Abstract

The novel all-optical unidirectional wavelength filters are studied by the finite-difference time-domain method, which are based on the two-dimensional square-lattice photonic crystal with the rectangular defects. Owing to the modes’ match and mismatch between the defect and the adjacent waveguides, the unidirectional propagation of the fundamental-mode light beam resonant at a certain frequency is obtained. Through merely altering the coupling region between the defect and the input waveguide, a unidirectional dual-branch waveguide filter is designed. This kind of devices has both the abilities of wavelength filtering and unidirectional light propagation, and may be potentially applied in the future all-optical complex integrated circuits.

© 2013 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  26. S. Fan, R. Baets, A. Petrov, Z. F. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, 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,” Science335, 38-b (2012).
  27. S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response to Comment on “Nonreciprocal Light Propagation in a Silicon Photonic Circuit”,” Science335(6064), 38–c, author reply 38 (2012).
    [CrossRef] [PubMed]

2012

S. Feng, C. Ren, Y. Q. Wang, and W. Z. Wang, “All-optical diode based on the self-collimation characteristics of the near-infrared photonic crystal heterojunctions,” Europhys. Lett.97(6), 64001 (2012).
[CrossRef]

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. H. Qi, “An All-Silicon Passive Optical Diode,” Science335(6067), 447–450 (2012).
[CrossRef] [PubMed]

S. Fan, R. Baets, A. Petrov, Z. F. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, 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,” Science335, 38-b (2012).

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response to Comment on “Nonreciprocal Light Propagation in a Silicon Photonic Circuit”,” Science335(6064), 38–c, author reply 38 (2012).
[CrossRef] [PubMed]

A. Cicek, M. B. Yucel, O. A. Kaya, and B. Ulug, “Refraction-based photonic crystal diode,” Opt. Lett.37(14), 2937–2939 (2012).
[CrossRef] [PubMed]

2011

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,” Science333(6043), 729–733 (2011).
[CrossRef] [PubMed]

C. C. Lu, X. Y. Hu, H. Yang, and Q. H. Gong, “Ultrahigh-contrast and wideband nanoscale photonic crystal all-optical diode,” Opt. Lett.36(23), 4668–4670 (2011).
[CrossRef] [PubMed]

C. Wang, C. Z. Zhou, and Z. Y. Li, “On-chip optical diode based on silicon photonic crystal heterojunctions,” Opt. Express19(27), 26948–26955 (2011).
[CrossRef] [PubMed]

X. F. Li, X. Ni, L. Feng, M. H. Lu, C. He, and Y. F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode,” Phys. Rev. Lett.106(8), 084301 (2011).
[CrossRef] [PubMed]

M. S. Kang, A. Butsch, and P. S. J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics5(9), 549–553 (2011).
[CrossRef]

2009

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics3(2), 91–94 (2009).
[CrossRef]

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature461(7265), 772–775 (2009).
[CrossRef] [PubMed]

2008

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]

F. D. M. Haldane and S. Raghu, “Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry,” Phys. Rev. Lett.100(1), 013904 (2008).
[CrossRef] [PubMed]

2007

A. Rostami, “Piecewise linear integrated optical device as an optical isolator using two-port nonlinear ring resonators,” Opt. Laser Technol.39(5), 1059–1065 (2007).
[CrossRef]

2006

2005

H. Takano, B. S. Song, T. Asano, and S. Noda, “Highly efficient in-plane channel drop filter in a two-dimensional heterophotonic crystal,” Appl. Phys. Lett.86(24), 241101 (2005).
[CrossRef]

2003

B. S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science300(5625), 1537 (2003).
[CrossRef] [PubMed]

M. Soljacić, C. Luo, J. D. Joannopoulos, and S. Fan, “Nonlinear photonic crystal microdevices for optical integration,” Opt. Lett.28(8), 637–639 (2003).
[CrossRef] [PubMed]

2001

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs,” Phys. Rev. Lett.87(25), 253902 (2001).
[CrossRef] [PubMed]

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett.79(3), 314 (2001).
[CrossRef]

2000

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature407(6804), 608–610 (2000).
[CrossRef] [PubMed]

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature407(6804), 608–610 (2000).
[CrossRef] [PubMed]

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, “Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide,” Appl. Phys. Lett.76(8), 952 (2000).
[CrossRef]

1998

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Channel Drop Tunneling through Localized States,” Phys. Rev. Lett.80(5), 960–963 (1998).
[CrossRef]

1987

E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett.58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett.58(23), 2486–2489 (1987).
[CrossRef] [PubMed]

Asano, T.

H. Takano, B. S. Song, T. Asano, and S. Noda, “Highly efficient in-plane channel drop filter in a two-dimensional heterophotonic crystal,” Appl. Phys. Lett.86(24), 241101 (2005).
[CrossRef]

B. S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science300(5625), 1537 (2003).
[CrossRef] [PubMed]

Assanto, G.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett.79(3), 314 (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,” Science333(6043), 729–733 (2011).
[CrossRef] [PubMed]

Baets, R.

S. Fan, R. Baets, A. Petrov, Z. F. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, 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,” Science335, 38-b (2012).

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response to Comment on “Nonreciprocal Light Propagation in a Silicon Photonic Circuit”,” Science335(6064), 38–c, author reply 38 (2012).
[CrossRef] [PubMed]

Brinkmeyer, E.

S. Fan, R. Baets, A. Petrov, Z. F. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, 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,” Science335, 38-b (2012).

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response to Comment on “Nonreciprocal Light Propagation in a Silicon Photonic Circuit”,” Science335(6064), 38–c, author reply 38 (2012).
[CrossRef] [PubMed]

Butsch, A.

M. S. Kang, A. Butsch, and P. S. J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics5(9), 549–553 (2011).
[CrossRef]

Chen, Y. F.

X. F. Li, X. Ni, L. Feng, M. H. Lu, C. He, and Y. F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode,” Phys. Rev. Lett.106(8), 084301 (2011).
[CrossRef] [PubMed]

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,” Science333(6043), 729–733 (2011).
[CrossRef] [PubMed]

Chong, Y.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature461(7265), 772–775 (2009).
[CrossRef] [PubMed]

Chutinan, A.

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature407(6804), 608–610 (2000).
[CrossRef] [PubMed]

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature407(6804), 608–610 (2000).
[CrossRef] [PubMed]

Cicek, A.

Doerr, C. R.

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response to Comment on “Nonreciprocal Light Propagation in a Silicon Photonic Circuit”,” Science335(6064), 38–c, author reply 38 (2012).
[CrossRef] [PubMed]

S. Fan, R. Baets, A. Petrov, Z. F. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, 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,” Science335, 38-b (2012).

Eich, M.

S. Fan, R. Baets, A. Petrov, Z. F. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, 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,” Science335, 38-b (2012).

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response to Comment on “Nonreciprocal Light Propagation in a Silicon Photonic Circuit”,” Science335(6064), 38–c, author reply 38 (2012).
[CrossRef] [PubMed]

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,” Science333(6043), 729–733 (2011).
[CrossRef] [PubMed]

Fan, L.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. H. Qi, “An All-Silicon Passive Optical Diode,” Science335(6067), 447–450 (2012).
[CrossRef] [PubMed]

Fan, S.

S. Fan, R. Baets, A. Petrov, Z. F. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, 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,” Science335, 38-b (2012).

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response to Comment on “Nonreciprocal Light Propagation in a Silicon Photonic Circuit”,” Science335(6064), 38–c, author reply 38 (2012).
[CrossRef] [PubMed]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics3(2), 91–94 (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]

M. Soljacić, C. Luo, J. D. Joannopoulos, and S. Fan, “Nonlinear photonic crystal microdevices for optical integration,” Opt. Lett.28(8), 637–639 (2003).
[CrossRef] [PubMed]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Channel Drop Tunneling through Localized States,” Phys. Rev. Lett.80(5), 960–963 (1998).
[CrossRef]

Fejer, M. M.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett.79(3), 314 (2001).
[CrossRef]

Feng, 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,” Science333(6043), 729–733 (2011).
[CrossRef] [PubMed]

X. F. Li, X. Ni, L. Feng, M. H. Lu, C. He, and Y. F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode,” Phys. Rev. Lett.106(8), 084301 (2011).
[CrossRef] [PubMed]

Feng, S.

S. Feng, C. Ren, Y. Q. Wang, and W. Z. Wang, “All-optical diode based on the self-collimation characteristics of the near-infrared photonic crystal heterojunctions,” Europhys. Lett.97(6), 64001 (2012).
[CrossRef]

Freude, W.

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response to Comment on “Nonreciprocal Light Propagation in a Silicon Photonic Circuit”,” Science335(6064), 38–c, author reply 38 (2012).
[CrossRef] [PubMed]

S. Fan, R. Baets, A. Petrov, Z. F. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, 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,” Science335, 38-b (2012).

Gallo, K.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett.79(3), 314 (2001).
[CrossRef]

Gong, Q. H.

Haldane, F. D. M.

F. D. M. Haldane and S. Raghu, “Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry,” Phys. Rev. Lett.100(1), 013904 (2008).
[CrossRef] [PubMed]

He, C.

X. F. Li, X. Ni, L. Feng, M. H. Lu, C. He, and Y. F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode,” Phys. Rev. Lett.106(8), 084301 (2011).
[CrossRef] [PubMed]

Hu, X. Y.

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,” Science333(6043), 729–733 (2011).
[CrossRef] [PubMed]

Imada, M.

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature407(6804), 608–610 (2000).
[CrossRef] [PubMed]

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature407(6804), 608–610 (2000).
[CrossRef] [PubMed]

Jalas, D.

S. Fan, R. Baets, A. Petrov, Z. F. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, 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,” Science335, 38-b (2012).

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response to Comment on “Nonreciprocal Light Propagation in a Silicon Photonic Circuit”,” Science335(6064), 38–c, author reply 38 (2012).
[CrossRef] [PubMed]

Joannopoulos, J. D.

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response to Comment on “Nonreciprocal Light Propagation in a Silicon Photonic Circuit”,” Science335(6064), 38–c, author reply 38 (2012).
[CrossRef] [PubMed]

S. Fan, R. Baets, A. Petrov, Z. F. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, 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,” Science335, 38-b (2012).

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature461(7265), 772–775 (2009).
[CrossRef] [PubMed]

M. Soljacić, C. Luo, J. D. Joannopoulos, and S. Fan, “Nonlinear photonic crystal microdevices for optical integration,” Opt. Lett.28(8), 637–639 (2003).
[CrossRef] [PubMed]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Channel Drop Tunneling through Localized States,” Phys. Rev. Lett.80(5), 960–963 (1998).
[CrossRef]

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett.58(23), 2486–2489 (1987).
[CrossRef] [PubMed]

Kang, M. S.

M. S. Kang, A. Butsch, and P. S. J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics5(9), 549–553 (2011).
[CrossRef]

Kaya, O. A.

Kosaka, H.

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, “Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide,” Appl. Phys. Lett.76(8), 952 (2000).
[CrossRef]

Krause, M.

S. Fan, R. Baets, A. Petrov, Z. F. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, 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,” Science335, 38-b (2012).

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response to Comment on “Nonreciprocal Light Propagation in a Silicon Photonic Circuit”,” Science335(6064), 38–c, author reply 38 (2012).
[CrossRef] [PubMed]

Lan, S.

Li, X. F.

X. F. Li, X. Ni, L. Feng, M. H. Lu, C. He, and Y. F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode,” Phys. Rev. Lett.106(8), 084301 (2011).
[CrossRef] [PubMed]

Li, Z. Y.

Lin, X. S.

Lu, C. C.

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,” Science333(6043), 729–733 (2011).
[CrossRef] [PubMed]

X. F. Li, X. Ni, L. Feng, M. H. Lu, C. He, and Y. F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode,” Phys. Rev. Lett.106(8), 084301 (2011).
[CrossRef] [PubMed]

Luo, C.

Melloni, A.

S. Fan, R. Baets, A. Petrov, Z. F. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, 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,” Science335, 38-b (2012).

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response to Comment on “Nonreciprocal Light Propagation in a Silicon Photonic Circuit”,” Science335(6064), 38–c, author reply 38 (2012).
[CrossRef] [PubMed]

Ni, X.

X. F. Li, X. Ni, L. Feng, M. H. Lu, C. He, and Y. F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode,” Phys. Rev. Lett.106(8), 084301 (2011).
[CrossRef] [PubMed]

Niu, B.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. H. Qi, “An All-Silicon Passive Optical Diode,” Science335(6067), 447–450 (2012).
[CrossRef] [PubMed]

Noda, S.

H. Takano, B. S. Song, T. Asano, and S. Noda, “Highly efficient in-plane channel drop filter in a two-dimensional heterophotonic crystal,” Appl. Phys. Lett.86(24), 241101 (2005).
[CrossRef]

B. S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science300(5625), 1537 (2003).
[CrossRef] [PubMed]

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature407(6804), 608–610 (2000).
[CrossRef] [PubMed]

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature407(6804), 608–610 (2000).
[CrossRef] [PubMed]

Notomi, M.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs,” Phys. Rev. Lett.87(25), 253902 (2001).
[CrossRef] [PubMed]

Parameswaran, K. R.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett.79(3), 314 (2001).
[CrossRef]

Petrov, A.

S. Fan, R. Baets, A. Petrov, Z. F. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, 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,” Science335, 38-b (2012).

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response to Comment on “Nonreciprocal Light Propagation in a Silicon Photonic Circuit”,” Science335(6064), 38–c, author reply 38 (2012).
[CrossRef] [PubMed]

Popovic, M.

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response to Comment on “Nonreciprocal Light Propagation in a Silicon Photonic Circuit”,” Science335(6064), 38–c, author reply 38 (2012).
[CrossRef] [PubMed]

S. Fan, R. Baets, A. Petrov, Z. F. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, 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,” Science335, 38-b (2012).

Qi, M. H.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. H. Qi, “An All-Silicon Passive Optical Diode,” Science335(6067), 447–450 (2012).
[CrossRef] [PubMed]

Raghu, S.

F. D. M. Haldane and S. Raghu, “Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry,” Phys. Rev. Lett.100(1), 013904 (2008).
[CrossRef] [PubMed]

Ren, C.

S. Feng, C. Ren, Y. Q. Wang, and W. Z. Wang, “All-optical diode based on the self-collimation characteristics of the near-infrared photonic crystal heterojunctions,” Europhys. Lett.97(6), 64001 (2012).
[CrossRef]

Renner, H.

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response to Comment on “Nonreciprocal Light Propagation in a Silicon Photonic Circuit”,” Science335(6064), 38–c, author reply 38 (2012).
[CrossRef] [PubMed]

S. Fan, R. Baets, A. Petrov, Z. F. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, 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,” Science335, 38-b (2012).

Rostami, A.

A. Rostami, “Piecewise linear integrated optical device as an optical isolator using two-port nonlinear ring resonators,” Opt. Laser Technol.39(5), 1059–1065 (2007).
[CrossRef]

Russell, P. S. J.

M. S. Kang, A. Butsch, and P. S. J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics5(9), 549–553 (2011).
[CrossRef]

Scherer, A.

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,” Science333(6043), 729–733 (2011).
[CrossRef] [PubMed]

Shen, H.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. H. Qi, “An All-Silicon Passive Optical Diode,” Science335(6067), 447–450 (2012).
[CrossRef] [PubMed]

Shinya, A.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs,” Phys. Rev. Lett.87(25), 253902 (2001).
[CrossRef] [PubMed]

Soljacic, M.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature461(7265), 772–775 (2009).
[CrossRef] [PubMed]

M. Soljacić, C. Luo, J. D. Joannopoulos, and S. Fan, “Nonlinear photonic crystal microdevices for optical integration,” Opt. Lett.28(8), 637–639 (2003).
[CrossRef] [PubMed]

Song, B. S.

H. Takano, B. S. Song, T. Asano, and S. Noda, “Highly efficient in-plane channel drop filter in a two-dimensional heterophotonic crystal,” Appl. Phys. Lett.86(24), 241101 (2005).
[CrossRef]

B. S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science300(5625), 1537 (2003).
[CrossRef] [PubMed]

Takahashi, C.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs,” Phys. Rev. Lett.87(25), 253902 (2001).
[CrossRef] [PubMed]

Takahashi, J.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs,” Phys. Rev. Lett.87(25), 253902 (2001).
[CrossRef] [PubMed]

Takano, H.

H. Takano, B. S. Song, T. Asano, and S. Noda, “Highly efficient in-plane channel drop filter in a two-dimensional heterophotonic crystal,” Appl. Phys. Lett.86(24), 241101 (2005).
[CrossRef]

Tokushima, M.

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, “Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide,” Appl. Phys. Lett.76(8), 952 (2000).
[CrossRef]

Tomita, A.

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, “Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide,” Appl. Phys. Lett.76(8), 952 (2000).
[CrossRef]

Ulug, B.

Vanwolleghem, M.

S. Fan, R. Baets, A. Petrov, Z. F. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, 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,” Science335, 38-b (2012).

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response to Comment on “Nonreciprocal Light Propagation in a Silicon Photonic Circuit”,” Science335(6064), 38–c, author reply 38 (2012).
[CrossRef] [PubMed]

Varghese, L. T.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. H. Qi, “An All-Silicon Passive Optical Diode,” Science335(6067), 447–450 (2012).
[CrossRef] [PubMed]

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]

Villeneuve, P. R.

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Channel Drop Tunneling through Localized States,” Phys. Rev. Lett.80(5), 960–963 (1998).
[CrossRef]

Wang, C.

Wang, J.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. H. Qi, “An All-Silicon Passive Optical Diode,” Science335(6067), 447–450 (2012).
[CrossRef] [PubMed]

Wang, W. Z.

S. Feng, C. Ren, Y. Q. Wang, and W. Z. Wang, “All-optical diode based on the self-collimation characteristics of the near-infrared photonic crystal heterojunctions,” Europhys. Lett.97(6), 64001 (2012).
[CrossRef]

Wang, Y. Q.

S. Feng, C. Ren, Y. Q. Wang, and W. Z. Wang, “All-optical diode based on the self-collimation characteristics of the near-infrared photonic crystal heterojunctions,” Europhys. Lett.97(6), 64001 (2012).
[CrossRef]

Wang, Z.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature461(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]

Weiner, A. M.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. H. Qi, “An All-Silicon Passive Optical Diode,” Science335(6067), 447–450 (2012).
[CrossRef] [PubMed]

Wu, W. Q.

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,” Science333(6043), 729–733 (2011).
[CrossRef] [PubMed]

Xuan, Y.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. H. Qi, “An All-Silicon Passive Optical Diode,” Science335(6067), 447–450 (2012).
[CrossRef] [PubMed]

Yablonovitch, E.

E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett.58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

Yamada, H.

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, “Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide,” Appl. Phys. Lett.76(8), 952 (2000).
[CrossRef]

Yamada, K.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs,” Phys. Rev. Lett.87(25), 253902 (2001).
[CrossRef] [PubMed]

Yang, H.

Yokohama, I.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs,” Phys. Rev. Lett.87(25), 253902 (2001).
[CrossRef] [PubMed]

Yu, Z.

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response to Comment on “Nonreciprocal Light Propagation in a Silicon Photonic Circuit”,” Science335(6064), 38–c, author reply 38 (2012).
[CrossRef] [PubMed]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics3(2), 91–94 (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]

Yu, Z. F.

S. Fan, R. Baets, A. Petrov, Z. F. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, 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,” Science335, 38-b (2012).

Yucel, M. B.

Zhou, C. Z.

Zhou, H.

Zhou, K. F.

Appl. Phys. Lett.

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, “Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide,” Appl. Phys. Lett.76(8), 952 (2000).
[CrossRef]

H. Takano, B. S. Song, T. Asano, and S. Noda, “Highly efficient in-plane channel drop filter in a two-dimensional heterophotonic crystal,” Appl. Phys. Lett.86(24), 241101 (2005).
[CrossRef]

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett.79(3), 314 (2001).
[CrossRef]

Europhys. Lett.

S. Feng, C. Ren, Y. Q. Wang, and W. Z. Wang, “All-optical diode based on the self-collimation characteristics of the near-infrared photonic crystal heterojunctions,” Europhys. Lett.97(6), 64001 (2012).
[CrossRef]

Nat. Photonics

M. S. Kang, A. Butsch, and P. S. J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics5(9), 549–553 (2011).
[CrossRef]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics3(2), 91–94 (2009).
[CrossRef]

Nature

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature461(7265), 772–775 (2009).
[CrossRef] [PubMed]

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature407(6804), 608–610 (2000).
[CrossRef] [PubMed]

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature407(6804), 608–610 (2000).
[CrossRef] [PubMed]

Opt. Express

Opt. Laser Technol.

A. Rostami, “Piecewise linear integrated optical device as an optical isolator using two-port nonlinear ring resonators,” Opt. Laser Technol.39(5), 1059–1065 (2007).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

X. F. Li, X. Ni, L. Feng, M. H. Lu, C. He, and Y. F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode,” Phys. Rev. Lett.106(8), 084301 (2011).
[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]

F. D. M. Haldane and S. Raghu, “Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry,” Phys. Rev. Lett.100(1), 013904 (2008).
[CrossRef] [PubMed]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Channel Drop Tunneling through Localized States,” Phys. Rev. Lett.80(5), 960–963 (1998).
[CrossRef]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs,” Phys. Rev. Lett.87(25), 253902 (2001).
[CrossRef] [PubMed]

E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett.58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett.58(23), 2486–2489 (1987).
[CrossRef] [PubMed]

Science

B. S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science300(5625), 1537 (2003).
[CrossRef] [PubMed]

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. H. Qi, “An All-Silicon Passive Optical Diode,” Science335(6067), 447–450 (2012).
[CrossRef] [PubMed]

S. Fan, R. Baets, A. Petrov, Z. F. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, 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,” Science335, 38-b (2012).

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response to Comment on “Nonreciprocal Light Propagation in a Silicon Photonic Circuit”,” Science335(6064), 38–c, author reply 38 (2012).
[CrossRef] [PubMed]

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,” Science333(6043), 729–733 (2011).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

Sketch map of the 2D square-lattice PC with a central rectangular defect, the two side lengths of which are 1.367a and 0.5a.

Fig. 2
Fig. 2

Electric field profiles of the defective modes for the resonant frequencies. (a) 0.3246 c/a, (b) 0.3300 c/a, (c) 0.3758 c/a, and (d) 0.3977 c/a. Red and blue regions represent the positive and negative values of the electric field.

Fig. 3
Fig. 3

Sketch map of the waveguides composed by removing one row of rods along the ГX direction of the PC (a), and removing one row of rods along the ГX direction and shifting the adjacent two rows on each side outward for the distances of 0.7a and 0.35a. The even modes (shown by the solid dots) and odd modes (shown by the hollow dots) for the waveguide structures shown in (a) and (b) are described in (c) and (d), respectively.

Fig. 4
Fig. 4

(a) Sketch map of the wavelength filter consisting of the rectangular defect and the two waveguides shown in Fig. 3. (b) Light transmittances through the wavelength filter device from a light beam at the normal incidence from the left side (shown by the solid line) and down side (shown by the dotted line) of the waveguide. The solid line represents the transmittance spectrum when the light beam is incident from the left side, and the dotted line shows that in rightward incidence.

Fig. 5
Fig. 5

Spatial distributions of the electric field at the frequencies of 0.3246 c/a and 0.3977 c/a through the structure shown in Fig. 4(a). (a) a fundamental-mode light beam for the frequency 0.3246 c/a at upward incidence, (b) a fundamental-mode light beam for 0.3246 c/a at rightward incidence, (c) a fundamental-mode light beam for 0.3977 c/a at upward incidence, (d) a fundamental-mode light beam for 0.3977 c/a at rightward incidence. (e) an odd-mode light beam for 0.3977 c/a at upward incidence. (f) an odd-mode light beam for 0.3977 c/a at rightward incidence. The arrows point at the directions of light propagation through the structure. The red and blue regions represent the positive and negative values of the electric field.

Fig. 6
Fig. 6

(a) Sketch map of the two-branch wavelength filter consisting of two rectangular defects, one input waveguide, and the two output waveguides. (b) Light transmittances through the wavelength filter from a fundamental-mode light beam at the normal incidence from the left side of the input W1-typed waveguide. The dotted line represents the transmission spectrum collected at the upper waveguide port, and the solid line shows that at the under waveguide port.

Fig. 7
Fig. 7

Spatial distributions of the electric field at the frequencies of 0.3758 c/a and 0.3977 c/a through the structure shown in Fig. 6(a) at normal incidence of the fundamental-mode light source. (a) 0.3758 c/a at rightward incidence, (b) 0.3758 c/a at leftward incidence, (c) 0.3977 c/a at rightward incidence, (d) 0.3977 c/a at leftward incidence. The white arrows point at the directions of light propagation.

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