Abstract

We propose on-chip optical isolators that provide large isolation ratios. The isolation mechanism is based on the interplay between magneto-optical effects and resonant delocalization. Our analysis predicts large isolation ratios in the range of 45 to 55dB between forward and backward propagating optical beams. Both analytical and numerical results are presented, and fabrication feasibility is also discussed.

© 2012 Optical Society of America

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  1. B. A. E. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
  2. R. Wolfe, R. A. Lieberman, V. J. Fratello, R. E. Scotti, and N. Kopylov, Appl. Phys. Lett. 56, 426 (1990).
    [CrossRef]
  3. M. Levy, R. M. Osgood, H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Fratello, IEEE Photonics Technol. Lett. 8, 903 (1996).
    [CrossRef]
  4. J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, Appl. Phys. Lett. 76, 2158 (2000).
    [CrossRef]
  5. V. Zayets, M. C. Debnath, and K. Ando, J. Opt. Soc. Am. B 22, 281 (2005).
    [CrossRef]
  6. M. C. Tien, T. Mizumoto, P. Pintus, H. Kromer, and J. E. Bowers, Opt. Express 19, 11740 (2011).
    [CrossRef]
  7. Z. Yu and S. Fan, Nat. Photonics 3, 91 (2009).
    [CrossRef]
  8. M. S. Kang, A. Butsch, and P. St. J. Russell, Nat. Photonics 5, 549 (2011).
    [CrossRef]
  9. H. Lira, Z. Yu, S. Fan, and M. Lipson, Phys. Rev. Lett. 109, 033901 (2012).
    [CrossRef]
  10. H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodoulides, Phys Rev. A. 82, 043803 (2010).
    [CrossRef]
  11. L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
    [CrossRef]
  12. P. Kumar and M. Levy, Opt. Lett. 37, 3762 (2012).
    [CrossRef]
  13. P. Kumar and M. Levy, Opt. Lett. 36, 4359 (2011).
    [CrossRef]
  14. M. Levy and P. Kumar, Opt. Lett. 35, 3147 (2010).
    [CrossRef]
  15. R. El-Ganainy, D. N. Christodoulides, C. E. Rüter, and D. Kip, Opt. Lett. 36, 1464 (2011).
    [CrossRef]
  16. C. Zener, Proc. R. Soc. London A 145, 523 (1934).
    [CrossRef]
  17. U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701 (1998).
    [CrossRef]
  18. T. Pertsch, P. Dannberg, W. Elflein, and A. Bräuer, Phys. Rev. Lett. 83, 4752 (1999).
    [CrossRef]
  19. D. H. Dunlap and V. M. Kenkre, Phys. Rev. B 34, 3625 (1986).
    [CrossRef]
  20. S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
    [CrossRef]
  21. A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, Nat. Phys. 5, 271 (2009).
    [CrossRef]
  22. V. M. Kenkre and S. Raghavan, J. Opt. B 2, 686 (2000).
    [CrossRef]
  23. T. Shintaku, A. Tate, and S. Mino, Appl. Phys. Lett. 71, 1640 (1997).
    [CrossRef]
  24. K. G. Makris and D. N. Christodoulides, Phys. Rev. E. 73, 036616 (2006).
    [CrossRef]
  25. A. Joushaghani, R. Iyer, J. K. S. Poon, and J. S. Aitchison, Phys. Rev. Lett. 109, 103901 (2012).
    [CrossRef]

2012 (4)

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

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

P. Kumar and M. Levy, Opt. Lett. 37, 3762 (2012).
[CrossRef]

A. Joushaghani, R. Iyer, J. K. S. Poon, and J. S. Aitchison, Phys. Rev. Lett. 109, 103901 (2012).
[CrossRef]

2011 (4)

2010 (2)

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodoulides, Phys Rev. A. 82, 043803 (2010).
[CrossRef]

M. Levy and P. Kumar, Opt. Lett. 35, 3147 (2010).
[CrossRef]

2009 (2)

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

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, Nat. Phys. 5, 271 (2009).
[CrossRef]

2006 (2)

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef]

K. G. Makris and D. N. Christodoulides, Phys. Rev. E. 73, 036616 (2006).
[CrossRef]

2005 (1)

2000 (2)

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, Appl. Phys. Lett. 76, 2158 (2000).
[CrossRef]

V. M. Kenkre and S. Raghavan, J. Opt. B 2, 686 (2000).
[CrossRef]

1999 (1)

T. Pertsch, P. Dannberg, W. Elflein, and A. Bräuer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

1998 (1)

1997 (1)

T. Shintaku, A. Tate, and S. Mino, Appl. Phys. Lett. 71, 1640 (1997).
[CrossRef]

1996 (1)

M. Levy, R. M. Osgood, H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Fratello, IEEE Photonics Technol. Lett. 8, 903 (1996).
[CrossRef]

1990 (1)

R. Wolfe, R. A. Lieberman, V. J. Fratello, R. E. Scotti, and N. Kopylov, Appl. Phys. Lett. 56, 426 (1990).
[CrossRef]

1986 (1)

D. H. Dunlap and V. M. Kenkre, Phys. Rev. B 34, 3625 (1986).
[CrossRef]

1934 (1)

C. Zener, Proc. R. Soc. London A 145, 523 (1934).
[CrossRef]

Aitchison, J. S.

A. Joushaghani, R. Iyer, J. K. S. Poon, and J. S. Aitchison, Phys. Rev. Lett. 109, 103901 (2012).
[CrossRef]

Ando, K.

Bowers, J. E.

Bräuer, A.

T. Pertsch, P. Dannberg, W. Elflein, and A. Bräuer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

Butsch, A.

M. S. Kang, A. Butsch, and P. St. J. Russell, Nat. Photonics 5, 549 (2011).
[CrossRef]

Cadieu, F. J.

M. Levy, R. M. Osgood, H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Fratello, IEEE Photonics Technol. Lett. 8, 903 (1996).
[CrossRef]

Christodoulides, D. N.

R. El-Ganainy, D. N. Christodoulides, C. E. Rüter, and D. Kip, Opt. Lett. 36, 1464 (2011).
[CrossRef]

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodoulides, Phys Rev. A. 82, 043803 (2010).
[CrossRef]

K. G. Makris and D. N. Christodoulides, Phys. Rev. E. 73, 036616 (2006).
[CrossRef]

Cianci, E.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef]

Dannberg, P.

T. Pertsch, P. Dannberg, W. Elflein, and A. Bräuer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

Debnath, M. C.

Dotsch, H.

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, Appl. Phys. Lett. 76, 2158 (2000).
[CrossRef]

Dreisow, F.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, Nat. Phys. 5, 271 (2009).
[CrossRef]

Dunlap, D. H.

D. H. Dunlap and V. M. Kenkre, Phys. Rev. B 34, 3625 (1986).
[CrossRef]

Elflein, W.

T. Pertsch, P. Dannberg, W. Elflein, and A. Bräuer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

El-Ganainy, R.

R. El-Ganainy, D. N. Christodoulides, C. E. Rüter, and D. Kip, Opt. Lett. 36, 1464 (2011).
[CrossRef]

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodoulides, Phys Rev. A. 82, 043803 (2010).
[CrossRef]

Fan, L.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[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]

Foglietti, V.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef]

Fratello, V. J.

M. Levy, R. M. Osgood, H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Fratello, IEEE Photonics Technol. Lett. 8, 903 (1996).
[CrossRef]

R. Wolfe, R. A. Lieberman, V. J. Fratello, R. E. Scotti, and N. Kopylov, Appl. Phys. Lett. 56, 426 (1990).
[CrossRef]

Fujita, J.

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, Appl. Phys. Lett. 76, 2158 (2000).
[CrossRef]

Garanovich, I. L.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, Nat. Phys. 5, 271 (2009).
[CrossRef]

Hegde, H.

M. Levy, R. M. Osgood, H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Fratello, IEEE Photonics Technol. Lett. 8, 903 (1996).
[CrossRef]

Heinrich, M.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, Nat. Phys. 5, 271 (2009).
[CrossRef]

Iyer, R.

A. Joushaghani, R. Iyer, J. K. S. Poon, and J. S. Aitchison, Phys. Rev. Lett. 109, 103901 (2012).
[CrossRef]

Joushaghani, A.

A. Joushaghani, R. Iyer, J. K. S. Poon, and J. S. Aitchison, Phys. Rev. Lett. 109, 103901 (2012).
[CrossRef]

Kang, M. S.

M. S. Kang, A. Butsch, and P. St. J. Russell, Nat. Photonics 5, 549 (2011).
[CrossRef]

Kenkre, V. M.

V. M. Kenkre and S. Raghavan, J. Opt. B 2, 686 (2000).
[CrossRef]

D. H. Dunlap and V. M. Kenkre, Phys. Rev. B 34, 3625 (1986).
[CrossRef]

Kip, D.

Kivshar, Y. S.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, Nat. Phys. 5, 271 (2009).
[CrossRef]

Kopylov, N.

R. Wolfe, R. A. Lieberman, V. J. Fratello, R. E. Scotti, and N. Kopylov, Appl. Phys. Lett. 56, 426 (1990).
[CrossRef]

Kottos, T.

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodoulides, Phys Rev. A. 82, 043803 (2010).
[CrossRef]

Kromer, H.

Kumar, P.

Laporta, P.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef]

Lederer, F.

Levy, M.

P. Kumar and M. Levy, Opt. Lett. 37, 3762 (2012).
[CrossRef]

P. Kumar and M. Levy, Opt. Lett. 36, 4359 (2011).
[CrossRef]

M. Levy and P. Kumar, Opt. Lett. 35, 3147 (2010).
[CrossRef]

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, Appl. Phys. Lett. 76, 2158 (2000).
[CrossRef]

M. Levy, R. M. Osgood, H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Fratello, IEEE Photonics Technol. Lett. 8, 903 (1996).
[CrossRef]

Lieberman, R. A.

R. Wolfe, R. A. Lieberman, V. J. Fratello, R. E. Scotti, and N. Kopylov, Appl. Phys. Lett. 56, 426 (1990).
[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]

Lobino, M.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef]

Longhi, S.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef]

Makris, K. G.

K. G. Makris and D. N. Christodoulides, Phys. Rev. E. 73, 036616 (2006).
[CrossRef]

Marangoni, M.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef]

Mino, S.

T. Shintaku, A. Tate, and S. Mino, Appl. Phys. Lett. 71, 1640 (1997).
[CrossRef]

Mizumoto, T.

Niu, B.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

Nolte, S.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, Nat. Phys. 5, 271 (2009).
[CrossRef]

Osgood, R. M.

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, Appl. Phys. Lett. 76, 2158 (2000).
[CrossRef]

M. Levy, R. M. Osgood, H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Fratello, IEEE Photonics Technol. Lett. 8, 903 (1996).
[CrossRef]

Pertsch, T.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, Nat. Phys. 5, 271 (2009).
[CrossRef]

T. Pertsch, P. Dannberg, W. Elflein, and A. Bräuer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701 (1998).
[CrossRef]

Peschel, U.

Pintus, P.

Poon, J. K. S.

A. Joushaghani, R. Iyer, J. K. S. Poon, and J. S. Aitchison, Phys. Rev. Lett. 109, 103901 (2012).
[CrossRef]

Qi, M.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

Raghavan, S.

V. M. Kenkre and S. Raghavan, J. Opt. B 2, 686 (2000).
[CrossRef]

Ramezani, H.

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodoulides, Phys Rev. A. 82, 043803 (2010).
[CrossRef]

Ramponi, R.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef]

Russell, P. St. J.

M. S. Kang, A. Butsch, and P. St. J. Russell, Nat. Photonics 5, 549 (2011).
[CrossRef]

Rüter, C. E.

Saleh, B. A. E.

B. A. E. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).

Scotti, R. E.

R. Wolfe, R. A. Lieberman, V. J. Fratello, R. E. Scotti, and N. Kopylov, Appl. Phys. Lett. 56, 426 (1990).
[CrossRef]

Shen, H.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

Shintaku, T.

T. Shintaku, A. Tate, and S. Mino, Appl. Phys. Lett. 71, 1640 (1997).
[CrossRef]

Sukhorukov, A. A.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, Nat. Phys. 5, 271 (2009).
[CrossRef]

Szameit, A.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, Nat. Phys. 5, 271 (2009).
[CrossRef]

Tate, A.

T. Shintaku, A. Tate, and S. Mino, Appl. Phys. Lett. 71, 1640 (1997).
[CrossRef]

Teich, M. C.

B. A. E. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).

Tien, M. C.

Tünnermann, A.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, Nat. Phys. 5, 271 (2009).
[CrossRef]

Varghese, L. T.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

Wang, J.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

Weiner, A. M.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

Wilkens, L.

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, Appl. Phys. Lett. 76, 2158 (2000).
[CrossRef]

Wolfe, R.

M. Levy, R. M. Osgood, H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Fratello, IEEE Photonics Technol. Lett. 8, 903 (1996).
[CrossRef]

R. Wolfe, R. A. Lieberman, V. J. Fratello, R. E. Scotti, and N. Kopylov, Appl. Phys. Lett. 56, 426 (1990).
[CrossRef]

Xuan, Y.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

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]

Zayets, V.

Zener, C.

C. Zener, Proc. R. Soc. London A 145, 523 (1934).
[CrossRef]

Appl. Phys. Lett. (3)

R. Wolfe, R. A. Lieberman, V. J. Fratello, R. E. Scotti, and N. Kopylov, Appl. Phys. Lett. 56, 426 (1990).
[CrossRef]

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, Appl. Phys. Lett. 76, 2158 (2000).
[CrossRef]

T. Shintaku, A. Tate, and S. Mino, Appl. Phys. Lett. 71, 1640 (1997).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

M. Levy, R. M. Osgood, H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Fratello, IEEE Photonics Technol. Lett. 8, 903 (1996).
[CrossRef]

J. Opt. B (1)

V. M. Kenkre and S. Raghavan, J. Opt. B 2, 686 (2000).
[CrossRef]

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

Nat. Photonics (2)

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

M. S. Kang, A. Butsch, and P. St. J. Russell, Nat. Photonics 5, 549 (2011).
[CrossRef]

Nat. Phys. (1)

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, Nat. Phys. 5, 271 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (5)

Phys Rev. A. (1)

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodoulides, Phys Rev. A. 82, 043803 (2010).
[CrossRef]

Phys. Rev. B (1)

D. H. Dunlap and V. M. Kenkre, Phys. Rev. B 34, 3625 (1986).
[CrossRef]

Phys. Rev. E. (1)

K. G. Makris and D. N. Christodoulides, Phys. Rev. E. 73, 036616 (2006).
[CrossRef]

Phys. Rev. Lett. (4)

A. Joushaghani, R. Iyer, J. K. S. Poon, and J. S. Aitchison, Phys. Rev. Lett. 109, 103901 (2012).
[CrossRef]

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef]

T. Pertsch, P. Dannberg, W. Elflein, and A. Bräuer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

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

Proc. R. Soc. London A (1)

C. Zener, Proc. R. Soc. London A 145, 523 (1934).
[CrossRef]

Science (1)

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

Other (1)

B. A. E. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).

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Figures (3)

Fig. 1.
Fig. 1.

Schematic of the proposed optical isolator structure consisting of modulated Bloch array. Magnetic films are deposited on top of the waveguides (not shown here) in order to introduce nonreciprocity. The descending order of waveguide width provides effective index ramping. In our simulations, 17 waveguide channels are considered, but here we show only 5.

Fig. 2.
Fig. 2.

Impulse response (for an input optical beam at the central channel) in the (a) forward propagation direction and (b) backward propagation direction. For the design parameters presented in the text, optical revivals are obtained in the forward direction (a), while RD takes place in the backward propagation. In this latter case, the interplay between backward diffraction and boundary reflections leads to destructive interference at the middle channel.

Fig. 3.
Fig. 3.

Intensity evolution in both the forward (blue curve that ends at 0 dB) and the backward (red curve ending at 45dB) propagation directions. Intensities are measured in decibels with respect to the input optical intensity. Evidently, at a normalized propagation distance of z6.5, optical isolation ratios of 45dB are obtained.

Equations (3)

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idφn(p)(z)dz+κp(z)[φn+1(p)(z)+φn1(p)(z)]+nβpφn(p)(z)=0.
u(z)=κ0βsin(βz)+ε0zcos(βz)sin(Γz)dz,
v(z)=κ0β[1cos(βz)]+ε0zsin(βz)sin(Γz)dz.

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