Abstract

We show that optical Tamm states (OTSs) with nonreciprocal dispersion can be formed at the boundary separating two different magnetophotonic crystals magnetized in the Voigt geometry. At the frequencies of the Tamm states, one-way optical tunneling can be achieved. The nonreciprocity features of OTSs originate from the simultaneous violation of reciprocity, time-reversal, and all related spatial symmetries in the system. Our predictions are confirmed by the nonreciprocal dispersion of interface modes, unidirectional transmission spectra, and field distributions for our system. Such theoretical results may provide a mechanism to create compact optical isolators.

© 2013 Optical Society of America

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  1. J. A. Polo and A. Lakhtakia, Laser Photon. Rev. 5, 234 (2011).
    [CrossRef]
  2. S. Kawata, Near-Field Optics and Surface Plasmon Polaritons (Springer, 2001).
  3. M. I. D’yakonov, Sov. Phys. JETP 67, 714 (1988).
  4. D. Artigas and L. Torner, Phys. Rev. Lett. 94, 013901 (2005).
    [CrossRef]
  5. A. V. Kavokin, I. A. Shelykh, and G. Malpuech, Phys. Rev. B 72, 233102 (2005).
    [CrossRef]
  6. A. P. Vinogradov, A. V. Dorofeenko, S. G. Erokhin, M. Inoue, A. A. Lisyansky, A. M. Merzlikin, and A. B. Granovsky, Phys. Rev. B 74, 045128 (2006).
    [CrossRef]
  7. T. Goto, A. V. Dorofeenko, A. M. Merzlikin, A. V. Baryshev, A. P. Vinogradov, M. Inoue, A. A. Lisyansky, and A. B. Granovsky, Phys. Rev. Lett. 101, 113902 (2008).
    [CrossRef]
  8. Y. Hatsugai, Phys. Rev. Lett. 71, 3697 (1993).
    [CrossRef]
  9. S. Raghu and F. D. M. Haldane, Phys. Rev. A 78, 033834 (2008).
    [CrossRef]
  10. F. D. M. Haldane and S. Raghu, Phys. Rev. Lett. 100, 013904 (2008).
    [CrossRef]
  11. Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, Nature 461, 772 (2009).
    [CrossRef]
  12. Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, Phys. Rev. Lett. 106, 093903 (2011).
    [CrossRef]
  13. Z. Yu, G. Veronis, Z. Wang, and S. Fan, Phys. Rev. Lett. 100, 023902 (2008).
    [CrossRef]
  14. A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, Phys. Rev. Lett. 105, 126804 (2010).
    [CrossRef]
  15. X. Ao, Z. Lin, and C. T. Chan, Phys. Rev. B 80, 033105 (2009).
    [CrossRef]
  16. Z. Yu and S. Fan, Nat. Photonics 3, 91 (2009).
    [CrossRef]
  17. H. Lira, Z. Yu, S. Fan, and M. Lipson, Phys. Rev. Lett. 109, 033901 (2012).
    [CrossRef]
  18. K. Liu, L. Shen, and S. He, Opt. Lett. 37, 4110 (2012).
    [CrossRef]
  19. H. Zhu and C. Jiang, Opt. Express 18, 6914 (2010).
    [CrossRef]
  20. A. B. Khanikaev, A. V. Baryshev, M. Inoue, and Y. S. Kivshar, Appl. Phys. Lett. 95, 011101 (2009).
    [CrossRef]
  21. M. Liscidini and J. E. Sipe, J. Opt. Soc. Am. B 26, 279 (2009).
    [CrossRef]
  22. H. Y. Dong, J. Wang, and T. J. Cui, Phys. Rev. B 87, 045406 (2013).
    [CrossRef]
  23. P. Yeh, Optical Waves in Layered Media, 2nd ed. (Wiley, 2005).
  24. I. Iorsh, A. Orlov, P. Belov, and Y. Kivshar, Appl. Phys. Lett. 99, 151914 (2011).
    [CrossRef]
  25. R. Nishino and S. Yamada, J. Appl. Phys. 105, 083108 (2009).
    [CrossRef]
  26. Z. Yu, Z. Wang, and S. Fan, Appl. Phys. Lett. 90, 121133 (2007).
    [CrossRef]
  27. A. B. Khanikaev and M. J. Steel, Opt. Express 17, 5265 (2009).
    [CrossRef]
  28. A. Figotin and I. Vitebsky, Phys. Rev. E 63, 066609 (2001).
    [CrossRef]

2013 (1)

H. Y. Dong, J. Wang, and T. J. Cui, Phys. Rev. B 87, 045406 (2013).
[CrossRef]

2012 (2)

H. Lira, Z. Yu, S. Fan, and M. Lipson, Phys. Rev. Lett. 109, 033901 (2012).
[CrossRef]

K. Liu, L. Shen, and S. He, Opt. Lett. 37, 4110 (2012).
[CrossRef]

2011 (3)

Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef]

J. A. Polo and A. Lakhtakia, Laser Photon. Rev. 5, 234 (2011).
[CrossRef]

I. Iorsh, A. Orlov, P. Belov, and Y. Kivshar, Appl. Phys. Lett. 99, 151914 (2011).
[CrossRef]

2010 (2)

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, Phys. Rev. Lett. 105, 126804 (2010).
[CrossRef]

H. Zhu and C. Jiang, Opt. Express 18, 6914 (2010).
[CrossRef]

2009 (7)

A. B. Khanikaev, A. V. Baryshev, M. Inoue, and Y. S. Kivshar, Appl. Phys. Lett. 95, 011101 (2009).
[CrossRef]

M. Liscidini and J. E. Sipe, J. Opt. Soc. Am. B 26, 279 (2009).
[CrossRef]

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, Nature 461, 772 (2009).
[CrossRef]

X. Ao, Z. Lin, and C. T. Chan, Phys. Rev. B 80, 033105 (2009).
[CrossRef]

Z. Yu and S. Fan, Nat. Photonics 3, 91 (2009).
[CrossRef]

A. B. Khanikaev and M. J. Steel, Opt. Express 17, 5265 (2009).
[CrossRef]

R. Nishino and S. Yamada, J. Appl. Phys. 105, 083108 (2009).
[CrossRef]

2008 (4)

Z. Yu, G. Veronis, Z. Wang, and S. Fan, Phys. Rev. Lett. 100, 023902 (2008).
[CrossRef]

T. Goto, A. V. Dorofeenko, A. M. Merzlikin, A. V. Baryshev, A. P. Vinogradov, M. Inoue, A. A. Lisyansky, and A. B. Granovsky, Phys. Rev. Lett. 101, 113902 (2008).
[CrossRef]

S. Raghu and F. D. M. Haldane, Phys. Rev. A 78, 033834 (2008).
[CrossRef]

F. D. M. Haldane and S. Raghu, Phys. Rev. Lett. 100, 013904 (2008).
[CrossRef]

2007 (1)

Z. Yu, Z. Wang, and S. Fan, Appl. Phys. Lett. 90, 121133 (2007).
[CrossRef]

2006 (1)

A. P. Vinogradov, A. V. Dorofeenko, S. G. Erokhin, M. Inoue, A. A. Lisyansky, A. M. Merzlikin, and A. B. Granovsky, Phys. Rev. B 74, 045128 (2006).
[CrossRef]

2005 (2)

D. Artigas and L. Torner, Phys. Rev. Lett. 94, 013901 (2005).
[CrossRef]

A. V. Kavokin, I. A. Shelykh, and G. Malpuech, Phys. Rev. B 72, 233102 (2005).
[CrossRef]

2001 (1)

A. Figotin and I. Vitebsky, Phys. Rev. E 63, 066609 (2001).
[CrossRef]

1993 (1)

Y. Hatsugai, Phys. Rev. Lett. 71, 3697 (1993).
[CrossRef]

1988 (1)

M. I. D’yakonov, Sov. Phys. JETP 67, 714 (1988).

Ao, X.

X. Ao, Z. Lin, and C. T. Chan, Phys. Rev. B 80, 033105 (2009).
[CrossRef]

Artigas, D.

D. Artigas and L. Torner, Phys. Rev. Lett. 94, 013901 (2005).
[CrossRef]

Baryshev, A. V.

A. B. Khanikaev, A. V. Baryshev, M. Inoue, and Y. S. Kivshar, Appl. Phys. Lett. 95, 011101 (2009).
[CrossRef]

T. Goto, A. V. Dorofeenko, A. M. Merzlikin, A. V. Baryshev, A. P. Vinogradov, M. Inoue, A. A. Lisyansky, and A. B. Granovsky, Phys. Rev. Lett. 101, 113902 (2008).
[CrossRef]

Belov, P.

I. Iorsh, A. Orlov, P. Belov, and Y. Kivshar, Appl. Phys. Lett. 99, 151914 (2011).
[CrossRef]

Chan, C. T.

Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef]

X. Ao, Z. Lin, and C. T. Chan, Phys. Rev. B 80, 033105 (2009).
[CrossRef]

Chong, Y.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, Nature 461, 772 (2009).
[CrossRef]

Cui, T. J.

H. Y. Dong, J. Wang, and T. J. Cui, Phys. Rev. B 87, 045406 (2013).
[CrossRef]

D’yakonov, M. I.

M. I. D’yakonov, Sov. Phys. JETP 67, 714 (1988).

Dong, H. Y.

H. Y. Dong, J. Wang, and T. J. Cui, Phys. Rev. B 87, 045406 (2013).
[CrossRef]

Dorofeenko, A. V.

T. Goto, A. V. Dorofeenko, A. M. Merzlikin, A. V. Baryshev, A. P. Vinogradov, M. Inoue, A. A. Lisyansky, and A. B. Granovsky, Phys. Rev. Lett. 101, 113902 (2008).
[CrossRef]

A. P. Vinogradov, A. V. Dorofeenko, S. G. Erokhin, M. Inoue, A. A. Lisyansky, A. M. Merzlikin, and A. B. Granovsky, Phys. Rev. B 74, 045128 (2006).
[CrossRef]

Erokhin, S. G.

A. P. Vinogradov, A. V. Dorofeenko, S. G. Erokhin, M. Inoue, A. A. Lisyansky, A. M. Merzlikin, and A. B. Granovsky, Phys. Rev. B 74, 045128 (2006).
[CrossRef]

Fan, S.

H. Lira, Z. Yu, S. Fan, and M. Lipson, Phys. Rev. Lett. 109, 033901 (2012).
[CrossRef]

Z. Yu and S. Fan, Nat. Photonics 3, 91 (2009).
[CrossRef]

Z. Yu, G. Veronis, Z. Wang, and S. Fan, Phys. Rev. Lett. 100, 023902 (2008).
[CrossRef]

Z. Yu, Z. Wang, and S. Fan, Appl. Phys. Lett. 90, 121133 (2007).
[CrossRef]

Figotin, A.

A. Figotin and I. Vitebsky, Phys. Rev. E 63, 066609 (2001).
[CrossRef]

Goto, T.

T. Goto, A. V. Dorofeenko, A. M. Merzlikin, A. V. Baryshev, A. P. Vinogradov, M. Inoue, A. A. Lisyansky, and A. B. Granovsky, Phys. Rev. Lett. 101, 113902 (2008).
[CrossRef]

Granovsky, A. B.

T. Goto, A. V. Dorofeenko, A. M. Merzlikin, A. V. Baryshev, A. P. Vinogradov, M. Inoue, A. A. Lisyansky, and A. B. Granovsky, Phys. Rev. Lett. 101, 113902 (2008).
[CrossRef]

A. P. Vinogradov, A. V. Dorofeenko, S. G. Erokhin, M. Inoue, A. A. Lisyansky, A. M. Merzlikin, and A. B. Granovsky, Phys. Rev. B 74, 045128 (2006).
[CrossRef]

Haldane, F. D. M.

S. Raghu and F. D. M. Haldane, Phys. Rev. A 78, 033834 (2008).
[CrossRef]

F. D. M. Haldane and S. Raghu, Phys. Rev. Lett. 100, 013904 (2008).
[CrossRef]

Hatsugai, Y.

Y. Hatsugai, Phys. Rev. Lett. 71, 3697 (1993).
[CrossRef]

He, S.

Inoue, M.

A. B. Khanikaev, A. V. Baryshev, M. Inoue, and Y. S. Kivshar, Appl. Phys. Lett. 95, 011101 (2009).
[CrossRef]

T. Goto, A. V. Dorofeenko, A. M. Merzlikin, A. V. Baryshev, A. P. Vinogradov, M. Inoue, A. A. Lisyansky, and A. B. Granovsky, Phys. Rev. Lett. 101, 113902 (2008).
[CrossRef]

A. P. Vinogradov, A. V. Dorofeenko, S. G. Erokhin, M. Inoue, A. A. Lisyansky, A. M. Merzlikin, and A. B. Granovsky, Phys. Rev. B 74, 045128 (2006).
[CrossRef]

Iorsh, I.

I. Iorsh, A. Orlov, P. Belov, and Y. Kivshar, Appl. Phys. Lett. 99, 151914 (2011).
[CrossRef]

Jiang, C.

Joannopoulos, J. D.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, Nature 461, 772 (2009).
[CrossRef]

Kavokin, A. V.

A. V. Kavokin, I. A. Shelykh, and G. Malpuech, Phys. Rev. B 72, 233102 (2005).
[CrossRef]

Kawata, S.

S. Kawata, Near-Field Optics and Surface Plasmon Polaritons (Springer, 2001).

Khanikaev, A. B.

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, Phys. Rev. Lett. 105, 126804 (2010).
[CrossRef]

A. B. Khanikaev, A. V. Baryshev, M. Inoue, and Y. S. Kivshar, Appl. Phys. Lett. 95, 011101 (2009).
[CrossRef]

A. B. Khanikaev and M. J. Steel, Opt. Express 17, 5265 (2009).
[CrossRef]

Kivshar, Y.

I. Iorsh, A. Orlov, P. Belov, and Y. Kivshar, Appl. Phys. Lett. 99, 151914 (2011).
[CrossRef]

Kivshar, Y. S.

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, Phys. Rev. Lett. 105, 126804 (2010).
[CrossRef]

A. B. Khanikaev, A. V. Baryshev, M. Inoue, and Y. S. Kivshar, Appl. Phys. Lett. 95, 011101 (2009).
[CrossRef]

Lakhtakia, A.

J. A. Polo and A. Lakhtakia, Laser Photon. Rev. 5, 234 (2011).
[CrossRef]

Lin, Z.

Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef]

X. Ao, Z. Lin, and C. T. Chan, Phys. Rev. B 80, 033105 (2009).
[CrossRef]

Lipson, M.

H. Lira, Z. Yu, S. Fan, and M. Lipson, Phys. Rev. Lett. 109, 033901 (2012).
[CrossRef]

Lira, H.

H. Lira, Z. Yu, S. Fan, and M. Lipson, Phys. Rev. Lett. 109, 033901 (2012).
[CrossRef]

Liscidini, M.

Lisyansky, A. A.

T. Goto, A. V. Dorofeenko, A. M. Merzlikin, A. V. Baryshev, A. P. Vinogradov, M. Inoue, A. A. Lisyansky, and A. B. Granovsky, Phys. Rev. Lett. 101, 113902 (2008).
[CrossRef]

A. P. Vinogradov, A. V. Dorofeenko, S. G. Erokhin, M. Inoue, A. A. Lisyansky, A. M. Merzlikin, and A. B. Granovsky, Phys. Rev. B 74, 045128 (2006).
[CrossRef]

Liu, K.

Malpuech, G.

A. V. Kavokin, I. A. Shelykh, and G. Malpuech, Phys. Rev. B 72, 233102 (2005).
[CrossRef]

Merzlikin, A. M.

T. Goto, A. V. Dorofeenko, A. M. Merzlikin, A. V. Baryshev, A. P. Vinogradov, M. Inoue, A. A. Lisyansky, and A. B. Granovsky, Phys. Rev. Lett. 101, 113902 (2008).
[CrossRef]

A. P. Vinogradov, A. V. Dorofeenko, S. G. Erokhin, M. Inoue, A. A. Lisyansky, A. M. Merzlikin, and A. B. Granovsky, Phys. Rev. B 74, 045128 (2006).
[CrossRef]

Mousavi, S. H.

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, Phys. Rev. Lett. 105, 126804 (2010).
[CrossRef]

Nishino, R.

R. Nishino and S. Yamada, J. Appl. Phys. 105, 083108 (2009).
[CrossRef]

Orlov, A.

I. Iorsh, A. Orlov, P. Belov, and Y. Kivshar, Appl. Phys. Lett. 99, 151914 (2011).
[CrossRef]

Polo, J. A.

J. A. Polo and A. Lakhtakia, Laser Photon. Rev. 5, 234 (2011).
[CrossRef]

Poo, Y.

Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef]

Raghu, S.

F. D. M. Haldane and S. Raghu, Phys. Rev. Lett. 100, 013904 (2008).
[CrossRef]

S. Raghu and F. D. M. Haldane, Phys. Rev. A 78, 033834 (2008).
[CrossRef]

Shelykh, I. A.

A. V. Kavokin, I. A. Shelykh, and G. Malpuech, Phys. Rev. B 72, 233102 (2005).
[CrossRef]

Shen, L.

Shvets, G.

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, Phys. Rev. Lett. 105, 126804 (2010).
[CrossRef]

Sipe, J. E.

Soljacic, M.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, Nature 461, 772 (2009).
[CrossRef]

Steel, M. J.

Torner, L.

D. Artigas and L. Torner, Phys. Rev. Lett. 94, 013901 (2005).
[CrossRef]

Veronis, G.

Z. Yu, G. Veronis, Z. Wang, and S. Fan, Phys. Rev. Lett. 100, 023902 (2008).
[CrossRef]

Vinogradov, A. P.

T. Goto, A. V. Dorofeenko, A. M. Merzlikin, A. V. Baryshev, A. P. Vinogradov, M. Inoue, A. A. Lisyansky, and A. B. Granovsky, Phys. Rev. Lett. 101, 113902 (2008).
[CrossRef]

A. P. Vinogradov, A. V. Dorofeenko, S. G. Erokhin, M. Inoue, A. A. Lisyansky, A. M. Merzlikin, and A. B. Granovsky, Phys. Rev. B 74, 045128 (2006).
[CrossRef]

Vitebsky, I.

A. Figotin and I. Vitebsky, Phys. Rev. E 63, 066609 (2001).
[CrossRef]

Wang, J.

H. Y. Dong, J. Wang, and T. J. Cui, Phys. Rev. B 87, 045406 (2013).
[CrossRef]

Wang, Z.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, Nature 461, 772 (2009).
[CrossRef]

Z. Yu, G. Veronis, Z. Wang, and S. Fan, Phys. Rev. Lett. 100, 023902 (2008).
[CrossRef]

Z. Yu, Z. Wang, and S. Fan, Appl. Phys. Lett. 90, 121133 (2007).
[CrossRef]

Wu, R.

Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef]

Yamada, S.

R. Nishino and S. Yamada, J. Appl. Phys. 105, 083108 (2009).
[CrossRef]

Yang, Y.

Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef]

Yeh, P.

P. Yeh, Optical Waves in Layered Media, 2nd ed. (Wiley, 2005).

Yu, Z.

H. Lira, Z. Yu, S. Fan, and M. Lipson, Phys. Rev. Lett. 109, 033901 (2012).
[CrossRef]

Z. Yu and S. Fan, Nat. Photonics 3, 91 (2009).
[CrossRef]

Z. Yu, G. Veronis, Z. Wang, and S. Fan, Phys. Rev. Lett. 100, 023902 (2008).
[CrossRef]

Z. Yu, Z. Wang, and S. Fan, Appl. Phys. Lett. 90, 121133 (2007).
[CrossRef]

Zhu, H.

Appl. Phys. Lett. (3)

A. B. Khanikaev, A. V. Baryshev, M. Inoue, and Y. S. Kivshar, Appl. Phys. Lett. 95, 011101 (2009).
[CrossRef]

I. Iorsh, A. Orlov, P. Belov, and Y. Kivshar, Appl. Phys. Lett. 99, 151914 (2011).
[CrossRef]

Z. Yu, Z. Wang, and S. Fan, Appl. Phys. Lett. 90, 121133 (2007).
[CrossRef]

J. Appl. Phys. (1)

R. Nishino and S. Yamada, J. Appl. Phys. 105, 083108 (2009).
[CrossRef]

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

Laser Photon. Rev. (1)

J. A. Polo and A. Lakhtakia, Laser Photon. Rev. 5, 234 (2011).
[CrossRef]

Nat. Photonics (1)

Z. Yu and S. Fan, Nat. Photonics 3, 91 (2009).
[CrossRef]

Nature (1)

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, Nature 461, 772 (2009).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. A (1)

S. Raghu and F. D. M. Haldane, Phys. Rev. A 78, 033834 (2008).
[CrossRef]

Phys. Rev. B (4)

A. V. Kavokin, I. A. Shelykh, and G. Malpuech, Phys. Rev. B 72, 233102 (2005).
[CrossRef]

A. P. Vinogradov, A. V. Dorofeenko, S. G. Erokhin, M. Inoue, A. A. Lisyansky, A. M. Merzlikin, and A. B. Granovsky, Phys. Rev. B 74, 045128 (2006).
[CrossRef]

X. Ao, Z. Lin, and C. T. Chan, Phys. Rev. B 80, 033105 (2009).
[CrossRef]

H. Y. Dong, J. Wang, and T. J. Cui, Phys. Rev. B 87, 045406 (2013).
[CrossRef]

Phys. Rev. E (1)

A. Figotin and I. Vitebsky, Phys. Rev. E 63, 066609 (2001).
[CrossRef]

Phys. Rev. Lett. (8)

T. Goto, A. V. Dorofeenko, A. M. Merzlikin, A. V. Baryshev, A. P. Vinogradov, M. Inoue, A. A. Lisyansky, and A. B. Granovsky, Phys. Rev. Lett. 101, 113902 (2008).
[CrossRef]

Y. Hatsugai, Phys. Rev. Lett. 71, 3697 (1993).
[CrossRef]

D. Artigas and L. Torner, Phys. Rev. Lett. 94, 013901 (2005).
[CrossRef]

F. D. M. Haldane and S. Raghu, Phys. Rev. Lett. 100, 013904 (2008).
[CrossRef]

H. Lira, Z. Yu, S. Fan, and M. Lipson, Phys. Rev. Lett. 109, 033901 (2012).
[CrossRef]

Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef]

Z. Yu, G. Veronis, Z. Wang, and S. Fan, Phys. Rev. Lett. 100, 023902 (2008).
[CrossRef]

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, Phys. Rev. Lett. 105, 126804 (2010).
[CrossRef]

Sov. Phys. JETP (1)

M. I. D’yakonov, Sov. Phys. JETP 67, 714 (1988).

Other (2)

S. Kawata, Near-Field Optics and Surface Plasmon Polaritons (Springer, 2001).

P. Yeh, Optical Waves in Layered Media, 2nd ed. (Wiley, 2005).

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Figures (5)

Fig. 1.
Fig. 1.

Geometry of an interface separating two different semi-infinite MPCs formed by alternating magneto-optical and isotropic dielectric layers.

Fig. 2.
Fig. 2.

Dispersion of OTSs at the interface between two semi-infinite MPCs. Red and blue lines correspond to kx>0 and kx<0 propagating OTSs, respectively. The white region depicts the overlapping stop-band of MPC1 and MPC2, while green and yellow regions correspond to pass-bands of an infinite MPC1 and MPC2, respectively. The light line for free space (black line) is also shown.

Fig. 3.
Fig. 3.

Out-of-plane magnetic field patterns at the energy E+=1.525eV for the finite-size structure having eight pairs of layers in MPC1 and 33 pairs of layers in MPC2, under front illumination (a) and back illumination (b), when the in-plane component of wave vector |kx|=3μm1.

Fig. 4.
Fig. 4.

Transmission spectra of our model structure calculated with different in-plane components of wave vector, (a)–(d) |kx|=1,2,3,4μm1. Red and blue lines show the forward and backward illumination of light beams, respectively. The dotted and dashed lines correspond to the transmission spectrum of single MPC1 or MPC2 in vacuum. One can observe the sharp peaks within the stop band of the structure, which are associated with nonreciprocal OTSs, occurs at different energies.

Fig. 5.
Fig. 5.

Nonreciprocity in absorption (a) and transmission (b) for the same structure as Fig. 4, except that the loss effect is considered for the magneto-optical layer in MPCs. Here we assume the magneto-optical layers with the same loss, ϵ2=ϵ3=ϵ. Black and red lines show the cases for ϵ=i0.001 and ϵ=i0.01, respectively.

Equations (3)

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M^ij=ϵj2Δj22ϵjkzj(Fj*+FiFj*Fi*FjFiFj+Fi*),
eiKRΛR=12[(TR11+TR22)±(TR22TR11)2+4TR12TR21],
ikz4eiKLΛLTL11TL12eiKLΛLTL11+TL12=ikz1eiKRΛRTR11TR12eiKRΛRTR11+TR12,

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