Abstract

A nonlinear phase defect inserted in a coherent coupler can realize an effective all-optical diode. Basic features, design criteria, and suggested implementations are discussed with reference to Kerr-like media.

© 2008 Optical Society of America

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  1. J. Fujita, M. Levy, J. R. M. Osgood, L. Wilkens, and H. Dotsch, Appl. Phys. Lett. 76, 2158 (2000).
    [Crossref]
  2. Y. Yazaki, Y. Shoji, and T. Mizumoto, Jpn. J. Appl. Phys., Part 1 46, 5460 (2007).
    [Crossref]
  3. N. Kono, K. Kakihara, K. Saitoh, and M. Koshiba, Opt. Express 15, 7737 (2007).
    [Crossref] [PubMed]
  4. Z. Yu, Z. Wang, and S. Fan, Appl. Phys. Lett. 90, 121133 (2007).
    [Crossref]
  5. T. Amemiya, H. Shimizu, M. Yokoyama, P. N. Hai, M. Tanaka, and Y. Nakano, Appl. Opt. 46, 5784 (2007).
    [Crossref] [PubMed]
  6. C. G. Trevino-Palacios, G. I. Stegeman, and P. Baldi, Opt. Lett. 21, 1442 (1996).
    [Crossref] [PubMed]
  7. J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, Nat. Mater. 4, 383 (2005).
    [Crossref] [PubMed]
  8. Y. Matsuhisa, Y. Huang, Y. Zhou, S.-T. Wu, Y. Takao, A. Fujii, and M. Ozaki, Opt. Express 15, 616 (2007).
    [Crossref] [PubMed]
  9. G. Shvets, Appl. Phys. Lett. 89, 141127 (2006).
    [Crossref]
  10. A. H. Gevorgyan and M. Z. Harutyunyan, Phys. Rev. E 76, 031701 (2007).
    [Crossref]
  11. J. Y. Chen, J. Optoelectron. Adv. Mater. 9, 2437 (2007).
  12. S. Mujumdar and H. Ramachandran, Opt. Lett. 26, 929 (2001).
    [Crossref]
  13. A. Rostami, Opt. Laser Technol. 39, 1059 (2007).
    [Crossref]
  14. M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, Phys. Rev. E 71, 037602 (2005).
    [Crossref]
  15. M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, Appl. Phys. Lett. 66, 2324 (1995).
    [Crossref]
  16. X.-H. Jia, J. Opt. Soc. Am. B 24, 2746 (2007).
    [Crossref]
  17. X.-S. Lin, W.-Q. Wu, H. Zhou, K.-F. Zhou, and S. Lan, Opt. Express 14, 2429 (2006).
    [Crossref] [PubMed]
  18. A. E. Miroshnichenko, I. Pinkevych, and Y. S. Kivshar, Opt. Express 14, 2839 (2006).
    [Crossref] [PubMed]
  19. D. Alexander, J. Bruce III, C. Zuhlke, B. Koch, R. Rudebusch, J. Deogun, and H. Hamza, Opt. Lett. 31, 1957 (2006).
    [Crossref] [PubMed]
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    [Crossref]
  21. S. M. Jensen, IEEE J. Quantum Electron. 18, 1580 (1982).
    [Crossref]
  22. A. A. Maĭer, Sov. J. Quantum Electron. 14, 101 (1984).
    [Crossref]
  23. J. S. Aitchison, A. Villeneuve, and G. Stegeman, J. Nonlinear Opt. Phys. Mater. 4, 871 (1995).
    [Crossref]
  24. I. L. Garanovich and A. A. Sukhorukov, Opt. Lett. 32, 475 (2007).
    [Crossref] [PubMed]
  25. E. Caglioti, S. Trillo, S. Wabnitz, B. Daino, and G. I. Stegeman, Appl. Phys. Lett. 51, 293 (1987).
    [Crossref]
  26. E. M. Wright, S. W. Koch, J. E. Ehrlich, C. T. Seaton, and G. I. Stegeman, Appl. Phys. Lett. 52, 2127 (1988).
    [Crossref]
  27. D. R. Heatley, E. M. Wright, J. E. Ehrlich, and G. I. Stegeman, Opt. Lett. 13, 419 (1988).
    [Crossref] [PubMed]
  28. G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. VanStryland, Appl. Phys. Lett. 62, 1323 (1993).
    [Crossref]
  29. Y. Baek, R. Schiek, G. Stegeman, G. Assanto, and W. Sohler, Appl. Phys. Lett. 72, 3405 (1998).
    [Crossref]
  30. S. Trillo and S. Wabnitz, Appl. Phys. Lett. 49, 752 (1986).
    [Crossref]
  31. Y. P. Svirko and N. I. Zheludev, Opt. Lett. 20, 1809 (1995).
    [Crossref] [PubMed]

2007 (10)

2006 (4)

2005 (2)

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, Nat. Mater. 4, 383 (2005).
[Crossref] [PubMed]

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, Phys. Rev. E 71, 037602 (2005).
[Crossref]

2001 (2)

S. Mujumdar and H. Ramachandran, Opt. Lett. 26, 929 (2001).
[Crossref]

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001).
[Crossref]

2000 (1)

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

1998 (1)

Y. Baek, R. Schiek, G. Stegeman, G. Assanto, and W. Sohler, Appl. Phys. Lett. 72, 3405 (1998).
[Crossref]

1996 (1)

1995 (3)

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, Appl. Phys. Lett. 66, 2324 (1995).
[Crossref]

J. S. Aitchison, A. Villeneuve, and G. Stegeman, J. Nonlinear Opt. Phys. Mater. 4, 871 (1995).
[Crossref]

Y. P. Svirko and N. I. Zheludev, Opt. Lett. 20, 1809 (1995).
[Crossref] [PubMed]

1993 (1)

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. VanStryland, Appl. Phys. Lett. 62, 1323 (1993).
[Crossref]

1988 (2)

E. M. Wright, S. W. Koch, J. E. Ehrlich, C. T. Seaton, and G. I. Stegeman, Appl. Phys. Lett. 52, 2127 (1988).
[Crossref]

D. R. Heatley, E. M. Wright, J. E. Ehrlich, and G. I. Stegeman, Opt. Lett. 13, 419 (1988).
[Crossref] [PubMed]

1987 (1)

E. Caglioti, S. Trillo, S. Wabnitz, B. Daino, and G. I. Stegeman, Appl. Phys. Lett. 51, 293 (1987).
[Crossref]

1986 (1)

S. Trillo and S. Wabnitz, Appl. Phys. Lett. 49, 752 (1986).
[Crossref]

1984 (1)

A. A. Maĭer, Sov. J. Quantum Electron. 14, 101 (1984).
[Crossref]

1982 (1)

S. M. Jensen, IEEE J. Quantum Electron. 18, 1580 (1982).
[Crossref]

Aitchison, J. S.

J. S. Aitchison, A. Villeneuve, and G. Stegeman, J. Nonlinear Opt. Phys. Mater. 4, 871 (1995).
[Crossref]

Alexander, D.

Amemiya, T.

Assanto, G.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001).
[Crossref]

Y. Baek, R. Schiek, G. Stegeman, G. Assanto, and W. Sohler, Appl. Phys. Lett. 72, 3405 (1998).
[Crossref]

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. VanStryland, Appl. Phys. Lett. 62, 1323 (1993).
[Crossref]

Baek, Y.

Y. Baek, R. Schiek, G. Stegeman, G. Assanto, and W. Sohler, Appl. Phys. Lett. 72, 3405 (1998).
[Crossref]

Baldi, P.

Bloemer, M. J.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, Appl. Phys. Lett. 66, 2324 (1995).
[Crossref]

Bowden, C. M.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, Appl. Phys. Lett. 66, 2324 (1995).
[Crossref]

Bruce, J.

Caglioti, E.

E. Caglioti, S. Trillo, S. Wabnitz, B. Daino, and G. I. Stegeman, Appl. Phys. Lett. 51, 293 (1987).
[Crossref]

Chen, J. Y.

J. Y. Chen, J. Optoelectron. Adv. Mater. 9, 2437 (2007).

Daino, B.

E. Caglioti, S. Trillo, S. Wabnitz, B. Daino, and G. I. Stegeman, Appl. Phys. Lett. 51, 293 (1987).
[Crossref]

Deogun, J.

Dotsch, H.

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

Dowling, J. P.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, Appl. Phys. Lett. 66, 2324 (1995).
[Crossref]

Ehrlich, J. E.

E. M. Wright, S. W. Koch, J. E. Ehrlich, C. T. Seaton, and G. I. Stegeman, Appl. Phys. Lett. 52, 2127 (1988).
[Crossref]

D. R. Heatley, E. M. Wright, J. E. Ehrlich, and G. I. Stegeman, Opt. Lett. 13, 419 (1988).
[Crossref] [PubMed]

Fan, S.

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

Feise, M. W.

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, Phys. Rev. E 71, 037602 (2005).
[Crossref]

Fejer, M. M.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001).
[Crossref]

Fujii, A.

Fujita, J.

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

Gallo, K.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001).
[Crossref]

Garanovich, I. L.

Gevorgyan, A. H.

A. H. Gevorgyan and M. Z. Harutyunyan, Phys. Rev. E 76, 031701 (2007).
[Crossref]

Hai, P. N.

Hamza, H.

Harutyunyan, M. Z.

A. H. Gevorgyan and M. Z. Harutyunyan, Phys. Rev. E 76, 031701 (2007).
[Crossref]

Heatley, D. R.

Huang, Y.

Hwang, J.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, Nat. Mater. 4, 383 (2005).
[Crossref] [PubMed]

Ishikawa, K.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, Nat. Mater. 4, 383 (2005).
[Crossref] [PubMed]

Jensen, S. M.

S. M. Jensen, IEEE J. Quantum Electron. 18, 1580 (1982).
[Crossref]

Jia, X.-H.

Kakihara, K.

Kivshar, Y. S.

A. E. Miroshnichenko, I. Pinkevych, and Y. S. Kivshar, Opt. Express 14, 2839 (2006).
[Crossref] [PubMed]

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, Phys. Rev. E 71, 037602 (2005).
[Crossref]

Koch, B.

Koch, S. W.

E. M. Wright, S. W. Koch, J. E. Ehrlich, C. T. Seaton, and G. I. Stegeman, Appl. Phys. Lett. 52, 2127 (1988).
[Crossref]

Kono, N.

Koshiba, M.

Lan, S.

Levy, M.

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

Lin, X.-S.

Maier, A. A.

A. A. Maĭer, Sov. J. Quantum Electron. 14, 101 (1984).
[Crossref]

Matsuhisa, Y.

Miroshnichenko, A. E.

Mizumoto, T.

Y. Yazaki, Y. Shoji, and T. Mizumoto, Jpn. J. Appl. Phys., Part 1 46, 5460 (2007).
[Crossref]

Mujumdar, S.

Nakano, Y.

Nishimura, S.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, Nat. Mater. 4, 383 (2005).
[Crossref] [PubMed]

Osgood, J. R. M.

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

Ozaki, M.

Parameswaran, K. R.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001).
[Crossref]

Park, B.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, Nat. Mater. 4, 383 (2005).
[Crossref] [PubMed]

Pinkevych, I.

Ramachandran, H.

Rostami, A.

A. Rostami, Opt. Laser Technol. 39, 1059 (2007).
[Crossref]

Rudebusch, R.

Saitoh, K.

Scalora, M.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, Appl. Phys. Lett. 66, 2324 (1995).
[Crossref]

Schiek, R.

Y. Baek, R. Schiek, G. Stegeman, G. Assanto, and W. Sohler, Appl. Phys. Lett. 72, 3405 (1998).
[Crossref]

Seaton, C. T.

E. M. Wright, S. W. Koch, J. E. Ehrlich, C. T. Seaton, and G. I. Stegeman, Appl. Phys. Lett. 52, 2127 (1988).
[Crossref]

Shadrivov, I. V.

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, Phys. Rev. E 71, 037602 (2005).
[Crossref]

Sheik-Bahae, M.

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. VanStryland, Appl. Phys. Lett. 62, 1323 (1993).
[Crossref]

Shimizu, H.

Shoji, Y.

Y. Yazaki, Y. Shoji, and T. Mizumoto, Jpn. J. Appl. Phys., Part 1 46, 5460 (2007).
[Crossref]

Shvets, G.

G. Shvets, Appl. Phys. Lett. 89, 141127 (2006).
[Crossref]

Sohler, W.

Y. Baek, R. Schiek, G. Stegeman, G. Assanto, and W. Sohler, Appl. Phys. Lett. 72, 3405 (1998).
[Crossref]

Song, M. H.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, Nat. Mater. 4, 383 (2005).
[Crossref] [PubMed]

Stegeman, G.

Y. Baek, R. Schiek, G. Stegeman, G. Assanto, and W. Sohler, Appl. Phys. Lett. 72, 3405 (1998).
[Crossref]

J. S. Aitchison, A. Villeneuve, and G. Stegeman, J. Nonlinear Opt. Phys. Mater. 4, 871 (1995).
[Crossref]

Stegeman, G. I.

C. G. Trevino-Palacios, G. I. Stegeman, and P. Baldi, Opt. Lett. 21, 1442 (1996).
[Crossref] [PubMed]

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. VanStryland, Appl. Phys. Lett. 62, 1323 (1993).
[Crossref]

E. M. Wright, S. W. Koch, J. E. Ehrlich, C. T. Seaton, and G. I. Stegeman, Appl. Phys. Lett. 52, 2127 (1988).
[Crossref]

D. R. Heatley, E. M. Wright, J. E. Ehrlich, and G. I. Stegeman, Opt. Lett. 13, 419 (1988).
[Crossref] [PubMed]

E. Caglioti, S. Trillo, S. Wabnitz, B. Daino, and G. I. Stegeman, Appl. Phys. Lett. 51, 293 (1987).
[Crossref]

Sukhorukov, A. A.

Svirko, Y. P.

Takanishi, Y.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, Nat. Mater. 4, 383 (2005).
[Crossref] [PubMed]

Takao, Y.

Takezoe, H.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, Nat. Mater. 4, 383 (2005).
[Crossref] [PubMed]

Tanaka, M.

Tocci, M. D.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, Appl. Phys. Lett. 66, 2324 (1995).
[Crossref]

Toyooka, T.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, Nat. Mater. 4, 383 (2005).
[Crossref] [PubMed]

Trevino-Palacios, C. G.

Trillo, S.

E. Caglioti, S. Trillo, S. Wabnitz, B. Daino, and G. I. Stegeman, Appl. Phys. Lett. 51, 293 (1987).
[Crossref]

S. Trillo and S. Wabnitz, Appl. Phys. Lett. 49, 752 (1986).
[Crossref]

VanStryland, E.

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. VanStryland, Appl. Phys. Lett. 62, 1323 (1993).
[Crossref]

Villeneuve, A.

J. S. Aitchison, A. Villeneuve, and G. Stegeman, J. Nonlinear Opt. Phys. Mater. 4, 871 (1995).
[Crossref]

Wabnitz, S.

E. Caglioti, S. Trillo, S. Wabnitz, B. Daino, and G. I. Stegeman, Appl. Phys. Lett. 51, 293 (1987).
[Crossref]

S. Trillo and S. Wabnitz, Appl. Phys. Lett. 49, 752 (1986).
[Crossref]

Wang, Z.

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

Wilkens, L.

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

Wright, E. M.

D. R. Heatley, E. M. Wright, J. E. Ehrlich, and G. I. Stegeman, Opt. Lett. 13, 419 (1988).
[Crossref] [PubMed]

E. M. Wright, S. W. Koch, J. E. Ehrlich, C. T. Seaton, and G. I. Stegeman, Appl. Phys. Lett. 52, 2127 (1988).
[Crossref]

Wu, J. W.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, Nat. Mater. 4, 383 (2005).
[Crossref] [PubMed]

Wu, S.-T.

Wu, W.-Q.

Yazaki, Y.

Y. Yazaki, Y. Shoji, and T. Mizumoto, Jpn. J. Appl. Phys., Part 1 46, 5460 (2007).
[Crossref]

Yokoyama, M.

Yu, Z.

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

Zheludev, N. I.

Zhou, H.

Zhou, K.-F.

Zhou, Y.

Zuhlke, C.

Appl. Opt. (1)

Appl. Phys. Lett. (10)

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

G. Shvets, Appl. Phys. Lett. 89, 141127 (2006).
[Crossref]

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, Appl. Phys. Lett. 66, 2324 (1995).
[Crossref]

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001).
[Crossref]

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. VanStryland, Appl. Phys. Lett. 62, 1323 (1993).
[Crossref]

Y. Baek, R. Schiek, G. Stegeman, G. Assanto, and W. Sohler, Appl. Phys. Lett. 72, 3405 (1998).
[Crossref]

S. Trillo and S. Wabnitz, Appl. Phys. Lett. 49, 752 (1986).
[Crossref]

E. Caglioti, S. Trillo, S. Wabnitz, B. Daino, and G. I. Stegeman, Appl. Phys. Lett. 51, 293 (1987).
[Crossref]

E. M. Wright, S. W. Koch, J. E. Ehrlich, C. T. Seaton, and G. I. Stegeman, Appl. Phys. Lett. 52, 2127 (1988).
[Crossref]

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

IEEE J. Quantum Electron. (1)

S. M. Jensen, IEEE J. Quantum Electron. 18, 1580 (1982).
[Crossref]

J. Nonlinear Opt. Phys. Mater. (1)

J. S. Aitchison, A. Villeneuve, and G. Stegeman, J. Nonlinear Opt. Phys. Mater. 4, 871 (1995).
[Crossref]

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

J. Optoelectron. Adv. Mater. (1)

J. Y. Chen, J. Optoelectron. Adv. Mater. 9, 2437 (2007).

Jpn. J. Appl. Phys., Part 1 (1)

Y. Yazaki, Y. Shoji, and T. Mizumoto, Jpn. J. Appl. Phys., Part 1 46, 5460 (2007).
[Crossref]

Nat. Mater. (1)

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, Nat. Mater. 4, 383 (2005).
[Crossref] [PubMed]

Opt. Express (4)

Opt. Laser Technol. (1)

A. Rostami, Opt. Laser Technol. 39, 1059 (2007).
[Crossref]

Opt. Lett. (6)

Phys. Rev. E (2)

A. H. Gevorgyan and M. Z. Harutyunyan, Phys. Rev. E 76, 031701 (2007).
[Crossref]

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, Phys. Rev. E 71, 037602 (2005).
[Crossref]

Sov. J. Quantum Electron. (1)

A. A. Maĭer, Sov. J. Quantum Electron. 14, 101 (1984).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1

Sketch of the DC with a dephasing at η = η 0 in waveguide A. On the right is the index profile used in the ( 1 + 1 ) D simulations. We take guide A as both the input and output ports.

Fig. 2
Fig. 2

(a) Maximum contrast C r versus η 0 and L (in units of half-beat lengths). (b) t for forward (dashed curve) and backward ( t B , solid curve) propagation versus η 0 and (c) actual contrast C (dashed curve) and product C t B (solid curve) versus η 0 , for L = 0.5 and Δ Φ = 3 π P A ( η 0 ) , with P A in = 1 . The optimum is η 0 = 0.196 , as from Eqs. (5).

Fig. 3
Fig. 3

(a) Graphs of C (solid curve) and product C t (dashed curve) versus Δ β NL ( P A in ) from CMT. Circles and stars (crosses and triangles) are C t ( C ) from BPM in local and nonlocal cases (see text), respectively. (b) Solid (dashed) curve, transmission t versus Δ β NL ( P A in ) for reverse (forward) propagation. Circle and stars (crosses and triangles) show BPM computed t in the forward (backward) case, for local and nonlocal media, respectively.

Fig. 4
Fig. 4

Power evolution computed with a ( 1 + 1 ) D BPM at λ = 1064 nm for (a) forward ( z = 0 ) and (b) backward propagation. The beat length L b = π c is 94 μ m , L L b = 105 μ m , and the Kerr section is inserted between z 1 = 0.196 L b 38 μ m and z 2 = z 1 + Δ η L b 49 μ m [ Δ η = 0.06 from Eq. (6)]. Here C = 0.90 and C t = 0.75 . The solid (dashed) curve refers to power transmission in guide A (B).

Fig. 5
Fig. 5

As in Fig. 4 but with z 2 = z 1 + Δ η L b 113 μ m (i.e., Δ η = 0.4 ), L L b = 169 μ m , C = 0.96 , and C t = 0.84 .

Equations (7)

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d F ( z ) d z = [ d A ( z ) d z d B ( z ) d z ] = [ i c B A B e i Δ β z i c A B A e i Δ β z ] ,
T PM ( η ) = [ cos ( π η ) i sin ( π η ) i sin ( π η ) cos ( π η ) ] ,
T A A 2 = 1 2 { 1 + cos ( 2 π η 0 ) cos [ 2 π ( L η 0 ) ] } 1 2 cos Δ Φ sin ( 2 π η 0 ) sin [ 2 π ( L η 0 ) ] .
C r = ( t max t min ) ( t max + t min ) ,
Δ Φ F = 2 π = Δ Φ [ P A in cos 2 ( π η 0 ) ] ,
Δ Φ R = π = Δ Φ { P A in cos 2 [ π ( 0.5 η 0 ) ] } .
Δ η ( 6 c ω n eff M ) 1 n 2 P A in ,

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