Abstract

In this paper, we present a compact broadband design for reciprocal optical diode in linear two-dimensional air-hole photonic crystal waveguide. The forward even-to-odd mode conversion and backward blockade of even mode are achieved by introducing the functional region with 1.2a ×2.8a area. The inside dielectric distribution is obtained by finite element method combining geometry projection method and the method of moving asymptotes. In our design, only one asymmetrically deformed air hole locates in the functional region. The parabola-like unidirectionality keeps higher than 15dB within the operational bandwidth 0.01c/a (about 40nm when 1550nm is the center wavelength), and the maximum value reaches approximate 24 dB near the center frequency. Meanwhile, the forward transmission efficiency keeps higher than 89.9%. Moreover, the optical diode effect of the proposed design is validated in three-dimensional model and the tolerance of the imperfection in fabricating is demonstrated as well. This compact broadband optical diode can contribute to the all-optical integrated circuits.

© 2016 Optical Society of America

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2016 (1)

F. Callewaert, S. Butun, Z. Li, and K. Aydin, “Inverse design of an ultra-compact broadband optical diode based on asymmetric spatial mode conversion,” Sci. Rep. 6, 32577 (2016).
[Crossref] [PubMed]

2015 (2)

H. Ye, J. Q. N. Zhang, Z. Y. Yu, D. L. Wang, and Z. H. Chen, “Realizing mode conversion and optical diode effect by coupling photonic crystal waveguides with cavity,” Chin. Phys. B 24(9), 094214 (2015).
[Crossref]

H. Ye, D. Wang, Z. Yu, J. Zhang, and Z. Chen, “Ultra-compact broadband mode converter and optical diode based on linear rod-type photonic crystal waveguide,” Opt. Express 23(8), 9673–9680 (2015).
[Crossref] [PubMed]

2014 (3)

2013 (3)

D. Jalas, A. Petrov, M. Eich, W. Freude, S. H. Fan, Z. F. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is - and what is not - an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

S. Feng and Y. Wang, “Unidirectional reciprocal wavelength filters based on the square-lattice photonic crystal structures with the rectangular defects,” Opt. Express 21(1), 220–228 (2013).
[Crossref] [PubMed]

A. Khavasi, M. Rezaei, A. P. Fard, and K. Mehrany, “A heuristic approach to the realization of the wide-band optical diode effect in photonic crystal waveguides,” J. Opt. 15(7), 075501 (2013).
[Crossref]

2012 (6)

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

J. Xu, X. Zhuang, P. Guo, W. Huang, W. Hu, Q. Zhang, Q. Wan, X. Zhu, Z. Yang, L. Tong, X. Duan, and A. Pan, “Asymmetric light propagation in composition-graded semiconductor nanowires,” Sci. Rep. 2, 820 (2012).
[Crossref] [PubMed]

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (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]

D. A. B. Miller, “All linear optical devices are mode converters,” Opt. Express 20(21), 23985–23993 (2012).
[Crossref] [PubMed]

V. Liu, D. A. B. Miller, and S. Fan, “Ultra-compact photonic crystal waveguide spatial mode converter and its connection to the optical diode effect,” Opt. Express 20(27), 28388–28397 (2012).
[Crossref] [PubMed]

2011 (4)

L. Bi, J. J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

C. C. Lu, X. Y. Hu, Y. B. Zhang, Z. Q. Li, X. A. Xu, H. Yang, and Q. H. Gong, “Ultralow power all-optical diode in photonic crystal heterostructures with broken spatial inversion symmetry,” Appl. Phys. Lett. 99(5), 051107 (2011).
[Crossref]

D. Wang, Z. Yu, Y. Liu, P. Lu, L. Han, H. Feng, X. Guo, and H. Ye, “The optimal structure of two dimensional photonic crystals with the large absolute band gap,” Opt. Express 19(20), 19346–19353 (2011).
[Crossref] [PubMed]

C. Wang, C. Z. Zhou, and Z. Y. Li, “On-chip optical diode based on silicon photonic crystal heterojunctions,” Opt. Express 19(27), 26948–26955 (2011).
[Crossref] [PubMed]

2009 (1)

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[Crossref] [PubMed]

2008 (3)

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]

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]

W. R. Frei, H. T. Johnson, and K. D. Choquette, “Optimization of a single defect photonic crystal laser cavity,” J. Appl. Phys. 103(3), 033102 (2008).
[Crossref]

2006 (2)

X. S. Lin, W. Q. Wu, H. Zhou, K. F. Zhou, and S. Lan, “Enhancement of unidirectional transmission through the coupling of nonlinear photonic crystal defects,” Opt. Express 14(6), 2429–2439 (2006).
[Crossref] [PubMed]

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[Crossref] [PubMed]

2005 (1)

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater. 4(5), 383–387 (2005).
[Crossref] [PubMed]

1987 (1)

K. Svanberg, “The method of moving asymptotes-a new method for structural optimization,” Int. J. Numer. Methods Eng. 24(2), 359–373 (1987).
[Crossref]

Aydin, K.

F. Callewaert, S. Butun, Z. Li, and K. Aydin, “Inverse design of an ultra-compact broadband optical diode based on asymmetric spatial mode conversion,” Sci. Rep. 6, 32577 (2016).
[Crossref] [PubMed]

Baets, R.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. H. Fan, Z. F. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is - and what is not - an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

Bi, L.

L. Bi, J. J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

Bulgakov, E. N.

Butun, S.

F. Callewaert, S. Butun, Z. Li, and K. Aydin, “Inverse design of an ultra-compact broadband optical diode based on asymmetric spatial mode conversion,” Sci. Rep. 6, 32577 (2016).
[Crossref] [PubMed]

Callewaert, F.

F. Callewaert, S. Butun, Z. Li, and K. Aydin, “Inverse design of an ultra-compact broadband optical diode based on asymmetric spatial mode conversion,” Sci. Rep. 6, 32577 (2016).
[Crossref] [PubMed]

Chen, Y.

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[Crossref] [PubMed]

Chen, Z.

Chen, Z. H.

H. Ye, J. Q. N. Zhang, Z. Y. Yu, D. L. Wang, and Z. H. Chen, “Realizing mode conversion and optical diode effect by coupling photonic crystal waveguides with cavity,” Chin. Phys. B 24(9), 094214 (2015).
[Crossref]

Chong, Y.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[Crossref] [PubMed]

Choquette, K. D.

W. R. Frei, H. T. Johnson, and K. D. Choquette, “Optimization of a single defect photonic crystal laser cavity,” J. Appl. Phys. 103(3), 033102 (2008).
[Crossref]

Cicek, A.

Ding, Y.

Dionne, G. F.

L. Bi, J. J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

Doerr, C. R.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. H. Fan, Z. F. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is - and what is not - an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

Duan, X.

J. Xu, X. Zhuang, P. Guo, W. Huang, W. Hu, Q. Zhang, Q. Wan, X. Zhu, Z. Yang, L. Tong, X. Duan, and A. Pan, “Asymmetric light propagation in composition-graded semiconductor nanowires,” Sci. Rep. 2, 820 (2012).
[Crossref] [PubMed]

Eich, M.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. H. Fan, Z. F. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is - and what is not - an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

Elesin, Y.

Fan, L.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[Crossref] [PubMed]

Fan, S.

V. Liu, D. A. B. Miller, and S. Fan, “Ultra-compact photonic crystal waveguide spatial mode converter and its connection to the optical diode effect,” Opt. Express 20(27), 28388–28397 (2012).
[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]

Fan, S. H.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. H. Fan, Z. F. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is - and what is not - an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

Fard, A. P.

A. Khavasi, M. Rezaei, A. P. Fard, and K. Mehrany, “A heuristic approach to the realization of the wide-band optical diode effect in photonic crystal waveguides,” J. Opt. 15(7), 075501 (2013).
[Crossref]

Fedotov, V. A.

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[Crossref] [PubMed]

Feng, H.

Feng, S.

Frandsen, L. H.

Frei, W. R.

W. R. Frei, H. T. Johnson, and K. D. Choquette, “Optimization of a single defect photonic crystal laser cavity,” J. Appl. Phys. 103(3), 033102 (2008).
[Crossref]

Frellsen, L. F.

Freude, W.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. H. Fan, Z. F. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is - and what is not - an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

Gong, Q. H.

C. C. Lu, X. Y. Hu, Y. B. Zhang, Z. Q. Li, X. A. Xu, H. Yang, and Q. H. Gong, “Ultralow power all-optical diode in photonic crystal heterostructures with broken spatial inversion symmetry,” Appl. Phys. Lett. 99(5), 051107 (2011).
[Crossref]

Gu, D. Y.

Guo, P.

J. Xu, X. Zhuang, P. Guo, W. Huang, W. Hu, Q. Zhang, Q. Wan, X. Zhu, Z. Yang, L. Tong, X. Duan, and A. Pan, “Asymmetric light propagation in composition-graded semiconductor nanowires,” Sci. Rep. 2, 820 (2012).
[Crossref] [PubMed]

Guo, S. Q.

Guo, X.

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]

Han, L.

Hu, J. J.

L. Bi, J. J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

Hu, W.

J. Xu, X. Zhuang, P. Guo, W. Huang, W. Hu, Q. Zhang, Q. Wan, X. Zhu, Z. Yang, L. Tong, X. Duan, and A. Pan, “Asymmetric light propagation in composition-graded semiconductor nanowires,” Sci. Rep. 2, 820 (2012).
[Crossref] [PubMed]

Hu, W. S.

Hu, X. Y.

C. C. Lu, X. Y. Hu, Y. B. Zhang, Z. Q. Li, X. A. Xu, H. Yang, and Q. H. Gong, “Ultralow power all-optical diode in photonic crystal heterostructures with broken spatial inversion symmetry,” Appl. Phys. Lett. 99(5), 051107 (2011).
[Crossref]

Huang, W.

J. Xu, X. Zhuang, P. Guo, W. Huang, W. Hu, Q. Zhang, Q. Wan, X. Zhu, Z. Yang, L. Tong, X. Duan, and A. Pan, “Asymmetric light propagation in composition-graded semiconductor nanowires,” Sci. Rep. 2, 820 (2012).
[Crossref] [PubMed]

Hwang, J.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater. 4(5), 383–387 (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, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater. 4(5), 383–387 (2005).
[Crossref] [PubMed]

Jalas, D.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. H. Fan, Z. F. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is - and what is not - an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

Jiang, C.

Jiang, P.

L. Bi, J. J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

Joannopoulos, J. D.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. H. Fan, Z. F. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is - and what is not - an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[Crossref] [PubMed]

Johnson, H. T.

W. R. Frei, H. T. Johnson, and K. D. Choquette, “Optimization of a single defect photonic crystal laser cavity,” J. Appl. Phys. 103(3), 033102 (2008).
[Crossref]

Kaya, O. A.

Khavasi, A.

A. Khavasi, M. Rezaei, A. P. Fard, and K. Mehrany, “A heuristic approach to the realization of the wide-band optical diode effect in photonic crystal waveguides,” J. Opt. 15(7), 075501 (2013).
[Crossref]

Kim, D. H.

L. Bi, J. J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

Kimerling, L. C.

L. Bi, J. J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

Lan, S.

Li, Z.

F. Callewaert, S. Butun, Z. Li, and K. Aydin, “Inverse design of an ultra-compact broadband optical diode based on asymmetric spatial mode conversion,” Sci. Rep. 6, 32577 (2016).
[Crossref] [PubMed]

Li, Z. Q.

C. C. Lu, X. Y. Hu, Y. B. Zhang, Z. Q. Li, X. A. Xu, H. Yang, and Q. H. Gong, “Ultralow power all-optical diode in photonic crystal heterostructures with broken spatial inversion symmetry,” Appl. Phys. Lett. 99(5), 051107 (2011).
[Crossref]

Li, Z. Y.

Lin, X. S.

Liu, V.

Liu, Y.

Lu, C. C.

C. C. Lu, X. Y. Hu, Y. B. Zhang, Z. Q. Li, X. A. Xu, H. Yang, and Q. H. Gong, “Ultralow power all-optical diode in photonic crystal heterostructures with broken spatial inversion symmetry,” Appl. Phys. Lett. 99(5), 051107 (2011).
[Crossref]

Lu, J.

Lu, P.

Mehrany, K.

A. Khavasi, M. Rezaei, A. P. Fard, and K. Mehrany, “A heuristic approach to the realization of the wide-band optical diode effect in photonic crystal waveguides,” J. Opt. 15(7), 075501 (2013).
[Crossref]

Melloni, A.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. H. Fan, Z. F. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is - and what is not - an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

Miller, D. A. B.

Mitrovic, M.

Mladyonov, P. L.

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[Crossref] [PubMed]

Nishimura, S.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater. 4(5), 383–387 (2005).
[Crossref] [PubMed]

Niu, B.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[Crossref] [PubMed]

Pan, A.

J. Xu, X. Zhuang, P. Guo, W. Huang, W. Hu, Q. Zhang, Q. Wan, X. Zhu, Z. Yang, L. Tong, X. Duan, and A. Pan, “Asymmetric light propagation in composition-graded semiconductor nanowires,” Sci. Rep. 2, 820 (2012).
[Crossref] [PubMed]

Park, B.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater. 4(5), 383–387 (2005).
[Crossref] [PubMed]

Petrov, A.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. H. Fan, Z. F. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is - and what is not - an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

Popovic, M.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. H. Fan, Z. F. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is - and what is not - an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

Prosvirnin, S. L.

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[Crossref] [PubMed]

Qi, M.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[Crossref] [PubMed]

Qin, Y. L.

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, H. L.

Renner, H.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. H. Fan, Z. F. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is - and what is not - an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

Rezaei, M.

A. Khavasi, M. Rezaei, A. P. Fard, and K. Mehrany, “A heuristic approach to the realization of the wide-band optical diode effect in photonic crystal waveguides,” J. Opt. 15(7), 075501 (2013).
[Crossref]

Rogacheva, A. V.

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[Crossref] [PubMed]

Ross, C. A.

L. Bi, J. J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

Sadreev, A. F.

Shen, H.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[Crossref] [PubMed]

Sigmund, O.

Soljacic, M.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[Crossref] [PubMed]

Song, M. H.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater. 4(5), 383–387 (2005).
[Crossref] [PubMed]

Svanberg, K.

K. Svanberg, “The method of moving asymptotes-a new method for structural optimization,” Int. J. Numer. Methods Eng. 24(2), 359–373 (1987).
[Crossref]

Takanishi, Y.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater. 4(5), 383–387 (2005).
[Crossref] [PubMed]

Takezoe, H.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater. 4(5), 383–387 (2005).
[Crossref] [PubMed]

Tong, L.

J. Xu, X. Zhuang, P. Guo, W. Huang, W. Hu, Q. Zhang, Q. Wan, X. Zhu, Z. Yang, L. Tong, X. Duan, and A. Pan, “Asymmetric light propagation in composition-graded semiconductor nanowires,” Sci. Rep. 2, 820 (2012).
[Crossref] [PubMed]

Toyooka, T.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater. 4(5), 383–387 (2005).
[Crossref] [PubMed]

Ulug, B.

Vanwolleghem, M.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. H. Fan, Z. F. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is - and what is not - an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

Varghese, L. T.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335(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]

Wan, Q.

J. Xu, X. Zhuang, P. Guo, W. Huang, W. Hu, Q. Zhang, Q. Wan, X. Zhu, Z. Yang, L. Tong, X. Duan, and A. Pan, “Asymmetric light propagation in composition-graded semiconductor nanowires,” Sci. Rep. 2, 820 (2012).
[Crossref] [PubMed]

Wang, C.

Wang, D.

Wang, D. L.

H. Ye, J. Q. N. Zhang, Z. Y. Yu, D. L. Wang, and Z. H. Chen, “Realizing mode conversion and optical diode effect by coupling photonic crystal waveguides with cavity,” Chin. Phys. B 24(9), 094214 (2015).
[Crossref]

Wang, J.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[Crossref] [PubMed]

Wang, Y.

Wang, Z.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(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. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[Crossref] [PubMed]

Wen, H.

Wu, J. W.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater. 4(5), 383–387 (2005).
[Crossref] [PubMed]

Wu, W. Q.

Xu, J.

J. Xu, X. Zhuang, P. Guo, W. Huang, W. Hu, Q. Zhang, Q. Wan, X. Zhu, Z. Yang, L. Tong, X. Duan, and A. Pan, “Asymmetric light propagation in composition-graded semiconductor nanowires,” Sci. Rep. 2, 820 (2012).
[Crossref] [PubMed]

Xu, X. A.

C. C. Lu, X. Y. Hu, Y. B. Zhang, Z. Q. Li, X. A. Xu, H. Yang, and Q. H. Gong, “Ultralow power all-optical diode in photonic crystal heterostructures with broken spatial inversion symmetry,” Appl. Phys. Lett. 99(5), 051107 (2011).
[Crossref]

Xuan, Y.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[Crossref] [PubMed]

Yang, H.

C. C. Lu, X. Y. Hu, Y. B. Zhang, Z. Q. Li, X. A. Xu, H. Yang, and Q. H. Gong, “Ultralow power all-optical diode in photonic crystal heterostructures with broken spatial inversion symmetry,” Appl. Phys. Lett. 99(5), 051107 (2011).
[Crossref]

Yang, Z.

J. Xu, X. Zhuang, P. Guo, W. Huang, W. Hu, Q. Zhang, Q. Wan, X. Zhu, Z. Yang, L. Tong, X. Duan, and A. Pan, “Asymmetric light propagation in composition-graded semiconductor nanowires,” Sci. Rep. 2, 820 (2012).
[Crossref] [PubMed]

Ye, H.

Yu, Z.

Yu, Z. F.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. H. Fan, Z. F. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is - and what is not - an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

Yu, Z. Y.

H. Ye, J. Q. N. Zhang, Z. Y. Yu, D. L. Wang, and Z. H. Chen, “Realizing mode conversion and optical diode effect by coupling photonic crystal waveguides with cavity,” Chin. Phys. B 24(9), 094214 (2015).
[Crossref]

Yucel, M. B.

Yvind, K.

Zhang, J.

Zhang, J. Q. N.

H. Ye, J. Q. N. Zhang, Z. Y. Yu, D. L. Wang, and Z. H. Chen, “Realizing mode conversion and optical diode effect by coupling photonic crystal waveguides with cavity,” Chin. Phys. B 24(9), 094214 (2015).
[Crossref]

Zhang, Q.

J. Xu, X. Zhuang, P. Guo, W. Huang, W. Hu, Q. Zhang, Q. Wan, X. Zhu, Z. Yang, L. Tong, X. Duan, and A. Pan, “Asymmetric light propagation in composition-graded semiconductor nanowires,” Sci. Rep. 2, 820 (2012).
[Crossref] [PubMed]

Zhang, Y. B.

C. C. Lu, X. Y. Hu, Y. B. Zhang, Z. Q. Li, X. A. Xu, H. Yang, and Q. H. Gong, “Ultralow power all-optical diode in photonic crystal heterostructures with broken spatial inversion symmetry,” Appl. Phys. Lett. 99(5), 051107 (2011).
[Crossref]

Zheludev, N. I.

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[Crossref] [PubMed]

Zhong, X. L.

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

Zhou, C. Z.

Zhou, H.

Zhou, K. F.

Zhou, S. L.

Zhu, X.

J. Xu, X. Zhuang, P. Guo, W. Huang, W. Hu, Q. Zhang, Q. Wan, X. Zhu, Z. Yang, L. Tong, X. Duan, and A. Pan, “Asymmetric light propagation in composition-graded semiconductor nanowires,” Sci. Rep. 2, 820 (2012).
[Crossref] [PubMed]

Zhuang, X.

J. Xu, X. Zhuang, P. Guo, W. Huang, W. Hu, Q. Zhang, Q. Wan, X. Zhu, Z. Yang, L. Tong, X. Duan, and A. Pan, “Asymmetric light propagation in composition-graded semiconductor nanowires,” Sci. Rep. 2, 820 (2012).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

C. C. Lu, X. Y. Hu, Y. B. Zhang, Z. Q. Li, X. A. Xu, H. Yang, and Q. H. Gong, “Ultralow power all-optical diode in photonic crystal heterostructures with broken spatial inversion symmetry,” Appl. Phys. Lett. 99(5), 051107 (2011).
[Crossref]

Chin. Opt. Lett. (1)

Chin. Phys. B (1)

H. Ye, J. Q. N. Zhang, Z. Y. Yu, D. L. Wang, and Z. H. Chen, “Realizing mode conversion and optical diode effect by coupling photonic crystal waveguides with cavity,” Chin. Phys. B 24(9), 094214 (2015).
[Crossref]

Int. J. Numer. Methods Eng. (1)

K. Svanberg, “The method of moving asymptotes-a new method for structural optimization,” Int. J. Numer. Methods Eng. 24(2), 359–373 (1987).
[Crossref]

J. Appl. Phys. (1)

W. R. Frei, H. T. Johnson, and K. D. Choquette, “Optimization of a single defect photonic crystal laser cavity,” J. Appl. Phys. 103(3), 033102 (2008).
[Crossref]

J. Opt. (1)

A. Khavasi, M. Rezaei, A. P. Fard, and K. Mehrany, “A heuristic approach to the realization of the wide-band optical diode effect in photonic crystal waveguides,” J. Opt. 15(7), 075501 (2013).
[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, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater. 4(5), 383–387 (2005).
[Crossref] [PubMed]

Nat. Photonics (2)

L. Bi, J. J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

D. Jalas, A. Petrov, M. Eich, W. Freude, S. H. Fan, Z. F. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is - and what is not - an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

Nature (1)

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[Crossref] [PubMed]

Opt. Express (8)

X. S. Lin, W. Q. Wu, H. Zhou, K. F. Zhou, and S. Lan, “Enhancement of unidirectional transmission through the coupling of nonlinear photonic crystal defects,” Opt. Express 14(6), 2429–2439 (2006).
[Crossref] [PubMed]

D. A. B. Miller, “All linear optical devices are mode converters,” Opt. Express 20(21), 23985–23993 (2012).
[Crossref] [PubMed]

S. Feng and Y. Wang, “Unidirectional reciprocal wavelength filters based on the square-lattice photonic crystal structures with the rectangular defects,” Opt. Express 21(1), 220–228 (2013).
[Crossref] [PubMed]

V. Liu, D. A. B. Miller, and S. Fan, “Ultra-compact photonic crystal waveguide spatial mode converter and its connection to the optical diode effect,” Opt. Express 20(27), 28388–28397 (2012).
[Crossref] [PubMed]

H. Ye, D. Wang, Z. Yu, J. Zhang, and Z. Chen, “Ultra-compact broadband mode converter and optical diode based on linear rod-type photonic crystal waveguide,” Opt. Express 23(8), 9673–9680 (2015).
[Crossref] [PubMed]

D. Wang, Z. Yu, Y. Liu, P. Lu, L. Han, H. Feng, X. Guo, and H. Ye, “The optimal structure of two dimensional photonic crystals with the large absolute band gap,” Opt. Express 19(20), 19346–19353 (2011).
[Crossref] [PubMed]

C. Wang, C. Z. Zhou, and Z. Y. Li, “On-chip optical diode based on silicon photonic crystal heterojunctions,” Opt. Express 19(27), 26948–26955 (2011).
[Crossref] [PubMed]

L. H. Frandsen, Y. Elesin, L. F. Frellsen, M. Mitrovic, Y. Ding, O. Sigmund, and K. Yvind, “Topology optimized mode conversion in a photonic crystal waveguide fabricated in silicon-on-insulator material,” Opt. Express 22(7), 8525–8532 (2014).
[Crossref] [PubMed]

Opt. Lett. (2)

Phys. Rev. Lett. (3)

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[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]

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]

Sci. Rep. (3)

J. Xu, X. Zhuang, P. Guo, W. Huang, W. Hu, Q. Zhang, Q. Wan, X. Zhu, Z. Yang, L. Tong, X. Duan, and A. Pan, “Asymmetric light propagation in composition-graded semiconductor nanowires,” Sci. Rep. 2, 820 (2012).
[Crossref] [PubMed]

F. Callewaert, S. Butun, Z. Li, and K. Aydin, “Inverse design of an ultra-compact broadband optical diode based on asymmetric spatial mode conversion,” Sci. Rep. 6, 32577 (2016).
[Crossref] [PubMed]

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

Science (1)

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1 (a) The design of the multimode PhC waveguide (b) Dispersion curves of TE polarization (c) Magnetic field Hz for even mode and odd mode propagated in designed PhC waveguide at f = 0.36c/a (d) Transmission efficiency of even mode (solid line) and odd mode (dashed line). The shadow region represents the chosen operational frequency region of optical diode.
Fig. 2
Fig. 2 (a) Schematic structure of the proposed optical diode, including two conventional silicon waveguides, a PhC waveguide and a functional region. The area of functional region is 1.2a × 2.8a. (b) The zoomed-in functional region with the obtained dielectric distribution. The boundaries of the air hole are plotted as solid lines (smoothed results) and circles (directly from GPM).
Fig. 3
Fig. 3 Simulated magnetic field Hz and power flux (x-direction) at center frequency 0.36c/a in (a) forward direction and (b) backward direction.
Fig. 4
Fig. 4 (a) Transmission efficiency of forward and backward even mode propagation. (b) The output power flux of odd mode in forward direction.
Fig. 5
Fig. 5 The unidirectionality in dB as a function of frequency calculated by FEM, 2D FDTD and 3D FDTD.
Fig. 6
Fig. 6 (a) The unidirectionality of perfect and imperfect samples at 1550 nm center wavelength. (b) The upper and lower boundaries of the corresponding imperfect samples: expanding ( + 10nm), shrinking(−10nm), and random fluctuations #1 and #3.

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