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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 5 — Mar. 2, 2009
  • pp: 3490–3499
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Tailoring radiative and non-radiative losses of thin nanostructured plasmonic waveguides

Cyrille Billaudeau, Stéphane Collin, Fabrice Pardo, Nathalie Bardou, and Jean-Luc Pelouard  »View Author Affiliations


Optics Express, Vol. 17, Issue 5, pp. 3490-3499 (2009)
http://dx.doi.org/10.1364/OE.17.003490


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Abstract

Thin nanostructured metal films allow to control radiative and non-radiative losses of surface plasmon polariton modes without changing their group velocities. This effect is studied in plasmonic waveguides made of thin gold films drilled with very narrow slits and deposited on a GaAs substrate. The analysis is supported by high-resolution angle-resolved transmission measurements and rigorous electromagnetic calculations. We show that the excitation of air/gold and gold/GaAs surface waves leads to Fano-type resonances with specific light localization into the slits. As a result, gold/GaAs surface waves induce a modulation of radiative and non-radiative losses of air/gold surface waves. The minimum and maximum of the Fano-type resonance introduce two propagation regimes. In the radiative propagation regime, the losses due to the absorption are negligible, whereas an efficient inhibition of free-space coupling is demonstrated in low-loss propagation regime.

© 2009 Optical Society of America

1. Introduction

A single metal/dielectric interface between two semi-infinite media is probably the simplest optical waveguide. Light propagates along the interface in the form of surface waves called surface plasmon polaritons (SPP), as a result of the interaction between photons and the free electrons of the metal [1

1. H. Raether, ed, Surfaceplasmons (Springer, Berlin, 1988).

]. The huge development of plasmonic (or SPP) waveguides during the last decade originates in their unique property to confine light at a single interface [2

2. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature (London) 424, 824–830 (2003). [CrossRef]

]. It has been the key for the realization of efficient bio-sensing devices [3

3. R. L. Rich and D. G. Myszka, “Advances in surface plasmon resonance biosensor analysis,” Curr. Opin. Biotech. 11, 54–61 (2000). [CrossRef] [PubMed]

, 4

4. R. Slavik and J. Homola, “Ultrahigh resolution long range surface plasmon-based sensor,” Sen. Act. B: Chem 123, 10–12 (2007). [CrossRef]

] and quantum cascade lasers in the far infrared and THz ranges [5

5. C. Sirtori, C. Gmachl, F. Capasso, J. Faist, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long-wavelength (A ≃ 8 - 11.5 μm) semiconductor lasers with waveguides based on surface plasmons,” Opt. Lett. 23, 1366–1368 (1998). [CrossRef]

, 6

6. L. Mahler, A. Tredicucci, R. Kohler, F. Beltram, H. E. Beere, E. H. Linfield, and D. A. Ritchie, “High-performance operation of single-mode terahertz quantum cascade lasers with metallic gratings,” Appl. Phys. Lett. 87, 181101 (2005). [CrossRef]

]. In practice, simple plasmonic waveguides are made of thin metal stripes of width in the micrometer range [7

7. B. Lamprecht, J. R. Krenn, G. Schider, H. Ditlbacher, M. Salerno, N. Felidj, A. Leitner, F. R. Aussenegg, and J. C. Weeber, “Surface plasmon propagation in microscale metal stripes,” Appl. Phys. Lett. 79, 51–53 (2001). [CrossRef]

, 8

8. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of asymmetric structures,” Phys. Rev. B 63, 125417 (2001). [CrossRef]

, 9

9. A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljacic, “Surface-Plasmon-Assisted Guiding of Broadband Slow and Subwavelength Light in Air,” Phys. Rev. Lett. 95, 063901 (2005). [CrossRef] [PubMed]

, 10

10. R. Zia, M. D. Selker, and M. L. Brongersma, “Leaky and bound modes of surface plasmon waveguides,” Phys. Rev. B 71, 165431 (2005). [CrossRef]

, 11

11. J.-C. Weeber, Y. Lacroute, and A. Dereux, “Optical near-field distributions of surface plasmon waveguide modes,” Phys. Rev. B 68, 115401 (2003). [CrossRef]

]. They allow light confinement at the sub-wavelength scale in direction perpendicular to the metal surface and at the wavelength scale in the transverse direction. Many recent researches were devoted to the achievement of two-dimensional light confinement perpendicular to the propagation direction. A wide variety of plasmonic waveguides have been proposed: metal nanowires [12

12. H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver Nanowires as Surface Plasmon Resonators,” Phys. Rev. Lett. 95, 257403 (2005). [CrossRef] [PubMed]

], metal nanoparticles chains [13

13. J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leit-ner, F. R. Aussenegg, and C. Girard, “Squeezing the Optical Near-Field Zone by Plasmon Coupling of Metallic Nanoparticles,” Phys. Rev. Lett. 82, 2590–2593 (1999). [CrossRef]

, 14

14. S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nature Materials 2, 229–232 (2003). [CrossRef] [PubMed]

], plasmonic bandgap structures [15

15. S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, “Waveguiding in Surface Plasmon Polariton Band Gap Structures,” Phys. Rev. Lett. 86, 3008–3011 (2001). [CrossRef] [PubMed]

], subwavelength metal grooves [16

16. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel Plasmon-Polariton Guiding by Sub-wavelength Metal Grooves,” Phys. Rev. Lett. 95, 046802 (2005). [CrossRef] [PubMed]

], and nanoscale gaps in metal structures [17

17. H. T. Miyazaki and Y. Kurokawa, “Squeezing Visible Light Waves into a 3-nm-Thick and 55-nm-Long Plasmon Cavity,” Phys. Rev. Lett. 96, 097401 (2006). [CrossRef] [PubMed]

]. Based on these concepts, subwave-length passive and active optical components have also been proposed [18

18. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature (London) 440, 508–511 (2006). [CrossRef]

, 19

19. T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. 85, 5833–5835 (2004). [CrossRef]

, 20

20. A. V. Krasavin, K. F. MacDonald, N. I. Zheludev, and A. V. Zayats, “High-contrast modulation of light with light by control of surface plasmon polariton wave coupling,” Appl. Phys. Lett. 85, 3369–3371 (2004). [CrossRef]

]. However, the integration of plasmonic waveguides in photonic circuits and devices suffers from two major limitations [21

21. E. Ozbay, “Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions,” Science 311, 189–193 (2006). [CrossRef] [PubMed]

]: the metal absorption (non-radiative losses), and the control of the free-space (radiative) coupling of surface plasmon polaritons.

Fig. 1. (a) Schematic view of the nanostructured metallic waveguide made of a gold grating with subwavelength slits (period d, slit width a, thickness t) deposited on a GaAs substrate. Surface plasmon polaritons (SPP) propagating in x-direction on air/metal and metal/substrate interfaces are schematically represented in red. (b) Scanning electron microscope image of the sample. (c) Dispersion curves of SPP propagating along flat semi-infinite air/metal (dark) and GaAs/metal (grey) interfaces. (d) Schematic diagram of SPP dispersion curves for air/metal and metal/substrate interfaces with slightly perturbating periodical patterns.

2. Dispersion diagram of a thin 1D nanostructured plasmonic waveguide

2.1. Experimental and numerical methods

Thin gold metallic gratings have been fabricated on GaAs substrates, with nanoscale slit width a = 160 nm, period d = 2.9 μm, and metal thickness t = 40 nm (Figs. 1(a) and 1(b)). They have been prepared by electron-beam lithography using a double lift-off technique described in reference [26

26. C. Billaudeau, S. Collin, C. Sauvan, N. Bardou, F. Pardo, and J.-L. Pelouard, “Angle-resolved transmission measurements through anisotropic 2D plasmonic crystals,” Opt. Lett. 33, 165–167 (2008). [CrossRef] [PubMed]

]. The area of typical grating is 2 × 2 mm2. A scanning electron microscope image of the grating is shown in Fig. 1(b).

Angle-resolved transmission measurements have been optimized for high angle resolution [26

26. C. Billaudeau, S. Collin, C. Sauvan, N. Bardou, F. Pardo, and J.-L. Pelouard, “Angle-resolved transmission measurements through anisotropic 2D plasmonic crystals,” Opt. Lett. 33, 165–167 (2008). [CrossRef] [PubMed]

]. The light was linearly polarized and focused on the sample using an elliptical mirror. The incident spot diameter was 1.7 mm, and the angular resolution was set to Δθ = ±0.3°. Zero-order transmission measurements have been carried out from θ = 0° to θ = 45° in 0.1° increments, by means of a Fourier transform spectrometer (Bruker Equinox 55) and an InSb detector in the 1 μm - 5.4 μm wavelength range. In the following, we plot the absolute transmission intensity through the whole sample (metallic grating on GaAs substrate). The spectral resolution was set to 10 cm-1 in order to eliminate the Fabry-Perot resonances that occur in the 350 μm-thick GaAs substrate.

2.2. Evidence of air/gold and gold/GaAs plasmonic bands

Figure 2 shows the measured (a) and calculated (b) TM-polarized zero-order transmission intensity as a function of the wavenumber σ = 1/λ and the in-plane wavevector kx = k 0 sin θ, where k 0 = 2πσ. An excellent agreement is found between experimental and numerical results. Both transmission diagrams exhibit two series of bands with two different slopes. They clearly reveal the dispersion curves of SPP propagating on both the air/gold interface and the gold/GaAs interface.

The two series of dispersion curves can be described as follows. At the resonance, transmission is enhanced due to the coupling between SPP and diffracted waves. This phenomenon occurs when k (p) x ≈ ±kspp, where k (p) x = k 0 sin θ + p2π/d is the in-plane wavevector of the p-order diffracted wave (p = 0, ± 1,…), and kspp=k0/1εd+1εm is the wavevector of SPP propagating on a flat semi-infinite metal-dielectric interface (see the dispersion relation in Fig. 1(c)), εd and εm are the permittivities of the dielectric and metallic media, respectively. Since gold is a high conductivity metal, the slope of SPP bands is approximately proportional to 1/n where n is the optical index of the dielectric medium (n = 1 in air and n ≃ 3.4 in the GaAs substrate). The resulting plasmonic band structure is schematically represented in Fig. 1(d) for air/metal and substrate/metal periodically modulated surfaces. In the following, Ap (respect. Sp) plasmonic bands refer to SPP modes coupled to the p-order diffracted wave in the air (respect. in the substrate).

It is remarkable to observe numerous plasmonic bands in Fig 2(a). In particular, metal/substrate Sp plasmonic bands are distinguishable up to p = ±8 orders in experiments. The metal absorption increases with σ, and induces a broadening of SPP resonances, which is clearly seen in Fig. 2.

2.3. Plasmonic band gap

The coupling between two counter-propagating surface waves of the same interface gives rise to plasmonic band gaps at the center and at the boundaries of the first Brillouin zone (kx = 0 and kx = ±π/d) [24

24. S. C. Kitson, W. L. Barnes, and J. R. Sambles, “Full Photonic Band Gap for Surface Modes in the Visible,” Phys. Rev. Lett. 77, 2670–2673 (1996). [CrossRef] [PubMed]

]. As an example, the plasmonic band gap due to the coupling between A+1 and A-2 modes is shown in insets of Figs. 2(a) and 2(b). In this case, the tiny slits (a/d = 5.5%) induces an extremely narrow gap (δσ/σ ≃ 1.6% according to experimental data). In this example, the high-energy coupled-mode is radiative (bright dot), whereas the low-energy mode is non-radiative. It is worth noting that the plasmonic band gap between Sp bands does not appear in transmission spectra since the resonance widths are much greater than the expected band gaps.

2.4. Fano resonances

Plasmonic resonances shown in Fig. 2 are characterized as Fano resonances, featuring both a minimum and a maximum in transmission spectra (respectively dark and bright bands in transmission diagrams) [32

32. D. Maystre, in Electromagnetic Surface Modes edited by A. D. Boardman (Wiley, New-York, 1982), chap. 17.

]. Theoretical investigations of transmission metallic gratings have shown that surface resonances can be associated to poles and zeros of an isolated interface [33

33. P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404 (2003). [CrossRef]

]. Here both interfaces are uncoupled in the most part of the dispersion diagram since the upper and lower interfaces of the grating are different in nature. Then, in the spectral proximity of surface resonances, the transmission intensity through the whole structure can be approximated by:

Fig. 2. Transmission intensity measurements (left (a)) and calculations (right (b)) as a function of the wavenumber σ = 1/λ and the in-plane wavevector kx, in TM polarization through a gold grating on a GaAs substrate (d = 2.9 μm, a = 160 nm, t = 40 nm). Insets: detailed view of the intersection between A+1 and A-2 dispersion curves at the boudaries of the first Brillouin zone. A detailed view of the white dashed-dotted frames are shown in Figs. 4(a) and 4(b).
T=βωω0ωωp2,
(1)

where ωp and ω 0 are complex-value frequencies of poles and zeros, respectively, and β is a normalization factor.

The maps of the magnetic field intensity illustrate the light-grating interactions around Fano resonances (see A and B in Fig. 3). In case (A) of transmission minimum, the magnetic field Hy (and the tangential electric field component Ex) is nearly zero around the slits as the result of destructive interference between the incident light and the SPP wave. It drastically reduces the electromagnetic coupling between the upper and lower side of the grating through the apertures. On the contrary, in case (B) of transmission maximum, the magnetic field intensity is increased into the slits due to constructive interference between the incident light and the SPP wave, enabling enhanced radiative coupling.

The interaction between Ap and Sp Fano resonances is studied in the following section. A striking feature of transmission diagrams is the absence of band gap phenomenon at the intersections between air/metal (A-2) and substrate/metal (Sp) plasmonic bands. Nevertheless we shall show that the coupling between both surface modes induces a modification of radiative and non-radiative losses and that these modulations originate from the peculiar field distribution at the Fano resonances.

Fig. 3. Left: calculated transmission spectrum around a Fano resonance of air/metal surface mode (incident angle θ = 16°). Right: map of the magnetic field intensity at the minimum transmission wavelength (A) and at the maximum transmission wavelength (B). Red regions show high intensity regions. Dark rectangles show the metallic grating.

3. Enhancement and inhibition of the radiative coupling of surface waves

In this section, we focus our study on the A-2 SPP mode schematically represented in red in Fig. 1(d), and we analyze the coupling between surface waves propagating on the two different interfaces.

3.1. Evidence of two (radiative/low-loss) propagation regimes

Detailled views of Figs. 2(a) and 2(b) are shown in Figs. 4(a) and 4(b). Transmission diagrams plotted in Figs. 4(a) and 4(b) exhibit intensity modulations along the bright band of the A-2 dispersion curve. Both maxima and minima are located at the intersections between the A-2 mode and the gold/GaAs (S+5, S-6, S+6) SPP modes. They can be explained as follows.

Light transmission enhancement is evidenced at the intersections between the A-2 bright band and one of the Sp bright bands (red arrows in Fig. 4). This is a signature of the enhancement of the radiative coupling of SPP modes to free-space plane waves. Both air/metal and substrate/metal SPP waves are involved in the resonance and coupled together. Light transmission inhibition occurs at the crossing of the A-2 bright band and Sp dark bands (blue arrows in Fig. 4). In this case, the air/metal SPP wave is nearly uncoupled to the substrate side of the grating. The decrease of transmission intensity reveals the diminution of the radiative losses of SPP resonances [36

36. F. Marquier, J. J. Greffet, S. Collin, F. Pardo, and J. L. Pelouard, “Resonant transmission through a metallic film due to coupled modes,” Opt. Express 13, 70–76 (2005). [CrossRef] [PubMed]

, 37

37. C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, “Femtosecond Light Transmission and Subradiant Damping in Plasmonic Crystals,” Phys. Rev. Lett. 94, 113901 (2005). [CrossRef] [PubMed]

].

We emphasize that the inhibition of the radiative coupling of air/metal surface modes is due to the zero of the Fano resonance of metal/substrate surface modes (dark bands). As explained above, the zero of Fano resonances is associated to a nearly zero electromagnetic field intensity in the apertures, see Fig. 3 (A). The narrow slits represent the diffracting feature of the structure, so that the stationary minimum of the field in the vicinity of the slits induces an inhibition of the field emitted by the grating.

Hence, light transmission modulation evidences two different regimes for the propagation of surface waves: radiative propagation regime and low loss propagation regime. They are schematically depicted in Fig. 4 (red and blue frames). It must be noticed that the interaction between Ap and Sp modes has a strong effect on the enhancement and inhibition of light transmission despite the absence of coupled mode and bandgap opening. Moreover, this coupling exists with surface waves propagating in the same or opposite directions, their different group velocities remaining unperturbated.

Fig. 4. Detailed view of transmission intensity measurements (left (a)) and calculations (right (b)) as a function of the wavenumber σ and the in-plane wavevector kx. The intensity modulation along the A-2 SPP band (diagonal) reveals two different propagation regimes: radiative modes induced by a coupling between air/metal and substrate/metal surface waves (red frames), and low-loss modes involving only air/metal surface waves (blue frames).

3.2. Propagation length

3.3. Radiative and non-radiative losses

To further analyze non-monotonous variations of the propagation length, we have distinguished radiative and non-radiative losses of SPP modes. Radiative losses are calculated by neglecting the metal absorption [30

30. S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. A (Special Issue on Electromagnetic Optics) 4, S154–S160 (2002).

] (the imaginary part of νm is set to 0). They take into account all the (transmitted and reflected) propagating diffracted waves. Figure 6 shows a comparison of the resulting radiative propagation length Λr (green) to the propagation length Λ of the real structure (red). It is found that both curves merge in the case of radiative propagation regime (minima of Λ): non-radiative losses due to metal absorption are negligible, and the radiative efficiency Λ/Λr is close to 1. On the other hand, the difference between the red and green curves for longer propagation lengths evidences the strong inhibition of radiative emission of SPP waves in case of low loss propagation regimes (Λ/Λr = 0.25 at σ = 0.544 μm-1).

3.4. Inhibition of free-space coupling

The inhibition of free-space coupling is further illustrated in 3Fig. 7. The propagation length (A) of the A-2 surface modes is compared to the propagation length of surface modes of (coutinuous) metal films without slit, with different thicknesses. We consider the leaky mode propagating on the air-side of the metal film. In the case of non-radiative propagation regimes (maxima of the red curve), it is found that the propagation losses are very close to the continuous film with the same thickness (t = 40 nm) despite numerous radiative channels due to diffracted waves propagating in the substrate and in the air. For instance, the propagation length of the A-2 mode reaches A = 165 μm at σ = 0.544 μm (λ = 1.84 μm) which corresponds to 86 % of the value of the same structure without slit.

Fig. 5. The inverse transmission intensities 1/T(σ) along the A-2 SPP bright band are extracted from Figs. 4(a) and 4(b). They are reported in (a) (measurements, black points) and (b) (calculations, red points) and compared to the theoretical propagation length ? (red solid lines).
Fig. 6. Calculated propagation length of SPP on nanostructured plasmonic waveguides with a lossy metal (red solid line) and a lossless metal (green solid line). Dark arrows show radiative (R) and non-radiative low-loss (NR) propagation regimes.
Fig. 7. Comparison between the propagation length of surface modes on nanostructured plasmonic waveguides (red line), non-structured (continuous) metal films with the same thickness (t = 40 nm, dark line) and with smaller thicknesses (t = 25 nm and t = 37 nm).

In case of continuous metal films, radiative losses of air/metal surface plasmons can also occur via evanescent coupling through the metal film into plane waves propagating in the substrate. Obviously, the thinner the metal layer, the greater the radiative losses. Figure 7 shows that the modulations of losses of the A-2 mode follow the losses of metal films with thicknesses in the range t = 25 – 37 nm.

4. Conclusion

In conclusion, we have shown that thin metallic gratings with very narrow slits deposited on a dielectric substrate support two different propagation regimes, leading to a modulation of the propagation length. This property originates in the coupling between Fano resonances of air/metal and substrate/metal surface modes. The radiative propagation regime shows negligible absorption losses, whereas low loss propagation regime allows propagation lengths above 150 μm in the 1.5 – 2 μm wavelength range. The theoretical analysis of radiative and non-radiative losses show that free-space coupling of SPP modes can be inhibited efficiently in case of non-radiative propagation regimes.

It has to be emphasized that thin plasmonic waveguides enable to control radiative and non radiative losses without modification of the group velocity of surface modes. This is very different from classical plasmonic crystals, in which radiative losses can be modified via coupled modes having low group velocities. These properties open a route toward the design of nanostructured plasmonic waveguides with finely tuned radiative losses. Propagation lengths above 100 μm makes feasible the integration of thin nanostructured plasmonic waveguides in photonic circuits [18

18. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature (London) 440, 508–511 (2006). [CrossRef]

, 19

19. T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. 85, 5833–5835 (2004). [CrossRef]

, 20

20. A. V. Krasavin, K. F. MacDonald, N. I. Zheludev, and A. V. Zayats, “High-contrast modulation of light with light by control of surface plasmon polariton wave coupling,” Appl. Phys. Lett. 85, 3369–3371 (2004). [CrossRef]

]. The ability to control the trade-off between propagation length and light emission is also of high importance in surface-emitting devices like quantum cascade lasers [5

5. C. Sirtori, C. Gmachl, F. Capasso, J. Faist, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long-wavelength (A ≃ 8 - 11.5 μm) semiconductor lasers with waveguides based on surface plasmons,” Opt. Lett. 23, 1366–1368 (1998). [CrossRef]

, 6

6. L. Mahler, A. Tredicucci, R. Kohler, F. Beltram, H. E. Beere, E. H. Linfield, and D. A. Ritchie, “High-performance operation of single-mode terahertz quantum cascade lasers with metallic gratings,” Appl. Phys. Lett. 87, 181101 (2005). [CrossRef]

].

References and links

1.

H. Raether, ed, Surfaceplasmons (Springer, Berlin, 1988).

2.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature (London) 424, 824–830 (2003). [CrossRef]

3.

R. L. Rich and D. G. Myszka, “Advances in surface plasmon resonance biosensor analysis,” Curr. Opin. Biotech. 11, 54–61 (2000). [CrossRef] [PubMed]

4.

R. Slavik and J. Homola, “Ultrahigh resolution long range surface plasmon-based sensor,” Sen. Act. B: Chem 123, 10–12 (2007). [CrossRef]

5.

C. Sirtori, C. Gmachl, F. Capasso, J. Faist, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long-wavelength (A ≃ 8 - 11.5 μm) semiconductor lasers with waveguides based on surface plasmons,” Opt. Lett. 23, 1366–1368 (1998). [CrossRef]

6.

L. Mahler, A. Tredicucci, R. Kohler, F. Beltram, H. E. Beere, E. H. Linfield, and D. A. Ritchie, “High-performance operation of single-mode terahertz quantum cascade lasers with metallic gratings,” Appl. Phys. Lett. 87, 181101 (2005). [CrossRef]

7.

B. Lamprecht, J. R. Krenn, G. Schider, H. Ditlbacher, M. Salerno, N. Felidj, A. Leitner, F. R. Aussenegg, and J. C. Weeber, “Surface plasmon propagation in microscale metal stripes,” Appl. Phys. Lett. 79, 51–53 (2001). [CrossRef]

8.

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of asymmetric structures,” Phys. Rev. B 63, 125417 (2001). [CrossRef]

9.

A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljacic, “Surface-Plasmon-Assisted Guiding of Broadband Slow and Subwavelength Light in Air,” Phys. Rev. Lett. 95, 063901 (2005). [CrossRef] [PubMed]

10.

R. Zia, M. D. Selker, and M. L. Brongersma, “Leaky and bound modes of surface plasmon waveguides,” Phys. Rev. B 71, 165431 (2005). [CrossRef]

11.

J.-C. Weeber, Y. Lacroute, and A. Dereux, “Optical near-field distributions of surface plasmon waveguide modes,” Phys. Rev. B 68, 115401 (2003). [CrossRef]

12.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver Nanowires as Surface Plasmon Resonators,” Phys. Rev. Lett. 95, 257403 (2005). [CrossRef] [PubMed]

13.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leit-ner, F. R. Aussenegg, and C. Girard, “Squeezing the Optical Near-Field Zone by Plasmon Coupling of Metallic Nanoparticles,” Phys. Rev. Lett. 82, 2590–2593 (1999). [CrossRef]

14.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nature Materials 2, 229–232 (2003). [CrossRef] [PubMed]

15.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, “Waveguiding in Surface Plasmon Polariton Band Gap Structures,” Phys. Rev. Lett. 86, 3008–3011 (2001). [CrossRef] [PubMed]

16.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel Plasmon-Polariton Guiding by Sub-wavelength Metal Grooves,” Phys. Rev. Lett. 95, 046802 (2005). [CrossRef] [PubMed]

17.

H. T. Miyazaki and Y. Kurokawa, “Squeezing Visible Light Waves into a 3-nm-Thick and 55-nm-Long Plasmon Cavity,” Phys. Rev. Lett. 96, 097401 (2006). [CrossRef] [PubMed]

18.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature (London) 440, 508–511 (2006). [CrossRef]

19.

T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. 85, 5833–5835 (2004). [CrossRef]

20.

A. V. Krasavin, K. F. MacDonald, N. I. Zheludev, and A. V. Zayats, “High-contrast modulation of light with light by control of surface plasmon polariton wave coupling,” Appl. Phys. Lett. 85, 3369–3371 (2004). [CrossRef]

21.

E. Ozbay, “Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions,” Science 311, 189–193 (2006). [CrossRef] [PubMed]

22.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking Surface Plasmons with Structured Surfaces,” Science 305, 847–848 (2004). [CrossRef] [PubMed]

23.

F. J. Garcia-Vidal, L. Martín-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A 7, S97–S101 (2005). [CrossRef]

24.

S. C. Kitson, W. L. Barnes, and J. R. Sambles, “Full Photonic Band Gap for Surface Modes in the Visible,” Phys. Rev. Lett. 77, 2670–2673 (1996). [CrossRef] [PubMed]

25.

C. Sauvan, C. Billaudeau, S. Collin, N. Bardou, F. Pardo, J.-L. Pelouard, and P. Lalanne, “Surface plasmon coupling on metallic film perforated by two-dimensional rectangular hole array,” Appl. Phys. Lett. 92, 011125 (2008). [CrossRef]

26.

C. Billaudeau, S. Collin, C. Sauvan, N. Bardou, F. Pardo, and J.-L. Pelouard, “Angle-resolved transmission measurements through anisotropic 2D plasmonic crystals,” Opt. Lett. 33, 165–167 (2008). [CrossRef] [PubMed]

27.

C. Billaudeau, S. Collin, F. Pardo, N. Bardou, and J.-L. Pelouard, “Toward tunable light propagation and emission in thin nanostructured plasmonic waveguides,” Appl. Phys. Lett. 92, 041111 (2008). [CrossRef]

28.

M. M. J. Treacy, “Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B 66, 195105 (2002). [CrossRef]

29.

K. G. Lee and Q-Han Park, “Coupling of Surface Plasmon Polaritons and Light in Metallic Nanoslits,” Phys. Rev. Lett. 95, 103902 (2005). [CrossRef] [PubMed]

30.

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. A (Special Issue on Electromagnetic Optics) 4, S154–S160 (2002).

31.

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, Orlando, 1985).

32.

D. Maystre, in Electromagnetic Surface Modes edited by A. D. Boardman (Wiley, New-York, 1982), chap. 17.

33.

P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404 (2003). [CrossRef]

34.

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

35.

M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67, 085415 (2003). [CrossRef]

36.

F. Marquier, J. J. Greffet, S. Collin, F. Pardo, and J. L. Pelouard, “Resonant transmission through a metallic film due to coupled modes,” Opt. Express 13, 70–76 (2005). [CrossRef] [PubMed]

37.

C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, “Femtosecond Light Transmission and Subradiant Damping in Plasmonic Crystals,” Phys. Rev. Lett. 94, 113901 (2005). [CrossRef] [PubMed]

OCIS Codes
(230.7370) Optical devices : Waveguides
(240.6680) Optics at surfaces : Surface plasmons
(260.3910) Physical optics : Metal optics
(160.4236) Materials : Nanomaterials
(050.5298) Diffraction and gratings : Photonic crystals

ToC Category:
Optics at Surfaces

History
Original Manuscript: October 15, 2008
Revised Manuscript: December 15, 2008
Manuscript Accepted: January 5, 2009
Published: February 23, 2009

Citation
Cyrille Billaudeau, Stéphane Collin, Fabrice Pardo, Nathalie Bardou, and Jean-Luc Pelouard, "Tailoring radiative and non-radiative losses of thin nanostructured plasmonic waveguides," Opt. Express 17, 3490-3499 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-5-3490


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References

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  21. E. Ozbay, "Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions," Science 311, 189-193 (2006). [CrossRef] [PubMed]
  22. J. B. Pendry, L. Martın-Moreno, and F. J. Garcia-Vidal, "Mimicking Surface Plasmons with Structured Surfaces," Science 305, 847-848 (2004). [CrossRef] [PubMed]
  23. F. J. Garcia-Vidal, L. Martın-Moreno, and J. B. Pendry, "Surfaces with holes in them: new plasmonic metamaterials," J. Opt. A 7, S97-S101 (2005). [CrossRef]
  24. S. C. Kitson,W. L. Barnes, and J. R. Sambles, "Full Photonic Band Gap for Surface Modes in the Visible," Phys. Rev. Lett. 77, 2670-2673 (1996). [CrossRef] [PubMed]
  25. C. Sauvan, C. Billaudeau, S. Collin, N. Bardou, F. Pardo, and J.-L. Pelouard, P. Lalanne, "Surface plasmon coupling on metallic film perforated by two-dimensional rectangular hole array," Appl. Phys. Lett. 92, 011125 (2008). [CrossRef]
  26. C. Billaudeau, S. Collin, C. Sauvan, N. Bardou, F. Pardo, and J.-L. Pelouard, "Angle-resolved transmission measurements through anisotropic 2D plasmonic crystals," Opt. Lett. 33, 165-167 (2008). [CrossRef] [PubMed]
  27. C. Billaudeau, S. Collin, F. Pardo, N. Bardou, and J.-L. Pelouard, "Toward tunable light propagation and emission in thin nanostructured plasmonic waveguides," Appl. Phys. Lett. 92, 041111 (2008). [CrossRef]
  28. M. M. J. Treacy, "Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings," Phys. Rev. B 66, 195105 (2002). [CrossRef]
  29. K. G. Lee and Q-Han Park, "Coupling of Surface Plasmon Polaritons and Light in Metallic Nanoslits," Phys. Rev. Lett. 95, 103902 (2005). [CrossRef] [PubMed]
  30. S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, "Horizontal and vertical surface resonances in transmission metallic gratings," J. Opt. A(Special Issue on Electromagnetic Optics) 4, S154-S160 (2002).
  31. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, Orlando, 1985).
  32. D. Maystre, in Electromagnetic Surface Modes edited by A. D. Boardman (Wiley, New-York, 1982), chap. 17.
  33. P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, "Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures," Phys. Rev. B 68, 125404 (2003). [CrossRef]
  34. C. Genet, M. P. van Exter, and J. P. F. Woerdman, "Fano-type interpretation of red shifts and red tails in hole array transmission spectra," Opt. Commun. 225, 331-336 (2003). [CrossRef]
  35. M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, "Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes," Phys. Rev. B 67, 085415 (2003). [CrossRef]
  36. F. Marquier, J. J. Greffet, S. Collin, F. Pardo, and J. L. Pelouard, "Resonant transmission through a metallic film due to coupled modes," Opt. Express 13, 70-76 (2005). [CrossRef] [PubMed]
  37. C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, "Femtosecond Light Transmission and Subradiant Damping in Plasmonic Crystals," Phys. Rev. Lett. 94, 113901 (2005). [CrossRef] [PubMed]

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