Abstract

The dependence of the optical responses of microcavity-type one-dimensional (1D) photonic crystals and 1D magnetophotonic crystals (1D-MPCs) on the arrangement order ratio (AOR), which is the ratio of the first and second layers’ refractive indexes of Bragg reflectors, is studied. It is demonstrated that the optical properties of two microcavity structures resulting from exchanging the order of Bragg reflector layers so that they have the same optical contrast ratios and different AORs would be different. This difference will be more noticeable in the case of microcavity type 1D-MPCs. Regarding the arrangement-dependent magneto-optical properties of the structures, we can propose the efficient Bragg reflectors with high transmittance enhanced Faraday rotation.

© 2013 Optical Society of America

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    [CrossRef]

2012 (3)

2011 (2)

T. Sun, J. Luo, P. Xu, and L. Gao, “Independently tunable transmission-type magneto-optical isolators based on multilayers containing magnetic materials,” Phys. Lett. A 375, 2185–2188 (2011).
[CrossRef]

L. Dong, H. Jiang, H. Chen, and Y. Shi, “Tunnelling-based Faraday rotation effect enhancement,” J. Phys. D 44, 145402 (2011).
[CrossRef]

2009 (1)

T. V. Murzina, I. E. Razdolski, O. A. Aktsipetrov, A. M. Grishin, and S. I. Khartsev, “Nonlinear magneto-optical effects in all-garnet magnetophotonic crystals,” J. Magn. Magn. Mater. 321, 836–839 (2009).
[CrossRef]

2008 (1)

I. L. Lyubchanskii, N. N. Dadoenkova, A. E. Zabolotin, Y. P. Lee, and Th. Rasing, “Optical bistability in one-dimensional magnetic photonic crystal with two defect layers,” J. Appl. Phys. 103, 07B321 (2008).
[CrossRef]

2007 (1)

S. I. Khartsev and A. M. Grishin, “High performance [Bi3Fe5O12/Sm3Ga5O12]m magneto-optical photonic crystals,” J. Appl. Phys. 101, 053906 (2007).
[CrossRef]

2006 (2)

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

A. G. Zhdanov, A. A. Fedyanin, O. A. Aktsipetrov, D. Kobayashi, H. Uchida, and M. Inoue, “Enhancement of Faraday rotation at photonic-band-gap edge in garnet-based magnetophotonic crystals,” J. Magn. Magn. Mater. 300, e253–e256 (2006).
[CrossRef]

2004 (1)

S. Kahl and A. M. Grishin, “Enhanced Faraday rotation in all-garnet magneto-optical photonic crystal,” Appl. Phys. Lett. 84, 1438–1440 (2004).
[CrossRef]

2003 (1)

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, 3906–3911 (2003).
[CrossRef]

2001 (1)

2000 (1)

M. J. Steel, M. Levy, and R. M. Osgood, “High transmission enhanced Faraday rotation in one-dimensional photonic crystals with defects,” IEEE Photon. Technol. Lett. 12, 1171–1173 (2000).
[CrossRef]

1999 (2)

1997 (2)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals,” Solid State Commun. 102, 165–173 (1997).
[CrossRef]

M. Inoue and T. Fujii, “A theoretical analysis of magneto-optical Faraday effect of YIG films with random multilayer structures,” J. Appl. Phys. 81, 5659–5661 (1997).
[CrossRef]

1996 (1)

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699–702 (1996).
[CrossRef]

1987 (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062(1987).
[CrossRef]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef]

1979 (1)

H. Soda, K. Iga, C. Kitahara, and Y. Suematsu, “GaInAsP/InP surface emitting injection Lasers,” Jpn. J. Appl. Phys. 18, 2329–2330 (1979).

1975 (1)

D. R. Scifres, R. D. Burnham, and W. Streifer, “Highly collimated laser beams from electrically pumped SH GaAs/GaAlAs distributed-feedback lasers,” Appl. Phys. Lett. 26, 48–50 (1975).
[CrossRef]

1964 (1)

1950 (1)

F. Abeles, “Recherches sur la propagation des ondes electro-magnetiques,” Ann. Chim. Phys. 5, 596–640 and 706–782 (1950).

1888 (1)

L. Rayleigh, “On the remarkable phenomenon of crystalline reflexion described by Prof. Stokes,” Philos. Mag. 26(160), 256–265 (1888).
[CrossRef]

1846 (1)

M. Faraday, “Experimental researches in electricity. Nineteenth Series,” Phil. Trans. R. Soc. London 136, 1–20 (1846).
[CrossRef]

Abe, M.

M. Inoue, K. Arai, T. Fujii, and M. Abe, “One-dimensional magnetophotonic crystals,” J. Appl. Phys. 85, 5768–5770 (1999).
[CrossRef]

Abeles, F.

F. Abeles, “Recherches sur la propagation des ondes electro-magnetiques,” Ann. Chim. Phys. 5, 596–640 and 706–782 (1950).

Aktsipetrov, O.

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

Aktsipetrov, O. A.

T. V. Murzina, I. E. Razdolski, O. A. Aktsipetrov, A. M. Grishin, and S. I. Khartsev, “Nonlinear magneto-optical effects in all-garnet magnetophotonic crystals,” J. Magn. Magn. Mater. 321, 836–839 (2009).
[CrossRef]

A. G. Zhdanov, A. A. Fedyanin, O. A. Aktsipetrov, D. Kobayashi, H. Uchida, and M. Inoue, “Enhancement of Faraday rotation at photonic-band-gap edge in garnet-based magnetophotonic crystals,” J. Magn. Magn. Mater. 300, e253–e256 (2006).
[CrossRef]

Arai, K.

M. Inoue, K. Arai, T. Fujii, and M. Abe, “One-dimensional magnetophotonic crystals,” J. Appl. Phys. 85, 5768–5770 (1999).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Baryshev, A.

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

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Brand, S.

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699–702 (1996).
[CrossRef]

Burnham, R. D.

D. R. Scifres, R. D. Burnham, and W. Streifer, “Highly collimated laser beams from electrically pumped SH GaAs/GaAlAs distributed-feedback lasers,” Appl. Phys. Lett. 26, 48–50 (1975).
[CrossRef]

Chen, H.

L. Dong, H. Jiang, H. Chen, and Y. Shi, “Tunnelling-based Faraday rotation effect enhancement,” J. Phys. D 44, 145402 (2011).
[CrossRef]

Dadoenkova, N. N.

I. L. Lyubchanskii, N. N. Dadoenkova, A. E. Zabolotin, Y. P. Lee, and Th. Rasing, “Optical bistability in one-dimensional magnetic photonic crystal with two defect layers,” J. Appl. Phys. 103, 07B321 (2008).
[CrossRef]

De La Rue, R. M.

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699–702 (1996).
[CrossRef]

Dmitriev, V.

Dong, L.

L. Dong, H. Jiang, H. Chen, and Y. Shi, “Tunnelling-based Faraday rotation effect enhancement,” J. Phys. D 44, 145402 (2011).
[CrossRef]

Egawa, M.

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, 3906–3911 (2003).
[CrossRef]

Fan, S.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals,” Solid State Commun. 102, 165–173 (1997).
[CrossRef]

Faraday, M.

M. Faraday, “Experimental researches in electricity. Nineteenth Series,” Phil. Trans. R. Soc. London 136, 1–20 (1846).
[CrossRef]

Fedyanin, A.

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

Fedyanin, A. A.

A. G. Zhdanov, A. A. Fedyanin, O. A. Aktsipetrov, D. Kobayashi, H. Uchida, and M. Inoue, “Enhancement of Faraday rotation at photonic-band-gap edge in garnet-based magnetophotonic crystals,” J. Magn. Magn. Mater. 300, e253–e256 (2006).
[CrossRef]

Fujii, T.

M. Inoue, K. Arai, T. Fujii, and M. Abe, “One-dimensional magnetophotonic crystals,” J. Appl. Phys. 85, 5768–5770 (1999).
[CrossRef]

M. Inoue and T. Fujii, “A theoretical analysis of magneto-optical Faraday effect of YIG films with random multilayer structures,” J. Appl. Phys. 81, 5659–5661 (1997).
[CrossRef]

Fujikawa, R.

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

Fujita, J.

Gao, L.

T. Sun, J. Luo, P. Xu, and L. Gao, “Independently tunable transmission-type magneto-optical isolators based on multilayers containing magnetic materials,” Phys. Lett. A 375, 2185–2188 (2011).
[CrossRef]

Ghadiri, H.

Ghanaatshoar, M.

Goto, T.

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

Granovsky, A.

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

Grishin, A. M.

T. V. Murzina, I. E. Razdolski, O. A. Aktsipetrov, A. M. Grishin, and S. I. Khartsev, “Nonlinear magneto-optical effects in all-garnet magnetophotonic crystals,” J. Magn. Magn. Mater. 321, 836–839 (2009).
[CrossRef]

S. I. Khartsev and A. M. Grishin, “High performance [Bi3Fe5O12/Sm3Ga5O12]m magneto-optical photonic crystals,” J. Appl. Phys. 101, 053906 (2007).
[CrossRef]

S. Kahl and A. M. Grishin, “Enhanced Faraday rotation in all-garnet magneto-optical photonic crystal,” Appl. Phys. Lett. 84, 1438–1440 (2004).
[CrossRef]

Herriott, D. R.

Iga, K.

H. Soda, K. Iga, C. Kitahara, and Y. Suematsu, “GaInAsP/InP surface emitting injection Lasers,” Jpn. J. Appl. Phys. 18, 2329–2330 (1979).

Inoue, M.

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

A. G. Zhdanov, A. A. Fedyanin, O. A. Aktsipetrov, D. Kobayashi, H. Uchida, and M. Inoue, “Enhancement of Faraday rotation at photonic-band-gap edge in garnet-based magnetophotonic crystals,” J. Magn. Magn. Mater. 300, e253–e256 (2006).
[CrossRef]

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

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, 3906–3911 (2003).
[CrossRef]

M. Inoue, K. Arai, T. Fujii, and M. Abe, “One-dimensional magnetophotonic crystals,” J. Appl. Phys. 85, 5768–5770 (1999).
[CrossRef]

M. Inoue and T. Fujii, “A theoretical analysis of magneto-optical Faraday effect of YIG films with random multilayer structures,” J. Appl. Phys. 81, 5659–5661 (1997).
[CrossRef]

Jiang, H.

L. Dong, H. Jiang, H. Chen, and Y. Shi, “Tunnelling-based Faraday rotation effect enhancement,” J. Phys. D 44, 145402 (2011).
[CrossRef]

Joannopoulos, J. D.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals,” Solid State Commun. 102, 165–173 (1997).
[CrossRef]

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef]

Kahl, S.

S. Kahl and A. M. Grishin, “Enhanced Faraday rotation in all-garnet magneto-optical photonic crystal,” Appl. Phys. Lett. 84, 1438–1440 (2004).
[CrossRef]

Kato, H.

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, 3906–3911 (2003).
[CrossRef]

Kawakatsu, M. N.

Khanikaev, A.

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

Khartsev, S. I.

T. V. Murzina, I. E. Razdolski, O. A. Aktsipetrov, A. M. Grishin, and S. I. Khartsev, “Nonlinear magneto-optical effects in all-garnet magnetophotonic crystals,” J. Magn. Magn. Mater. 321, 836–839 (2009).
[CrossRef]

S. I. Khartsev and A. M. Grishin, “High performance [Bi3Fe5O12/Sm3Ga5O12]m magneto-optical photonic crystals,” J. Appl. Phys. 101, 053906 (2007).
[CrossRef]

Kitahara, C.

H. Soda, K. Iga, C. Kitahara, and Y. Suematsu, “GaInAsP/InP surface emitting injection Lasers,” Jpn. J. Appl. Phys. 18, 2329–2330 (1979).

Kobayashi, D.

A. G. Zhdanov, A. A. Fedyanin, O. A. Aktsipetrov, D. Kobayashi, H. Uchida, and M. Inoue, “Enhancement of Faraday rotation at photonic-band-gap edge in garnet-based magnetophotonic crystals,” J. Magn. Magn. Mater. 300, e253–e256 (2006).
[CrossRef]

Krauss, T. F.

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699–702 (1996).
[CrossRef]

Lee, Y. P.

I. L. Lyubchanskii, N. N. Dadoenkova, A. E. Zabolotin, Y. P. Lee, and Th. Rasing, “Optical bistability in one-dimensional magnetic photonic crystal with two defect layers,” J. Appl. Phys. 103, 07B321 (2008).
[CrossRef]

Levy, M.

M. Levy, H. C. Yang, M. J. Steel, and J. Fujita, “Flat top response in one-dimensional magnetic photonic band gap structures with Faraday rotation enhancement,” J. Lightwave Technol. 19, 1964–1969 (2001).
[CrossRef]

M. J. Steel, M. Levy, and R. M. Osgood, “High transmission enhanced Faraday rotation in one-dimensional photonic crystals with defects,” IEEE Photon. Technol. Lett. 12, 1171–1173 (2000).
[CrossRef]

Lim, P. B.

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

Luo, J.

T. Sun, J. Luo, P. Xu, and L. Gao, “Independently tunable transmission-type magneto-optical isolators based on multilayers containing magnetic materials,” Phys. Lett. A 375, 2185–2188 (2011).
[CrossRef]

Lyubchanskii, I. L.

I. L. Lyubchanskii, N. N. Dadoenkova, A. E. Zabolotin, Y. P. Lee, and Th. Rasing, “Optical bistability in one-dimensional magnetic photonic crystal with two defect layers,” J. Appl. Phys. 103, 07B321 (2008).
[CrossRef]

Matsushita, T.

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, 3906–3911 (2003).
[CrossRef]

Murzina, T.

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

Murzina, T. V.

T. V. Murzina, I. E. Razdolski, O. A. Aktsipetrov, A. M. Grishin, and S. I. Khartsev, “Nonlinear magneto-optical effects in all-garnet magnetophotonic crystals,” J. Magn. Magn. Mater. 321, 836–839 (2009).
[CrossRef]

Nishimura, K.

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, 3906–3911 (2003).
[CrossRef]

Osgood, R. M.

M. J. Steel, M. Levy, and R. M. Osgood, “High transmission enhanced Faraday rotation in one-dimensional photonic crystals with defects,” IEEE Photon. Technol. Lett. 12, 1171–1173 (2000).
[CrossRef]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1998).

Rasing, Th.

I. L. Lyubchanskii, N. N. Dadoenkova, A. E. Zabolotin, Y. P. Lee, and Th. Rasing, “Optical bistability in one-dimensional magnetic photonic crystal with two defect layers,” J. Appl. Phys. 103, 07B321 (2008).
[CrossRef]

Rayleigh, L.

L. Rayleigh, “On the remarkable phenomenon of crystalline reflexion described by Prof. Stokes,” Philos. Mag. 26(160), 256–265 (1888).
[CrossRef]

Razdolski, I. E.

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[CrossRef]

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H. Soda, K. Iga, C. Kitahara, and Y. Suematsu, “GaInAsP/InP surface emitting injection Lasers,” Jpn. J. Appl. Phys. 18, 2329–2330 (1979).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of a microcavity structure composed of A and B dielectric Bragg reflectors and a microcavity layer D.

Fig. 2.
Fig. 2.

Transmittance spectra of 1D-PC with the (A/B)5TiO2(B/A)5 structure for (a) η=0.5, 0.6, 0.7, 0.8 and (b) η=2.0, 1.67, 1.43, 1.25. Enlarged transmittance spectra near design wavelength for mentioned η (c) and η (d).

Fig. 3.
Fig. 3.

Transmittance spectra of 1D-MPC with the (A/B)5Bi:YIG(B/A)5 structure for (a) η=0.5, 0.6, 0.7, 0.8 and (b) η=2.0, 1.67, 1.43, 1.25. Enlarged transmittance spectra near design wavelength for mentioned η (c) and η (d).

Fig. 4.
Fig. 4.

Total FR spectra of 1D-MPC with the (A/B)5Bi:YIG(B/A)5 structure for η=0.5, 0.6, 0.7, 0.8 and η=2.0, 1.67, 1.43, 1.25. The magneto-optical figure of merit Q is represented for each structure. It is assumed that an external magnetic field (7 kOe) is applied perpendicularly on the structure to provide the saturated magnetization of Bi:YIG.

Fig. 5.
Fig. 5.

Trade-off relationships between FR and transmittance for a 1D-MPC with the (A/B)5Bi:YIG(B/A)5 structure at design wavelength. Transmittance (a) and total FR (b) as a function of η. Transmittance (c) and total FR (d) as a function of η. The vertical red lines that are labeled by numbers 1–5 are related to the materials of Table 1.

Tables (1)

Tables Icon

Table 1. Proposed Materials to Use in Bragg Reflectors with Refractive Index of nMgF2=1.38, nTiO2=2.49, nSiO2=1.54, nZrO2=2.14, nAl2O3=1.75 at λ=720nm

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

ε˜D=(εxxεxy0εyxεyy000εzz).
τ(z0+L)=ϕτ(z0),
τ(z)|z=z0=[1001]eik(zz0)+C1[1001]eik(zz0)+C2[0110]eik(zz0),
τ(z)|z=z0+L=C3[1001]eik(zz0L)+C4[0110]eik(zz0L),
T=|C3|2+|C4|2,
ΘF=12tan1(2Re(χ)1|χ|2)withχ=C4C3.

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