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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 27 — Dec. 19, 2011
  • pp: 26850–26858
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Microcavity enhanced optical absorption in subwavelength slits

Changjun Min, Liu Yang, and Georgios Veronis  »View Author Affiliations


Optics Express, Vol. 19, Issue 27, pp. 26850-26858 (2011)
http://dx.doi.org/10.1364/OE.19.026850


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Abstract

We introduce a compact submicron structure consisting of multiple optical microcavities at both the entrance and exit sides of a subwavelength plasmonic slit filled with an absorbing material. We show that such microcavity structures at the entrance side of the slit can greatly enhance the coupling of the incident light into the slit, by improving the impedance matching between the incident plane wave and the slit mode. In addition, the microcavity structures can also increase the reflectivities at both sides of the slit, and therefore the resonant field enhancement. Thus, such structures can greatly enhance the absorption cross section of the slit. An optimized submicron structure consisting of two microcavities at each of the entrance and exit sides of the slit leads to ~9.3 times absorption enhancement at the optical communication wavelength compared to an optimized slit without microcavities.

© 2011 OSA

1. Introduction

Following the observation of extraordinary optical transmission through arrays of subwavelength apertures in metallic films [1

1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]

], there has been enormous interest in the properties of plasmonic structures consisting of subwavelength apertures [2

2. T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, “Enhanced light transmission through a single subwavelength aperture,” Opt. Lett. 26(24), 1972–1974 (2001). [CrossRef] [PubMed]

8

8. F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010). [CrossRef]

]. Resonant subwavelength plasmonic apertures can efficiently concentrate light into deep subwavelength regions, and therefore significantly enhance the optical transmission through the apertures [3

3. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002). [CrossRef] [PubMed]

8

8. F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010). [CrossRef]

], or the absorption in the apertures [9

9. Z. Yu, G. Veronis, and S. Fan, andM. L. Brongersma “Design of mid-infrared photodetectors enhanced by surface plasmons on grating structures,” Appl. Phys. Lett. 89(15), 151116 (2006). [CrossRef]

,10

10. J. S. White, G. Veronis, Z. Yu, E. S. Barnard, A. Chandran, S. Fan, and M. L. Brongersma, “Extraordinary optical absorption through subwavelength slits,” Opt. Lett. 34(5), 686–688 (2009). [CrossRef] [PubMed]

]. In addition, grating structures, consisting of periodic arrays of grooves patterned on the metal film surrounding the aperture, are commonly used to enhance the coupling of incident light into the aperture through the excitation of surface plasmons [3

3. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002). [CrossRef] [PubMed]

,7

7. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]

,9

9. Z. Yu, G. Veronis, and S. Fan, andM. L. Brongersma “Design of mid-infrared photodetectors enhanced by surface plasmons on grating structures,” Appl. Phys. Lett. 89(15), 151116 (2006). [CrossRef]

,11

11. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90(16), 167401 (2003). [CrossRef] [PubMed]

18

18. B. Guo, G. Song, and L. Chen, “Plasmonic very-small-aperture lasers,” Appl. Phys. Lett. 91(2), 021103 (2007). [CrossRef]

]. For efficient surface plasmon excitation, however, the period of the grating has to be equal to the surface plasmon wavelength, and several grating periods are required. Thus, such structures need to be several microns long to operate at optical frequencies.

In this paper, we show that a compact submicron structure consisting of multiple optical microcavities at both the entrance and exit sides of a subwavelength plasmonic slit filled with an absorbing material can greatly enhance the absorption cross section of the slit. Our reference structure is a single optimized subwavelength slit in a metal film deposited on a substrate. We show that such microcavity structures at the entrance side of the slit can greatly enhance the coupling of the incident light into the slit, by improving the impedance matching between the incident plane wave and the slit mode. In addition, the microcavity structures can increase the reflectivities at both sides of the slit, and therefore the resonant field enhancement in the slit. An optimized submicron structure consisting of two microcavities at each of the entrance and exit sides of the slit leads to ~9.3 times absorption enhancement at the optical communication wavelength compared to the optimized reference slit without microcavities. We also show that, while the microcavity enhanced structures are optimized at a single wavelength, the operation wavelength range for high absorption is broad.

The remainder of the paper is organized as follows. In Section 2, we define the absorption cross section and absorption enhancement factor of the slit, and employ single-mode scattering matrix theory to account for their behavior. The results obtained for the reference structure of a slit without microcavities, as well as for the microcavity enhanced structures are presented in Section 3. Finally, our conclusions are summarized in Section 4.

2. Absorption cross section and absorption enhancement factor

We consider a structure consisting of a single slit in a silver film with N microcavities at the entrance side, and M microcavities at the exit side of the slit deposited on a silica substrate (Fig. 1(a)
Fig. 1 (a) Schematic of a structure consisting of a slit in a silver film with N microcavities at the entrance side, and M microcavities at the exit side of the slit deposited on a silica substrate. The slit is filled with germanium, while the microcavities are filled with silica. (b) Schematic of a bulk germanium photodetector with an anti-reflection coating. (c) Schematic defining the transmission cross section σT of a silver-germanium-silver waveguide through the structure above the entrance side of the slit of Fig. 1(a) for a normally incident plane wave from air. (d) Schematic defining the reflection coefficient r1 of the fundamental TM mode of a silver-germanium-silver waveguide at the interface of such a waveguide with the structure above the entrance side of the slit of Fig. 1(a). (e) Schematic defining the reflection coefficient r2 of the fundamental TM mode of a silver-germanium-silver waveguide at the interface of such a waveguide with the structure below the exit side of the slit of Fig. 1(a).
). The slit is filled with germanium, which is one of the most promising materials for near-infrared photodetectors in integrated optical circuits [21

21. L. Cao, J. S. Park, P. Fan, B. Clemens, and M. L. Brongersma, “Resonant germanium nanoantenna photodetectors,” Nano Lett. 10(4), 1229–1233 (2010). [CrossRef] [PubMed]

], while the microcavities are filled with silica. We consider compact structures in which all microcavity dimensions are limited to less than 1μm.

We use a two-dimensional finite-difference frequency-domain (FDFD) method [22

22. G. Veronis and S. Fan, “Overview of simulation techniques for plasmonic devices,” in Surface Plasmon Nanophotonics, Mark L. Brongersma and Pieter G. Kik, eds. (Springer, 2007).

] to numerically calculate the absorption in the material filling the slit. This method allows us to directly use experimental data for the frequency-dependent dielectric constant of metals such as silver [23

23. E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985).

], including both the real and imaginary parts, with no approximation. We use perfectly matched layer (PML) absorbing boundary conditions at all boundaries of the simulation domain [24

24. J. Jin, The Finite Element Method in Electromagnetics (Wiley, New York, 2002).

]. We also use the total-field-scattered-field formulation to simulate the response of the structure to a normally incident plane wave input [25

25. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed., (Artech House, Norwood, 2005).

].

For comparison of different configurations, we define the absorption cross section σA of the slit as the total light power absorbed by the material (germanium) in the slit, normalized by the incident plane wave power flux [9

9. Z. Yu, G. Veronis, and S. Fan, andM. L. Brongersma “Design of mid-infrared photodetectors enhanced by surface plasmons on grating structures,” Appl. Phys. Lett. 89(15), 151116 (2006). [CrossRef]

]. In two dimensions, the cross section is in the unit of length. We also calculate the absorption cross section for the same volume of germanium in a uniform thick slab with an anti-reflection coating, which is a typical configuration for conventional photodetectors [9

9. Z. Yu, G. Veronis, and S. Fan, andM. L. Brongersma “Design of mid-infrared photodetectors enhanced by surface plasmons on grating structures,” Appl. Phys. Lett. 89(15), 151116 (2006). [CrossRef]

] (Fig. 1(b)). The ratio between these two absorption cross sections defines the absorption enhancement factor η, which is a measure of the enhancement of the light absorption for a unit volume of absorbing material.

We employ single-mode scattering matrix theory to account for the absorption cross section σA of the slit in the structure of Fig. 1(a) [26

26. S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, “Transmission line and equivalent circuit models for plasmonic waveguide components,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1462–1472 (2008). [CrossRef]

]. We define the transmission cross section σT of a silver-germanium-silver metal-dielectric-metal (MDM) waveguide of width w (in the unit of length in two dimensions) as the transmitted power into the waveguide from the structure above the entrance side of the slit of Fig. 1(a), normalized by the incident plane wave power flux (Fig. 1(c)). We also define r1 (r2) as the complex magnetic field reflection coefficient for the fundamental propagating TM mode in a silver-germanium-silver MDM waveguide of width w at the interface of such a waveguide with the structure above the entrance side (below the exit side) of the slit of Fig. 1(a) (Figs. 1(d) and 1(e)). We use FDFD to numerically extract σT, r1, and r2 [26

26. S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, “Transmission line and equivalent circuit models for plasmonic waveguide components,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1462–1472 (2008). [CrossRef]

]. The absorption cross section σA of the slit can then be calculated using scattering matrix theory as:
σA=fGeσT(1|exp(γL)|2)(1+|r2exp(γL)|2)|1r1r2exp(2γL)|2,
(1)
where γ is the complex wave vector of the fundamental propagating TM mode in a silver-germanium-silver MDM waveguide of width w, L is the length of the slit, and fGe is the ratio of the power absorbed in germanium to the total power absorbed in the slit, which also includes the power absorbed in the metal. Based on Eq. (1), we observe that, for fixed slit dimensions, γ, L and fGe are fixed, so that the absorption cross section σA of the slit is solely determined by σT, r1, and r2. These three parameters in turn can be tuned by adjusting the geometrical dimensions of the microcavities at the entrance and exit sides of the slit.

In addition, the absorption cross section for the same volume of germanium in a conventional bulk photodetector with anti-reflection coating (Fig. 1(b)) isσA,bulk=w(1|exp(γ0L)|2),

Where γ0 is the complex wave vector of a plane wave propagating in germanium. Thus, the absorption enhancement factor for the slit is

ησAσA,bulk=fGeσT(1|exp(γL|2)(1+|r2exp(γL)|2)w(1|exp(γ0L|2)|1r1r2exp(2γL)|2=η1η2η3  ,
(2)

where η1fGe(1|exp(γL)|2)1|exp(γ0L)|2,  η2σTw, and  η31+|r2exp(γL)|2|1r1r2exp(2γL)|2. We note that η1 is fixed when the slit dimensions w and L are fixed, and does not depend on the microcavity structures above and below the slit. As an example, for a silver-germanium-silver slit with w = 50 nm, L = 122 nm at λ0 = 1.55μm we find η1~1.42. In addition, η2 is the transmission cross section enhancement factor of the MDM waveguide with respect to its geometrical cross section, associated with the microcavities above the entrance side of the slit. Finally, η3 is the resonance enhancement factor, associated with the slit resonance. We note that η3 is a function of the reflection coefficients r1 and r2 at both sides of the slit, and therefore depends on both the structure above and the structure below the slit. We also observe that the resonance enhancement factor η3 is maximized for |r1|,|r2|→1, and when the slit resonance condition arg(r1) + arg(r2)−2Im(γ)L = −2 is satisfied, where m is an integer. We note, however, that there is a tradeoff between the resonance enhancement factor η3, and the transmission cross section enhancement factor η2. As a result, in the optimized structures we have |r1|<1 in all cases.

3. Results

We first consider our reference structure consisting of a single subwavelength slit in a metal film deposited on a substrate (Fig. 2(a)
Fig. 2 (a) Schematic of a structure consisting of a single slit in a silver film deposited on a silica substrate. The slit is filled with germanium. (b) Absorption cross section σA in units of w (black line and circles), and absorption enhancement factor η (red line and circles) for the structure of Fig. 2(a) as a function of slit length L calculated using FDFD (circles) and scattering matrix theory (solid line). Results are shown for w = 50nm and λ0 = 1.55μm.
). In Fig. 2(b), we show the absorption cross section σA, and the absorption enhancement factor η for the structure of Fig. 2(a) as a function of the slit length L calculated using FDFD. We observe that, as the slit length L increases, both the absorption cross section and the absorption enhancement factor exhibit peaks, corresponding to the Fabry-Pérot resonances in the slit. In Fig. 2(b) we also show σA and η calculated using scattering matrix theory (Eqs. (1), (2)). We observe that there is excellent agreement between the scattering matrix theory results and the exact results obtained using FDFD. Similarly, excellent agreement between the results of these two methods is observed for all the structures considered in this paper (Table 1

Table 1. Absorption enhancement factor η, transmission cross section enhancement factor η2, resonance enhancement factor η3, and reflection coefficients r1,r2. Also shown is the absorption cross section σA in units of w, calculated using scattering matrix theory and FDFD. Results are shown for the optimized structures of Fig. 1(a) with (N, M) = (0, 0), (1, 0), (1, 1), and (2, 2).

table-icon
View This Table
). The maximum absorption enhancement factor η of ~43.9 with respect to a conventional photodetector is obtained at the first peak (L = 122nm), due to the strong electromagnetic field enhancement associated with the Fabry-Pérot resonance in the slit [10

10. J. S. White, G. Veronis, Z. Yu, E. S. Barnard, A. Chandran, S. Fan, and M. L. Brongersma, “Extraordinary optical absorption through subwavelength slits,” Opt. Lett. 34(5), 686–688 (2009). [CrossRef] [PubMed]

]. For such a structure, the transmission cross section enhancement factor is η2~0.96 (Table 1). In other words, the transmission cross section of a silver-germanium-silver MDM waveguide with w = 50 nm at λ0 = 1.55μm is approximately equal to its geometrical cross section. In addition, the resonance enhancement factor is η3~32.3 (Table 1). Such large resonance enhancement is due to the strong reflectivities r1, r2 at both sides of the slit (Table 1), associated with the strong impedance mismatch between the fundamental MDM mode in the slit and propagating plane waves in air and in the silica substrate [9

9. Z. Yu, G. Veronis, and S. Fan, andM. L. Brongersma “Design of mid-infrared photodetectors enhanced by surface plasmons on grating structures,” Appl. Phys. Lett. 89(15), 151116 (2006). [CrossRef]

].

To further enhance the absorption cross section of the slit, we consider structures with multiple microcavities at both the entrance and exit sides of the slit (Fig. 1(a)). More specifically, we use the genetic optimization algorithm to optimize the widths and lengths of all microcavities in a (N = 2, M = 2) structure. As before, the dimensions of the structures at both the entrance and the exit sides of the slit are limited to less than 1μm. The maximum absorption cross section for such a structure is found to be σA~2.295w, and the corresponding absorption enhancement factor is η~410.6 (Table 1). We observe that the use of multiple microcavities at the entrance side of the slit (N = 2, M = 2) increases the transmission cross section enhancement factor η2 compared to the single microcavity (N = 1, M = 1) structure (Table 1). This is due to the fact that multiple-section structures can improve the impedance matching and therefore the coupling between optical modes [28

28. G. Veronis and S. Fan, “Theoretical investigation of compact couplers between dielectric slab waveguides and two-dimensional metal-dielectric-metal plasmonic waveguides,” Opt. Express 15(3), 1211–1221 (2007). [CrossRef] [PubMed]

]. In addition, the use of multiple microcavities at the entrance and exit sides of the slit (N = 2, M = 2) also increases the corresponding reflectivities |r1|2 and |r2|2 compared to the single microcavity (N = 1, M = 1) structure (Table 1). Thus, a large resonance enhancement factor η3~97.9 is obtained (Table 1). This is due to the fact that multiple-section structures can be more finely tuned than single-section structures, and can therefore provide larger resonantly enhanced reflectivity. This is analogous to the multilayer Bragg reflectors which can provide larger reflectivity compared to single layer structures. Overall, the optimized (N = 2, M = 2) structure results in ~3.1 times larger transmission cross section enhancement factor η2, ~3 times larger resonance enhancement factor η3, and therefore ~9.3 times larger absorption cross section compared to the optimized reference slit without microcavities (Fig. 2(a)).

In Figs. 4(a)
Fig. 4 (a) Profile of the magnetic field amplitude enhancement with respect to the field amplitude of the incident plane wave for the optimized structure of Fig. 1(a) with N = M = 1. Results are shown for (wT1, dT1, wB1, dB1) = (300, 260, 860, 380) nm. All other parameters are as in Fig. 3(b). (b) Profile of the magnetic field amplitude enhancement with respect to the field amplitude of the incident plane wave for the optimized structure of Fig. 1(a) with N = M = 2. Results are shown for (wT1, dT1, wT2, dT2, wB1, dB1, wB2, dB2) = (1000, 390, 540, 200, 660, 220, 180, 210) nm. All other parameters are as in Fig. 3(b).
and 4(b), we show the magnetic field profile for the (N = 1, M = 1) and (N = 2, M = 2) cases, respectively, with dimensions optimized for maximum absorption cross section σA. We find that, as the number of microcavities increases, the field in the microcavities at the entrance side is stronger, due to the fact that more incident light is collected in the microcavities. The maximum magnetic field amplitude enhancement in the slit with respect to the incident plane wave is ~23 and ~40 for the (N = 1, M = 1) and (N = 2, M = 2) cases, respectively.

The microcavity-enhanced structures were optimized at a single wavelength of λ0 = 1.55μm. In Fig. 5
Fig. 5 Absorption cross section σA in units of w as a function of wavelength for the optimized structures of Fig. 1(a) with N = M = 0 (black line), N = M = 1 (red line), and N = M = 2 (green line). All other parameters for the N = M = 0, N = M = 1, and N = M = 2 cases are as in Figs. 3(b), 4(a), and 4(b), respectively.
, we show the absorption cross section σA as a function of incident wavelength for the optimized structures of Fig. 2(a) (N = M = 0), Fig. 4(a) (N = M = 1), and Fig. 4(b) (N = M = 2). We observe that the operation wavelength range for high absorption is broad. For example, the full width at half maximum (FWHM) of the absorption peak in the (N = M = 2) case is ~50nm. This is due to the fact that in all cases the enhanced absorption is not associated with any strong resonances. In other words, the quality factors Q of the microcavities are low.

4. Conclusions

In this paper, we investigated compact submicron structures consisting of multiple optical microcavities at both the entrance and exit sides of a subwavelength plasmonic slit filled with an absorbing material, with the goal to increase the absorption in the slit. Our reference structure consisted of a single subwavelength slit in a metal film deposited on a substrate. For such a structure, the maximum absorption enhancement factor with respect to a conventional photodetector is η~43.9, and the absorption enhancement is due to the large resonant field enhancement in the slit, associated with the strong reflectivities at both sides of the slit.

To further enhance the absorption in the slit, we first considered a structure with a single microcavity at the entrance side of the slit. We found that the microcavity greatly enhances the coupling of the incident light into the slit, by improving the impedance matching between the incident plane wave and the slit mode. On the other hand, the microcavity reduces the reflectivity at the entrance side of the slit, and therefore the resonance enhancement factor. Overall, the use of an optimized single microcavity at the entrance side of the slit resulted in an absorption enhancement factor of η~75.7, which is ~1.7 times larger compared to the slit without a microcavity. We then considered a structure with a single microcavity at each of the entrance and exit sides of the slit. We found that the microcavity at the exit side of the slit results in larger reflectivity, and therefore larger resonant field enhancement. Overall, the use of an optimized single microcavity at both the entrance and exit sides of the slit resulted in an absorption enhancement factor of η~133.6 which is ~3 times larger compared to the slit without a microcavity.

We finally considered structures with multiple microcavities at both the entrance and exit sides of the slit. We found that the use of multiple microcavities at the entrance side of the slit further enhances the coupling of the incident light into the slit through improved impedance matching. In addition, the use of multiple microcavities at the entrance and exit sides of the slit also increases the reflectivities at both sides of the slit, and therefore the resonant field enhancement. Overall, the use of two optimized microcavities at both the entrance and exit sides of the slit resulted in an absorption enhancement factor of η~410.6 which is ~9.3 times larger compared to the slit without a microcavity. We also found that, while the microcavity-enhanced structures were optimized at a single wavelength, the operation wavelength range for high absorption is broad.

As final remarks, we note that for the fabrication of each microcavity of the structure, one can make first a silica ridge using lithography and etching processes. This step can then be followed by metal deposition and lift-off processes to form the metal parts of the microcavity [9

9. Z. Yu, G. Veronis, and S. Fan, andM. L. Brongersma “Design of mid-infrared photodetectors enhanced by surface plasmons on grating structures,” Appl. Phys. Lett. 89(15), 151116 (2006). [CrossRef]

].

Acknowledgments

This research was supported by the Louisiana Board of Regents (contracts LEQSF(2009-12)-RD-A-08 and NSF(2010)-PFUND-187), and the National Science Foundation (Award No. 1102301).

References and links

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2.

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3.

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9.

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J. Jin, The Finite Element Method in Electromagnetics (Wiley, New York, 2002).

25.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed., (Artech House, Norwood, 2005).

26.

S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, “Transmission line and equivalent circuit models for plasmonic waveguide components,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1462–1472 (2008). [CrossRef]

27.

K. Krishnakumar, “Micro-genetic algorithms for stationary and non-stationary function optimization,” Proc. SPIE 1196, 289–296 (1989).

28.

G. Veronis and S. Fan, “Theoretical investigation of compact couplers between dielectric slab waveguides and two-dimensional metal-dielectric-metal plasmonic waveguides,” Opt. Express 15(3), 1211–1221 (2007). [CrossRef] [PubMed]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(260.3910) Physical optics : Metal optics
(260.5740) Physical optics : Resonance

ToC Category:
Physical Optics

History
Original Manuscript: October 13, 2011
Revised Manuscript: December 8, 2011
Manuscript Accepted: December 8, 2011
Published: December 15, 2011

Virtual Issues
Vol. 7, Iss. 2 Virtual Journal for Biomedical Optics

Citation
Changjun Min, Liu Yang, and Georgios Veronis, "Microcavity enhanced optical absorption in subwavelength slits," Opt. Express 19, 26850-26858 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-27-26850


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References

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  27. K. Krishnakumar, “Micro-genetic algorithms for stationary and non-stationary function optimization,” Proc. SPIE1196, 289–296 (1989).
  28. G. Veronis and S. Fan, “Theoretical investigation of compact couplers between dielectric slab waveguides and two-dimensional metal-dielectric-metal plasmonic waveguides,” Opt. Express15(3), 1211–1221 (2007). [CrossRef] [PubMed]

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