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PHYSICAL REVIEW B 70, 012407 (2004)

Magnetization-induced second-harmonic generation in magnetophotonic crystals
T. V. Murzina, R. V. Kapra, T. V. Dolgova, A. A. Fedyanin, and O. A. Aktsipetrov*
Department of Physics, Moscow State University, 119992 Moscow, Russia

K. Nishimura, H. Uchida, and M. Inoue
Toyohashi University of Technology, 441-8580 Toyohashi, Japan (Received 12 February 2004; published 21 July 2004) Magnetization-induced second-harmonic generation is observed in magnetic photonic-crystal microcavities. The microcavity is formed from a half-wavelength-thick Bi-substituted yttrium-iron-garnet film sandwiched between two high-finesse dielectric Bragg reflectors. The transversal nonlinear magneto-optical Kerr effect reveals itself in magnetization-induced variations of the intensity and the relative phase of the second-harmonic wave. The variations reach the factor of 4 in intensity and 180° in phase for opposite directions of the dc-magnetic field. The longitudinal and polar nonlinear magneto-optical Kerr effects manifest themselves in the considerable, up to 50°, rotation of the second-harmonic wave polarization. DOI: 10.1103/PhysRevB.70.012407 PACS number(s): 78.20.Ls, 42.65. k, 42.70.Qs

Ferrite garnets are intensively studied magnetic materials.1 Due to the high magneto-optical response, small saturating fields, and transparency in the visible and IR spectral regions2 they find widespread use as optical isolators, optical switchers, magnetic-field sensors, and materials for magneto-optical imaging and detection.3 Doping the garnet films by Bi atoms strongly varies their magneto-optical response, e.g., Faraday rotation.4 Magnetic nonlinear-optical effects are affected even more strongly by Bi-substitution since it distorts the garnet lattice, breaks cubic lattice symmetry, and makes garnet films macroscopically noncentrosymmetric.5,6 In magnetic materials with broken space-inversion and time-reversal symmetries, the quadratic optical susceptibility tensor 2 becomes a function of the magnetization vector M and can be expanded into the series over M, 2 = 2,0 + 2,1 · M + Ї. The nonmagnetic and magnetization-induced electric-dipole contributions to the quadratic nonlinear-optical polarization, which are governed by the tensor 2,0 and the pseudotensor 2,1 , respectively, coexist leading to magnetization-induced second-harmonic generation (MSHG).7 MSHG was observed in magnetic garnet films in the late 1980's (Ref. 5) and then studied in garnet films of various composition.8,9 However, MSHG in reflection, that is, the nonlinear magneto-optical Kerr effect (NOMOKE), has not been used for magnetic garnet films except for in Ref. 5 which reported the magnetizationinduced rotation of the second-harmonic (SH) wave polarization for the polar NOMOKE. This is in contrast with numerous NOMOKE studies of metallic magnetic systems: ultrathin films10 and crystal surfaces11 in UHV conditions, planar nanostructures,12 and nanoparticles.13 MSHG in reflection from garnet film is induced in a thin surface layer with the thickness of an order of the inverted wave-vector sum k2 +2k -1. This is supposed to be responsible for a weak NOMOKE in garnets in comparison with MSHG detected in transmission through the film. In the case of multiple-reflection interference the nonlinear interaction length increases to the larger scale of an order of k2 -2k -1. Such a configuration of the Kerr effect measure0163-1829/2004/70(1)/012407(4)/$22.50

ments, which is similar to the transmission (Faraday) configuration, should lead to enhancement of NOMOKE. Microscopic-scale control of multiple reflection is achievable by means of a special class of photonic band gap (PBG) materials14 called photonic-crystal microcavities possessing optical resonant transitions inside the PBG. Microcavity effects give rise to enhancement of the resonant optical field and bring about a drastic increase in the second-harmonic generation (SHG) efficiency.15,16 A new class of PBG structures containing ferromagnetic materials and being controlled by a dc-magnetic field are magnetophotonic crystals and microcavities (MMC).17 Localization of the resonant electromagnetic field in the magnetic spacer leads to enhancement of the polar NOMOKE (Ref. 18) and the Faraday rotation.17 In this paper, the nonlinear magneto-optical Kerr effect is studied in magnetic microcavities formed from dielectric Bragg reflectors and a magnetic garnet spacer. Magnetization-induced variation of the SH intensity, rotation of the SH wave polarization, and the shift of the relative SH phase are observed at the wavelength (angular) resonance of the fundamental radiation with the microcavity mode. The symmetry properties of 2,0 and 2,1 (pseudo)tensors allow the clear separation of the magneto-optical effects. Namely, magnetization-induced changes in the SH intensity and relative phase are observed in the transversal configuration, while the SH wave polarization rotation is obtained in the longitudinal and polar configurations. Bragg reflectors of the MMC are fabricated by RF sputtering of five repeats of MC / 4-thick SiO2 and Ta2O5 layer pairs, where MC denotes the PBG center at the normal incidence. The MC / 2-thick cavity spacer is a Bi-substituted yttrium-iron-garnet Bi1.0Y2.0Fe5Ox Bi : YIG layer with a thickness of 195 and 245 nm that correspond to MC 900 nm and MC 1115 nm, respectively. The coercivity of the MMC measured in a vibrating sample magnetometer is 30 Oe. Saturating magnetic field is slightly above 100 Oe and indicates the easy-magnetization axis aligned along the MMC plane.
©2004 The American Physical Society

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FIG. 1. The SHG spectra of the MMC with MC sured in the p-in, p-out and s-in, p-out polarization open and filled circles, respectively. Inset: Spectra of (filled circles) and the Faraday rotation angle (open sured at the normal incidence.

900 nm meacombinations, transmittance circles) mea-

The polarized output of an optical parametric generator directed at an angle of incidence =30° is used for wavelength-domain SHG spectroscopy. The pulse duration is 2 ns, the energy is below 5 mJ/pulse, and the fundamental is tunable from 730 to 1050 nm. Wave-vector wavelength domain SHG spectroscopy is performed by changing the angle of incidence of the 10-ns-YAG : Nd3+ laser output at 1064 nm with an energy below 10 mJ/pulse. A saturating dc-magnetic field of a strength up to 2 kOe providing the single-domain state is applied tangentially to MMC for the longitudinal and transversal NOMOKE or normal to the sample for the polar NOMOKE. The inset in Fig. 1 shows the transmittance and Faraday rotation spectra of MMC. Low transmittance, down to 0.002, is observed in the spectral region from 750 to 1000 nm corresponding to the photonic band gap of the MMC. The PBG spectral width and attenuation in the PBG are determined by the number of layers and the refractive index difference in the Bragg reflectors. The peak in transmittance at 910 nm is attributed to the microcavity mode and shows a high quality 75. The Faraday rotation spectrum has factor of MMC, Q a peak at the mode as well, where the rotation angle is enhanced up to -1.5°. It corresponds to an effective value of -7.7° / m, which is approximately 50 times larger than that for the single Bi:YIG film on the substrate at these wavelengths. The SHG spectra for s- and p-polarized fundamental rainterval from diation are presented in Fig. 1. Peaks in the 850 to 880 nm separated by 10 nm are observed. The peaks correlate with the microcavity mode, which is spectrally shifted to shorter fundamental wavelength for oblique angles -2 = MC 1- nYIG sin2 1/2 deof incidence and observed at pending on the refractive index nYIG of the Bi:YIG spacer. The SH intensity I2 at the MMC mode is enhanced by a factor of 103 at least, in comparison with that outside PBG, where fundamental wave propagation is allowed. No I2 in-

FIG. 2. Intensity effects in MSHG: Transversal NOMOKE measured in the p-in, p-out polarization combination for opposite directions of magnetic field, solid and open circles, respectively. Triangles: the spectra of the SHG magnetic contrast in the spectral (angular) vicinity of the microcavity mode. (a) Wavelength-domain MSHG spectroscopy, MC 900 nm. (b) Angular MSHG spectroscopy, MC 1115 nm.

crease is observed at the spectral region of the PBG edge. The Q factor of the SHG resonances Q2 = 0 / , where 0 denotes the resonant fundamental wavelength and is the full width at half maximum, is equal to 160 ± 5, approximately twice as large as Q . Figure 2 shows the SH intensity as a function of the fundamental wavelength [panel (a)] and of the angle of incidence [panel (b)] measured in the spectral (angular) vicinity of the microcavity mode in the transversal configuration. For opposite magnetic field directions I2 is enhanced by a factor of 2 in wavelength-domain spectra and by a factor of 4 in angular spectra and no spectral shifts of the SHG resonances are observed. The spectra of the SHG magnetic contrast + - + - = I 2 - I 2 / I 2 + I 2 , where + and - denote the directions of the field, are shown in Figs. 2(a) and 2(b). achieves the value of 0.3 and 0.65 in the wavelength and wave-vector domains, respectively, and is spectrally independent in the vicinity of the mode. Magnetization-induced changes of the relative phase of the SH wave are observed using SHG interferometry.19 The SHG interference patterns are obtained by translating the SHG reference sample, which is a 30-nm-thick indium tin oxide film deposited on a fused quartz plate, along the laser beam. The SHG interference patterns measured for the opposite field directions are shifted by almost a half of a period.

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FIG. 3. Phase effects in MSHG: The magnetization-induced shift of the relative SH phase measured in the transversal configuration at the angular vicinity of the mode of the MMC with MC 1115 nm. Inset: Raw SHG interference patterns for opposite field directions measured at =28°.

The magnetization-induced shifts of the relative SH phase, which are shown in Fig. 3, are slightly smaller than 180° and almost constant in . The dependences of the SH intensity on the rotation angle of the analyzer axis measured for the opposite field directions at the mode are shown in the insets of Fig. 4. The longitudinal NOMOKE manifests itself in magnetization-induced rotation of the SH wave polarization up to 50°. The polar NOMOKE spectrum is shown in

FIG. 4. Polarization effects in MSHG: The spectrum of the SH wave polarization rotation upon the reversing the magnetic field direction in the polar configuration measured for the MMC with MC 900 nm. Top inset. The longitudinal NOMOKE -- the SH polarization diagrams measured for the s-polarized fundamental radiation at = 870 nm. Bottom inset: the polar NOMOKE -- the SH polarization diagrams measured for the p-polarized fundamental radiation at = 868 nm. = 0 corresponds to the p-polarized SH wave. Curves are the fit to intensity of the linear polarized wave.

Fig. 4. Tuning across the microcavity mode leads to a gradual increase of from 1° to 7°. The SiO2 /Ta2O5 Bragg reflectors are supposed to be the linear media since I2 is negligible at the PBG edge, where the phase-matched SHG from reflectors is expected.16,20 Dipole nonlinear sources are localized in the ferromagnetic Bi:YIG spacer. The latter is considered as the in-plane isotropic film with the m symmetry. Let us determine the z axis of the Cartesian frame as the film normal and xz as the plane of incidence. The 2,0 tensor, defining the nonmagNM netic component of the quadratic polarization P2 ,i 2,0 = ijk E j Ek , has three nonequivalent elements zzz, zxx = zyy and xxz = yyz. The 2,1 pseudotensor, describing M the magnetization-induced quadratic polarization P2 ,i 2,1 21 = ijkL E j Ek M L, has six nonequivalent elements xzzY = - yzzX, zxzY =- zyzX, yxzZ =- xyzZ, yyyX =- xxxY , yxyY = - xxyX, and xyyY =- yxxX. The symmetry considered is confirmed by a negligible I2 value measured in the transversal configuration for the s-in, s-out and p-in, s-out polarization combinations, in which both magnetization-induced and nonmagnetic SHG contributions are expected to be zero. The primary mechanism of the SHG enhancement in MMC is localization of the resonant fundamental radiation in the garnet spacer. The spectral splitting of the SHG peaks for s- and p-polarized fundamental waves is associated with the splitting of the microcavity modes for these polarization states that can be the manifestation of the stressinduced anisotropy of the Bi:YIG layer1 and inequality of the zz and yy elements of the permittivity tensor. The variations of I2 , which are odd in M, are observed only in the transversal configuration as M = 0, M Y ,0 . In the p-in, p-out polarization combination, the nonmagnetic NM NM SH field E2 induced by P2 interferes with magnetM M ization-induced SH field E2 exp i M generated by P2 . The SH intensity I2 ± M Y contains the cross term NM M ±2E2 E2 cos M depending on the relative phase M beNM M tween E2 and E2 and changing the sign for the opposite field directions. This term, known as the internal homodyne cross term,22 leads to the linear in M variation of I2 . The constant value of in the spectral vicinity of the mode indiNM M cates that E2 and E2 are enhanced similarly due to the fundamental field localization. A large value is attributed to a small M value that is due to absorption in garnet films. In fact, in transparent materials 2,0 is a real but 2,1 is an NM M imaginary tensor and the fields E2 and E2 generated in the same point do not interfere. Magnetization-induced shift of the relative SH phase, which is close to 180° for opposite directions of M, also indicates that M is close to 0° or to 180°. The spectral dependence of M leading to different values observed in the wavelength and wavevector-domain spectra is attributed to the Bi:YIG absorption at the SH NM M wavelength. The ratio E2 / E2 can be estimated as for small refraction angle in the xxxY M Y / 2 zxx tan 0.65 and M 0, it gives a ratio of Bi:YIG layer. For xxxY M Y / zxx 0.15. The nonmagnetic and magnetization-induced SH fields are polarized orthogonally in the polar and longitudinal NM M configurations. In this case E2 is p-polarized and E2 is s-polarized. NOMOKE appears in the rotation of the po-

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larization plane of the total SH wave. The SH intensity NM E2 cos depends on the analyzer angle as I2 M 2 , where the phase shift M describes + E2 exp i M sin the SH field ellipticity. Since the SH intensity vanishes for some value, the SH wave is considered as linearly polarized with M 0. The angle of rotation of the SH wave polarization upon the field direction reversing is estimated as and depends on the relation between the corresponding 2,0 and 2,1 elements. For the longitudinal NOMOKE and s-polarized fundamental radiation . For 2 arctan yyyXM X / zyy sin 2 =48°, it gives yyyXM X / zyy 0.1 that is close to the xxxY M Y / zxx ratio estimated for the transversal NOMOKE. In the polar configuration, the magnetization-induced rotation of the SH wave polarization is yielded by the combined effect of generation of s-polarized magnetizationinduced SH field induced by the yxzZ element and Faraday rotation of the SH and fundamental waves.23 Tuning through the microcavity mode of the p-polarized wave enhances the Faraday rotation of the fundamental radiation due to the multiple reflection in the Bi:YIG spacer.17 This leads to the appearance of the s-polarized fundamental radiation and generation of the s-polarized SH wave via a nonmagnetic yyz element. The best condition for this magnetizationinduced polarization plane rotation is achieved as the s and p modes are overlapped leading to the spectral dependence of . The value can be estimated for small angles of incidence as23 /2+ 2 , where yxzZM Z / zxx + and 2 are the linear (Faraday) rotation angles of the fun-

damental and SH waves polarizations, respectively. In conclusion, magnetization-induced second-harmonic generation is observed in magnetic photonic-crystal microcavities with the spacer formed from bismuth-doped yttriumiron garnet. Localization of the fundamental radiation, resonant with the microcavity mode, in the garnet spacer enhances the absolute values of both nonmagnetic (crystallographic) and magnetization-induced SHG in reflection from the Bi:YIG microcavity manyfold. This allows the observation of transversal and longitudinal nonlinear magnetooptical Kerr effects in magnetic garnet films. The transversal NOMOKE reveals itself in the magnetization-induced variation of the SH intensity with the magnetic contrast up to 0.65, and in the large, close to 180°, shift of the relative SH phase. The large, up to 50°, magnetization-induced rotation of the SH wave polarization plane is observed for the longitudinal NOMOKE. Multiple-reflection interference of the resonant fundamental radiation enhances the Faraday rotation of the fundamental wave polarization. This results in the enhancement of the SH wave polarization rotation in the polar configuration of the magnetic field. This work was supported in part by the Russian Foundation for Basic Research (Grants No. 04-02-16847 and 04-0217059), the Presidential Grant for Leading Russian Science Schools (Grant No. 1604.2003.2) INTAS Grant No. 03­51­ 3784 and the Grant-In-Aid from the Ministry of Education, Science, Culture and Sport of Japan (Grants No. 14205045 and 14655119).

*URL: http://www.shg.ru
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