Abstract

We report a kind of broadband electromagnetic boundary mode at an interface of anti-parallel magnetized media, which can only propagate in one direction perpendicular to the magnetization and parallel to the interface. The unidirectionality of this mode originates from the permeability or permittivity tensor introduced by magnetization. We theoretically and numerically analyze the existence of the unidirectional mode, and point out that this mode can exist in both gyromagnetic and gyroelectric medium. We also propose a one-way waveguide based on this unidirectional mode, which may realize a new kind of electromagnetic isolation differing from those existing ones.

© 2010 OSA

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    [CrossRef]
  3. P. K. Amiri, B. Rejaei, Z. Yan, M. Vroubel, L. Dok Won, and S. X. Wang, “Nonreciprocal Spin Waves in Co-Ta-Zr Films and Multilayers,” IEEE Trans. Magn. 45(10), 4215–4218 (2009).
    [CrossRef]
  4. B. K. Kuanr, V. Veerakumar, R. Marson, S. R. Mishra, R. E. Camley, and Z. Celinski, “Nonreciprocal microwave devices based on magnetic nanowires,” Appl. Phys. Lett. 94(20), 202505 (2009).
    [CrossRef]
  5. A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
    [CrossRef] [PubMed]
  6. C. J. Barrelet, A. B. Greytak, and C. M. Lieber, “Nanowire Photonic Circuit Elements,” Nano Lett. 4(10), 1981–1985 (2004).
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  7. Y. Okamura, H. Inuzuka, T. Kikuchi, and S. Yamamoto, “Nonreciprocal propagation in magnetooptic YIG rib waveguides,” J. Lightwave Technol. 4(7), 711–714 (1986).
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  8. B. L. Johnson and R. E. Camley, “Nonreciprocal propagation of surface waves in quasiperiodic superlattices,” Phys. Rev. B 44(3), 1225–1231 (1991).
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  9. A. F. Popkov, M. Fehndrich, O. Zhuromskyy, and H. Dötsch, “Nonreciprocal light channeling in a film by a magnetic nonuniformity akin to a Néel domain wall,” J. Appl. Phys. 84(6), 3020 (1998).
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  12. W. V. Parys, B. Moeyersoon, D. V. Thourhout, R. Baets, M. Vanwolleghem, B. Dagens, J. Decobert, O. L. Gouezigou, D. Make, R. Vanheertum, and L. Lagae, “Transverse magnetic mode nonreciprocal propagation in an amplifying AlGaInAs/InP optical waveguide isolator,” Appl. Phys. Lett. 88(7), 071115 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  36. J. R. Goldman, T. D. Ladd, F. Yamaguchi, and Y. Yamamoto, “Magnet designs for a crystal-lattice quantum computer,” Appl. Phys., A Mater. Sci. Process. 71, 11–17 (2000).
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    [CrossRef] [PubMed]
  39. B. Bai, Y. Svirko, J. Turunen, and T. Vallius, “Optical activity in planar chiral metamaterials: Theoretical study,” Phys. Rev. A 76(2), 023811 (2007).
    [CrossRef]

2009 (8)

P. K. Amiri, B. Rejaei, Z. Yan, M. Vroubel, L. Dok Won, and S. X. Wang, “Nonreciprocal Spin Waves in Co-Ta-Zr Films and Multilayers,” IEEE Trans. Magn. 45(10), 4215–4218 (2009).
[CrossRef]

B. K. Kuanr, V. Veerakumar, R. Marson, S. R. Mishra, R. E. Camley, and Z. Celinski, “Nonreciprocal microwave devices based on magnetic nanowires,” Appl. Phys. Lett. 94(20), 202505 (2009).
[CrossRef]

J. Montoya, K. Parameswaran, J. Hensley, M. Allen, and R. Ram, “Surface plasmon isolator based on nonreciprocal coupling,” J. Appl. Phys. 106(2), 023108 (2009).
[CrossRef]

Z. Yu and S. Fan, “Optical isolation based on nonreciprocal phase shift induced by interband photonic transitions,” Appl. Phys. Lett. 94(17), 171116 (2009).
[CrossRef]

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[CrossRef] [PubMed]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3(2), 91–94 (2009).
[CrossRef]

A. E. Serebryannikov and E. Ozbay, “Isolation and one-way effects in diffraction on dielectric gratings with plasmonic inserts,” Opt. Express 17(1), 278–292 (2009).
[CrossRef] [PubMed]

S. M. Drezdzon and T. Yoshie, “On-chip waveguide isolator based on bismuth iron garnet operating via nonreciprocal single-mode cutoff,” Opt. Express 17(11), 9276–9281 (2009).
[CrossRef] [PubMed]

2008 (10)

H. Zhou, X. Jiang, J. Yang, Q. Zhou, T. Yu, and M. Wang, “Wavelength-Selective Optical Waveguide Isolator Based on Nonreciprocal Ring-Coupled Mach?Zehnder Interferometer,” J. Lightwave Technol. 26(17), 3166–3172 (2008).
[CrossRef]

H. Takeda and S. John, “Compact optical one-way waveguide isolators for photonic-band-gap microchips,” Phys. Rev. A 78(2), 023804 (2008).
[CrossRef]

Z. Yu, G. Veronis, Z. Wang, and 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(2), 023902 (2008).
[CrossRef] [PubMed]

T. R. Zaman, X. Guo, and R. J. Ram, “Semiconductor Waveguide Isolators,” J. Lightwave Technol. 26(2), 291–301 (2008).
[CrossRef]

L. Tang, S. M. Drezdzon, and T. Yoshie, “Single-mode waveguide optical isolator based on direction-dependent cutoff frequency,” Opt. Express 16(20), 16202–16208 (2008).
[CrossRef] [PubMed]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljacić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100(1), 013905 (2008).
[CrossRef] [PubMed]

Y. Shoji, T. Mizumoto, H. Yokoi, I.-W. Hsieh, J. Richard, and M. Osgood, “Magneto-optical isolator with silicon waveguides fabricated by direct bonding,” Appl. Phys. Lett. 92(7), 071117 (2008).
[CrossRef]

A. Potts, W. Zhang, and D. M. Bagnall, “Nonreciprocal diffraction through dielectric gratings with two-dimensional chirality,” Phys. Rev. A 77(4), 043816 (2008).
[CrossRef]

H. Shimizu, S. Yoshida, and S. Goto, “Semiconductor Waveguide Optical Isolators Towards Larger Optical Isolation Utilizing Nonreciprocal Phase Shift by Ferromagnetic Co,” IEEE Photon. Technol. Lett. 20(18), 1554–1556 (2008).
[CrossRef]

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[CrossRef] [PubMed]

2007 (5)

N. Kono, K. Kakihara, K. Saitoh, and M. Koshiba, “Nonreciprocal microresonators for the miniaturization of optical waveguide isolators,” Opt. Express 15(12), 7737–7751 (2007).
[CrossRef] [PubMed]

Y. Shoji and T. Mizumoto, “Wideband operation of Mach-Zehnder interferomertic magneto-optical isolator using phase adjustment,” Opt. Express 15(20), 13446–13450 (2007).
[CrossRef] [PubMed]

Y. Shoji, I. W. Hsieh, J. R. M. Osgood, and T. Mizumoto, “Polarization-Independent Magneto-Optical Waveguide Isolator Using TM-Mode Nonreciprocal Phase Shift,” J. Lightwave Technol. 25(10), 3108–3113 (2007).
[CrossRef]

B. Bai, Y. Svirko, J. Turunen, and T. Vallius, “Optical activity in planar chiral metamaterials: Theoretical study,” Phys. Rev. A 76(2), 023811 (2007).
[CrossRef]

J. B. González-Díaz, A. García-Martín, G. Armelles, J. M. García-Martín, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76(15), 153402 (2007).
[CrossRef]

2006 (1)

W. V. Parys, B. Moeyersoon, D. V. Thourhout, R. Baets, M. Vanwolleghem, B. Dagens, J. Decobert, O. L. Gouezigou, D. Make, R. Vanheertum, and L. Lagae, “Transverse magnetic mode nonreciprocal propagation in an amplifying AlGaInAs/InP optical waveguide isolator,” Appl. Phys. Lett. 88(7), 071115 (2006).
[CrossRef]

2004 (4)

C. J. Barrelet, A. B. Greytak, and C. M. Lieber, “Nanowire Photonic Circuit Elements,” Nano Lett. 4(10), 1981–1985 (2004).
[CrossRef]

C. Brosseau, S. Mallégol, P. Quéffelec, and J. Ben Youssef, “Nonreciprocal electromagnetic properties of nanocomposites at microwave frequencies,” Phys. Rev. B 70(9), 092401 (2004).
[CrossRef]

J. B. Pendry, “A chiral route to negative refraction,” Science 306(5700), 1353–1355 (2004).
[CrossRef] [PubMed]

R. L. Espinola, T. Izuhara, M.-C. Tsai, R. M. Osgood, and H. Dötsch, “Magneto-optical nonreciprocal phase shift in garnet/silicon-on-insulator waveguides,” Opt. Lett. 29(9), 941–943 (2004).
[CrossRef] [PubMed]

2002 (1)

P. A. Belov, S. A. Tretyakov, and A. J. Viitanen, “Nonreciprocal microwave band-gap structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(1), 016608 (2002).
[CrossRef] [PubMed]

2001 (2)

2000 (2)

J. R. Goldman, T. D. Ladd, F. Yamaguchi, and Y. Yamamoto, “Magnet designs for a crystal-lattice quantum computer,” Appl. Phys., A Mater. Sci. Process. 71, 11–17 (2000).

J. Fujita, M. Levy, J. R. M. Osgood, L. Wilkens, and H. Dötsch, “Waveguide optical isolator based on Mach–Zehnder interferometer,” Appl. Phys. Lett. 76(16), 2158–2160 (2000).
[CrossRef]

1998 (2)

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(20), 2508–2510 (1998).
[CrossRef]

A. F. Popkov, M. Fehndrich, O. Zhuromskyy, and H. Dötsch, “Nonreciprocal light channeling in a film by a magnetic nonuniformity akin to a Néel domain wall,” J. Appl. Phys. 84(6), 3020 (1998).
[CrossRef]

1991 (1)

B. L. Johnson and R. E. Camley, “Nonreciprocal propagation of surface waves in quasiperiodic superlattices,” Phys. Rev. B 44(3), 1225–1231 (1991).
[CrossRef]

1987 (1)

R. E. Camley, “Nonreciprocal Surface wave,” Surf. Sci. Rep. 7(3-4), 103–187 (1987).
[CrossRef]

1986 (1)

Y. Okamura, H. Inuzuka, T. Kikuchi, and S. Yamamoto, “Nonreciprocal propagation in magnetooptic YIG rib waveguides,” J. Lightwave Technol. 4(7), 711–714 (1986).
[CrossRef]

Allen, M.

J. Montoya, K. Parameswaran, J. Hensley, M. Allen, and R. Ram, “Surface plasmon isolator based on nonreciprocal coupling,” J. Appl. Phys. 106(2), 023108 (2009).
[CrossRef]

Amiri, P. K.

P. K. Amiri, B. Rejaei, Z. Yan, M. Vroubel, L. Dok Won, and S. X. Wang, “Nonreciprocal Spin Waves in Co-Ta-Zr Films and Multilayers,” IEEE Trans. Magn. 45(10), 4215–4218 (2009).
[CrossRef]

Armelles, G.

J. B. González-Díaz, A. García-Martín, G. Armelles, J. M. García-Martín, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76(15), 153402 (2007).
[CrossRef]

Baets, R.

W. V. Parys, B. Moeyersoon, D. V. Thourhout, R. Baets, M. Vanwolleghem, B. Dagens, J. Decobert, O. L. Gouezigou, D. Make, R. Vanheertum, and L. Lagae, “Transverse magnetic mode nonreciprocal propagation in an amplifying AlGaInAs/InP optical waveguide isolator,” Appl. Phys. Lett. 88(7), 071115 (2006).
[CrossRef]

Bagnall, D. M.

A. Potts, W. Zhang, and D. M. Bagnall, “Nonreciprocal diffraction through dielectric gratings with two-dimensional chirality,” Phys. Rev. A 77(4), 043816 (2008).
[CrossRef]

Bai, B.

B. Bai, Y. Svirko, J. Turunen, and T. Vallius, “Optical activity in planar chiral metamaterials: Theoretical study,” Phys. Rev. A 76(2), 023811 (2007).
[CrossRef]

Barrelet, C. J.

C. J. Barrelet, A. B. Greytak, and C. M. Lieber, “Nanowire Photonic Circuit Elements,” Nano Lett. 4(10), 1981–1985 (2004).
[CrossRef]

Belov, P. A.

P. A. Belov, S. A. Tretyakov, and A. J. Viitanen, “Nonreciprocal microwave band-gap structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(1), 016608 (2002).
[CrossRef] [PubMed]

Ben Youssef, J.

C. Brosseau, S. Mallégol, P. Quéffelec, and J. Ben Youssef, “Nonreciprocal electromagnetic properties of nanocomposites at microwave frequencies,” Phys. Rev. B 70(9), 092401 (2004).
[CrossRef]

Brosseau, C.

C. Brosseau, S. Mallégol, P. Quéffelec, and J. Ben Youssef, “Nonreciprocal electromagnetic properties of nanocomposites at microwave frequencies,” Phys. Rev. B 70(9), 092401 (2004).
[CrossRef]

Camley, R. E.

B. K. Kuanr, V. Veerakumar, R. Marson, S. R. Mishra, R. E. Camley, and Z. Celinski, “Nonreciprocal microwave devices based on magnetic nanowires,” Appl. Phys. Lett. 94(20), 202505 (2009).
[CrossRef]

B. L. Johnson and R. E. Camley, “Nonreciprocal propagation of surface waves in quasiperiodic superlattices,” Phys. Rev. B 44(3), 1225–1231 (1991).
[CrossRef]

R. E. Camley, “Nonreciprocal Surface wave,” Surf. Sci. Rep. 7(3-4), 103–187 (1987).
[CrossRef]

Cebollada, A.

J. B. González-Díaz, A. García-Martín, G. Armelles, J. M. García-Martín, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76(15), 153402 (2007).
[CrossRef]

Celinski, Z.

B. K. Kuanr, V. Veerakumar, R. Marson, S. R. Mishra, R. E. Camley, and Z. Celinski, “Nonreciprocal microwave devices based on magnetic nanowires,” Appl. Phys. Lett. 94(20), 202505 (2009).
[CrossRef]

Chong, Y.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[CrossRef] [PubMed]

Chong, Y. D.

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljacić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100(1), 013905 (2008).
[CrossRef] [PubMed]

Clarke, R.

J. B. González-Díaz, A. García-Martín, G. Armelles, J. M. García-Martín, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76(15), 153402 (2007).
[CrossRef]

Clavero, C.

J. B. González-Díaz, A. García-Martín, G. Armelles, J. M. García-Martín, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76(15), 153402 (2007).
[CrossRef]

Cryan, M. J.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[CrossRef] [PubMed]

Dagens, B.

W. V. Parys, B. Moeyersoon, D. V. Thourhout, R. Baets, M. Vanwolleghem, B. Dagens, J. Decobert, O. L. Gouezigou, D. Make, R. Vanheertum, and L. Lagae, “Transverse magnetic mode nonreciprocal propagation in an amplifying AlGaInAs/InP optical waveguide isolator,” Appl. Phys. Lett. 88(7), 071115 (2006).
[CrossRef]

Decobert, J.

W. V. Parys, B. Moeyersoon, D. V. Thourhout, R. Baets, M. Vanwolleghem, B. Dagens, J. Decobert, O. L. Gouezigou, D. Make, R. Vanheertum, and L. Lagae, “Transverse magnetic mode nonreciprocal propagation in an amplifying AlGaInAs/InP optical waveguide isolator,” Appl. Phys. Lett. 88(7), 071115 (2006).
[CrossRef]

Dok Won, L.

P. K. Amiri, B. Rejaei, Z. Yan, M. Vroubel, L. Dok Won, and S. X. Wang, “Nonreciprocal Spin Waves in Co-Ta-Zr Films and Multilayers,” IEEE Trans. Magn. 45(10), 4215–4218 (2009).
[CrossRef]

Dötsch, H.

R. L. Espinola, T. Izuhara, M.-C. Tsai, R. M. Osgood, and H. Dötsch, “Magneto-optical nonreciprocal phase shift in garnet/silicon-on-insulator waveguides,” Opt. Lett. 29(9), 941–943 (2004).
[CrossRef] [PubMed]

O. Zhuromskyy, H. Dötsch, M. Lohmeyer, L. Wilkens, and P. Hertel, “Magnetooptical Waveguides with Polarization-Independent Nonreciprocal PhaseShift,” J. Lightwave Technol. 19(2), 214–221 (2001).
[CrossRef]

J. Fujita, M. Levy, J. R. M. Osgood, L. Wilkens, and H. Dötsch, “Waveguide optical isolator based on Mach–Zehnder interferometer,” Appl. Phys. Lett. 76(16), 2158–2160 (2000).
[CrossRef]

A. F. Popkov, M. Fehndrich, O. Zhuromskyy, and H. Dötsch, “Nonreciprocal light channeling in a film by a magnetic nonuniformity akin to a Néel domain wall,” J. Appl. Phys. 84(6), 3020 (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(20), 2508–2510 (1998).
[CrossRef]

Drezdzon, S. M.

Espinola, R. L.

Fan, S.

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3(2), 91–94 (2009).
[CrossRef]

Z. Yu and S. Fan, “Optical isolation based on nonreciprocal phase shift induced by interband photonic transitions,” Appl. Phys. Lett. 94(17), 171116 (2009).
[CrossRef]

Z. Yu, G. Veronis, Z. Wang, and 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(2), 023902 (2008).
[CrossRef] [PubMed]

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(20), 2508–2510 (1998).
[CrossRef]

A. F. Popkov, M. Fehndrich, O. Zhuromskyy, and H. Dötsch, “Nonreciprocal light channeling in a film by a magnetic nonuniformity akin to a Néel domain wall,” J. Appl. Phys. 84(6), 3020 (1998).
[CrossRef]

Figotin, A.

A. Figotin and I. Vitebsky, “Nonreciprocal magnetic photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(6), 066609 (2001).
[CrossRef] [PubMed]

Fujita, J.

J. Fujita, M. Levy, J. R. M. Osgood, L. Wilkens, and H. Dötsch, “Waveguide optical isolator based on Mach–Zehnder interferometer,” Appl. Phys. Lett. 76(16), 2158–2160 (2000).
[CrossRef]

García-Martín, A.

J. B. González-Díaz, A. García-Martín, G. Armelles, J. M. García-Martín, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76(15), 153402 (2007).
[CrossRef]

García-Martín, J. M.

J. B. González-Díaz, A. García-Martín, G. Armelles, J. M. García-Martín, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76(15), 153402 (2007).
[CrossRef]

Goldman, J. R.

J. R. Goldman, T. D. Ladd, F. Yamaguchi, and Y. Yamamoto, “Magnet designs for a crystal-lattice quantum computer,” Appl. Phys., A Mater. Sci. Process. 71, 11–17 (2000).

González-Díaz, J. B.

J. B. González-Díaz, A. García-Martín, G. Armelles, J. M. García-Martín, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76(15), 153402 (2007).
[CrossRef]

Goto, S.

H. Shimizu, S. Yoshida, and S. Goto, “Semiconductor Waveguide Optical Isolators Towards Larger Optical Isolation Utilizing Nonreciprocal Phase Shift by Ferromagnetic Co,” IEEE Photon. Technol. Lett. 20(18), 1554–1556 (2008).
[CrossRef]

Gouezigou, O. L.

W. V. Parys, B. Moeyersoon, D. V. Thourhout, R. Baets, M. Vanwolleghem, B. Dagens, J. Decobert, O. L. Gouezigou, D. Make, R. Vanheertum, and L. Lagae, “Transverse magnetic mode nonreciprocal propagation in an amplifying AlGaInAs/InP optical waveguide isolator,” Appl. Phys. Lett. 88(7), 071115 (2006).
[CrossRef]

Greytak, A. B.

C. J. Barrelet, A. B. Greytak, and C. M. Lieber, “Nanowire Photonic Circuit Elements,” Nano Lett. 4(10), 1981–1985 (2004).
[CrossRef]

Guo, X.

Hensley, J.

J. Montoya, K. Parameswaran, J. Hensley, M. Allen, and R. Ram, “Surface plasmon isolator based on nonreciprocal coupling,” J. Appl. Phys. 106(2), 023108 (2009).
[CrossRef]

Hertel, P.

Hsieh, I. W.

Hsieh, I.-W.

Y. Shoji, T. Mizumoto, H. Yokoi, I.-W. Hsieh, J. Richard, and M. Osgood, “Magneto-optical isolator with silicon waveguides fabricated by direct bonding,” Appl. Phys. Lett. 92(7), 071117 (2008).
[CrossRef]

Inuzuka, H.

Y. Okamura, H. Inuzuka, T. Kikuchi, and S. Yamamoto, “Nonreciprocal propagation in magnetooptic YIG rib waveguides,” J. Lightwave Technol. 4(7), 711–714 (1986).
[CrossRef]

Izuhara, T.

Jiang, X.

Joannopoulos, J. D.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[CrossRef] [PubMed]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljacić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100(1), 013905 (2008).
[CrossRef] [PubMed]

John, S.

H. Takeda and S. John, “Compact optical one-way waveguide isolators for photonic-band-gap microchips,” Phys. Rev. A 78(2), 023804 (2008).
[CrossRef]

Johnson, B. L.

B. L. Johnson and R. E. Camley, “Nonreciprocal propagation of surface waves in quasiperiodic superlattices,” Phys. Rev. B 44(3), 1225–1231 (1991).
[CrossRef]

Kakihara, K.

Kikuchi, T.

Y. Okamura, H. Inuzuka, T. Kikuchi, and S. Yamamoto, “Nonreciprocal propagation in magnetooptic YIG rib waveguides,” J. Lightwave Technol. 4(7), 711–714 (1986).
[CrossRef]

Kono, N.

Koshiba, M.

Kuanr, B. K.

B. K. Kuanr, V. Veerakumar, R. Marson, S. R. Mishra, R. E. Camley, and Z. Celinski, “Nonreciprocal microwave devices based on magnetic nanowires,” Appl. Phys. Lett. 94(20), 202505 (2009).
[CrossRef]

Kumah, D. P.

J. B. González-Díaz, A. García-Martín, G. Armelles, J. M. García-Martín, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76(15), 153402 (2007).
[CrossRef]

Ladd, T. D.

J. R. Goldman, T. D. Ladd, F. Yamaguchi, and Y. Yamamoto, “Magnet designs for a crystal-lattice quantum computer,” Appl. Phys., A Mater. Sci. Process. 71, 11–17 (2000).

Lagae, L.

W. V. Parys, B. Moeyersoon, D. V. Thourhout, R. Baets, M. Vanwolleghem, B. Dagens, J. Decobert, O. L. Gouezigou, D. Make, R. Vanheertum, and L. Lagae, “Transverse magnetic mode nonreciprocal propagation in an amplifying AlGaInAs/InP optical waveguide isolator,” Appl. Phys. Lett. 88(7), 071115 (2006).
[CrossRef]

Levy, M.

J. Fujita, M. Levy, J. R. M. Osgood, L. Wilkens, and H. Dötsch, “Waveguide optical isolator based on Mach–Zehnder interferometer,” Appl. Phys. Lett. 76(16), 2158–2160 (2000).
[CrossRef]

Lieber, C. M.

C. J. Barrelet, A. B. Greytak, and C. M. Lieber, “Nanowire Photonic Circuit Elements,” Nano Lett. 4(10), 1981–1985 (2004).
[CrossRef]

Lohmeyer, M.

O. Zhuromskyy, H. Dötsch, M. Lohmeyer, L. Wilkens, and P. Hertel, “Magnetooptical Waveguides with Polarization-Independent Nonreciprocal PhaseShift,” J. Lightwave Technol. 19(2), 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(20), 2508–2510 (1998).
[CrossRef]

Lukaszew, R. A.

J. B. González-Díaz, A. García-Martín, G. Armelles, J. M. García-Martín, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76(15), 153402 (2007).
[CrossRef]

Make, D.

W. V. Parys, B. Moeyersoon, D. V. Thourhout, R. Baets, M. Vanwolleghem, B. Dagens, J. Decobert, O. L. Gouezigou, D. Make, R. Vanheertum, and L. Lagae, “Transverse magnetic mode nonreciprocal propagation in an amplifying AlGaInAs/InP optical waveguide isolator,” Appl. Phys. Lett. 88(7), 071115 (2006).
[CrossRef]

Mallégol, S.

C. Brosseau, S. Mallégol, P. Quéffelec, and J. Ben Youssef, “Nonreciprocal electromagnetic properties of nanocomposites at microwave frequencies,” Phys. Rev. B 70(9), 092401 (2004).
[CrossRef]

Marson, R.

B. K. Kuanr, V. Veerakumar, R. Marson, S. R. Mishra, R. E. Camley, and Z. Celinski, “Nonreciprocal microwave devices based on magnetic nanowires,” Appl. Phys. Lett. 94(20), 202505 (2009).
[CrossRef]

Mishra, S. R.

B. K. Kuanr, V. Veerakumar, R. Marson, S. R. Mishra, R. E. Camley, and Z. Celinski, “Nonreciprocal microwave devices based on magnetic nanowires,” Appl. Phys. Lett. 94(20), 202505 (2009).
[CrossRef]

Mizumoto, T.

Moeyersoon, B.

W. V. Parys, B. Moeyersoon, D. V. Thourhout, R. Baets, M. Vanwolleghem, B. Dagens, J. Decobert, O. L. Gouezigou, D. Make, R. Vanheertum, and L. Lagae, “Transverse magnetic mode nonreciprocal propagation in an amplifying AlGaInAs/InP optical waveguide isolator,” Appl. Phys. Lett. 88(7), 071115 (2006).
[CrossRef]

Montoya, J.

J. Montoya, K. Parameswaran, J. Hensley, M. Allen, and R. Ram, “Surface plasmon isolator based on nonreciprocal coupling,” J. Appl. Phys. 106(2), 023108 (2009).
[CrossRef]

O’Brien, J. L.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[CrossRef] [PubMed]

Okamura, Y.

Y. Okamura, H. Inuzuka, T. Kikuchi, and S. Yamamoto, “Nonreciprocal propagation in magnetooptic YIG rib waveguides,” J. Lightwave Technol. 4(7), 711–714 (1986).
[CrossRef]

Osgood, J. R. M.

Y. Shoji, I. W. Hsieh, J. R. M. Osgood, and T. Mizumoto, “Polarization-Independent Magneto-Optical Waveguide Isolator Using TM-Mode Nonreciprocal Phase Shift,” J. Lightwave Technol. 25(10), 3108–3113 (2007).
[CrossRef]

J. Fujita, M. Levy, J. R. M. Osgood, L. Wilkens, and H. Dötsch, “Waveguide optical isolator based on Mach–Zehnder interferometer,” Appl. Phys. Lett. 76(16), 2158–2160 (2000).
[CrossRef]

Osgood, M.

Y. Shoji, T. Mizumoto, H. Yokoi, I.-W. Hsieh, J. Richard, and M. Osgood, “Magneto-optical isolator with silicon waveguides fabricated by direct bonding,” Appl. Phys. Lett. 92(7), 071117 (2008).
[CrossRef]

Osgood, R. M.

Ozbay, E.

Parameswaran, K.

J. Montoya, K. Parameswaran, J. Hensley, M. Allen, and R. Ram, “Surface plasmon isolator based on nonreciprocal coupling,” J. Appl. Phys. 106(2), 023108 (2009).
[CrossRef]

Parys, W. V.

W. V. Parys, B. Moeyersoon, D. V. Thourhout, R. Baets, M. Vanwolleghem, B. Dagens, J. Decobert, O. L. Gouezigou, D. Make, R. Vanheertum, and L. Lagae, “Transverse magnetic mode nonreciprocal propagation in an amplifying AlGaInAs/InP optical waveguide isolator,” Appl. Phys. Lett. 88(7), 071115 (2006).
[CrossRef]

Pendry, J. B.

J. B. Pendry, “A chiral route to negative refraction,” Science 306(5700), 1353–1355 (2004).
[CrossRef] [PubMed]

Politi, A.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[CrossRef] [PubMed]

Popkov, A. F.

A. F. Popkov, M. Fehndrich, O. Zhuromskyy, and H. Dötsch, “Nonreciprocal light channeling in a film by a magnetic nonuniformity akin to a Néel domain wall,” J. Appl. Phys. 84(6), 3020 (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(20), 2508–2510 (1998).
[CrossRef]

Potts, A.

A. Potts, W. Zhang, and D. M. Bagnall, “Nonreciprocal diffraction through dielectric gratings with two-dimensional chirality,” Phys. Rev. A 77(4), 043816 (2008).
[CrossRef]

Quéffelec, P.

C. Brosseau, S. Mallégol, P. Quéffelec, and J. Ben Youssef, “Nonreciprocal electromagnetic properties of nanocomposites at microwave frequencies,” Phys. Rev. B 70(9), 092401 (2004).
[CrossRef]

Ram, R.

J. Montoya, K. Parameswaran, J. Hensley, M. Allen, and R. Ram, “Surface plasmon isolator based on nonreciprocal coupling,” J. Appl. Phys. 106(2), 023108 (2009).
[CrossRef]

Ram, R. J.

Rarity, J. G.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[CrossRef] [PubMed]

Rejaei, B.

P. K. Amiri, B. Rejaei, Z. Yan, M. Vroubel, L. Dok Won, and S. X. Wang, “Nonreciprocal Spin Waves in Co-Ta-Zr Films and Multilayers,” IEEE Trans. Magn. 45(10), 4215–4218 (2009).
[CrossRef]

Richard, J.

Y. Shoji, T. Mizumoto, H. Yokoi, I.-W. Hsieh, J. Richard, and M. Osgood, “Magneto-optical isolator with silicon waveguides fabricated by direct bonding,” Appl. Phys. Lett. 92(7), 071117 (2008).
[CrossRef]

Saitoh, K.

Serebryannikov, A. E.

Shimizu, H.

H. Shimizu, S. Yoshida, and S. Goto, “Semiconductor Waveguide Optical Isolators Towards Larger Optical Isolation Utilizing Nonreciprocal Phase Shift by Ferromagnetic Co,” IEEE Photon. Technol. Lett. 20(18), 1554–1556 (2008).
[CrossRef]

Shoji, Y.

Skuza, J. R.

J. B. González-Díaz, A. García-Martín, G. Armelles, J. M. García-Martín, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76(15), 153402 (2007).
[CrossRef]

Soljacic, M.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[CrossRef] [PubMed]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljacić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100(1), 013905 (2008).
[CrossRef] [PubMed]

Svirko, Y.

B. Bai, Y. Svirko, J. Turunen, and T. Vallius, “Optical activity in planar chiral metamaterials: Theoretical study,” Phys. Rev. A 76(2), 023811 (2007).
[CrossRef]

Takeda, H.

H. Takeda and S. John, “Compact optical one-way waveguide isolators for photonic-band-gap microchips,” Phys. Rev. A 78(2), 023804 (2008).
[CrossRef]

Tang, L.

Thourhout, D. V.

W. V. Parys, B. Moeyersoon, D. V. Thourhout, R. Baets, M. Vanwolleghem, B. Dagens, J. Decobert, O. L. Gouezigou, D. Make, R. Vanheertum, and L. Lagae, “Transverse magnetic mode nonreciprocal propagation in an amplifying AlGaInAs/InP optical waveguide isolator,” Appl. Phys. Lett. 88(7), 071115 (2006).
[CrossRef]

Tretyakov, S. A.

P. A. Belov, S. A. Tretyakov, and A. J. Viitanen, “Nonreciprocal microwave band-gap structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(1), 016608 (2002).
[CrossRef] [PubMed]

Tsai, M.-C.

Turunen, J.

B. Bai, Y. Svirko, J. Turunen, and T. Vallius, “Optical activity in planar chiral metamaterials: Theoretical study,” Phys. Rev. A 76(2), 023811 (2007).
[CrossRef]

Vallius, T.

B. Bai, Y. Svirko, J. Turunen, and T. Vallius, “Optical activity in planar chiral metamaterials: Theoretical study,” Phys. Rev. A 76(2), 023811 (2007).
[CrossRef]

Vanheertum, R.

W. V. Parys, B. Moeyersoon, D. V. Thourhout, R. Baets, M. Vanwolleghem, B. Dagens, J. Decobert, O. L. Gouezigou, D. Make, R. Vanheertum, and L. Lagae, “Transverse magnetic mode nonreciprocal propagation in an amplifying AlGaInAs/InP optical waveguide isolator,” Appl. Phys. Lett. 88(7), 071115 (2006).
[CrossRef]

Vanwolleghem, M.

W. V. Parys, B. Moeyersoon, D. V. Thourhout, R. Baets, M. Vanwolleghem, B. Dagens, J. Decobert, O. L. Gouezigou, D. Make, R. Vanheertum, and L. Lagae, “Transverse magnetic mode nonreciprocal propagation in an amplifying AlGaInAs/InP optical waveguide isolator,” Appl. Phys. Lett. 88(7), 071115 (2006).
[CrossRef]

Veerakumar, V.

B. K. Kuanr, V. Veerakumar, R. Marson, S. R. Mishra, R. E. Camley, and Z. Celinski, “Nonreciprocal microwave devices based on magnetic nanowires,” Appl. Phys. Lett. 94(20), 202505 (2009).
[CrossRef]

Veronis, G.

Z. Yu, G. Veronis, Z. Wang, and 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(2), 023902 (2008).
[CrossRef] [PubMed]

Viitanen, A. J.

P. A. Belov, S. A. Tretyakov, and A. J. Viitanen, “Nonreciprocal microwave band-gap structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(1), 016608 (2002).
[CrossRef] [PubMed]

Vitebsky, I.

A. Figotin and I. Vitebsky, “Nonreciprocal magnetic photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(6), 066609 (2001).
[CrossRef] [PubMed]

Vroubel, M.

P. K. Amiri, B. Rejaei, Z. Yan, M. Vroubel, L. Dok Won, and S. X. Wang, “Nonreciprocal Spin Waves in Co-Ta-Zr Films and Multilayers,” IEEE Trans. Magn. 45(10), 4215–4218 (2009).
[CrossRef]

Wang, M.

Wang, S. X.

P. K. Amiri, B. Rejaei, Z. Yan, M. Vroubel, L. Dok Won, and S. X. Wang, “Nonreciprocal Spin Waves in Co-Ta-Zr Films and Multilayers,” IEEE Trans. Magn. 45(10), 4215–4218 (2009).
[CrossRef]

Wang, Z.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[CrossRef] [PubMed]

Z. Yu, G. Veronis, Z. Wang, and 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(2), 023902 (2008).
[CrossRef] [PubMed]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljacić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100(1), 013905 (2008).
[CrossRef] [PubMed]

Wilkens, L.

O. Zhuromskyy, H. Dötsch, M. Lohmeyer, L. Wilkens, and P. Hertel, “Magnetooptical Waveguides with Polarization-Independent Nonreciprocal PhaseShift,” J. Lightwave Technol. 19(2), 214–221 (2001).
[CrossRef]

J. Fujita, M. Levy, J. R. M. Osgood, L. Wilkens, and H. Dötsch, “Waveguide optical isolator based on Mach–Zehnder interferometer,” Appl. Phys. Lett. 76(16), 2158–2160 (2000).
[CrossRef]

Yamaguchi, F.

J. R. Goldman, T. D. Ladd, F. Yamaguchi, and Y. Yamamoto, “Magnet designs for a crystal-lattice quantum computer,” Appl. Phys., A Mater. Sci. Process. 71, 11–17 (2000).

Yamamoto, S.

Y. Okamura, H. Inuzuka, T. Kikuchi, and S. Yamamoto, “Nonreciprocal propagation in magnetooptic YIG rib waveguides,” J. Lightwave Technol. 4(7), 711–714 (1986).
[CrossRef]

Yamamoto, Y.

J. R. Goldman, T. D. Ladd, F. Yamaguchi, and Y. Yamamoto, “Magnet designs for a crystal-lattice quantum computer,” Appl. Phys., A Mater. Sci. Process. 71, 11–17 (2000).

Yan, Z.

P. K. Amiri, B. Rejaei, Z. Yan, M. Vroubel, L. Dok Won, and S. X. Wang, “Nonreciprocal Spin Waves in Co-Ta-Zr Films and Multilayers,” IEEE Trans. Magn. 45(10), 4215–4218 (2009).
[CrossRef]

Yang, J.

Yokoi, H.

Y. Shoji, T. Mizumoto, H. Yokoi, I.-W. Hsieh, J. Richard, and M. Osgood, “Magneto-optical isolator with silicon waveguides fabricated by direct bonding,” Appl. Phys. Lett. 92(7), 071117 (2008).
[CrossRef]

Yoshida, S.

H. Shimizu, S. Yoshida, and S. Goto, “Semiconductor Waveguide Optical Isolators Towards Larger Optical Isolation Utilizing Nonreciprocal Phase Shift by Ferromagnetic Co,” IEEE Photon. Technol. Lett. 20(18), 1554–1556 (2008).
[CrossRef]

Yoshie, T.

Yu, S.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[CrossRef] [PubMed]

Yu, T.

Yu, Z.

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3(2), 91–94 (2009).
[CrossRef]

Z. Yu and S. Fan, “Optical isolation based on nonreciprocal phase shift induced by interband photonic transitions,” Appl. Phys. Lett. 94(17), 171116 (2009).
[CrossRef]

Z. Yu, G. Veronis, Z. Wang, and 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(2), 023902 (2008).
[CrossRef] [PubMed]

Zaman, T. R.

Zhang, W.

A. Potts, W. Zhang, and D. M. Bagnall, “Nonreciprocal diffraction through dielectric gratings with two-dimensional chirality,” Phys. Rev. A 77(4), 043816 (2008).
[CrossRef]

Zhou, H.

Zhou, Q.

Zhuromskyy, O.

O. Zhuromskyy, H. Dötsch, M. Lohmeyer, L. Wilkens, and P. Hertel, “Magnetooptical Waveguides with Polarization-Independent Nonreciprocal PhaseShift,” J. Lightwave Technol. 19(2), 214–221 (2001).
[CrossRef]

A. F. Popkov, M. Fehndrich, O. Zhuromskyy, and H. Dötsch, “Nonreciprocal light channeling in a film by a magnetic nonuniformity akin to a Néel domain wall,” J. Appl. Phys. 84(6), 3020 (1998).
[CrossRef]

Appl. Phys. Lett. (6)

B. K. Kuanr, V. Veerakumar, R. Marson, S. R. Mishra, R. E. Camley, and Z. Celinski, “Nonreciprocal microwave devices based on magnetic nanowires,” Appl. Phys. Lett. 94(20), 202505 (2009).
[CrossRef]

W. V. Parys, B. Moeyersoon, D. V. Thourhout, R. Baets, M. Vanwolleghem, B. Dagens, J. Decobert, O. L. Gouezigou, D. Make, R. Vanheertum, and L. Lagae, “Transverse magnetic mode nonreciprocal propagation in an amplifying AlGaInAs/InP optical waveguide isolator,” Appl. Phys. Lett. 88(7), 071115 (2006).
[CrossRef]

Y. Shoji, T. Mizumoto, H. Yokoi, I.-W. Hsieh, J. Richard, and M. Osgood, “Magneto-optical isolator with silicon waveguides fabricated by direct bonding,” Appl. Phys. Lett. 92(7), 071117 (2008).
[CrossRef]

Z. Yu and S. Fan, “Optical isolation based on nonreciprocal phase shift induced by interband photonic transitions,” Appl. Phys. Lett. 94(17), 171116 (2009).
[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(20), 2508–2510 (1998).
[CrossRef]

J. Fujita, M. Levy, J. R. M. Osgood, L. Wilkens, and H. Dötsch, “Waveguide optical isolator based on Mach–Zehnder interferometer,” Appl. Phys. Lett. 76(16), 2158–2160 (2000).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Magnetic domain wall and steady-state field pattern for unidirectional mode. The external magnetic field for y>0 and y<0 are applied along + z and -z, respectively. A TE polarized (Ez ) point source, indicated by the big arrow in (a), is located at the domain wall. Ez field pattern is indicated with blue-red color map in (a)-(e), while H field pattern is shown in (a) with arrows grid. At very boundary of the domain wall we can observe a unidirectional boundary mode, which is exactly a TEM mode. Different frequencies 0.050, 0.075, 0.100, 0.125 and 0.150 ( × 2 π c / a ) are utilized to show the unidirectional phenomenon, which are shown in (a), (b), (c), (d) and (e), respectively.

Fig. 2
Fig. 2

Deviation cases from anti-symmetrical profile of domain wall. Partly demagnetization case with μ 1 = 6 and μ 2 = 2 for y>0 is shown in (a); and unmagnetization case with μ 1 = 1 and μ 2 = 0 for y>0 is shown in (b). Operating frequency is chosen as 0.2 × 2 π c / a for clearly demonstration, where a is the normalized length.

Fig. 3
Fig. 3

Isolator based on unidirectional boundary mode at the domain wall. The isolator is connected with two reciprocal waveguide, which work as input and output ports. The mechanism of this isolator is shown in (a), and the forward and backward transmitting steady-state field patterns are shown in (b) and (c). Operating frequency is 0.05 × 2 π c / a , where a is the waveguide's width.

Fig. 4
Fig. 4

Forward and backward transmission (a), and the isolation ratio (b) for our example isolator. In (a), the blue line represents the forward transmission and the red one represents the backward counterpart. The magnified backward transmission is plotted in the inside box. (b) shows the high isolation ratio in a wide frequency range.

Equations (6)

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ε = ε 0 [ ε 1 i ε 2 0 i ε 2 ε 1 0 0 0 1 ] , μ = μ 0 [ μ 1 i μ 2 0 i μ 2 μ 1 0 0 0 1 ] .
H ( > ) ( r ; t ) = A ( 0 , 0 , 1 ) exp[i k x α y i ω t ]
Ε ( > ) ( r ; t ) = A i ω [ ε ˜ 1 α + ε ˜ 2 k ,  i( ε ˜ 2 α + ε ˜ 1 k ), 0 ] exp[i k x α y i ω t ]
H ( < ) ( r ; t ) = B ( 0 , 0 , 1 ) exp[i k x + β y i ω t ]
Ε ( < ) ( r ; t ) = A i ω [ ( ε ˜ 1 β + ε ˜ 2 k ) ,  i( ε ˜ 2 β + ε ˜ 1 k ), 0 ] exp[i k x + β y i ω t ]
k = ε ˜ 1 ε ˜ 2 α = α Q E .

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