- Email: [email protected]
Magnetooptical properties of perforated metallic films
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 310 (2007) e843–e845 www.elsevier.com/locate/jmmm
Magnetooptical properties of perforated metallic films V.I. Belotelova,b,, L.L. Doskolovichc, V.A. Kotovc, A.K. Zvezdina a
General Physics Institute RAS, 38 Vavilov Street, Moscow 119991, Russia b M.V. Lomonosov Moscow State University, Moscow 119992, Russia c Image Processing Systems Institute RAS, 151, Molodog. Street, Samara 443001, Russia Available online 17 November 2006
Abstract It is shown that optical transmittance and the magnetooptical (MO) Faraday rotation in the heterostructure of a periodically perforated metallic layer attached to a smooth magnetic dielectric thin film demonstrate resonance dependences on the wavelength and magnetic-film thickness. It is possible to adjust geometrical and MO parameters of the system in order to get these resonance peaks close in wavelength and get enhanced Faraday rotation (by a factor of 5–10) along with sufficient transmittance (30–40%). The phenomenon is explained in terms of the excitation of the surface plasmon polaritons waves coupled with waveguided modes of the magnetic film. r 2006 Elsevier B.V. All rights reserved. PACS: 42.25.Fx; 42.79.Dj; 78.67.n; 78.20.Ls Keywords: Surface plasmon polariton; Magneto-optical effect; Extraordinary transmission
At present, control of the near-infrared and visible light on a submicronic scale by means of the magnetooptical (MO) effects attracts much attention. It can be realized, for example, through the Faraday effect. At the same time, the value of the Faraday effect is not always high enough. In addition, the condition of simultaneous high transmission and Faraday rotation, which is of prime importance for optical devices, is often difficult to fulfill, especially for the visible spectral range. That is why the search for new mechanisms of the Faraday rotation enhancement is a quite urgent task. In this work we investigate the possibility of MO effects enhancement in planar plasmonic systems—nanostructured materials with optical properties strongly affected by surface plasmon polaritons (SPP) [1]. One of the prominent features of such materials is the effect of the extraordinary optical transmission (EOT), which has been revealed and extensively studied in the past several years [1,2]. However, magnetooptics of plasmonic systems with the EOT phenomenon has been considered so far only in several works [3,4], and no pronounced MO effects Corresponding author. M.V. Lomonosov Moscow State University, Moscow 119992, Russia. Tel.: +7 495 9391134; fax: +7 495 9305270. E-mail address: [email protected] (V.I. Belotelov).
0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.10.851
increase was found. Experiments on Co films perforated by the periodic subwavelength hole arrays revealed that the MO Kerr effect in the spectral range of the anomalous transmission band is even about one order smaller than in uniform Co films of the same thickness [4]. In contrast to previous studies we consider the heterostructure (Fig. 1), where the perforated metal is not magnetized itself, but all MO properties of the structure are due to the uniform dielectric magnetic film attached to the metallic one. The choice of this configuration is mainly dedicated by the fact that ferromagnetic metals such as Co, Ni, and Fe have fairly large optical absorption, which substantially suppresses all plasmonic effects. For example at the incident light of wavelength l ¼ 900 nm the propagation distance of the generated SPP on the silica/Co interface is only around 2 mm, while for the silica/Au interface it is ten times larger. At the same time, for the EOT phenomenon the SPP propagation distance must be much higher than the period of the holes array, which is a fraction of micron. Consequently, for Co or other metal ferromagnetics this condition is not well satisfied. The main idea of the current research is to organize the most favorable conditions for the SPP generation and EOT phenomenon and to introduce simultaneously enhanced
ARTICLE IN PRESS V.I. Belotelov et al. / Journal of Magnetism and Magnetic Materials 310 (2007) e843–e845
k
0.25
d
r
M
h Fig. 1. Problem configuration. Light with wave vector k is normally incident onto metal-dielectric bilayer. Metallic plate (upper layer) is periodically perforated with the square holes, constituting a square lattice of period d. The size of each hole is r. Dielectric layer (lower layer) of thickness h is magnetized perpendicular to the film plane.
MO effects. We solve this problem by choosing the configuration, already presented in Fig. 1, and taking Au for the metallic layer and Bi-substituted yttrium iron garnet (BiYIG) magnetized uniformly along the Z-axis for the dielectric one. For numerical modeling of the electromagnetic wave diffraction by such a system, we used a rigorous coupledwave analysis [5]. In our calculus we employed a straightforward generalization of this method onto the case of 2-D multilayered structures. In the modal approach to the computation of electromagnetic field in each grating layer, we employed the correct rules of Fourier factorization introduced in Ref. [5]. Using this method we obtain satisfactory convergence for a multilayered structure containing crossed binary-relief binary grating made from highly reflecting metal. The system was optimized to obtain substantial enhancement of the Faraday angle FF along with high transmittance. Transmittance spectrum of the Au/BiYIG bilayer has several EOT resonances (Fig. 2), which are related to the light coupling with surface waves in the films—SPPs on the Au/BiYIG interface and quasi-guided modes in the BiYIG film. For a fixed wavelength, such coupling should be possible only for a discrete set of the film thickness h, for which quasi-guided modes have propagation wave numbers matching with SPPs wave number and the period of the inverse lattice of the grating in accordance with the momentum conservation law. It is verified by the strong dependence of the transmittance peak position on the film thickness h found in the considered systems. Coming to the MO properties of the system, we should point out that the medium’s gyrotropy should have significant influence on the polarization of the transmitted or reflected light. The latter is confirmed by the results of simulation of Faraday effects presented in Fig. 2. Pronounced MO effects enhancement is found at lmax ¼ 967 nm, which is very close to the wavelength of the transmittance resonance. Namely, the Faraday rotation gets a negative value of FF ¼ 0.781. This corresponds to an order of magnitude enhancement of the Faraday
Transmittance
0.20
0.6 0.4 0.2
0.15
0.0
0.10
-0.2 -0.4
0.05
-0.6
Faraday rotation (deg.)
e844
-0.8 0.00 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 Wavelength (µm) Fig. 2. Optical transmittance (blue line) and the Faraday rotation (red solid line) spectra of the bilayer system of perforated Au film of thickness 68.1 nm and uniform BiYIG film of thickness 117.6 nm, d ¼ 750 nm, r ¼ 393.5 nm (see Fig. 1). The Faraday rotation of the single magnetic layer of thickness 117.6 nm placed in optically matched surrounding medium is 0.091. Components of BiYIG dielectric tensor are m ¼ 5:5 and g ¼ 0:01 i0:0015 [6]; dielectric data for Au are taken from Ref. [7].
rotation, in comparison with the same single magnetic layer surrounded by optically matched medium. The analysis of the transmittance and the Faraday effect dependences on the magnetic-film thickness h reveals that for any wavelength of the incident light from the range where plasmon resonances exist, it is possible to adjust the thickness h to get significant Faraday rotation enhancement simultaneous with low light ellipticity, and relatively high transmission. This conclusion is of great importance for future applications of the described bilayered materials. The increase of the Faraday effect is explained by the fact that the magnetized dielectric plate is a kind of MO waveguide, for which TM-mode–TE-mode conversion takes place. The thickness of the dielectric film has a proper value for supporting one of the waveguided modes, which coupled with SPP effective length of the MO interaction increases and light polarization rotation gets significantly increased. It is important to emphasize here that in a standard MO dielectric waveguide magnetized perpendicular to its surfaces, TE–TM modes conversion does not arise, and consequently the MO effect in the considered system is purely due to the complex electromagnetic field of SPP and guided wave in the magnetic film. To conclude, we have studied the optical properties of bilayered systems consisting of metal and dielectric layers, the metallic plate being periodically perforated with hole arrays and the dielectric plate being magnetized in polar geometry. The effect of the extraordinary transmittance and MO Faraday effect is found. This phenomenon results from the formation of the coupled SPP and quasi-guided wave at resonance wavelengths. This work is supported by RFBR (No. 04-01-96517, 0502-17308, 05-02-17064, 06-02-17507), Russian President Grant for young scientists (MK-3804.2005.2), CRDF
ARTICLE IN PRESS V.I. Belotelov et al. / Journal of Magnetism and Magnetic Materials 310 (2007) e843–e845
RUE1-005064-SA-05, and nonprofitable scientific foundation ‘‘Dynasty’’. References [1] T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, P.A. Wolff, Nature 391 (1998) 667. [2] W.L. Barnes, W.A. Murray, J. Dintinger, E. Devaux, T.W. Ebbesen, Phys. Rev. Lett. 92 (2005) 107401.
e845
[3] Y.M. Strelniker, D.J. Bergman, Phys. Rev. B 59 (1999) R12763. [4] M. Diwekar, V. Kamaev, J. Shi, Z.V. Vardeny, Appl. Phys. Lett. 84 (2004) 3112. [5] B. Bai, L. Li, J. Opt. Soc. Am. A 22 (2005) 654. [6] A. Zvezdin, V. Kotov, in: Modern Magnetooptics and Magnetooptical Materials, IOP Publishing, Bristol/Oxford/Amsterdam, 1997. [7] D. Palik, in: Handbook of Optical Constants of Solids, Edward Academic Press, 1985.
Journal of Magnetism and Magnetic Materials 310 (2007) e843–e845 www.elsevier.com/locate/jmmm
Magnetooptical properties of perforated metallic films V.I. Belotelova,b,, L.L. Doskolovichc, V.A. Kotovc, A.K. Zvezdina a
General Physics Institute RAS, 38 Vavilov Street, Moscow 119991, Russia b M.V. Lomonosov Moscow State University, Moscow 119992, Russia c Image Processing Systems Institute RAS, 151, Molodog. Street, Samara 443001, Russia Available online 17 November 2006
Abstract It is shown that optical transmittance and the magnetooptical (MO) Faraday rotation in the heterostructure of a periodically perforated metallic layer attached to a smooth magnetic dielectric thin film demonstrate resonance dependences on the wavelength and magnetic-film thickness. It is possible to adjust geometrical and MO parameters of the system in order to get these resonance peaks close in wavelength and get enhanced Faraday rotation (by a factor of 5–10) along with sufficient transmittance (30–40%). The phenomenon is explained in terms of the excitation of the surface plasmon polaritons waves coupled with waveguided modes of the magnetic film. r 2006 Elsevier B.V. All rights reserved. PACS: 42.25.Fx; 42.79.Dj; 78.67.n; 78.20.Ls Keywords: Surface plasmon polariton; Magneto-optical effect; Extraordinary transmission
At present, control of the near-infrared and visible light on a submicronic scale by means of the magnetooptical (MO) effects attracts much attention. It can be realized, for example, through the Faraday effect. At the same time, the value of the Faraday effect is not always high enough. In addition, the condition of simultaneous high transmission and Faraday rotation, which is of prime importance for optical devices, is often difficult to fulfill, especially for the visible spectral range. That is why the search for new mechanisms of the Faraday rotation enhancement is a quite urgent task. In this work we investigate the possibility of MO effects enhancement in planar plasmonic systems—nanostructured materials with optical properties strongly affected by surface plasmon polaritons (SPP) [1]. One of the prominent features of such materials is the effect of the extraordinary optical transmission (EOT), which has been revealed and extensively studied in the past several years [1,2]. However, magnetooptics of plasmonic systems with the EOT phenomenon has been considered so far only in several works [3,4], and no pronounced MO effects Corresponding author. M.V. Lomonosov Moscow State University, Moscow 119992, Russia. Tel.: +7 495 9391134; fax: +7 495 9305270. E-mail address: [email protected] (V.I. Belotelov).
0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.10.851
increase was found. Experiments on Co films perforated by the periodic subwavelength hole arrays revealed that the MO Kerr effect in the spectral range of the anomalous transmission band is even about one order smaller than in uniform Co films of the same thickness [4]. In contrast to previous studies we consider the heterostructure (Fig. 1), where the perforated metal is not magnetized itself, but all MO properties of the structure are due to the uniform dielectric magnetic film attached to the metallic one. The choice of this configuration is mainly dedicated by the fact that ferromagnetic metals such as Co, Ni, and Fe have fairly large optical absorption, which substantially suppresses all plasmonic effects. For example at the incident light of wavelength l ¼ 900 nm the propagation distance of the generated SPP on the silica/Co interface is only around 2 mm, while for the silica/Au interface it is ten times larger. At the same time, for the EOT phenomenon the SPP propagation distance must be much higher than the period of the holes array, which is a fraction of micron. Consequently, for Co or other metal ferromagnetics this condition is not well satisfied. The main idea of the current research is to organize the most favorable conditions for the SPP generation and EOT phenomenon and to introduce simultaneously enhanced
ARTICLE IN PRESS V.I. Belotelov et al. / Journal of Magnetism and Magnetic Materials 310 (2007) e843–e845
k
0.25
d
r
M
h Fig. 1. Problem configuration. Light with wave vector k is normally incident onto metal-dielectric bilayer. Metallic plate (upper layer) is periodically perforated with the square holes, constituting a square lattice of period d. The size of each hole is r. Dielectric layer (lower layer) of thickness h is magnetized perpendicular to the film plane.
MO effects. We solve this problem by choosing the configuration, already presented in Fig. 1, and taking Au for the metallic layer and Bi-substituted yttrium iron garnet (BiYIG) magnetized uniformly along the Z-axis for the dielectric one. For numerical modeling of the electromagnetic wave diffraction by such a system, we used a rigorous coupledwave analysis [5]. In our calculus we employed a straightforward generalization of this method onto the case of 2-D multilayered structures. In the modal approach to the computation of electromagnetic field in each grating layer, we employed the correct rules of Fourier factorization introduced in Ref. [5]. Using this method we obtain satisfactory convergence for a multilayered structure containing crossed binary-relief binary grating made from highly reflecting metal. The system was optimized to obtain substantial enhancement of the Faraday angle FF along with high transmittance. Transmittance spectrum of the Au/BiYIG bilayer has several EOT resonances (Fig. 2), which are related to the light coupling with surface waves in the films—SPPs on the Au/BiYIG interface and quasi-guided modes in the BiYIG film. For a fixed wavelength, such coupling should be possible only for a discrete set of the film thickness h, for which quasi-guided modes have propagation wave numbers matching with SPPs wave number and the period of the inverse lattice of the grating in accordance with the momentum conservation law. It is verified by the strong dependence of the transmittance peak position on the film thickness h found in the considered systems. Coming to the MO properties of the system, we should point out that the medium’s gyrotropy should have significant influence on the polarization of the transmitted or reflected light. The latter is confirmed by the results of simulation of Faraday effects presented in Fig. 2. Pronounced MO effects enhancement is found at lmax ¼ 967 nm, which is very close to the wavelength of the transmittance resonance. Namely, the Faraday rotation gets a negative value of FF ¼ 0.781. This corresponds to an order of magnitude enhancement of the Faraday
Transmittance
0.20
0.6 0.4 0.2
0.15
0.0
0.10
-0.2 -0.4
0.05
-0.6
Faraday rotation (deg.)
e844
-0.8 0.00 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 Wavelength (µm) Fig. 2. Optical transmittance (blue line) and the Faraday rotation (red solid line) spectra of the bilayer system of perforated Au film of thickness 68.1 nm and uniform BiYIG film of thickness 117.6 nm, d ¼ 750 nm, r ¼ 393.5 nm (see Fig. 1). The Faraday rotation of the single magnetic layer of thickness 117.6 nm placed in optically matched surrounding medium is 0.091. Components of BiYIG dielectric tensor are m ¼ 5:5 and g ¼ 0:01 i0:0015 [6]; dielectric data for Au are taken from Ref. [7].
rotation, in comparison with the same single magnetic layer surrounded by optically matched medium. The analysis of the transmittance and the Faraday effect dependences on the magnetic-film thickness h reveals that for any wavelength of the incident light from the range where plasmon resonances exist, it is possible to adjust the thickness h to get significant Faraday rotation enhancement simultaneous with low light ellipticity, and relatively high transmission. This conclusion is of great importance for future applications of the described bilayered materials. The increase of the Faraday effect is explained by the fact that the magnetized dielectric plate is a kind of MO waveguide, for which TM-mode–TE-mode conversion takes place. The thickness of the dielectric film has a proper value for supporting one of the waveguided modes, which coupled with SPP effective length of the MO interaction increases and light polarization rotation gets significantly increased. It is important to emphasize here that in a standard MO dielectric waveguide magnetized perpendicular to its surfaces, TE–TM modes conversion does not arise, and consequently the MO effect in the considered system is purely due to the complex electromagnetic field of SPP and guided wave in the magnetic film. To conclude, we have studied the optical properties of bilayered systems consisting of metal and dielectric layers, the metallic plate being periodically perforated with hole arrays and the dielectric plate being magnetized in polar geometry. The effect of the extraordinary transmittance and MO Faraday effect is found. This phenomenon results from the formation of the coupled SPP and quasi-guided wave at resonance wavelengths. This work is supported by RFBR (No. 04-01-96517, 0502-17308, 05-02-17064, 06-02-17507), Russian President Grant for young scientists (MK-3804.2005.2), CRDF
ARTICLE IN PRESS V.I. Belotelov et al. / Journal of Magnetism and Magnetic Materials 310 (2007) e843–e845
RUE1-005064-SA-05, and nonprofitable scientific foundation ‘‘Dynasty’’. References [1] T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, P.A. Wolff, Nature 391 (1998) 667. [2] W.L. Barnes, W.A. Murray, J. Dintinger, E. Devaux, T.W. Ebbesen, Phys. Rev. Lett. 92 (2005) 107401.
e845
[3] Y.M. Strelniker, D.J. Bergman, Phys. Rev. B 59 (1999) R12763. [4] M. Diwekar, V. Kamaev, J. Shi, Z.V. Vardeny, Appl. Phys. Lett. 84 (2004) 3112. [5] B. Bai, L. Li, J. Opt. Soc. Am. A 22 (2005) 654. [6] A. Zvezdin, V. Kotov, in: Modern Magnetooptics and Magnetooptical Materials, IOP Publishing, Bristol/Oxford/Amsterdam, 1997. [7] D. Palik, in: Handbook of Optical Constants of Solids, Edward Academic Press, 1985.