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JOURNAL OF APPLIED PHYSICS

VOLUME 95, NUMBER 11

1 JUNE 2004

Nonlinear magneto-optical Kerr effect in garnet magnetophotonic crystals
T. V. Dolgova,a) A. A. Fedyanin, and O. A. Aktsipetrov
Department of Physics, Moscow State University, Moscow, 119992, Russia

K. Nishimura, H. Uchida, and M. Inoue
Department of Electrical and Electronic Engineering, Toyohashi University of Technology, Toyohashi, Japan

Presented on 9 January 2003 Magnetization-induced second-harmonic SH generation is studied in magnetophotonic crystals formed from a magnetic garnet spacer located between two dielectric Bragg reflectors, at the resonance of the fundamental radiation with the cavity mode. Longitudinal nonlinear magneto-optical Kerr effect manifests itself in the rotation of the polarization plane of a reflected SH wave which reaches a value up to 250°/ m. A magnetization-induced variation of the SH intensity is observed in transversal configuration with magnetic contrast up to 0.3. © 2004 American Institute of Physics. DOI: 10.1063/1.1667838

INTRODUCTION

EXPERIMENT

Lately magnetophotonic crystals MPC attract considerable attention owing to combining the advantages of photonic band-gap PBG structures1 and magnetic materials. The former allows one to control light propagation while the characteristics of the latter can be manipulated by an external magnetic field. This opens up prospectives for using the MPC in magneto-optical devices, such as isolators, ultrafast switches, and spatial light modulators.2 The MPCs, consisting of two nonmagnetic dielectric Bragg reflectors and ferromagnetic spacer--magnetophotonic microcavities, have recently been proposed and designed.3 The microcavities have the pass mode inside the PBG and localize the optical field of a certain wavelength inside the cavity spacer. Multiple reflections in the magnetic spacer lead to the increase of magneto-optical Faraday and Kerr effects.4 Localization of the optical field gives rise to the enhancement of magnetization-induced second-harmonic generation MSHG . Typically, in magnetic noncentrosymmetric materials, magnetization-induced changes in the parameters of second-harmonic SH radiation, such as its amplitude intensity , polarization, and relative phase, are several orders of magnitude larger than in the magneto-optical Kerr effect and the Faraday effect.5,6 Moreover, the SH wave polarization rotation up to 7° in Bi-doped yttrium ­ iron ­ garnet Bi:YIG microcavities was recently observed in the polar configuration of a magnetic field application for the wavelength resonant with the cavity mode.7,8 However, the MSHG effects in tangential configurations of magnetic field application are expected to be much stronger, since the easy magnetization axes is in the film plane. In this article, magnetic nonlinear-optical effects in tangential configurations of the magnetic field application are measured in Bi:YIG magnetophotonic microcavity.
a

The magnetophotonic microcavities are formed from two dielectric Bragg reflectors and a microcavity spacer Fig. 1 . Bragg reflectors are fabricated from five pairs of alternating quarter-wavelength-thick SiO2 and Ta2 O5 layers. The microcavity spacer is Bi-substituted yttrium ­ iron ­ garnet layer, Bi1.0Y2.5Fe5 Ox , with the half-wavelength thickness. The sample is grown on a glass substrate by the rf sputtering of corresponding targets in an Ar atmosphere with a sputtering pressure of 6 mTorr. Before the fabrication of the top Bragg reflector, the sample is annealed in air at 700 °C for 20 min for residual oxidation and crystallization of Bi:YIG film. The cavity mode is expected at approximately 850 nm under the normal incidence. Figure 1 shows a field-emission scanning electron microscope image of the MPC sample cleavage. The image demonstrates the high quality of the interfaces and good periodicity of the reflectors. The sample structure is clearly seen. The sample is characterized by the linear transmission solid circles in Fig. 2 and Faraday rotation open circles in Fig. 2 spectra. The small transmission observed in the spectral interval from approximately 750 nm to 1000 nm corre-

Electronic mail: tata@shg.ru 7330

FIG. 1. Field-emission scanning electron microscope image of the MPC sample. © 2004 American Institute of Physics

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TABLE I. The non zero elements of tensor ( 2,0) and pseudotensor ( 2,1) for m medium distributed over the magnetization direction and polarization combinations of fundamental and SH generation light. M s s p p s p s p 0 , 0
X

M 0

Y

M 0 0

Z

1 0
zy y

yyy X

xy y Y y zzX xxxY

y xxX

0 ,

y xzZ xzzY

0
zzz

,

0

,

xzx zxx

,

zxzY

FIG. 2. Spectra of the transmittance filled circles and the Faraday rotation angle open circles measured in Bi:YIG-based MPC at the normal incidence.

Fresnel rhombus. The polarization of the SH radiation is controlled by a Glan prism analyzer. The saturating dc-magnetic field up to 2 kOe is applied to the microcavity using a permanent FeNdB magnet along the surface for the longitudinal and transversal configurations of nonlinear magneto-optical Kerr effect NOMOKE .
RESULTS AND DISCUSSION

sponds to the PBG of the MPC. The PBG spectral width and the drop of the transmission coefficient inside the PBG are determined by the number of periods and refractive index difference in the SiO2 /Ta2 O5 Bragg reflectors. The sharp peak in transmittance at 900 nm is attributed to the microcavity mode and shows the high-quality factor of the MPC. A small redshift of its spectral position from the center of the PBG indicates that the optical thickness of the Bi:YIG layer is slightly larger than a half-wavelength. The spectrum of the Faraday rotation angle of the linearly polarized wave also has a peak at the microcavity mode where rotation enhances till approximately 1.5°. It corresponds to effective value of 7.7°/ m that is approximately 50 times larger than the Faraday rotation angle for the single Bi:YIG films at these wavelengths. The linearly polarized output of a tunable ns-parametric generator/amplifier operating from 730 nm to 1050 nm is used as a fundamental radiation. The pulse duration is approximately 2 ns and the energy is below 5 mJ/pulse. The SH radiation reflected from the MPC is selected by a series of glass filters BG39 and detected by a photomultiplier tube and a boxcar. The polarization of the fundamental radiation is controlled by a Glan prism polarizer and varied by a

Figure 3 shows dependences of the SH intensity on the orientation of the analyzer axis measured for two opposite directions of saturating magnetic field applied in the longitudinal geometry of NOMOKE. The fundamental wavelength corresponds to the microcavity mode. The SH wave is strongly linearly polarized. The magnetic field application leads only to the rotation of the SH wave polarization. The angle of polarization rotation is 38° for an angle of incidence of 30° and almost 50° for 15° incidence. Second-harmonic SHG generation is produced by the (2) quadratic nonlinear polarization P2 at the doubled frequency of the fundamental radiation E which is given in dipole approximation by: P22
(2) 2

:E E ,

1

where is the quadratic dipole susceptibility tensor. In magnetic materials, (2) becomes the function of magnetization vector, M. Phenomenologically, the function (2) ( M) can be expanded into the series over M:
2 2,0 ( 2,0) 2,1

·M

2,2

: MM ... .

2

FIG. 3. SH polarization diagrams measured for two opposite directions open and solid circles of magnetic field applied in the longitudinal configuration. The angle of incidence of s-polarized fundamental radiation is 15° panel a or 30° panel b . The zeroth value of the analyzer angle corresponds to the p-polarized SH wave. Curves are the fit to intensity of the linearly polarized wave.

describes the nonmagnetic crystallographic Tensor contribution to (2) , pseudotensor ( 2,1) governs the magnetic contribution, which is odd in magnetization, and tensor ( 2,2) is responsible for the term, which is even in M. In the studied magnetic microcavity, the dielectric Bragg reflectors are supposed to be linear and all dipole nonlinear sources are localized in the magnetic spacer. The Bi:YIG spacer is considered as an isotropic film in its plane and anisotropic along the normal. The corresponding symmetry group is m . The nonzero elements of pseudo tensors are given in the Cartesian frame e x , e y , e z with the z axis being a normal to the film and the plane xz is the plane of incidence. ( 2,0) has three nonequivalent elements, zzz , zxx ( 2,1) has six nonequivalent zy y , xxz yy z and 9 elements, , xzzY y zzX zxzY zyz X , y xzZ , , xyz Z yyy X xxxY yxyY xx y X , xy yY y xxX , where capital subscript corresponds to the magnetization vector component.


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The odd magnetization-induced variations in the SH intensity can be observed only in the transversal NOMOKE configuration as M (0,M Y ,0) . The interference between crystallographic and magnetization-induced SHG contributions provides the presence of the cross term which is linear in magnetization. Figure 4 b shows intensity of MSHG as a function of the fundamental wavelength measured in the geometry of transversal NOMOKE for the p-in, p-out polarization combination in the spectral vicinity of the microcavity mode. The spectra for two opposite directions of the saturating magnetic field are obtained by changing the field direction several times at each spectral position as is shown in the inset of Fig. 4 and averaging the resulting intensities. The SH intensity is enhanced as the fundamental wave is in the resonance with the microcavity mode. The ratio of the intensities for two directions of the magnetic field is almost 2. Figure 4 a shows the spectral dependence of the magnetic contrast (I I )/( I I ) , where and in the SH intensity, denote directions of the field. achieves values of 0.3 and appears to be almost spectrally independent. The changing of the magnetic field direction varies only the SH intensity and no spectral shifts of SHG resonances are observed.

CONCLUSIONS

FIG. 4. Panel a: The spectrum of SHG magnetic contrast in the spectral vicinity of the microcavity mode. Panel b: The SHG spectra measured in transversal NOMOKE configuration for the p-in, p-out polarization combination and shown by solid and open circles for two opposite directions of the saturating magnetic field. Inset: the SH intensity for alternating opposite directions of magnetic field for the fixed fundamental wavelength.

Table I shows the nonzero elements of ( 2,0) and ( 2,1) for isotropic film distributed over the magnetization direction and polarization combinations of fundamental and SHG light. In the longitudinal configuration M ( M X ,0,0 ) magnetization-induced and crystallographic SHG terms are polarized orthogonally with respect to each other. The resulting polarization plane is determined by a vector sum of the two contributions. This leads to the rotation of the SH field polarization plane depending on the sign of the magnetic field applied. The rotation angle is given by tg F sin ·
yyy X

In conclusion, nonlinear magneto-optical Kerr effect is studied in one-dimensional MPCs formed from SiO2 /Ta2 O5 Bragg reflectors and half-wavelength-thick Bi-doped yttrium iron garnet microcavity spacer. Strong magnetizationinduced variations in polarization plane of the SH wave are observed in the longitudinal configuration of NOMOKE. The polarization plane rotation for two opposite directions of the magnetic field achieves 48° for 15° incidence. Magnetic contrast up to 0.3 is observed in the transversal configuration. The work is supported by a Grant-In-Aid from the Ministry of Education, Science, Culture, and Sport of Japan Grant Nos. 14205045 and 14655119 , the Russian Foundation for Basic Research, and the Presidential Grant for Leading Russian Science Schools.

1

2

3 4

M

X

5

,

3

6 7

zy y

where F ( ) is a weak function of the angle of incidence . According to Eq. 3 , increases with the decrease in . Using experimental values of , the (2) components ratio is estimated to be yyy X M X / zy y 0.05.

8

9

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