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Advances in Optics and Photonics

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  • Editor: Bahaa E. A. Saleh
  • Vol. 1, Iss. 3 — Nov. 1, 2009
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Optical Antennas

Palash Bharadwaj, Bradley Deutsch, and Lukas Novotny  »View Author Affiliations


Advances in Optics and Photonics, Vol. 1, Issue 3, pp. 438-483 (2009)
http://dx.doi.org/10.1364/AOP.1.000438


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Abstract

Optical antennas are an emerging concept in physical optics. Similar to radiowave and microwave antennas, their purpose is to convert the energy of free propagating radiation to localized energy, and vice versa. Optical antennas exploit the unique properties of metal nanostructures, which behave as strongly coupled plasmas at optical frequencies. The tutorial provides an account of the historical origins and the basic concepts and parameters associated with optical antennas. It also reviews recent work in the field and discusses areas of application, such as light-emitting devices, photovoltaics, and spectroscopy.

© 2009 Optical Society of America

1. Introduction

In optical science and engineering, light is commonly controlled by redirecting the wave fronts of propagating radiation by means of lenses, mirrors, and diffractive elements. This type of manipulation relies on the wave nature of electromagnetic fields and is therefore not amenable to controlling fields on the subwavelength scale. In contrast, radiowave and microwave technology predominantly makes use of antennas to manipulate electromagnetic fields, controlling them on the subwavelength scale and interfacing efficiently between propagating radiation and localized fields.

While antennas are a key enabling technology for devices like cellular phones and televisions using electromagnetic radiation in the radiowave or microwave regime, their optical analog is basically nonexistent in today’s technology. However, recent research in nano-optics and plasmonics has generated considerable interest in the optical antenna concept, and several studies are currently focused on how to translate established radiowave and microwave antenna theories into the optical frequency regime.

The absence of optical antennas in technological applications is primarily associated with their small scale. Antennas have characteristic dimensions of the order of a wavelength of light, demanding fabrication accuracies better than 10nm. The advent of nanoscience and nanotechnology provides access to this length scale with the use of novel top-down nanofabrication tools (e.g. focused ion beam milling and electron-beam lithography) and bottom-up self-assembly schemes. The fabrication of optical antenna structures is an emerging opportunity for novel optoelectronic devices.

Given their wide applicability, the absence of optical antennas in current technology is conspicuous. Even as their fabrication becomes feasible, material challenges associated with optical antennas remain. For example, the penetration of radiation into metals can no longer be neglected. The electromagnetic response is then dictated by collective electron oscillations (plasmons) characteristic of a strongly coupled plasma. These collective excitations make a direct downscaling of traditional antenna designs impossible and demand the careful study of surface modes in metal nanostructures.

The introduction of the antenna concept into the optical frequency regime will provide access to new technological applications. Optical antennas will likely be employed to enhance absorption cross sections and quantum yields in photovoltaics, to release energy efficiently from nanoscale light-emitting devices, to boost the efficiency of photochemical or photophysical detectors, and to increase spatial resolution in optical microscopy. In this tutorial, we define the optical antenna, outline its physical properties, and review relevant history and recent work. The field of optical antennas is in its infancy, and new studies and developments are evolving at a rapid pace. Therefore, we do not intend a state-of-the-art review. Rather, we hope to establish language pertaining to optical antennas and to provide historical and future perspectives.

We will begin in Section 2 with a short history of antennas and show how the concept of optical antennas was motivated by microscopy. In Section 3 we derive physical properties of optical antennas in analogy to radiowave or microwave antennas, and we derive several antenna parameters for the example of a spherical nanoparticle. We also discuss wavelength scaling, nonlinear properties of optical antennas, and their effect on atomic or molecular systems. Finally, in Section 4 we outline applications of optical antennas and review some recent developments in the field.

2. Antenna History

The word antenna has had an interesting history that is worth reviewing. It was first introduced in a translation of Aristotle’s writings in 1476 [2

2. Aristotle, De Animalibus, Theodorus Gaza, trans. (Johannes de Colonia and Johannes Manthen, 1476).

]. Aristotle used the Greek word keraiai to refer to the “horns” of insects [3

3. Aristotle, History of Animals (c. 340 B.C.E.).

], which Theodorus Gaza translated into the Latin-derived antenna, used to designate a sailing yard of a lateen. Antenna probably derives from the prefix an, “up,” and the Indo-European root ten, “to stretch” [4

4. T. G. Tucker, “Antemna, antenna,” in A Concise Etymological Dictionary of Latin (Max Niemeyer Verlag, 1931), p. 19.

, 5

5. C. Watkins, “ten-,” in The American Heritage Dictionary of Indo-European Roots (Houghton Mifflin, 2000), p. 90.

]. The verbs tan (Sanskrit), tendere (Latin), teinein (Greek), dehnen (German) and tyanut’ (Russian), all meaning “to stretch,” as well as modern English words such as tension, tent, pretend, tenacious, and tendon all trace their origins back to this root verb. Etymologically then, an antenna is that which stretches or extends up [6

6. E. Klein, “Antenna,” in A Comprehensive Etymological Dictionary of the English Language (Elsevier, 1966), p. 82.

].

Evidence suggests that the term antenna first found only casual verbal use in English, and that it took about a decade before it was popularly used in scientific work. Marconi did not refer to antennas in his patents, but he makes use of the term in his Nobel Prize speech of 1909 [10

10. G. Marconi, “Wireless telegraphic communication,” Nobel Lecture, December 11, 1909.

]. The term can also be found in George W. Pierce’s article of 1904 [11

11. G. W. Pierce, “Experiments on resonance in wireless telegraph circuits,” Phys. Rev. 19, 196–217 (1904).

] and in John A. Fleming’s 1902 entry in the Encyclopedia Britannica XXXIII referring to Marconi’s work [12

12. J. A. Fleming, “Telegraphy,” The New Volumes of the Encyclopedia Britannica, 10th ed., vol. XXXIII (1902).

].

The first document we are aware of that uses the word antenna for an electromagnetic transmitter is a paper by André-Eugène Blondel titled “Sur la théorie des antennes dans la télégraphie sans fil,” presented in 1898 at a meeting of the Association Française pour l’Avancement des Sciences. Blondel, the inventor of the oscillograph, also refers to antennas in a letter that he sent to H. Poincaré in August 1898 [13

13. S. Walter, E. Bolmont, and A. Coret, “La correspondance entre Henri Poincaré et les physiciens, chimistes et ingénieurs,” in Publications of the Henri Poincaré Archives (Birkhäuser, 2007), chap. 8. [CrossRef]

]. We also find the term antenna in the book by André Broca titled La télégraphie sans fils published in French in 1899 [14

14. A. Broca, La télégraphie sans fils (Gauthier Villars, 1899).

]. Broca states that an antenna is a means for concentrating electromagnetic waves and defines it as “the vertical long-wire pole of an excitation source.” The other pole is considered to be grounded. He writes that “the extremity of the antenna is a point of escape for electromagnetic energy” and that an antenna is also needed on the receiving end, similar to Benjamin Franklin’s lightning rod [15

15. B. Franklin, in The Papers of Benjamin Franklin, L. W. Labaree, ed. (Yale Univ. Press, 1961), vol. 3, pp. 156–164.

]. The term antenna is also used in a 1900 French patent by Manuel Rodriguez Garcia [16

16. M. C. H. E. Rodriguez-Garcia, “Systéme de télégraphie sans fil par ondes hertziennes,” French Patent 301264 (June 14, 1900).

] and in subsequent U.S. patents filed in 1901 [17

17. E. Ducretet, “Transmitting and receiving apparatus for Hertzian waves,” U.S. Patent 726413 (April 28, 1903).

, 18

18. M. C. H. E. Rodriguez-Garcia, “Wireless telegraphy,” U.S. Patent 795762 (July 25, 1905).

].

2.1. Optical Antennas

While radio antennas were developed as solutions to a communication problem, the invention of optical antennas was motivated by microscopy. In analogy to its radiowave and microwave counterparts, we define the optical antenna as a device designed to efficiently convert free-propagating optical radiation to localized energy, and vice versa. In the context of microscopy, an optical antenna effectively replaces a conventional focusing lens or objective, concentrating external laser radiation to dimensions smaller than the diffraction limit.  

Optical antenna: a device designed to efficiently convert free-propagating optical radiation to localized energy, and vice versa.

In a letter dated April 22, 1928, Edward Hutchinson Synge described to Albert Einstein a microscopic method in which the field scattered from a tiny particle could be used as a light source [20

20. L. Novotny, “The history of near-field optics,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2007), vol. 50, pp. 137–184. [CrossRef]

]. The particle would convert free-propagating optical radiation into a localized field that would interact with a sample surface. Thinking of the surface as a receiver, the particle can be viewed as an optical antenna. Synge’s description was likely inspired by the development of dark-field microscopy, a technique invented at the turn of the twentieth century by the Austrian chemist Richard Adolf Zsigmondy [21

21. Nobel Lectures, Chemistry 1922–1941 (Elsevier, 1966).

].

John Wessel was unfamiliar with Synge’s work when he wrote in 1985, “The particle serves as an antenna that receives an incoming electromagnetic field [22

22. J. Wessel, “Surface-enhanced optical microscopy,” J. Opt. Soc. Am. B 2, 1538–1540 (1985). [CrossRef]

],” making him the first to mention explicitly the analogy of local microscopic light sources to classical antennas—a concept that has since been thoroughly explored [23

23. P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006). [CrossRef]

, 24

24. S. Kühn, U. Hakanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97, 017402 (2006). [CrossRef] [PubMed]

]. The invention of scanning tunneling microscopy [25

25. G. Binnig and H. Rohrer, “Scanning tunneling microscopy,” Helv. Phys. Acta 55, 726–735 (1982).

] and the discovery of surface enhanced Raman scattering (SERS) [26

26. M. Fleischmann, P. J. Hendra, and A. J. McQuillian, “Raman spectra of pyridine adsorbed at a silver electrode,” Chem. Phys. Lett. 26, 163–166 (1974). [CrossRef]

, 27

27. D. L. Jeanmaire and R. P. V. Duyne, “Surface Raman spectroelectrochemistry: part I. Heterocyclic, aromatic, and aliphatic amines adsorbed on the anodized silver electrode,” J. Electroanal. Chem. 84, 1–20 (1977). [CrossRef]

, 28

28. M. G. Albrecht and J. A. Creighton, “Anomalously intense Raman spectra of pyridine at a silver electrode,” J. Am. Chem. Soc. 99, 5215–5217 (1977). [CrossRef]

] most likely inspired Wessel’s idea. The quest for an understanding of SERS gave rise to many theoretical studies aimed at predicting the electromagnetic field enhancement near laser-irradiated metal particles and clusters [29

29. J. Gersten and A. Nitzan, “Electromagnetic theory of enhanced Raman scattering of molecules adsorbed on rough surfaces,” J. Chem. Phys. 73, 3023–3037 (1980). [CrossRef]

, 30

30. A. Wokaun, J. Gordon, and P. Liao, “Radiation damping in surface-enhanced Raman scattering,” Phys. Rev. Lett. 48, 957–960 (1982). [CrossRef]

, 31

31. A. D. Boardman, ed., Electromagnetic Surface Modes (Wiley, 1982).

, 32

32. H. Metiu, Surface Enhanced Spectroscopy, vol. 17 of Progress in Surface Science, I. Prigogine and S. A. Rice, eds. (Pergamon, 1984), pp. 153–320.

, 33

33. M. Meier, A. Wokaun, and P. F. Liao, “Enhanced fields on rough surfaces: dipolar interactions among particles of sizes exceeding the Raleigh limit,” J. Opt. Soc. Am. B 2, 931–949 (1985). [CrossRef]

]. This era can be considered the first phase of what is now called nanoplasmonics. In 1988 Ulrich Ch. Fischer and Dieter W. Pohl carried out an experiment similar to Synge’s and Wessel’s proposals [34

34. U. C. Fischer and D. W. Pohl, “Observation on single-particle plasmons by near-field optical microscopy,” Phys. Rev. Lett. 62, 458–461 (1989). [CrossRef] [PubMed]

]. Instead of a solid metal particle, they used a gold-coated polystyrene particle as a local light source, a structure that was later extensively developed and is now called a gold nanoshell [35

35. J. Jackson, S. Westcott, L. Hirsch, J. West, and N. Halas, “Controlling the surface enhanced Raman effect via the nanoshell geometry,” Appl. Phys. Lett. 82, 257–259 (2003). [CrossRef]

, 36

36. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 320, 419–422 (2003). [CrossRef]

]. Fischer and Pohl imaged a thin metal film with 320nm holes and demonstrated a spatial resolution of 50nm. Their results provide the first experimental evidence that near-field scanning optical microscopy as introduced by Synge is feasible. Ten years later, laser-irradiated metal tips were proposed as optical antenna probes for near-field microscopy and optical trapping [37

37. L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. 79, 645–648 (1997). [CrossRef]

, 38

38. L. Novotny, E. J. Sanchez, and X. S. Xie, “Near-field optical imaging using metal tips illuminated by higher-order Hermite–Gaussian beams,” Ultramicroscopy 71, 21–29 (1998). [CrossRef]

], and since then various antenna geometries have been studied (rods, bowties, etc.), some of which are reviewed below.

3. Physical Properties of Optical Antennas

Optical antennas are strongly analogous to their RF and microwave counterparts, but there are crucial differences in their physical properties and scaling behavior. Most of these differences arise because metals are not perfect conductors at optical frequencies, but are instead strongly correlated plasmas described as a free electron gas. Optical antennas are also not typically driven with galvanic transmission lines—localized oscillators are instead brought close to the feed point of the antennas, and electronic oscillations are driven capacitively [49

49. D. W. Pohl, “Near-field optics seen as an antenna problem,” in Near-field Optics, Principles and Applications, X. Zhu and M. Ohtsu, eds. (World Scientific, 2000), pp. 9–21. [CrossRef]

]. Moreover, optical antennas can take various unusual forms (tips, nanoparticles, etc.) and their properties may be strongly shape and material dependent owing to surface plasmon resonances.

The general problem statement of optical antenna theory is illustrated in Fig. 3. A receiver or transmitter interacts with free optical radiation via an optical antenna. The receiver or transmitter is ideally an elemental quantum absorber or emitter, such as an atom, ion, molecule, quantum dot, or defect center in a solid. The antenna enhances the interaction between the emitter or absorber and the radiation field. It therefore provides the prospect of controlling the light–matter interaction on the level of a single quantum system. The presence of the antenna modifies the properties of the receiver/transmitter, such as its transition rates and, in the case of a strong interaction, even the energy-level structure. Likewise, the antenna properties depend on those of the receiver–transmitter, and it becomes evident that the two must be regarded as a coupled system. In this section, we will address these issues and attempt to express them in terms of established antenna terminology.

3.1. Local Density of Electromagnetic States

Arguably, one of the most important quantities in a discussion of antennas is the impedance, defined in circuit theory in terms of source current I and voltage V as Z=VI. This definition assumes that the source is connected to the antenna via a current-carrying transmission line. But optical antennas are typically fed by localized light emitters, not by real currents. Thus, the definition of antenna input impedance needs some adjustments. A viable alternate definition involves the local density of electromagnetic states (LDOS), which can be expressed in terms of the Green’s function tensor G and which accounts for the energy dissipation of a dipole in an arbitrary inhomogeneous environment.

The total decay rate of a two-level quantum emitter located at ro and weakly coupled to the antenna can be represented by Fermi’s golden rule as [51

51. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge Univ. Press, 2006). [CrossRef]

]
Γ=πω3εo|g|p̂|e|2ρp(ro,ω),
(1)
where g|p̂|e is the transition dipole moment between the emitter’s excited state |e and ground state |g, ω is the transition frequency, and ρp denotes the partial density of electromagnetic states (LDOS). The latter can be expressed in terms of the system’s dyadic Green’s function G as [51

51. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge Univ. Press, 2006). [CrossRef]

, 52

52. K. Joulain, R. Carminati, J. P. Mulet, and J. J. Greffet, “Definition and measurement of the local density of electromagnetic states close to an interface,” Phys. Rev. B 68, 245405 (2003). [CrossRef]

]
ρp(ro,ω)=6ωπc2[npIm{G(ro,ro,ω)}np],
(2)
where np is a unit vector pointing in direction of p. The Green’s function used in Eq. (2) is indirectly defined by the electric field E at the observation point r generated by a dipole p located at ro,
E(r)=1εoω2c2G(r,ro,ω)p.
(3)
Notice that the Green’s function in Eq. (2) is evaluated at ro, which is the position of the emitter itself. This reflects the fact that the decay from the excited state happens in response to the emitter’s own field.

The total LDOS (ρ) is obtained by assuming that the quantum emitter has no preferred dipole axis (atom). Averaging Eq. (2) over different dipole orientations leads to
ρ(ro,ω)=ρp(ro,ω)=2ωπc2Im{Tr[G(ro,ro,ω)]},
(4)
where Tr denotes the trace. Thus, the excited state lifetime τ=1Γof the quantum emitter is determined by the Green’s function G of the system in which the emitter is embedded. The LDOS therefore accounts for the presence of the antenna and is a measure of its properties. In free space, i.e., in the absence of the antenna, we obtain ρp=ω2(π2c3) and Γo=ω3|g|p̂|e|2(3πεoc3). The observation that atomic decay rates are dependent on the local environment goes back to Purcell’s analysis in 1946 [53

53. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946). [CrossRef]

] and has since been measured for various systems, such as molecules near interfaces [54

54. K. H. Drexhage, M. Fleck, F. Shäfer, and W. Sperling, “Beeinflussung der Fluoreszenz eines Europium-chelates durch einen Spiegel,” Ber. Bunsenges. Phys. Chem. 20, 1179 (1966).

] or atoms in cavities [55

55. D. Kleppner, “Inhibited spontaneous emission,” Phys. Rev. Lett. 47, 233–236 (1981). [CrossRef]

, 56

56. P. Goy, J. Raimond, M. Gross, and S. Haroche, “Observation of cavity-enhanced single-atom spontaneous emission,” Phys. Rev. Lett. 50, 1903–1906 (1983). [CrossRef]

]. The origin for the modification of atomic decay rates is the interaction of the atom with its own secondary field—the field that arrives back at the atom’s location after being scattered in the local environment. This back-action also influences the energy states and transition frequencies [57

57. M. A. Wilson, P. Bushev, J. Eschner, F. Schmidt-Kaler, C. Becher, R. Blatt, and U. Dorner, “Vacuum-field level shifts in a single trapped ion mediated by a single distant mirror,” Phys. Rev. Lett. 91, 213602 (2003). [CrossRef] [PubMed]

, 58

58. O. Labeau, P. Tamarat, H. Courtois, G. S. Agarwal, and B. Lounis, “Laser-induced resonance shifts of single molecules self-coupled by a metallic surface,” Phys. Rev. Lett. 98, 143003 (2007). [CrossRef] [PubMed]

], but the effect is generally much smaller than the modification of transition rates.

3.2. Power Dissipation and Antenna Impedance

We now return to the circuit-theory definition of the impedance. The antenna resistance follows from the dissipated power according to Re{Z}=PI2. Since we have a driving dipole instead of a physical current, it is more useful to define Z in terms of the current density, jiωp, instead of the current, I. Equation (8) thus yields [60

60. J.-J. Greffet, Institut d'Optique, Paris, France (personal communication, 2008).

]
Re{Z}=π12εoρp(ro,ω).
(11)
Hence, the LDOS can be associated with the antenna resistance Re{Z}. The units of such a resistance are ohms per area instead of the usual ohms. Notice that Z depends on both the location ro and the orientation np of the receiving or transmitting dipole. As discussed by Greffet et al. [60

60. J.-J. Greffet, Institut d'Optique, Paris, France (personal communication, 2008).

], the imaginary part of Z accounts for the energy stored in the near field.

3.3. Antenna Efficiency, Directivity, and Gain

The power P in Eq. (8) accounts for the total dissipated power, which is the sum of radiated power Prad and power dissipated into heat and other channels (Ploss). The antenna radiation efficiency εrad is defined as
εrad=PradP=PradPrad+Ploss.
(12)
While P is most conveniently determined by calculating the field E at the dipole’s position according to Eq. (7), Prad requires the calculation of the energy flux through a surface enclosing both the dipole and the antenna.

It is useful to distinguish dissipation in the antenna and the transmitter, which is not accomplished by Eq. (12). We therefore define the intrinsic quantum yield of the emitter as
ηi=PradoPrado+Pintrinsiclosso,
(13)
where the superscripts o designate the absence of the antenna. With this definition of ηi we can rewrite Eq. (12) as
εrad=PradPradoPradPrado+PantennalossPrado+[1ηi]ηi.
(14)
For an emitter with ηi=1 (no intrinsic loss) the antenna can only reduce the efficiency. However, for emitters with low ηi we can effectively increase the overall efficiency, which holds promise for the optimization of light emitting devices.

To account for the angular distribution of the radiated power we define the normalized angular power density p(θ,φ), or radiation pattern, as
0π02πp(θ,φ)sinθdφdθ=Prad.
(15)
The directivity D is a measure of an antenna’s ability to concentrate radiated power into a certain direction. It corresponds to the angular power density relative to a hypothetical isotropic radiator. Formally,
D(θ,φ)=4πPradp(θ,φ).
(16)
When the direction (θ,φ) is not explicitly stated, one usually refers to the direction of maximum directivity, i.e., Dmax=(4πPrad)Max[p(θ,φ)].

Because the fields at a large distance from an antenna are transverse, they can be written in terms of two polarization directions, nθ and nφ. The partial directivities are then defined as
Dθ(θ,φ)=4πPradpθ(θ,φ),Dφ(θ,φ)=4πPradpφ(θ,φ).
(17)
Here, pθ and pφ are the normalized angular powers measured after polarizers aligned in direction nθ and nφ, respectively. Because nθnφ=0, we have
D(θ,φ)=Dθ(θ,φ)+Dφ(θ,φ).
(18)
The influence of an optical antenna on the radiation pattern of a single molecule was recently studied by van Hulst and co-workers [61

61. T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, and N. F. van Hulst, “λ/4 Resonance of an optical monopole antenna probed by single molecule fluorescence,” Nano Lett. 7, 28–33 (2007). [CrossRef]

, 62

62. T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. van Hulst, “Optical antennas direct single-molecule emission,” Nat. Photonics 2, 234–237 (2008). [CrossRef]

, 63

63. R. J. Moerland, N. F. van Hulst, H. Gersen, and L. Kuipers, “Probing the negative permittivity perfect lens at optical frequencies using near-field optics and single molecule detection,” Opt. Eng. 13, 1604–1614 (2005).

, 64

64. H. Gersen, M. F. García-Parajó, L. Novotny, J. A. Veerman, L. Kuipers, and N. F. van Hulst, “Influencing the angular emission of a single molecule,” Phys. Rev. Lett. 85, 5312 (2000). [CrossRef]

], and it was shown that the antenna provides a high level of control for the direction and polarization of the emitted photons.

The gain G of an antenna follows a definition similar to that of the directivity, but instead of normalizing with the radiated power Prad the gain is defined relative to the total power P, i.e.,
G=4πPp(θ,φ)=εradD.
(19)
D and G are usually measured in decibels. Since perfectly isotropic radiators do not exist in reality, it is often more practical to refer to an antenna of a known directional pattern. The relative gain is then defined as the ratio of the power gain in a given direction to the power gain of a reference antenna in the same direction. A dipole antenna is the standard choice as a reference because of its relatively simple radiation pattern. Bouhelier and co-workers recently characterized the relative gain of optical antennas made from metal nanoparticle dimers, using as a reference the dipolelike radiation from single nanoparticles [65

65. C. Huang, A. Bouhelier, G. C. des Francs, A. Bruyant, A. Guenot, E. Finot, J.-C. Weeber, and A. Dereux, “Gain, detuning, and radiation patterns of nanoparticle optical antennas,” Phys. Rev. B 78, 155407 (2008). [CrossRef]

].

3.4. Radiative Enhancement

The reciprocity theorem states that for a closed system (no incoming waves) with two separable and finite-sized current distributions j1 and j2, producing the fields E1 and E2, respectively, the following relationship holds [66

66. R. Carminati, M. Nieto-Vesperinas, and J.-J. Greffet, “Reciprocity of evanescent electromagnetic waves,” J. Opt. Soc. Am. A 15, 706–712 (1998). [CrossRef]

]:
Vj1E2dV=Vj2E1dV.
(20)
According to Eq. (6), for two dipoles this equation simplifies to
p1E2=p2E1.
(21)
We will use this equation to derive a relationship between the excitation rate Γexc of dipole p1 and its radiative rate Γrad, following the steps used by Taminiau et al. [67

67. T. H. Taminiau, F. D. Stefani, and N. F. van Hulst, “Enhanced directional excitation and emission of single emitters by a nano-optical Yagi-Uda antenna,” Opt. Express 16, 10858–10866 (2008). [CrossRef] [PubMed]

, 68

68. T. H. Taminiau and N. F. Van Hulst, ICFO—The Institute of Photonic Sciences, Castelldefels (Barcelona), Spain (personal communication, 2008).

].

Let us consider the situation depicted in Fig. 4 in which one dipole (p1) represents a quantum emitter or absorber near an optical antenna and the other dipole (p2) is a dummy dipole representing the location of a point detector. The separation between the two dipoles is assumed to be sufficiently large (kR1) to ensure that they interact only via their far fields. Furthermore, the direction of p2 is chosen to be transverse to the vector connecting the two dipoles.

In the classical picture, we assume that dipole p1 has been induced by the field E2 of dipole p2 according to p1=α1E2, where α1=α1np1np1 is the polarizability tensor. Here, np1 is the unit vector in the direction of p1. According to Eq. (7), the power absorbed by the particle at r1 is
Pexc=(ω2)Im{p1*E2(r1)}=(ω2)Im{α1}|np1E2(r1)|2.
(22)
We now substitute reciprocity relation (21) in the form p1np1E2=p2np2E1 and obtain
Pexc=(ω2)|p2p1|2Im{α1}|np2E1(r2)|2.
(23)
The term |np2E1(r2)|2 corresponds to the power a photodetector at r2 would read if it were placed behind a polarizer oriented in direction np2.

We now invoke the partial directivities defined in Eqs. (17). In terms of the field E evaluated at r2=(R,θ,φ) the partial directivity Dθ reads as
Dθ(θ,φ)=4π|nθE(R,θ,φ)|24π|E(R,θ,φ)|2dΩ,
(24)
where Ω is the unit solid angle and nθ the unit polar vector. Dφ(θ,φ), referring to radiation polarized in azimuthal direction nφ, is expressed similarly.

To proceed, we choose the dipole p2 to point in direction of nθ. Equation (23) can then be represented as
Pexc,θ(θ,φ)=(ω2)|p2p1|2Im{α1}Prad2πεocR2Dθ(θ,φ).
(25)
Here, Prad=(12)εocR24π|E(R,θ,φ)|2dΩ is the total radiated power. The left-hand side, Pexc,θ(θ,φ), specifies the power absorbed by dipole p1 when it is excited by the field of dipole p2 located at (R,θ,φ) and oriented in the nθ direction. Because kR1, the field exciting dipole p1 and the antenna is essentially a plane wave polarized in nθ.

We now remove the antenna and write an equation similar to Eq. (25). Dividing the two equations yields
Pexc,θ(θ,φ)Pexc,θo(θ,φ)=PradPradoDθ(θ,φ)Dθo(θ,φ),
(26)
where the superscript o carries the same meaning as in Eq. (15). Invoking the proportionality Eq. (10) between power P and transition rate Γ, we can represent the above equation as
Γexc,θ(θ,φ)Γexc,θo(θ,φ)=ΓradΓradoDθ(θ,φ)Dθo(θ,φ),
(27)
which states that the enhancement of the excitation rate due to the presence of the antenna is proportional to the enhancement of the radiative rate, a relationship that has been used qualitatively in various studies [67

67. T. H. Taminiau, F. D. Stefani, and N. F. van Hulst, “Enhanced directional excitation and emission of single emitters by a nano-optical Yagi-Uda antenna,” Opt. Express 16, 10858–10866 (2008). [CrossRef] [PubMed]

, 69

69. K. T. Shimizu, W. K. Woo, B. R. Fisher, H. J. Eisler, and M. G. Bawendi, “Surface-enhanced emission from single semiconductor nanocrystals,” Phys. Rev. Lett. 89, 117401 (2002). [CrossRef] [PubMed]

, 70

70. J. N. Farahani, D. W. Pohl, H.-J. Eisler, and B. Hecht, “Single quantum dot coupled to a scanning optical antenna: a tunable superemitter,” Phys. Rev. Lett. 95, 017402 (2005). [CrossRef] [PubMed]

, 71

71. P. Bharadwaj and L. Novotny, “Spectral dependence of single molecule fluorescence enhancement,” Opt. Express 15, 14266–14274 (2007). [CrossRef] [PubMed]

]. Note that the same analysis can be repeated with nφ instead of nθ, which corresponds to polarization rotated by 90°.

In most experiments, a quantum emitter is excited by focused laser radiation rather than a polarized plane wave from (θ,φ). In this case, the incident field can be written as an angular spectrum of plane waves and their mutual interferences accounted for to arrive at a correct relationship between Γexc and Γrad.

3.5. Antenna Aperture and Absorption Cross Section

The antenna aperture or effective area, A, describes the efficiency with which incident radiation is captured. It corresponds to the area of incident radiation that interacts with the antenna and is defined as
A(θ,φ,npol)=PexcI=σA(θ,φ,npol),
(28)
where Pexc denotes the power that excites the receiver and I is the intensity of radiation incident from (θ,φ) and polarized in direction npol. If the direction or polarization is not specified, one usually refers to that which yields the maximum aperture. Formally, A is equivalent to the absorption (or excitation) cross section σA.

In the absence of the antenna, the absorption cross section of a two-level system has a theoretical limit of σo=3λ2(2π) [72

72. R. Loudon, The Quantum Theory of Light, 2nd ed., Oxford Science Publications (Clarendon, 1983).

]. Typical values for dye molecules or quantum dots are of the order of σo1nm2. Thus, a planar array of molecules with nearest neighbor distances of 1nm would interact with all of the incident radiation.

The antenna increases the optical energy density that falls on a target and thereby increases its efficiency. For example, the overall efficiency of a photodetector can be improved when coupled to an optical antenna [73

73. L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D.-S. Ly-Gagnon, K. C. Saraswat, and D. A. B. Miller, “Nanometre-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2, 226–229 (2008). [CrossRef]

]. For a detector small compared with the wavelength λ the received power is calculated according to Eqs. (7, 22) as
Pexc=(ω2)Im{α}|npE|2.
(29)
Here, np is the unit vector in the direction of the absorption dipole p, and E is the field at the location of the detector. If we denote the field at the target in the absence of the antenna as Eo, we can represent the absorption cross section (antenna aperture) as
σ=σo|npE|2|npEo|2.
(30)
Here, σo is the absorption cross section in the absence of the antenna and E is the field at the target in presence of the antenna. Note that both σ and σo depend on the direction of incidence (θ,φ) and the polarization direction npol. According to Eq. (30) the enhancement of the absorption cross section, and aperture, corresponds to the local intensity enhancement factor.

Several studies have demonstrated that intensity enhancements of 104106 are feasible [37

37. L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. 79, 645–648 (1997). [CrossRef]

, 74

74. H. Xu, E. J. Bjernfeld, M. Käll, and L. Börjesson, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999). [CrossRef]

, 75

75. K. Li, M. I. Stockman, and D. J. Bergman, “Self-similar chain of metal nanospheres as an efficient nanolens,” Phys. Rev. Lett. 91, 227402 (2003). [CrossRef] [PubMed]

]. Using these values as working numbers we find that by use of optical antennas the areal density of discrete absorbers can be reduced by 4–6 orders of magnitude without sacrificing any loss of absorption. For example, a planar solar cell consisting of an array of antenna-coupled molecules or quantum dots spaced by 100nm to 1μm would interact with all of the incident radiation.

3.6. Example: Nanoparticle Antenna

Let us consider a spherical nanoparticle as a simple example of an optical antenna [23

23. P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006). [CrossRef]

, 24

24. S. Kühn, U. Hakanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97, 017402 (2006). [CrossRef] [PubMed]

, 71

71. P. Bharadwaj and L. Novotny, “Spectral dependence of single molecule fluorescence enhancement,” Opt. Express 15, 14266–14274 (2007). [CrossRef] [PubMed]

, 76

76. T. Kalkbrenner, U. Håkanson, A. Schädle, S. Burger, C. Henkel, and V. Sandoghdar, “Optical microscopy via spectral modifications of a nanoantenna,” Phys. Rev. Lett. 95, 200801 (2005). [CrossRef] [PubMed]

, 77

77. P. Bharadwaj, P. Anger, and L. Novotny, “Nanoplasmonic enhancement of single-molecule fluorescence,” Nanotechnology 18, 044017 (2007). [CrossRef]

]. The nanoparticle geometry allows straightforward analytical solutions [71

71. P. Bharadwaj and L. Novotny, “Spectral dependence of single molecule fluorescence enhancement,” Opt. Express 15, 14266–14274 (2007). [CrossRef] [PubMed]

]. The experimental situation along with the theoretical model is shown in Fig. 5. For simplicity, we assume that the dipole p of the molecule is pointing toward the nanoparticle in direction nz and that the incident field Eo is parallel to p. Furthermore, we assume that the intrinsic quantum yield of the molecule is unity, i.e., that the molecule radiates all the power that is supplied to it. The polarizability of the nanoparticle is approximated by its isotropic, quasi-static limit by α=4πεoa3[(ε(ω)1)(ε(ω)+2)], with a being the particle radius and ε the particle’s relative dielectric permittivity. The resonance condition arising from the denominator of this expression (Re{ε}=2) is the well-known localized surface plasmon resonance for a sphere [51

51. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge Univ. Press, 2006). [CrossRef]

]. Similar resonance conditions are calculated for nanoparticle antennas with other shapes (e.g., ellipsoids).

To first order, the field at the molecule’s origin due to the incident field Eo is
E=[I+k2εoα(ω)G(ro,rp,ω)]Eo=[1+2α̃(ω)a3(a+z)3]Eo,
(31)
where k=ωc, αp=α̃p4πεoa3, I is the unit tensor, and z is the separation between the molecule and the particle’s surface. Notice that in the dipole limit (aλ) α̃p depends only on the shape of the nanoparticle antenna and not on its size. We retain only the near-field term of the free-space Green’s function G and assume that retardation can be neglected. Similarly, the dipole induced in the nanoparticle due to the radiating molecule is
pp=k2εoαp(ω)G(rp,ro,ω)p=2α̃p(ω)a3(a+z)3p.
(32)
Using Eqs. (31, 32) we can derive various antenna parameters for the nanoparticle antenna.

1. Received Power. According to Eqs. (7, 22, 31) the normalized total power absorbed by the molecule is
PexcPexco=ΓexcΓexco=|1+2α̃p(ω)a3(a+z)3|2,
(33)
where we have used the proportionality between P and Γ according to Eq. (10). Po and Γo are calculated in the absence of the nanoparticle antenna.

2. Radiated Power. For a particle much smaller than the wavelength of radiation we can neglect the power radiated by higher-order multipoles. Therefore, the total power radiated by the molecule in presence of the antenna is proportional to the absolute square of the total dipole p+pp. Using Eq. (32) we find
PradPrado=ΓradΓrado=|p+pp|2|p|2=|1+2α̃p(ω)a3(a+z)3|2,
(34)
which is identical to the normalized excitation rate in Eq. (33).

3. Directivity. In the absence of the antenna the directivity of the molecule is defined by the dipole radiation pattern Do=Dθo=(32)sin2θ. The nanoparticle antenna does not change the directivity because the induced dipole moment pp points in the same direction as the molecular dipole, and because the two dipoles are closely spaced. Therefore,
D(θ,φ)=Dθ(θ,φ)=(32)sin2θ.
(35)
Because the directivities Dθ and Dθo are identical, Eq. (27) implies that the normalized excitation rate is the same as the normalized radiative rate, which also follows from Eqs. (33, 34). The situation would be more complicated if we considered a dipole p oriented at an angle to the z axis or an incident wave coming in from a different direction.

4. Efficiency. To calculate the radiation efficiency εrad we need to determine the power absorbed in the nanoparticle antenna. For small distances between molecule and particle the curvature of the particle’s surface can be neglected and the environment as seen by the molecule is a plane interface [78

78. G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984). [CrossRef]

, 32

32. H. Metiu, Surface Enhanced Spectroscopy, vol. 17 of Progress in Surface Science, I. Prigogine and S. A. Rice, eds. (Pergamon, 1984), pp. 153–320.

, 79

79. V. V. Klimov, M. Ducloy, and V. S. Letokhov, “Spontaneous emission in the presence of nanobodies,” Quantum Electron. 31, 569–586 (2001). [CrossRef]

]. From electrostatic image theory [51

51. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge Univ. Press, 2006). [CrossRef]

] the normalized absorbed power of a vertical dipole near a half-space with dielectric constant ε(ω) is [71

71. P. Bharadwaj and L. Novotny, “Spectral dependence of single molecule fluorescence enhancement,” Opt. Express 15, 14266–14274 (2007). [CrossRef] [PubMed]

]
PlossPrado=34Im[ε(ω)1ε(ω)+1]1(kz)3.
(36)
The resonance of the above expression is worth noting: losses incurred by the radiating dipole correspond to the excitation of surface plasmons along the planar surface given by the familiar condition Re{ε}=1. Unlike the dipolar localized surface plasmon resonance, this resonance is nonradiative, and the absorbed energy is ultimately lost as heat. Higher-order correction terms to Eq. (36) can be derived as outlined in the literature [32

32. H. Metiu, Surface Enhanced Spectroscopy, vol. 17 of Progress in Surface Science, I. Prigogine and S. A. Rice, eds. (Pergamon, 1984), pp. 153–320.

, 80

80. V. V. Klimov and V. S. Letokhov, “Electric and magnetic dipole transitions of an atom in the presence of spherical dielectric interface,” Laser Phys. 15, 61–73 (2005).

]. Combining Eqs. (34, 36), the radiation efficiency εrad can be calculated for different intrinsic quantum yields ηi. Figure 6 shows εrad for a molecule with different ηi as a function of separation z from a 80nm gold particle. Evidently, the lower ηi, the more the antenna increases the overall efficiency, an effect that was observed in 1983 by Wokaun et al. [81

81. A. Wokaun, H.-P. Lutz, A. P. King, U. P. Wild, and R. R. Ernst, “Energy transfer in surface enhanced luminescence,” J. Chem. Phys. 79, 509–514 (1983). [CrossRef]

]. However, the distance between molecule and antenna is very critical. For too large distances there is no interaction between molecule and antenna, and for too small distances all the energy is dissipated into heat. Much higher enhancements of the efficiency can be achieved with optimized antenna designs.

6. Aperture. The intensity incident on the antenna–molecule system is I=(12)εoc|Eo|2. Using the result in Eq. (33) and the expression for the received power in absence of the antenna, Pexco=(ω2)Im{α}|Eo|2, we find
σ=kεoIm{α(ω)}|1+2[ε(ω)1ε(ω)+2]a3(a+z)3|2.
(38)
Here, (kεo)Im{α} corresponds to the molecule’s cross section σo in the absence of the antenna.

The nanoparticle serves as a model antenna, and its predictions have been tested in recent experiments [23

23. P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006). [CrossRef]

, 24

24. S. Kühn, U. Hakanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97, 017402 (2006). [CrossRef] [PubMed]

, 71

71. P. Bharadwaj and L. Novotny, “Spectral dependence of single molecule fluorescence enhancement,” Opt. Express 15, 14266–14274 (2007). [CrossRef] [PubMed]

, 76

76. T. Kalkbrenner, U. Håkanson, A. Schädle, S. Burger, C. Henkel, and V. Sandoghdar, “Optical microscopy via spectral modifications of a nanoantenna,” Phys. Rev. Lett. 95, 200801 (2005). [CrossRef] [PubMed]

, 77

77. P. Bharadwaj, P. Anger, and L. Novotny, “Nanoplasmonic enhancement of single-molecule fluorescence,” Nanotechnology 18, 044017 (2007). [CrossRef]

]. Because the antenna parameters depend on the properties of the environment they can be used as local probes in spectroscopy and microscopy [76

76. T. Kalkbrenner, U. Håkanson, A. Schädle, S. Burger, C. Henkel, and V. Sandoghdar, “Optical microscopy via spectral modifications of a nanoantenna,” Phys. Rev. Lett. 95, 200801 (2005). [CrossRef] [PubMed]

].

3.7. Wavelength Scaling

The notion of an effective wavelength can be used to extend familiar design ideas and rules into the optical frequency regime. For example, the optical analog of the λ2 dipole antenna becomes a thin metal rod of length λeff2. Since λeff for a gold rod of radius 5nm is roughly λ5.3 [see Fig. 7(c)], this means that the length of a λ2 dipole antenna is surprisingly small, about λ10.6. One can similarly construct antenna arrays like the well-established Yagi–Uda antenna developed in the 1920s for the UHF–VHF region [67

67. T. H. Taminiau, F. D. Stefani, and N. F. van Hulst, “Enhanced directional excitation and emission of single emitters by a nano-optical Yagi-Uda antenna,” Opt. Express 16, 10858–10866 (2008). [CrossRef] [PubMed]

, 82

82. L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett. 98, 266802 (2007). [CrossRef] [PubMed]

].

Figure 7(a) shows the intensity distribution near a half-wave antenna of length L=110nm and radius R=5nm resonantly excited at λ=1170nm. The effective wavelength is λeff=220nm. The induced current density j=iωεo[ε(ω)1]E evaluated along the axis of the antenna is shown in Fig. 7(a). The current density can be accurately approximated by jcos[zπ(L+2R)]. The current is nearly 180° out of phase with respect to the exciting field.

The wavelength shortening from λ to λeff has interesting implications. For example, it implies that the radiation resistance of an optical half-wave antenna is of the order of just a few ohms [82

82. L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett. 98, 266802 (2007). [CrossRef] [PubMed]

, 84

84. P. J. Burke, S. Li, and Z. Yu, “Quantitative theory of nanowire and nanotube antenna performance,” IEEE Trans. Nanotech. 5, 314–334 (2006). [CrossRef]

, 85

85. A. Alù and N. Engheta, “Input impedance, nanocircuit loading, and radiation tuning of optical nanoantennas,” Phys. Rev. Lett. 101, 043901 (2008). [CrossRef] [PubMed]

]. To see this, we note that the radiation resistance of a thin-wire antenna is roughly Rrad=30π2(Lλ)2, with L being the antenna length. For a half-wave antenna at RFs L=λ2 and Rrad73Ω. However, for an optical half-wave antenna, L=λeff2 , and hence Rrad=(304)π2(λeffλ)2. In other words, the radiation resistance at optical frequencies is a factor of (λeffλ)2 smaller than at RFs. For λeff=λ5 we find Rrad=3Ω.

Interestingly, while the radiation resistance Rrad at optical frequencies is a factor (λeffλ)2 smaller than at RFs, the loss resistance Rloss is only a factor (λeffλ) smaller. This follows from Ploss=VI=RlossI2, with V=EL and IωεoIm{ε}E. Using L=λeff2 we obtain RlossλλeffIm{ε}. At RFs λeff=λ, and therefore the loss resistance is a factor (λeffλ) smaller at optical frequencies than at RFs. For metals with no loss (Im{ε}0) the resistance tends to infinity, implying that no current can flow for a given field E.

3.8. Influencing the Light–Matter Interaction

In the discussion so far we have assumed that the antenna does not influence the intrinsic properties of the emitter or transmitter. Modifications of the transition rates occurred because of a change in the LDOS and not because of a change in molecular polarizability α. However, the highly localized fields near the antenna open up new interaction mechanisms between light and matter, such as higher-order multipole transitions or momentum-forbidden transitions. These interactions are inaccessible in free space and have the potential to enrich optical spectroscopy and provide new strategies for optical sensing and detection.

In free space, the momentum of a photon with energy E=ω is pph=ωc. On the other hand, the momentum of an unbound electron with the same energy is pe=[2m*ω]12, which is a factor of [2m*c2(ω)]12102103 larger than the photon momentum. Therefore, the photon momentum can be neglected in electronic transitions; i.e., optically excited transitions are vertical in an electronic band diagram. However, near optical antennas the photon momentum is no longer defined by its free space value. Instead, the localized optical fields are associated with a broad momentum distribution whose bandwidth pph=πΔ is given by the spatial confinement Δ, which can be as small as 110nm. Thus, in the optical near field the photon momentum can be increased by a factor of λΔ100, which brings it into the range of the electron momentum, especially in materials with small effective mass m*. Hence, localized optical fields can give rise to diagonal transitions in an electronic band diagram, thereby increasing the overall absorption strength represented by Im{α}, which is useful for devices such as silicon solar cells (see Subsection 4.2). The increase of photon momentum in optical near fields has been discussed in the context of photoelectron emission [86

86. V. M. Shalaev, “Electromagnetic properties of small-particle composites,” Phys. Rep. 272, 61–137 (1996). [CrossRef]

] and photoluminescence (PL)[87

87. M. R. Beversluis, A. Bouhelier, and L. Novotny, “Continum generation from single gold nanostructures through near-field mediated intraband transitions,” Phys. Rev. B 68, 115433 (2003). [CrossRef]

].

The strong field confinement near optical antennas also has implications for selection rules in atomic or molecular systems. The light–matter interaction involves matrix elements of the form f|p̂Â|i, with p̂ and  being the momentum and the field operators, respectively. As long as the quantum wave functions of states |i and |f are much smaller than the spatial extent over which  varies, it is legitimate to pull  out of the matrix element. The remaining expression f|p̂|i is what defines the dipole approximation and leads to standard dipole selection rules. However, the localized fields near optical antennas give rise to spatial variations of  of a few nanometers, and hence it may no longer be legitimate to invoke the dipole approximation. This is especially the case in semiconductor nanostructures where the low effective mass gives rise to quantum orbitals with large spatial extent. In situations where the field confinement becomes comparable with quantum confinement it is possible to expand the light–matter interaction in a multipole series. Theoretical studies have shown that higher-order multipoles have different selection rules [88

88. J. R. Zurita-Sanchez and L. Novotny, “Multipolar interband absorption in a semiconductor quantum dot. I. Electric quadrupole enhancement,” J. Opt. Soc. Am. B 19, 1355–1362 (2002). [CrossRef]

, 89

89. J. R. Zurita-Sanchez and L. Novotny, “Multipolar interband absorption in a semiconductor quantum dot. II. Magnetic dipole enhancement,” J. Opt. Soc. Am. B 19, 2722–2726 (2002). [CrossRef]

]. Additional transition channels are opened up in near-field interactions, which can be exploited for boosting the sensitivity of photodetection. Once the field confinement becomes stronger than the quantum confinement the multipole series no longer converges, and transition rates are solely defined by the local overlap of ground state and excited state wave functions. In this limit, an optical antenna can be used to spatially map out the quantum wave functions, providing direct optical images of atomic orbitals. However, this would require antennas with field confinements of better than 1nm.

3.9. Nonlinear Antenna Behavior

Today, most optical antenna designs are based on the optical properties of metals. In the linear regime the behavior is well described by a free electron gas. Additional interband transitions give rise to the characteristic color of a metal. Nonlocal effects come into play when the size of the structures becomes comparable with the electron mean free path [90

90. I. A. Larkin, M. I. Stockman, M. Achermann, and V. I. Klimov, “Dipolar emitters at nanoscale proximity of metal surfaces: giant enhancement of relaxation,” Phys. Rev. B 69, 121403(R) (2004). [CrossRef]

, 91

91. J. Aizpurua and A. Rivacoba, “Nonlocal effects in the plasmons of nanowires and nanocavities excited by fast electron beams,” Phys. Rev. B 78, 035404 (2008). [CrossRef]

, 92

92. F. J. G. de Abajó, “Nonlocal effects in the plasmons of strongly interacting nanoparticles, dimers, and waveguides,” J. Phys. Chem. C 112, 17983–17987 (2008). [CrossRef]

, 93

93. J. Zuloaga, E. Prodan, and P. Nordlander, “Quantum description of the plasmon resonances of a nanoparticle dimer,” Nano Lett. 9, 88789 (2009). [CrossRef]

], such as close to corners, tips, and gaps. Interestingly, metals also have a very strong nonlinear response. For example, the third-order nonlinear susceptibility of gold (χ(3)1nm2V2) is more than 3 orders of magnitude larger than the susceptibility of the most nonlinear optical crystals, such as lithium niobate (LiNbO3) [94

94. R. A. Ganeev, I. A. Kulagin, A. I. Ryasnyansky, R. I. Tugushev, and T. Usmanov, “Characterization of nonlinear optical parameters of KDP, LiNbo3 and BBO crystals,” Opt. Commun. 229, 403–412 (2003). [CrossRef]

, 95

95. N. Bloembergen, W. K. Burns, and M. Matsuoka, “Reflected third harmonic generation by picosecond laser pulses,” Opt. Commun. 1, 195–198 (1969). [CrossRef]

, 96

96. J. Renger, R. Quidant, N. V. Hulst, and L. Novotny, “Optical four-wave mixing at planar noble metal surfaces,” submitted to Phys. Rev. Lett..

]. Laser systems employ nonlinear crystals instead of noble metals for frequency conversion because they are transparent, enabling them to be placed in a beam line, and because they allow phase matching—the coherent addition of the nonlinear response on propagation through a periodic crystal. For phase matching to occur the crystal needs to be many wavelengths in size. In plasmonics, one is usually more concerned with local nonlinear signals, and without the constraints associated with lasers, exploiting the nonlinearities of noble metal antenna structures may be favorable. Nonlinear plasmonics is a largely unexplored territory and only a few nonlinear interactions in noble metal nanostructures have been studied so far, including second-harmonic generation [97

97. A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90, 013903 (2003). [CrossRef] [PubMed]

, 98

98. M. Labardi, M. Allegrini, M. Zavelani-Rossi, D. Polli, G. Cerullo, S. D. Silvestri, and O. Svelto, “Highly efficient second-harmonic nanosource for near-field optics and microscopy,” Opt. Lett. 29, 62–64 (2004). [CrossRef] [PubMed]

], third-harmonic generation [99

99. M. Lippitz, M. A. van Dijk, and M. Orrit, “Third-harmonic generation from single gold nanoparticles,” Nano Lett. 5, 799 (2005). [CrossRef] [PubMed]

], two-photon excited luminescence (TPL) [87

87. M. R. Beversluis, A. Bouhelier, and L. Novotny, “Continum generation from single gold nanostructures through near-field mediated intraband transitions,” Phys. Rev. B 68, 115433 (2003). [CrossRef]

, 100

100. A. Bouhelier, M. R. Beversluis, and L. Novotny, “Characterization of nanoplasmonic structures by locally excited photoluminescence,” Appl. Phys. Lett. 83, 5041–5043 (2003). [CrossRef]

, 101

101. P. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005). [CrossRef] [PubMed]

, 102

102. P. Ghenuche, S. Cherukulappurath, T. H. Taminiau, N. F. van Hulst, and R. Quidant, “Spectroscopic mode mapping of resonant plasmon nanoantennas,” Phys. Rev. Lett. 101, 116805 (2008). [CrossRef] [PubMed]

], and four-wave mixing [103

103. M. Danckwerts and L. Novotny, “Optical frequency mixing at coupled gold nanoparticles,” Phys. Rev. Lett. 98, 026104 (2007). [CrossRef] [PubMed]

, 104

104. S. Palomba and L. Novotny, “Nonlinear excitation of surface plasmon polaritons by four-wave mixing,” Phys. Rev. Lett. 101, 056802 (2008). [CrossRef] [PubMed]

]. Figure 8 shows the spectrum of photons emitted from a pair of gold nanoparticles in touching contact irradiated with laser pulses of wavelength λ1=810nm and λ2=1210nm. The discrete peaks correspond to coherent nonlinear processes, whereas the broad continuum is associated with TPL. The intensity drop toward the red (λem>570nm) is due to the optical filters used to suppress the excitation lasers.

The high optical nonlinearities of metals bring many opportunities for nanoscale photonic devices. For example, the intensity of optical four-wave mixing in a gold nanoparticle junction spans 4 orders of magnitude with a gap variation of only 2nm [103

103. M. Danckwerts and L. Novotny, “Optical frequency mixing at coupled gold nanoparticles,” Phys. Rev. Lett. 98, 026104 (2007). [CrossRef] [PubMed]

] (see Fig. 9). Optical four-wave mixing uses two incident laser beams with frequencies ω1 and ω2 to produce radiation at frequency ω4WM=2ω1ω2. Figure 9(b) demonstrates that a pair of gold nanoparticles can be used as a spatially and temporally controllable photon source. The ability to generate local frequency conversion with high efficiency makes it possible to exploit frequency-selective interactions across the entire visible and IR spectrum while requiring only a single frequency excitation. Frequency-converted fields can be used to interact with nanoscale systems like single quantum dots, molecules, or ions. The challenge for optical antenna design is that the structures need to be resonant simultaneously at multiple wavelengths—the wavelengths of incoming radiation and the wavelengths of outgoing radiation. Nonlinear optical antennas hold promise for frequency conversion on a single-photon level and for single-photon transistors [106

106. D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys. 3, 807–812 (2007). [CrossRef]

]: devices that employ the energy of a single photon to switch between states.

3.10. Characterization of Optical Antennas

An alternative characterization modality uses the nonlinear responses of antennas mentioned in Subsection 3.9. TPL is a second-order process especially suited for mapping out intensity hot spots in antennas generating a high degree of field localization, such as the bowtie [121

121. K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: resonators for local field enhancement,” J. Appl. Phys. 94, 4632–4642 (2003). [CrossRef]

, 122

122. A. Sundaramurthy, K. B. Crozier, G. S. Kino, D. P. Fromm, P. J. Schuck, and W. E. Moerner, “Field enhancement and gap-dependent resonance in a system of two opposing tip-to-tip Au nanotriangles,” Phys. Rev. B 72, 165409 (2005). [CrossRef]

], half-wave [102

102. P. Ghenuche, S. Cherukulappurath, T. H. Taminiau, N. F. van Hulst, and R. Quidant, “Spectroscopic mode mapping of resonant plasmon nanoantennas,” Phys. Rev. Lett. 101, 116805 (2008). [CrossRef] [PubMed]

], or gap antennas [123

123. P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005). [CrossRef] [PubMed]

, 102

102. P. Ghenuche, S. Cherukulappurath, T. H. Taminiau, N. F. van Hulst, and R. Quidant, “Spectroscopic mode mapping of resonant plasmon nanoantennas,” Phys. Rev. Lett. 101, 116805 (2008). [CrossRef] [PubMed]

]. Figure 10 shows field intensities in antenna test structures revealed by far-field TPL measurements using femtosecond laser excitation. As expected, the strongest enhancements arise in the gap region when the incoming light is polarized along the length of the antenna. To increase the spatial resolution in TPL imaging, Bouhelier et al. employed a sharp tip to locally scatter the TPL signal generated by the antenna under study [100

100. A. Bouhelier, M. R. Beversluis, and L. Novotny, “Characterization of nanoplasmonic structures by locally excited photoluminescence,” Appl. Phys. Lett. 83, 5041–5043 (2003). [CrossRef]

]. The tip is raster scanned over the laser-irradiated antenna in close proximity, and the TPL intensity is measured as a function of the tip’s scan coordinates. In order not to perturb the antenna's behavior, care must be taken to avoid any strong interaction between the local scatterer and the antenna under study.

As an aside, one must note the difference in the role of the feed gap between the radio and optical regimes. The feed gap in a radio antenna is typically impedance matched to a generator (source) and is not a point of high localized energy density. This matching ensures that the two antenna segments do not feel a gap or discontinuity between them. The gap in an optical gap antenna, in contrast, is a region of high local field intensity and dictates the antenna’s overall optical response. It is a high impedance point due to the large LDOS (see Subsection 3.2), and the efforts over the years to engineer the gap for strongest field enhancement are a direct consequence. The mismatched gap can even be turned into an advantage as it provides a means to tune antenna properties, e.g., by loading the gap with various nanoloads [85

85. A. Alù and N. Engheta, “Input impedance, nanocircuit loading, and radiation tuning of optical nanoantennas,” Phys. Rev. Lett. 101, 043901 (2008). [CrossRef] [PubMed]

, 124

124. A. Alù and N. Engheta, “Hertzian plasmonic nanodimer as an efficient optical nanoantenna,” Phys. Rev. B 78, 195111 (2008). [CrossRef]

, 125

125. A. Alù and N. Engheta, “Tuning the scattering response of optical nanoantennas with nanocircuit loads,” Nat. Photonics 2, 307–310 (2008). [CrossRef]

]. Such a tuning may enable one to go beyond simple field enhancement and might lead to truly impedance-matched energy transfer between a localized source and the antenna.

4. Applications of Optical Antennas

Research in the field of optical antennas is currently driven by the need for high field enhancement, strong field localization, and large absorption cross sections. This includes antennas for high-resolution microscopy and spectroscopy, photovoltaics, light emission, and coherent control. In one way or another, optical antennas are used to make processes more efficient or to increase the specificity of gathered information. In this section, we review recent advances, highlight application areas, and discuss future developments in the field of optical antennas.

4.1. Antennas for Nanoscale Imaging and Spectroscopy

The hallmark of optical antennas, their ability to influence light on the nanometer scale, leads naturally to nanoimaging applications. In the context of nanoscale imaging, an optical antenna represents a near-field optical probe used to interact locally with an unknown sample surface. To acquire a near-field optical image, the optical antenna is guided over the sample surface in close proximity and an optical response (scattering, fluorescence, antenna detuning) is detected for each image pixel. In general, a near-field image recorded in this way renders the spatial distribution of the antenna–sample interaction strength, and not the properties of the sample. It is possible, however, to write the interaction between antenna and sample as a series of interaction orders [126

126. J. Sun, S. Carney, and J. Schotland, “Strong tip effects in near-field optical tomography,” J. Appl. Phys. 102, 103103 (2007). [CrossRef]

], and in many cases it is legitimate to retain only a single dominant term. For example, in scattering-based near-field microscopy, the antenna acts as a local perturbation that scatters away the field near the sample surface. Therefore, the antenna–sample interaction can be largely neglected. At the other extreme, in tip-enhanced near-field optical microscopy, the sample interacts predominantly with the locally enhanced antenna field, and the external irradiation can be largely ignored. In this regime the optical antenna acts as a nanoscale flashlight [127

127. E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, “Plasmonic laser antenna,” Appl. Phys. Lett. 89, 093120 (2006). [CrossRef]

] that can be used to perform local spectroscopy.

There is a considerable body of literature on microscopy and spectroscopy aided by antennas, which has been covered in several recent reviews [59

59. L. Novotny and S. J. Stranick, “Near-field optical microscopy and spectroscopy with pointed probes,” Annu. Rev. Phys. Chem. 57, 303–331 (2006). [CrossRef] [PubMed]

, 51

51. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge Univ. Press, 2006). [CrossRef]

, 82

82. L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett. 98, 266802 (2007). [CrossRef] [PubMed]

, 128

128. A. Hartschuh, M. R. Beversluis, A. Bouhelier, and L. Novotny, “Tip-enhanced optical spectroscopy,” Philos. Trans. R. Soc. London, Ser. A 362, 807–819 (2003). [CrossRef]

, 129

129. A. Hartschuh, “Tip-enhanced near-field optical microscopy,” Angew. Chem., Int. Ed. 47, 8178–8191 (2008). [CrossRef]

, 130

130. E. Bailo and V. Deckert, “Tip-enhanced Raman scattering,” Chem. Soc. Rev. 37, 921–930 (2008). [CrossRef] [PubMed]

, 131

131. E. Fort and S. Grésillon, “Surface enhanced fluorescence,” J. Phys. D 41, 013001 (2008). [CrossRef]

]. Our goal below is not to provide a comprehensive review of the field, but rather to convey the basic concepts with some examples.

4.1a. Scattering-Based Microscopy

The optical field near an irradiated sample consists of both propagating and evanescent field components. The inability of the imaging apparatus to collect the evanescent fields results in the resolution limit. The basic idea behind scattering based near-field microscopy is to locally convert the evanescent fields into propagating radiation by use of a scattering probe. The first experiments performed in the early 1990s used sharp metal tips [132

132. R. Bachelot, P. Gleyzes, and A. C. Boccara, “Near-field optical microscope based on local perturbation of a diffraction spot,” Opt. Lett. 20, 1924–1926 (1995). [CrossRef] [PubMed]

, 133

133. S. Kawata and Y. Inouye, “Scanning probe optical microscopy using a metallic probe tip,” Ultramicroscopy 57, 313–317 (1995). [CrossRef]

], although semiconducting atomic force microscopy tips have since become the prevalent choice. Samples that couple strongly with the illuminating laser radiation (e.g., due to plasmon or phonon resonances) are best suited for scattering microscopy studies. As a consequence, most studies to date have investigated metallic nanostructures excited in the visible or near-IR [134

134. B. Deutsch, R. Hillenbrand, and L. Novotny, “Near-field amplitude and phase recovery using phase-shifting interferometry,” Opt. Express 16, 494–501 (2008). [CrossRef] [PubMed]

, 135

135. R. Vogelgesang, J. Dorfmüller, R. Esteban, R. T. Weitz, A. Dmitriev, and K. Kern, “Plasmonic nanostructures in aperture-less scanning near-field optical microscopy (aSNOM),” Phys. Status Solidi B 245, 2255–2260 (2008). [CrossRef]

] and semiconductors in the mid-IR [136

136. A. Cvitkovic, N. Ocelic, J. Aizpurua, R. Guckenberger, and R. Hillenbrand, “Infrared imaging of single nanoparticles via strong field enhancement in a scanning nanogap,” Phys. Rev. Lett. 97, 060801 (2006). [CrossRef] [PubMed]

]. Driven by the need for efficient signal extraction from a large background, Knoll and Keilmann proposed modulating the tip vertically (at frequency Ω) and demodulating the signal at higher harmonics (nΩ) [137

137. B. Knoll and F. Keilmann, “Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy,” Opt. Commun. 182, 321–328 (2000). [CrossRef]

]. This technique was later combined with a heterodyne scheme to extract optical amplitude and phase information of the scattered light [138

138. R. Hillenbrand and F. Keilmann, “Complex optical constants on a subwavelength scale,” Phys. Rev. Lett. 85, 3029–3032 (2000). [CrossRef] [PubMed]

, 139

139. F. Keilmann and R. Hillenbrand, “Near-field microscopy by elastic light scattering from a tip,” Philos. Trans. R. Soc. London, Ser. A 362, 787–797 (2004). [CrossRef]

].

In most scattering-based approaches it is assumed that the incident light interacts more strongly with the sample surface than with the local probe. Therefore, the resulting images reflect primarily the properties of the sample. However, the sample properties always act back on the local probe and influence its properties. This back-action has been recently studied in an elegant experiment by Sandoghdar and co-workers using a local probe in the form of a single gold nanoparticle [76

76. T. Kalkbrenner, U. Håkanson, A. Schädle, S. Burger, C. Henkel, and V. Sandoghdar, “Optical microscopy via spectral modifications of a nanoantenna,” Phys. Rev. Lett. 95, 200801 (2005). [CrossRef] [PubMed]

]. The properties of this nanoparticle antenna, such as its resonance frequency and scattering strength, were found to be dependent on the local environment defined by the sample properties. Therefore, the antenna detuning becomes a local probe for the properties of the sample. An example of these studies is shown in Fig. 11, which renders a spatial map of the width of the antenna resonance recorded while scanning the nanoparticle antenna over a test structure. The nanoparticle antenna has also been recently used by Eng and co-workers to demonstrate scattering microscopy in the mid-IR using an 80nm gold nanoparticle [140

140. M. Wenzel, T. Härtling, P. Olk, S. C. Kehr, S. Grafström, S. Winnerl, M. Helm, and L. M. Eng, “Gold nanoparticle tips for optical field confinement in infrared scattering near-field optical microscopy,” Opt. Express 16, 12302–12312 (2008). [CrossRef] [PubMed]

].

4.1b. Spectroscopy Based on Local Field Enhancement

An effective antenna interacts strongly with incoming radiation and leads to a high degree of field localization. The localized fields have been used in several recent experiments as excitation sources for local spectroscopy, such as fluorescence, IR absorption, and Raman scattering.

Laser-excited fluorescence is a widely used analytical tool because fluorescence can be significantly redshifted from excitation (Stokes shift), rendering the signal essentially background free. Even though fluorescence does not typically reveal molecular information, and neither are fluorescent dyes particularly long-lived (photobleaching), it offers single-molecule sensitivity even without any antennas [141

141. X. S. Xie and J. K. Trautman, “Optical studies of single molecules at room temperature,” Annu. Rev. Phys. Chem. 49, 441–480 (1998). [CrossRef]

] because of the large absorption cross sections of fluorescent dyes (1015cm2). The fluorescence rate Γfl from a single emitter is determined by the excitation rate Γexc and the intrinsic quantum yield ηi of the emitter. ηi is defined analogously to Eq. (13) as Γrado(Γrado+Γnro), where Γrado and Γnro are the intrinsic radiative and nonradiative relaxation rates, respectively. In the absence of the antenna and far from saturation (weak excitation) the fluorescence rate is given by
Γfl=Γexcoηi=ΓexcΓradoΓrado+Γnro.
(40)
The antenna typically leads to an increase in Γexc due to local field enhancement and the associated increase of the LDOS. By reciprocity [cf. Eq. (27)], an increase in Γexc is accompanied by an increase of Γrad [24

24. S. Kühn, U. Hakanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97, 017402 (2006). [CrossRef] [PubMed]

, 53

53. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946). [CrossRef]

, 142

142. J. R. Lakowicz, J. Malicka, I. Gryczynski, Z. Gryczynski, and C. D. Geddes, “Radiative decay engineering: the role of photonic mode density in biotechnology,” J. Phys. D 36, R240–R249 (2003). [CrossRef]

, 143

143. O. L. Muskens, V. Giannini, J. A. Sánchez-Gil, and J. G. Rivas, “Strong enhancement of the radiative decay rate of emitters by single plasmonic nanoantennas,” Nano Lett. 7, 2871–2875 (2007). [CrossRef] [PubMed]

]. However, the presence of the antenna also increases Γnr because of nonradiative energy transfer from the excited molecule to the antenna [144

144. H. Kuhn, “Classical aspects of energy transfer in molecular systems,” J. Chem. Phys. 53, 101–108 (1970). [CrossRef]

, 145

145. R. R. Chance, A. Prock, and R. Silbey, “Lifetime of an emitting molecule near a partially reflecting surface,” J. Chem. Phys. 60, 2744–2748 (1974). [CrossRef]

, 146

146. M. Thomas, J.-J. Greffet, R. Carminati, and J. R. Arias-Gonzalez, “Single-molecule spontaneous emission close to absorbing nanostructures,” Appl. Phys. Lett. 85, 3863–3865 (2004). [CrossRef]

]. Good emitters have ηi1, which cannot be further increased by an optical antenna. Therefore, an antenna-induced increase in fluorescence is basically a result of an increase in Γexc. On the other hand, for poor emitters with ηi1 (i.e., ΓnroΓrado), the antenna can end up enhancing both the excitation rate and the efficiency (see Fig. 6), leading to much higher net fluorescence enhancements than those for good emitters [81

81. A. Wokaun, H.-P. Lutz, A. P. King, U. P. Wild, and R. R. Ernst, “Energy transfer in surface enhanced luminescence,” J. Chem. Phys. 79, 509–514 (1983). [CrossRef]

, 147

147. J. R. Lakowicz, “Radiative decay engineering 5: metal-enhanced fluorescence and plasmon emission,” Anal. Biochem. 337, 171–194 (2005). [CrossRef] [PubMed]

].

Hartschuh et al. studied PL from single-walled carbon nanotubes and reported PL enhancements of around 100, using sharp gold tips [148

148. A. Hartschuh, H. Qian, A. J. Meixner, N. Anderson, and L. Novotny, “Nanoscale optical imaging of excitons in single-walled carbon nanotubes,” Nano Lett. 5, 2310 (2005). [CrossRef] [PubMed]

, 149

149. H. Qian, C. Georgi, N. Anderson, A. A. Green, M. C. Hersam, L. Novotny, and A. Hartschuh, “Exciton transfer and propagation in carbon nanotubes studied by near-field optical microscopy,” Nano Lett. 8, 1363–1367 (2008). [CrossRef] [PubMed]

, 150

150. H. Qian, P. T. Araujo, C. Georgi, T. Gokus, N. Hartmann, A. A. Green, A. Jorio, M. C. Hersam, L. Novotny, and A. Hartschuh, “Visualizing the local optical response of semiconducting carbon nanotubes to DNA-wrapping,” Nano Lett. 8, 2706–2711 (2008). [CrossRef] [PubMed]

] (Fig. 12). Such high enhancements are consistent with the low intrinsic PL quantum yield of 103 experimentally observed for single-walled carbon nanotubes, which is a result of large intrinsic Γnr [151

151. F. Wang, G. Dukovic, L. E. Brus, and T. F. Heinz, “Time-resolved fluorescence of carbon nanotubes and its implication for radiative lifetimes,” Phys. Rev. Lett. 92, 177401 (2004). [CrossRef] [PubMed]

]. Tam et al. used single silica-gold core-shell particles (nanoshells) for plasmonic fluorescence enhancement of adsorbed molecules with low ηi in the near-IR [152

152. F. Tam, G. P. Goodrich, B. R. Johnson, and N. J. Halas, “Plasmonic enhancement of molecular fluorescence,” Nano Lett. 7, 496501 (2007). [CrossRef]

]. Silicon quantum dots, which also have a low intrinsic quantum yield, have been studied by the groups of Atwater and Polman, and the luminescence was shown to increase close to patterned silver islands [153

153. J. S. Biteen, N. Lewis, H. Atwater, H. Mertens, and A. Polman, “Spectral tuning of plasmon-enhanced silicon quantum dot luminescence,” Appl. Phys. Lett. 88, 131109 (2006). [CrossRef]

, 154

154. H. Mertens, J. S. Biteen, H. A. Atwater, and A. Polman, “Polarization-selective plasmon-enhanced silicon quantum-dot luminescence,” Nano Lett. 6, 2622–2625 (2006). [CrossRef] [PubMed]

].

The key to having efficient antennas for fluorescence enhancement is to minimize nonradiative losses in the metal (quenching). Extended structures, such as sharp metal tips, allow relaxation of an excited emitter into propagating surface plasmons along the tip and therefore lead to high losses [155

155. N. A. Issa and R. Guckenberger, “Fluorescence near metal tips: the roles of energy transfer and surface plasmon polaritons,” Opt. Express 15, 12131–12144 (2007). [CrossRef] [PubMed]

]. Confined nanostructures such as noble metal nanoparticles strike a balance between strong field enhancement and low absorption and are thus ideal for fluorescence applications. Enhancements of up to 20 have been reported by using gold and silver nanoparticles on single fluorophores [24

24. S. Kühn, U. Hakanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97, 017402 (2006). [CrossRef] [PubMed]

, 23

23. P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006). [CrossRef]

, 77

77. P. Bharadwaj, P. Anger, and L. Novotny, “Nanoplasmonic enhancement of single-molecule fluorescence,” Nanotechnology 18, 044017 (2007). [CrossRef]

]. Spectral dependence of Γexc and Γnr has been investigated to clarify the role of surface plasmon resonance in nanoparticle antennas [71

71. P. Bharadwaj and L. Novotny, “Spectral dependence of single molecule fluorescence enhancement,” Opt. Express 15, 14266–14274 (2007). [CrossRef] [PubMed]

, 156

156. Y. Chen, K. Munechika, and D. S. Ginger, “Dependence of fluorescence intensity on the spectral overlap between fluorophores and plasmon resonant single silver nanoparticles,” Nano Lett. 7, 690–696 (2007). [CrossRef] [PubMed]

, 157

157. Y. Chen, K. Munechika, I. J.-L. Plante, A. M. Munro, S. E. Skrabalak, Y. Xia, and D. S. Ginger, “Excitation enhancement of CdSe quantum dots by single metal nanoparticles,” Appl. Phys. Lett. 93, 053106 (2008). [CrossRef]

]. Biological moieties with sizes comparable with the size of the antenna are of particular interest in fluorescence imaging [158

158. M. F. Garcia-Parajo, “Optical antennas focus in on biology,” Nat. Photonics 2, 201–203 (2008). [CrossRef]

], and single proteins have recently been visualized in physiological conditions by using a single gold nanoparticle [159

159. C. Höppener and L. Novotny, “Antenna-based optical imaging of single Ca2+ transmembrane proteins in liquids,” Nano Lett. 8, 642–646 (2008). [CrossRef]

, 160

160. C. Höppener and L. Novotny, “Imaging of membrane proteins using antenna-based optical microscopy,” Nanotechnology 19, 384012 (2008). [CrossRef] [PubMed]

].

In contrast to fluorescence, the vibrational spectra provided by Raman scattering define a unique chemical fingerprint for the material under study. However, Raman scattering cross sections are 10–15 orders of magnitude smaller than typical fluorescence cross sections of dye molecules. Therefore, the effect is generally too weak to detect, and to achieve single molecule sensitivity it is necessary to invoke enhancement mechanisms such as resonance enhancement or field enhancement. Raman scattering involves the absorption and emission of photons almost identical in energy, and a nearby antenna can amplify both the incoming field and the outgoing field. The total Raman scattering enhancement is therefore proportional to the fourth power of the field enhancement [163

163. R. Esteban, M. Laroche, and J.-J. Greffet, “Influence of metallic nanoparticles on upconversion processes,” J. Appl. Phys. 105, 033107 (2009). [CrossRef]

]. Recent studies of SERS revealed that junctions in colloidal nanoparticle clusters can have extremely high field enhancements (103), leading to Raman enhancements as high as 1014, sufficient even to detect a single molecule [164

164. S. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface enhanced Raman scattering,” Science 275, 1102 (1997). [CrossRef] [PubMed]

, 165

165. K. Kneipp, Y. Wang, H. Kneipp, I. Itzkan, R. R. Dasary, and M. S. Feld, “Single molecule detection using surface enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997). [CrossRef]

, 166

166. A. M. Michaels, J. Jiang, and L. Brus, “Ag nanocrystal junctions as the site for surface-enhanced Raman scattering of single Rhodamine 6G molecules,” J. Phys. C 104, 11965–11971 (2000).

]. In addition to field enhancement, a chemical contribution to SERS is well known [167

167. M. Moskovits, “Surface-enhanced Raman spectroscopy: a brief retrospective,” J. Raman Spectrosc. 36, 485–496 (2005). [CrossRef]

], and well-characterized antennas can be useful in separating chemical and electromagnetic contributions in the Raman enhancement mechanism [168

168. D. P. Fromm, A. Sundaramurthy, A. Kinkhabwala, P. J. Schuck, G. S. Kino, and W. E. Moerner, “Exploring the chemical enhancement for surface-enhanced Raman scattering with Au bowtie nanoantennas,” J. Chem. Phys. 124, 061101 (2006). [CrossRef]

].

4.2. Antennas for Photovoltaics

The traditional approach to photovoltaics is to use light for generating charge carriers in a semiconductor. The spatial separation of the charge carriers defines a current in an external circuit. For maximum efficiency it is important to absorb most of the incoming radiation, necessitating a minimum material thickness, which forms the primary cost determinant. There are at least three distinct ways in which nanoparticle antennas can interact with a photoactive substrate when placed in close proximity to it, as illustrated in Fig. 15. Plasmonic nanoparticles have large optical cross sections and can efficiently collect and scatter photons into the far field, some of which may become coupled into in-plane waveguide modes in the photoactive material [186

186. H. R. Stuart and D. G. Hall, “Absorption enhancement in silicon-on-insulator waveguides using metal island films,” Appl. Phys. Lett. 69, 2327–2329 (1996). [CrossRef]

, 187

187. K. R. Catchpole and S. Pillai, “Absorption enhancement due to scattering by dipoles into silicon waveguides,” J. Appl. Phys. 100, 044504 (2006). [CrossRef]

]. This leads first to an increased effective optical path length and greater photon absorption probability. Second, the spatially localized high-momentum near-field photons created in the immediate vicinity of an optical antenna can directly excite electron–hole pairs in an indirect gap semiconductor (like silicon) even without phonon assistance [188

188. M. Kirkengen, J. Bergli, and Y. M. Galperin, “Direct generation of charge carriers in c-Si solar cells due to embedded nanoparticles,” J. Appl. Phys. 102, 093713 (2007). [CrossRef]

], thereby increasing light absorption per unit thickness. Last, there is the possibility of direct charge-carrier injection from the nanoparticle into the semiconductor.

Making use of the first two effects, Stuart and Hall were the first to show increased absorption using metal nanoparticles in a 165nm thick silicon-on-insulator material [186

186. H. R. Stuart and D. G. Hall, “Absorption enhancement in silicon-on-insulator waveguides using metal island films,” Appl. Phys. Lett. 69, 2327–2329 (1996). [CrossRef]

]. More recently, Pillai et al. demonstrated 16-fold absorption enhancement at λ=1050nm by depositing >100nm silver particles on thin film silicon-on-insulator cells [189

189. S. Pillai, K. Catchpole, T. Trupke, and M. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101, 093105 (2007). [CrossRef]

], while Atwater and co-workers also saw an improvement in the performance of GaAs thin film solar cells by decorating them with silver nanoparticles [190

190. K. Nakayama, K. Tanabe, and H. A. Atwater, “Plasmonic nanoparticle enhanced light absorption in GaAs solar cells,” Appl. Phys. Lett. 93, 121904 (2008). [CrossRef]

]. Lim et al. explored the effect of spherical gold nanoparticles on optically thick silicon and found a positive effect most likely due to increased waveguiding [191

191. S. H. Lim, W. Mar, P. Matheu, D. Derkacs, and E. T. Yu, “Photocurrent spectroscopy of optical absorption enhancement in silicon photodiodes via scattering from surface plasmon polaritons in gold nanoparticles,” J. Appl. Phys. 101, 104309 (2007). [CrossRef]

]. Hägglund et al. investigated thick silicon further by using gold nanodisks and highlighted the problem of increased losses at the plasmon resonance wavelength, which can more than compensate for an increase of absorption in silicon [192

192. C. Hägglund, M. Zäch, G. Petersson, and B. Kasemo, “Electromagnetic coupling of light into a silicon solar cell by nanodisk plasmons,” Appl. Phys. Lett. 92, 053110 (2008). [CrossRef]

]. Improvements in the performance of organic solar cells [193

193. A. J. Morfa, K. L. Rowlen, T. H. Reilly, M. J. Romero, and J. van de Lagemaat, “Plasmon-enhanced solar energy conversion in organic bulk heterojunction photovoltaics,” Phys. Rev. E 92, 013504 (2008).

, 194

194. S.-S. Kim, S.-I. Na, J. Jo, D.-Y. Kim, and Y.-C. Nah, “Plasmon enhanced performance of organic solar cells using electrodeposited Ag nanoparticles,” Appl. Phys. Lett. 93, 073307 (2008). [CrossRef]

] and InPInGasAsP quantum-well solar cells [195

195. D. Derkacs, W. V. Chen, P. M. Matheu, S. H. Lim, P. K. L. Yu, and E. T. Yu, “Nanoparticle-induced light scattering for improved performance of quantum-well solar cells,” Appl. Phys. Lett. 93, 091107 (2008). [CrossRef]

] have also been reported recently. In all of these examples, the inclusion of nanoparticles in the solar cell structure leads to a reduction in the absorption-mandated thickness requirement for the photoconductive material. A reduced thickness is favorable, especially for organic semiconductors, since it allows a higher fraction of photogenerated carriers to reach the outer world (electrodes) without being lost to undesirable recombination events. A good review of recent developments is given by Catchpole and Polman [196

196. K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express 16, 21793–21800 (2008). [CrossRef] [PubMed]

].

Another attractive class of photovoltaic cells is the dye-sensitized solar cell or Grätzel cell [197

197. B. O’Regan and M. Grätzel, “A low-cost, high-efficiency solar cell based on dye-sensitized colloidal TiO2 films,” Nature 353, 737–740 (1991). [CrossRef]

]. These cells employ extremely fast charge injection from a dye into the conduction band of a large bandgap semiconductor, typically TiO2, instead of the usual approach of generating electron–hole pairs in the semiconductor directly. Early attempts at incorporating metal nanostructures in Grätzel cells gave mixed results [198

198. G. Zhao, H. Kozuka, and T. Yoko, “Effects of the incorporation of silver and gold nanoparticles on the photoanodic properties of rose bengal sensitized TiO2 film electrodes prepared by sol-gel method,” Sol. Energy Mater. Sol. Cells 46, 219–231 (1997). [CrossRef]

, 199

199. C. Wen, K. Ishikawa, M. Kishima, and K. Yamada, “Effects of silver particles on the photovoltaic properties of dye-sensitized TiO2 thin films,” Sol. Energy Mater. Sol. Cells 61, 339–351 (2000). [CrossRef]

]. Hägglund et al. [200

200. C. Hägglund, M. Zäch, and B. Kasemo, “Enhanced charge carrier generation in dye sensitized solar cells by nanoparticle plasmons,” Appl. Phys. Lett. 92, 013113 (2008). [CrossRef]

] systematically explored this issue by sensitizing a model dye-sensitized solar cell system of flat TiO2 film with nanofabricated gold ellipsoids, as shown in Fig. 16. They found evidence for plasmonically enhanced charge generation rate from the dye, which was attributed to a combination of near-field and far-field effects [200

200. C. Hägglund, M. Zäch, and B. Kasemo, “Enhanced charge carrier generation in dye sensitized solar cells by nanoparticle plasmons,” Appl. Phys. Lett. 92, 013113 (2008). [CrossRef]

]. Adopting a different approach and improving on initial experiments by Kozuka et al. [201

201. H. Kozuka, G. Zhao, and T. Yoko, “Sol-gel preparation and photoelectrochemical properties of TiO2 films containing Au and Ag metal particles,” Thin Solid Films 277, 147–154 (1996). [CrossRef]

], Tian and Tatsuma have replaced the dye completely by gold nanoparticles and made use of direct photocarrier injection from the nanoparticles into TiO2 to get photon-to-current conversion efficiencies as high as 20% [202

202. Y. Tian and T. Tatsuma, “Mechanisms and applications of plasmon-induced charge separation at TiO2 films loaded with gold nanoparticles,” J. Am. Chem. Soc. 127, 7632–7637 (2005). [CrossRef] [PubMed]

]. A scenario combining the two effects of direct charge injection and absorption enhancement of the dye in a nanoparticle-enriched Grätzel cell should be easily realizable.

4.3. Antennas for Light Emission

Because of reciprocity, optical antennas increase not only the efficiency of light absorption but also the efficiency of light emission. They stand to improve inherently low-efficiency lighting schemes like organic LEDs (OLEDs), silicon-based lighting, and solid-state lighting in the yellow and green spectral region.

Typically, an OLED comprises an active organic semiconductor sandwiched between two electrodes. The charges injected from the electrodes recombine as electron–hole pairs (excitons) and then transfer their energy to light-emitting dopants. Despite the simplicity of the system, OLED technology faces several challenges, and optical antenna structures might provide solutions for some of them. Nominally one quarter of excitons are formed in a singlet (spin-zero) state, and three quarters are in a triplet (spin-one) state. However, in most cases the light-emitting dopants can only convert the energy of singlet states into photons, and the energy associated with triplet states is dissipated as heat. The triplet states not only reduce the efficiency but are also believed to reduce the longevity of a device. Optical antennas have the potential to quench the triplet state lifetimes, thereby increasing the long-term stability of OLEDs. Another limitation in OLEDs is that some of the energy released in the recombination process becomes trapped in the conducting electrodes as surface plasmons and is eventually dissipated into heat. By patterning the electrodes with arrays of holes, this energy can be released from surface plasmon modes and emitted into free space [203

203. S. Wedge, J. A. E. Wasey, and W. L. Barnes, “Coupled surface plasmon-polariton mediated photoluminescence from a top-emitting organic light-emitting structure,” Appl. Phys. Lett. 85, 182–184 (2004). [CrossRef]

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]. Liu et al. show a factor-seven improvement in the electroluminescence quantum efficiency of an OLED device [204

204. C. Liu, V. Kamaev, and Z. V. Vardenya, “Efficiency enhancement of an organic light-emitting diode with a cathode forming two-dimensional periodic hole array,” Appl. Phys. Lett. 86, 143501 (2005). [CrossRef]

]. They attribute this phenomenon to the enhanced transmission of the electroluminescence through the perforated electrode. Perforations in such a metal act as antennas, allowing plasmon modes to couple to propagating radiation.

A similar effect can be achieved by using metallic particles instead of holes and has found success in the field of silicon lighting. Philip Ball’s 2001 review of the state of silicon light emission lists quantum dots and texture engineering as ways to increase the emission efficiency, but makes no mention of the use of antennas or metallic nanoparticles [206

206. P. Ball, “Let there be light,” Nature 409, 974–976 (2001). [CrossRef] [PubMed]

]. Two years earlier, W. L. Barnes had suggested using periodically textured metal films for light extraction from a semiconductor, using an angular emission argument [207

207. W. Barnes, “Electromagnetic crystals for surface plasmon polaritons and the extraction of light from emissive devices,” J. Lightwave Technol. 17, 2170–2182 (1999). [CrossRef]

]. The first experimental demonstration of such a solution was reported in 2005 by Pillai et al. [208

208. S. Pillai, K. R. Catchpole, T. Trupke, G. Zhang, J. Zhao, and M. A. Green, “Enhanced emission from Si-based light emitting diodes using surface plasmons,” Appl. Phys. Lett. 88, 161102 (2006). [CrossRef]

], who showed a threefold enhancement over the full electroluminescence spectrum of a silicon emitter with silver nanoparticle islands on its surface. Figure 17, which shows a device partially covered with the islands, vividly illustrates the enhancement effect. After one year, they published an improvement to sevenfold enhancement [189

189. S. Pillai, K. Catchpole, T. Trupke, and M. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101, 093105 (2007). [CrossRef]

]. Their analysis focuses on surface plasmon polaritons in the particles as a coupling mechanism between the incident and local fields. The particles function as a random array of transmitting optical antennas.

Optical antennas can also be used to enhance the efficiency of solid-state devices at wavelengths where we lack emission-efficient materials. Today’s high-efficiency solid-state lighting devices use the remarkable properties of LEDs composed of InGaN and AlGaInP [209

209. Basic Research Needs for Solid-State Lighting, Report of the Basic Energy Sciences Workshop on Solid-State Lighting (U.S. Department of Energy,2006), http://www.sc.doe.gov/bes/reports/files/SSL_rpt.pdf.

]. The former has a high emission yield in the blue–green spectral region [210

210. S. Nakamura, T. Mukai, and M. Senoh, “Candela-class high-brightness InGaNAlGaN double-heterostructure blue-light-emitting diodes,” Appl. Phys. Lett. 64, 1687–1689 (1994). [CrossRef]

], and the latter possesses a high emission efficiency in the red. For white light illumination one also requires emission in the green–yellow spectral region, but, unfortunately, InGaN turns out to have a low quantum efficiency in this region [211

211. C. Wetzel, T. Salagaj, T. Detchprohm, P. Li, and J. S. Nelson, “GaInNGaN growth optimization for high power green light emitting diodes,” Appl. Phys. Lett. 85, 866–868 (2004). [CrossRef]

]. Near the peak sensitivity of the human eye (wavelength 550nm) the external efficiency is only about 5%. Besides the low quantum efficiency in the green–yellow region, InGaN also possesses an efficiency roll-off at high electron–hole injection densities, limiting the performance of high-power LEDs. One avenue for increasing the emission yield in the green–yellow spectral region is the introduction of phosphors such as Y3Al5O12:Ce3+ (YAG) that are pumped by the blue emission of InGaN [212

212. P. Schlotter, R. Schmidt, and J. Schneider, “Luminescence conversion of blue light mmitting diodes,” Appl. Phys. A 64, 417 (1997). [CrossRef]

]. However, the introduction of phosphors brings other challenges such as saturation and photochemical stability.

Optical antennas in the form of nanoparticles with suitably engineered plasmonic modes are able to improve the efficiency of low quantum yield emitters and might prove beneficial in solid-state lighting applications. The improvements for a simple spherical nanoparticle antenna have been discussed in Subsection 3.6 (see Fig. 6), and much better efficiency enhancements can be expected for improved antenna geometries. Besides the potential for increasing quantum efficiencies, optical antennas might also enable higher extraction efficiencies by providing a means to extract photons from the source region.

All of these applications involve devices with inherently low efficiency. As shown in Subsection 3.6, antennas can only hurt devices with inherently high efficiency. The limitations of metallic nanoparticles in light-emitting devices are pointed out by Sun et al. [213

213. J. Sun, J. Khurgin, and R. Soref, “Plasmonic light-emission enhancement with isolated metal nanoparticles and their coupled arrays,” J. Opt. Soc. Am. B 25, 1748–1755 (2008). [CrossRef]

]. They consider an InGaNGaN active quantum well in a dielectric medium and model the luminescence with and without a silver nanosphere. Their goal is to optimize the emitter–nanosphere separation and the size of the nanosphere. Finding a result similar to Eq. (14), Sun et al. thus conclude that nanoparticle antennas may be useful for detection and instrumentation, but that they hold little promise for efficient, large-area emitters.

Optical antennas may make low-cost but inefficient devices like OLEDs and silicon LEDs feasible, and they offer a way to patch up missing colors in efficient solid-state lighting. Developments in these directions are underway in various laboratories, and it will be interesting to see in which applications the optical antenna concept ultimately finds use.

4.4. Antennas for Coherent Control

So far we have discussed the ability of optical antennas to couple propagating far fields to localized near fields and vice versa, but we have ignored their interesting temporal dynamics. The broad spectral response associated with plasmons in metals corresponds to dynamics in the range of hundreds of attoseconds [214

214. M. Stockman, M. Kling, U. Kleinberg, and F. Krausz, “Attosecond nanoplasmonic-field microscope,” Nat. Photonics 1, 539–544 (2007). [CrossRef]

], which makes optical antennas useful tools for ultrafast applications like nanoscale computing, time-resolved spectroscopy, or selective chemical bonding. In short, the rapid response of the free-electron gas in a metal provides a means for controlling the dynamics of a system on the quantum level. Quantum control has been an active area of research recently, and many strategies have been suggested [215

215. H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, “Whither the future of controlling quantum phenomena?” Science 288, 824–828 (2000). [CrossRef] [PubMed]

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, 218

218. M. Stockman, D. Bergman, and T. Kobayashi, “Coherent control of nanoscale localization of ultrafast optical excitation in nanosystems,” Phys. Rev. B 69, 054202 (2004). [CrossRef]

, 219

219. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007). [CrossRef] [PubMed]

]. Ultrafast plasmonics is particularly promising, but it requires the ability to control local field distributions temporally and spatially.

The antenna properties of metal nanostructures provide a convenient way to control plasmon dynamics. A pulse of light incident on a nanostructure imprints temporally dependent amplitude, phase, and polarization information on the structure. Stockman et al. showed that ultrafast pulse shaping can achieve many degrees of freedom to control the fields associated with the surface plasmons [220

220. M. I. Stockman, S. V. Faleev, and D. J. Bergman, “Coherently controlled femtosecond energy localization on nanoscale,” Appl. Phys. B 74, S63–S67 (2002). [CrossRef]

, 221

221. M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93, 137404 (2004). [CrossRef] [PubMed]

, 222

222. M. I. Stockman, “Ultrafast nanoplasmonics under coherent control,” New J. Phys. 10, 025031 (2008). [CrossRef]

]. Three main strategies are used to achieve the desired control of surface plasmon oscillations. First, if the Green’s function of the plasmonic system is known exactly, the incident field parameters can be solved for. Stockman showed that the Green’s function has separable dependencies on geometry and material properties [222

222. M. I. Stockman, “Ultrafast nanoplasmonics under coherent control,” New J. Phys. 10, 025031 (2008). [CrossRef]

] and can in principle be calculated. Second, time-reversal techniques provide a way to concentrate fields to an arbitrary pattern in a sample without cumbersome calculations [222

222. M. I. Stockman, “Ultrafast nanoplasmonics under coherent control,” New J. Phys. 10, 025031 (2008). [CrossRef]

]. Using this method, model emitters (i.e. fluorescent dipoles) generate plasmons in the antenna structure, which then radiate into the near and far field. If these fields are recorded, they can be time reversed and played back, thus reconstructing the original excitation. One serious challenge associated with time-reversal approaches is that the near field, which contains essential reconstruction information, is difficult to measure, owing to its exponential distance dependence. But since the plasmons are relatively long lived, the antenna serves as a reverberating structure, slowly emitting energy into the far field to be recorded. Finally, if the system is configured in a feedback loop, learning algorithms can be used to find the optimal pulse shapes and polarizations for the desired effects [223

223. T. Brixner, F. G. de Abajo, J. Schneider, and W. Pfeiffer, “Nanoscopic ultrafast space-time-resolved spectroscopy,” Phys. Rev. Lett. 95, 093901 (2005). [CrossRef] [PubMed]

, 224

224. M. Sukharev and T. Seideman, “Phase and polarization control as a route to plasmonic nanodevices,” Nano Lett. 6, 715–719 (2006). [CrossRef] [PubMed]

]. This method was used recently in the first experimental demonstration of dynamic localization of surface plasmon fields in an antenna-type nanostructure by Aeschlimann et al. [225

225. M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. G. de Abajó, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446, 301–304 (2007). [CrossRef] [PubMed]

]. As illustrated in Fig. 18, photoelectron maximization and minimization leads to localization in different regions of the nanostructure. These experiments prove that the electromagnetic modes of an optical antenna can be controlled in time and space by pulsed laser excitation.

Applications such as nanoscale sensing, high-resolution spectroscopy, and optical logic require strongly confined and enhanced fields [222

222. M. I. Stockman, “Ultrafast nanoplasmonics under coherent control,” New J. Phys. 10, 025031 (2008). [CrossRef]

], and the possibility to coherently control the electromagnetic response of an optical antenna opens the door to temporally and spatially influence these fields.

5. Conclusions and Outlook

The study of optical antennas is still in its infancy. While some properties directly derive from classical antenna theory, the direct downscaling of antenna designs into the optical regime is not possible because radiation penetrates into metals and gives rise to plasma oscillations. In general, an optical antenna is designed to increase the interaction area of a local absorber or emitter with free radiation, thereby making the light–matter interaction more efficient. This is accounted for in quantities such as the LDOS, the antenna impedance, or the antenna aperture.

As in canonical antenna theory, there is no universal antenna design. Instead, optical antennas have to be optimized separately for each application. However, to achieve the best efficiency the internal energy dissipation of any antenna must be minimized. For a quantum emitter such as an atom, molecule, or ion, a good antenna yields a low nonradiative decay rate.

So far, most of the progress in fabrication of the more complicated antenna designs has been in the IR, where electron-beam lithography is relatively commonplace. Fabrication and testing at visible wavelengths is in its beginning states, but shows promise.

New ideas and developments are emerging at a rapid pace, and it is clear that the optical antenna concept will provide new opportunities for optoelectronic architectures and devices. Today, the building blocks for optical antennas are plasmonic nanostructures. These can be fabricated from the bottom up by colloidal chemistry or from the top down with established nanofabrication techniques, such as electron-beam lithography or focused ion-beam milling. It is also conceivable that future optical antenna designs will draw inspiration from biological systems such as light harvesting proteins in photosynthesis.

Acknowledgments

This work was funded by the U.S. Department of Energy (DOE) (DE-FG02-01ER15204) and the National Science Foundation (NSF) (ECCS-0651079). We thank Tim Taminiau, Niek van Hulst, and Jean-Jacques Greffet for valuable discussions, and Barbara Schirmer and Alexandre Bouhelier for help with patent and literature searches.

Figures

Fig. 1 Antenna-based optical interactions: (a) antenna-coupled LED, (b) antenna-coupled photovoltaics, (c) antenna-coupled spectroscopy.
Fig. 2 Examples of IR optical antennas fabricated by Boreman and co-workers: (a) asymmetric spiral antenna [45], (b) microstrip dipole antenna [46], (c) square spiral antenna [43], (d) phased-array antenna [47].
Fig. 3 Problem statement of optical antenna theory. A receiver or transmitter (atom, ion, molecule...) interacts with free optical radiation via an optical antenna.
Fig. 4 Illustration of reciprocity between two point emitters. The excitation rate Γexc of p1 is related to its radiative decay rate Γrad and its directivity D(θ,φ).
Fig. 5 (a) An optical antenna in the form of a gold or silver nanoparticle attached to the end of a pointed glass tip is interacting with a single molecule. The inset shows an scanning electron microscope image of a 80nm gold particle attached to a glass tip. (b) Theoretical model.
Fig. 6 Radiation efficiency εrad as a function of separation between a gold nanoparticle antenna and a molecule with different quantum efficiencies ηi. The lower ηi is, the higher the radiation enhancement can be. The curves are scaled to the same maximum value.
Fig. 7 Effective wavelength scaling for linear gold antennas. (a) Intensity distribution (E2, factor of 2 between contour lines) for a gold half-wave antenna irradiated with a plane wave (λ=1150nm). (b) Amplitude and phase of the current density (j) evaluated along the axis of the antenna. (c) Effective wavelength scaling for gold rods of different radii (5, 10, and 20nm).
Fig. 8 Spectrum of photons emitted from a pair of gold nanoparticles irradiated with laser pulses of wavelength λ1=810nm and λ2=1210nm. Each peak is associated with a different nonlinear process. From [105].
Fig. 9 (a) Four-wave mixing photon count rate (λ4WM=639nm) as a function of the separation of two 60nm gold nanoparticles. Inset, detailed view on a log-log scale. Dots are data, and the curves are power-law fits. The kink in the curve indicates the formation of a conductive bridge. (b) Photon bursts generated by modulating the interparticle separation. Reprinted with permission from [103]. © 2007 American Physical Society.
Fig. 10 Two-photon excited luminescence as a tool to characterize field intensity distributions in optical antennas. (a) Resonantly excited linear nanostrip antenna showing field enhancement at the ends. (b) TPL from a gap antenna, indicating a strong field enhancement in the gap for incoming light polarized along the long axis. Reprinted with permission from [102]. © 2008 American Physical Society.
Fig. 11 Microscopy using environment-induced spectral changes of an optical antenna. (a) Schematic of the experiment. A white light source illuminates a 100nm gold nanoparticle antenna from the side. (b) A spatial map of the width of the antenna’s plasmon resonance recorded by raster scanning the nanoparticle antenna over a sample consisting of a circular hole in a layer of 8nm thick chromium (see inset). Adapted with permission from [76]. © 2005 American Physical Society.
Fig. 12 PL from carbon nanotubes enhanced with gold tips. (a) Sample topography consisting of a DNA-wrapped nanotube on mica. (b) Corresponding PL image formed by integrating the signal from 850 to 1050nm (laser excitation is at 633nm). (c) Variations of the peak emission frequency due to DNA wrapping. Reprinted with permission from [150]. © 2008 American Chemical Society.
Fig. 13 Single-molecule fluorescence imaging using a λ4 monopole antenna fabricated on the end face of an aperture-type near-field probe. (a) Electron micrographs showing monopoles of different lengths, resonant at correspondingly different wavelengths. From [61]. (b) Spatial fluorescence map of randomly oriented single molecules. The emitted polarization is color coded: red, horizontal; green, vertical; yellow, unpolarized. Scale bar, 1μm. Adapted from [62] by permission from Macmillan Publishers Ltd., Nature Photonics, © 2008.
Fig. 14 Tip-enhanced Raman spectroscopy of a single-walled carbon nanotube. (a) Topographic image. The scale bar denotes 200nm. (b) Near-field Raman spectra recorded at the locations marked in (a). The radial breathing mode frequency changes from 251 to 191cm1, revealing a structural transition (inset) from a semiconducting (10, 3) tube to a metallic (12, 6) tube. Reprinted with permission from [172]. © 2007 American Chemical Society.
Fig. 15 Schematic of different types of antenna effects in photovoltaics. (a) Far-field scattering, leading to a prolonged optical path. (b) Near-field scattering, causing locally increased absorption, and (c) direct injection of photoexcited carriers into the semiconductor. From [185].
Fig. 16 A dye-sensitized solar cell decorated with gold nanodisk antennas for improved absorption of light. (a) Schematic of the device. Excitation of the dye molecules adsorbed on TiO2 is amplified near an antenna, leading to enhanced carrier injection from the dyes into the TiO2. (b), (c) Electron micrographs showing electrical contacts and gold nanodisks fabricated on top of thin TiO2. Reprinted with permission from [200]. © 2008 American Institute of Physics.
Fig. 17 (a) Scanning electron microscope image of a silicon-on-insulator LED with silver nanoparticles on its surface. (b) Electroluminescence from an LED partially coated with silver nanoparticles. Brighter areas correspond to stronger electroluminescence intensity. Reprinted with permission from [208]. © 2008 American Institute of Physics.
Fig. 18 Coherent control of photoelectron generation in an optical antenna structure. (a) Photoelectron distribution for an incident p-polarized pulse with no coherent control. (b) Electron micrograph of the test structure. (c) Photoelectron distribution for excitation pulse shown in (d). (e) Photoelectron distribution for excitation pulse shown in (f). Adapted from [225] by permission from Macmillan Publishers Ltd., Nature, © 2007.
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ToC Category:
Micro-optical Devices

History
Original Manuscript: March 12, 2009
Revised Manuscript: July 4, 2009
Manuscript Accepted: July 8, 2009
Published: August 11, 2009

Virtual Issues
(2009) Advances in Optics and Photonics

Citation
Palash Bharadwaj, Bradley Deutsch, and Lukas Novotny, "Optical Antennas," Adv. Opt. Photon. 1, 438-483 (2009)
http://www.opticsinfobase.org/aop/abstract.cfm?URI=aop-1-3-438


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