Tunable asymmetric mode conversion using the dark-mode of three-mode waveguide system

Joonsoo Kim; Seung-Yeol Lee; Yohan Lee; Hwi Kim; Byoungho Lee

doi:10.1364/OE.22.028683

Tunable asymmetric mode conversion using the dark-mode of three-mode waveguide system

Joonsoo Kim, Seung-Yeol Lee, Yohan Lee, Hwi Kim, and Byoungho Lee

Optics Express
Vol. 22,
Issue 23,
pp. 28683-28696
(2014)
•https://doi.org/10.1364/OE.22.028683

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Joonsoo Kim, Seung-Yeol Lee, Yohan Lee, Hwi Kim, and Byoungho Lee, "Tunable asymmetric mode conversion using the dark-mode of three-mode waveguide system," Opt. Express 22, 28683-28696 (2014)

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Related Topics
Table of Contents Category
- Integrated Optics
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Coherent optical effects (030.1670)
- Gratings (050.2770)
- Integrated optics devices (130.3120)
- Waveguides, planar (230.7390)

About this Article
History
- Original Manuscript: September 16, 2014
- Revised Manuscript: October 27, 2014
- Manuscript Accepted: November 4, 2014
- Published: November 10, 2014

Accessible

Open Access

Abstract

A design scheme for low-reflection asymmetric mode conversion structure in three-mode waveguide system is proposed. By using a dark-mode of three-mode system, which can be interpreted in terms of destructive interference of transition amplitudes, the transmission characteristics for forward and backward directions can be designed separately. After explanation of the proposed design scheme, we demonstrate an example of asymmetric mode converter that consists of two gratings. The proposed scheme may be useful for the design of tunable asymmetric transmission devices due to its design flexibility and efficient design process.

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References

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Publication

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(6043), 729–733 (2011).
[Crossref] [PubMed]
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(2), 108–113 (2012).
[Crossref] [PubMed]
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, “Comment on Nonreciprocal light propagation in a silicon photonic circuit,” Science 335(6064), 38 (2012).
[Crossref] [PubMed]
L. Feng, M. Ayache, J. Huang, and Y.-L. Xu, “Response to comments on Nonreciprocal light propagation in a silicon photonic circuit,” Science 335(6064), 38 (2012).
[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]
A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, and N. I. Zheludev, “Nanostructured metal film with asymmetric optical transmission,” Nano Lett. 8(9), 2940–2943 (2008).
[Crossref] [PubMed]
R. Singh, E. Plum, C. Menzel, C. Rockstuhl, A. K. Azad, R. A. Cheville, F. Lederer, W. Zhang, and N. I. Zheludev, “Terahertz metamaterial with asymmetric transmission,” Phys. Rev. B 80(15), 153104 (2009).
[Crossref]
C. Menzel, C. Helgert, C. Rockstuhl, E.-B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, “Asymmetric transmission of linearly polarized light at optical metamaterials,” Phys. Rev. Lett. 104(25), 253902 (2010).
[Crossref] [PubMed]
M. Mutlu, A. E. Akosman, A. E. Serebryannikov, and E. Ozbay, “Asymmetric transmission of linearly polarized waves and polarization angle dependent wave rotation using a chiral metamaterial,” Opt. Express 19(15), 14290–14299 (2011).
[Crossref] [PubMed]
M. Kang, J. Chen, H.-X. Cui, Y. Li, and H.-T. Wang, “Asymmetric transmission for linearly polarized electromagnetic radiation,” Opt. Express 19(9), 8347–8356 (2011).
[Crossref] [PubMed]
E. Plum, V. A. Fedotov, and N. I. Zheludev, “Asymmetric transmission: a generic property of two-dimensional periodic patterns,” J. Opt. 13(2), 024006 (2011).
[Crossref]
C. Huang, Y. Feng, J. Zhao, Z. Wang, and T. Jiang, “Asymmetric electromagnetic wave transmission of linear polarization via polarization conversion through chiral metamaterial structures,” Phys. Rev. B 85(19), 195131 (2012).
[Crossref]
M. Mutlu, A. E. Akosman, A. E. Serebryannikov, and E. Ozbay, “Diodelike asymmetric transmission of linearly polarized waves using magnetoelectric coupling and electromagnetic wave tunneling,” Phys. Rev. Lett. 108(21), 213905 (2012).
[Crossref] [PubMed]
J. Shi, X. Liu, S. Yu, T. Lv, Z. Zhu, H. F. Ma, and T. J. Cui, “Dual-band asymmetric transmission of linear polarization in bilayered chiral metamaterial,” Appl. Phys. Lett. 102(19), 191905 (2013).
[Crossref]
C. Pfeiffer, C. Zhang, V. Ray, L. J. Guo, and A. Grbic, “High performance bianisotropic metasurfaces: asymmetric transmission of light,” Phys. Rev. Lett. 113(2), 023902 (2014).
[Crossref] [PubMed]
S. Cakmakyapan, A. E. Serebryannikov, H. Caglayan, and E. Ozbay, “One-way transmission through the subwavelength slit in nonsymmetric metallic gratings,” Opt. Lett. 35(15), 2597–2599 (2010).
[Crossref] [PubMed]
J. Xu, C. Cheng, M. Kang, J. Chen, Z. Zheng, Y.-X. Fan, and H.-T. Wang, “Unidirectional optical transmission in dual-metal gratings in the absence of anisotropic and nonlinear materials,” Opt. Lett. 36(10), 1905–1907 (2011).
[Crossref] [PubMed]
S. Cakmakyapan, H. Caglayan, A. E. Serebryannikov, and E. Ozbay, “Experimental validation of strong directional selectivity in nonsymmetric metallic gratings with a subwavelength slit,” Appl. Phys. Lett. 98(5), 051103 (2011).
[Crossref]
E. Battal, T. A. Yogurt, and A. K. Okyay, “Ultrahigh contrast one-way optical transmission through a subwavelength slit,” Plasmonics 8(2), 509–513 (2013).
[Crossref]
M. Stolarek, D. Yavorskiy, R. Kotyński, C. J. Zapata Rodríguez, J. Łusakowski, and T. Szoplik, “Asymmetric transmission of terahertz radiation through a double grating,” Opt. Lett. 38(6), 839–841 (2013).
[Crossref] [PubMed]
Z. Cao, X. Qi, G. Zhang, and J. Bai, “Asymmetric light propagation in transverse separation modulated photonic lattices,” Opt. Lett. 38(17), 3212–3215 (2013).
[Crossref] [PubMed]
A. E. Serebryannikov, E. Ozbay, and S. Nojima, “Asymmetric transmission of terahertz waves using polar dielectrics,” Opt. Express 22(3), 3075–3088 (2014).
[Crossref] [PubMed]
T. Xu and H. J. Lezec, “Visible-frequency asymmetric transmission devices incorporating a hyperbolic metamaterial,” Nat. Commun. 5, 4141 (2014).
[Crossref] [PubMed]
C. Lu, X. Hu, Y. Zhang, Z. Li, X. Xu, H. Yang, and Q. Gong, “Ultralow power all-optical diode in photonic crytal heterostructures with broken spatial inversion symmetry,” Appl. Phys. Lett. 99(5), 051107 (2011).
[Crossref]
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]
C. Lu, X. Hu, H. Yang, and Q. Gong, “Ultrahigh-contrast and wideband nanoscale photonic crystal all-optical diode,” Opt. Lett. 36(23), 4668–4670 (2011).
[Crossref] [PubMed]
H. Kurt, D. Yilmaz, A. E. Akosman, and E. Ozbay, “Asymmetric light propagation in chirped photonic crystal waveguides,” Opt. Express 20(18), 20635–20646 (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]
V. Kuzmiak and A. A. Maradudin, “Asymmetric transmission of surface plasmon polaritons,” Phys. Rev. A 86(4), 043805 (2012).
[Crossref]
C. Wang, X.-L. Zhong, and Z.-Y. Li, “Linear and passive silicon optical isolator,” Sci. Rep. 2, 674 (2012).
[PubMed]
A. Cicek and B. Ulug, “Coupling between opposite-parity modes in parallel photonic crystal waveguides and its application in unidirectional light transmission,” Appl. Phys. B 113(4), 619–626 (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]
I. H. Giden, D. Yilmaz, M. Turduev, H. Kurt, E. Çolak, and E. Ozbay, “Theoretical and experimental investigations of asymmetric light transport in graded index photonic crystal waveguides,” Appl. Phys. Lett. 104(3), 031116 (2014).
[Crossref]
A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010).
[Crossref]
B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref] [PubMed]
N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, “Metamaterial analog of electromagnetically induced transparency,” Phys. Rev. Lett. 101(25), 253903 (2008).
[Crossref] [PubMed]
J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat Commun 3, 1151 (2012).
[Crossref] [PubMed]
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H.-C. Liu and A. Yariv, “Grating induced transparency (GIT) and the dark mode in optical waveguides,” Opt. Express 17(14), 11710–11718 (2009).
[Crossref] [PubMed]
K. Xia, M. Alamri, and M. S. Zubairy, “Ultrabroadband nonreciprocal transverse energy flow of light in linear passive photonic circuits,” Opt. Express 21(22), 25619–25631 (2013).
[Crossref] [PubMed]
H. Kim, J. Park, and B. Lee, Fourier Modal Method and Its Applications in Computational Nanophotonics (CRC Press, 2012).
A. Yariv, “Couple-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9(9), 919–933 (1973).
[Crossref]
H. A. Haus and W. Huang, “Coupled-mode theory,” Proc. IEEE 79(10), 1505–1518 (1991).
[Crossref]

2014 (4)

C. Pfeiffer, C. Zhang, V. Ray, L. J. Guo, and A. Grbic, “High performance bianisotropic metasurfaces: asymmetric transmission of light,” Phys. Rev. Lett. 113(2), 023902 (2014).
[Crossref] [PubMed]

T. Xu and H. J. Lezec, “Visible-frequency asymmetric transmission devices incorporating a hyperbolic metamaterial,” Nat. Commun. 5, 4141 (2014).
[Crossref] [PubMed]

I. H. Giden, D. Yilmaz, M. Turduev, H. Kurt, E. Çolak, and E. Ozbay, “Theoretical and experimental investigations of asymmetric light transport in graded index photonic crystal waveguides,” Appl. Phys. Lett. 104(3), 031116 (2014).
[Crossref]

A. E. Serebryannikov, E. Ozbay, and S. Nojima, “Asymmetric transmission of terahertz waves using polar dielectrics,” Opt. Express 22(3), 3075–3088 (2014).
[Crossref] [PubMed]

2013 (7)

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]

M. Stolarek, D. Yavorskiy, R. Kotyński, C. J. Zapata Rodríguez, J. Łusakowski, and T. Szoplik, “Asymmetric transmission of terahertz radiation through a double grating,” Opt. Lett. 38(6), 839–841 (2013).
[Crossref] [PubMed]

Z. Cao, X. Qi, G. Zhang, and J. Bai, “Asymmetric light propagation in transverse separation modulated photonic lattices,” Opt. Lett. 38(17), 3212–3215 (2013).
[Crossref] [PubMed]

K. Xia, M. Alamri, and M. S. Zubairy, “Ultrabroadband nonreciprocal transverse energy flow of light in linear passive photonic circuits,” Opt. Express 21(22), 25619–25631 (2013).
[Crossref] [PubMed]

E. Battal, T. A. Yogurt, and A. K. Okyay, “Ultrahigh contrast one-way optical transmission through a subwavelength slit,” Plasmonics 8(2), 509–513 (2013).
[Crossref]

A. Cicek and B. Ulug, “Coupling between opposite-parity modes in parallel photonic crystal waveguides and its application in unidirectional light transmission,” Appl. Phys. B 113(4), 619–626 (2013).
[Crossref]

J. Shi, X. Liu, S. Yu, T. Lv, Z. Zhu, H. F. Ma, and T. J. Cui, “Dual-band asymmetric transmission of linear polarization in bilayered chiral metamaterial,” Appl. Phys. Lett. 102(19), 191905 (2013).
[Crossref]

2012 (10)

C. Huang, Y. Feng, J. Zhao, Z. Wang, and T. Jiang, “Asymmetric electromagnetic wave transmission of linear polarization via polarization conversion through chiral metamaterial structures,” Phys. Rev. B 85(19), 195131 (2012).
[Crossref]

M. Mutlu, A. E. Akosman, A. E. Serebryannikov, and E. Ozbay, “Diodelike asymmetric transmission of linearly polarized waves using magnetoelectric coupling and electromagnetic wave tunneling,” Phys. Rev. Lett. 108(21), 213905 (2012).
[Crossref] [PubMed]

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(2), 108–113 (2012).
[Crossref] [PubMed]

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, “Comment on Nonreciprocal light propagation in a silicon photonic circuit,” Science 335(6064), 38 (2012).
[Crossref] [PubMed]

L. Feng, M. Ayache, J. Huang, and Y.-L. Xu, “Response to comments on Nonreciprocal light propagation in a silicon photonic circuit,” Science 335(6064), 38 (2012).
[Crossref] [PubMed]

V. Kuzmiak and A. A. Maradudin, “Asymmetric transmission of surface plasmon polaritons,” Phys. Rev. A 86(4), 043805 (2012).
[Crossref]

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

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat Commun 3, 1151 (2012).
[Crossref] [PubMed]

H. Kurt, D. Yilmaz, A. E. Akosman, and E. Ozbay, “Asymmetric light propagation in chirped photonic crystal waveguides,” Opt. Express 20(18), 20635–20646 (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 (9)

M. Kang, J. Chen, H.-X. Cui, Y. Li, and H.-T. Wang, “Asymmetric transmission for linearly polarized electromagnetic radiation,” Opt. Express 19(9), 8347–8356 (2011).
[Crossref] [PubMed]

J. Xu, C. Cheng, M. Kang, J. Chen, Z. Zheng, Y.-X. Fan, and H.-T. Wang, “Unidirectional optical transmission in dual-metal gratings in the absence of anisotropic and nonlinear materials,” Opt. Lett. 36(10), 1905–1907 (2011).
[Crossref] [PubMed]

M. Mutlu, A. E. Akosman, A. E. Serebryannikov, and E. Ozbay, “Asymmetric transmission of linearly polarized waves and polarization angle dependent wave rotation using a chiral metamaterial,” Opt. Express 19(15), 14290–14299 (2011).
[Crossref] [PubMed]

C. Lu, X. Hu, H. Yang, and Q. 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. Express 19(27), 26948–26955 (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,” Science 333(6043), 729–733 (2011).
[Crossref] [PubMed]

E. Plum, V. A. Fedotov, and N. I. Zheludev, “Asymmetric transmission: a generic property of two-dimensional periodic patterns,” J. Opt. 13(2), 024006 (2011).
[Crossref]

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

S. Cakmakyapan, H. Caglayan, A. E. Serebryannikov, and E. Ozbay, “Experimental validation of strong directional selectivity in nonsymmetric metallic gratings with a subwavelength slit,” Appl. Phys. Lett. 98(5), 051103 (2011).
[Crossref]

2010 (4)

C. Menzel, C. Helgert, C. Rockstuhl, E.-B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, “Asymmetric transmission of linearly polarized light at optical metamaterials,” Phys. Rev. Lett. 104(25), 253902 (2010).
[Crossref] [PubMed]

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010).
[Crossref]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref] [PubMed]

S. Cakmakyapan, A. E. Serebryannikov, H. Caglayan, and E. Ozbay, “One-way transmission through the subwavelength slit in nonsymmetric metallic gratings,” Opt. Lett. 35(15), 2597–2599 (2010).
[Crossref] [PubMed]

2009 (2)

H.-C. Liu and A. Yariv, “Grating induced transparency (GIT) and the dark mode in optical waveguides,” Opt. Express 17(14), 11710–11718 (2009).
[Crossref] [PubMed]

R. Singh, E. Plum, C. Menzel, C. Rockstuhl, A. K. Azad, R. A. Cheville, F. Lederer, W. Zhang, and N. I. Zheludev, “Terahertz metamaterial with asymmetric transmission,” Phys. Rev. B 80(15), 153104 (2009).
[Crossref]

2008 (2)

A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, and N. I. Zheludev, “Nanostructured metal film with asymmetric optical transmission,” Nano Lett. 8(9), 2940–2943 (2008).
[Crossref] [PubMed]

N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, “Metamaterial analog of electromagnetically induced transparency,” Phys. Rev. Lett. 101(25), 253903 (2008).
[Crossref] [PubMed]

2006 (1)

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]

1991 (1)

H. A. Haus and W. Huang, “Coupled-mode theory,” Proc. IEEE 79(10), 1505–1518 (1991).
[Crossref]

1973 (1)

A. Yariv, “Couple-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9(9), 919–933 (1973).
[Crossref]

Akosman, A. E.

H. Kurt, D. Yilmaz, A. E. Akosman, and E. Ozbay, “Asymmetric light propagation in chirped photonic crystal waveguides,” Opt. Express 20(18), 20635–20646 (2012).
[Crossref] [PubMed]

Alamri, M.

Almeida, V. R.

Ayache, M.

L. Feng, M. Ayache, J. Huang, and Y.-L. Xu, “Response to comments on Nonreciprocal light propagation in a silicon photonic circuit,” Science 335(6064), 38 (2012).
[Crossref] [PubMed]

Azad, A. K.

Baets, R.

Bai, J.

Z. Cao, X. Qi, G. Zhang, and J. Bai, “Asymmetric light propagation in transverse separation modulated photonic lattices,” Opt. Lett. 38(17), 3212–3215 (2013).
[Crossref] [PubMed]

Battal, E.

E. Battal, T. A. Yogurt, and A. K. Okyay, “Ultrahigh contrast one-way optical transmission through a subwavelength slit,” Plasmonics 8(2), 509–513 (2013).
[Crossref]

Brinkmeyer, E.

Caglayan, H.

Cakmakyapan, S.

Cao, Z.

Z. Cao, X. Qi, G. Zhang, and J. Bai, “Asymmetric light propagation in transverse separation modulated photonic lattices,” Opt. Lett. 38(17), 3212–3215 (2013).
[Crossref] [PubMed]

Chen, H.-T.

Chen, J.

M. Kang, J. Chen, H.-X. Cui, Y. Li, and H.-T. Wang, “Asymmetric transmission for linearly polarized electromagnetic radiation,” Opt. Express 19(9), 8347–8356 (2011).
[Crossref] [PubMed]

Chen, Y.

Chen, Y.-F.

Cheng, C.

Cheville, R. A.

Chong, C. T.

Cicek, A.

Çolak, E.

Cui, H.-X.

M. Kang, J. Chen, H.-X. Cui, Y. Li, and H.-T. Wang, “Asymmetric transmission for linearly polarized electromagnetic radiation,” Opt. Express 19(9), 8347–8356 (2011).
[Crossref] [PubMed]

Cui, T. J.

Doerr, C. R.

Eich, M.

Fainman, Y.

Fan, S.

Fan, Y.-X.

Fedotov, V. A.

E. Plum, V. A. Fedotov, and N. I. Zheludev, “Asymmetric transmission: a generic property of two-dimensional periodic patterns,” J. Opt. 13(2), 024006 (2011).
[Crossref]

Fegadolli, W. S.

Feng, L.

L. Feng, M. Ayache, J. Huang, and Y.-L. Xu, “Response to comments on Nonreciprocal light propagation in a silicon photonic circuit,” Science 335(6064), 38 (2012).
[Crossref] [PubMed]

Feng, S.

Feng, Y.

Flach, S.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010).
[Crossref]

Freude, W.

Giden, I. H.

Giessen, H.

Gong, Q.

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

Grbic, A.

Gu, J.

Guo, L. J.

Halas, N. J.

Han, J.

Haus, H. A.

H. A. Haus and W. Huang, “Coupled-mode theory,” Proc. IEEE 79(10), 1505–1518 (1991).
[Crossref]

Helgert, C.

Hu, X.

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

Huang, C.

Huang, J.

L. Feng, M. Ayache, J. Huang, and Y.-L. Xu, “Response to comments on Nonreciprocal light propagation in a silicon photonic circuit,” Science 335(6064), 38 (2012).
[Crossref] [PubMed]

Huang, W.

H. A. Haus and W. Huang, “Coupled-mode theory,” Proc. IEEE 79(10), 1505–1518 (1991).
[Crossref]

Jalas, D.

Jiang, T.

Joannopoulos, J. D.

Kang, M.

M. Kang, J. Chen, H.-X. Cui, Y. Li, and H.-T. Wang, “Asymmetric transmission for linearly polarized electromagnetic radiation,” Opt. Express 19(9), 8347–8356 (2011).
[Crossref] [PubMed]

Khardikov, V. V.

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Appl. Phys. B (1)

Appl. Phys. Lett. (4)

IEEE J. Quantum Electron. (1)

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J. Opt. (1)

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Nano Lett. (1)

Nat Commun (1)

Nat. Commun. (1)

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[Crossref] [PubMed]

Nat. Mater. (2)

Opt. Express (9)

M. Kang, J. Chen, H.-X. Cui, Y. Li, and H.-T. Wang, “Asymmetric transmission for linearly polarized electromagnetic radiation,” Opt. Express 19(9), 8347–8356 (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]

A. E. Serebryannikov, E. Ozbay, and S. Nojima, “Asymmetric transmission of terahertz waves using polar dielectrics,” Opt. Express 22(3), 3075–3088 (2014).
[Crossref] [PubMed]

H. Kurt, D. Yilmaz, A. E. Akosman, and E. Ozbay, “Asymmetric light propagation in chirped photonic crystal waveguides,” Opt. Express 20(18), 20635–20646 (2012).
[Crossref] [PubMed]

H.-C. Liu and A. Yariv, “Grating induced transparency (GIT) and the dark mode in optical waveguides,” Opt. Express 17(14), 11710–11718 (2009).
[Crossref] [PubMed]

Opt. Lett. (5)

Z. Cao, X. Qi, G. Zhang, and J. Bai, “Asymmetric light propagation in transverse separation modulated photonic lattices,” Opt. Lett. 38(17), 3212–3215 (2013).
[Crossref] [PubMed]

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

Phys. Rev. A (1)

V. Kuzmiak and A. A. Maradudin, “Asymmetric transmission of surface plasmon polaritons,” Phys. Rev. A 86(4), 043805 (2012).
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Phys. Rev. B (2)

Phys. Rev. Lett. (5)

Plasmonics (1)

E. Battal, T. A. Yogurt, and A. K. Okyay, “Ultrahigh contrast one-way optical transmission through a subwavelength slit,” Plasmonics 8(2), 509–513 (2013).
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Rev. Mod. Phys. (1)

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Sci. Rep. (1)

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

Science (3)

L. Feng, M. Ayache, J. Huang, and Y.-L. Xu, “Response to comments on Nonreciprocal light propagation in a silicon photonic circuit,” Science 335(6064), 38 (2012).
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Other (2)

H. Kim, J. Park, and B. Lee, Fourier Modal Method and Its Applications in Computational Nanophotonics (CRC Press, 2012).

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Fig. 1 (a) A schematic of the proposed device. A silicon waveguide (ε_Si = 12.15) of width w₁ = 400 nm and a SiO₂ waveguide

(ε_{{SiO}_{2}}

= 2.25) of width w₂ = 400 nm are aligned in parallel with an air gap of width g = 100 nm. The half-infinite areas above the waveguide II and beneath the waveguide I are set to air. (b) When mode 1 is incident from the left, the grating α converts mode 1 to the dark-mode at the grating β and the dark-mode appears at the output because the dark-mode is stationary in the grating β. (c) When mode 1 is incident from the right, mode transitions in the grating β is not prohibited. As a result, various linear combinations of modes 1, 2 and 3 can appear at the output.

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Fig. 2 (a) The dispersion relations of three modes considered in our configuration. The widths of two waveguide are adjusted so that

Δ k_{23} \approx Δ k_{12}

for simultaneous coupling of modes. Normalized power flow inside the grating β when (b)

Λ_{β} = 1530 nm

and (c)

Λ_{β} = 1550 nm .

Electric field (E_y) distribution inside the grating β when (d)

Λ_{β} = 1530 nm

and (e)

Λ_{β} = 1550 nm .

Mode 2 is launched from the left and the waveguide centered at x = 0 is the waveguide II.

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Fig. 3 (a) Normalized power flow in the grating β when the dark-mode is launched. (b) E_y field distribution of the dark-mode in the grating β. Normalized power flow of mode 3 in grating β when there is (c) a variation of normalized input power flow of mode 3 (P_3,in) and (d) a variation of relative phase of mode 3 (Δφ) with respect to the exact dark-mode condition at the entrance of grating β.

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Fig. 4 (a) Normalized power flow inside the grating α tuned for the transition from modes 1 to 3. (b) Normalized power flow through two cascaded gratings when a wrong value of D is chosen (D = 5.6 μm). (c) Normalized power transmission after the two cascaded gratings depending on D. The length of the grating β is 40 periods. (d) Normalized power flow inside two cascaded gratings when D = 5.25 μm.

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Fig. 5 (a) Normalized power flows inside the cascaded grating when the length of the grating β is set to 40 periods for the right-to-left propagation case. (b) Normalized power flows inside the grating β for the case of mode 1 incidence. Normalized power flows inside the cascaded gratings when the length of the grating β is set to 11 periods (c) for the left-to-right and (d) right-to-left propagation cases. (e) and (f) are those for the left-to-right and right-to-left propagation when the length of the grating β is set to 16 periods.

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Fig. 6 E_y field distributions on two cascaded gratings for mode 1 incidence when the length of the grating β is set to 11 periods (a) for left-to-right and (b) right-to-left propagation cases. (c) and (d) are those when the length of the grating is set to 16 periods for left-to-right and right-to-left propagation cases, respectively. The field distributions of input and output are shown at the upper parts of each figure.

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Equations (10)

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\begin{array}{l} i k_{1} \frac{d a_{1}}{d z} = μ_{12} a_{2} e^{i Δ_{12} z} + μ_{13} a_{3} e^{i Δ_{13} z}, \\ i k_{2} \frac{d a_{2}}{d z} = μ_{12}^{*} a_{1} e^{- i Δ_{12} z} + μ_{23} a_{3} e^{i Δ_{23} z}, \\ i k_{3} \frac{d a_{3}}{d z} = μ_{13}^{*} a_{1} e^{- i Δ_{13} z} + μ_{23}^{*} a_{2} e^{- i Δ_{23} z}, \end{array}

i \frac{d}{d z} [\begin{array}{l} a_{1} \\ a_{2} \\ a_{3} \end{array}] = [\begin{matrix} 0 & μ_{12} e^{i Δ z} / k_{1} & 0 \\ μ_{12}^{*} e^{- i Δ z} / k_{2} & 0 & μ_{23} e^{- i Δ z} / k_{2} \\ 0 & μ_{23}^{*} e^{i Δ z} / k_{3} & 0 \end{matrix}] [\begin{array}{l} a_{1} \\ a_{2} \\ a_{3} \end{array}] .

i \frac{d}{d z} [\begin{array}{l} a_{1} \\ a_{2} \\ a_{3} \end{array}] = [\begin{matrix} 0 & 0 & μ_{13}^{(α)} / k_{1} \\ 0 & 0 & 0 \\ μ_{13}^{(α)}^{*} / k_{3} & 0 & 0 \end{matrix}] [\begin{array}{l} a_{1} \\ a_{2} \\ a_{3} \end{array}],

\begin{array}{l} a_{1} (z) = a_{1} (0) \cos Ω_{13}^{(α)} z - i \sqrt{\frac{k_{3} μ_{13}^{(α)}}{k_{1} μ_{13}^{(α)}^{*}}} a_{3} (0) \sin Ω_{13}^{(α)} z, \\ a_{2} (z) = a_{2} (0), \\ a_{3} (z) = a_{3} (0) \cos Ω_{13}^{(α)} z - i \sqrt{\frac{k_{1} μ_{13}^{(α)}^{*}}{k_{3} μ_{13}^{(α)}}} a_{1} (0) \sin Ω_{13}^{(α)} z, \end{array}

[\begin{matrix} \cos Ω_{13}^{(α)} L_{α} \\ 0 \\ - i \sqrt{μ_{13}^{(α)}^{*} k_{1} / μ_{13}^{(α)} k_{3}} \sin Ω_{13}^{(α)} L_{α} \end{matrix}] = N [\begin{matrix} μ_{23}^{(β)} e^{- i 2 π (L_{α} + D) / Λ_{β}} \\ 0 \\ - μ_{12}^{(β)}^{*} e^{i 2 π (L_{α} + D) / Λ_{β}} \end{matrix}],

\begin{array}{l} [\begin{matrix} a_{1} \\ a_{2} e^{i Δ z} \\ a_{3} \end{matrix}] = C_{1} [\begin{matrix} μ_{23}^{(β)} \\ 0 \\ - μ_{12}^{(β)}^{*} \end{matrix}] + C_{2} [\begin{matrix} μ_{12}^{(β)} / k_{1} \\ Ω_{-} \\ μ_{23}^{(β)}^{*} / k_{3} \end{matrix}] \exp (- i Ω_{-} z) + C_{3} [\begin{matrix} μ_{12}^{(β)} / k_{1} \\ - Ω_{+} \\ μ_{23}^{(β)}^{*} / k_{3} \end{matrix}] \exp (i Ω_{+} z), \\ C_{1} = \frac{μ_{23}^{(β)}^{*}}{{| μ_{23}^{(β)} |}^{2} + k_{3} {| μ_{12}^{(β)} |}^{2} / k_{1}} a_{1} (0) - \frac{μ_{12}^{(β)}}{{| μ_{12}^{(β)} |}^{2} + k_{1} {| μ_{23}^{(β)} |}^{2} / k_{3}} a_{3} (0), \\ C_{2} = \frac{k_{3} μ_{12}^{(β)}^{*}}{{| μ_{23}^{(β)} |}^{2} + k_{3} {| μ_{12}^{(β)} |}^{2} / k_{1}} \frac{Ω_{+}}{2 Ω} a_{1} (0) + \frac{1}{2 Ω} a_{2} (0) + \frac{k_{1} μ_{23}^{(β)}}{{| μ_{12}^{(β)} |}^{2} + k_{1} {| μ_{23}^{(β)} |}^{2} / k_{3}} \frac{Ω_{+}}{2 Ω} a_{3} (0), \\ C_{3} = \frac{k_{3} μ_{12}^{(β)}^{*}}{{| μ_{23}^{(β)} |}^{2} + k_{3} {| μ_{12}^{(β)} |}^{2} / k_{1}} \frac{Ω_{-}}{2 Ω} a_{1} (0) - \frac{1}{2 Ω} a_{2} (0) + \frac{k_{1} μ_{23}^{(β)}}{{| μ_{12}^{(β)} |}^{2} + k_{1} {| μ_{23}^{(β)} |}^{2} / k_{3}} \frac{Ω_{-}}{2 Ω} a_{3} (0), \end{array}

\begin{array}{l} | a_{1} | = \cos Ω_{13}^{(α)} L_{α}, \\ | a_{2} | = \frac{k_{3} | μ_{12}^{(β)} |}{{| μ_{23}^{(β)} |}^{2} + k_{3} {| μ_{12}^{(β)} |}^{2} / k_{1}} (\frac{Ω_{12}^{(β)}^{2} + Ω_{23}^{(β)}^{2}}{Ω} \sin Ω L_{β}) . \end{array}

[\begin{matrix} a_{1} (z) \\ a_{2} (z) \\ a_{3} (z) \end{matrix}] = [\begin{matrix} - (i μ_{12}^{(β)} / k_{1} Ω) e^{i Δ z / 2} \cos Ω z \\ e^{- i Δ z / 2} \cos Ω z + i (Δ / 2 Ω) e^{- i Δ z / 2} \sin Ω z \\ - (i μ_{23}^{(β)}^{*} / k_{3} Ω) e^{i Δ z / 2} \cos Ω z \end{matrix}] .

\begin{array}{l} \frac{d a_{1}}{d z} = i \frac{Ω}{2} a_{2} e^{i Δ z}, \\ \frac{d a_{2}}{d z} = i \frac{Ω}{2} a_{1} e^{- i Δ z}, \end{array}

{| a_{1} (z) |}^{2} = (\frac{1 + {(κ Ω - Δ)}^{2}}{2} - \frac{(κ^{2} - 1) Ω^{2} - 2 Δ κ Ω)}{2 (Ω^{2} + Δ^{2})} \cos (\sqrt{Ω^{2} + Δ^{2}} z)) {| a_{1} (0) |}^{2} .