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JETP Letters, Vol. 76, No. 8, 2002, pp. 527­531. Translated from Pis'ma v Zhurnal èksperimental'nooe i Teoreticheskooe Fiziki, Vol. 76, No. 8, 2002, pp. 609­613. Original Russian Text Copyright © 2002 by Fedyanin, Yoshida, Nishimura, Marowsky, Inoue, Aktsipetrov.

Magnetization-Induced Second Harmonic Generation in Magnetophotonic Microcavities Based on Ferrite Garnets
A. A. Fedyanin1, T. Yoshida2, K. Nishimura2, G. Marowsky3, M. Inoue2, and O. A. Aktsipetrov1, *
1Moscow

State University, Vorob'evy gory, Moscow, 119992 Russia * e-mail: aktsip@shg.ru 2Toyohashi University of Technology, 441-8580 Toyohashi, Japan 3Laser-Laboratorium GÆttingen, D-37077 GÆttingen, Germany
Received September 25, 2002

Magnetization-induced second harmonic generation was observed in magnetophotonic microcavities consisting of a ferromagnetic yttrium­iron garnet layer surrounded by nonmagnetic photonic crystals (Bragg reflectors). At resonance between the fundamental radiation and the microcavity mode in the geometry of polar magnetooptical Kerr effect, the polarization rotation for the second harmonic was found to be (18.5 ± 0.5)°/µm for the fundamental radiation with a wavelength of 825 nm. © 2002 MAIK "Nauka / Interperiodica". PACS numbers: 42.65.Ky; 42.70.Qs; 75.75.+a

Magnetization-induced second harmonic generation (MSHG) is one of the fundamental phenomena in nonlinear magneto-optics. It is associated with the involvement of the spin subsystem and the spin­orbit interaction in the formation of the electronic quadratic nonlinear optical response of magnets [1]. This phenomenon was used to develop an efficient method of studying magnetic surfaces and thin films [2]. The sensitivity of this method is caused by the symmetry selection rule for MSHG in the bulk of centrosymmetric media; many important magnetic materials belong to such media. Magnetization-induced changes in the parameters of SH radiation such as its amplitude (intensity), polarization, and phase in typical experimental situations prove to be several orders of magnitude larger than in the magnetooptical Kerr effect and the Faraday effect. Since the first observation of MSHG in ferrite garnet films [3] and its theoretical prediction in [4], the magnetization-induced SH was extensively studied at metal surfaces and thin films [5­ 8], as well as in thin films of magnetic insulators, primarily, of yttrium­iron garnets [9, 10]. In last years, much attention has been given to studying MSHG in magnetic nanoparticles [2, 11, 12]. The methods developed in the last years for manufacturing structures with an artificial photonic band gap {photonic crystals and microcavities (MC) [13]} made it possible to study nonlinear optical phenomena which are associated with the specificity of light propagation in such microstructures [14]. For example, in the case of MC, the spatial localization of resonant electromag-

netic radiation in the vicinity of microcavity layer strengthens the generation of optical harmonics, as was recently observed experimentally for the second and third harmonics in microcavities based on porous silicon [15, 16]. Of special interest is the study of nonlinear optical effects in magnetic microstructures with photonic band gap because of the expected enhancement of their magnetization-induced response. However, methods of growing such objects were developed only recently [17, 18]. In this work, the enhancement of MSHG was studied experimentally in magnetic microcavities based on photonic crystals. A high quality of the nonmagnetic Bragg reflectors grown from silicon oxide and tantalum oxide layers causes strong localization of electromagnetic field in a ferromagnetic yttrium­iron garnet MC layer and enhances the gain in MSHG, which manifests itself in a many-fold amplification of the rotation of SH polarization. Magnetophotonic MC samples were composed of a half-wave 190-nm-thick bismuth-doped polycrystalline yttrium­iron garnet (Bi:YIG) layer surrounded by two Bragg reflectors consisting of five pairs of alternating quarter-wave SiO2 and Ta2O5 layers 135 and 95 nm in thickness, respectively. The expected spectral position of the microcavity mode in the grown MC was about 850 nm at the normal incidence, and the center of the photonic band gap and its width were about 780 and 200 nm, respectively. When manufacturing MC, SiO2/Ta2O5 photonic crystal was first grown on a fused silica substrate by magnetron sputtering. Then a

0021-3640/02/7608-0527$22.00 © 2002 MAIK "Nauka / Interperiodica"


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FEDYANIN et al.

Bi:YIG

NONE

COMPO

15.0 kV â 30.000

100 nm

WD 7.0 mm

SiO2

Ta2O5

Fig. 1. Electron microscope image of the magnetophotonic microcavity cleavage.

Fig. 2. Linear reflection coefficients measured for the s- and p-polarized fundamental waves (light and dark circles, respectively) at an angle of incidence of 30°. Arrows indicate spectral positions of the MC mode for these polarizations. Inset: scheme of experimental geometry, applied magnetic field, and the MC frame of reference.

Bi:YIG film was deposited. After annealing at a temperature of 725°C for 10 min, a polycrystalline ferromagnetic garnet layer was formed. At the final stage, the capping photonic crystal was deposited on the MC garnet layer. The structure of the grown magnetophotonic MC is seen in its electron microscope image

(Fig. 1). It demonstrates a high homogeneity of the layers constituting MC and well-defined interfaces between the layers. Experiments on MSHG spectroscopy were performed using linearly polarized radiation from an optical parametric oscillator with a pulse duration of about 4 ns and a pulse energy of 5 mJ. The fundamental radiation wavelength was tuned in the range from 750 to 950 nm. The polarization of fundamental radiation was varied by a Fresnel rhomb and monitored by a Glan prism. The polarization of the reflected SH radiation was monitored by another Glan prism. The saturating magnetic field on the order of 2 kOe was applied in the geometry of polar magnetooptical Kerr effect using a permanent magnet made from NdFeB. The SH radiation was separated by a set of glass BG39 filters and detected by a photomultiplier. The angle of incidence of the fundamental radiation on the sample was 30°. The spectra of the coefficients Rs and Rp of linear reflection from a magnetophotonic MC for the s- and ppolarized radiation in the vicinity of the MC mode are shown in Fig. 2. For wavelengths shorter than 900 nm, both spectra demonstrate high reflectance corresponding to the photonic band gap. A dip in the reflection spectrum at 823 nm and 813 nm for the s and p polarization, respectively, indicates the spectral position of the MC mode for the chosen polarization. The fundamental radiation with these wavelengths efficiently penetrates into the MC, where it is localized in the vicinity of MC layer because of a multiple-beam interference. The spectral splitting of the mode is likely caused by the anisotropy of dielectric constant of the Bi:YIG layer, because the p-polarized fundamental radiation, contrary to the s-polarized radiation, is a superposition of the tangential and normal electromagnetic field components. Figure 3 presents the intensity of the p-polarized SH radiation generated by the fundamental radiation polarized at an angle of 45° to the s- and p-polarized waves. The spectrum shows two distinct peaks at 862 nm and 810 nm, which are close to the positions of the MC mode for the fundamental s and p components. This resonant SH enhancement is caused by the alternate localization of the fundamental s and p components inside the MC layer. Negligible SH intensities at the fundamental wavelengths near the edge of photonic bandgap, where the phase-matching conditions are fulfilled for the SH generation in photonic crystal mirrors, indicate that Bragg reflectors do not make contribution to the observed SH radiation signal. To within the experimental accuracy, the intensity of s-polarized SH radiation in the absence of an external magnetic field was zero for any polarization of fundamental radiation. Figure 3 also demonstrates the optical rotation (upon changing the direction of the applied magnetic field) 2 of the SH radiation generated by the p-polarized fundamental radiation. The spectral range of 2 is limited by a decrease in the SH intensity, because the
JETP LETTERS Vol. 76 No. 8 2002


MAGNETIZATION-INDUCED SECOND HARMONIC GENERATION

529

fundamental radiation and the MC mode are then off resonance. At the fundamental wavelength 795 nm corresponding to the short-wavelength edge of the MC mode for the p-polarized wave, the rotation angle of SH wave polarization is about 2.8°. The tuning of the fundamental wavelength to the long-wavelength edge of the mode results in a monotonic increase in 2 to ~7.0°. This corresponds to the Kerr rotation of 2 /2 18.5°/µm for 825 nm. The magnetization-induced rotation of SH wave polarization is caused by the appearance of magnetic components in the quadratic susceptibility of the ferrite garnet layer, resulting in the generation of s-polarized SH component and its enhancement due to the localization of fundamental radiation in the MC layer. Another mechanism of the rotation of SH wave polarization amounts to the Kerr rotation of the fundamental wave polarization and its enhancement due to the resonance with the MC mode. The multiple-beam interference of the resonant fundamental radiation inside the ferromagnetic MC layer brings about additive increase in the magnetization-induced rotation of fundamental wave polarization and appearance of the s-polarized component in the initially p-polarized fundamental field. In the description of MSHG from the magnetophotonic MC, it is assumed that the polycrystalline ferrite garnet MC layer with in-plane isotropy is the only source of the dipole SH radiation. The nature of quadratic nonlinearity of ferrite garnet can be associated with the inhomogeneous deformations arising in the direction normal to the layer while annealing. Let us denote by z the normal coordinate to the plane of MC layer and by zx the plane of incidence. Then the set of nonzero components of quadratic susceptibility of the garnet layer is written as zzz,
(2) (2) xzx

Fig. 3. Dark circles are for the angle 2 of magnetizationinduced, polarization rotation measured for the SH wave generated by the p-polarized fundamental wave upon changing the direction of the saturating magnetic field. Light circles are for the intensity I2 of the p-polarized SH wave generated by the fundamental radiation with a mixed polarization (in arbitrary units). Insets: schematically illustrated mechanisms of magnetization-induced rotation of the SH wave. (I) Generation of magnetization-induced s-polarized SH field E
( 2 ), M yxz 2 p 2 s

caused by the magnetic component


of quadratic susceptibility; (II) Kerr rotation E p of the fundamental wave polarization; and (III) Kerr rotation E of the SH wave polarization plane.

=

(2) yzy

,



(2) zxx

=

(2) zyy

.

(1)

In the absence of magnetic field, the SH radiation generated by the p-polarized fundamental field with the amplitude E p = { E x , 0, E z } E p { F x , 0, F z } in a film with in-plane isotropy is strictly p-polarized due to the symmetry properties of the quadratic susceptibility 2 2 2 tensor. The SH wave amplitude E p = { E x , 0, E z } E
2 p

{F

2 x

, 0, F E
2 p

2 z

} is given by
2 2 2 (2) zxx (2) zzz

= G(E p ) ( F z (F x )
(2) xzx 2 2

of quadratic susceptibility. This component is nonzero for the isotropic layer in the geometry of polar Kerr effect [19]. Additionally, the fundamental wave undergoes Kerr rotation inside the MC layer, so that fundamental fields of both (s and p) polarizations coexist inside it. Because of this, the s-polarized SH field can (2) be generated by the nonmagnetic component yzy of quadratic susceptibility. Finally, the polarization rotation for the initially p-polarized SH field can be due to the linear magnetooptical Kerr effect at the SH frequency. Therefore, in the presence of magnetic field, the amplitude of s-polarized SH wave of purely magnetization-induced nature is given by E s (M) = G(E p ) ( F x F z + Fz
(2) yzy 2 2 2 ( 2 ), M yxz L

+ F x F x Fz

2

(2) ),

+ F z (F z )

where G is the proportionality coefficient equivalent to the Green's function for a multilayer medium. It accounts for the result of integration over the MC layer and the geometric factors. In the polar geometry, the applied magnetic field induces s-polarized SH field, ( 2 ), M which is generated by the magnetic component yxz
JETP LETTERS Vol. 76 No. 8 2002

sin ( /2 ) ) + E p sin ( 2 /2 ) ,
L

(3)

where and 2 are the angles of rotation (due to a change in the magnetic-field direction) caused by the magnetooptical Kerr effect for the fundamental and SH radiations and M is the normal component of the mag-


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FEDYANIN et al.

netization vector of the ferrite garnet MC layer. The weak magnetic-field dependence of the G and F coefficients is ignored in Eq. (3). The intensity of the total SH field is determined by the superposition of the p- and s-polarized SH waves: I 2 () = E
2 p

exp ( i ) cos + E s (M) sin ,

2

2

(4)

where is the analyzer-axis rotation angle measured from the p-polarization direction and is the phase shift between the SH p and s components, which are, generally, complex quantities. The experimental polarization diagrams demonstrate that the SH wave is linearly polarized, so that one can set = 0 with a good accuracy. Then the polarization rotation upon changing the direction of magnetic field can be written for the SH wave as tan
2

the propagation of the s-polarized fundamental wave is forbidden in the MC, one has = 0, and the nonzero 2 values are caused by the generation of s-polarized magnetization-induced SH by the magnetic component ( 2 ), M yxz of the quadratic susceptibility and by the linear Kerr rotation of SH wave polarization. Independent L experimental measurements give 2 ~ 1°. Hence, the experimental 2 values at the edges of the spectral range can be used to estimate the ratio yxz / xzx ~ 0.04 of the magnetic and nonmagnetic components of quadratic susceptibility and the characteristic Kerr rotation angle /2 22.0°/µm ( 825 nm) for the fundamental wave in the ferrite­garnet MC layer. Taking into account that our model is rather crude, the estimate ( 2 ), M (2) obtained for yxz / xzx can be considered as being in good agreement with the estimate 0.1 made in [12] for ferrite garnet nanoparticles. The values are approximately 50 times larger those obtained for ferrite garnet films at the same wavelengths. In summary, the magnetization-induced second harmonic generation has been investigated in the magnetophotonic bandgap microstructures--microcavities based on bismuth-doped yttrium iron garnet. At resonance with the MC mode, the spatial localization of an electromagnetic field inside the ferromagnetic MC enhances magnetization-induced second harmonic. Spectroscopic study of MSHG near the MC mode in the geometry of polar magnetooptical Kerr effect has demonstrated a giant amplification, up to 18.5°/µm, of the rotation of SH wave polarization for the resonant fundamental radiation at the wavelength 825 nm. This work was supported by the Russian Foundation for Basic Research (project nos. 01-02-16746, 01-0217524, 01-02-04018, 00-02-16253). REFERENCES
1. K. N. Bennemann, J. Magn. Magn. Mater. 200, 679 (1999). 2. O. A. Aktsipetrov, Colloids Surf., A 202, 165 (2002). 3. O. A. Aktsipetrov, O. V. Braginskioe, and D. A. Esikov, Kvantovaya èlektron. (Moscow) 17, 320 (1990). 4. N. N. Akhmediev, S. B. Borisov, A. K. Zvezdin, et al., Fiz. Tverd. Tela (Leningrad) 27, 1075 (1985) [Sov. Phys. Solid State 27, 650 (1985)]. 5. J. Reif, J. C. Zink, C.-M. Schneider, and J. Kirshner, Phys. Rev. Lett. 67, 2878 (1991). 6. J. Hohlfeld, E. Matthias, R. Knorren, and K. H. Bennemann, Phys. Rev. Lett. 78, 4861 (1997). 7. Q. Y. Jin, H. Regensburger, R. Vollmer, and J. Kirschner, Phys. Rev. Lett. 80, 4056 (1998). 8. U. Conrad, J. GÝdde, V. JÄnhke, and E. Mattias, Phys. Rev. B 63, 144 417 (2001). 9. O. A. Aktsipetrov, V. A. Aleshkevich, A. V. Melnikov, et al., J. Magn. Magn. Mater. 165, 421 (1997).
JETP LETTERS Vol. 76 No. 8 2002
( 2 ), M (2)

2 Es / E
(2)

2

2 p

F x yxz + yzy sin ( /2 ) = 2 ------------------------------------------------------------------------------------------------------------ (5) 2 2 ­1 ( 2 ) 2 (2) 2 (2) F z (F x ) ( F z ) zxx + F x F x xzx + F z F z zzz +2 sin ( 2 /2 ) ,
L

( 2 ), M

where the second-order magnetization-induced contri2 bution to E p is ignored. Assume that the components of nonmagnetic quadratic susceptibility are of the same order and that the quantities in the numerator are real. L Then, for small Kerr rotation angles 2 , , and 2 and small angles of incidence on the MC layer ( F Fz 0 and F x , F is obtained for 2:
2 2 x 2 z

,

1), the following estimate

yxz L ------------ + /2 + 2 . (2) xzx

( 2 ), M

(6)

The spectral dependence of the first term in Eq. (6) can be ignored, because the fundamental wavelength-tuning range is small enough for the noticeable spectral dependence to appear in the quadratic susceptibility L components. The quantity 2 can also be assumed to be constant, because no resonance features are observed at the SH wavelength in the linear reflection spectrum of the magnetophotonic MC. For this reason, the spectral dependence 2() is completely due to the Kerr rotation of fundamental radiation occurring at resonance with the MC mode. The maximum of magnetization-induced rotation of SH polarization corresponds to the largest spectral overlap between the modes for the s- and p-polarized fundamental waves. For this reason, 2 increases monotonically upon tuning the fundamental wavelength from the p-mode maximum to the overlap of the p and s MC modes. At the short-wavelength edge of the 2() spectrum, where


MAGNETIZATION-INDUCED SECOND HARMONIC GENERATION 10. V. V. Pavlov, R. V. Pisarev, A. Kirilyuk, and Th. Rasing, Phys. Rev. Lett. 78, 2004 (1997). 11. T. V. Murzina, E. A. Ganshina, S. V. Guschin, et al., Appl. Phys. Lett. 73, 3769 (1998). 12. T. V. Murzina, A. A. Nikulin, O. A. Aktsipetrov, et al., Appl. Phys. Lett. 79, 1309 (2001). 13. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, Princeton, 1995). 14. K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, Berlin, 2001). 15. T. V. Dolgova, A. I. Maoedykovskioe, M. G. Martem'yanov, et al., Pis'ma Zh. èksp. Teor. Fiz. 73, 8 (2001) [JETP Lett. 73, 6 (2001)].

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16. T. V. Dolgova, A. I. Maoedykovskioe, M. G. Martem'yanov, et al., Pis'ma Zh. èksp. Teor. Fiz. 75, 17 (2002) [JETP Lett. 75, 15 (2002)]. 17. M. Inoue, K. Arai, T. Fujii, and M. Abe, J. Appl. Phys. 83, 6768 (1998). 18. M. Inoue, K. Arai, T. Fujii, and M. Abe, J. Appl. Phys. 85, 5768 (1999). 19. R.-P. Pan, H. D. Wei, and Y. R. Shen, Phys. Rev. B 39, 1229 (1989).

Translated by V. Sakun

JETP LETTERS

Vol. 76

No. 8

2002