Abstract

In this article, an efficient method of asymmetric conversion of guided modes is investigated. From a basic excitation consisting of (mainly) the lowest-order mode of the input multimode strip waveguide, we achieve a conversion efficiency of 60% on average, in the forward propagation case, while the backward propagation is suppressed below 10%. The analytical formulation is based on electromagnetic wave theory with orthogonality relations. Affirmative results between the theoretical and numerical findings based on time and frequency domain analysis are observed. The results of this study will increase the ease of implementing an optical isolator if the breaking time-reversal symmetry could be achieved by nonlinear optics or magneto-optic configurations.

© 2013 Optical Society of America

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    [CrossRef]
  2. 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, 013905 (2008).
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    [CrossRef]
  14. C. Wang, X. L. Zhong, and Z. Y. Li, “Linear and passive silicon optical isolator,” Sci. Rep. 2, 674 (2012).
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    [CrossRef]
  16. H. Kurt, D. Yilmaz, A. Akosman, and E. Ozbay, “Asymmetric light propagation in chirped photonic crystal waveguides,” Opt. Express 20, 20635–20646 (2012).
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    [CrossRef]
  25. A. A. Maznev, A. G. Every, and O. B. Wright, “Reciprocity in reflection and transmission: what is a ‘phonon diode’?” Wave Motion 50, 776–784 (2013).
    [CrossRef]
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    [CrossRef]
  27. C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989), Chap. 7.
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    [CrossRef]

2013 (1)

A. A. Maznev, A. G. Every, and O. B. Wright, “Reciprocity in reflection and transmission: what is a ‘phonon diode’?” Wave Motion 50, 776–784 (2013).
[CrossRef]

2012 (5)

K. Üstün and H. Kurt, “Slow light structure with enhanced delay–bandwidth product,” J. Opt. Soc. Am. B 29, 2403–2409 (2012).
[CrossRef]

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. B. Oliveira, V. R. Almeida, Y. F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2012).
[CrossRef]

J. Yu, H. Chen, Y. Wu, and S. Liu, “Magnetically manipulable perfect unidirectional absorber based on nonreciprocal magnetic surface plasmon,” Europhys. Lett. 100, 47007 (2012).
[CrossRef]

C. Wang, X. L. Zhong, and Z. Y. Li, “Linear and passive silicon optical isolator,” Sci. Rep. 2, 674 (2012).

H. Kurt, D. Yilmaz, A. Akosman, and E. Ozbay, “Asymmetric light propagation in chirped photonic crystal waveguides,” Opt. Express 20, 20635–20646 (2012).
[CrossRef]

2011 (6)

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on nonreciprocal light propagation in a silicon photonic circuit,” Science 335, 38-b (2011).

C. Husko, T. D. Vo, B. Corcoran, J. Li, T. F. Krauss, and B. J. Eggleton, “Ultracompact all-optical XOR logic gate in a slow-light silicon photonic crystal waveguide,” Opt. Express 19, 20681–20690 (2011).
[CrossRef]

S. Y. Liu, W. L. Lu, Z. F. Lin, and S. T. Chui, “Molding reflection from metamaterials based on magnetic surface plasmons,” Phys. Rev. B 84, 045425 (2011).
[CrossRef]

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

K. Üstün and H. Kurt, “Compact coupling of light from conventional photonic wire to slow light waveguides,” J. Appl. Phys. 110, 113109 (2011).
[CrossRef]

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333, 729–733 (2011).
[CrossRef]

2010 (3)

2009 (3)

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

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

A. E. Serebryannikov, “One-way diffraction effects in photonic crystal gratings made of isotropic materials,” Phys. Rev. B 80, 155117 (2009).
[CrossRef]

2008 (2)

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, 013905 (2008).
[CrossRef]

T. F. Krauss, “Why do we need slow light?” Nat. Photonics 2, 448–450 (2008).
[CrossRef]

2007 (1)

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2, 35–38 (2007).
[CrossRef]

2006 (1)

2004 (2)

S. Pereira, P. Chak, J. E. Sipe, L. Tkeshelashvili, and K. Busch, “All-optical diode in an asymmetrically apodized Kerr nonlinear microresonator system,” Photon. Nanostr. Fundam. Appl. 2, 181–190 (2004).
[CrossRef]

R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67, 717–754 (2004).
[CrossRef]

2001 (2)

K. Gallo and G. Assanto, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett. 79, 314–316 (2001).
[CrossRef]

S. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[CrossRef]

Akosman, A.

Almeida, V. R.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. B. Oliveira, V. R. Almeida, Y. F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2012).
[CrossRef]

Assanto, G.

K. Gallo and G. Assanto, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett. 79, 314–316 (2001).
[CrossRef]

Ayache, M.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333, 729–733 (2011).
[CrossRef]

Baets, R.

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on nonreciprocal light propagation in a silicon photonic circuit,” Science 335, 38-b (2011).

Balanis, C. A.

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989), Chap. 7.

Brinkmeyer, E.

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on nonreciprocal light propagation in a silicon photonic circuit,” Science 335, 38-b (2011).

Busch, K.

S. Pereira, P. Chak, J. E. Sipe, L. Tkeshelashvili, and K. Busch, “All-optical diode in an asymmetrically apodized Kerr nonlinear microresonator system,” Photon. Nanostr. Fundam. Appl. 2, 181–190 (2004).
[CrossRef]

Cao, H.

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

Chak, P.

S. Pereira, P. Chak, J. E. Sipe, L. Tkeshelashvili, and K. Busch, “All-optical diode in an asymmetrically apodized Kerr nonlinear microresonator system,” Photon. Nanostr. Fundam. Appl. 2, 181–190 (2004).
[CrossRef]

Chen, H.

J. Yu, H. Chen, Y. Wu, and S. Liu, “Magnetically manipulable perfect unidirectional absorber based on nonreciprocal magnetic surface plasmon,” Europhys. Lett. 100, 47007 (2012).
[CrossRef]

Chen, Y. F.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. B. Oliveira, V. R. Almeida, Y. F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2012).
[CrossRef]

Chen, Y.-F.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333, 729–733 (2011).
[CrossRef]

Chong, Y.

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

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, 013905 (2008).
[CrossRef]

Christodoulides, D. N.

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

Chui, S. T.

S. Y. Liu, W. L. Lu, Z. F. Lin, and S. T. Chui, “Molding reflection from metamaterials based on magnetic surface plasmons,” Phys. Rev. B 84, 045425 (2011).
[CrossRef]

S. Y. Liu, W. L. Lu, Z. F. Lin, and S. T. Chui, “Magnetically controllable unidirectional electromagnetic waveguiding devices designed with metamaterials,” Appl. Phys. Lett. 97, 201113 (2010).
[CrossRef]

Collin, R. E.

R. E. Collin, Field Theory of Guided Waves (McGraw-Hill, 1960).

Corcoran, B.

Doerr, C. R.

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on nonreciprocal light propagation in a silicon photonic circuit,” Science 335, 38-b (2011).

Eggleton, B. J.

Eich, M.

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on nonreciprocal light propagation in a silicon photonic circuit,” Science 335, 38-b (2011).

Eichelkraut, T.

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

Every, A. G.

A. A. Maznev, A. G. Every, and O. B. Wright, “Reciprocity in reflection and transmission: what is a ‘phonon diode’?” Wave Motion 50, 776–784 (2013).
[CrossRef]

Fainman, Y.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333, 729–733 (2011).
[CrossRef]

Fan, S.

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on nonreciprocal light propagation in a silicon photonic circuit,” Science 335, 38-b (2011).

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

Fegadolli, W. S.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. B. Oliveira, V. R. Almeida, Y. F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2012).
[CrossRef]

Feng, L.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. B. Oliveira, V. R. Almeida, Y. F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2012).
[CrossRef]

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333, 729–733 (2011).
[CrossRef]

Foster, M. A.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2, 35–38 (2007).
[CrossRef]

Freude, W.

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on nonreciprocal light propagation in a silicon photonic circuit,” Science 335, 38-b (2011).

Gaeta, A. L.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2, 35–38 (2007).
[CrossRef]

Gallo, K.

K. Gallo and G. Assanto, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett. 79, 314–316 (2001).
[CrossRef]

Geraghty, D. F.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2, 35–38 (2007).
[CrossRef]

Huang, J.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333, 729–733 (2011).
[CrossRef]

Husko, C.

Jalas, D.

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on nonreciprocal light propagation in a silicon photonic circuit,” Science 335, 38-b (2011).

Joannopoulos, J.

Joannopoulos, J. D.

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on nonreciprocal light propagation in a silicon photonic circuit,” Science 335, 38-b (2011).

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

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, 013905 (2008).
[CrossRef]

Johnson, S.

Kottos, T.

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

Krause, M.

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on nonreciprocal light propagation in a silicon photonic circuit,” Science 335, 38-b (2011).

Krauss, T. F.

Kurt, H.

Lan, S.

Li, J.

Li, Z. Y.

C. Wang, X. L. Zhong, and Z. Y. Li, “Linear and passive silicon optical isolator,” Sci. Rep. 2, 674 (2012).

Lin, X.-S.

Lin, X.-W.

Lin, Z.

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

Lin, Z. F.

S. Y. Liu, W. L. Lu, Z. F. Lin, and S. T. Chui, “Molding reflection from metamaterials based on magnetic surface plasmons,” Phys. Rev. B 84, 045425 (2011).
[CrossRef]

S. Y. Liu, W. L. Lu, Z. F. Lin, and S. T. Chui, “Magnetically controllable unidirectional electromagnetic waveguiding devices designed with metamaterials,” Appl. Phys. Lett. 97, 201113 (2010).
[CrossRef]

Lipson, M.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2, 35–38 (2007).
[CrossRef]

Liu, S.

J. Yu, H. Chen, Y. Wu, and S. Liu, “Magnetically manipulable perfect unidirectional absorber based on nonreciprocal magnetic surface plasmon,” Europhys. Lett. 100, 47007 (2012).
[CrossRef]

Liu, S. Y.

S. Y. Liu, W. L. Lu, Z. F. Lin, and S. T. Chui, “Molding reflection from metamaterials based on magnetic surface plasmons,” Phys. Rev. B 84, 045425 (2011).
[CrossRef]

S. Y. Liu, W. L. Lu, Z. F. Lin, and S. T. Chui, “Magnetically controllable unidirectional electromagnetic waveguiding devices designed with metamaterials,” Appl. Phys. Lett. 97, 201113 (2010).
[CrossRef]

Lu, M. H.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. B. Oliveira, V. R. Almeida, Y. F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2012).
[CrossRef]

Lu, M.-H.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333, 729–733 (2011).
[CrossRef]

Lu, W. L.

S. Y. Liu, W. L. Lu, Z. F. Lin, and S. T. Chui, “Molding reflection from metamaterials based on magnetic surface plasmons,” Phys. Rev. B 84, 045425 (2011).
[CrossRef]

S. Y. Liu, W. L. Lu, Z. F. Lin, and S. T. Chui, “Magnetically controllable unidirectional electromagnetic waveguiding devices designed with metamaterials,” Appl. Phys. Lett. 97, 201113 (2010).
[CrossRef]

Lu, Y.-Q.

Maznev, A. A.

A. A. Maznev, A. G. Every, and O. B. Wright, “Reciprocity in reflection and transmission: what is a ‘phonon diode’?” Wave Motion 50, 776–784 (2013).
[CrossRef]

Melloni, A.

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on nonreciprocal light propagation in a silicon photonic circuit,” Science 335, 38-b (2011).

Oliveira, J. E. B.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. B. Oliveira, V. R. Almeida, Y. F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2012).
[CrossRef]

Ozbay, E.

Pereira, S.

S. Pereira, P. Chak, J. E. Sipe, L. Tkeshelashvili, and K. Busch, “All-optical diode in an asymmetrically apodized Kerr nonlinear microresonator system,” Photon. Nanostr. Fundam. Appl. 2, 181–190 (2004).
[CrossRef]

Petrov, A.

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on nonreciprocal light propagation in a silicon photonic circuit,” Science 335, 38-b (2011).

Popovic, M.

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on nonreciprocal light propagation in a silicon photonic circuit,” Science 335, 38-b (2011).

Potton, R. J.

R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67, 717–754 (2004).
[CrossRef]

Qian, X.-S.

Ramezani, H.

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

Renner, H.

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on nonreciprocal light propagation in a silicon photonic circuit,” Science 335, 38-b (2011).

Salem, R.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2, 35–38 (2007).
[CrossRef]

Scherer, A.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. B. Oliveira, V. R. Almeida, Y. F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2012).
[CrossRef]

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333, 729–733 (2011).
[CrossRef]

Serebryannikov, A. E.

A. E. Serebryannikov, “One-way diffraction effects in photonic crystal gratings made of isotropic materials,” Phys. Rev. B 80, 155117 (2009).
[CrossRef]

Sipe, J. E.

S. Pereira, P. Chak, J. E. Sipe, L. Tkeshelashvili, and K. Busch, “All-optical diode in an asymmetrically apodized Kerr nonlinear microresonator system,” Photon. Nanostr. Fundam. Appl. 2, 181–190 (2004).
[CrossRef]

Soljacic, M.

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

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, 013905 (2008).
[CrossRef]

Song, X.-S.

Tkeshelashvili, L.

S. Pereira, P. Chak, J. E. Sipe, L. Tkeshelashvili, and K. Busch, “All-optical diode in an asymmetrically apodized Kerr nonlinear microresonator system,” Photon. Nanostr. Fundam. Appl. 2, 181–190 (2004).
[CrossRef]

Turner, A. C.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2, 35–38 (2007).
[CrossRef]

Üstün, K.

Vanwolleghem, M.

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on nonreciprocal light propagation in a silicon photonic circuit,” Science 335, 38-b (2011).

Vo, T. D.

Wang, C.

C. Wang, X. L. Zhong, and Z. Y. Li, “Linear and passive silicon optical isolator,” Sci. Rep. 2, 674 (2012).

Wang, Q.

Wang, Z.

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

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, 013905 (2008).
[CrossRef]

Wright, O. B.

A. A. Maznev, A. G. Every, and O. B. Wright, “Reciprocity in reflection and transmission: what is a ‘phonon diode’?” Wave Motion 50, 776–784 (2013).
[CrossRef]

Wu, W.-Q.

Wu, Y.

J. Yu, H. Chen, Y. Wu, and S. Liu, “Magnetically manipulable perfect unidirectional absorber based on nonreciprocal magnetic surface plasmon,” Europhys. Lett. 100, 47007 (2012).
[CrossRef]

Xu, F.

Xu, Y. L.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. B. Oliveira, V. R. Almeida, Y. F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2012).
[CrossRef]

Xu, Y.-L.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333, 729–733 (2011).
[CrossRef]

Yilmaz, D.

Yu, J.

J. Yu, H. Chen, Y. Wu, and S. Liu, “Magnetically manipulable perfect unidirectional absorber based on nonreciprocal magnetic surface plasmon,” Europhys. Lett. 100, 47007 (2012).
[CrossRef]

Yu, Z.

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on nonreciprocal light propagation in a silicon photonic circuit,” Science 335, 38-b (2011).

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

Yu, Z.-Y.

Zhong, X. L.

C. Wang, X. L. Zhong, and Z. Y. Li, “Linear and passive silicon optical isolator,” Sci. Rep. 2, 674 (2012).

Zhou, H.

Zhou, K.-F.

Appl. Phys. Lett. (2)

S. Y. Liu, W. L. Lu, Z. F. Lin, and S. T. Chui, “Magnetically controllable unidirectional electromagnetic waveguiding devices designed with metamaterials,” Appl. Phys. Lett. 97, 201113 (2010).
[CrossRef]

K. Gallo and G. Assanto, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett. 79, 314–316 (2001).
[CrossRef]

Europhys. Lett. (1)

J. Yu, H. Chen, Y. Wu, and S. Liu, “Magnetically manipulable perfect unidirectional absorber based on nonreciprocal magnetic surface plasmon,” Europhys. Lett. 100, 47007 (2012).
[CrossRef]

J. Appl. Phys. (1)

K. Üstün and H. Kurt, “Compact coupling of light from conventional photonic wire to slow light waveguides,” J. Appl. Phys. 110, 113109 (2011).
[CrossRef]

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

Nat. Mater. (1)

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. B. Oliveira, V. R. Almeida, Y. F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2012).
[CrossRef]

Nat. Photonics (3)

T. F. Krauss, “Why do we need slow light?” Nat. Photonics 2, 448–450 (2008).
[CrossRef]

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2, 35–38 (2007).
[CrossRef]

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

Nature (1)

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

Opt. Express (5)

Opt. Lett. (1)

Photon. Nanostr. Fundam. Appl. (1)

S. Pereira, P. Chak, J. E. Sipe, L. Tkeshelashvili, and K. Busch, “All-optical diode in an asymmetrically apodized Kerr nonlinear microresonator system,” Photon. Nanostr. Fundam. Appl. 2, 181–190 (2004).
[CrossRef]

Phys. Rev. B (2)

S. Y. Liu, W. L. Lu, Z. F. Lin, and S. T. Chui, “Molding reflection from metamaterials based on magnetic surface plasmons,” Phys. Rev. B 84, 045425 (2011).
[CrossRef]

A. E. Serebryannikov, “One-way diffraction effects in photonic crystal gratings made of isotropic materials,” Phys. Rev. B 80, 155117 (2009).
[CrossRef]

Phys. Rev. Lett. (2)

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, 013905 (2008).
[CrossRef]

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

Rep. Prog. Phys. (1)

R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67, 717–754 (2004).
[CrossRef]

Sci. Rep. (1)

C. Wang, X. L. Zhong, and Z. Y. Li, “Linear and passive silicon optical isolator,” Sci. Rep. 2, 674 (2012).

Science (2)

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333, 729–733 (2011).
[CrossRef]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on nonreciprocal light propagation in a silicon photonic circuit,” Science 335, 38-b (2011).

Wave Motion (1)

A. A. Maznev, A. G. Every, and O. B. Wright, “Reciprocity in reflection and transmission: what is a ‘phonon diode’?” Wave Motion 50, 776–784 (2013).
[CrossRef]

Other (2)

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989), Chap. 7.

R. E. Collin, Field Theory of Guided Waves (McGraw-Hill, 1960).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Initial PC waveguide structure. The structure has an input coupler at the left, but there is no special configuration at the output. Part A shows the slow light PC waveguide given in [26]. Part B is the tapered input coupling region. Part C is the output configuration with a new eigenfield. (b) Forward traveling wave at the output. As seen in the figure, the higher-order modes are dominant compared to the fundamental mode. (c) Excitation from the output. The light wave cannot penetrate into the PC waveguide structure, because it mainly contains the fundamental mode and slow light mode excitation with tapering being absent on the right-hand side. (d) Clearer look for the exit region (part C). (e) The dispersion diagram of the slow light PC waveguide given in part A. The vertical axis shows the normalized frequency. The linear region of the band given in thick red color in the dispersion diagram is of interest.

Fig. 2.
Fig. 2.

(a) Forward transmission spectra for different numbers of holes as r2=0.33a. (b) Corresponding contrast ratios. Note that the scale of the graph ranges from 0.95 to 1.0.

Fig. 3.
Fig. 3.

Backward and forward transmission spectra for the 3D case and the corresponding contrast ratio.

Fig. 4.
Fig. 4.

(a)–(d) Fourier space mode profiles of the first, third, fifth, and seventh order modes of the output waveguide at a/λ=0.2155, respectively. (e) FDTD mode profile at the output waveguide, which is a superposition of (a)–(d) as shown by numbers. The unit of the wave vectors kx and ky is (2π/a).

Tables (1)

Tables Icon

Table 1. Comparison of Coupling Coefficients Derived from FDTD Results and EMT

Equations (16)

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×E=jωμH,
×H=jω(ε1+Δε)E,
×Ein=jωμHin,
×Hin=jωε1Ein.
×Es=jωμHs,
×Hs=jω(ε1+Δε)Es+Js,
Ein=a1Epc+Eo1Hin=a1Hpc+Ho1,
Es=a2Epc+Eo2Hs=a2Hpc+Ho2,
E=Es+Ein=(a1+a2)Epc+irrelevanttermsH=Hs+Hin=(a1+a2)Hpc+irrelevantterms.
(Es×Hs*)=Hs*×EsEs×Hs*=jωμHs*Hs+jω(ε1+Δε)EsEs*EsJs*
·((a2Epc+Eo2)×(a2Hpc+Ho2)*)=jωμ(a2Hpc+Ho2)*(a2Hpc+Ho2)+jω(ε1+Δε)(a2Epc+Eo2)(a2Epc+Eo2)*(a2Epc+Eo2)Js*.
RHS=jωμ|a2|2|Hpc|2jωμ|Ho2|2jωμa2*Hpc*Ho2jωμa2HpcHo2*+jω(ε1+Δε)|a2|2|Epc|2+jω(ε1+Δε)|Eo2|2+jω(ε1+Δε)a2*Epc*Eo2+jω(ε1+Δε)a2EpcEo2*a2EpcJs*Eo2Js*.
(|a2|2Epc×Hpc*)=jωμ|a2|2|Hpc|2+jω(ε1+Δε)|a2|2|Epc|2a2EpcJs*
(|a2|2Epc×Hpc*)=a2EpcJs*.
|a2|2(Epc×Hpc*)dS=a2EpcJs*dV.
a2=[(EpcJs*dV)/((Epc×Hpc*)dS)]*

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