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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 15 — Jul. 23, 2007
  • pp: 9575–9583
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Effect of surface plasmon resonance on the optical activity of chiral metal nanogratings

K. Konishi, T. Sugimoto, B. Bai, Y. Svirko, and M. Kuwata-Gonokami  »View Author Affiliations


Optics Express, Vol. 15, Issue 15, pp. 9575-9583 (2007)
http://dx.doi.org/10.1364/OE.15.009575


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Abstract

We examine the mechanism responsible for the optical activity of a two-dimensional array of gold nanostructures with no mirror symmetry on a dielectric substrate. Measurements with different incident angles, polarizations and sample orientations allow us to reveal that observed polarization effect is enhanced by surface plasmon resonance. By performing numerical simulation with rigorous diffraction theory we also show that the grating chirality can be described in terms of the non-coplanarity of the electric field vectors at the front (air-metal) and back (substrate-metal) sides of the grating layer.

© 2007 Optical Society of America

1. Introduction

The optical response of a metal nanograting can be manipulated by changing the resonance frequencies of conduction electron oscillations at the metal-dielectric interface (surface plasmon resonances) [1

1. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Grating (Springer-Verlag, Berlin, 1988).

]. A grating structure enables resonant coupling between photons with small lateral momentum and surface plasmons that gives rise to strong optical effects such as enhanced light transmission through subwavelength holes [2

2. 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]

], suppression of light extinction [3

3. S. Linden, J. Kuhl, and H. Giessen, “Controlling the Interaction between Light and Gold Nanoparticles: Slelective Suppression of Excitation,” Phys. Rev. Lett. 86, 4688–4691 (2001). [CrossRef] [PubMed]

] and other linear and nonlinear optical phenomena [4

4. S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005). [CrossRef]

6

6. C. Anceau, S. Brasselet, J. Zyss, and P. Gadenne, “Local second-harmonic generation enhancement on gold nanostructures probed by two-photon microscopy,” Opt. Lett. 28, 713–715 (2003). [CrossRef] [PubMed]

].

Our results have been extended to double-layered structures with which a strong polarization effect was obtained. In Ref. 10, a pair of mutually twisted unconnected metal patterns acts as a chiral object and shows gyrotropy. Recently, enhanced gyrotropy in the visible and near-IR spectral range has been demonstrated with submicron-period two dimensional arrays of similar structures [11

11. E. Plum, V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, and Y. Chen, “Giant optical gyrotropy due to electromagnetic coupling,” Appl. Phys. Lett. 90, 223113 (2007). [CrossRef]

]. The untwisted metal double layer structures also shows strong polarization effects induced by local magnetic-dipole moments due to antisymmetric oscillation modes of the two layers [12

12. M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. 32, 856–858 (2007). [CrossRef] [PubMed]

]. In the experiments described in Ref. 10–12, single-layered structures have also been examined but only small signals have been detected and the mechanism of enhanced optical activity in the single-layered structure [9

9. M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, “Giant Optical Activity in Quasi-Two-Dimentional Planar Nanostructures,” Phys. Rev. Lett. 95, 227401 (2005). [CrossRef] [PubMed]

] has not been clarified. The simplicity of the single-layered structure is beneficial for applications and thus it is important to find proper conditions to obtain enhanced polarization effects.

In this letter, we visualize the role of surface plasmon resonance and chiral morphology on the observed polarization effect by performing transmission and polarization rotation measurements at oblique incidence. We also calculate the electric field distribution at the air-metal and metal-substrate interfaces induced by a linearly polarized plane wave at normal incidence. The calculation shows that, in a metal grating, the imbalance of the interface coupling effects results in a strong twisting of the electric field vector.

2. Samples and experimental setup

Nanogratings with a period of 500 nm were fabricated using electron beam lithography, lift-off and argon sputter etching processes. The sample consists of a fused silica substrate, a 3 nm thick chromium adhesion layer, a 95 nm thick gold layer, and a 23 nm thick chromium cover layer. All gratings were designed to possess a four-fold rotational symmetry about the substrate normal, however they still exhibit a weak anisotropy due to a slight astigmatism of the electron beam. Since all observed polarization phenomena are reciprocal [9

9. M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, “Giant Optical Activity in Quasi-Two-Dimentional Planar Nanostructures,” Phys. Rev. Lett. 95, 227401 (2005). [CrossRef] [PubMed]

], the magnetization of anti-ferromagnetic chromium layers does not affect the morphology-sensitive effects discussed in this paper.

Fig. 1. Experimental scheme. Light from tungsten lamps was horizontally polarized. SEM image shows grating composed of left-twisted gammadions. We rotated the sample around the X- and Y- axis for s- and p- polarized measurement, respectively [13].

Transmission and polarization measurements were performed in a wavelength range from 550 nm to 900 nm by slicing the tungsten lamp emission and applying a polarization modulation technique [14

14. K. Sato, “Measurement of Magneto-Optical Kerr Effect Using Piezo-Birefringent Modulator,” Jpn. J. Appl. Phys. 20, 2403–2409 (1981). [CrossRef]

]. We measured the grating composed of left-twisted gammadions as shown in Fig. 1. In order to distinguish between the different mechanisms of polarization change, we rotate the grating around the substrate normal. The angle of incidence was changed from -7° to +7° with 1° increment by rotating the sample about the X- and Y-axes.

3. Measurement of transmission spectra

Figure 2 shows transmission spectra of the chiral nanograting with left-twisted gammadions measured for s- and p-polarized incident light. We plotted the spectra in the (E,kx) plane, where E is the photon energy and kx=(2π/λ)sinψ is the in-plane component of the incident wavevector. The transmission spectrum for the s-polarized light shows a weak dependence on the incident angle (see Fig. 2(a)). In contrast, the spectrum for the p-polarized light shows a pronounced dependence on ψ. Specifically, one can observe from Fig. 2(b) the splitting of the transmission dip at a non-zero ψ. The magnitude of the splitting is increased with the increase of the incident angle. This is a clear signature of a lifting of the degeneracy of surface plasmons generated by the p-polarized light wave [15

15. W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface Plasmon Polaritons and Their Role in the Enhanced Transmission of Light through Periodic Arrays of Subwavelength Holes in a Metal Film,” Phys. Rev. Lett. 92, 107401 (2004). [CrossRef] [PubMed]

].

According to Ref. 16, when the incident light wave is s-polarized, the resonance wavelength λ s ψ for the lowest mode (i 2+j 2=1, where integers i and j represent the mode indices in X and Y directions) of the grating with a square lattice is given by

(λψsa)2=ε1(λψs)ε2ε1(λψs)+ε2sin2ψ,
(1)

where ε 1 and ε 2 are the permittivities of the metal and dielectric (air or substrate) respectively, a is the grating period and ψ is the incidence angle. Therefore at a small incidence angle, the shift of the resonance wavelength from that measured at ψ=0 is proportional to ψ 2. That is why we did not observe a strong dependence of the resonance wavelength on the incidence angle in our experiment. However, when the incident light is p-polarized, the resonance wavelength λ p ψ for the lowest modes (i 2+j 2=1) at incidence angle ψ is given by

λψpa=ε1(λψp)ε2ε1(λψp)+ε2±sinψ.
(2)
Fig. 2. Transmission spectra of s-polarized (a) and p-polarized (b) measurement.

This equation describes the splitting of the transmission dip at non-zero incident angle and shows that the shift of the resonance wavelengths for both branches from that measured at ψ=0 is proportional to ψ. Taking into account the frequency dispersion of the dielectric constant of gold [17

17. D. W. Lynch and W. R. Hunter, “Gold(Au)” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1984).

] and ε 2=2.13, we can derive that, in a nanograting with a period a=500 nm, the surface plasmon modes with i 2+j 2=1 and i 2+j 2=2 at the gold-silica interface are located in the vicinity of 780 and 600 nm, respectively. It is necessary to note that in Eqs. (1) and (2), we ignore the coupling between the plasmon modes localized at different interfaces [18

18. S. A. Darmanyan and A. V. Zayats, “Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: An analytical study,” Phys. Rev. B. 67, 035424 (2003). [CrossRef]

] and the inter-particle coupling that induces the anti-crossing at the folding points [19

19. W. L. Barns, T. W. Preist, S. C. Kiston, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B. 54, 6227–6244 (1996). [CrossRef]

].

4. Measurement of polarization rotation spectra

In order to distinguish polarization effects originating from the specific sense of twist and from the residual anisotropy, we measured the polarization rotation of the transmitted light beam as a function of the sample azimuth angle φ (see Fig.1). For example, the azimuth dependence of the polarization rotation at a wavelength of 720 nm is shown in Fig. 3. The polarization rotation Δ as a function of the azimuth angle can be described by the following equation:

Fig. 3. Sample azimuth angle dependence of the polarization rotation measured at 720nm for incident angle of 0° (a), +3° (b), and +7°(c). Blue curves are the fitting curves with formula of Eq. (3).
Δ=θ+Asin(2φ+B)+Csin(4φ+D)
(3)

where the fitting parameters θ, A, B, C, and D have a pronounced dependence on ψ. At normal incidence, C is zero and the offset θ in Eq. (3) gives the chirality-induced polarization rotation [9

9. M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, “Giant Optical Activity in Quasi-Two-Dimentional Planar Nanostructures,” Phys. Rev. Lett. 95, 227401 (2005). [CrossRef] [PubMed]

], so only sin 2φ dependence appears. At ψ≠0, C does not vanish and both the chirality and anisotropy of the grating contribute to all terms in the right-hand side of Eq. (3), so that a sin 4φ dependence also appears. The dependences are clearly observed in Fig. 3. As a result, the dependence of polarization rotation on the azimuthal angle φ resembles that in a chiral biaxial crystal when the light propagation direction does not coincide with the optical axes. However, since at small incidence angles θ are still dominated by the grating chirality, we focus on this term in the following analysis.

Fig. 4. Polarization rotation spectra of s-polarized(a) and p-polarized(b) measurement.

Spectra of the offset θ for incident angles varying from -7° to +7° are shown in Fig. 4. By comparing the polarization rotation spectra with the transmission spectra (Fig. 2), we can see an evident correspondence between their resonance and angular dependence features. For example, there is a splitting of resonance at 1.6 eV for the p-polarized case, and much smaller splitting of resonance (if any) at 2.0 eV for the s-polarized case. This is an evidence of a relation between the surface plasmon resonance and enhanced polarization rotation.

5. Discussion

Optical activity is a first-order spatial dispersion effect that originates from the non-locality of light-matter interaction [20

20. L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (New York, Pergamon Press1960).

]. Microscopic theory of optical activity was formulated by Born who showed the role of the retardation of a radiation field in chiral molecules [21

21. M. Born, Optik (Springer, Berlin, 1930).

]. In quasi-planar structures, the importance of the three dimensional configuration can be visualized using a classical model of paired displaced coupled oscillators in a non-coplanar geometry [22

22. Y. Svirko, N. Zheludev, and M. Osipov, “Layered chiral metallic microstructures with inductive coupling,” Appl. Phys. Lett. 78, 498–500 (2001). [CrossRef]

]. In order to employ theoretical approaches developed for molecular systems to describe qualitatively the optical activity in chiral metal nanogratings, one can notice that in a metal nanograting, the incident light excites collective oscillation of conduction electrons at both the metal-air and metal-dielectric interfaces (surface plasmons). Although these oscillations with different resonance frequencies are displaced in space by the thickness of the metal layer, they are coupled together due to mode overlapping inside or at the edges of metal nanostructures. If the symmetry of the plasmon modes allows electron oscillations at the front and back sides of the grating in non-parallel directions, this coupling can give rise to a polarization rotation of the transmitted wave. However, such non-parallel oscillations of electrons at grating surfaces do not necessarily result in optical activity due to the fact that in the wave zone, the transmitted wave is determined by secondary waves produced by electron oscillations in the unit cell of the grating. Since the phase and amplitude of these oscillations depend on the shape of the metal nanostructures and vary across the unit cell, the polarization effect in the transmitted wave may be canceled due to the symmetry of the oscillation pattern. This is in strong contrast with molecular optical activity, where the chiral object (molecule) is much smaller than the optical wavelength and all molecules equally contribute to the polarization rotation of the transmitted wave.

The above qualitative picture can be formulated in terms of the first-order spatial dispersion effects contributing to the light-matter interaction energy. When a light wave propagating in the z-direction interacts with a quasi two-dimensional metallic medium of thickness D located in the XY plane, the energy density associated with first-order spatial dispersion effects of the light-matter interaction can be presented in terms of the electric field strength at the front and back surfaces:

UNON(r)0D(E·[×E])dz=f(d,δ)(n·[Eair(r)×Esub(r)]),
(4)

where the angular brackets stand for average over the light wave period, n is a unit vector along the substrate normal, and Eair(r) and Esub(r) are the electric field strengths at the air-metal and substrate-metal interfaces at the point r={x,y} of the layer surface. f(d,δ) characterizes the chirality and overlapping of the modes localized at different interfaces and depends on the thickness D and penetration depth δ. The non-vanishing UNON(r)implies that ξ(r)≡(n·〈 [E air(rE sub(r)]〉)≠0, i.e. E air(r) and E sub(r) should not be parallel. At the front and back surfaces of the nanograting, the electric field distribution depends on the shape of nanostructures, while its magnitude is strongly enhanced at the frequency of the relevant surface plasmon resonance. The asymmetry of the air-metal-substrate structure results in non-parallel electric field vectors at the front and back surfaces setting UNON to be non-zero across the grating.

Fig. 5. (a). Schematic diagram of the electric filed distribution at normal incidence. Incident light is 752nm and Y-polarization. The geometrical parameters are given by a=295nm, b=207nm and c=88nm, and film thickness correspond to the value which is indicated in the Sec. 2. (b) (c) Numerically calculated ξ(r) for Y-polarized incident light at λ=752nm with lefttwisted pattern and cross pattern. Both (b) and (c) used same scale.
Fig. 6. (a). Transmission spectra. (b). Polarization rotation spectra. Both spectra are of left-twisted gammadion at normal incidence.

The transmission and polarization rotation spectra at normal incidence are shown in Figs. 6(a) and 6(b) in the spectral range form 700 nm to 900 nm. Although the sensitivity of the polarization effect to the imperfectness of the manufactured gammadion structure did result in some discrepancy between theory and experiment, we can see that results of the numerical simulation well reproduce the spectral profile of experimental results and that the enhancement of polarization rotation by surface plasmon resonance is evident.

Figure 5(a) shows the distribution of the electric field strength at both interfaces at 752 nm, which corresponds to the peak wavelength nearest to the surface plasmon resonance in the calculated polarization rotation spectrum (Fig. 6(b)). One can observe from Fig. 5(a) that the distribution of the electric field strength at the interface depends on the nanostructure shapes so that ξ(x,y) is non-zero at a number of points for both achiral and chiral nanostructures (see Figs. 5(b), 6(c)). However, the ξ(x,y) pattern over the unite cell has a two-fold rotation axis and two-fold rotation inversion axis in the chiral and achiral gratings, respectively.

In order to evaluate the non-coplanarity of the induced field at the front and back interfaces of the grating, we can introduce a “field twist parameter,”

Ξ=1AE2celldxdyξ(x,y),
(5)

where A is the unit cell area and E is the electric field of the incident wave. The symmetry of the ξ(x,y) pattern results in Ξ=0 for the achiral grating and Ξ≠0 for the chiral grating.

One can observe from Fig. 7 that the field twist parameter vanishes for the grating composed of achiral nanostructures and has the same magnitude but opposite sign for gratings composed of nanostructures with right and left senses of twist. Such a behavior coincides with the observed relationship between polarization rotation and the sense of twist of the structure.

In some recent reports on double-layered structures, no significant polarization effect in a single-layered structure sample has been observed [10

10. A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheldev, “Giant Gyrotropy due to Electromagnetic-Field Coupling in a Bilayered Chiral Structure,” Phys. Rev. Lett. 97, 117401 (2006). [CrossRef]

, 11

11. E. Plum, V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, and Y. Chen, “Giant optical gyrotropy due to electromagnetic coupling,” Appl. Phys. Lett. 90, 223113 (2007). [CrossRef]

, 12

12. M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. 32, 856–858 (2007). [CrossRef] [PubMed]

]. In Ref. 10, polarization effects have been examined in the microwave region with a single- and a double-layered chiral metal structure. At microwave frequencies, the anomalously high imaginary part of the dielectric index of the metal virtually removes any difference between metal-dielectric and metal-air interfaces giving rise to a symmetry plane that forbids the polarization rotation of the transmitted wave. Therefore the chirality manifests itself in the polarization of the transmitted microwave field only for double-layered structures with mutual twist. The authors of Ref. [12

12. M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. 32, 856–858 (2007). [CrossRef] [PubMed]

] compared the polarization effects of single- and double-layered structures in the optical wave length region and no significant effect was detected for single-layered structures. One can see from Fig. 6(b) that the chirality-induced polarization rotation in single-layered structures is about one order of magnitude smaller than that reported in Ref. [12

12. M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. 32, 856–858 (2007). [CrossRef] [PubMed]

], i.e. it is below the limit of sensitivity polarization measurement setup in Ref. [12

12. M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. 32, 856–858 (2007). [CrossRef] [PubMed]

]. The authors of Ref. [11

11. E. Plum, V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, and Y. Chen, “Giant optical gyrotropy due to electromagnetic coupling,” Appl. Phys. Lett. 90, 223113 (2007). [CrossRef]

] also examined polarization effects on single- and double-layered twisted structures and did not detect strong effects for single-layered structures. Our angle-dependent spectroscopic measurements clearly evidence the role of surface plasmon excitation on the enhancement of optical activity in single layer structures. Since the resonance conditions of surface plasmons depend on the detailed structure including thickness, shape and period of the structures, the magnitude of the polarization effects should severely depend on the samples. Thus the results of Refs. [10

10. A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheldev, “Giant Gyrotropy due to Electromagnetic-Field Coupling in a Bilayered Chiral Structure,” Phys. Rev. Lett. 97, 117401 (2006). [CrossRef]

12

12. M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. 32, 856–858 (2007). [CrossRef] [PubMed]

] are not contradicting our results.

Fig. 7. Spectra of field twist parameter (see text in Sec. 5). Numerical values of structures for calculation are provided in Fig. 5 and the text in the Sec. 5.

6. Conclusion

In conclusion, by performing systematic polarization rotation and transmission measurements with different incident angles and sample orientations, we visualized the relationship between local field enhancement due to surface plasmon resonance and the giant optical rotatory power of chiral metal nanogratings. A numerical simulation technique allows us to introduce a measure of optical activity to characterize the chiral morphology of the structure. The field distribution clearly shows that surface plasmons excited on the air-metal-substrate interfaces of nanostructures play an essential role on the enhancement of optical activity. Another interesting aspect of the chiral nanogratings is their ability to control the transverse mode of the beam. In particular, mode conversion [25

25. A. V. Krasavin, A. S. Schwanecke, N. I. Zheludev, M. Reichelt, T. Stroucken, S. W. Koch, and E. M. Wright, “Polarization conversion and “focusing” of light propagating through a small chiral hole in a metallic screen,” Appl. Phys. Lett. 86, 201105 (2005). [CrossRef]

] and mode sensitive interaction with planar chiral structures [26

26. T. Ohno and S. Miyanishi, “Study of surface plasmon chirality induced by Archimedes’ spiral grooves,” Opt. Express 14, 6285–6290 (2006). [CrossRef] [PubMed]

] have been discussed. Combination of the morphology effects and the transverse mode sensitive interactions may lead to further novel chirality-induced polarization phenomena.

Acknowledgments

We thank Konstantin Jefimovs for samples preparation and Jean Benoit Héroux for discussion. We acknowledge support by a Grant-in-Aid for Scientific Research (S) and Research Fellowships for Young Scientist (K.K) from the Japan Society for the Promotion of Science, Special Coordination Funds for Promoting Science and Technology (SCF) commissioned by the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan and the Academy of Finland (grant #115781).

References and links

1.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Grating (Springer-Verlag, Berlin, 1988).

2.

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]

3.

S. Linden, J. Kuhl, and H. Giessen, “Controlling the Interaction between Light and Gold Nanoparticles: Slelective Suppression of Excitation,” Phys. Rev. Lett. 86, 4688–4691 (2001). [CrossRef] [PubMed]

4.

S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005). [CrossRef]

5.

J. Elliott, I. I. Smolyaninov, N. I. Zheludev, and A. V. Zayats, “Polarization control of optical transmission of a periodic array of elliptical nanohole in a metal film,” Opt. Exp. 29, 1414–1416 (2004).

6.

C. Anceau, S. Brasselet, J. Zyss, and P. Gadenne, “Local second-harmonic generation enhancement on gold nanostructures probed by two-photon microscopy,” Opt. Lett. 28, 713–715 (2003). [CrossRef] [PubMed]

7.

A. Papakostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, and N. I. Zheludev, “Optical Manifestations of Planar Chirality,” Phys. Rev. Lett. 90, 107404 (2003). [CrossRef] [PubMed]

8.

A. S. Schwanecke, A. Krasavin, D. M. Bagnall, A. Potts, A. V. Zayats, and N. I. Zheludev, “Broken Time Reversal of Light Interaction with Planar Chiral Nanostructures,” Phys. Rev. Lett. 91, 247404 (2003). [CrossRef] [PubMed]

9.

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, “Giant Optical Activity in Quasi-Two-Dimentional Planar Nanostructures,” Phys. Rev. Lett. 95, 227401 (2005). [CrossRef] [PubMed]

10.

A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheldev, “Giant Gyrotropy due to Electromagnetic-Field Coupling in a Bilayered Chiral Structure,” Phys. Rev. Lett. 97, 117401 (2006). [CrossRef]

11.

E. Plum, V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, and Y. Chen, “Giant optical gyrotropy due to electromagnetic coupling,” Appl. Phys. Lett. 90, 223113 (2007). [CrossRef]

12.

M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. 32, 856–858 (2007). [CrossRef] [PubMed]

13.

In the inset of Fig. 1 of Ref. 8, images of the left- and right-twisted structures were exchanged by mistake.

14.

K. Sato, “Measurement of Magneto-Optical Kerr Effect Using Piezo-Birefringent Modulator,” Jpn. J. Appl. Phys. 20, 2403–2409 (1981). [CrossRef]

15.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface Plasmon Polaritons and Their Role in the Enhanced Transmission of Light through Periodic Arrays of Subwavelength Holes in a Metal Film,” Phys. Rev. Lett. 92, 107401 (2004). [CrossRef] [PubMed]

16.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B. 58, 6779–6782 (1998). [CrossRef]

17.

D. W. Lynch and W. R. Hunter, “Gold(Au)” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1984).

18.

S. A. Darmanyan and A. V. Zayats, “Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: An analytical study,” Phys. Rev. B. 67, 035424 (2003). [CrossRef]

19.

W. L. Barns, T. W. Preist, S. C. Kiston, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B. 54, 6227–6244 (1996). [CrossRef]

20.

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (New York, Pergamon Press1960).

21.

M. Born, Optik (Springer, Berlin, 1930).

22.

Y. Svirko, N. Zheludev, and M. Osipov, “Layered chiral metallic microstructures with inductive coupling,” Appl. Phys. Lett. 78, 498–500 (2001). [CrossRef]

23.

B. Bai and L. Li, “Group-theoretic approach to enhancing the Fourier modal method for crossed gratings with C4 symmetry,” J. Opt. A: Pure Appl. Opt. 7, 783–789 (2005). [CrossRef]

24.

R. C. Weast, M. J. Astle, and W.H. Beyer, CRC Handbook of Chemistry and Physics, 64 th ed. (CRC Press, Florida, 1984).

25.

A. V. Krasavin, A. S. Schwanecke, N. I. Zheludev, M. Reichelt, T. Stroucken, S. W. Koch, and E. M. Wright, “Polarization conversion and “focusing” of light propagating through a small chiral hole in a metallic screen,” Appl. Phys. Lett. 86, 201105 (2005). [CrossRef]

26.

T. Ohno and S. Miyanishi, “Study of surface plasmon chirality induced by Archimedes’ spiral grooves,” Opt. Express 14, 6285–6290 (2006). [CrossRef] [PubMed]

OCIS Codes
(230.3990) Optical devices : Micro-optical devices
(240.6680) Optics at surfaces : Surface plasmons

ToC Category:
Optics at Surfaces

History
Original Manuscript: May 7, 2007
Revised Manuscript: June 7, 2007
Manuscript Accepted: July 9, 2007
Published: July 18, 2007

Citation
K. Konishi, T. Sugimoto, B. Bai, Y. Svirko, and M. Kuwata-Gonokami, "Effect of surface plasmon resonance on the optical activity of chiral metal nanogratings," Opt. Express 15, 9575-9583 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-15-9575


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References

  1. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Grating (Springer-Verlag, Berlin, 1988).
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