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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 21 — Oct. 13, 2008
  • pp: 16529–16537
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Spectral properties of plasmonic resonator antennas

Edward S. Barnard, Justin S. White, Anu Chandran, and Mark L. Brongersma  »View Author Affiliations


Optics Express, Vol. 16, Issue 21, pp. 16529-16537 (2008)
http://dx.doi.org/10.1364/OE.16.016529


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Abstract

A theoretical study of the optical properties of metallic nano-strip antennas is presented. Such strips exhibit retardation-based resonances resulting from the constructive interference of counter propagating short-range surface plasmon-polaritons (SR-SPPs) that reflect from the antenna terminations. A Fabry-Pérot model was formulated that successfully predicts both the peak position and spectral shape of their optical resonances. This model requires knowledge of the SR-SPP reflection amplitude and phase pickup upon reflection from the structure terminations. These quantities were first estimated using an intuitive Fresnel reflection model and then calculated exactly using full-field simulations based on the finite-difference frequency-domain (FDFD) method. With only three dimensionless scaling parameters, the Fabry-Pérot model provides simple design rules for engineering resonant properties of such plasmonic resonator antennas.

© 2008 Optical Society of America

1. Introduction

Recent advances in nanofabrication techniques have enabled the realization of a wide variety of metallic nanostructure shapes and sizes [1

1. S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photon. 1, 641–648 (2007). [CrossRef]

]. Such structures provide a unique and effective means to concentrate and manipulate light at the nanoscale through the excitation of collective electron oscillations known as surface plasmons (SPs). In order to take full advantage of this class of objects, it would be desirable to formulate simple design rules that can capture the essence of their operation, while hiding much of the internal complexity [2

2. N. Engheta, A. Salandrino, and A. Alù, “Circuit elements at optical frequencies: Nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95, 095504 (2005). [CrossRef] [PubMed]

, 3

3. M. L. Brongersma, “Plasmonics: Engineering optical nanoantennas,” Nat. Photon. 2, 270–272 (2008). [CrossRef]

]. Deep subwave-length metallic nanoparticles exhibit localized SP excitations which are electrostatic in nature and fairly well understood [4

4. F. Wang and Y. R. Shen, “General properties of local plasmons in metal nanostructures,” Phys. Rev. Let. 97, 206806 (2006). [CrossRef]

, 5

5. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).

]. Such particles are already extensively used to concentrate light and have enabled a wide variety of optical sensing and spectroscopy techniques, most notably Surface Enhanced Raman Spectroscopy (SERS) [6

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

, 7

7. J. B. Jackson and N. J. Halas, “Surface-enhanced raman scattering on tunable plasmonic nanoparticle substrates,” Proc. Nat. Acad. Sci. U.S.A. 101, 17930–17935 (2004). [CrossRef]

, 8

8. G. Laurent, N. Félidj, S. Truong, J. Aubard, G. Lévi, J. Krenn, A. Hohenau, A. Leitner, and F. Aussenegg, “Imaging surface plasmon of gold nanoparticle arrays by far-field raman scattering,” Nano Lett. 5, 253–258 (2005). [CrossRef] [PubMed]

].

More recently, metallic waveguide structures, such as wires and strips, have also gained significant interest for their ability to support propagating SPs known as surface plasmonpolaritons (SPPs). These SPPs are electron density waves propagating at a metal-dielectric interface that exhibit a strong coupling to electromagnetic fields. The metallic nanostructures that support SPPs thus can serve as miniature optical waveguides and their use for chipscale optical information transport has been suggested [9

9. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter.” Opt. Lett. 22, 475–7 (1997). [CrossRef] [PubMed]

, 10

10. H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators.” Phys. Rev. Lett. 95, 257403–4 (2005). [CrossRef] [PubMed]

, 11

11. R. Zia, A. Chandran, and M. L. Brongersma, “Dielectric waveguide model for guided surface polaritons,” Opt. Lett. 30, 1473–1475 (2005). [CrossRef] [PubMed]

, 12

12. R. Zia, J. A. Schuller, and M. L. Brongersma, “Near-field characterization of guided polariton propagation and cutoff in surface plasmon waveguides,” Phys. Rev. B. 74, 165415 (2006). [CrossRef]

, 13

13. R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9, 20–27 (2006).

]. In addition, it has recently been shown that retardation-based optical resonators can be constructed by truncating such waveguides to wavelength-scale dimensions [14

14. G. W. Bryant, F. J. García de Abajo, and J. Aizpurua, “Mapping the plasmon resonances of metallic nanoantennas,” Nano Lett. 8, 631–636 (2008). [CrossRef] [PubMed]

, 15

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

, 16

16. T. Søndergaard and S. I. Bozhevolnyi, “Strip and gap plasmon polariton optical resonators,” Phys. Status Solidi B 245, 9–19 (2008). [CrossRef]

]. Local field-enhancements can be achieved in these truncated structures through the excitation and constructive interference of SPP waves that propagate back and forth between the terminations [16

16. T. Søndergaard and S. I. Bozhevolnyi, “Strip and gap plasmon polariton optical resonators,” Phys. Status Solidi B 245, 9–19 (2008). [CrossRef]

]. Because of their high radiation efficiency, these resonators can also be thought of as optical analogs to traditional microwave antennas [17

17. C. A. Balanis, Antenna Theory : Analysis and Design (John Wiley, 2005), 3rd ed.

]. As these structures behave as both resonators and antennas, they can logically be termed plasmonic resonator antennas (PRAs) in analogy to dielectric resonator antennas [18

18. R. K. Mongia and P. Bhartia, “Dielectric resonator antennas — a review and general design relations for resonant frequency and bandwidth,” Int. J. of Microwave Millimeter-Wave Eng. 4, 230–247 (1994). [CrossRef]

]. This type of resonator antenna has effectively been used for Raman spectroscopy and non-linear optics applications [19

19. P. J. 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, 017402–4 (2005). [CrossRef] [PubMed]

, 20

20. P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas.” Science 308, 1607–9 (2005). [CrossRef] [PubMed]

]. The resonant lengths of these PRAs are strongly dependent on the SPP wavelength and reflection phase [21

21. G. Della Valle, T. Søndergaard, and S. I. Bozhevolnyi, “Plasmon-polariton nano-strip resonators: from visible to infra-red,” Opt. Express 16, 6867–6876 (2008). [CrossRef] [PubMed]

]. While the calculation of the SPP wavelength can be accomplished using well-established techniques [22

22. E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969). [CrossRef]

, 23

23. E. Anemogiannis, E. Glytsis, and T. K. Gaylord, “Determination of guided and leaky modes in lossless and lossy planar multilayer optical waveguides: reflection pole method and wavevector density method,” J. Lightwave Technol. 17, 929 (1999). [CrossRef]

], the direct calculation of reflection phase has only been performed more recently for the case of SPPs on thick metal films and for gap SPPs [24

24. R. Gordon, “Vectorial method for calculating the fresnel reflection of surface plasmon polaritons,” Phys. Rev. B. 74, 153417 (2006). [CrossRef]

, 25

25. R. Gordon, “Light in a subwavelength slit in a metal: Propagation and reflection,” Phys. Rev. B. 73, 153405 (2006). [CrossRef]

]. In addition, recent work has provided indirect estimates of reflection phase for SPPs on strips from their resonant response to optical excitation [21

21. G. Della Valle, T. Søndergaard, and S. I. Bozhevolnyi, “Plasmon-polariton nano-strip resonators: from visible to infra-red,” Opt. Express 16, 6867–6876 (2008). [CrossRef] [PubMed]

, 26

26. T. Søndergaard, J. Beermann, A. Boltasseva, and S. I. Bozhevolnyi, “Slow-plasmon resonant-nanostrip antennas: Analysis and demonstration,” Phys. Rev. B. 77, 115420 (2008). [CrossRef]

].

In this paper, we directly calculate both the reflection amplitude and phase for thin metal film terminations using an intuitive Fresnel reflection model and full-field electromagnetic simulations. To our knowledge this is the first direct calculation of these reflection parameters for an SR-SPP reflecting off a terminated thin metal film. We then develop a Fabry-Pérot model that uses these parameters to predict the peak position and spectral shape of the field-intensity resonances for metallic strips (truncated films) of different width, thickness, and optical material properties.

2. Optical properties of metallic films and strips

Fig. 1. Trends in the guiding and reflection properties of short range surface plasmonpolaritions (SR-SPPs) supported by truncated silver films with normalized metal thickness, t/λo. The blue dotted, green dashed, and red solid curves show the trends for εm values that correspond to silver at 500, 600, and 700 nm free-space wavelengths respectively. (a) Real part of the effective index, nspp, of SR-SPP mode. (b) Mode size of the SR-SPP. (c) Reflection amplitude for an SR-SPP reflecting off of a silver film truncation. (d) Phase pickup for an SR-SPP reflecting off of a silver film truncation. (c) & (d): The thin lines were calculated with the Fresnel reflection model and the thick lines were obtained from full-field simulations.

In contrast to SR-SPPs, the LR-SPP modes are poorly confined, exhibit low mode indices, and provide little field enhancement [16

16. T. Søndergaard and S. I. Bozhevolnyi, “Strip and gap plasmon polariton optical resonators,” Phys. Status Solidi B 245, 9–19 (2008). [CrossRef]

]. LR-SPPs are ideally suited for the realization of low-loss plasmonic components [28

28. A. Boltasseva, S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, “Compact Bragg gratings for long-range surface plasmon polaritons,” J. Lightwave Technol. 24, 912 (2006). [CrossRef]

], but not for strip PRAs and thus these modes are not further considered in this paper.

3. Fabry-Pérot resonator model

A metallic strip, such as shown in Fig. 3(a), can be generated by truncating a silver film of thickness t to a width w. When top-illuminated with the electric field polarized along the x-direction, SR-SPPs will be excited at the truncations and start propagating back and forth between the antenna end-faces. When the SR-SPP encounters an end-face it will partially reflect and partially scatter into free-space modes. For a properly chosen strip width, constructive interference of multiply-reflected SR-SPPs will occur and generate resonantly enhanced fields in the vicinity of the strip.

It was recently suggested that the metal strip can be treated as a Fabry-Pérot resonator for SR-SPPs where the reflection phase can dramatically affect the resonance condition [16

16. T. Søndergaard and S. I. Bozhevolnyi, “Strip and gap plasmon polariton optical resonators,” Phys. Status Solidi B 245, 9–19 (2008). [CrossRef]

]. In this study we will provide further evidence that wavelength-scale metallic structures behave as SR-SPP resonators. This is a valuable conclusion as it allows for a more intuitive way of thinking about this class of structures. Since the properties of SR-SPPs can be captured in just a few normalized geometric and materials parameters (w/λo, t/λo, and εm/εd), it also enables a complete description of the resonant optical properties of metal strips in terms of these normalized quantities. For example, the resonant width of a metal strip can be written in terms of the SR-SPP wavelength (λ spp=λo/nspp) and reflection phase which only depend on t/λo and εm/εd. On resonance, the round trip phase must be equal to an integer multiple of 2π. For the case of the metal strip this implies that (2π/λ spp)2w res,m+2ϕ=m2π where m is the order of the resonance. This then leads to

wres,m=mπϕ(tλo,εmεd)2πλonspp(tλo,εmεd)
(1)

From the equation, it is clear that a larger nspp or a larger ϕ will result in a shorter wres,m. It is worth noting that for structures exhibiting large reflection phases, our microwave intuition that suggests w res,1=λo/2 is insufficient to predict their resonant widths. Below we will show that reflection phases exceeding π/2 can be expected in this system which can cause shifts in the resonance width, w res,1, from λ spp/2 to less than λ spp/4.

One of the most exciting characteristics of nano-strip resonators is their ability to generate local field enhancements for the resonant widths, w res,m. With the Fabry-Pérot model, the dependence of the field intensity at the end-faces, |E end|2, can be found by summing contributions from the multiply-reflected SR-SPPs that were launched onto the strip. A simple addition of these fields gives

Eend2(1reiϕeiksppw)(1eiksppw)1r2ei2ϕei2ksppw2.
(2)

In this equation we express |E end|2 as a proportionality rather than an equality since the (possibly frequency-dependent) coupling efficiency of the incident wave into SR-SPPs is unknown. Note that for symmetry reasons only odd modes (m=1,3,5…) can be excited in the considered top-illumination geometry. Through a careful comparison to full-field simulations, we will show that the frequency dependence of the coupling efficiency is weak and the Fabry-Pérot resonances occur where exp[i2k spp w+i2ϕ] is close to unity, i.e. where Eq. (1) holds, and the quantity in Eq. (2) is maximized. Note that the numerator in Eq. (2) gives rise to an asymmetric line-shape as a function of w and slightly shifts (by less than 5%) the resonance maximum from the w res,m predicted by Eq. (1). Interestingly, the weak frequency dependence of the coupling also enables an accurate prediction of the resonant line-shape and thus the quality factor, Q.

4. Determination of reflection amplitude and phase

In order to test the validity of the Fabry-Pérot model, we first estimate the amplitude and phase of SR-SPP reflection off of a film truncation using a Fresnel reflectivity model. In this simple estimate, we treat the metal film as a uniform medium with an effective complex refractive index n spp=k spp/ko, where k spp is the in-plane wave vector of the SR-SPP supported by the film. Reflections from a termination are then obtained by considering a plane wave propagating in a uniform medium of n spp and reflecting off a dielectric with an index equal to that of the embedding medium (n=1 in our case). The reflection amplitude, |r|, and phase pickup, ϕ, for the SR-SPP wave can now be calculated based on this effective index contrast using the well-known Fresnel equations [29

29. E. Hecht, Optics (Addison Wesley, 2001), 4th ed.

]:

r=reiϕ=nspp1nspp+1.
(3)

The thin lines in Fig. 1(c) show the dependence of the reflection amplitude on thickness for the same εm values as in Fig. 1(a) and (b). For sufficiently thick films, the reflection parameters asymptote as the SR-SPP becomes more like a SPP on a semi-infinite metal film. However, as the film thickness is decreased, the increase in the SR-SPP mode index leads to a larger reflection amplitude that tend towards unity for films that are thinner than just a few percent of the free-space wavelength. Within the confines of the Fresnel reflection model, the reflection phase would be equal to zero for the case of a lossless metal. However, real metals exhibit loss and give rise to a non-negligible phase pickup. For low-loss noble metals this Fresnel reflection model predicts a small phase pickup as seen in Fig. 1(d) for silver.

The Fresnel reflection model (Eq. (3)) is expected to underestimate the reflection amplitude and phase because it does not take into account the significant mode mismatch between the SR-SPP mode and the free-space modes it couples to at the end-faces. Fig. 1(b) shows that the mode size can drop well below the free-space wavelength and modifications of the reflection properties should be expected. To analyze these effects and more accurately predict the end-face reflection properties, we performed full-field finite-difference frequency-domain (FDFD) simulations [30

30. G. Veronis and S. Fan, “Overview of simulation techniques for plasmonic devices,” in “Surface Plasmon Nanophotonics,”, vol. 131, M. L. Brongersma and P. G. Kik, eds. (Springer, 2007), pp. 169–182.

] to calculate the reflection amplitude and phase. FDFD allows for the use of frequency-dependent optical constants determined from experiments [27

27. A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for verticalcavity optoelectronic devices,” Appl. Opt. 37, 5271 (1998). [CrossRef]

]. Fig. 2(a) shows the simulated geometry consisting of a semi-infinite metal film with an abrupt truncation at which the SR-SPP will partially reflect and partially scatter into free-space modes. To calculate |r| and ϕ at a frequency and film thickness of interest, we launch an analytically-derived SR-SPP mode [22

22. E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969). [CrossRef]

] from xo towards the end-face of the slab at xe and monitor its reflection at xm.

Fig. 2. Full-field simulation of an SR-SPP reflecting off of a metal film truncation. (a) Schematic of the simulation geometry showing the truncated metal film with the SR-SPP launch point (xo), end-face (xe), and measurement point (xm). (b) Incident, (c) total, and (d) reflected (total minus incident) tangential electric field, Ex, for a 30 nm thick silver film excited with a SR-SPP mode with a wavelength of λ spp=465 nm (free-space λo=550nm).

To illustrate the procedure, Fig. 2(b) shows the tangential electric field distribution of the incident, forward-propagatingwave, Ex,i(x,y) for a 30 nmthick silver film at an excitation (free-space) wavelength of 550 nm. Upon reaching the end-face, the SR-SPP scatters and produces a total field E x,tot(x,y) as shown in Fig. 2(c). Fig. 2(d) shows that near the strip the difference field, E x,tot(x,y)-Ex,i(x,y), is dominated by contributions from a backward-propagating, reflected SR-SPP, as is expected for such a strongly bound mode. For this reason we call this difference field the reflected field Ex,r(x,y). Sufficiently far from the end-face and within the metal film Ex,r only has contributions from the reflected SR-SPP wave. In those locations, (xm,ym), the phase and amplitude of the SR-SPP reflections can be directly computed from our simulated field patterns. To determine the reflection amplitude, |r|, and phase, ϕ, we first write out the incident, Ex,i, and reflected, Ex,r, SR-SPP fields:

Ex,i(x,y)=Ex,o(y)eikspp(xxo)
(4)
Ex,r(x,y)=Ex,o(y)reikspp(xexo)eiϕeikspp(xex).
(5)

It is then straightforward to show that the complex reflection coefficient, r, for the SR-SPP is given by the ratio of the incident and reflected fields as

r=reiϕ=Ex,r(xm,ym)Ex,i(xm,ym)ei2kspp(xmxe).
(6)

The thick lines in Fig. 1(c) and (d) show the dependence of the simulated reflection amplitude and phase on film thickness. These curves exhibit similar qualitative behavior as those obtained from the Fresnel reflection model (thin lines). However, the full-field simulations properly take into account the significant decrease in mode size with decreasing film thickness (Fig. 1(b)) and thus predict stronger reflections and substantially larger reflection phases. The rapid decrease in |r| with increasing film thickness can be explained by both the decrease in the SPP effective index and the concurrent spreading of the SR-SPP mode into the surrounding dielectric. The increased mode overlap of the now larger SR-SPP mode gives rise to better coupling to freespace modes and thus a reduced reflection.

Unlike the Fresnel reflection model, these full-field simulations show a very significant ϕ, in some cases exceeding π/2. Similar to the Fresnel reflection model, the reflection phase pickup again tends towards zero as the metal thickness is decreased. This limit can be explained by the fact that the reflection becomes almost perfect (r → 1). For large film thicknesses (t/λ o) the reflection phase increases and approaches the phase pickup of a single-interface (semi-infinite) SPP reflection as the surface modes decouple.

5. Fabry-Pérot resonances in local field enhancement

Fig. 3. Resonance behavior of 30 nm thick silver strips and comparison with Fabry-Pérot models. Dashed blue lines correspond to the Fresnel reflection Fabry-Pérot model and solid red lines correspond to Fabry-Pérot model with phase and reflection coefficient from fullfield simulations. The dashed green indicates cuts from the full-field strip resonance map. (a) Schematic of the simulated strip geometry. (b) Slice of resonance map and (c) Fabry-Pérot model vs. strip width, w, at λo=550 nm. (d) Slice of resonance map and (e) Fabry-Pérot model vs. excitation wavelength, λo, at w=0.8µm. (f) Resonance map of 30 nm thick silver strips from full-field simulations. |E end|2 is shown as a density plot, overlayed with predicted resonance peaks from Fabry-Pérot models.
Fig. 4. Field intensity distributions (|E|2/|Eo|2) for the lowest order resonances (m=1,3, 5) of 30 nm thick silver strips at an illumination wavelength of λo=550 nm. For this excitation wavelength w res,1=130 nm is shown in (a), w res,3=575 nm is shown in (b), and w res,5=1040 nm is shown in (c).

Figure 3(c) shows three resonances in the local field enhancement. From Eq. (1) the spacing between these odd order resonances in w res,m is expected to match the SR-SPP wavelength of λ spp=465 nm for the considered excitation wavelength of λo=550 nm. The differences between w res,1 and w res,3 is 445 nm, just 4.3% smaller than the SR-SPP wavelength. This similarity to the surface plasmon wavelength was used previously to argue that metal strips behave as SR-SPP resonators [31

31. S. I. Bozhevolnyi and T. Søndergaard, “General properties of slow-plasmon resonant nanostructures: nanoantennas and resonators,” Opt. Express 15, 10869 (2007). [CrossRef] [PubMed]

]. It is worth noting that the difference between the m=3 and m=5 resonance widths is less than 1 nm from the SR-SPP wavelength. This indicates that for wide strips the local field intensity enhancement can fully be attributed to resonating SR-SPPs and that narrow strips are dominantly, but not purely SR-SPP resonators.

In Fig. 3(b) and (d) we have also calculated the local intensity enhancement obtained the Fabry-Pérot model (Eq. (2)). The dashed blue lines were calculated using |r| and ϕ from the Fresnel reflection model. For this simple model the Fabry-Pérot resonance peaks occur at too large a width or too short a wavelength when compared to the full-field simulations because this model significantly underestimates the phase pickup upon reflection. The solid red curves in these Figs. were obtained by taking |r| and φ from full-field reflection simulations as shown in Fig. 2. With these more accurate reflection parameters the Fabry-Pérot model predicts peak positions and spectral shapes that are in agreement with full-field simulations of strips. The small observed deviations in the line-shape and peak position may be attributed to minor contributions on the local intensity from other modes as well as to the frequency-dependence of the coupling efficiency for free-space waves into SR-SPPs. The close agreement between the full-field simulations and the Fabry-Pérot model further confirm that wavelength-scale strips behave as resonators for SR-SPPs. It also shows that intuitive Fabry-Pérot models can effectively be used to predict not only the resonance positions, but also their line-shapes.

6. Conclusions

This study on the optical properties of metallic strips has provided further evidence that wavelength-scale metallic structures behave as SR-SPP resonators. This is a valuable conclusion as the properties of SR-SPPs can be captured in terms of just a few normalized geometric and materials parameters (w/λo, t/λo, and εm/εd). Moreover, it allows for the SR-SPP reflection amplitudes and phases to be described in terms of these parameters. This in-turn enables the construction of an intuitive Fabry-Pérot model capable of predicting the position and line-shapes of resonant metallic structures for a wide variety of choices for the metal, surrounding dielectric, and structure geometries. Although we have only verified applicability for strips, it is expected that these models can effectively be extended to other wavelengths-scale structures of different cross-sectional shape. We anticipate that the presented concepts will provides optical engineers with a powerful framework for designing the properties of this exciting new class of resonators.

Acknowledgments

The authors acknowledge support from a National Science Foundation Graduate Research fellowship, the Stanford Global Climate and Energy Project, and the National Science Foundation.

References and links

1.

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photon. 1, 641–648 (2007). [CrossRef]

2.

N. Engheta, A. Salandrino, and A. Alù, “Circuit elements at optical frequencies: Nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95, 095504 (2005). [CrossRef] [PubMed]

3.

M. L. Brongersma, “Plasmonics: Engineering optical nanoantennas,” Nat. Photon. 2, 270–272 (2008). [CrossRef]

4.

F. Wang and Y. R. Shen, “General properties of local plasmons in metal nanostructures,” Phys. Rev. Let. 97, 206806 (2006). [CrossRef]

5.

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).

6.

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

7.

J. B. Jackson and N. J. Halas, “Surface-enhanced raman scattering on tunable plasmonic nanoparticle substrates,” Proc. Nat. Acad. Sci. U.S.A. 101, 17930–17935 (2004). [CrossRef]

8.

G. Laurent, N. Félidj, S. Truong, J. Aubard, G. Lévi, J. Krenn, A. Hohenau, A. Leitner, and F. Aussenegg, “Imaging surface plasmon of gold nanoparticle arrays by far-field raman scattering,” Nano Lett. 5, 253–258 (2005). [CrossRef] [PubMed]

9.

J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter.” Opt. Lett. 22, 475–7 (1997). [CrossRef] [PubMed]

10.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators.” Phys. Rev. Lett. 95, 257403–4 (2005). [CrossRef] [PubMed]

11.

R. Zia, A. Chandran, and M. L. Brongersma, “Dielectric waveguide model for guided surface polaritons,” Opt. Lett. 30, 1473–1475 (2005). [CrossRef] [PubMed]

12.

R. Zia, J. A. Schuller, and M. L. Brongersma, “Near-field characterization of guided polariton propagation and cutoff in surface plasmon waveguides,” Phys. Rev. B. 74, 165415 (2006). [CrossRef]

13.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9, 20–27 (2006).

14.

G. W. Bryant, F. J. García de Abajo, and J. Aizpurua, “Mapping the plasmon resonances of metallic nanoantennas,” Nano Lett. 8, 631–636 (2008). [CrossRef] [PubMed]

15.

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

16.

T. Søndergaard and S. I. Bozhevolnyi, “Strip and gap plasmon polariton optical resonators,” Phys. Status Solidi B 245, 9–19 (2008). [CrossRef]

17.

C. A. Balanis, Antenna Theory : Analysis and Design (John Wiley, 2005), 3rd ed.

18.

R. K. Mongia and P. Bhartia, “Dielectric resonator antennas — a review and general design relations for resonant frequency and bandwidth,” Int. J. of Microwave Millimeter-Wave Eng. 4, 230–247 (1994). [CrossRef]

19.

P. J. 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, 017402–4 (2005). [CrossRef] [PubMed]

20.

P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas.” Science 308, 1607–9 (2005). [CrossRef] [PubMed]

21.

G. Della Valle, T. Søndergaard, and S. I. Bozhevolnyi, “Plasmon-polariton nano-strip resonators: from visible to infra-red,” Opt. Express 16, 6867–6876 (2008). [CrossRef] [PubMed]

22.

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969). [CrossRef]

23.

E. Anemogiannis, E. Glytsis, and T. K. Gaylord, “Determination of guided and leaky modes in lossless and lossy planar multilayer optical waveguides: reflection pole method and wavevector density method,” J. Lightwave Technol. 17, 929 (1999). [CrossRef]

24.

R. Gordon, “Vectorial method for calculating the fresnel reflection of surface plasmon polaritons,” Phys. Rev. B. 74, 153417 (2006). [CrossRef]

25.

R. Gordon, “Light in a subwavelength slit in a metal: Propagation and reflection,” Phys. Rev. B. 73, 153405 (2006). [CrossRef]

26.

T. Søndergaard, J. Beermann, A. Boltasseva, and S. I. Bozhevolnyi, “Slow-plasmon resonant-nanostrip antennas: Analysis and demonstration,” Phys. Rev. B. 77, 115420 (2008). [CrossRef]

27.

A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for verticalcavity optoelectronic devices,” Appl. Opt. 37, 5271 (1998). [CrossRef]

28.

A. Boltasseva, S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, “Compact Bragg gratings for long-range surface plasmon polaritons,” J. Lightwave Technol. 24, 912 (2006). [CrossRef]

29.

E. Hecht, Optics (Addison Wesley, 2001), 4th ed.

30.

G. Veronis and S. Fan, “Overview of simulation techniques for plasmonic devices,” in “Surface Plasmon Nanophotonics,”, vol. 131, M. L. Brongersma and P. G. Kik, eds. (Springer, 2007), pp. 169–182.

31.

S. I. Bozhevolnyi and T. Søndergaard, “General properties of slow-plasmon resonant nanostructures: nanoantennas and resonators,” Opt. Express 15, 10869 (2007). [CrossRef] [PubMed]

OCIS Codes
(050.2230) Diffraction and gratings : Fabry-Perot
(140.4780) Lasers and laser optics : Optical resonators
(240.6680) Optics at surfaces : Surface plasmons
(260.3910) Physical optics : Metal optics

ToC Category:
Optics at Surfaces

History
Original Manuscript: September 16, 2008
Revised Manuscript: September 26, 2008
Manuscript Accepted: September 28, 2008
Published: October 1, 2008

Citation
Edward S. Barnard, Justin S. White, Anu Chandran, and Mark L. Brongersma, "Spectral properties of plasmonic resonator antennas," Opt. Express 16, 16529-16537 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-21-16529


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References

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  24. R. Gordon, "Vectorial method for calculating the fresnel reflection of surface plasmon polaritons," Phys. Rev. B. 74, 153417 (2006). [CrossRef]
  25. R. Gordon, "Light in a subwavelength slit in a metal: Propagation and reflection," Phys. Rev. B. 73, 153405 (2006). [CrossRef]
  26. T. Søndergaard, J. Beermann, A. Boltasseva, and S. I. Bozhevolnyi, "Slow-plasmon resonant-nanostrip antennas: Analysis and demonstration," Phys. Rev. B. 77, 115420 (2008). [CrossRef]
  27. A. D. Rakiíc, A. B. Djurisi�?, J. M. Elazar, and M. L. Majewski, "Optical properties of metallic films for verticalcavity optoelectronic devices," Appl. Opt. 37, 5271 (1998). [CrossRef]
  28. A. Boltasseva, S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, "Compact Bragg gratings for long-range surface plasmon polaritons," J. Lightwave Technol. 24, 912 (2006). [CrossRef]
  29. E. Hecht, Optics (Addison Wesley, 2001), 4th ed.
  30. G. Veronis and S. Fan, "Overview of simulation techniques for plasmonic devices," in Surface Plasmon Nanophotonics, vol. 131, M. L. Brongersma and P. G. Kik, eds. (Springer, 2007), pp. 169-182.
  31. S. I. Bozhevolnyi and T. Søndergaard, "General properties of slow-plasmon resonant nanostructures: nanoantennas and resonators," Opt. Express 15, 10869 (2007). [CrossRef] [PubMed]

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