Effect of surface plasmon resonance on the optical ... - OSA Publishing

Effect of surface plasmon resonance on the optical activity of chiral metal nanogratings K. Konishi1, T. Sugimoto1, B. Bai2, Y. Svirko2, and M. Kuwata-Gonokami1* 1 Department of Applied Physics, University of Tokyo, and Core Research for Evolutional Science and Technology (CREST), JST, 113-8656, Tokyo, Japan 2 Department of Physics and Mathematics, University of Joensuu, Joensuu, P.O. Box 111, Finland * Corresponding author: [email protected]

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 noncoplanarity of the electric field vectors at the front (air-metal) and back (substrate-metal) sides of the grating layer. ©2007 Optical Society of America OCIS codes: (230.3990) Microstructure devices; (240.6680) Surface plasmons.

References and links 1. 2. 3. 4. 5. 6. 7. 8. 9.

10. 11. 12. 13. 14. 15.

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H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Grating (Springer-Verlag, Berlin, 1988). 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). 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). S. A. Maier, and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005). 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). 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). 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). 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). 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). 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). 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). M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. 32, 856-858 (2007). In the inset of Fig. 1 of Ref. 8, images of the left- and right-twisted structures were exchanged by mistake. K. Sato, “Measurement of Magneto-Optical Kerr Effect Using Piezo-Birefringent Modulator,” Jpn. J. Appl. Phys. 20, 2403-2409 (1981). 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). 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). D. W. Lynch, and W. R. Hunter, “Gold(Au)” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1984).

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Received 7 May 2007; revised 7 Jun 2007; accepted 9 Jul 2007; published 18 Jul 2007

23 July 2007 / Vol. 15, No. 15 / OPTICS EXPRESS 9575

18.

19. 20. 21. 22. 23. 24. 25.

26.

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). 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). L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (New York, Pergamon Press 1960). M. Born, Optik (Springer, Berlin, 1930). Y. Svirko, N. Zheludev, and M. Osipov, “Layered chiral metallic microstructures with inductive coupling,” Appl. Phys. Lett. 78, 498-500 (2001). 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). R. C. Weast, M. J. Astle, and W.H. Beyer, CRC Handbook of Chemistry and Physics, 64 th ed. (CRC Press, Florida, 1984). 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). T. Ohno and S. Miyanishi, “Study of surface plasmon chirality induced by Archimedes’ spiral grooves,” Opt. Express 14, 6285-6290 (2006).

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]. 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], suppression of light extinction [3] and other linear and nonlinear optical phenomena [4-6]. Observation of the polarization-sensitive diffraction in a chiral grating composed of a twodimensional (2D) array of metal nanostructures with no mirror symmetry has resulted in controversial claims related to a possible time reversibility violation in the interaction of light with chiral 2D structures [7, 8]. However, in our recent transmission experiments [9], we have clearly demonstrated reciprocity of the polarization effect. We have shown in particular that the presence of a substrate makes a planar chiral grating a three-dimensional medium that exhibits optical activity with a giant optical rotational power (~104 deg./mm). 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]. 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]. 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] 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 airmetal 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-

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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].

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], the magnetization of anti-ferromagnetic chromium layers does not affect the morphologysensitive effects discussed in this paper. 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]. 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]. According to Ref. 16, when the incident light wave is s-polarized, the resonance 2 2 wavelength λψ for the lowest mode ( i + j = 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

s

⎛ λψ ⎜ ⎜ a ⎝

s

⎞ ⎟ ⎟ ⎠

2

ε1 (λψs )ε 2 = − sin 2 ψ s ε1 (λψ ) + ε 2

,

(1)

ε1 and ε 2

are the permittivities of the metal and dielectric (air or substrate)

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where

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Fig. 2. Transmission spectra of s-polarized (a) and p-polarized (b) measurement.

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 toψ . 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 p2

polarized, the resonance wavelength angle

ψ

λψp

2 2 for the lowest modes ( i + j = 1 ) at incidence

is given by

λψp

ε1 (λψp )ε 2 = ± sinψ a ε1 (λψp ) + ε 2

.

(2)

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

constant of gold [17] and

ψ . Taking into account the frequency dispersion of the dielectric ε 2 = 2.13, we can derive that, in a nanograting with a period a =

2 2 2 2 500 nm, the surface plasmon modes with i + j = 1 and i + j = 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] and the inter-particle coupling that induces the anti-crossing at the folding points [19].

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

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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).

polarization rotation Δ as a function of the azimuth angle can be described by the following equation:

Δ = θ + A sin(2ϕ + B ) + C sin(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], 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

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

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

U NON ( r ) ∝ ∫

( E ⋅ [∇ × E ])

(

)

dz = f (d , δ ) n ⋅ [ E air (r ) × E sub (r )] ,

(4)

0

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 airmetal 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 U NON ( r ) implies

(

)

that ξ ( r ) ≡ n ⋅ [ E air ( r ) × E sub ( r ) ] ≠ 0 , i.e. Eair(r) and Esub(r) should not be parallel. At the front and back surfaces of the nanograting, the electric field distribution depends on the shape #82763 - $15.00 USD

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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 nonparallel electric field vectors at the front and back surfaces setting U NON to be non-zero across the grating. By using a rigorous Fourier modal method for crossed gratings with four-fold rotational symmetry (see Ref. [23] for details), we calculated the electric field distribution over the unit cell surface when a Y-polarized (see Fig. 5) light wave propagates along the grating normal. In the calculation of the electric field distribution we employed ellipsometric data for a thin gold film, while refractive index of chromium and silica are obtained from Ref. [24].

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.

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)% 10 ( ec 8 na tti 6 m sn ar 4 T .)g 0.6 ed ( 0.4 onit 0.2 at or 0.0 no it - 0.2 az ria- 0.4 lo P

700

(a) Experiment Calculation

(b) Experiment Calculat ion/ 12

750

800

850

Wavelength (nm)

900

Fig. 6. (a). Transmission spectra. (b). Polarization rotation spectra. Both spectra are of lefttwisted 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 twofold 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=

1 A E2

∫ dxdyξ ( x, y ) ,

(5)

cell

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, 11, 12]. 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 #82763 - $15.00 USD

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.)u .a 0.06 ( re 0.04 te 0.02 m ar ap 0.00 ts - 0.02 i tw- 0.04 lde iF - 0.06 700

Left Cross Right

750

800

850

900

Wavelength (nm) 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.

microwave field only for double-layered structures with mutual twist. The authors of Ref. [12] 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], i.e. it is below the limit of sensitivity polarization measurement setup in Ref. [12]. The authors of Ref. [11] 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. [10-12] are not contradicting our results. 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] and mode sensitive interaction with planar chiral structures [26] 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).

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