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Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 8, Iss. 3 — Apr. 4, 2013
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An absorption-based superconducting nano-detector as a near-field optical probe

Qiang Wang and Michiel J. A. de Dood  »View Author Affiliations


Optics Express, Vol. 21, Issue 3, pp. 3682-3692 (2013)
http://dx.doi.org/10.1364/OE.21.003682


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Abstract

We investigate the use of a superconducting nano-detector as a novel near-field probe. In contrast to conventional scanning near-field optical microscopes, the nano-detector absorbs and detects photons in the near-field. We show that this absorption-based probe has a higher collection efficiency and investigate the details of the interaction between the nano detector and the dipole emitter. To this end, we introduce a multipole model to describe the interaction. Calculations of the local density of states show that the nano-detector does not strongly modify the emission rate of a dipole, especially when compared to traditional metal probes.

© 2013 OSA

1. Introduction

Near-field optical microscopes have been used to probe the fluorescence of a single molecule and the evanescent near-field of a large variety of nanophotonic structures [1

1. R. C. Dunn, “Near-field scanning optical microscopy,” Chem. Rev. 99(10), 2891–2928 (1999). [CrossRef] [PubMed]

,2

2. V. Sandoghdar, B. Buchler, P. Kramper, S. Götzinger, O. Benson, and M. Kafesaki, “Scanning near-field optical studies of photonic devices,” in Photonic Crystals: Advances in Design, Fabrication, and Characterization, K. Busch, S. Lölkes, R. B. Wehrspohn and H. Föll eds. (Wiley-VCH Verlag GmbH & Co. KGaA, 2006).

]. Because near-field probes interact with evanescent waves the resolution of these microscopes is not limited by the diffraction limit that holds for propagating waves. Conventional near-field microscopes probe the optical near-field with a metal tip [3

3. F. Keilmann and R. Hillenbrand, “Near-field microscopy by elastic light scattering from a tip,” Philos. Transact. A Math. Phys. Eng. Sci. 362(1817), 787–805 (2004). [CrossRef] [PubMed]

], a metal particle [4

4. T. Kalkbrenner, M. Ramstein, J. Mlynek, and V. Sandoghdar, “A single gold particle as a probe for apertureless scanning near-field optical microscopy,” J. Microsc. 202(1), 72–76 (2001). [CrossRef] [PubMed]

] or a metal coated tip with a sub-wavelength hole [5

5. B. Hecht, B. Sick, U. P. Wild, V. Decker, R. Zenobi, O. J. F. Martin, and D. W. Pohl, “Scanning near-field optical microscopy with aperture probes: fundamentals and applications,” J. Chem. Phys. 112(18), 7761–7774 (2000). [CrossRef]

]. These probes are positioned in the near-field and scanned in the lateral directions. These tips either scatter the light directly into the optical far field, or through a sub-wavelength aperture connected to an optical fiber where it is detected by a photosensitive detector in the far-field.

To attain sub-wavelength lateral resolution, the size of the aperture or tip should be smaller than the wavelength. This makes near-field probes based on scattering inherently inefficient because light scattering from sub-wavelength metal particles is an inefficient process. For particles that are much smaller than the wavelength, Rayleigh scattering occurs and the scattering decreases as d6/λ4, where d is the dimension of the particle and λ is the wavelength. This low collection efficiency makes near-field studies of quantum optics an extremely challenging task, because detection of weak light with a small collection efficiency (i.e., missing out many photons) introduces noise [6

6. C. H. Henry and R. F. Kazarinov, “Quantum noise in photonics,” Rev. Mod. Phys. 68(3), 801–853 (1996). [CrossRef]

]. Similarly in experiments on single molecules the total number of photons emitted by a molecule is given by the ratio τ1/2/τrad, where τ1/2 is the half life of a molecule due to bleaching and τrad is the radiative lifetime [7

7. E. Betzig and R. J. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science 262(5138), 1422–1425 (1993). [CrossRef] [PubMed]

].

Since the absorption of a small particle scales with its volume, i.e. as d3, an intrinsically much more efficient near-field nano-detector can be constructed. Recently, superconducting nano-detectors have been demonstrated that absorb a single photon and create a measurable electronic pulse for each absorbed photon [8

8. G. N. Gol’tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. 79(6), 705–707 (2001). [CrossRef]

]. This type of detector is based on optical absorption and detection of single photons directly in the near-field.

In this paper we consider a detector made of a 4 nm thick NbN film grown on a GaAs substrate, i.e. identical to the square nano-detector reported in the Ref. 9

9. D. Bitauld, F. Marsili, A. Gaggero, F. Mattioli, R. Leoni, S. J. Nejad, F. Lévy, and A. Fiore, “Nanoscale optical detector with single-photon and multiphoton sensitivity,” Nano Lett. 10(8), 2977–2981 (2010). [CrossRef] [PubMed]

. Photons can be detected only in the constricted area where the current through the detector is close to the critical current of the superconductor at cryogenic temperatures.

2. Scattering and absorption by a near-field probe

Conventional scanning near-field optical microscopes (SNOMs) can be subdivided into two major types: aperture based SNOMs and scattering type SNOMs [10

10. A. Rasmussen and V. Deckert, “New dimension in nano-imaging: breaking through the diffraction limit with scanning near-field optical microscopy,” Anal. Bioanal. Chem. 381(1), 165–172 (2005). [CrossRef] [PubMed]

]. The aperture based SNOMs make use of a subwavelength hole in a metal film or metal-clad fiber tip [11

11. F. Zenhausern, M. P. O’Boyle, and H. K. Wickramasinghe, “Apertureless near-field optical microscope,” Appl. Phys. Lett. 65(13), 1623–1625 (1994). [CrossRef]

15

15. J. Smajic and C. Hafner, “Numerical analysis of a SNOM tip based on a partially cladded optical fiber,” Opt. Express 19(23), 23140–23152 (2011). [CrossRef] [PubMed]

]. The transmission through a subwavelength hole in a good conductor is extremely low and is proportional to a6/λ4 (a/λ << 1) [16

16. H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66(7-8), 163–182 (1944). [CrossRef]

], where a is the radius of the aperture, and λ is the wavelength of light. Similarly, the scattering type SNOMs make use of light scattering of the sharp end of a metal clad tip to scatter the optical near-field directly onto a far-field detector. To estimate the performance of this type of SNOMs the probe is considered to be a sphere [17

17. I. S. Averbukh, B. M. Chernobrod, O. A. Sedletsky, and Y. Prior, “Coherent near field optical microscopy,” Opt. Commun. 174(1-4), 33–41 (2000). [CrossRef]

], and the tip’s scattering cross section is then given by Mie theory. For a subwavelength sphere one can apply the Rayleigh limit (a/λ << 1) to calculate the scattering cross section σ = 8π|αeff|2/(3λ4) [18

18. C. F. Bohren and D. R. Huffman, “Particles small compared with the wavelength,” in Absorption and scattering of light by small particles. (Wiley & Sons, 1983).

], where
αeff=α(1β)/(1αβ32πr3)orαeff=α(1+β)/(1αβ16πr3),
(1)
which represents the effective polarizability of the sphere close to the surface of a substrate. The applied electric field is either parallel or perpendicular to the surface as shown in Fig. 1
Fig. 1 Absorption cross section for a NbN sphere close to a GaAs substrate, as compared to a Ag sphere. Calculations are done at λ = 1.0 μm, as a function of sphere radius. The inset shows a sphere with a radius of a at distance z = 10 nm from the semi-infinite substrate. The particle is excited by an external electric field E parallel to the interface. In the Rayleigh limit (a/λ << 1), the absorption cross section is much larger than the scattering cross section. Because of the larger imaginary part of the dielectric constant of NbN, the absorption cross section of a NbN sphere is 10 times larger than that of a Ag sphere.
. In Eq. (1) the polarizability of a sphere α = 4πa3(εsp – 1)/(εsp + 2), β = (εsb – 1)/(εsb + 1), where εsp and εsb are the complex dielectric constants of the sphere and the substrate, and a is the radius of the sphere [18

18. C. F. Bohren and D. R. Huffman, “Particles small compared with the wavelength,” in Absorption and scattering of light by small particles. (Wiley & Sons, 1983).

,19

19. B. Knoll and F. Keilmann, “Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy,” Opt. Commun. 182(4-6), 321–328 (2000). [CrossRef]

].

To date, scattering SNOMs have been used successfully in experiments using Ag clad tips at near-infrared wavelengths. Figure 1 compares the calculated scattering and absorption cross section for a Ag and a NbN sphere close to a GaAs substrate (refractive index 3.5). Calculations are shown for light with a wavelength of 1.0 μm, as a function of the radius a of the sphere. The air gap between the sphere and the substrate is kept constant at z = 10 nm as the radius of the sphere is varied. In these calculations we assume a dielectric constant of εAg = – 45.6 + 2.9i for the Ag sphere [20

20. D. W. Lynch and W. R. Hunter, “Comments on the optical constants of metals and an introduction to the data for several metals,” in Handbook of Optical Constants of Solids I, E. D. Palik, ed. (Academic, 1998).

] and εNbN = – 8.2 + 31.4i for NbN [21

21. E. F. C. Driessen and M. J. A. de Dood, “The perfect absorber,” Appl. Phys. Lett. 94(17), 171109 (2009). [CrossRef]

]. The inset in Fig. 1 shows a schematic of the geometry used in the calculation: The sphere, which models (the tip of the) scanning probe, is located above a GaAs substrate and is excited at normal incidence light with polarization parallel to the substrate’s surface. In this geometry, the tip induces a surface charge in the substrate that can be described by an image dipole at a distance r from the surface [19

19. B. Knoll and F. Keilmann, “Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy,” Opt. Commun. 182(4-6), 321–328 (2000). [CrossRef]

].

As can be seen in Fig. 1, the scattering cross sections of a NbN and a Ag sphere are comparable in the Rayleigh limit. This reflects the fact that both materials provide a large dielectric constant |ε| and scattering depends on the absolute value of the polarizability. The absorption cross section of a sphere much smaller than the wavelength is proportional to the volume of the particle, and exceeds the scattering cross section by several orders of magnitude. The absorption cross section of a NbN sphere exceeds the absorption cross section of a comparable Ag sphere by more than an order of magnitude for all sizes. For a realistic, 20 nm diameter tip, the absorption of a NbN sphere is 4 orders of magnitude larger than the scattering of either a NbN or a Ag sphere. Additional calculations (not shown) for vertical polarization and for Au or Al metal are very similar to those presented in Fig. 1. A SNOM, based on a NbN nano-detector, that would be able to absorb and detect the radiation directly in the optical near-field would thus comprise a great advantage over current SNOM technology.

A real detector that can operate in the optical near-field could be based on a thin strip of strongly absorbing NbN material that is tapered down to a constriction which forms the active area [9

9. D. Bitauld, F. Marsili, A. Gaggero, F. Mattioli, R. Leoni, S. J. Nejad, F. Lévy, and A. Fiore, “Nanoscale optical detector with single-photon and multiphoton sensitivity,” Nano Lett. 10(8), 2977–2981 (2010). [CrossRef] [PubMed]

]. Figure 2
Fig. 2 Comparison of the absorption cross section for a square and spherical NbN nano-detector as a function of size a at λ = 1.0 μm. Simulations are used to calculate the absorption of a square detector, both at λ = 1.0 μm. In the optical near-field (a/λ <<1), the absorption of a NbN square is higher than that of a sphere. The inset shows a schematic picture of a realistic NbN nano-detector: a 4 nm thick NbN film is grown on a GaAs substrate. A bowtie shape with a nanoscale square constriction serving as the detector active area is patterned in the film.
compares the absorption cross section of a square detector of size a × a with the absorption of a NbN sphere of radius a. A schematic drawing of the NbN nano-detector is shown in the inset of Fig. 2. The absorption of the NbN sphere is calculated using the Rayleigh approximation for small particles, while the results of a square on a substrate, excluding the wire, are based on finite-difference-time-domain (FDTD) simulations. The FDTD calculation includes a 3-dimensional model of the square NbN detector close to a semi-infinite GaAs substrate. The detector is illuminated at normal incidence by a plane wave with the electric field parallel to the GaAs substrate surface. We monitor the power absorption in the detector and the total intensity of the illumination. From this we calculate the absorption cross section of the square detector. As can be seen from the figure, the absorption of the square NbN detector is larger than that of the sphere, even though the geometrical cross section of the sphere (πa2) is larger than that of the detector (a2).

3. Interaction between a NbN detector and a dipole emitter

To evaluate the performance of a SNOM using FDTD we perform simulation of a scanning probe with a light source in the near-field. To this end we place a dipole emitter on a GaAs substrate to mimic the single-photon emission from an atom or a quantum dot. Figure 3
Fig. 3 Physical model used in FDTD simulations of detector sensitivity and resolution. The NbN nano-detector is located above a dipole emitter (point source) with a dipole moment along X-direction. The emitter (λ = 1.0 μm) is placed on the semi-infinite GaAs substrate. Charge areas are induced inside the nano-detector and in the substrate underneath the emitter.
shows the geometry and the 3-dimensional coordinate system used in these simulations. On the surface of a semi-infinite GaAs substrate, a point dipole source is placed at the origin, with its dipole moment along the X-direction, i.e. in the plane of the surface. The square block of NbN represents the nano-detector (50 nm × 50 nm × 4 nm constriction), and is situated above the dipole source. Both the detector and the emitter are centered on the Z axis.

Several dipole-based models have been put forward to describe the interaction between the tip of the probe in SNOM and the sample [19

19. B. Knoll and F. Keilmann, “Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy,” Opt. Commun. 182(4-6), 321–328 (2000). [CrossRef]

,22

22. M. Esslinger and R. Vogelgesang, “Reciprocity theory of apertureless scanning near-field optical microscopy with point-dipole probes,” ACS Nano 6(9), 8173–8182 (2012). [CrossRef] [PubMed]

,23

23. A. J. L. Adam, N. C. J. van der Valk, and P. C. M. Planken, “Measurement and calculation of the near field of a terahertz apertureless scanning optical microscope,” J. Opt. Soc. Am. B 24(5), 1080–1090 (2007). [CrossRef]

]. For a scattering SNOM as described in Ref. 19

19. B. Knoll and F. Keilmann, “Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy,” Opt. Commun. 182(4-6), 321–328 (2000). [CrossRef]

, an analytical dipole model can describe the interaction between the probe tip and a point sample. Within these models, the probe tip is treated as a polarizable sphere that interacts with a dipole source on a substrate. When the distance between the sphere and the dipole becomes much smaller than the wavelength, a charge area is induced inside the tip by the electric field of the dipole, and the electric potential generated by this charge area can be expressed by a multipole expansion [24

24. J. D. Jackson, “Multipoles, electrostatics of macroscopic media, dielectrics,” in Classical Electrodynamics. (Wiley & Sons, 1983).

]:
φ(R)=14πεo[QRp·1R+16D:1R+...],
(2)
where φ(R) is the electric potential at the position R (R=x2+y2+z2) and the distance from the dipole source to the detector is equal to z, εo is dielectric constant in vacuum, Q is total induced charge, vector pis the dipole moment, and the tensorD relates to the quadrupole contribution to the field.

The first term in the brackets of Eq. (2) reflects the electric potential generated by the total amount of induced charge Q in the detector. For a dipole source with no net charge the amounts of positive and negative induced charge should be equal and this term vanishes.

Within the dipole approximation we only keep the second term in Eq. (2), i.e. the dipole moment, and neglect all higher order terms in the multipole expansion. We do, however, include the electric field of the induced dipole in the probe that induces surface charges in the sample. This contribution is equivalent to an image dipole in the substrate underneath the dipole source at a distance of 2z from the probe [19

19. B. Knoll and F. Keilmann, “Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy,” Opt. Commun. 182(4-6), 321–328 (2000). [CrossRef]

].

The image dipole has a dipole moment p’ = – βp, where β = (εsb – 1)/(εsb + 1) [19

19. B. Knoll and F. Keilmann, “Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy,” Opt. Commun. 182(4-6), 321–328 (2000). [CrossRef]

, 25

25. L. Novotny and B. Hecht, “Dipole emission near planar interfaces,” in Principles of Nano-optics. (Cambridge University Press, 2006).

], and εsb = 12.25 is the dielectric constant of the GaAs substrate. The total field includes the original dipole field and the contribution from the image dipole fields. The effective polarizability for the probe-sample system (parallel to the substrate) is then given by Eq. (1).

With this effective polarizability, the scattering and absorption cross section are calculated in a straightforward way. Results of this calculation are shown in Fig. 1.

Figure 4 (a)
Fig. 4 Calculated absorption of a point dipole as a function of distance between the nano-detector and the substrate. Calculations are done for a wavelength λ = 1.0 μm with the radiation power of the dipole source fixed at 1 W. The FDTD results are compared with two models: a dipole (a) and mutipole (b) model.
shows the absorption in the detector as a function of the distance between the detector and the dipole. Calculations based on the dipole approximation and complete FDTD are compared. As can be seen in Fig. 4 (a), a large deviation exists between the absorption calculated by the dipole model and by FDTD for distances z < 10 nm. We explain this deviation by the square shape of the detector instead of a simple sphere for the SNOM tip. In a square detector a more complex image charge distribution exists in the film. This charge distribution cannot be described by an induced dipole only. In order to describe the image charge more accurately, we include a quadrupole moment in the expression given by Eq. (2). Figure 4(b) shows the absorption in the detector using a multipole expansion and FDTD simulations. Compared to the dipole model above, the mutipole model, that includes a quadrupole moment, fits the FDTD curve very well.

To analyze this contribution in a concise way we consider a dipole moment in the X direction (see Fig. 3) that creates an induced dipolep in the nano-detector, which is mirrored and points in the –X-direction. For the dipole and its induced dipole oriented along the X direction the Ey component of the field in the XZ-plane is zero and the electric field is strongly concentrated at the center of the constriction. At this position the field contains only nonzero Ex and Ez components. Hence we limit our model to the component D13 of the tensorD. The induced quadrupole moment in the detector can then be defined as:
D13=V3xzρ(x,y,z)dxdydz=ηEx2+Ez2,
(3)
where we have introduced a tuning parameter η that we determine from the comparison of the model with FDTD simulations.

Again, an image charge is induced below the emitter as shown in Fig. 3, with p’ = – βp and D’ = βD [25

25. L. Novotny and B. Hecht, “Dipole emission near planar interfaces,” in Principles of Nano-optics. (Cambridge University Press, 2006).

], where β = (εsb – 1)/(εsb + 1).

The total electric field E(Ex,Ey,Ez) inside the nano-detector contains a contribution from the dipole emitter and the image charge and can be expressed as:
E=Eemitter+Eimage,
(4)
which can be solved analytically. To obtain the absorption in the detector we numerically integrate|E|2over the volume of the nano-detector and multiply the result by the imaginary part of the dielectric constant [26

26. J. D. Jackson, “Radiating systems, multipole fields and radiation,” in Classical Electrodynamics. (Wiley & Sons, 1983).

]. We neglect phase changes of the electric field in our model, because the near-field of a radiant dipole can be treated as a static electric dipole field as long as kr << 1 (k is the wave vector and r is the distance from the dipole) [27

27. J. D. Jackson, “Maxwell equations, macroscopic electromagnetism, conservation laws,” in Classical Electrodynamics. (Wiley & Sons, 1983).

].

At distances larger than 20 nm the interaction between the detector and the dipole emitter is very weak. In this case both the multipole model and FDTD calculations yield almost identical curves with the same tendency that reflects the rapid decay of the electric field of the dipole source with distance. From the comparison of the multipole model and FDTD calculations we find a value η = 14.5 for the tuning parameter in Eq. (3). We note that a very small deviation remains in Fig. 4(b). We attribute this deviation to the fact that our multipole model does not include the finite size of the detector. In the multipole model we ignore the boundaries of the detector based on the assumption that the quadrupole field decays very strongly towards the edge of the detector.

For practical applications of the novel, absorption-based, SNOM tip it is important to consider the spatial resolution. To this end, we performed additional FDTD calculations (not shown). To estimate the resolution we investigate the response of the detector to two dipole sources separated by a distance D. For a detector at a height z = 10 nm from the surface we find that two sources at a distance D = 60 nm can be resolved, limited by the transverse size of the detector. We chose the height of 10 nm to find a compromise between the near-field probe affecting the dipole emitter and a degradation of the resolution that occurs for larger heights of the detector from the substrate. The most favorable situation is reached for a detector that is as far away as possible, without significantly degrading the resolution. In principle, the spatial resolution can be improved via nanofabrication of smaller detectors by reducing the constriction area of the wire further. However, it is currently unclear how this affects the operation of the detector and what the practical limitations on the active area of the detector are when the resistive region (“hot spot”) in the detector is taken into account [9

9. D. Bitauld, F. Marsili, A. Gaggero, F. Mattioli, R. Leoni, S. J. Nejad, F. Lévy, and A. Fiore, “Nanoscale optical detector with single-photon and multiphoton sensitivity,” Nano Lett. 10(8), 2977–2981 (2010). [CrossRef] [PubMed]

]. The 50 nm constriction considered in this work has been studied experimentally [9

9. D. Bitauld, F. Marsili, A. Gaggero, F. Mattioli, R. Leoni, S. J. Nejad, F. Lévy, and A. Fiore, “Nanoscale optical detector with single-photon and multiphoton sensitivity,” Nano Lett. 10(8), 2977–2981 (2010). [CrossRef] [PubMed]

] and a spatial resolution of ~500 nm has been demonstrated to resolve the optical far-field.

4. The detector’s influence on the dipole source/emitter

In order to estimate the change in emission rate we calculate the LDOS for a simple system consisting of a thin (4 nm thick) NbN film on a semi-infinite GaAs substrate. We are primarily interested in the near-field interaction where the distance between the emitter and the detector is comparable or smaller than the lateral size of the detector. In this near-field regime the change in the decay rate of an emitter close to the detector is expected to be very similar to the change in decay rate induced by an infinite large slab. For the slab configuration, the LDOS can be calculated with relative ease using an analytical expression of the Green’s function.

The LDOSρ(R,ω) can be calculated by taking the imaginary part of the trace of the Green’s dyadic G(R,R',ω) of the system [31

31. K. Joulain, R. Carminati, J. Mulet, and J. Greffet, “Definition and measurement of the local density of electromagnetic states close to an interface,” Phys. Rev. B 68(24), 245405 (2003). [CrossRef]

]. This quantity is evaluated at the positionR=R', where R' is the location of the emitter with transition frequency ω:

ρ(R,ω)=ωπc2ImTr[G(R,R,ω)].
(5)

We use the Green’s dyadicG(R,R,ω)given by the approach of Ref. 28

28. K. H. Drexhage, “Influence of a dielectric interface on fluorescence decay time,” J. Lumin. 1(2), 693–701 (1970). [CrossRef]

that separates the dyadic into a nonscattering partGo(R,R,ω)and a scattering partGs(R,R,ω). The detailed expressions for these quantities can be found in Ref. 30

30. R. R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys. 37, 1–65 (1978). [CrossRef]

. For a planar interface with an emitter at a distance z from the interface the Green’s dyadic at the position of the emitter can be significantly simplified. In cylindrical coordinates we obtain:
G(z,z,ω)=i4π0dλ[(c1'ei2h1z+1)λ2h1erer+(λf1'ei2h1z)h12k12eϕeϕ+(f1'ei2h1z+1)λ3k12h1ezez],
(6)
wherec1'=(h1R1h2)/(h1R1+h2),f1'=(S1h1ε2h2ε1)/(S1h1ε2+h2ε1), withR1andS1 defined as R1=(h2ih3tanθ)/(h3ih2tanθ), and S1=(h2ε3ih3ε2tanθ)/(h3ε2ih2ε3tanθ). In these expressions, kj denotes the wave vector in j-th layer, hj is the vertical component of the wave vector and the phase change in the second (middle) layer is θ. These quantities are given bykj2=εj(ω/c)2, hj2=kj2λ2 and θ=h2d2 respectively, in which c is the speed of light in vacuum, and ε j is the dielectric constant of j-th layer, and d2 is the thickness of the second layer [30

30. R. R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys. 37, 1–65 (1978). [CrossRef]

].

Figure 5
Fig. 5 Normalized life time of an emitter close to a 4 nm thick metal film as a function of distance from the substrate. Calculation are shown for a NbN, Au, Ag and Al film at λ = 1.0 μm. In the near field (distance < 50 nm), the emitter close to NbN behaves differently from those close to the other three metal films. The inset shows the variations in emitter lifetime for larger distances.
compares the normalized life time of an emitter calculated as a function of distance for an emitter close to a 4 nm thick NbN, Au, Ag and Al film. Calculations are shown for a wavelength of 1.0 μm. The normalized lifetime is obtained by dividing spontaneous decay rate in free space by the spontaneous decay rate of the dipole emitter as obtained from the Green’s function:
Γ(z)ω2ImTrG(z,z,ω).
(7)
The proportionality constant is divided out by normalization to the life time of the dipole in free space.

The curves in Fig. 5 show that the lifetime of the emitter close to the NbN film is much higher for distances below 50 nm compared to the lifetime close to a thin metal film of Au, Ag or Al. This makes a NbN detector a very interesting near-field probe because it has a relatively high detection efficiency while leaving the emission rate of the dipole unaffected. We attribute the relatively weak coupling of the NbN detector to the strong damping in the material that excludes strong energy transfer to the film via surface plasmon. We emphasize that all thin films have comparable reflectivity while only Au, Ag and Al support low loss surface plasmon modes. This inset shows the calculated normalized life time for larger distances up to 1.0 μm. For larger distances all curves show characteristic oscillations with a periodicity of λ/4 for an emitter close to a mirror [28

28. K. H. Drexhage, “Influence of a dielectric interface on fluorescence decay time,” J. Lumin. 1(2), 693–701 (1970). [CrossRef]

]. The modulation of the oscillation around a normalized lifetime of 1.0 is a consequence of self interference between the emitted radiation and radiation reflected by the mirror. These similar oscillations for the different materials are a signature of the fact that reflectivity of the different thin films is comparable.

To further investigate the role of surface plasmon in the near-field interaction for a dipole close to a thin film we calculated the LDOS as a function of frequency for different materials. Figure 6
Fig. 6 Local density of states (LDOS) at the position of the emitter as a function of frequency for different metal substrates. Results are shown for a 4 nm thick NbN film and a 4 nm thick Ag film on a semi-infinite GaAs substrate as shown in the inset. The distance between the emitter and the film is set to 5 nm and 10 nm which are in the near-field of the emitter leading to a strong coupling to surface plasmon modes of the Ag film.
shows the calculated LDOS for a 4 nm thick NbN film compared to a 4 nm thick Ag film as a function of frequency. Calculations are shown for a dipole at a constant distance of 5 nm and 10 nm from the metal surface. As can be seen, the calculations for the Ag film show a sharply double peaked structure at angular frequencies close to 3 × 1015 and 7 × 1015 rad/s, while the calculations for NbN show a relatively small maximum around a frequency of 7 × 1015 rad/s.

To calculate these data we use two different modified Drude models [20

20. D. W. Lynch and W. R. Hunter, “Comments on the optical constants of metals and an introduction to the data for several metals,” in Handbook of Optical Constants of Solids I, E. D. Palik, ed. (Academic, 1998).

,32

32. K. Tanabe, H. Asano, Y. Katoh, and O. Michikami, “Ellipsometric and optical reflectivity studies of reactively sputtered NbN thin films,” J. Appl. Phys. 63(5), 1733 (1988). [CrossRef]

] to describe the dielectric constant of NbN and Ag as a function of frequency:
εNbN(ω)=εNbNhighεNbNhighωNbNp2ω2+iγNbNω,
(8)
εAg(ω)=εAghigh(εAgstaticεAghigh)ωAgp2ω2+iγAgω,
(9)
where ωNbNp = 5.28 × 1015 rad/s and ωAgp = 1.72 × 1016 rad/s are plasma frequencies; γNbN = 3.77 × 1015 rad/s and γAg = 2.3 × 1013 are the damping constants of the plasma excitation; εNbNhigh = 12.5 andεAghigh = 5.45 are the relative permittivity in the high frequency limit and εAgstatic = 6.18 is the relative permittivity in the static limit for Ag.

The data in Fig. 6 show that for low angular frequencies below 1015 rad/s (wavelength larger than 1.8 μm), all curves of the LDOS are very smooth and nearly constant. For frequencies above 1016 rad/s (wavelength shorter than 180 nm), all curves approach a LDOS that is proportional to ω2. In the relevant spectral range between angular frequencies of 1015 and 1016 rad/s (wavelength range from 180 to 1800 nm) the calculation for a NbN and a Ag film are markedly different.

The Ag system has two peaks due to the localized surface plasmon. Those sharp fluctuations in LDOS come from the strong energy coupling between the emitter and the Ag film, and this will enhance the energy transfer from the emitter to the Ag that reduces the lifetime of the emitter. These large fluctuations show that the surface plasmon has a profound effect on the emitter and the field that is emitted. In contrast, the LDOS for NbN film shows a much smoother frequency dependence and therefore perturbs the original field much weaker.

5. Conclusions

We have introduced a novel, absorption-based, near-field probe based on a NbN nano detector that absorbs and detects single photons directly in the near-field. This nano-detector has a higher detection efficiency compared to conventional scanning near-field optical microscopes because it is based on the physical process of absorption instead of scattering. We calculate an enhancement of 1~2 orders by comparing the absorption of a NbN detector with the scattering cross section of a Ag particle using Mie theory in the Rayleigh limit. We introduced a multipole model to describe the near-field interaction between a square NbN detector and a dipole emitter on a GaAs substrate and find that this analytical model fits well with FDTD simulations. From the calculations and FDTD simulations we find that a spatial resolution of ~60 nm can be achieved for a detector at 10 nm distance from the substrate. This resolution is limited by the detector size and may be improved for smaller detectors. Further research on nano-detectors smaller than 50 nm × 50 nm is needed to provide an answer if the active area of the detector can be reduced further.

A nano-detector close to an emitter also influences the decay rate of that emitter. For good metals with low-loss large enhancements in the local field can be achieved if the emitter couples to a plasmon mode. For a near-field probe this strong perturbation of the emitter is undesired. We use a Green's function formalism to calculate and compare the change in decay rate for a nano-detector versus other, commonly used, metals in SNOM tips (Ag, Au and Al). We find that the life time of an emitter that emits at λ = 1.0 μm is only mildly decreased when the emitter is close to a NbN, while a strong reduction in lifetime occurs for an emitter close to other metals. To explain this difference, we calculate the LDOS at the position of the emitter close to NbN and Ag film as a function of frequency of the emitter and show that the surface plasmon on the Ag film causes a strong energy transfer, reducing the life time of the emitter. In contrast, the NbN film has a much weaker coupling to the emitter and does not have a well-developed plasmon mode.

This novel nano-detector could be integrated with a cantilever or a tuning fork as a detection probe. To this end, the superconducting nano-detector should operate in a cryostat (~4 K) to create a near-field scanning optical microscope with high spatial resolution and single-photon and multiphoton sensitivity [9

9. D. Bitauld, F. Marsili, A. Gaggero, F. Mattioli, R. Leoni, S. J. Nejad, F. Lévy, and A. Fiore, “Nanoscale optical detector with single-photon and multiphoton sensitivity,” Nano Lett. 10(8), 2977–2981 (2010). [CrossRef] [PubMed]

]. This opens new possibilities to explore single emitters, quantum light and optical antenna structures at the nanoscale.

Acknowledgments

We thank Jelmer Renema and Martin van Exter for discussions, and we also thank Amdrea Fiore of Eindhoven University of Technology for discussions. This research was supported by the foundation for Fundamental Research on Matter (FOM) and The Netherlands Organisation for Scientific (NWO).

References and links

1.

R. C. Dunn, “Near-field scanning optical microscopy,” Chem. Rev. 99(10), 2891–2928 (1999). [CrossRef] [PubMed]

2.

V. Sandoghdar, B. Buchler, P. Kramper, S. Götzinger, O. Benson, and M. Kafesaki, “Scanning near-field optical studies of photonic devices,” in Photonic Crystals: Advances in Design, Fabrication, and Characterization, K. Busch, S. Lölkes, R. B. Wehrspohn and H. Föll eds. (Wiley-VCH Verlag GmbH & Co. KGaA, 2006).

3.

F. Keilmann and R. Hillenbrand, “Near-field microscopy by elastic light scattering from a tip,” Philos. Transact. A Math. Phys. Eng. Sci. 362(1817), 787–805 (2004). [CrossRef] [PubMed]

4.

T. Kalkbrenner, M. Ramstein, J. Mlynek, and V. Sandoghdar, “A single gold particle as a probe for apertureless scanning near-field optical microscopy,” J. Microsc. 202(1), 72–76 (2001). [CrossRef] [PubMed]

5.

B. Hecht, B. Sick, U. P. Wild, V. Decker, R. Zenobi, O. J. F. Martin, and D. W. Pohl, “Scanning near-field optical microscopy with aperture probes: fundamentals and applications,” J. Chem. Phys. 112(18), 7761–7774 (2000). [CrossRef]

6.

C. H. Henry and R. F. Kazarinov, “Quantum noise in photonics,” Rev. Mod. Phys. 68(3), 801–853 (1996). [CrossRef]

7.

E. Betzig and R. J. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science 262(5138), 1422–1425 (1993). [CrossRef] [PubMed]

8.

G. N. Gol’tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. 79(6), 705–707 (2001). [CrossRef]

9.

D. Bitauld, F. Marsili, A. Gaggero, F. Mattioli, R. Leoni, S. J. Nejad, F. Lévy, and A. Fiore, “Nanoscale optical detector with single-photon and multiphoton sensitivity,” Nano Lett. 10(8), 2977–2981 (2010). [CrossRef] [PubMed]

10.

A. Rasmussen and V. Deckert, “New dimension in nano-imaging: breaking through the diffraction limit with scanning near-field optical microscopy,” Anal. Bioanal. Chem. 381(1), 165–172 (2005). [CrossRef] [PubMed]

11.

F. Zenhausern, M. P. O’Boyle, and H. K. Wickramasinghe, “Apertureless near-field optical microscope,” Appl. Phys. Lett. 65(13), 1623–1625 (1994). [CrossRef]

12.

A. V. Zayats and V. Sandoghdar, “Apertureless near-field optical microscopy via local second-harmonic generation,” J. Microsc. 202(1), 94–99 (2001). [CrossRef] [PubMed]

13.

T. Vo-Dinh, J. P. Alarie, B. M. Cullum, and G. D. Griffin, “Antibody-based nanoprobe for measurement of a fluorescent analyte in a single cell,” Nat. Biotechnol. 18(7), 764–767 (2000). [CrossRef] [PubMed]

14.

Y. Zhang, A. Dhawan, and T. Vo Dinh, “Design and fabrication of fiber-optic nanoprobes for optical sensing,” Nanoscale Res. Lett. 6, 18–23 (2011).

15.

J. Smajic and C. Hafner, “Numerical analysis of a SNOM tip based on a partially cladded optical fiber,” Opt. Express 19(23), 23140–23152 (2011). [CrossRef] [PubMed]

16.

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66(7-8), 163–182 (1944). [CrossRef]

17.

I. S. Averbukh, B. M. Chernobrod, O. A. Sedletsky, and Y. Prior, “Coherent near field optical microscopy,” Opt. Commun. 174(1-4), 33–41 (2000). [CrossRef]

18.

C. F. Bohren and D. R. Huffman, “Particles small compared with the wavelength,” in Absorption and scattering of light by small particles. (Wiley & Sons, 1983).

19.

B. Knoll and F. Keilmann, “Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy,” Opt. Commun. 182(4-6), 321–328 (2000). [CrossRef]

20.

D. W. Lynch and W. R. Hunter, “Comments on the optical constants of metals and an introduction to the data for several metals,” in Handbook of Optical Constants of Solids I, E. D. Palik, ed. (Academic, 1998).

21.

E. F. C. Driessen and M. J. A. de Dood, “The perfect absorber,” Appl. Phys. Lett. 94(17), 171109 (2009). [CrossRef]

22.

M. Esslinger and R. Vogelgesang, “Reciprocity theory of apertureless scanning near-field optical microscopy with point-dipole probes,” ACS Nano 6(9), 8173–8182 (2012). [CrossRef] [PubMed]

23.

A. J. L. Adam, N. C. J. van der Valk, and P. C. M. Planken, “Measurement and calculation of the near field of a terahertz apertureless scanning optical microscope,” J. Opt. Soc. Am. B 24(5), 1080–1090 (2007). [CrossRef]

24.

J. D. Jackson, “Multipoles, electrostatics of macroscopic media, dielectrics,” in Classical Electrodynamics. (Wiley & Sons, 1983).

25.

L. Novotny and B. Hecht, “Dipole emission near planar interfaces,” in Principles of Nano-optics. (Cambridge University Press, 2006).

26.

J. D. Jackson, “Radiating systems, multipole fields and radiation,” in Classical Electrodynamics. (Wiley & Sons, 1983).

27.

J. D. Jackson, “Maxwell equations, macroscopic electromagnetism, conservation laws,” in Classical Electrodynamics. (Wiley & Sons, 1983).

28.

K. H. Drexhage, “Influence of a dielectric interface on fluorescence decay time,” J. Lumin. 1(2), 693–701 (1970). [CrossRef]

29.

K. H. Drexhage, “Interaction of light with monomolecular dye layers,” Prog. Opt. 12, 165–232 (1974).

30.

R. R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys. 37, 1–65 (1978). [CrossRef]

31.

K. Joulain, R. Carminati, J. Mulet, and J. Greffet, “Definition and measurement of the local density of electromagnetic states close to an interface,” Phys. Rev. B 68(24), 245405 (2003). [CrossRef]

32.

K. Tanabe, H. Asano, Y. Katoh, and O. Michikami, “Ellipsometric and optical reflectivity studies of reactively sputtered NbN thin films,” J. Appl. Phys. 63(5), 1733 (1988). [CrossRef]

OCIS Codes
(230.0040) Optical devices : Detectors
(270.5570) Quantum optics : Quantum detectors
(180.4243) Microscopy : Near-field microscopy

ToC Category:
Detectors

History
Original Manuscript: December 3, 2012
Revised Manuscript: January 26, 2013
Manuscript Accepted: January 26, 2013
Published: February 6, 2013

Virtual Issues
Vol. 8, Iss. 3 Virtual Journal for Biomedical Optics

Citation
Qiang Wang and Michiel J. A. de Dood, "An absorption-based superconducting nano-detector as a near-field optical probe," Opt. Express 21, 3682-3692 (2013)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-21-3-3682


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References

  1. R. C. Dunn, “Near-field scanning optical microscopy,” Chem. Rev.99(10), 2891–2928 (1999). [CrossRef] [PubMed]
  2. V. Sandoghdar, B. Buchler, P. Kramper, S. Götzinger, O. Benson, and M. Kafesaki, “Scanning near-field optical studies of photonic devices,” in Photonic Crystals: Advances in Design, Fabrication, and Characterization, K. Busch, S. Lölkes, R. B. Wehrspohn and H. Föll eds. (Wiley-VCH Verlag GmbH & Co. KGaA, 2006).
  3. F. Keilmann and R. Hillenbrand, “Near-field microscopy by elastic light scattering from a tip,” Philos. Transact. A Math. Phys. Eng. Sci.362(1817), 787–805 (2004). [CrossRef] [PubMed]
  4. T. Kalkbrenner, M. Ramstein, J. Mlynek, and V. Sandoghdar, “A single gold particle as a probe for apertureless scanning near-field optical microscopy,” J. Microsc.202(1), 72–76 (2001). [CrossRef] [PubMed]
  5. B. Hecht, B. Sick, U. P. Wild, V. Decker, R. Zenobi, O. J. F. Martin, and D. W. Pohl, “Scanning near-field optical microscopy with aperture probes: fundamentals and applications,” J. Chem. Phys.112(18), 7761–7774 (2000). [CrossRef]
  6. C. H. Henry and R. F. Kazarinov, “Quantum noise in photonics,” Rev. Mod. Phys.68(3), 801–853 (1996). [CrossRef]
  7. E. Betzig and R. J. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science262(5138), 1422–1425 (1993). [CrossRef] [PubMed]
  8. G. N. Gol’tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett.79(6), 705–707 (2001). [CrossRef]
  9. D. Bitauld, F. Marsili, A. Gaggero, F. Mattioli, R. Leoni, S. J. Nejad, F. Lévy, and A. Fiore, “Nanoscale optical detector with single-photon and multiphoton sensitivity,” Nano Lett.10(8), 2977–2981 (2010). [CrossRef] [PubMed]
  10. A. Rasmussen and V. Deckert, “New dimension in nano-imaging: breaking through the diffraction limit with scanning near-field optical microscopy,” Anal. Bioanal. Chem.381(1), 165–172 (2005). [CrossRef] [PubMed]
  11. F. Zenhausern, M. P. O’Boyle, and H. K. Wickramasinghe, “Apertureless near-field optical microscope,” Appl. Phys. Lett.65(13), 1623–1625 (1994). [CrossRef]
  12. A. V. Zayats and V. Sandoghdar, “Apertureless near-field optical microscopy via local second-harmonic generation,” J. Microsc.202(1), 94–99 (2001). [CrossRef] [PubMed]
  13. T. Vo-Dinh, J. P. Alarie, B. M. Cullum, and G. D. Griffin, “Antibody-based nanoprobe for measurement of a fluorescent analyte in a single cell,” Nat. Biotechnol.18(7), 764–767 (2000). [CrossRef] [PubMed]
  14. Y. Zhang, A. Dhawan, and T. Vo Dinh, “Design and fabrication of fiber-optic nanoprobes for optical sensing,” Nanoscale Res. Lett.6, 18–23 (2011).
  15. J. Smajic and C. Hafner, “Numerical analysis of a SNOM tip based on a partially cladded optical fiber,” Opt. Express19(23), 23140–23152 (2011). [CrossRef] [PubMed]
  16. H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev.66(7-8), 163–182 (1944). [CrossRef]
  17. I. S. Averbukh, B. M. Chernobrod, O. A. Sedletsky, and Y. Prior, “Coherent near field optical microscopy,” Opt. Commun.174(1-4), 33–41 (2000). [CrossRef]
  18. C. F. Bohren and D. R. Huffman, “Particles small compared with the wavelength,” in Absorption and scattering of light by small particles. (Wiley & Sons, 1983).
  19. B. Knoll and F. Keilmann, “Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy,” Opt. Commun.182(4-6), 321–328 (2000). [CrossRef]
  20. D. W. Lynch and W. R. Hunter, “Comments on the optical constants of metals and an introduction to the data for several metals,” in Handbook of Optical Constants of Solids I, E. D. Palik, ed. (Academic, 1998).
  21. E. F. C. Driessen and M. J. A. de Dood, “The perfect absorber,” Appl. Phys. Lett.94(17), 171109 (2009). [CrossRef]
  22. M. Esslinger and R. Vogelgesang, “Reciprocity theory of apertureless scanning near-field optical microscopy with point-dipole probes,” ACS Nano6(9), 8173–8182 (2012). [CrossRef] [PubMed]
  23. A. J. L. Adam, N. C. J. van der Valk, and P. C. M. Planken, “Measurement and calculation of the near field of a terahertz apertureless scanning optical microscope,” J. Opt. Soc. Am. B24(5), 1080–1090 (2007). [CrossRef]
  24. J. D. Jackson, “Multipoles, electrostatics of macroscopic media, dielectrics,” in Classical Electrodynamics. (Wiley & Sons, 1983).
  25. L. Novotny and B. Hecht, “Dipole emission near planar interfaces,” in Principles of Nano-optics. (Cambridge University Press, 2006).
  26. J. D. Jackson, “Radiating systems, multipole fields and radiation,” in Classical Electrodynamics. (Wiley & Sons, 1983).
  27. J. D. Jackson, “Maxwell equations, macroscopic electromagnetism, conservation laws,” in Classical Electrodynamics. (Wiley & Sons, 1983).
  28. K. H. Drexhage, “Influence of a dielectric interface on fluorescence decay time,” J. Lumin.1(2), 693–701 (1970). [CrossRef]
  29. K. H. Drexhage, “Interaction of light with monomolecular dye layers,” Prog. Opt.12, 165–232 (1974).
  30. R. R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys.37, 1–65 (1978). [CrossRef]
  31. K. Joulain, R. Carminati, J. Mulet, and J. Greffet, “Definition and measurement of the local density of electromagnetic states close to an interface,” Phys. Rev. B68(24), 245405 (2003). [CrossRef]
  32. K. Tanabe, H. Asano, Y. Katoh, and O. Michikami, “Ellipsometric and optical reflectivity studies of reactively sputtered NbN thin films,” J. Appl. Phys.63(5), 1733 (1988). [CrossRef]

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