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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 13 — Jun. 23, 2008
  • pp: 9708–9713
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Surface plasmon microcavity for resonant transmission through a slit in a gold film

Qiao Min and Reuven Gordon  »View Author Affiliations


Optics Express, Vol. 16, Issue 13, pp. 9708-9713 (2008)
http://dx.doi.org/10.1364/OE.16.009708


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Abstract

We demonstrate the use of a compact surface plasmon (SP) microcavity formed in a 300 nm thick gold film to resonantly enhance the optical transmission through a subwavelength slit. Focussed ion beam milling is used to create 200 nm deep SP microcavities, with widths between 800 nm to 1300 nm, each with a 180 nm slit in its center. The experimentally-measured TM polarized optical transmission has a wavelength-dependent peak that has similarities with finite-difference time-domain calculations in terms of peak-position and enhancement factors of peak transmission. The calculations show, by observing the near-field distributions, the interaction between the SP microcavity standing waves and the slit to create enhanced transmission. The SP microcavity demonstrated here is easily fabricated and may be optimized for future applications in surface-enhanced Raman scattering, nonlinear optics and surface plasmon resonance sensors.

© 2008 Optical Society of America

1. Introduction

The demonstration of extraordinary optical transmission through subwavelength apertures has renewed the interest in resonant structures using metals that support surface plasmon polaritons (SPPs) [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, 667–669 (1998). [CrossRef]

,2

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

]. Wavelength-dependent enhanced transmission has been demonstrated for periodic hole arrays [1–3

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, 667–669 (1998). [CrossRef]

], and for a single hole or a slit surrounded by periodic surface structures [4–6

4. 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, 820–822 (2002). [CrossRef] [PubMed]

]. Both those approaches used Bragg resonances to couple the normally incident light into the SPPs. Another approach is to use Bragg resonances to act as a SPPs reflector in the plane [7–9

7. M. U. Gonzalez, A. L. Stepanov, J. C. Weeber, A. Hohenau, A. Dereux, R. Quidant, and J. R. Krenn, “Analysis of the angular acceptance of surface plasmon Bragg mirrors,” Opt. Lett. 32, 2704–2706 (2007). [CrossRef] [PubMed]

], which has been used to enhance the subwavelength aperture array optical transmission [10

10. P. Marthandam and R. Gordon, “Plasmonic Bragg reflectors for enhanced extraordinary optical transmission through nano-hole arrays in a gold film,” Opt. Express 15, 12995–13002 (2007). [CrossRef] [PubMed]

].

For an even more compact reflector device with resonant transmission, here we propose using the highly reflective gold as a simple mirror, and thereby forming a compact surface plasmon (SP) microcavity. The SP microcavity is created by trench milling in a gold film. Other narrower trench structures have been proposed for channel plasmon polaritons waveguides [11–13

11. I. M. Lee, J. Jung, J. Park, H. Kim, and B. Lee, “Dispersion characteristics of channel plasmon polariton waveguides with step-trench-type grooves,” Opt. Express 15, 16596–16603 (2007). [CrossRef] [PubMed]

]; those structures used a different polarization state and they relied on lateral guiding the SPPs [14

14. Y. Q. Fu, W. Zhou, L. E. N. Lim, C. Du, H. Shi, C. Wang, and X. Luo, “Influence of V-shaped plasmonic nanostructures on beam propagation,” Appl Phys B-Lasers 86, 461–466 (2007). [CrossRef]

], which is not the topic of this work. Here, the trench is used simply to form mirror side-walls, and thereby to create a microcavity. Due to the surface localization of the SPPs, the trench side-walls are good reflectors, even for depths of only a few hundred nanometers [15

15. H. A. Jamid and S. J. Al-Bader, “Reflection and transmission of surface plasmon mode at a step discontinuity,” IEEE Photon. Technol. Lett. 9, 220–222 (1997). [CrossRef]

]. As a result, compact SP microcavities can be easily created using this approach. Recently, a theory was presented for enhanced coupling between plasmonic transmission lines by using a gold microcavity [16

16. P. Ginzburg and M. Orenstein, “Plasmonic transmission lines: from micro to nano scale with λ/4 impedance matching,” Opt. Express 15, 6762–6767, (2007). [CrossRef] [PubMed]

]. In that work, the transverse resonances of a corresponding periodic slit-array were considered to explain the enhanced coupling. Here, we present experimental observations and calculations of a SP microcavity enhanced transmission through a slit for the case of free-space coupling.

In this paper, we demonstrate the use of a SP microcavity formed in a gold film to resonantly enhance the transmission of light through a slit. The optical transmission is measured experimentally for SP microcavities fabricated with various widths, each having a central slit. The observed resonant transmission peak wavelengths agree well with finite-difference time-domain (FDTD) calculations. The FDTD calculations allow for near-field visualization of the SP standing waves within the SP microcavity. These near-field images elucidate the interaction between the SP microcavity and the slit in the center of the microcavity.

2. Experimental and calculation methods

2.1 Focussed-ion beam fabrication

Figure 1 shows the scanning electron microscope image of a fabricated SP microcavity with a slit and a schematic representation of the structure. Focussed ion beam (FIB) milling was used to fabricate the SP microcavity structures. The FIB milled through a 300 nm deep gold film evaporated on a glass substrate. There was a 5 nm thick chromium layer deposited to assist adhesion between the gold layer and glass substrate. A gallium beam current of 30 pA at 30 kV was used for milling. The gallium beam spot size was 7 nm. The mill rate of the gold film was calibrated using energy-dispersive x-ray analysis and it was found to be 110 nm/ms.

We fabricated six SP microcavity structures of 200 nm depth and of variable widths from 800 nm to 1300 nm. The length of these structures was 15 µm. In the middle of each structure, a 180 nm slit was milled entirely through the gold film. From past work, the 200 nm high walls of the microcavity were estimated to give 50% reflection, while having strong coupling to the input radiation through scattering [15

15. H. A. Jamid and S. J. Al-Bader, “Reflection and transmission of surface plasmon mode at a step discontinuity,” IEEE Photon. Technol. Lett. 9, 220–222 (1997). [CrossRef]

].

Fig. 1. Scanning electron microscope image of w=1300 nm wide SP microcavity (200 nm depth) with central slit (180 nm width, 100 nm depth) and a schematic representation.

2.2 Optical transmission setup

The transmission spectra were recorded using a fiber-optic coupled spectrometer. The source was focused with normal incidence onto the SP microcavity structure with a slit. An illumination spot size of 30 µm was obtained using a combination of an iris and a 20× microscope objective. A polarizer was used to control the polarization of the incident light. The zeroth order transmission was collected with a 100 µm diameter core fiber placed 1.5 mm from the sample. Positioning of the fiber core and gold slide were achieved using XYZ translation stages.

2.3 FDTD calculations

FDTD was used to calculate electromagnetic transmission characteristics of the SP microcavity structure with a slit [17

17. Lumerical Solutions, Inc.,. http://www.lumerical.com.

]. The dispersion of the gold was captured using a Drude model. A small mesh-size of 2 nm was chosen to accurately capture SP effects, as was verified by finite-difference mode calculations and repeating the calculations with varying grid sizes (both smaller and larger). Perfectly matched layer boundary conditions were used on all sides of the calculation domain. The Courant stability factor was 0.99. To reproduce the conditions of the experiment, a broadband plane wave source (500 nm to 900 nm) was normally incident on the top surface of the SP microcavity structure, with electric field polarization in the x-direction. Near-field and transmission monitors were used to visualize standing waves within the microcavity and to quantify the transmission spectrum.

3. Results and discussion

3.1 Measured transmission spectra

Figure 2 shows the measured transmission spectra from different width SP microcavities, with incident polarization in the x-direction, normalized to the white-light source spectrum. There was no additional normalization to account for the width of the microcavity; however, the lengths of all the structures were the same. All of the structures were measured under the same conditions and the results were repeatable. The transmission for a single slit in a 100 nm gold film without a microcavity is also shown for direct quantitative comparison. (For the orthogonal polarization, no transmission was detectable, which is expected because of the reduced TE transmission through a subwavelength slit.) Resonant transmission peaks were observed with wavelength that increases as cavity width increases. For example, for a cavity width of 1300 nm, the transmission peak was at 750 nm wavelength (shown with the blue curve in Fig. 2). This resonant transmission peak was approximately 170 nm wide. There appears to be some additional structurally-dependent transmission features for shorter wavelengths (below 600 nm); however, these effects were obscured by the transmission of gold close to the plasma frequency. The measured transmission is reduced at longer wavelengths due to greater diffraction from the slit. This is an experimental artifact that arises because the 100 µm core fiber collects the transmitted light 1.5 mm from the slit. In essence, this is a zeroth-order transmission measurement.

Fig. 2. Measured transmission spectra for different surface plasmon microcavity widths.

3.2 Calculated transmission spectra

The calculated resonant transmission peak widths were smaller than in the experiments, which may be attributed to additional losses from surface roughness that is present in real fabrication. We have repeated our calculations without the slit and we still observe strong SPPs resonances inside the cavity; for example, the 1300 nm wide slit showed 72% as large a transverse magnetic field without the slit as compared to with the slit. This implies that the side walls play an important part in coupling to the input radiation, as well as the coupling as the central slit.

Fig. 3. FDTD calculated transmission spectra, normalized to power incident on slit, for different SP microcavity widths.

3.3 Discussion

From the experimental and calculation results, the SP microcavity shows a resonant enhancement of the optical transmission through a slit. The experiment showed a maximum transmission enhancement of 2× with respect to the single slit and the calculations showed a maximum enhancement of 2.6×, both for the 1100 nm array. The discrepancy can be mostly attributed to fabrication tolerances (see Fig. 1). There is good quantitative agreement in the wavelength of peak transmission between experiment and calculations. The resonant enhancement is expected from coupling of the slit to standing-wave resonances of the SP microcavity, which is formed by the 200 nm tall side walls.

The SP microcavity is similar to the plane-wave microcavity, except that plane-waves are replaced with SPPs. This should shift the resonances to longer wavelengths; however, the transmission peak resonances were actually observed at shorter wavelengths. To explore this further, we consider the field distribution within the cavity for different wavelengths.

Figure 4 shows the near-field distribution of the transverse magnetic field squared magnitude for the 1300 nm cavity. It should be noted that similar features have been observed in a complimentary plasmonic cavity structure [19

19. T. Søndergaard and S. Bozhevolnyi, “Slow-plasmon resonant nanostructures: Scattering and field enhancements,” Phys. Rev. B 75, 073402, (2007). [CrossRef]

]. Figure 4(a) shows the near-field for 640 nm – a wavelength that is shorter than the transmission resonance peak. It is clear from this figure that the intensity maxima are away from the slit (on each side), which reduces the coupling to the slit and the overall transmission. Figure 2(b) is at the transmission resonance peak wavelength of 730 nm. It is clear from this figure that the slit introduces a strong negative phase-shift and reflection to the SPPs mode [20

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

], which produces 3 peaks near the slit. There is also a strong intensity variation seen within the slit, which corresponds to resonances within the slit from the reflection at each end. These features are associated with the slit, and they perturb the cavity to blue-shift the resonant wavelength away from the expected values of a regular microcavity. Figure 4(c) shows the near-field distribution at 840 nm, where the SPPs is closely matched to the second order resonance of the 1300 nm wide cavity. While this does not give the largest transmission, since the coupling to the slit is not optimized, the standing wave within the cavity is seen clearly.

There may be additional resonance effects from changing the height of the cavity side-walls coming from modes in the vertical z-direction in addition to resonant modes we observe in the horizontal x-direction [16

16. P. Ginzburg and M. Orenstein, “Plasmonic transmission lines: from micro to nano scale with λ/4 impedance matching,” Opt. Express 15, 6762–6767, (2007). [CrossRef] [PubMed]

]. This influences only slightly the resonance wavelength for the short and wide cavities considered here – the resonances are mainly from the transverse SPPs propagation. For example, we varied the depth of the side-walls by 100 nm for the 1300 nm cavity in the FDTD calculations and found that the peak shift was only 20 nm.

Fig. 4. Transverse magnetic field (perpendicular to imaging plane) profile of 1300 nm structure for three wavelengths: (a) 640 nm, (b) 730 nm and (c) 840 nm. Scale bar is the same for all three images.

The reflection of a 200 nm step for a gold surface was calculated using FDTD. For 750 nm wavelength, the reflection was 0.76 and the phase of reflection was 171° (close to 180° expected for a perfect electric conductor, which contributes a 1.7% shift to the resonant wavelength). For the 1300 nm cavity, ignoring the influence of the slit and the SPPs loss, this gives an optimal quality factor (Q) of 6.6. Considering this, the FWHM of the transmission resonances should be approximately 110 nm. In the FDTD calculations for the 1300 nm cavity, the transmission peak FWHM (subtracting the slit-only transmission) was 150 nm, which is larger due to material loss and scattering loss from the slit. In the experiment, the FWHM of the 1300 nm cavity peak transmission (subtracting the slit-only transmission) was 15% larger still, likely due to roughness from fabrication. The transmission resonance has an asymmetric shape, which is characteristic of Fano resonances found in similar plasmonic systems [21

21. C. Genet, M.P. van Exter, and J.P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Comm. 225, 331–336, (2003). [CrossRef]

]. The present structure was not optimized for achieving a large quality factor because of the additional losses necessary from the slit to measure the transmission. Without the slit, the quality factor (from calculations) increases to 14.3; however, there is an intrinsic limitation from metal losses that limits plasmonic microcavities. The SPPs propagation length divided by the SPPs wavelength is an approximate upper bound for the quality factor imposed by plasmonic damping.

4. Conclusions

The optical transmission through a slit was resonantly enhanced, by a factor of 2, by forming a SP microcavity around the slit. Wavelength tuning of the transmission maxima was achieved by varying the width of the microcavity. FDTD calculations were also performed that agreed quantitatively with the experiments. The resonance transmission wavelength was dependent on the cavity width, and influenced by the presence of the slit. The compact SP microcavity geometry proposed here is easily fabricated and it may be used to provide wavelength-sensitive transmission. By extending the SP microcavity approach presented here, it is easy to envision future devices for enhancing local electromagnetic fields and for providing refractive index sensitive peak shifts. Those optimized SP microcavity structures can be applied to surface-enhanced Raman scattering, nonlinear optics and surface plasmon resonance sensors [22–27

22. K. Kneipp, H. Kneipp, I. Itzkan, R. R. Dasari, and M. S. Feld, “Ultrasensitive Chemical Analysis by Raman Spectroscopy,” Chem. Rev. 99, 2957–2976 (1999). [CrossRef]

].

Acknowledgments

The authors thank Prof. Karen L. Kavanagh for use of Simon Fraser University’s Nano-Imaging Facility, and Nicki Humphry-Baker for SEM images. The authors acknowledge funding from CIPI, NSERC, CFI and BCKDF.

References and links

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, 667–669 (1998). [CrossRef]

2.

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

3.

Y. T. Chang, T. H. Chuang, M. W. Tsai, M. J. Lai, and S. C. Lee, “Observation of Fabry-Perot-type surface plasmon on Ag film with perforated short-range 3×3 hole array arranged in long-range periodic structure,” Appl. Phys. Lett. 90, 253106 (2007). [CrossRef]

4.

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, 820–822 (2002). [CrossRef] [PubMed]

5.

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, 1972–1974 (2001). [CrossRef]

6.

L. Martin-Moreno, F. J. Garcia-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, 167401 (2003). [CrossRef] [PubMed]

7.

M. U. Gonzalez, A. L. Stepanov, J. C. Weeber, A. Hohenau, A. Dereux, R. Quidant, and J. R. Krenn, “Analysis of the angular acceptance of surface plasmon Bragg mirrors,” Opt. Lett. 32, 2704–2706 (2007). [CrossRef] [PubMed]

8.

M. U. Gonzalez, J. C. Weeber, A. L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, “Design, near-field characterization, and modeling of 45 circle surface-plasmon Bragg mirrors,” Phys. Rev. B 73, 155416 (2006). [CrossRef]

9.

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. 81, 1762–1764 (2002). [CrossRef]

10.

P. Marthandam and R. Gordon, “Plasmonic Bragg reflectors for enhanced extraordinary optical transmission through nano-hole arrays in a gold film,” Opt. Express 15, 12995–13002 (2007). [CrossRef] [PubMed]

11.

I. M. Lee, J. Jung, J. Park, H. Kim, and B. Lee, “Dispersion characteristics of channel plasmon polariton waveguides with step-trench-type grooves,” Opt. Express 15, 16596–16603 (2007). [CrossRef] [PubMed]

12.

E. Feigenbaum and M. Orenstein, “Modeling of complementary (void) plasmon waveguiding,” J. Lightwave Technol. 25, 2547–2562 (2007). [CrossRef]

13.

Y. Satuby and M. Orenstein, “Surface-Plasmon-Polariton modes in deep metallic trenches- measurement and analysis,” Opt. Express 15, 4247–4252 (2007). [CrossRef] [PubMed]

14.

Y. Q. Fu, W. Zhou, L. E. N. Lim, C. Du, H. Shi, C. Wang, and X. Luo, “Influence of V-shaped plasmonic nanostructures on beam propagation,” Appl Phys B-Lasers 86, 461–466 (2007). [CrossRef]

15.

H. A. Jamid and S. J. Al-Bader, “Reflection and transmission of surface plasmon mode at a step discontinuity,” IEEE Photon. Technol. Lett. 9, 220–222 (1997). [CrossRef]

16.

P. Ginzburg and M. Orenstein, “Plasmonic transmission lines: from micro to nano scale with λ/4 impedance matching,” Opt. Express 15, 6762–6767, (2007). [CrossRef] [PubMed]

17.

Lumerical Solutions, Inc.,. http://www.lumerical.com.

18.

P. B. Johnson and R. W. Christy, “Optical-Constants of Noble-Metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]

19.

T. Søndergaard and S. Bozhevolnyi, “Slow-plasmon resonant nanostructures: Scattering and field enhancements,” Phys. Rev. B 75, 073402, (2007). [CrossRef]

20.

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

21.

C. Genet, M.P. van Exter, and J.P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Comm. 225, 331–336, (2003). [CrossRef]

22.

K. Kneipp, H. Kneipp, I. Itzkan, R. R. Dasari, and M. S. Feld, “Ultrasensitive Chemical Analysis by Raman Spectroscopy,” Chem. Rev. 99, 2957–2976 (1999). [CrossRef]

23.

A. Lesuffleur, L. K. S. Kumar, A. G. Brolo, K. L. Kavanagh, and R. Gordon, “Apex-enhanced Raman spectroscopy using double-hole arrays in a gold film,” J Phys Chem C 111, 2347–2350 (2007). [CrossRef]

24.

F. Mahdavi, Y. Liu, and S. Blair, “Modeling fluorescence enhancement from metallic nanocavities,” Plasmonics 2, 129–141 (2007). [CrossRef]

25.

A. G. Brolo, S. C. Kwok, M. G. Moffitt, R. Gordon, J. Riordon, and K. L. Kavanagh, “Enhanced Fluorescence from Arrays of Nanoholes in a Gold Film,” J. Am. Chem. Soc. 127, 14936–14941, (2005). [CrossRef] [PubMed]

26.

G. W. Lu, B. L. Cheng, H. Shen, Y. L. Zhou, Z. H. Chen, G. Z. Yang, O. Tillement, S. Roux, and P. Perriat, “Fabry-Perot type sensor with surface plasmon resonance,” Appl. Phys. Lett. 89, 223904 (2006). [CrossRef]

27.

A. G. Brolo, R. Gordon, B. Leathem, and K. L. Kavanagh, “films Surface plasmon sensor based on the enhanced light transmission through arrays of nanoholes in gold”, Langmuir 20, 4813–4815, (2004). [CrossRef]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(240.6690) Optics at surfaces : Surface waves
(250.5300) Optoelectronics : Photonic integrated circuits

ToC Category:
Optics at Surfaces

History
Original Manuscript: March 18, 2008
Revised Manuscript: April 24, 2008
Manuscript Accepted: June 13, 2008
Published: June 17, 2008

Citation
Qiao Min and Reuven Gordon, "Surface plasmon microcavity for resonant transmission through a slit in a gold film," Opt. Express 16, 9708-9713 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-13-9708


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References

  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, 667-669 (1998). [CrossRef]
  2. C. Genet, and T. W. Ebbesen, "Light in tiny holes," Nature 445, 39-46 (2007). [CrossRef] [PubMed]
  3. Y. T. Chang, T. H. Chuang, M. W. Tsai, M. J. Lai, and S. C. Lee, "Observation of Fabry-Perot-type surface plasmon on Ag film with perforated short-range 3x3 hole array arranged in long-range periodic structure," Appl. Phys. Lett. 90, 253106 (2007). [CrossRef]
  4. 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, 820-822 (2002). [CrossRef] [PubMed]
  5. 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, 1972-1974 (2001). [CrossRef]
  6. L. Martin-Moreno, F. J. Garcia-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, 167401 (2003). [CrossRef] [PubMed]
  7. M. U. Gonzalez, A. L. Stepanov, J. C. Weeber, A. Hohenau, A. Dereux, R. Quidant, and J. R. Krenn, "Analysis of the angular acceptance of surface plasmon Bragg mirrors," Opt. Lett. 32, 2704-2706 (2007). [CrossRef] [PubMed]
  8. M. U. Gonzalez, J. C. Weeber, A. L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, "Design, near-field characterization, and modeling of 45 circle surface-plasmon Bragg mirrors," Phys. Rev. B 73, 155416 (2006). [CrossRef]
  9. H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, "Two-dimensional optics with surface plasmon polaritons," Appl. Phys. Lett. 81, 1762-1764 (2002). [CrossRef]
  10. P. Marthandam and R. Gordon, "Plasmonic Bragg reflectors for enhanced extraordinary optical transmission through nano-hole arrays in a gold film," Opt. Express 15, 12995-13002 (2007). [CrossRef] [PubMed]
  11. I. M. Lee, J. Jung, J. Park, H. Kim, and B. Lee, "Dispersion characteristics of channel plasmon polariton waveguides with step-trench-type grooves," Opt. Express 15, 16596-16603 (2007). [CrossRef] [PubMed]
  12. E. Feigenbaum and M. Orenstein, "Modeling of complementary (void) plasmon waveguiding," J. Lightwave Technol. 25, 2547-2562 (2007). [CrossRef]
  13. Y. Satuby and M. Orenstein, "Surface-Plasmon-Polariton modes in deep metallic trenches- measurement and analysis," Opt. Express 15, 4247-4252 (2007). [CrossRef] [PubMed]
  14. Y. Q. Fu, W. Zhou, L. E. N. Lim, C. Du, H. Shi, C. Wang, and X. Luo, "Influence of V-shaped plasmonic nanostructures on beam propagation," Appl Phys B-Lasers 86, 461-466 (2007). [CrossRef]
  15. H. A. Jamid and S. J. Al-Bader, "Reflection and transmission of surface plasmon mode at a step discontinuity," IEEE Photon. Technol. Lett. 9, 220-222 (1997). [CrossRef]
  16. P. Ginzburg, and M. Orenstein, "Plasmonic transmission lines: from micro to nano scale with ?/4 impedance matching," Opt. Express 15, 6762-6767, (2007). [CrossRef] [PubMed]
  17. Lumerical Solutions, Inc., http://www.lumerical.com.
  18. P. B. Johnson and R. W. Christy, "Optical-Constants of Noble-Metals," Phys. Rev. B 6, 4370-4379 (1972). [CrossRef]
  19. T. Søndergaard and S. Bozhevolnyi, "Slow-plasmon resonant nanostructures: Scattering and ??eld enhancements," Phys. Rev. B 75, 073402 (2007). [CrossRef]
  20. R. Gordon, "Light in a subwavelength slit in a metal: Propagation and reflection," Phys. Rev. B 73, 153405 (2006). [CrossRef]
  21. C. Genet, M. P. van Exter, and J. P. Woerdman, "Fano-type interpretation of red shifts and red tails in hole array transmission spectra," Opt. Commun. 225, 331-336, (2003). [CrossRef]
  22. K. Kneipp, H. Kneipp, I. Itzkan, R. R. Dasari, and M. S. Feld, "Ultrasensitive Chemical Analysis by Raman Spectroscopy, " Chem. Rev. 99, 2957 - 2976 (1999). [CrossRef]
  23. A. Lesuffleur, L. K. S. Kumar, A. G. Brolo, K. L. Kavanagh, and R. Gordon, "Apex-enhanced Raman spectroscopy using double-hole arrays in a gold film," J Phys Chem C 111, 2347-2350 (2007). [CrossRef]
  24. F. Mahdavi, Y. Liu, and S. Blair, "Modeling fluorescence enhancement from metallic nanocavities," Plasmonics 2, 129-141 (2007). [CrossRef]
  25. A. G. Brolo, S. C. Kwok, M. G. Moffitt, R. Gordon, J. Riordon, and K. L. Kavanagh, "Enhanced Fluorescence from Arrays of Nanoholes in a Gold Film," J. Am. Chem. Soc. 127, 14936-14941 (2005). [CrossRef] [PubMed]
  26. G. W. Lu, B. L. Cheng, H. Shen, Y. L. Zhou, Z. H. Chen, G. Z. Yang, O. Tillement, S. Roux, and P. Perriat, "Fabry-Perot type sensor with surface plasmon resonance," Appl. Phys. Lett. 89, 223904 (2006). [CrossRef]
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