Abstract

We propose a nonreciprocal waveguide with different wavevectors for forward and backward propagations. Utilizing this nonreciprocal waveguide, we further compose a nonreciprocal micro-ring resonator, which possesses different phase shifts for clockwise and anticlockwise circulatings. Using this nonreciprocal resonator, more than 20 dB optical isolation can be achieved. This work demonstrates that on-chip optical isolations can be accomplished with simple nonreciprocal resonator components, which can show promising applications for integrated optoelectronic systems.

© 2011 IEEE

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  1. M. Soljac˘ić, J. D. Joannopoulos, "Enhancement of nonlinear effects using photonic crystals," Nature Mater. 3, 211-219 (2004).
  2. L. Pavesi, D. J. Lockwood, Silicon Photonics (Springer, 2004).
  3. V. R. Almeida, C. A. Barrios, R. R. Panepucci, M. Lipson, "All-optical control of light on a silicon chip," Nature 431, 1081-1084 (2004).
  4. H. Dötsch, "Applications of magneto-optical waveguides in integrated optics: Review," J. Opt. Soc. Amer. B 22, 240-253 (2005).
  5. T. R. Zaman, X. Guo, R. J. Ram, "Semiconductor waveguide isolators," J. Lightw. Technol. 26, 291-301 (2008).
  6. N. Bahlmann, "Improved design of magnetooptic Rib waveguides for optical isolators," J. Lightw. Technol. 16, 818-823 (1998).
  7. V. Priye, B. P. Pal, K. Thyagarajan, "Analysis and design of a novel leaky YIG film guided wave optical isolator," J. Lightw. Technol. 16, 246-250 (1998).
  8. V. Zayets, M. C. Debnath, K. Ando, "Optical isolation in Cd$_{1 - {\rm x}}$Mn$_{x}$Te magneto-optical waveguide grown on GaAs substrate," J. Opt. Soc. Amer. B 22, 281-285 (2005).
  9. T. Amemiya, "Semiconductor waveguide optical isolator based on nonreciprocal loss induced by ferromagnetic MnAs," Appl. Phys. Lett. 89, 021104 (2006).
  10. W. V. Parys, "Transverse magnetic mode nonreciprocal propagation in an amplifying AlGaInAs/InP optical waveguide isolator," Appl. Phys. Lett. 88, (2006) Art. ID 071115.
  11. H. Shimizu, Y. Nakano, "Fabrication and characterization of an InGaAsp/InP active waveguide optical isolator with 14.7 dB/mm TE mode nonreciprocal attenuation," J. Lightw. Technol. 24, 38-43 (2006).
  12. T. Amemiya, H. Shimizu, P. N. Hai, M. Tanaka, Y. Nakano, "Nonreciprocal propagation of light without external magnetic fields in a semiconductor waveguide isolator with a MnAs layer," J. Magn. Magn. Mater. 310, 2161-2163 (2007).
  13. M. Vanwolleghem, P. Gogol, P. Beauvillain, W. V. Parys, R. Baets, "Design and optimization of a monolithically integratable InP-based optical waveguide isolator," J. Opt. Soc. Amer. B 24, 94 (2007).
  14. S. M. Drezdzon, T. Yoshie, "On-chip waveguide isolator based on bismuth iron garnet operating via nonreciprocal single-modecutoff," Opt. Exp. 17, 9276-9281 (2009).
  15. H. Shimizu, S. Goto, "Evanescent semiconductor active optical isolators for low insertion loss and high gain saturation power," J. Lightw. Technol. 28, 1414-1419 (2010).
  16. O. Zhuromskyy, "Analysis of polarization independent Mach-Zehnder-type integrated optical isolator," J. Lightw. Technol. 17, 1200-1205 (1999).
  17. J. Fujita, M. Levy, J. R. M. Osgood, "Waveguide optical isolator based on Mach–Zehnder interferometer," Appl. Phys. Lett. 76, 2158-2160 (2000).
  18. H. Yokoi, Y. Shoji, E. Shin, T. Mizumoto, "Interferometric optical isolator employing a nonreciprocal phase shift operated in a unidirectional magnetic field," Appl. Opt. 43, 4745-4752 (2004).
  19. Y. Shoji, I. W. Hsieh, J. R. M. Osgood, T. Mizumoto, "Polarization-independent magneto-optical waveguide isolator using TM-mode nonreciprocal phase shift," J. Lightw. Technol. 25, 3108-3113 (2007).
  20. Y. Shoji, T. Mizumoto, "Wideband operation of Mach–Zehnder interferomertic magneto-optical isolator using phase adjustment," Opt. Exp. 15, 13446-13450 (2007).
  21. Y. Shoji, T. Mizumoto, "Ultra-wideband design of waveguide magneto-optical isolator operating in 1.31$\mu$m and 1.55$\mu$m band," Opt. Exp. 15, 639-645 (2007).
  22. H. Shimizu, S. Yoshida, S. Goto, "Semiconductor waveguide optical isolators towards larger optical isolation utilizing nonreciprocal phase shift by ferromagnetic Co," IEEE Photon. Technol. Lett. 20, 1554-1556 (2008).
  23. Y. Shoji, T. Mizumoto, H. Yokoi, I.-W. Hsieh, J. Richard, M. Osgood, "Magneto-optical isolator with silicon waveguides fabricated by direct bonding," Appl. Phys. Lett. 92, (2008) Art. ID 071117.
  24. H. Zhou, "Wavelength-selective optical waveguide isolator based on nonreciprocal ring-coupled mach-zehnder interferometer," J. Lightw. Technol. 26, 3166-3172 (2008).
  25. Z. Wang, S. Fan, "Magneto-optical defects in two-dimensional photonic crystals," Appl. Phys. B 81, 369-375 (2005).
  26. Z. Wang, S. Fan, "Suppressing the effect of disorders using time-reversal symmetry breaking in magneto-optical photonic crystals: An illustration with a four-port circulator," Photon. Nanostruct.: Fundam. Appl. 4, 132-140 (2006).
  27. H. Takeda, S. John, "Compact optical one-way waveguide isolators for photonic-band-gap microchips," Phys. Rev. A 78, (2008) Art. ID 023804.
  28. N. Kono, K. Kakihara, K. Saitoh, M. Koshiba, "Nonreciprocal microresonators for the miniaturization of optical waveguide isolators," Opt. Exp. 15, 7737-7751 (2007).
  29. A. Rostami, "Piecewise linear integrated optical device as an optical isolator using two-port nonlinear ring resonators," Opt. Laser Technol. 39, 1059-1065 (2007).
  30. X.-S. Lin, J.-H. Yan, L.-J. Wu, S. Lan, "High transmission contrast for single resonator based all-optical diodes with pump-assisting," Opt. Exp. 16, 20949-20954 (2008).
  31. A. Alberucci, G. Assanto, "All-optical isolation by directional coupling," Opt. Lett. 33, 1641-1643 (2008).
  32. J. B. Khurgin, "Optical isolating action in surface plasmon polaritons," Appl. Phys. Lett. 89, (2006) Art. ID 251115.
  33. J. Montoya, K. Parameswaran, J. Hensley, M. Allen, R. Ram, "Surface plasmon isolator based on nonreciprocal coupling," J. Appl. Phys. 106, (2009) Art. ID 023108.
  34. A. E. Serebryannikov, E. Ozbay, "Isolation and one-way effects in diffraction on dielectric gratings with plasmonic inserts," Opt. Exp. 17, 278-292 (2009).
  35. Z. Yu, S. Fan, "Optical isolation based on nonreciprocal phase shift induced by interband photonic transitions," Appl. Phys. Lett. 94, (2009) Art. ID 171116.
  36. Z. Yu, S. Fan, "Complete optical isolation created by indirect interband photonic transitions," Nature Photon. 3, 91-94 (2009).
  37. Z. Yu, S. Fan, "Integrated nonmagnetic optical isolators based on photonic transitions," IEEE J. Sel. Topics Quantum Electron. 16, 459-466 (2010).
  38. F. D. M. Haldane, S. Raghu, "Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry," Phys. Rev. Lett. 100, 013904 (2008).
  39. Z. Wang, Y. D. Chong, J. D. Joannopoulos, M. Soljac˘ić, "Reflection-free one-way edge modes in a gyromagnetic photonic crystal," Phys. Rev. Lett. 100, (2008) Art. ID 013905.
  40. Z. Yu, G. Veronis, Z. Wang, S. Fan, "One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal," Phys. Rev. Lett. 100, 023902 (2008).
  41. Z. Wang, Y. Chong, J. D. Joannopoulos, M. Soljac˘ić, "Observation of unidirectional backscattering-immune topological electromagnetic states," Nature 461, 772-775 (2009).
  42. H. Zhu, C. Jiang, "Extraordinary coupling into one-way magneto-optical photonic crystal waveguide," J. Lightw. Technol. 29, 708-713 (2011).
  43. D. G. Rabus, Integrated Ring Resonators (Springer, 2007).
  44. H. Zhu, C. Jiang, "Broadband unidirectional electromagnetic mode at interface of anti-parallel magnetized media," Opt. Exp. 18, 6914-6921 (2010).
  45. Z. Yu, Z. Wang, S. Fan, "One-way total reflection with one-dimensional magneto-optical photonic crystals," Appl. Phys. Lett. 90, (2007) Art. ID 121133.
  46. J. R. Goldman, T. D. Ladd, F. Yamaguchi, Y. Yamamoto, "Magnet designs for a crystal-lattice quantum computer," Appl. Phys. A 71, 11-17 (2000).
  47. N. Adachi, V. P. Denysenkov, S. I. Khartsev, A. M. Grishin, T. Okuda, "Epitaxial Bi$_{3}$Fe$_{5}$O$_{12}$ (001) films grown by pulsed laser deposition and reactive ion beam sputtering techniques," J. Appl. Phys. 88, 2734-2739 (2000).
  48. T. Tepper, C. A. Ross, "Pulsed laser deposition and refractive index measurement of fully substituted bismuth iron garnet films," J. Crystal Growth 255, 324-331 (2003).
  49. K. Okamoto, Fundamentals of Optical Waveguides (Elsevier, 2006).

2011 (1)

H. Zhu, C. Jiang, "Extraordinary coupling into one-way magneto-optical photonic crystal waveguide," J. Lightw. Technol. 29, 708-713 (2011).

2010 (3)

H. Zhu, C. Jiang, "Broadband unidirectional electromagnetic mode at interface of anti-parallel magnetized media," Opt. Exp. 18, 6914-6921 (2010).

H. Shimizu, S. Goto, "Evanescent semiconductor active optical isolators for low insertion loss and high gain saturation power," J. Lightw. Technol. 28, 1414-1419 (2010).

Z. Yu, S. Fan, "Integrated nonmagnetic optical isolators based on photonic transitions," IEEE J. Sel. Topics Quantum Electron. 16, 459-466 (2010).

2009 (6)

J. Montoya, K. Parameswaran, J. Hensley, M. Allen, R. Ram, "Surface plasmon isolator based on nonreciprocal coupling," J. Appl. Phys. 106, (2009) Art. ID 023108.

A. E. Serebryannikov, E. Ozbay, "Isolation and one-way effects in diffraction on dielectric gratings with plasmonic inserts," Opt. Exp. 17, 278-292 (2009).

Z. Yu, S. Fan, "Optical isolation based on nonreciprocal phase shift induced by interband photonic transitions," Appl. Phys. Lett. 94, (2009) Art. ID 171116.

Z. Yu, S. Fan, "Complete optical isolation created by indirect interband photonic transitions," Nature Photon. 3, 91-94 (2009).

S. M. Drezdzon, T. Yoshie, "On-chip waveguide isolator based on bismuth iron garnet operating via nonreciprocal single-modecutoff," Opt. Exp. 17, 9276-9281 (2009).

Z. Wang, Y. Chong, J. D. Joannopoulos, M. Soljac˘ić, "Observation of unidirectional backscattering-immune topological electromagnetic states," Nature 461, 772-775 (2009).

2008 (10)

X.-S. Lin, J.-H. Yan, L.-J. Wu, S. Lan, "High transmission contrast for single resonator based all-optical diodes with pump-assisting," Opt. Exp. 16, 20949-20954 (2008).

A. Alberucci, G. Assanto, "All-optical isolation by directional coupling," Opt. Lett. 33, 1641-1643 (2008).

T. R. Zaman, X. Guo, R. J. Ram, "Semiconductor waveguide isolators," J. Lightw. Technol. 26, 291-301 (2008).

F. D. M. Haldane, S. Raghu, "Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry," Phys. Rev. Lett. 100, 013904 (2008).

Z. Wang, Y. D. Chong, J. D. Joannopoulos, M. Soljac˘ić, "Reflection-free one-way edge modes in a gyromagnetic photonic crystal," Phys. Rev. Lett. 100, (2008) Art. ID 013905.

Z. Yu, G. Veronis, Z. Wang, S. Fan, "One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal," Phys. Rev. Lett. 100, 023902 (2008).

H. Shimizu, S. Yoshida, S. Goto, "Semiconductor waveguide optical isolators towards larger optical isolation utilizing nonreciprocal phase shift by ferromagnetic Co," IEEE Photon. Technol. Lett. 20, 1554-1556 (2008).

Y. Shoji, T. Mizumoto, H. Yokoi, I.-W. Hsieh, J. Richard, M. Osgood, "Magneto-optical isolator with silicon waveguides fabricated by direct bonding," Appl. Phys. Lett. 92, (2008) Art. ID 071117.

H. Zhou, "Wavelength-selective optical waveguide isolator based on nonreciprocal ring-coupled mach-zehnder interferometer," J. Lightw. Technol. 26, 3166-3172 (2008).

H. Takeda, S. John, "Compact optical one-way waveguide isolators for photonic-band-gap microchips," Phys. Rev. A 78, (2008) Art. ID 023804.

2007 (8)

N. Kono, K. Kakihara, K. Saitoh, M. Koshiba, "Nonreciprocal microresonators for the miniaturization of optical waveguide isolators," Opt. Exp. 15, 7737-7751 (2007).

A. Rostami, "Piecewise linear integrated optical device as an optical isolator using two-port nonlinear ring resonators," Opt. Laser Technol. 39, 1059-1065 (2007).

Y. Shoji, I. W. Hsieh, J. R. M. Osgood, T. Mizumoto, "Polarization-independent magneto-optical waveguide isolator using TM-mode nonreciprocal phase shift," J. Lightw. Technol. 25, 3108-3113 (2007).

Y. Shoji, T. Mizumoto, "Wideband operation of Mach–Zehnder interferomertic magneto-optical isolator using phase adjustment," Opt. Exp. 15, 13446-13450 (2007).

Y. Shoji, T. Mizumoto, "Ultra-wideband design of waveguide magneto-optical isolator operating in 1.31$\mu$m and 1.55$\mu$m band," Opt. Exp. 15, 639-645 (2007).

T. Amemiya, H. Shimizu, P. N. Hai, M. Tanaka, Y. Nakano, "Nonreciprocal propagation of light without external magnetic fields in a semiconductor waveguide isolator with a MnAs layer," J. Magn. Magn. Mater. 310, 2161-2163 (2007).

M. Vanwolleghem, P. Gogol, P. Beauvillain, W. V. Parys, R. Baets, "Design and optimization of a monolithically integratable InP-based optical waveguide isolator," J. Opt. Soc. Amer. B 24, 94 (2007).

Z. Yu, Z. Wang, S. Fan, "One-way total reflection with one-dimensional magneto-optical photonic crystals," Appl. Phys. Lett. 90, (2007) Art. ID 121133.

2006 (5)

J. B. Khurgin, "Optical isolating action in surface plasmon polaritons," Appl. Phys. Lett. 89, (2006) Art. ID 251115.

T. Amemiya, "Semiconductor waveguide optical isolator based on nonreciprocal loss induced by ferromagnetic MnAs," Appl. Phys. Lett. 89, 021104 (2006).

W. V. Parys, "Transverse magnetic mode nonreciprocal propagation in an amplifying AlGaInAs/InP optical waveguide isolator," Appl. Phys. Lett. 88, (2006) Art. ID 071115.

H. Shimizu, Y. Nakano, "Fabrication and characterization of an InGaAsp/InP active waveguide optical isolator with 14.7 dB/mm TE mode nonreciprocal attenuation," J. Lightw. Technol. 24, 38-43 (2006).

Z. Wang, S. Fan, "Suppressing the effect of disorders using time-reversal symmetry breaking in magneto-optical photonic crystals: An illustration with a four-port circulator," Photon. Nanostruct.: Fundam. Appl. 4, 132-140 (2006).

2005 (3)

Z. Wang, S. Fan, "Magneto-optical defects in two-dimensional photonic crystals," Appl. Phys. B 81, 369-375 (2005).

H. Dötsch, "Applications of magneto-optical waveguides in integrated optics: Review," J. Opt. Soc. Amer. B 22, 240-253 (2005).

V. Zayets, M. C. Debnath, K. Ando, "Optical isolation in Cd$_{1 - {\rm x}}$Mn$_{x}$Te magneto-optical waveguide grown on GaAs substrate," J. Opt. Soc. Amer. B 22, 281-285 (2005).

2004 (3)

M. Soljac˘ić, J. D. Joannopoulos, "Enhancement of nonlinear effects using photonic crystals," Nature Mater. 3, 211-219 (2004).

V. R. Almeida, C. A. Barrios, R. R. Panepucci, M. Lipson, "All-optical control of light on a silicon chip," Nature 431, 1081-1084 (2004).

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

2003 (1)

T. Tepper, C. A. Ross, "Pulsed laser deposition and refractive index measurement of fully substituted bismuth iron garnet films," J. Crystal Growth 255, 324-331 (2003).

2000 (3)

J. R. Goldman, T. D. Ladd, F. Yamaguchi, Y. Yamamoto, "Magnet designs for a crystal-lattice quantum computer," Appl. Phys. A 71, 11-17 (2000).

N. Adachi, V. P. Denysenkov, S. I. Khartsev, A. M. Grishin, T. Okuda, "Epitaxial Bi$_{3}$Fe$_{5}$O$_{12}$ (001) films grown by pulsed laser deposition and reactive ion beam sputtering techniques," J. Appl. Phys. 88, 2734-2739 (2000).

J. Fujita, M. Levy, J. R. M. Osgood, "Waveguide optical isolator based on Mach–Zehnder interferometer," Appl. Phys. Lett. 76, 2158-2160 (2000).

1999 (1)

O. Zhuromskyy, "Analysis of polarization independent Mach-Zehnder-type integrated optical isolator," J. Lightw. Technol. 17, 1200-1205 (1999).

1998 (2)

N. Bahlmann, "Improved design of magnetooptic Rib waveguides for optical isolators," J. Lightw. Technol. 16, 818-823 (1998).

V. Priye, B. P. Pal, K. Thyagarajan, "Analysis and design of a novel leaky YIG film guided wave optical isolator," J. Lightw. Technol. 16, 246-250 (1998).

Appl. Phys. Lett. (1)

Z. Yu, S. Fan, "Optical isolation based on nonreciprocal phase shift induced by interband photonic transitions," Appl. Phys. Lett. 94, (2009) Art. ID 171116.

Appl. Opt. (1)

Appl. Phys. A (1)

J. R. Goldman, T. D. Ladd, F. Yamaguchi, Y. Yamamoto, "Magnet designs for a crystal-lattice quantum computer," Appl. Phys. A 71, 11-17 (2000).

Appl. Phys. B (1)

Z. Wang, S. Fan, "Magneto-optical defects in two-dimensional photonic crystals," Appl. Phys. B 81, 369-375 (2005).

Appl. Phys. Lett. (6)

J. Fujita, M. Levy, J. R. M. Osgood, "Waveguide optical isolator based on Mach–Zehnder interferometer," Appl. Phys. Lett. 76, 2158-2160 (2000).

Y. Shoji, T. Mizumoto, H. Yokoi, I.-W. Hsieh, J. Richard, M. Osgood, "Magneto-optical isolator with silicon waveguides fabricated by direct bonding," Appl. Phys. Lett. 92, (2008) Art. ID 071117.

J. B. Khurgin, "Optical isolating action in surface plasmon polaritons," Appl. Phys. Lett. 89, (2006) Art. ID 251115.

T. Amemiya, "Semiconductor waveguide optical isolator based on nonreciprocal loss induced by ferromagnetic MnAs," Appl. Phys. Lett. 89, 021104 (2006).

W. V. Parys, "Transverse magnetic mode nonreciprocal propagation in an amplifying AlGaInAs/InP optical waveguide isolator," Appl. Phys. Lett. 88, (2006) Art. ID 071115.

Z. Yu, Z. Wang, S. Fan, "One-way total reflection with one-dimensional magneto-optical photonic crystals," Appl. Phys. Lett. 90, (2007) Art. ID 121133.

IEEE J. Sel. Topics Quantum Electron. (1)

Z. Yu, S. Fan, "Integrated nonmagnetic optical isolators based on photonic transitions," IEEE J. Sel. Topics Quantum Electron. 16, 459-466 (2010).

IEEE Photon. Technol. Lett. (1)

H. Shimizu, S. Yoshida, S. Goto, "Semiconductor waveguide optical isolators towards larger optical isolation utilizing nonreciprocal phase shift by ferromagnetic Co," IEEE Photon. Technol. Lett. 20, 1554-1556 (2008).

J. Lightw. Technol. (1)

V. Priye, B. P. Pal, K. Thyagarajan, "Analysis and design of a novel leaky YIG film guided wave optical isolator," J. Lightw. Technol. 16, 246-250 (1998).

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

H. Dötsch, "Applications of magneto-optical waveguides in integrated optics: Review," J. Opt. Soc. Amer. B 22, 240-253 (2005).

J. Appl. Phys. (2)

J. Montoya, K. Parameswaran, J. Hensley, M. Allen, R. Ram, "Surface plasmon isolator based on nonreciprocal coupling," J. Appl. Phys. 106, (2009) Art. ID 023108.

N. Adachi, V. P. Denysenkov, S. I. Khartsev, A. M. Grishin, T. Okuda, "Epitaxial Bi$_{3}$Fe$_{5}$O$_{12}$ (001) films grown by pulsed laser deposition and reactive ion beam sputtering techniques," J. Appl. Phys. 88, 2734-2739 (2000).

J. Crystal Growth (1)

T. Tepper, C. A. Ross, "Pulsed laser deposition and refractive index measurement of fully substituted bismuth iron garnet films," J. Crystal Growth 255, 324-331 (2003).

J. Lightw. Technol. (1)

N. Bahlmann, "Improved design of magnetooptic Rib waveguides for optical isolators," J. Lightw. Technol. 16, 818-823 (1998).

J. Lightw. Technol. (7)

T. R. Zaman, X. Guo, R. J. Ram, "Semiconductor waveguide isolators," J. Lightw. Technol. 26, 291-301 (2008).

H. Shimizu, Y. Nakano, "Fabrication and characterization of an InGaAsp/InP active waveguide optical isolator with 14.7 dB/mm TE mode nonreciprocal attenuation," J. Lightw. Technol. 24, 38-43 (2006).

Y. Shoji, I. W. Hsieh, J. R. M. Osgood, T. Mizumoto, "Polarization-independent magneto-optical waveguide isolator using TM-mode nonreciprocal phase shift," J. Lightw. Technol. 25, 3108-3113 (2007).

H. Shimizu, S. Goto, "Evanescent semiconductor active optical isolators for low insertion loss and high gain saturation power," J. Lightw. Technol. 28, 1414-1419 (2010).

O. Zhuromskyy, "Analysis of polarization independent Mach-Zehnder-type integrated optical isolator," J. Lightw. Technol. 17, 1200-1205 (1999).

H. Zhou, "Wavelength-selective optical waveguide isolator based on nonreciprocal ring-coupled mach-zehnder interferometer," J. Lightw. Technol. 26, 3166-3172 (2008).

H. Zhu, C. Jiang, "Extraordinary coupling into one-way magneto-optical photonic crystal waveguide," J. Lightw. Technol. 29, 708-713 (2011).

J. Magn. Magn. Mater. (1)

T. Amemiya, H. Shimizu, P. N. Hai, M. Tanaka, Y. Nakano, "Nonreciprocal propagation of light without external magnetic fields in a semiconductor waveguide isolator with a MnAs layer," J. Magn. Magn. Mater. 310, 2161-2163 (2007).

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

M. Vanwolleghem, P. Gogol, P. Beauvillain, W. V. Parys, R. Baets, "Design and optimization of a monolithically integratable InP-based optical waveguide isolator," J. Opt. Soc. Amer. B 24, 94 (2007).

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

V. Zayets, M. C. Debnath, K. Ando, "Optical isolation in Cd$_{1 - {\rm x}}$Mn$_{x}$Te magneto-optical waveguide grown on GaAs substrate," J. Opt. Soc. Amer. B 22, 281-285 (2005).

Nature (2)

V. R. Almeida, C. A. Barrios, R. R. Panepucci, M. Lipson, "All-optical control of light on a silicon chip," Nature 431, 1081-1084 (2004).

Z. Wang, Y. Chong, J. D. Joannopoulos, M. Soljac˘ić, "Observation of unidirectional backscattering-immune topological electromagnetic states," Nature 461, 772-775 (2009).

Nature Mater. (1)

M. Soljac˘ić, J. D. Joannopoulos, "Enhancement of nonlinear effects using photonic crystals," Nature Mater. 3, 211-219 (2004).

Nature Photon. (1)

Z. Yu, S. Fan, "Complete optical isolation created by indirect interband photonic transitions," Nature Photon. 3, 91-94 (2009).

Opt. Exp. (3)

A. E. Serebryannikov, E. Ozbay, "Isolation and one-way effects in diffraction on dielectric gratings with plasmonic inserts," Opt. Exp. 17, 278-292 (2009).

Y. Shoji, T. Mizumoto, "Ultra-wideband design of waveguide magneto-optical isolator operating in 1.31$\mu$m and 1.55$\mu$m band," Opt. Exp. 15, 639-645 (2007).

H. Zhu, C. Jiang, "Broadband unidirectional electromagnetic mode at interface of anti-parallel magnetized media," Opt. Exp. 18, 6914-6921 (2010).

Opt. Exp. (4)

N. Kono, K. Kakihara, K. Saitoh, M. Koshiba, "Nonreciprocal microresonators for the miniaturization of optical waveguide isolators," Opt. Exp. 15, 7737-7751 (2007).

X.-S. Lin, J.-H. Yan, L.-J. Wu, S. Lan, "High transmission contrast for single resonator based all-optical diodes with pump-assisting," Opt. Exp. 16, 20949-20954 (2008).

S. M. Drezdzon, T. Yoshie, "On-chip waveguide isolator based on bismuth iron garnet operating via nonreciprocal single-modecutoff," Opt. Exp. 17, 9276-9281 (2009).

Y. Shoji, T. Mizumoto, "Wideband operation of Mach–Zehnder interferomertic magneto-optical isolator using phase adjustment," Opt. Exp. 15, 13446-13450 (2007).

Opt. Laser Technol. (1)

A. Rostami, "Piecewise linear integrated optical device as an optical isolator using two-port nonlinear ring resonators," Opt. Laser Technol. 39, 1059-1065 (2007).

Opt. Lett. (1)

Photon. Nanostruct.: Fundam. Appl. (1)

Z. Wang, S. Fan, "Suppressing the effect of disorders using time-reversal symmetry breaking in magneto-optical photonic crystals: An illustration with a four-port circulator," Photon. Nanostruct.: Fundam. Appl. 4, 132-140 (2006).

Phys. Rev. Lett. (1)

Z. Wang, Y. D. Chong, J. D. Joannopoulos, M. Soljac˘ić, "Reflection-free one-way edge modes in a gyromagnetic photonic crystal," Phys. Rev. Lett. 100, (2008) Art. ID 013905.

Phys. Rev. A (1)

H. Takeda, S. John, "Compact optical one-way waveguide isolators for photonic-band-gap microchips," Phys. Rev. A 78, (2008) Art. ID 023804.

Phys. Rev. Lett. (2)

F. D. M. Haldane, S. Raghu, "Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry," Phys. Rev. Lett. 100, 013904 (2008).

Z. Yu, G. Veronis, Z. Wang, S. Fan, "One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal," Phys. Rev. Lett. 100, 023902 (2008).

Other (3)

D. G. Rabus, Integrated Ring Resonators (Springer, 2007).

K. Okamoto, Fundamentals of Optical Waveguides (Elsevier, 2006).

L. Pavesi, D. J. Lockwood, Silicon Photonics (Springer, 2004).

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