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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 17 — Aug. 26, 2013
  • pp: 19648–19656
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Para-magneto- and electro-optic microcavities for blue wavelength modulation

Taichi Goto, Ryosuke Isogai, and M. Inoue  »View Author Affiliations


Optics Express, Vol. 21, Issue 17, pp. 19648-19656 (2013)
http://dx.doi.org/10.1364/OE.21.019648


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Abstract

We report on microcavities comprising para-magnetic garnet and electro-optic films (MPMEO) for modulation of the polarization rotation angle of light at near-UV wavelengths with a slight intensity change, with applying a low voltage. The MPMEO are composed of para-magnetic garnet and electro-optic films sandwiched between two Bragg mirrors. The microcavity states in MPMEO are split and yield both the large rotation angle and high optical efficiency. Significant enhancement and modulation by applied voltages are verified through a conventional matrix calculation approach. High optical efficiency (>90%) and large modulation (~90 degree) of the polarization rotation are proved.

© 2013 OSA

1. Introduction

The non-reciprocal rotation of polarized light is one of the unique characteristics of magnetooptical (MO) materials that cannot be observed in other material systems. Hence, the MO is widely used and studied in optical isolator [1

1. B. Stadler, K. Vaccaro, P. Yip, J. Lorenzo, L. Yi-Qun, and M. Cherif, “Integration of magneto-optical garnet films by metal-organic chemical vapor deposition,” IEEE Trans. Magn. 38(3), 1564–1567 (2002). [CrossRef]

, 2

2. T. Goto, M. C. Onbaşlı, and C. A. Ross, “Magneto-optical properties of cerium substituted yttrium iron garnet films with reduced thermal budget for monolithic photonic integrated circuits,” Opt. Express 20(27), 28507–28517 (2012). [CrossRef] [PubMed]

] or modulators [3

3. Z. Wang and S. Fan, “Optical circulators in two-dimensional magneto-optical photonic crystals,” Opt. Lett. 30(15), 1989–1991 (2005). [CrossRef] [PubMed]

, 4

4. M. Inoue, A. B. Khanikaev, and A. B. Baryshev, Nanoscale Magnetic Materials and Applications (Springer, 2009).

] for optical circuit [5

5. Y. Urino, T. Shimizu, M. Okano, N. Hatori, M. Ishizaka, T. Yamamoto, T. Baba, T. Akagawa, S. Akiyama, T. Usuki, D. Okamoto, M. Miura, M. Noguchi, J. Fujikata, D. Shimura, H. Okayama, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, E. Saito, T. Nakamura, and Y. Arakawa, “First demonstration of high density optical interconnects integrated with lasers, optical modulators, and photodetectors on single silicon substrate,” Opt. Express 19(26), B159–B165 (2011). [CrossRef] [PubMed]

], laser processing [6

6. H. Yoshida, K. Tsubakimoto, Y. Fujimoto, K. Mikami, H. Fujita, N. Miyanaga, H. Nozawa, H. Yagi, T. Yanagitani, Y. Nagata, and H. Kinoshita, “Optical properties and Faraday effect of ceramic terbium gallium garnet for a room temperature Faraday rotator,” Opt. Express 19(16), 15181–15187 (2011). [CrossRef] [PubMed]

], etc. From a macroscopic view, MO effects originate from a refractive index difference between right- and left-circularly-polarized (RCP and LCP) light beams in these materials [4

4. M. Inoue, A. B. Khanikaev, and A. B. Baryshev, Nanoscale Magnetic Materials and Applications (Springer, 2009).

]. The well-known MO material is rare-earth-substituted yttrium iron garnet (R:YIG), has a large refractive index difference (off-diagonal permittivity elements) caused by the Fe3+ ion transition in blue light and at shorter wavelengths (<450 nm) [7

7. S. Wittekoek, T. J. A. Popma, J. M. Robertson, and P. F. Bongers, “Magneto-optic spectra and the dielectric tensor elements of bismuth-substituted iron garnets at photon energies between 2.2-5.2 eV,” Phys. Rev. B 12(7), 2777–2788 (1975). [CrossRef]

]. However, their large absorption hinder their potential use in devices, so for short-wavelength modulation bulk para-magneto-optic (para-MO) materials, e.g. terbium gallium garnet (Tb3Gd5O12, TGG) or terbium aluminum garnet (Tb3Al5O12, TAG), are extensively used [6

6. H. Yoshida, K. Tsubakimoto, Y. Fujimoto, K. Mikami, H. Fujita, N. Miyanaga, H. Nozawa, H. Yagi, T. Yanagitani, Y. Nagata, and H. Kinoshita, “Optical properties and Faraday effect of ceramic terbium gallium garnet for a room temperature Faraday rotator,” Opt. Express 19(16), 15181–15187 (2011). [CrossRef] [PubMed]

, 8

8. M. Geho, T. Sekijima, and T. Fujii, “Growth of terbium aluminum garnet (Tb3Al5O12; TAG) single crystals by the hybrid laser floating zone machine,” J. Cryst. Growth 267(1-2), 188–193 (2004). [CrossRef]

] because of high transparency in spite of the large external magnetic field. These para-MO bulk are several centimeter thick to obtain sufficient polarization rotation angle for device applications. This size requirement is one of the largest issues, so any short-wavelength modulation using para-MO materials in nano or micro scale devices have not been reported so far. In addition, a high temperature risk caused by a large external magnetic field generated by an electromagnet would occur in the case where the magnetization in the para-MO material is switched.

To address these two issues, we propose the use of microcavities with MO films, so called one-dimensional magnetophotonic crystals (MPCs) [9

9. M. Inoue, R. Fujikawa, A. V. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, “Magnetophotonic crystals,” J. Phys. D 39(8), R151–R161 (2006). [CrossRef]

11

11. M. Levy and R. Li, “Polarization rotation enhancement and scattering mechanisms in waveguide magnetophotonic crystals,” Appl. Phys. Lett. 89(12), 121113 (2006). [CrossRef]

]. The microcavity modes are spectrally located inside the photonic band gaps and are associated with sharp transmission and reflection peaks in the spectra. These localized modes are strongly coupled to the magnetic constituents of the MPCs, and can enhance their linear and nonlinear MO responses because of the multiple reflections within the microcavities. Therefore, MPCs comprising para-MO materials can also enhance the MO responses; in other words, it can reduce the thickness of para-MO material. In actual, a microcavity comprising TGG was fabricated by sputtering and it showed ~50 times enhanced Verdet constant (ς = –8170 deg/T•cm) at a wavelength of 435 nm [12

12. K. Yamada, T. Goto, Y. Suzuki, H. Sato, A. Kume, S. Mito, H. Takagi, and M. Inoue, “Fabrication of magnetophotonic crystals with paramagnetic garnet films,” J. Magn. Soc. Jpn. 35(3), 199–202 (2011). [CrossRef]

].

Second, to overcome the high temperature risk caused by a large external magnetic field generated by an electromagnet, MPCs with inserted electro-optic (EO) films are considered to be effective following theoretical [13

13. T. Goto, H. Sato, H. Takagi, A. V. Baryshev, and M. Inoue, “Novel magnetophotonic crystals controlled by the electro-optic effect for non-reciprocal high-speed modulators,” J. Appl. Phys. 109(7), 07B756 (2011). [CrossRef]

] and experimental approaches [14

14. T. Goto, R. Hashimoto, R. Isogai, Y. Suzuki, R. Araki, H. Takagi, and M. Inoue, “Fabrication of Microcavity with Magneto- and Electro-Optical Film,” J. Magn. Soc. Jpn. 36(3), 197–201 (2012). [CrossRef]

]. The EO film stacked on the MO film can change its refractive index with the applied voltage, which can vary the existing mode not only inside the EO film but also inside the MO film because of the interference, resulting in a slight MO modulation with the applied voltage [15

15. Y. S. Dadoenkova, I. L. Lyubachanskii, Y. P. Lee, and T. Rasing, “Electric field controlled Faraday rotation in an electro-optic/magneto-optic bilayer,” Appl. Phys. Lett. 97(1), 011901 (2010). [CrossRef]

]. However in this case, the working wavelength is limited at the near-IR region because of the small rotation angle or the large absorption. To improve the performances, the use of the microcavity mode was proposed. The MO-EO microcavity shows high polarization angle modulation and low power consumption with a slight change in reflectivity. Such performance was achieved with the combination of non-reciprocity and spectral peak shift from the MO and EO effects [13

13. T. Goto, H. Sato, H. Takagi, A. V. Baryshev, and M. Inoue, “Novel magnetophotonic crystals controlled by the electro-optic effect for non-reciprocal high-speed modulators,” J. Appl. Phys. 109(7), 07B756 (2011). [CrossRef]

]. A microcavity mode in MPC, shown as a spectral reflection peak within the photonic band gap, is split because of the MO effect, but a polarization rotation angle spectral peak is not. This results in high reflectivity with large rotation angle at the center of the split spectral reflection peaks, i.e. at the rotation angle spectral peak. The spectral positions for the whole peaks are shifted by EO effect with the applied voltage (the refractive index of the EO layer can be controlled with the voltage applied in parallel to the incident light direction). This is the working principle of the MO-EO microcavity.

In this paper, a para-magnetic garnet was used in the MO-EO microcavity. We optimized the structures and revealed the characteristics of microcavities with para-magnetic garnet and EO materials (hereafter MPMEO) as a pixel of spatial light modulators (SLMs) [16

16. D. Dudley, W. M. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) applications,” Proc. SPIE 4985, 14–25 (2003). [CrossRef]

19

19. K. Iwasaki, H. Mochizuki, H. Umezawa, and M. Inoue, “Practical magneto-optic spatial light modulator with single magnetic domain pixels,” IEEE Trans. Magn. 44(11), 3296–3299 (2008). [CrossRef]

], Fig. 1
Fig. 1 Sketch of SLM with a microcavity comprising para-magnetic garnet and electro-optic layers (MPMEO).
, using a conventional calculation method: a 4 × 4 matrix approach [9

9. M. Inoue, R. Fujikawa, A. V. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, “Magnetophotonic crystals,” J. Phys. D 39(8), R151–R161 (2006). [CrossRef]

]. The results given here allow us to conclude that the MPMEO can modulate short-wavelength light extensively with only a small voltage.

2. Calculation method: 4 × 4 matrix approach

The optical and MO responses were calculated with a conventional 4 × 4 matrix approach. The incident light entering perpendicular to the film at z = z0 is linearly polarized along the x direction, Fig. 2
Fig. 2 System configuration used in the calculations.
, and has a plane waveform. Kato et al. described the detailed of this method in [20

20. H. Kato, T. Matsushita, A. Takayama, M. Egawa, K. Nishimura, and M. Inoue, “Theoretical analysis of optical and magneto-optical properties of one-dimensional magnetophotonic crystals,” J. Appl. Phys. 93(7), 3906–3911 (2003). [CrossRef]

]. To deal with the combination of the para-MO and EO effects, several variables were modified.

2.1 MO material

We used TGG as a MO material in the calculations because of its large Verdet constant and low absorption. The permittivity tensor ε˜of the magnetized isotropic MO material is written as:
ε˜=(ε1iε20iε2ε1000ε3),
(1)
where
ε1=ε1'+iε1''=(n2κ2)+i(2nκ),
(2)
ε2=ε2'iε2''=(nΔκ+κΔn)i(nΔn+κΔκ),
(3)
with the refractive index n, the extinction coefficient κ (the complex refractive indexN=n+iκ). The refractive index difference between RCP and LCP lights is Δn, and the extinction coefficient difference is Δκ.

The Verdet constant ς and the refractive index difference Δn have a proportional relationship, can be described like:
θ=πΔndλ0,
(4)
θ=ςdH,
(5)
with the rotation angle θ, the wavelength of the light in a vacuum λ0, the film thickness d, the external magnetic field H. As the para-MO film, we used TGG, and the optical and MO parameters were obtained from [8

8. M. Geho, T. Sekijima, and T. Fujii, “Growth of terbium aluminum garnet (Tb3Al5O12; TAG) single crystals by the hybrid laser floating zone machine,” J. Cryst. Growth 267(1-2), 188–193 (2004). [CrossRef]

, 21

21. U. Schlarb and B. Sugg, “Refractive index of terbium gallium garnet,” Phys. Status Solidi B 182, K91–K93 (1994).

, 22

22. F. Guo, J. Ru, H. Li, N. Zhuang, B. Zhao, and J. Chen, “Growth and magneto-optical properties of LiTb(MoO4)2 crystal,” Appl. Phys. B 94(3), 437–441 (2009). [CrossRef]

]. TGG magnetized along the z direction (parallel to the light beam) is a uniaxial crystal with 4 (C4) point group symmetry. At a wavelength of 405 nm, the film’s Verdet constant is ς = –213 (deg/T•cm) [8

8. M. Geho, T. Sekijima, and T. Fujii, “Growth of terbium aluminum garnet (Tb3Al5O12; TAG) single crystals by the hybrid laser floating zone machine,” J. Cryst. Growth 267(1-2), 188–193 (2004). [CrossRef]

]. Note that the direction of the positive Verdet constant is a clockwise rotation. The Δnvalue of TGG was derived from Eq. (4) and (5), and was shown in Table 1

Table 1. Material parameters used in the calculations

table-icon
View This Table
. The external magnetic field was assumed as H = 10 kOe.

2.2 EO material

We used lithium tantalate (LiTaO3, LTO) as the EO material because it has a large linear EO effect and a low extinction coefficient at the working wavelength [23

23. W. L. Bond, “Measurement of the refractive indices of several crystals,” J. Appl. Phys. 36(5), 1674–1677 (1965). [CrossRef]

, 24

24. Y. Furukawa, K. Kitamura, K. Niwa, H. Hatano, P. Bernasconi, G. Montemezzani, and P. Gunter, “Stoichiometric LiTaO3 for dynamic holography in Near UV wavelength range,” Jpn. J. Appl. Phys. 38(Part 1, No. 3B), 1816–1819 (1999). [CrossRef]

]. Unpolarized LTO is a uniaxial crystal with 3m (C3v) point group symmetry [25

25. A. Yariv, Optical Electronics in Modern Communications (Oxford University, 1997).

]. We assumed the c axis, i.e. extraordinary axis, of LTO was parallel to z axis, and LTO was polarized along the uniaxial z direction with the voltage applied along the z direction. In this study, the incident light is also parallel to the z axis, then the ordinary refractive index no of LTO in [23

23. W. L. Bond, “Measurement of the refractive indices of several crystals,” J. Appl. Phys. 36(5), 1674–1677 (1965). [CrossRef]

] was used, Table 1.

Yariv described the EO effects in [25

25. A. Yariv, Optical Electronics in Modern Communications (Oxford University, 1997).

]. The change in these coefficients by applied electric field E (where E1 = Ex, E2 = Ey, E3 = Ez) is
Δ(1n2)i=j=13rijEj.
(6)
The rij is the 6 × 3 electro-optic tensor for the EO material. The EO tensor for LTO is:
r˜=[0r22r130r22r1300r330r420r4200r2200].
(7)
As mentioned above, the refractive index in the x and y directions are the ordinary one no, and the refractive index in the z direction is the extraordinary one ne. We choose the direction of the applied filed E parallel to the z axis, so Ex = Ey = 0. Then the refractive index ellipsoid is
(1no2+r13Ez)1x2+(1no2+r13Ez)2y2+(1ne2+r33Ez)3z2=1.
(8)
In our configuration, the incident angle of the light beam is perpendicular to the surface, so we can neglect the effects from nz. The refractive index with applying field along the z direction Ez can be described as:
1nx2(=1ny2)=1no2+r13Ez.
(9)
With using a series expansion, this equation can be described as:
nx(=ny)=nono3r13Ez2,
(10)
which can be also described:
nx(=ny)=nono3r13V2dLTO,
(11)
with the applied voltage V in the z direction, and the LTO thickness dLTO. In the calculation, we used the Pockels constant r13 = 7.62 × 10−12 (m/V) at room temperature [26

26. J. L. Casson, K. T. Gahagan, D. A. Scrymgeour, R. K. Jain, J. M. Robinson, V. Gopalan, and R. K. Sander, “Electro-optic coefficients of lithium tantalate at near-infrared wavelengths,” J. Opt. Soc. Am. B 21(11), 1948–1952 (2004). [CrossRef]

]. The Verdet constant of LTO (ς = –4.4 deg/T•cm) [27

27. S. Kase and K. Ohi, “Optical absorption and interband Faraday rotation in LiTaO3 and LiNbO3,” Ferroelectrics 8(1), 419–420 (1974). [CrossRef]

] was 100 times smaller than TGG, so in this study this was not taken into account.

2.3 Structures

Figure 3
Fig. 3 Cross-sectional sketch of the MPMEO used in the calculations.
shows the model of the MPMEO used in this study. The microcavity has defect layers and two Bragg mirrors (BM) made of Ta2O5 (T) and SiO2 (S). The thicknesses of each layer in the BMs were set so that their optical thicknesses were equal to λ0/4 for the working wavelength of λ0 = 405 nm. The defect layer was composed of TGG and LTO films. Here, the optical thicknesses (physical thicknesses) of the TGG and LTO films were chosen to be 10 × λ0/2 (~1002 nm) and λ0/2 (~89 nm), respectively. The LTO film was sandwiched between two transparent indium tin oxide (ITO) electrodes. The optical parameters of T, S, and the substituted gadolinium gallium garnet [(GdCa)3(GaMgZr)5O12, SGGG] substrate were determined by ellipsometry measurements, Table 1. On the incident side of the substrate, there was an anti-reflection (AR) coating. The whole structure can be described like: AR/SGGG/(T/S)f/TGG/LTO/(S/T)r, with the repetition numbers f and r for front and rear BM. For simplicity in the present analysis, we did not take any change in the optical parameters of the transparent electrodes into account.

Two options were available for the use of the MPMEO: transmission or reflection type microcavities (hereafter T-type and R-type). To compare the two types, a figure of merit (FOM) was defined using the polarization rotation angle θ and whichever was the larger value of the light intensity I between transmissivity and reflectivity as:
FOM=|θ|×I.
(12)
Here the ellipticity of light was not included because of the fact that both transmitted and reflected light show the ellipticity of 0 at a resonant wavelength [28

28. T. Goto and M. Inoue, “Magnetophotonic crystal comprising electro-optical layer for controlling helicity of light,” J. Appl. Phys. 111(7), 07A913 (2012). [CrossRef]

].

3. Transmission and reflection types

The calculation results, with a matrix approach written in C++ language showed the transmission (or reflection), rotation angle, and FOM spectra. Figure 4
Fig. 4 (a) Transmissivity, polarization rotation angle and FOM of T-type microcavities versus the repetition number f ( = r) of BMs. (b) Reflectivity, polarization rotation angle and FOM of R-type microcavities versus the repetition number f of the front BMs.
shows the results of the T-type and R-type MPMEO as functions of the repetition numbers f of the BMs. For T-type, f equals r, but for R-type, r is set at 20 so that all of the light can be reflected back in the incident direction. The absolute value of rotation angle is increased as the increasing of BM repetition numbers. Although the FOM of the T-type tends to decrease, the FOM of the R-type tends to increase as the repetition numbers increase. This tendency can be understood when we look at the spectra in the vicinity of the localized wavelengths, Fig. 5
Fig. 5 Transmission and polarization rotation angle of spectra in T-type microcavities, AR/SGGG/(T/S)f/TGG/LTO/(S/T)f, where f = 8–10. (b) Reflectivity and polarization rotation angle of R-type microcavity, AR/SGGG/(T/S)f/TGG/LTO/(S/T)20, where f = 8–10.
. The split transmission and reflection spectral peaks produce decreasing and increasing light intensities, respectively. This is because of the refractive index difference between the RCP and LCP light beams [13

13. T. Goto, H. Sato, H. Takagi, A. V. Baryshev, and M. Inoue, “Novel magnetophotonic crystals controlled by the electro-optic effect for non-reciprocal high-speed modulators,” J. Appl. Phys. 109(7), 07B756 (2011). [CrossRef]

]. The increased Q factor of the microcavities makes the peak separation clear. Overall, the R-type was found to be better than the T-type, and f = 9 is the closest condition to obtain the 90 degree rotation angle, which is required in modulators. R-type’s performances were similar (except the resonant spectral position) in case where the incidence of light was oblique from 90 (normal incidence) to 50 degree.

4. Defects thicknesses

With regard to further optimization, the contribution of TGG and LTO thicknesses in R-type MPMEO were comprehensively examined, Fig. 6
Fig. 6 Reflectivity (a) and polarization rotation angle (b) dependences on the TGG and LTO thicknesses in the microcavities with AR/SGGG/(T/S)9/TGG/LTO/(S/T)20 structure.
. We cannot see a large contribution from the LTO thickness. That layer thickness was thus determined to have a minimum value of 89 nm, which equals an optical thickness of λ0/2, to decrease the required voltage for its electronic polarization.

When the LTO thickness was fixed at 89 nm, the reflectivity and rotation angle dependence on the TGG thickness were then examined and are shown in Fig. 7
Fig. 7 Dependence of reflectivity and rotation angle on the TGG thickness in the microcavities.
. The reflectivity does not changed with the TGG thickness, so we can optimize that only with the rotation angle magnitude. For instance, a SLM requires a 90 degree rotation angle to produce its maximum contrast. Hence, the optical thickness (physical thickness) of the TGG layer was set at 8 × λ0/2 (802 nm), which gives a rotation angle of 93 degree.

5. Responses for the applied voltage

We finally determined the entire structure of the MPMEO, AR/SGGG/(T/S)9/TGG/LTO/(S/T)20 with optical thicknesses (physical thicknesses) of 8 × λ0/2 (~802 nm) and λ0/2 (~89 nm) for TGG and LTO, respectively. When a small voltage is applied to the LTO, the alternating optical path length in the microcavity caused by the EO effect can shift the localized peak to a shorter wavelength. In Fig. 8
Fig. 8 Change of reflectivity and polarization rotation angle with the applied voltage to the LTO film in the microcavity with ~802 nm thick TGG and ~89 nm thick LTO.
, one can see polarization rotation angle modulation versus a low applied voltage, with negligibly small change of reflectivity.

6. Conclusion

We have reported that MPMEO comprising TGG and LTO achieve high-performance modulation of blue and shorter wavelength light (<450 nm). It should be noted that we do not need to change the direction of magnetization, but can control the polarization rotation angle using a small voltage. The performance shown here cannot be accomplished by using any other system.

These calculated results open the availability of paramagnetic garnets in micro or nano scale devices as potential polarization modulators for blue and near-UV light beams.

Acknowledgments

TG acknowledges the Japan Society for the Promotion of Science (JSPS) Postdoctoral Fellowships for Research Abroad.

References and links

1.

B. Stadler, K. Vaccaro, P. Yip, J. Lorenzo, L. Yi-Qun, and M. Cherif, “Integration of magneto-optical garnet films by metal-organic chemical vapor deposition,” IEEE Trans. Magn. 38(3), 1564–1567 (2002). [CrossRef]

2.

T. Goto, M. C. Onbaşlı, and C. A. Ross, “Magneto-optical properties of cerium substituted yttrium iron garnet films with reduced thermal budget for monolithic photonic integrated circuits,” Opt. Express 20(27), 28507–28517 (2012). [CrossRef] [PubMed]

3.

Z. Wang and S. Fan, “Optical circulators in two-dimensional magneto-optical photonic crystals,” Opt. Lett. 30(15), 1989–1991 (2005). [CrossRef] [PubMed]

4.

M. Inoue, A. B. Khanikaev, and A. B. Baryshev, Nanoscale Magnetic Materials and Applications (Springer, 2009).

5.

Y. Urino, T. Shimizu, M. Okano, N. Hatori, M. Ishizaka, T. Yamamoto, T. Baba, T. Akagawa, S. Akiyama, T. Usuki, D. Okamoto, M. Miura, M. Noguchi, J. Fujikata, D. Shimura, H. Okayama, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, E. Saito, T. Nakamura, and Y. Arakawa, “First demonstration of high density optical interconnects integrated with lasers, optical modulators, and photodetectors on single silicon substrate,” Opt. Express 19(26), B159–B165 (2011). [CrossRef] [PubMed]

6.

H. Yoshida, K. Tsubakimoto, Y. Fujimoto, K. Mikami, H. Fujita, N. Miyanaga, H. Nozawa, H. Yagi, T. Yanagitani, Y. Nagata, and H. Kinoshita, “Optical properties and Faraday effect of ceramic terbium gallium garnet for a room temperature Faraday rotator,” Opt. Express 19(16), 15181–15187 (2011). [CrossRef] [PubMed]

7.

S. Wittekoek, T. J. A. Popma, J. M. Robertson, and P. F. Bongers, “Magneto-optic spectra and the dielectric tensor elements of bismuth-substituted iron garnets at photon energies between 2.2-5.2 eV,” Phys. Rev. B 12(7), 2777–2788 (1975). [CrossRef]

8.

M. Geho, T. Sekijima, and T. Fujii, “Growth of terbium aluminum garnet (Tb3Al5O12; TAG) single crystals by the hybrid laser floating zone machine,” J. Cryst. Growth 267(1-2), 188–193 (2004). [CrossRef]

9.

M. Inoue, R. Fujikawa, A. V. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, “Magnetophotonic crystals,” J. Phys. D 39(8), R151–R161 (2006). [CrossRef]

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A. M. Grishin and S. I. Khartsev, “All-garnet magneto-optical photonic crystals,” J. Magn. Soc. Jpn. 32(2_2), 140–145 (2008). [CrossRef]

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M. Levy and R. Li, “Polarization rotation enhancement and scattering mechanisms in waveguide magnetophotonic crystals,” Appl. Phys. Lett. 89(12), 121113 (2006). [CrossRef]

12.

K. Yamada, T. Goto, Y. Suzuki, H. Sato, A. Kume, S. Mito, H. Takagi, and M. Inoue, “Fabrication of magnetophotonic crystals with paramagnetic garnet films,” J. Magn. Soc. Jpn. 35(3), 199–202 (2011). [CrossRef]

13.

T. Goto, H. Sato, H. Takagi, A. V. Baryshev, and M. Inoue, “Novel magnetophotonic crystals controlled by the electro-optic effect for non-reciprocal high-speed modulators,” J. Appl. Phys. 109(7), 07B756 (2011). [CrossRef]

14.

T. Goto, R. Hashimoto, R. Isogai, Y. Suzuki, R. Araki, H. Takagi, and M. Inoue, “Fabrication of Microcavity with Magneto- and Electro-Optical Film,” J. Magn. Soc. Jpn. 36(3), 197–201 (2012). [CrossRef]

15.

Y. S. Dadoenkova, I. L. Lyubachanskii, Y. P. Lee, and T. Rasing, “Electric field controlled Faraday rotation in an electro-optic/magneto-optic bilayer,” Appl. Phys. Lett. 97(1), 011901 (2010). [CrossRef]

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N. Itoh, Y. Kawabata, M. Koden, S. Miyoshi, T. Numao, M. Shigeta, M. Sugino, M. J. Bradshaw, C. V. Brown, A. Graham, S. D. Haslam, J. R. Hughes, J. C. Jones, D. G. McDonnell, A. J. Slaney, P. Bonnett, P. A. Gass, E. P. Rayens, and D. Ulrich, “17-in. video-rate full-color FLCD,” Journal of ITE 53(8), 1136–1141 (1999). [CrossRef]

18.

C. Greenlee, J. Luo, K. Leedy, B. Bayraktaroglu, R. A. Norwood, M. Fallahi, A. K. Y. Jen, and N. Peyghambarian, “Electro-optic polymer spatial light modulator based on a Fabry-Perot interferometer configuration,” Opt. Express 19(13), 12750–12758 (2011). [CrossRef] [PubMed]

19.

K. Iwasaki, H. Mochizuki, H. Umezawa, and M. Inoue, “Practical magneto-optic spatial light modulator with single magnetic domain pixels,” IEEE Trans. Magn. 44(11), 3296–3299 (2008). [CrossRef]

20.

H. Kato, T. Matsushita, A. Takayama, M. Egawa, K. Nishimura, and M. Inoue, “Theoretical analysis of optical and magneto-optical properties of one-dimensional magnetophotonic crystals,” J. Appl. Phys. 93(7), 3906–3911 (2003). [CrossRef]

21.

U. Schlarb and B. Sugg, “Refractive index of terbium gallium garnet,” Phys. Status Solidi B 182, K91–K93 (1994).

22.

F. Guo, J. Ru, H. Li, N. Zhuang, B. Zhao, and J. Chen, “Growth and magneto-optical properties of LiTb(MoO4)2 crystal,” Appl. Phys. B 94(3), 437–441 (2009). [CrossRef]

23.

W. L. Bond, “Measurement of the refractive indices of several crystals,” J. Appl. Phys. 36(5), 1674–1677 (1965). [CrossRef]

24.

Y. Furukawa, K. Kitamura, K. Niwa, H. Hatano, P. Bernasconi, G. Montemezzani, and P. Gunter, “Stoichiometric LiTaO3 for dynamic holography in Near UV wavelength range,” Jpn. J. Appl. Phys. 38(Part 1, No. 3B), 1816–1819 (1999). [CrossRef]

25.

A. Yariv, Optical Electronics in Modern Communications (Oxford University, 1997).

26.

J. L. Casson, K. T. Gahagan, D. A. Scrymgeour, R. K. Jain, J. M. Robinson, V. Gopalan, and R. K. Sander, “Electro-optic coefficients of lithium tantalate at near-infrared wavelengths,” J. Opt. Soc. Am. B 21(11), 1948–1952 (2004). [CrossRef]

27.

S. Kase and K. Ohi, “Optical absorption and interband Faraday rotation in LiTaO3 and LiNbO3,” Ferroelectrics 8(1), 419–420 (1974). [CrossRef]

28.

T. Goto and M. Inoue, “Magnetophotonic crystal comprising electro-optical layer for controlling helicity of light,” J. Appl. Phys. 111(7), 07A913 (2012). [CrossRef]

OCIS Codes
(160.3820) Materials : Magneto-optical materials
(070.6120) Fourier optics and signal processing : Spatial light modulators

ToC Category:
Optical Devices

History
Original Manuscript: April 22, 2013
Revised Manuscript: July 5, 2013
Manuscript Accepted: July 7, 2013
Published: August 14, 2013

Citation
Taichi Goto, Ryosuke Isogai, and M. Inoue, "Para-magneto- and electro-optic microcavities for blue wavelength modulation," Opt. Express 21, 19648-19656 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-17-19648


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References

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  13. T. Goto, H. Sato, H. Takagi, A. V. Baryshev, and M. Inoue, “Novel magnetophotonic crystals controlled by the electro-optic effect for non-reciprocal high-speed modulators,” J. Appl. Phys.109(7), 07B756 (2011). [CrossRef]
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  15. Y. S. Dadoenkova, I. L. Lyubachanskii, Y. P. Lee, and T. Rasing, “Electric field controlled Faraday rotation in an electro-optic/magneto-optic bilayer,” Appl. Phys. Lett.97(1), 011901 (2010). [CrossRef]
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  18. C. Greenlee, J. Luo, K. Leedy, B. Bayraktaroglu, R. A. Norwood, M. Fallahi, A. K. Y. Jen, and N. Peyghambarian, “Electro-optic polymer spatial light modulator based on a Fabry-Perot interferometer configuration,” Opt. Express19(13), 12750–12758 (2011). [CrossRef] [PubMed]
  19. K. Iwasaki, H. Mochizuki, H. Umezawa, and M. Inoue, “Practical magneto-optic spatial light modulator with single magnetic domain pixels,” IEEE Trans. Magn.44(11), 3296–3299 (2008). [CrossRef]
  20. H. Kato, T. Matsushita, A. Takayama, M. Egawa, K. Nishimura, and M. Inoue, “Theoretical analysis of optical and magneto-optical properties of one-dimensional magnetophotonic crystals,” J. Appl. Phys.93(7), 3906–3911 (2003). [CrossRef]
  21. U. Schlarb and B. Sugg, “Refractive index of terbium gallium garnet,” Phys. Status Solidi B182, K91–K93 (1994).
  22. F. Guo, J. Ru, H. Li, N. Zhuang, B. Zhao, and J. Chen, “Growth and magneto-optical properties of LiTb(MoO4)2 crystal,” Appl. Phys. B94(3), 437–441 (2009). [CrossRef]
  23. W. L. Bond, “Measurement of the refractive indices of several crystals,” J. Appl. Phys.36(5), 1674–1677 (1965). [CrossRef]
  24. Y. Furukawa, K. Kitamura, K. Niwa, H. Hatano, P. Bernasconi, G. Montemezzani, and P. Gunter, “Stoichiometric LiTaO3 for dynamic holography in Near UV wavelength range,” Jpn. J. Appl. Phys.38(Part 1, No. 3B), 1816–1819 (1999). [CrossRef]
  25. A. Yariv, Optical Electronics in Modern Communications (Oxford University, 1997).
  26. J. L. Casson, K. T. Gahagan, D. A. Scrymgeour, R. K. Jain, J. M. Robinson, V. Gopalan, and R. K. Sander, “Electro-optic coefficients of lithium tantalate at near-infrared wavelengths,” J. Opt. Soc. Am. B21(11), 1948–1952 (2004). [CrossRef]
  27. S. Kase and K. Ohi, “Optical absorption and interband Faraday rotation in LiTaO3 and LiNbO3,” Ferroelectrics8(1), 419–420 (1974). [CrossRef]
  28. T. Goto and M. Inoue, “Magnetophotonic crystal comprising electro-optical layer for controlling helicity of light,” J. Appl. Phys.111(7), 07A913 (2012). [CrossRef]

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