Abstract

A method based on Yeh’s rigorous 4×4 matrix algebra and a fast perturbation-theory-based method are proposed for modeling and optimization of an integrated magneto-optical (MO) waveguide isolator. The transverse MO Kerr effect in ferromagnetic Co90Fe10 is used to design the integrated isolator. Waveguide losses introduced by absorption in the MO metallic film are compensated for by optical gain in an InP-based semiconductor optical amplifier with a tensile strained multiple-quantum-well (MQW) active region. The desired device isolation, which originates from the nonreciprocity of the transverse MO effect, is obtained by operation of the device under appropriate current injection, leading to zero modal net gain in the forward direction while the device remains lossy in the backward direction. In the approach based on Yeh’s matrix formalism, phenomena such as the MO effects described by anisotropic permittivity tensors, waveguide losses in absorbing layers, and optical gain in the active layer are explicitly included. Numerical aspects of the resonant condition solution for waveguide modes are discussed. In the perturbation theory method, the MO nonreciprocal waveguide effects are calculated in a first-order scheme. The general models are applied in an example of a realistic InP-based MQW isolator with a Co90Fe10 MO layer, indicating that practical isolation ratios are achievable within reasonable levels of necessary material gain. Rigorous and perturbation models are compared, and good agreement is obtained. This result indicates that first-order perturbation theory modeling of integrated magneto-optics is accurate enough, even for devices that employ MO materials with relatively strong Voigt parameters.

© 2005 Optical Society of America

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2004

K. Postava, J. Pistora, and T. Yamaguchi, "Magneto-optic vector magnetometry for sensor applications," Sens. Actuators, A 110, 242-246 (2004).
[CrossRef]

2003

2002

M. Muñoz, T. M. Holden, F. H. Pollak, M. Kahn, D. Ritter, L. Kronik, and G. M. Cohen, "Optical constants of In0.53Ga0.47As/InP: experiment and modeling," J. Appl. Phys. 92, 5878-5885 (2002).
[CrossRef]

K. Postava, T. Yamaguchi, and R. Kantor, "Matrix description of coherent and incoherent light reflection and transmission by anisotropic multilayer structures," Appl. Opt. 41, 2521-2531 (2002).
[CrossRef] [PubMed]

H. Yokoi, T. Mizumoto, S. Kuroda, T. Ohtsuka, and Y. Nakano, "Elimination of a back-reflected TE mode in a TM-mode optical isolator with Mach-Zehnder interferometer," Appl. Opt. 41, 7045-7051 (2002).
[CrossRef] [PubMed]

T. Izuhara, J. Fujita, M. Levy, and R. M. Osgood, Jr., "Integration of magnetooptical waveguides onto a III-V semiconductor surface," IEEE Photonics Technol. Lett. 14, 167-169 (2002).
[CrossRef]

H. Shimizu and M. Tanaka, "Design of semiconductor-waveguide-type optical isolators using the nonreciprocal loss/gain in the magneto-optical waveguides having MnAs nanoclusters," Appl. Phys. Lett. 81, 5246-5248 (2002).
[CrossRef]

M. Levy, "The on-chip integration of magnetooptic waveguide isolators," IEEE J. Sel. Top. Quantum Electron. 8, 1300-1306 (2002).
[CrossRef]

2001

L. Wilkens, D. Träger, H. Dötsch, A. F. Popkov, and A. M. Alekseev, "Nonreciprocal phase shift of TE modes induced by a compensation wall in a magneto-optic rib waveguide," Appl. Phys. Lett. 79, 4292-4294 (2001).
[CrossRef]

O. Zhuromskyy, H. Dötsch, M. Lohmeyer, L. Wilkens, and P. Hertel, "Magnetooptical waveguide with polarization-independent nonreciprocal phaseshift," J. Lightwave Technol. 19, 214-221 (2001).
[CrossRef]

2000

H. Yokoi, T. Mizumoto, N. S. N. Futakuchi, and Y. Nakano, "Demonstration of an optical isolator with a semiconductor guiding layer that was obtained by use of a nonreciprocal phase shift," Appl. Opt. 39, 6158-6164 (2000).
[CrossRef]

J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dötsch, "Waveguide optical isolator based on Mach-Zehnder interferometer," Appl. Phys. Lett. 76, 2158-2160 (2000).
[CrossRef]

1999

K. Postava, J. Pistora, and S. Visnovský, "Magnetooptical effects in ultrathin structures at transversal magnetization," Czech. J. Phys., Sect. B 49, 1185-1204 (1999).
[CrossRef]

J. Pistora, K. Postava, and R. Sebesta, "Optical guided modes in sandwiches with ultrathin metallic films," J. Magn. Magn. Mater. 198-199, 683-685 (1999).
[CrossRef]

H. Yokoi, T. Mizumoto, M. Shimizu, T. Waniishi, N. Futakuchi, N. Kaida, and Y. Nakano, "Analysis of GaInAsP surfaces by contact-angle measurement for wafer direct bonding of garnet crystals," Jpn. J. Appl. Phys. 38, 4780-4783 (1999).
[CrossRef]

W. Zaets and K. Ando, "Optical waveguide isolator based on nonreciprocal loss/gain amplifier covered by ferromagnetic layer," IEEE Photonics Technol. Lett. 11, 1012-1014 (1999).
[CrossRef]

1998

T. Shintaku, "Integrated optical isolator based on efficient nonreciprocal radiation mode conversion," Appl. Phys. Lett. 73, 1946-1948 (1998).
[CrossRef]

A. F. Popkov, M. Fehndrich, M. Lohmeyer, and H. Dötsch, "Nonreciprocal TE-mode phase shift by domain walls in magnetooptic rib waveguides," Appl. Phys. Lett. 72, 2508-2510 (1998).
[CrossRef]

1997

T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, "Confinement factors and gain in optical amplifiers," IEEE J. Quantum Electron. 33, 1763-1766 (1997).
[CrossRef]

1994

M. Levy, R. Scarmozzino, R. M. Osgood, Jr., R. Wolfe, F. J. Cadieu, H. Hedge, C. J. Gutierrez, and G. A. Prinz, "Permanent magnet film magneto-optic waveguide isolator," J. Appl. Phys. 75, 6286-6288 (1994).
[CrossRef]

E. P. O'Reilly and A. R. Adams, "Band-structure engineering in strained semiconductor lasers," IEEE J. Quantum Electron. 30, 366-379 (1994).
[CrossRef]

1991

S. Visnovský, "Optics of magnetic multilayers," Czech. J. Phys., Sect. B 41, 663-694 (1991).
[CrossRef]

1990

M. Mansuripur, "Analysis of multilayer thin-film structures containing magneto-optic and anisotropic media at oblique incidence using 2×2 matrices," J. Appl. Phys. 67, 6466-6475 (1990).
[CrossRef]

J. Lafait, T. Yamaguchi, J. M. Frigerio, A. Bichri, and K. Driss-Khodja, "Effective medium equivalent to a symmetric multilayer at oblique incidence," Appl. Opt. 29, 2460-2465 (1990).
[CrossRef] [PubMed]

1986

S. Visnovský, "Magneto-optical permittivity tensor in crystals," Czech. J. Phys., Sect. B 36, 1424-1433 (1986).
[CrossRef]

S. Visnovský, "Magneto-optical ellipsometry," Czech. J. Phys., Sect. B 36, 625-650 (1986).
[CrossRef]

1980

P. Yeh, "Optics of anisotropic layered media: a new 4×4 matrix algebra," Surf. Sci. 96, 41-53 (1980).
[CrossRef]

1972

1950

F. Abeles, "Recherches sur la propagation des ondes electromagnetiques sinusoidales dans les milieux stratifies: application aux couches minces," Ann. Phys. 5, 596-640 (1950).

Abeles, F.

F. Abeles, "Recherches sur la propagation des ondes electromagnetiques sinusoidales dans les milieux stratifies: application aux couches minces," Ann. Phys. 5, 596-640 (1950).

Adams, A. R.

E. P. O'Reilly and A. R. Adams, "Band-structure engineering in strained semiconductor lasers," IEEE J. Quantum Electron. 30, 366-379 (1994).
[CrossRef]

Alekseev, A. M.

L. Wilkens, D. Träger, H. Dötsch, A. F. Popkov, and A. M. Alekseev, "Nonreciprocal phase shift of TE modes induced by a compensation wall in a magneto-optic rib waveguide," Appl. Phys. Lett. 79, 4292-4294 (2001).
[CrossRef]

Ando, K.

W. Zaets and K. Ando, "Optical waveguide isolator based on nonreciprocal loss/gain amplifier covered by ferromagnetic layer," IEEE Photonics Technol. Lett. 11, 1012-1014 (1999).
[CrossRef]

Berreman, D. W.

Bichri, A.

Blok, H.

T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, "Confinement factors and gain in optical amplifiers," IEEE J. Quantum Electron. 33, 1763-1766 (1997).
[CrossRef]

Cadieu, F. J.

M. Levy, R. Scarmozzino, R. M. Osgood, Jr., R. Wolfe, F. J. Cadieu, H. Hedge, C. J. Gutierrez, and G. A. Prinz, "Permanent magnet film magneto-optic waveguide isolator," J. Appl. Phys. 75, 6286-6288 (1994).
[CrossRef]

Cohen, G. M.

M. Muñoz, T. M. Holden, F. H. Pollak, M. Kahn, D. Ritter, L. Kronik, and G. M. Cohen, "Optical constants of In0.53Ga0.47As/InP: experiment and modeling," J. Appl. Phys. 92, 5878-5885 (2002).
[CrossRef]

Demeulenaere, B.

T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, "Confinement factors and gain in optical amplifiers," IEEE J. Quantum Electron. 33, 1763-1766 (1997).
[CrossRef]

Dötsch, H.

L. Wilkens, D. Träger, H. Dötsch, A. F. Popkov, and A. M. Alekseev, "Nonreciprocal phase shift of TE modes induced by a compensation wall in a magneto-optic rib waveguide," Appl. Phys. Lett. 79, 4292-4294 (2001).
[CrossRef]

O. Zhuromskyy, H. Dötsch, M. Lohmeyer, L. Wilkens, and P. Hertel, "Magnetooptical waveguide with polarization-independent nonreciprocal phaseshift," J. Lightwave Technol. 19, 214-221 (2001).
[CrossRef]

J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dötsch, "Waveguide optical isolator based on Mach-Zehnder interferometer," Appl. Phys. Lett. 76, 2158-2160 (2000).
[CrossRef]

A. F. Popkov, M. Fehndrich, M. Lohmeyer, and H. Dötsch, "Nonreciprocal TE-mode phase shift by domain walls in magnetooptic rib waveguides," Appl. Phys. Lett. 72, 2508-2510 (1998).
[CrossRef]

Driss-Khodja, K.

Fehndrich, M.

A. F. Popkov, M. Fehndrich, M. Lohmeyer, and H. Dötsch, "Nonreciprocal TE-mode phase shift by domain walls in magnetooptic rib waveguides," Appl. Phys. Lett. 72, 2508-2510 (1998).
[CrossRef]

Frigerio, J. M.

Fujita, J.

T. Izuhara, J. Fujita, M. Levy, and R. M. Osgood, Jr., "Integration of magnetooptical waveguides onto a III-V semiconductor surface," IEEE Photonics Technol. Lett. 14, 167-169 (2002).
[CrossRef]

J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dötsch, "Waveguide optical isolator based on Mach-Zehnder interferometer," Appl. Phys. Lett. 76, 2158-2160 (2000).
[CrossRef]

Futakuchi, N.

H. Yokoi, T. Mizumoto, M. Shimizu, T. Waniishi, N. Futakuchi, N. Kaida, and Y. Nakano, "Analysis of GaInAsP surfaces by contact-angle measurement for wafer direct bonding of garnet crystals," Jpn. J. Appl. Phys. 38, 4780-4783 (1999).
[CrossRef]

Futakuchi, N. S. N.

Gutierrez, C. J.

M. Levy, R. Scarmozzino, R. M. Osgood, Jr., R. Wolfe, F. J. Cadieu, H. Hedge, C. J. Gutierrez, and G. A. Prinz, "Permanent magnet film magneto-optic waveguide isolator," J. Appl. Phys. 75, 6286-6288 (1994).
[CrossRef]

Hedge, H.

M. Levy, R. Scarmozzino, R. M. Osgood, Jr., R. Wolfe, F. J. Cadieu, H. Hedge, C. J. Gutierrez, and G. A. Prinz, "Permanent magnet film magneto-optic waveguide isolator," J. Appl. Phys. 75, 6286-6288 (1994).
[CrossRef]

Hertel, P.

Holden, T. M.

M. Muñoz, T. M. Holden, F. H. Pollak, M. Kahn, D. Ritter, L. Kronik, and G. M. Cohen, "Optical constants of In0.53Ga0.47As/InP: experiment and modeling," J. Appl. Phys. 92, 5878-5885 (2002).
[CrossRef]

Izuhara, T.

T. Izuhara, J. Fujita, M. Levy, and R. M. Osgood, Jr., "Integration of magnetooptical waveguides onto a III-V semiconductor surface," IEEE Photonics Technol. Lett. 14, 167-169 (2002).
[CrossRef]

Kahn, M.

M. Muñoz, T. M. Holden, F. H. Pollak, M. Kahn, D. Ritter, L. Kronik, and G. M. Cohen, "Optical constants of In0.53Ga0.47As/InP: experiment and modeling," J. Appl. Phys. 92, 5878-5885 (2002).
[CrossRef]

Kaida, N.

H. Yokoi, T. Mizumoto, M. Shimizu, T. Waniishi, N. Futakuchi, N. Kaida, and Y. Nakano, "Analysis of GaInAsP surfaces by contact-angle measurement for wafer direct bonding of garnet crystals," Jpn. J. Appl. Phys. 38, 4780-4783 (1999).
[CrossRef]

Kantor, R.

Kronik, L.

M. Muñoz, T. M. Holden, F. H. Pollak, M. Kahn, D. Ritter, L. Kronik, and G. M. Cohen, "Optical constants of In0.53Ga0.47As/InP: experiment and modeling," J. Appl. Phys. 92, 5878-5885 (2002).
[CrossRef]

Kuroda, S.

Lafait, J.

Lenstra, D.

T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, "Confinement factors and gain in optical amplifiers," IEEE J. Quantum Electron. 33, 1763-1766 (1997).
[CrossRef]

Levy, M.

M. Levy, "The on-chip integration of magnetooptic waveguide isolators," IEEE J. Sel. Top. Quantum Electron. 8, 1300-1306 (2002).
[CrossRef]

T. Izuhara, J. Fujita, M. Levy, and R. M. Osgood, Jr., "Integration of magnetooptical waveguides onto a III-V semiconductor surface," IEEE Photonics Technol. Lett. 14, 167-169 (2002).
[CrossRef]

J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dötsch, "Waveguide optical isolator based on Mach-Zehnder interferometer," Appl. Phys. Lett. 76, 2158-2160 (2000).
[CrossRef]

M. Levy, R. Scarmozzino, R. M. Osgood, Jr., R. Wolfe, F. J. Cadieu, H. Hedge, C. J. Gutierrez, and G. A. Prinz, "Permanent magnet film magneto-optic waveguide isolator," J. Appl. Phys. 75, 6286-6288 (1994).
[CrossRef]

Lohmeyer, M.

O. Zhuromskyy, H. Dötsch, M. Lohmeyer, L. Wilkens, and P. Hertel, "Magnetooptical waveguide with polarization-independent nonreciprocal phaseshift," J. Lightwave Technol. 19, 214-221 (2001).
[CrossRef]

A. F. Popkov, M. Fehndrich, M. Lohmeyer, and H. Dötsch, "Nonreciprocal TE-mode phase shift by domain walls in magnetooptic rib waveguides," Appl. Phys. Lett. 72, 2508-2510 (1998).
[CrossRef]

Mansuripur, M.

M. Mansuripur, "Analysis of multilayer thin-film structures containing magneto-optic and anisotropic media at oblique incidence using 2×2 matrices," J. Appl. Phys. 67, 6466-6475 (1990).
[CrossRef]

Mizumoto, T.

Muñoz, M.

M. Muñoz, T. M. Holden, F. H. Pollak, M. Kahn, D. Ritter, L. Kronik, and G. M. Cohen, "Optical constants of In0.53Ga0.47As/InP: experiment and modeling," J. Appl. Phys. 92, 5878-5885 (2002).
[CrossRef]

Nakano, Y.

Ohtsuka, T.

O'Reilly , E. P.

E. P. O'Reilly and A. R. Adams, "Band-structure engineering in strained semiconductor lasers," IEEE J. Quantum Electron. 30, 366-379 (1994).
[CrossRef]

Osgood, R. M.

T. Izuhara, J. Fujita, M. Levy, and R. M. Osgood, Jr., "Integration of magnetooptical waveguides onto a III-V semiconductor surface," IEEE Photonics Technol. Lett. 14, 167-169 (2002).
[CrossRef]

J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dötsch, "Waveguide optical isolator based on Mach-Zehnder interferometer," Appl. Phys. Lett. 76, 2158-2160 (2000).
[CrossRef]

M. Levy, R. Scarmozzino, R. M. Osgood, Jr., R. Wolfe, F. J. Cadieu, H. Hedge, C. J. Gutierrez, and G. A. Prinz, "Permanent magnet film magneto-optic waveguide isolator," J. Appl. Phys. 75, 6286-6288 (1994).
[CrossRef]

Pistora, J.

K. Postava, J. Pistora, and T. Yamaguchi, "Magneto-optic vector magnetometry for sensor applications," Sens. Actuators, A 110, 242-246 (2004).
[CrossRef]

K. Postava, J. Pistora, and S. Visnovský, "Magnetooptical effects in ultrathin structures at transversal magnetization," Czech. J. Phys., Sect. B 49, 1185-1204 (1999).
[CrossRef]

J. Pistora, K. Postava, and R. Sebesta, "Optical guided modes in sandwiches with ultrathin metallic films," J. Magn. Magn. Mater. 198-199, 683-685 (1999).
[CrossRef]

Pollak, F. H.

M. Muñoz, T. M. Holden, F. H. Pollak, M. Kahn, D. Ritter, L. Kronik, and G. M. Cohen, "Optical constants of In0.53Ga0.47As/InP: experiment and modeling," J. Appl. Phys. 92, 5878-5885 (2002).
[CrossRef]

Popkov, A. F.

L. Wilkens, D. Träger, H. Dötsch, A. F. Popkov, and A. M. Alekseev, "Nonreciprocal phase shift of TE modes induced by a compensation wall in a magneto-optic rib waveguide," Appl. Phys. Lett. 79, 4292-4294 (2001).
[CrossRef]

A. F. Popkov, M. Fehndrich, M. Lohmeyer, and H. Dötsch, "Nonreciprocal TE-mode phase shift by domain walls in magnetooptic rib waveguides," Appl. Phys. Lett. 72, 2508-2510 (1998).
[CrossRef]

Postava, K.

K. Postava, J. Pistora, and T. Yamaguchi, "Magneto-optic vector magnetometry for sensor applications," Sens. Actuators, A 110, 242-246 (2004).
[CrossRef]

K. Postava, T. Yamaguchi, and R. Kantor, "Matrix description of coherent and incoherent light reflection and transmission by anisotropic multilayer structures," Appl. Opt. 41, 2521-2531 (2002).
[CrossRef] [PubMed]

K. Postava, J. Pistora, and S. Visnovský, "Magnetooptical effects in ultrathin structures at transversal magnetization," Czech. J. Phys., Sect. B 49, 1185-1204 (1999).
[CrossRef]

J. Pistora, K. Postava, and R. Sebesta, "Optical guided modes in sandwiches with ultrathin metallic films," J. Magn. Magn. Mater. 198-199, 683-685 (1999).
[CrossRef]

Prinz, G. A.

M. Levy, R. Scarmozzino, R. M. Osgood, Jr., R. Wolfe, F. J. Cadieu, H. Hedge, C. J. Gutierrez, and G. A. Prinz, "Permanent magnet film magneto-optic waveguide isolator," J. Appl. Phys. 75, 6286-6288 (1994).
[CrossRef]

Ritter, D.

M. Muñoz, T. M. Holden, F. H. Pollak, M. Kahn, D. Ritter, L. Kronik, and G. M. Cohen, "Optical constants of In0.53Ga0.47As/InP: experiment and modeling," J. Appl. Phys. 92, 5878-5885 (2002).
[CrossRef]

Scarmozzino, R.

M. Levy, R. Scarmozzino, R. M. Osgood, Jr., R. Wolfe, F. J. Cadieu, H. Hedge, C. J. Gutierrez, and G. A. Prinz, "Permanent magnet film magneto-optic waveguide isolator," J. Appl. Phys. 75, 6286-6288 (1994).
[CrossRef]

Sebesta, R.

J. Pistora, K. Postava, and R. Sebesta, "Optical guided modes in sandwiches with ultrathin metallic films," J. Magn. Magn. Mater. 198-199, 683-685 (1999).
[CrossRef]

Shimizu , H.

H. Shimizu and M. Tanaka, "Design of semiconductor-waveguide-type optical isolators using the nonreciprocal loss/gain in the magneto-optical waveguides having MnAs nanoclusters," Appl. Phys. Lett. 81, 5246-5248 (2002).
[CrossRef]

Shimizu, M.

H. Yokoi, T. Mizumoto, M. Shimizu, T. Waniishi, N. Futakuchi, N. Kaida, and Y. Nakano, "Analysis of GaInAsP surfaces by contact-angle measurement for wafer direct bonding of garnet crystals," Jpn. J. Appl. Phys. 38, 4780-4783 (1999).
[CrossRef]

Shintaku, T.

T. Shintaku, "Integrated optical isolator based on efficient nonreciprocal radiation mode conversion," Appl. Phys. Lett. 73, 1946-1948 (1998).
[CrossRef]

Shoji, Y.

Tanaka, M.

H. Shimizu and M. Tanaka, "Design of semiconductor-waveguide-type optical isolators using the nonreciprocal loss/gain in the magneto-optical waveguides having MnAs nanoclusters," Appl. Phys. Lett. 81, 5246-5248 (2002).
[CrossRef]

Träger, D.

L. Wilkens, D. Träger, H. Dötsch, A. F. Popkov, and A. M. Alekseev, "Nonreciprocal phase shift of TE modes induced by a compensation wall in a magneto-optic rib waveguide," Appl. Phys. Lett. 79, 4292-4294 (2001).
[CrossRef]

Visnovský, S.

K. Postava, J. Pistora, and S. Visnovský, "Magnetooptical effects in ultrathin structures at transversal magnetization," Czech. J. Phys., Sect. B 49, 1185-1204 (1999).
[CrossRef]

S. Visnovský, "Optics of magnetic multilayers," Czech. J. Phys., Sect. B 41, 663-694 (1991).
[CrossRef]

S. Visnovský, "Magneto-optical permittivity tensor in crystals," Czech. J. Phys., Sect. B 36, 1424-1433 (1986).
[CrossRef]

S. Visnovský, "Magneto-optical ellipsometry," Czech. J. Phys., Sect. B 36, 625-650 (1986).
[CrossRef]

Visser, T. D.

T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, "Confinement factors and gain in optical amplifiers," IEEE J. Quantum Electron. 33, 1763-1766 (1997).
[CrossRef]

Waniishi, T.

H. Yokoi, T. Mizumoto, M. Shimizu, T. Waniishi, N. Futakuchi, N. Kaida, and Y. Nakano, "Analysis of GaInAsP surfaces by contact-angle measurement for wafer direct bonding of garnet crystals," Jpn. J. Appl. Phys. 38, 4780-4783 (1999).
[CrossRef]

Wilkens, L.

L. Wilkens, D. Träger, H. Dötsch, A. F. Popkov, and A. M. Alekseev, "Nonreciprocal phase shift of TE modes induced by a compensation wall in a magneto-optic rib waveguide," Appl. Phys. Lett. 79, 4292-4294 (2001).
[CrossRef]

O. Zhuromskyy, H. Dötsch, M. Lohmeyer, L. Wilkens, and P. Hertel, "Magnetooptical waveguide with polarization-independent nonreciprocal phaseshift," J. Lightwave Technol. 19, 214-221 (2001).
[CrossRef]

J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dötsch, "Waveguide optical isolator based on Mach-Zehnder interferometer," Appl. Phys. Lett. 76, 2158-2160 (2000).
[CrossRef]

Wolfe, R.

M. Levy, R. Scarmozzino, R. M. Osgood, Jr., R. Wolfe, F. J. Cadieu, H. Hedge, C. J. Gutierrez, and G. A. Prinz, "Permanent magnet film magneto-optic waveguide isolator," J. Appl. Phys. 75, 6286-6288 (1994).
[CrossRef]

Yamaguchi, T.

Yeh, P.

P. Yeh, "Optics of anisotropic layered media: a new 4×4 matrix algebra," Surf. Sci. 96, 41-53 (1980).
[CrossRef]

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Zaets , W.

W. Zaets and K. Ando, "Optical waveguide isolator based on nonreciprocal loss/gain amplifier covered by ferromagnetic layer," IEEE Photonics Technol. Lett. 11, 1012-1014 (1999).
[CrossRef]

Zhuromskyy, O.

Ann. Phys.

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Appl. Phys. Lett.

J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dötsch, "Waveguide optical isolator based on Mach-Zehnder interferometer," Appl. Phys. Lett. 76, 2158-2160 (2000).
[CrossRef]

A. F. Popkov, M. Fehndrich, M. Lohmeyer, and H. Dötsch, "Nonreciprocal TE-mode phase shift by domain walls in magnetooptic rib waveguides," Appl. Phys. Lett. 72, 2508-2510 (1998).
[CrossRef]

T. Shintaku, "Integrated optical isolator based on efficient nonreciprocal radiation mode conversion," Appl. Phys. Lett. 73, 1946-1948 (1998).
[CrossRef]

L. Wilkens, D. Träger, H. Dötsch, A. F. Popkov, and A. M. Alekseev, "Nonreciprocal phase shift of TE modes induced by a compensation wall in a magneto-optic rib waveguide," Appl. Phys. Lett. 79, 4292-4294 (2001).
[CrossRef]

H. Shimizu and M. Tanaka, "Design of semiconductor-waveguide-type optical isolators using the nonreciprocal loss/gain in the magneto-optical waveguides having MnAs nanoclusters," Appl. Phys. Lett. 81, 5246-5248 (2002).
[CrossRef]

Czech. J. Phys., Sect. B

S. Visnovský, "Magneto-optical ellipsometry," Czech. J. Phys., Sect. B 36, 625-650 (1986).
[CrossRef]

S. Visnovský, "Magneto-optical permittivity tensor in crystals," Czech. J. Phys., Sect. B 36, 1424-1433 (1986).
[CrossRef]

S. Visnovský, "Optics of magnetic multilayers," Czech. J. Phys., Sect. B 41, 663-694 (1991).
[CrossRef]

K. Postava, J. Pistora, and S. Visnovský, "Magnetooptical effects in ultrathin structures at transversal magnetization," Czech. J. Phys., Sect. B 49, 1185-1204 (1999).
[CrossRef]

IEEE J. Quantum Electron.

T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, "Confinement factors and gain in optical amplifiers," IEEE J. Quantum Electron. 33, 1763-1766 (1997).
[CrossRef]

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[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

M. Levy, "The on-chip integration of magnetooptic waveguide isolators," IEEE J. Sel. Top. Quantum Electron. 8, 1300-1306 (2002).
[CrossRef]

IEEE Photonics Technol. Lett.

W. Zaets and K. Ando, "Optical waveguide isolator based on nonreciprocal loss/gain amplifier covered by ferromagnetic layer," IEEE Photonics Technol. Lett. 11, 1012-1014 (1999).
[CrossRef]

T. Izuhara, J. Fujita, M. Levy, and R. M. Osgood, Jr., "Integration of magnetooptical waveguides onto a III-V semiconductor surface," IEEE Photonics Technol. Lett. 14, 167-169 (2002).
[CrossRef]

J. Appl. Phys.

M. Levy, R. Scarmozzino, R. M. Osgood, Jr., R. Wolfe, F. J. Cadieu, H. Hedge, C. J. Gutierrez, and G. A. Prinz, "Permanent magnet film magneto-optic waveguide isolator," J. Appl. Phys. 75, 6286-6288 (1994).
[CrossRef]

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[CrossRef]

M. Muñoz, T. M. Holden, F. H. Pollak, M. Kahn, D. Ritter, L. Kronik, and G. M. Cohen, "Optical constants of In0.53Ga0.47As/InP: experiment and modeling," J. Appl. Phys. 92, 5878-5885 (2002).
[CrossRef]

J. Lightwave Technol.

J. Magn. Magn. Mater.

J. Pistora, K. Postava, and R. Sebesta, "Optical guided modes in sandwiches with ultrathin metallic films," J. Magn. Magn. Mater. 198-199, 683-685 (1999).
[CrossRef]

J. Opt. Soc. Am.

Jpn. J. Appl. Phys.

H. Yokoi, T. Mizumoto, M. Shimizu, T. Waniishi, N. Futakuchi, N. Kaida, and Y. Nakano, "Analysis of GaInAsP surfaces by contact-angle measurement for wafer direct bonding of garnet crystals," Jpn. J. Appl. Phys. 38, 4780-4783 (1999).
[CrossRef]

Sens. Actuators, A

K. Postava, J. Pistora, and T. Yamaguchi, "Magneto-optic vector magnetometry for sensor applications," Sens. Actuators, A 110, 242-246 (2004).
[CrossRef]

Surf. Sci.

P. Yeh, "Optics of anisotropic layered media: a new 4×4 matrix algebra," Surf. Sci. 96, 41-53 (1980).
[CrossRef]

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M. Takenaka and Y. Nakano, "Proposal of a novel semiconductor optical waveguide isolator," presented at the 11th International Conference on Indium Phosphide and Related Materials, Davos, Switzerland, May 16-20, 1999.

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J. Decobert, N. Lagay, C. Cuisin, and B. Dagens, "MOVPE growth of AlGaInAsInP highly tensile-strained MQW's for 1.3 µm low-threshold lasers," presented at the Twelfth International Conference on Metal Organic Vapor Phase Epitaxy, Maui, Hawaii, May 30-June 4, 2004.

M. Vanwolleghem, W. Van Parys, D. Van Thourhout, R. Baets, F. Lelarge, O. Gauthier-Lafaye, B. Thedrez, R. Wirix-Speetjens, and J. De Boeck, "Experimental verification of a novel integrated isolator concept," presented at the 29th European Conference on Optical Communication, Rimini, Italy, September 21-25, 2003.

M. Vanwolleghem, W. Van Parys, D. Van Thourhout, R. Baets, F. Lelarge, O. Gauthier-Lafaye, B. Thedrez, R. Wirix-Speetjens, and J. De Boeck, "First experimental demonstration of a monolithically integrated InP-based waveguide isolator," in Optical Fiber Communication Conference , Vols. 95/A and 95/B of the OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2004), paper TuE6.

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Figures (12)

Fig. 1
Fig. 1

Schematic of a two-dimensional cross section of a MO integrated isolator. A nonreciprocal gain shift originates from the transversal MO effect in a ferromagnetic metal film (M). Waveguide losses by the absorbing metal films are compensated for by optical gain in a MQW active region separated by an InP spacer layer. Both sides of the MO stripe waveguide are separated from the injection current by a polyimide isolating layer.

Fig. 2
Fig. 2

Multilayer structure of the waveguide and the coordinate system chosen.

Fig. 3
Fig. 3

Schematic of the application of Yeh’s matrix algebra to produce the waveguide resonant condition and a solution of the inverse problem.

Fig. 4
Fig. 4

Four eigenmodes propagating in an anisotropic layer.

Fig. 5
Fig. 5

Multilayer structure of the waveguide isolator and the coordinate system chosen. Optical and MO constants for the wavelength of 1300 nm were obtained from Refs. 39-42.

Fig. 6
Fig. 6

Waveguide term |M33| as a function of R(neff) and I(neff) for the structure shown in Fig. 5. A thickness of the InP spacer layer of t(2)=500 nm and zero gain of the active layer k=0 were used in the model. The sharp minimum corresponds to the guided mode that satisfies waveguide resonant condition M33=0. Searching the minimum of |M33| by use of the optimization algorithm gives the value neff=3.23195-j0.00416.

Fig. 7
Fig. 7

Gain of the waveguide as a function of the internal gain of the active layer. The difference between forward and backward regimes represents nonreciprocal properties of the transversal MO isolator. The structure of the waveguide is the same as that shown in Fig. 5. Whereas the gain of the active layer was adjusted to 1139 cm-1 (k=0.01178), the waveguide gain for the forward direction was equal to zero. Then the isolation of the device defined as backward losses was 24.4 cm-1 [corresponding to I(neff)=0.000252].

Fig. 8
Fig. 8

Device isolation as a function of active-layer thickness shown for the waveguide structure from Fig. 5. The three curves correspond to InP spacer layer thicknesses of 250, 500, and 750 nm.

Fig. 9
Fig. 9

Necessary internal gains of the active layer for compensation of waveguide absorption losses in the forward direction are shown for the same conditions as in Fig. 8.

Fig. 10
Fig. 10

Waveguide isolation and the necessary internal gains of the active layer as functions of MO layer thickness. The structure of the waveguide is the same as shown in Fig. 5.

Fig. 11
Fig. 11

Comparison of the perturbation theory and the rigorous approach based on Yeh’s formalism. Waveguide isolation is shown as a function of the factor of Voigt MO parameter Q=fQCoFe. The MO waveguide of a real Co90Fe10 film corresponds to f=1. Good agreement between the two approaches can be observed.

Fig. 12
Fig. 12

Optimization of the MWQ-based isolator described in Table 1. The lower and upper SCH layers are optimized by use of the merit function from Eq. (44) with m=1 for the InP spacer thickness as a constant parameter. For a given available internal gain of the QW structure (b), the optimal thicknesses of InP and SCH layers (c) can be obtained. (a), The corresponding isolation.

Tables (1)

Tables Icon

Table 1 Structure of the Modeled Isolator Based on Tensile Strained MQW Structurea

Equations (58)

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

k(n)×H0(n)=-ω0ˆ(n)E0(n),
k(n)×E0(n)=ωμ0μˆ(n)H0(n),
[Nˆ(n)[μˆ(n)]-1Nˆ(n)+ˆ(n)]E0(n)=0,
k(n)×E0(n)=k0Nˆ(n)E0(n)=k00-NzNyNz0-Nx(n)-NyNx(n)0E0(n),
xx(n)-neff2xy(n)xz(n)+neffNx(n)yx(n)yy(n)-neff2-Nx(n)2yz(n)zx(n)+neffNx(n)zy(n)zz(n)-Nx(n)2E0x(n)E0y(n)E0z(n)=0.
det{Nˆ(n)[μˆ(n)]-1Nˆ(n)+ˆ(n)}=0,
A(0)=[D(0)]-1D(1)P(1)[D(1)]-1[D(N)]-1D(N+1)A(N+1)=MA(N+1),
A(n)=A1(n)A2(n)A3(n)A4(n),
D(n)=e1y(n)e2y(n)e3y(n)e4y(n)h1z(n)h2z(n)h3z(n)h4z(n)e1z(n)e2z(n)e3z(n)e4z(n)h1y(n)h2y(n)h3y(n)h4y(n),
S(n)=D(n)P(n)[D(n)]-1
M=[D(0)]-1n=1NS(n)D(N+1).
Sjn=12R[E0j(n)×H0j(n)*]exp{2k0 I[Nxj(n)]x}.
I(Nx1)>0,I(Nx2)<0,I(Nx3)>0,
I(Nx4)<0,
0A2(0)0A4(0)=M11M12M13M14M21M22M23M24M31M32M33M34M41M42M43M44A1(N+1)0A3(N+1)0,
M11M33-M13M31=0.
ˆ(n)=(n)0-jQ(n)(n)0(n)0jQ(n)(n)0(n),
[(n)-neff2-Nx1,2(n)2]×[(n)-Q(n)2(n)-neff2-Nx3,4(n)2]=0.
Nx1(n)=-[(n)-neff2]1/2,e1(n)=010,
Nx2(n)=-Nx1(n),e2(n)=010,
Nx3(n)=-[(n)-neff2-Q(n)2(n)]1/2,
e3(n)=C3(n)jQ(n)(n)-neffNx3(n)0(n)-neff2,
Nx4(n)=-Nx3(n),e4(n)=C4(n)×jQ(n)(n)+neffNx3(n)0(n)-neff2,
D(n)=D11(n)D11(n)00D21(n)-D21(n)0000D33(n)D33(n)00D43(n)D44(n),
D11(n)=1,
D21(n)=Nx1(n),
D33(n)=(n)-neff2,
D43(n)=jQ(n)(n)neff-(n)Nx3(n),
D44(n)=jQ(n)(n)neff+(n)Nx3(n).
gain[1/cm]=22πλ[m]I(neff)100=0.12566I(neff)λ[m].
gain[dB/cm]=10ln 10gain[1/cm]=0.5458I(neff)λ[m].
×E(r)=-jωμ0H(r),
×H(r)=jω0r(ρ)E(r)+J(r),
J(r)=jω0Δˆ(ρ)·E(r),
Δˆ(ρ)=00-jrQ000+jrQ00.
Et(r)Ht(r)=iMCi(z)Et,i(r)Ht,i(r),
uz·[t×Et(r)]=-t·[uz×Et(r)]=-jωμ0Hz(r),
uz·[t×Ht(r)]=-t·[uz×Ht(r)]=jω0uz·[r(ρ)Iˆ+Δˆ(ρ)]·E(r),
-t·[uz×Et,i(r)]=-jωμ0Hz,i(r),
-t·[uz×Ht,i(r)]=jω0r(ρ)Ez,i(r).
Hz(r)=iMCi(z)Hz,i(r),
Ez(r)=1jω0r(ρ)-iMCi(z)t·[uz×Ht,i(r)]-jω0iMCi(z)Δˆzt(ρ)·Et,i(r)=iMCi(z)Ez,i-iMCi(z)Δˆzt(ρ)r(ρ)·Et,i(r).
12[ei(ρ)×hj(ρ)]·uzdS=δij,
14[e-i(ρ)×hj(ρ)-ej(ρ)×h-i(ρ)]·uzdS=δij.
Ci(z)=14[E-i(r)×H(r)-E(r)×H-i(r)]·uzdS.
·[E-i(r)×H(r)-E(r)×H-i(r)]=-E-i(r)·J(r).
t·[E-i(r)×H(r)-E(r)×H-i(r)]+ddz[E-i(r)×H(r)-E(r)×H-i(r)]·uzdS=E-i(r)·J(r)dS.
J=jω0r(ρ)Q(ρ)kMCk(z)[jEx,k(r)uz-jEz,k(r)ux-Q(ρ)Ex,k(r)ux].
dCi(z)dz=-jkMAikCk(z)exp[-j(βk-βi)z],
Aik=-jω04{r(ρ)Q(ρ)[ez,i(ρ)ex,k(ρ)+ex,i(ρ)ez,k(ρ)-jQ(ρ)ex,i(ρ)ex,k(ρ)]}dS.
dXi(z)dz=-jβiXi(z)-jkMAikXk(z).
dX¯(z)dz=-jA̿·X¯(z),
A̿ik=βiI̿+A̿ik.
Γ-βm=Amm+O(2),
(Γ-βi)Xi=Aim+O(2),im,
Xi=Aimβm-βi,im.
Δβm=-jω02r(ρ)Q(ρ)ex,m(ρ)ez,m(ρ)dS=ω02Δˆxz(ρ)ex,m(ρ)ez,m(ρ)dS.
Meritfunction=InternalgainIsolationm,

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