Abstract

A wideband design is proposed for nonreciprocal phase shift magneto-optical isolators based on Mach–Zehnder interferometers. The wavelength dependence of nonreciprocal phase difference between the backward waves propagating in two interferometer arms is compensated for by that of reciprocal phase difference. This is realized by introducing an appropriate phase bias in one of interferometer arms. Two design examples are presented with a backward loss of >30dB in the wavelength range of 1.401.63μm for a magnetic garnet waveguide isolator and of 1.4851.630μm for a Si-wire waveguide isolator.

© 2006 Optical Society of America

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  1. K. Ando, T. Okoshi, and N. Koshizuka, "Waveguide magneto-optic isolator fabricated by laser annealing," Appl. Phys. Lett. 53, 4-6 (1988).
    [CrossRef]
  2. M. Levy, R. M. Osgood, Jr., H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Ftratello, "Integrated optical isolators with sputter-deposited thin-film magnets," IEEE Photon. Technol. Lett. 8, 903-905 (1996).
    [CrossRef]
  3. M. Lohmeyer, N. Bahlmann, O. Zhuromskyy, H. Dötsch, and P. Hertel, "Phase-matched rectangular magneto-optic waveguides for applications in integrated optics isolators: numerical assessment," Opt. Commun. 158, 189-200 (1998).
    [CrossRef]
  4. D. C. Hutchings, "Prospects for the implementation of magneto-optic elements in optoelectronic integrated circuits: a personal perspective," J. Phys. D 36, 2222-2229 (2003).
    [CrossRef]
  5. F. Auracher and H. H. Witte, "A new design for an integrated optical isolator," Opt. Commun. 13, 435-438 (1975).
    [CrossRef]
  6. T. Mizumoto, K. Oochi, T. Harada, and Y. Naito, "Measurement of optical nonreciprocal phase shift in a Bi-substituted Gd3Fe5O12 film and application to waveguide-type optical circulator," J. Lightwave Technol. LT-4, 347-352 (1986).
  7. T. Mizumoto, S. Mashimo, T. Ida, and Y. Naito, "In-plane magnetized rare earth iron garnet for a waveguide optical isolator employing nonreciprocal phase shift," IEEE Trans. Magn. 29, 3417-3419 (1993).
    [CrossRef]
  8. 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]
  9. H. Dötsch, N. Bahlmann, O. Zhuromskyy, M. Hammer, L. Wilkens, R. Gerhardt, and P. Hertel, "Application of magneto-optical waveguides in integrated optics: review," J. Opt. Soc. Am. B 22, 240-253 (2005).
    [CrossRef]
  10. H. Yokoi, T. Mizumoto, T. Takano, and N. Shinjo, "Demonstration of an optical isolator by use of a nonreciprocal phase shift," Appl. Opt. 38, 7409-7413 (1999).
  11. H. Yokoi, T. Mizumoto, N. Shinjo, 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).
  12. H. Yokoi, T. Mizumoto, and Y. Shoji, "Optical nonreciprocal devices with a silicon guiding layer fabricated by wafer bonding," Appl. Opt. 42, 6605-6612 (2003).
  13. Y. Shoji, H. Yokoi, T. Mizumoto, "Ultracompact optical isolator with a silicon high index contrast waveguide," in Conference on Lasers and Electro-Optics (CLEO) (Optical Society of America, 2004), Vol. 2, pp. 285-287.
  14. H. Yokoi, Y. Shoji, E. Shin, and T. Mizumoto, "Interferometric optical isolator employing a nonreciprocal phase shift operated in a unidirectional magnetic field," Appl. Opt. 43, 4745-4752 (2004).
    [CrossRef]
  15. R. L. Espinola, T. Izuhara, M.-C. Tsai, and R. M. Osgood, Jr., "Magneto-optical nonreciprocal phase shift in garnet/silicon-on-insulator waveguides," Opt. Lett. 29, 941-943 (2004).
    [CrossRef]
  16. T. Shintaku, "Optical waveguide isolator based on nonreciprocal radiation," J. Appl. Phys. 76, 8155-8159 (1994).
    [CrossRef]
  17. J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dötsch, "Polarization-independent waveguide optical isolator based on nonreciprocal phase shift," IEEE Photon. Technol. Lett. 12, 1510-1512 (2000).
    [CrossRef]

2005 (1)

2004 (2)

2003 (2)

H. Yokoi, T. Mizumoto, and Y. Shoji, "Optical nonreciprocal devices with a silicon guiding layer fabricated by wafer bonding," Appl. Opt. 42, 6605-6612 (2003).

D. C. Hutchings, "Prospects for the implementation of magneto-optic elements in optoelectronic integrated circuits: a personal perspective," J. Phys. D 36, 2222-2229 (2003).
[CrossRef]

2000 (3)

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]

J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dötsch, "Polarization-independent waveguide optical isolator based on nonreciprocal phase shift," IEEE Photon. Technol. Lett. 12, 1510-1512 (2000).
[CrossRef]

H. Yokoi, T. Mizumoto, N. Shinjo, 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).

1999 (1)

1998 (1)

M. Lohmeyer, N. Bahlmann, O. Zhuromskyy, H. Dötsch, and P. Hertel, "Phase-matched rectangular magneto-optic waveguides for applications in integrated optics isolators: numerical assessment," Opt. Commun. 158, 189-200 (1998).
[CrossRef]

1996 (1)

M. Levy, R. M. Osgood, Jr., H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Ftratello, "Integrated optical isolators with sputter-deposited thin-film magnets," IEEE Photon. Technol. Lett. 8, 903-905 (1996).
[CrossRef]

1994 (1)

T. Shintaku, "Optical waveguide isolator based on nonreciprocal radiation," J. Appl. Phys. 76, 8155-8159 (1994).
[CrossRef]

1993 (1)

T. Mizumoto, S. Mashimo, T. Ida, and Y. Naito, "In-plane magnetized rare earth iron garnet for a waveguide optical isolator employing nonreciprocal phase shift," IEEE Trans. Magn. 29, 3417-3419 (1993).
[CrossRef]

1988 (1)

K. Ando, T. Okoshi, and N. Koshizuka, "Waveguide magneto-optic isolator fabricated by laser annealing," Appl. Phys. Lett. 53, 4-6 (1988).
[CrossRef]

1986 (1)

T. Mizumoto, K. Oochi, T. Harada, and Y. Naito, "Measurement of optical nonreciprocal phase shift in a Bi-substituted Gd3Fe5O12 film and application to waveguide-type optical circulator," J. Lightwave Technol. LT-4, 347-352 (1986).

1975 (1)

F. Auracher and H. H. Witte, "A new design for an integrated optical isolator," Opt. Commun. 13, 435-438 (1975).
[CrossRef]

Ando, K.

K. Ando, T. Okoshi, and N. Koshizuka, "Waveguide magneto-optic isolator fabricated by laser annealing," Appl. Phys. Lett. 53, 4-6 (1988).
[CrossRef]

Auracher, F.

F. Auracher and H. H. Witte, "A new design for an integrated optical isolator," Opt. Commun. 13, 435-438 (1975).
[CrossRef]

Bahlmann, N.

H. Dötsch, N. Bahlmann, O. Zhuromskyy, M. Hammer, L. Wilkens, R. Gerhardt, and P. Hertel, "Application of magneto-optical waveguides in integrated optics: review," J. Opt. Soc. Am. B 22, 240-253 (2005).
[CrossRef]

M. Lohmeyer, N. Bahlmann, O. Zhuromskyy, H. Dötsch, and P. Hertel, "Phase-matched rectangular magneto-optic waveguides for applications in integrated optics isolators: numerical assessment," Opt. Commun. 158, 189-200 (1998).
[CrossRef]

Cadieu, F. J.

M. Levy, R. M. Osgood, Jr., H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Ftratello, "Integrated optical isolators with sputter-deposited thin-film magnets," IEEE Photon. Technol. Lett. 8, 903-905 (1996).
[CrossRef]

Dötsch, H.

H. Dötsch, N. Bahlmann, O. Zhuromskyy, M. Hammer, L. Wilkens, R. Gerhardt, and P. Hertel, "Application of magneto-optical waveguides in integrated optics: review," J. Opt. Soc. Am. B 22, 240-253 (2005).
[CrossRef]

J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dötsch, "Polarization-independent waveguide optical isolator based on nonreciprocal phase shift," IEEE Photon. Technol. Lett. 12, 1510-1512 (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]

M. Lohmeyer, N. Bahlmann, O. Zhuromskyy, H. Dötsch, and P. Hertel, "Phase-matched rectangular magneto-optic waveguides for applications in integrated optics isolators: numerical assessment," Opt. Commun. 158, 189-200 (1998).
[CrossRef]

Espinola, R. L.

Ftratello, V. J.

M. Levy, R. M. Osgood, Jr., H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Ftratello, "Integrated optical isolators with sputter-deposited thin-film magnets," IEEE Photon. Technol. Lett. 8, 903-905 (1996).
[CrossRef]

Fujita, J.

J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dötsch, "Polarization-independent waveguide optical isolator based on nonreciprocal phase shift," IEEE Photon. Technol. Lett. 12, 1510-1512 (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]

Futakuchi, N.

Gerhardt, R.

Hammer, M.

Harada, T.

T. Mizumoto, K. Oochi, T. Harada, and Y. Naito, "Measurement of optical nonreciprocal phase shift in a Bi-substituted Gd3Fe5O12 film and application to waveguide-type optical circulator," J. Lightwave Technol. LT-4, 347-352 (1986).

Hegde, H.

M. Levy, R. M. Osgood, Jr., H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Ftratello, "Integrated optical isolators with sputter-deposited thin-film magnets," IEEE Photon. Technol. Lett. 8, 903-905 (1996).
[CrossRef]

Hertel, P.

H. Dötsch, N. Bahlmann, O. Zhuromskyy, M. Hammer, L. Wilkens, R. Gerhardt, and P. Hertel, "Application of magneto-optical waveguides in integrated optics: review," J. Opt. Soc. Am. B 22, 240-253 (2005).
[CrossRef]

M. Lohmeyer, N. Bahlmann, O. Zhuromskyy, H. Dötsch, and P. Hertel, "Phase-matched rectangular magneto-optic waveguides for applications in integrated optics isolators: numerical assessment," Opt. Commun. 158, 189-200 (1998).
[CrossRef]

Hutchings, D. C.

D. C. Hutchings, "Prospects for the implementation of magneto-optic elements in optoelectronic integrated circuits: a personal perspective," J. Phys. D 36, 2222-2229 (2003).
[CrossRef]

Ida, T.

T. Mizumoto, S. Mashimo, T. Ida, and Y. Naito, "In-plane magnetized rare earth iron garnet for a waveguide optical isolator employing nonreciprocal phase shift," IEEE Trans. Magn. 29, 3417-3419 (1993).
[CrossRef]

Izuhara, T.

Koshizuka, N.

K. Ando, T. Okoshi, and N. Koshizuka, "Waveguide magneto-optic isolator fabricated by laser annealing," Appl. Phys. Lett. 53, 4-6 (1988).
[CrossRef]

Levy, M.

J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dötsch, "Polarization-independent waveguide optical isolator based on nonreciprocal phase shift," IEEE Photon. Technol. Lett. 12, 1510-1512 (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]

M. Levy, R. M. Osgood, Jr., H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Ftratello, "Integrated optical isolators with sputter-deposited thin-film magnets," IEEE Photon. Technol. Lett. 8, 903-905 (1996).
[CrossRef]

Lohmeyer, M.

M. Lohmeyer, N. Bahlmann, O. Zhuromskyy, H. Dötsch, and P. Hertel, "Phase-matched rectangular magneto-optic waveguides for applications in integrated optics isolators: numerical assessment," Opt. Commun. 158, 189-200 (1998).
[CrossRef]

Mashimo, S.

T. Mizumoto, S. Mashimo, T. Ida, and Y. Naito, "In-plane magnetized rare earth iron garnet for a waveguide optical isolator employing nonreciprocal phase shift," IEEE Trans. Magn. 29, 3417-3419 (1993).
[CrossRef]

Mizumoto, T.

H. Yokoi, Y. Shoji, E. Shin, and T. Mizumoto, "Interferometric optical isolator employing a nonreciprocal phase shift operated in a unidirectional magnetic field," Appl. Opt. 43, 4745-4752 (2004).
[CrossRef]

H. Yokoi, T. Mizumoto, and Y. Shoji, "Optical nonreciprocal devices with a silicon guiding layer fabricated by wafer bonding," Appl. Opt. 42, 6605-6612 (2003).

H. Yokoi, T. Mizumoto, N. Shinjo, 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).

H. Yokoi, T. Mizumoto, T. Takano, and N. Shinjo, "Demonstration of an optical isolator by use of a nonreciprocal phase shift," Appl. Opt. 38, 7409-7413 (1999).

T. Mizumoto, S. Mashimo, T. Ida, and Y. Naito, "In-plane magnetized rare earth iron garnet for a waveguide optical isolator employing nonreciprocal phase shift," IEEE Trans. Magn. 29, 3417-3419 (1993).
[CrossRef]

T. Mizumoto, K. Oochi, T. Harada, and Y. Naito, "Measurement of optical nonreciprocal phase shift in a Bi-substituted Gd3Fe5O12 film and application to waveguide-type optical circulator," J. Lightwave Technol. LT-4, 347-352 (1986).

Y. Shoji, H. Yokoi, T. Mizumoto, "Ultracompact optical isolator with a silicon high index contrast waveguide," in Conference on Lasers and Electro-Optics (CLEO) (Optical Society of America, 2004), Vol. 2, pp. 285-287.

Naito, Y.

T. Mizumoto, S. Mashimo, T. Ida, and Y. Naito, "In-plane magnetized rare earth iron garnet for a waveguide optical isolator employing nonreciprocal phase shift," IEEE Trans. Magn. 29, 3417-3419 (1993).
[CrossRef]

T. Mizumoto, K. Oochi, T. Harada, and Y. Naito, "Measurement of optical nonreciprocal phase shift in a Bi-substituted Gd3Fe5O12 film and application to waveguide-type optical circulator," J. Lightwave Technol. LT-4, 347-352 (1986).

Nakano, Y.

Okoshi, T.

K. Ando, T. Okoshi, and N. Koshizuka, "Waveguide magneto-optic isolator fabricated by laser annealing," Appl. Phys. Lett. 53, 4-6 (1988).
[CrossRef]

Oochi, K.

T. Mizumoto, K. Oochi, T. Harada, and Y. Naito, "Measurement of optical nonreciprocal phase shift in a Bi-substituted Gd3Fe5O12 film and application to waveguide-type optical circulator," J. Lightwave Technol. LT-4, 347-352 (1986).

Osgood, R. M.

R. L. Espinola, T. Izuhara, M.-C. Tsai, and R. M. Osgood, Jr., "Magneto-optical nonreciprocal phase shift in garnet/silicon-on-insulator waveguides," Opt. Lett. 29, 941-943 (2004).
[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]

J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dötsch, "Polarization-independent waveguide optical isolator based on nonreciprocal phase shift," IEEE Photon. Technol. Lett. 12, 1510-1512 (2000).
[CrossRef]

M. Levy, R. M. Osgood, Jr., H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Ftratello, "Integrated optical isolators with sputter-deposited thin-film magnets," IEEE Photon. Technol. Lett. 8, 903-905 (1996).
[CrossRef]

Shin, E.

Shinjo, N.

Shintaku, T.

T. Shintaku, "Optical waveguide isolator based on nonreciprocal radiation," J. Appl. Phys. 76, 8155-8159 (1994).
[CrossRef]

Shoji, Y.

Takano, T.

Tsai, M.-C.

Wilkens, L.

H. Dötsch, N. Bahlmann, O. Zhuromskyy, M. Hammer, L. Wilkens, R. Gerhardt, and P. Hertel, "Application of magneto-optical waveguides in integrated optics: review," J. Opt. Soc. Am. B 22, 240-253 (2005).
[CrossRef]

J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dötsch, "Polarization-independent waveguide optical isolator based on nonreciprocal phase shift," IEEE Photon. Technol. Lett. 12, 1510-1512 (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]

Witte, H. H.

F. Auracher and H. H. Witte, "A new design for an integrated optical isolator," Opt. Commun. 13, 435-438 (1975).
[CrossRef]

Wolfe, R.

M. Levy, R. M. Osgood, Jr., H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Ftratello, "Integrated optical isolators with sputter-deposited thin-film magnets," IEEE Photon. Technol. Lett. 8, 903-905 (1996).
[CrossRef]

Yokoi, H.

Zhuromskyy, O.

H. Dötsch, N. Bahlmann, O. Zhuromskyy, M. Hammer, L. Wilkens, R. Gerhardt, and P. Hertel, "Application of magneto-optical waveguides in integrated optics: review," J. Opt. Soc. Am. B 22, 240-253 (2005).
[CrossRef]

M. Lohmeyer, N. Bahlmann, O. Zhuromskyy, H. Dötsch, and P. Hertel, "Phase-matched rectangular magneto-optic waveguides for applications in integrated optics isolators: numerical assessment," Opt. Commun. 158, 189-200 (1998).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. Lett. (2)

K. Ando, T. Okoshi, and N. Koshizuka, "Waveguide magneto-optic isolator fabricated by laser annealing," Appl. Phys. Lett. 53, 4-6 (1988).
[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]

IEEE Photon. Technol. Lett. (2)

M. Levy, R. M. Osgood, Jr., H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Ftratello, "Integrated optical isolators with sputter-deposited thin-film magnets," IEEE Photon. Technol. Lett. 8, 903-905 (1996).
[CrossRef]

J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dötsch, "Polarization-independent waveguide optical isolator based on nonreciprocal phase shift," IEEE Photon. Technol. Lett. 12, 1510-1512 (2000).
[CrossRef]

IEEE Trans. Magn. (1)

T. Mizumoto, S. Mashimo, T. Ida, and Y. Naito, "In-plane magnetized rare earth iron garnet for a waveguide optical isolator employing nonreciprocal phase shift," IEEE Trans. Magn. 29, 3417-3419 (1993).
[CrossRef]

J. Appl. Phys. (1)

T. Shintaku, "Optical waveguide isolator based on nonreciprocal radiation," J. Appl. Phys. 76, 8155-8159 (1994).
[CrossRef]

J. Lightwave Technol. (1)

T. Mizumoto, K. Oochi, T. Harada, and Y. Naito, "Measurement of optical nonreciprocal phase shift in a Bi-substituted Gd3Fe5O12 film and application to waveguide-type optical circulator," J. Lightwave Technol. LT-4, 347-352 (1986).

J. Opt. Soc. Am. B (1)

J. Phys. D (1)

D. C. Hutchings, "Prospects for the implementation of magneto-optic elements in optoelectronic integrated circuits: a personal perspective," J. Phys. D 36, 2222-2229 (2003).
[CrossRef]

Opt. Commun. (2)

F. Auracher and H. H. Witte, "A new design for an integrated optical isolator," Opt. Commun. 13, 435-438 (1975).
[CrossRef]

M. Lohmeyer, N. Bahlmann, O. Zhuromskyy, H. Dötsch, and P. Hertel, "Phase-matched rectangular magneto-optic waveguides for applications in integrated optics isolators: numerical assessment," Opt. Commun. 158, 189-200 (1998).
[CrossRef]

Opt. Lett. (1)

Other (1)

Y. Shoji, H. Yokoi, T. Mizumoto, "Ultracompact optical isolator with a silicon high index contrast waveguide," in Conference on Lasers and Electro-Optics (CLEO) (Optical Society of America, 2004), Vol. 2, pp. 285-287.

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Figures (11)

Fig. 1
Fig. 1

Schematic diagram of optical isolator employing nonreciprocal phase shift.

Fig. 2
Fig. 2

(a) Wavelength dependence of reciprocal and nonreciprocal phase differences and (b) total phase difference in a conventional MZI design.

Fig. 3
Fig. 3

Proposed configuration of a MZI isolator.

Fig. 4
Fig. 4

(a) Wavelength dependence of reciprocal and nonreciprocal phase differences and (b) total phase difference in a proposed MZI design.

Fig. 5
Fig. 5

Tailoring waveguide width and length to adjust a reciprocal phase difference.

Fig. 6
Fig. 6

Optical isolators employing nonreciprocal phase shift.

Fig. 7
Fig. 7

Wavelength dependence of (a) the Faraday rotation coefficient of Ce:YIG and the refractive indices of (b) Ce:YIG, (c) Si, and (d) SiO 2 .

Fig. 8
Fig. 8

The cross-sectional structure of the waveguide used in the calculation for (a) type-1 and (b) type-2 optical isolators.

Fig. 9
Fig. 9

Wavelength dependence of type-1 optical isolator: (a) forward loss and (b) backward loss. Solid and dotted lines show the characteristics of proposed and conventional design, respectively.

Fig. 10
Fig. 10

Wavelength dependence of type-2 optical isolator: (a) forward loss and (b) backward loss. Solid and dotted curves show the characteristics of proposed and conventional design, respectively.

Fig. 11
Fig. 11

Fabrication tolerance of type-2 optical isolator in (a), (b) conventional design and (c), (d) proposed design.

Equations (2)

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ε = [ ε x x 0 0 0 ε y y j ε y z 0 - j ε y z ε z z     ] ,
ε y z = 2 n Θ F k 0 .

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