Abstract

We will show that broadband unidirectional optical transmission with a total transmission maximum inside the band can be obtained for linearly polarized incident waves in the nonsymmetric photonic crystal gratings made of isotropic linear materials at a fixed nonzero or zero angle of incidence. Being based on the merging of diffraction and dispersion effects, the basic physical mechanism studied exploits the transmission channels associated with higher orders, for which asymmetry in the coupling conditions at the two grating interfaces appears when spatial inversion symmetry is broken. Total transmission in one direction and zero transmission in the opposite direction can be obtained due to hybridization of Fabry-Perot type resonances with a diffraction anomaly that yields a diode-like operation regime. Single-beam deflection and two-beam splitting can be obtained, for which transmission can be (nearly) total, if the corrugated side is illuminated. In contrast to the previous studies, it is also shown that unidirectional transmission can appear only at a fixed frequency and only due to diffractions, when total transmission occurs at the noncorrugated-side illumination, being in agreement with the Lorentz Lemma.

© 2012 OSA

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2011 (4)

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]

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]

M. Beruete, A. E. Serebryannikov, V. Torres, M. Navarro-Cia, and M. Sorolla, “Toward compact millimeter-wave diode in thin stacked hole array assisted by a dielectric grating,” Appl. Phys. Lett. 99(15), 154101 (2011).
[CrossRef]

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]

2010 (6)

K. Xiu-Bao, T. Wei, W. Zhan-Shan, W. Zhi-Guo, and C. Hong, “High efficiency one-way transmission by one-dimensional photonic crystals with graings on one side,” Chin. Phys. Lett. 27(7), 074204 (2010).
[CrossRef]

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]

A. O. Cakmak, E. Colak, A. E. Serebryannikov, and E. Ozbay, “Unidirectional transmission in photonic-crystal gratings at beam-type illumination,” Opt. Express 18(21), 22283–22298 (2010).
[CrossRef] [PubMed]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[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 metamaterilas,” Phys. Rev. Lett. 104(25), 253902 (2010).
[CrossRef]

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett. 96(11), 111111 (2010).
[CrossRef]

2009 (4)

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3(2), 91–94 (2009).
[CrossRef]

A. E. Serebryannikov, “One-way diffraction effects in photonic crystal gratings made of isotropic materials,” Phys. Rev. B 80(15), 155117 (2009).
[CrossRef]

A. E. Serebryannikov, A. Y. Petrov, and E. Ozbay, “Toward photonic crystal based spatial filters with wide angle ranges of total transmission,” Appl. Phys. Lett. 94(18), 181101 (2009).
[CrossRef]

A. E. Serebryannikov and E. Ozbay, “Unidirectional transmission in non-symmetric gratings containing metallic layers,” Opt. Express 17(16), 13335–13345 (2009).
[CrossRef] [PubMed]

2008 (2)

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljacić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100(1), 013905 (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]

2006 (3)

A. Figotin and I. Vitebskiy, “Electromagnetic unidirectionality and frozen modes in magnetic photonic crystals,” J. Magn. Magn. Mater. 300(1), 117–121 (2006).
[CrossRef]

G. Shvets, “Optical polarizer/isolator based on rectangular waveguide with helical grooves,” Appl. Phys. Lett. 89(14), 141127 (2006).
[CrossRef]

J.-Y. Chen and L.-W. Chen, “Color separating with integrated photonic band-gap optical diodes: a numerical study,” Opt. Express 14(22), 10733–10739 (2006).
[CrossRef] [PubMed]

2005 (2)

T. Magath and A. E. Serebryannikov, “Fast iterative, coupled-integral-equation technique for inhomogeneous profiled and periodic slabs,” J. Opt. Soc. Am. A 22(11), 2405–2418 (2005).
[CrossRef] [PubMed]

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis, “Negative refraction and superlens behavior in a two-dimensional photonic crystal,” Phys. Rev. B 71(8), 085106 (2005).
[CrossRef]

2004 (1)

S. K. Ibrahim, S. Bhandare, D. Sandel, H. Zhang, and R. Noe, “Non-magnetic 30dB integrated opical isolator in III/Vmaterial,” Electron. Lett. 40(20), 1293–1294 (2004).
[CrossRef]

2003 (3)

2002 (1)

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65(20), 201104 (2002).
[CrossRef]

1996 (1)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
[CrossRef] [PubMed]

1994 (1)

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76(4), 2023–2025 (1994).
[CrossRef]

Beruete, M.

M. Beruete, A. E. Serebryannikov, V. Torres, M. Navarro-Cia, and M. Sorolla, “Toward compact millimeter-wave diode in thin stacked hole array assisted by a dielectric grating,” Appl. Phys. Lett. 99(15), 154101 (2011).
[CrossRef]

Bhandare, S.

S. K. Ibrahim, S. Bhandare, D. Sandel, H. Zhang, and R. Noe, “Non-magnetic 30dB integrated opical isolator in III/Vmaterial,” Electron. Lett. 40(20), 1293–1294 (2004).
[CrossRef]

Bloemer, M. J.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76(4), 2023–2025 (1994).
[CrossRef]

Bowden, C. M.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76(4), 2023–2025 (1994).
[CrossRef]

Caglayan, H.

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]

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]

Cakmak, A. O.

Cakmakyapan, S.

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]

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]

Chen, J.-Y.

Chen, L.-W.

Chen, X.-L.

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett. 96(11), 111111 (2010).
[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]

Chen, Y.-F.

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett. 96(11), 111111 (2010).
[CrossRef]

Chong, Y. D.

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljacić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100(1), 013905 (2008).
[CrossRef] [PubMed]

Christodoulides, D. N.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[CrossRef]

Colak, E.

Dowling, J. P.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76(4), 2023–2025 (1994).
[CrossRef]

El-Ganainy, R.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[CrossRef]

Fan, S.

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3(2), 91–94 (2009).
[CrossRef]

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]

Feng, L.

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]

Figotin, A.

A. Figotin and I. Vitebskiy, “Electromagnetic unidirectionality and frozen modes in magnetic photonic crystals,” J. Magn. Magn. Mater. 300(1), 117–121 (2006).
[CrossRef]

Foteinopoulou, S.

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis, “Negative refraction and superlens behavior in a two-dimensional photonic crystal,” Phys. Rev. B 71(8), 085106 (2005).
[CrossRef]

Gong, Q.

Guven, K.

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis, “Negative refraction and superlens behavior in a two-dimensional photonic crystal,” Phys. Rev. B 71(8), 085106 (2005).
[CrossRef]

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]

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett. 96(11), 111111 (2010).
[CrossRef]

Helgert, C.

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

Holden, A. J.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
[CrossRef] [PubMed]

Hong, C.

K. Xiu-Bao, T. Wei, W. Zhan-Shan, W. Zhi-Guo, and C. Hong, “High efficiency one-way transmission by one-dimensional photonic crystals with graings on one side,” Chin. Phys. Lett. 27(7), 074204 (2010).
[CrossRef]

Hu, X.

Ibrahim, S. K.

S. K. Ibrahim, S. Bhandare, D. Sandel, H. Zhang, and R. Noe, “Non-magnetic 30dB integrated opical isolator in III/Vmaterial,” Electron. Lett. 40(20), 1293–1294 (2004).
[CrossRef]

Joannopoulos, J. D.

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljacić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100(1), 013905 (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]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65(20), 201104 (2002).
[CrossRef]

Johnson, S. G.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65(20), 201104 (2002).
[CrossRef]

Kip, D.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[CrossRef]

Kley, E.-B.

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

Lederer, F.

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

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]

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett. 96(11), 111111 (2010).
[CrossRef]

Lu, C.

Lu, M.-H.

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]

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett. 96(11), 111111 (2010).
[CrossRef]

Luo, C.

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]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65(20), 201104 (2002).
[CrossRef]

Magath, T.

Makris, K. G.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[CrossRef]

Menzel, C.

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

Moussa, R.

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis, “Negative refraction and superlens behavior in a two-dimensional photonic crystal,” Phys. Rev. B 71(8), 085106 (2005).
[CrossRef]

Navarro-Cia, M.

M. Beruete, A. E. Serebryannikov, V. Torres, M. Navarro-Cia, and M. Sorolla, “Toward compact millimeter-wave diode in thin stacked hole array assisted by a dielectric grating,” Appl. Phys. Lett. 99(15), 154101 (2011).
[CrossRef]

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]

Noe, R.

S. K. Ibrahim, S. Bhandare, D. Sandel, H. Zhang, and R. Noe, “Non-magnetic 30dB integrated opical isolator in III/Vmaterial,” Electron. Lett. 40(20), 1293–1294 (2004).
[CrossRef]

Ozbay, E.

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]

A. O. Cakmak, E. Colak, A. E. Serebryannikov, and E. Ozbay, “Unidirectional transmission in photonic-crystal gratings at beam-type illumination,” Opt. Express 18(21), 22283–22298 (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]

A. E. Serebryannikov and E. Ozbay, “Unidirectional transmission in non-symmetric gratings containing metallic layers,” Opt. Express 17(16), 13335–13345 (2009).
[CrossRef] [PubMed]

A. E. Serebryannikov, A. Y. Petrov, and E. Ozbay, “Toward photonic crystal based spatial filters with wide angle ranges of total transmission,” Appl. Phys. Lett. 94(18), 181101 (2009).
[CrossRef]

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis, “Negative refraction and superlens behavior in a two-dimensional photonic crystal,” Phys. Rev. B 71(8), 085106 (2005).
[CrossRef]

Pendry, J. B.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65(20), 201104 (2002).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
[CrossRef] [PubMed]

Pertsch, T.

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

Petrov, A. Y.

A. E. Serebryannikov, A. Y. Petrov, and E. Ozbay, “Toward photonic crystal based spatial filters with wide angle ranges of total transmission,” Appl. Phys. Lett. 94(18), 181101 (2009).
[CrossRef]

Piestun, R.

Qian, X.-S.

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett. 96(11), 111111 (2010).
[CrossRef]

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]

Rockstuhl, C.

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

Rüter, C. E.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[CrossRef]

Sandel, D.

S. K. Ibrahim, S. Bhandare, D. Sandel, H. Zhang, and R. Noe, “Non-magnetic 30dB integrated opical isolator in III/Vmaterial,” Electron. Lett. 40(20), 1293–1294 (2004).
[CrossRef]

Scalora, M.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76(4), 2023–2025 (1994).
[CrossRef]

Schurig, D.

D. Schurig and D. R. Smith, “Spatial filtering using media with indefinite permittivity and permeability tensors,” Appl. Phys. Lett. 82(14), 2215–2217 (2003).
[CrossRef]

Schwartz, B. T.

Segev, M.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[CrossRef]

Serebryannikov, A. E.

M. Beruete, A. E. Serebryannikov, V. Torres, M. Navarro-Cia, and M. Sorolla, “Toward compact millimeter-wave diode in thin stacked hole array assisted by a dielectric grating,” Appl. Phys. Lett. 99(15), 154101 (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]

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]

A. O. Cakmak, E. Colak, A. E. Serebryannikov, and E. Ozbay, “Unidirectional transmission in photonic-crystal gratings at beam-type illumination,” Opt. Express 18(21), 22283–22298 (2010).
[CrossRef] [PubMed]

A. E. Serebryannikov and E. Ozbay, “Unidirectional transmission in non-symmetric gratings containing metallic layers,” Opt. Express 17(16), 13335–13345 (2009).
[CrossRef] [PubMed]

A. E. Serebryannikov, A. Y. Petrov, and E. Ozbay, “Toward photonic crystal based spatial filters with wide angle ranges of total transmission,” Appl. Phys. Lett. 94(18), 181101 (2009).
[CrossRef]

A. E. Serebryannikov, “One-way diffraction effects in photonic crystal gratings made of isotropic materials,” Phys. Rev. B 80(15), 155117 (2009).
[CrossRef]

T. Magath and A. E. Serebryannikov, “Fast iterative, coupled-integral-equation technique for inhomogeneous profiled and periodic slabs,” J. Opt. Soc. Am. A 22(11), 2405–2418 (2005).
[CrossRef] [PubMed]

Shvets, G.

G. Shvets, “Optical polarizer/isolator based on rectangular waveguide with helical grooves,” Appl. Phys. Lett. 89(14), 141127 (2006).
[CrossRef]

Smith, D. R.

D. Schurig and D. R. Smith, “Spatial filtering using media with indefinite permittivity and permeability tensors,” Appl. Phys. Lett. 82(14), 2215–2217 (2003).
[CrossRef]

Soljacic, M.

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljacić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100(1), 013905 (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]

Sorolla, M.

M. Beruete, A. E. Serebryannikov, V. Torres, M. Navarro-Cia, and M. Sorolla, “Toward compact millimeter-wave diode in thin stacked hole array assisted by a dielectric grating,” Appl. Phys. Lett. 99(15), 154101 (2011).
[CrossRef]

Soukoulis, C. M.

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis, “Negative refraction and superlens behavior in a two-dimensional photonic crystal,” Phys. Rev. B 71(8), 085106 (2005).
[CrossRef]

Stewart, W. J.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
[CrossRef] [PubMed]

Torres, V.

M. Beruete, A. E. Serebryannikov, V. Torres, M. Navarro-Cia, and M. Sorolla, “Toward compact millimeter-wave diode in thin stacked hole array assisted by a dielectric grating,” Appl. Phys. Lett. 99(15), 154101 (2011).
[CrossRef]

Tünnermann, A.

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

Tuttle, G.

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis, “Negative refraction and superlens behavior in a two-dimensional photonic crystal,” Phys. Rev. B 71(8), 085106 (2005).
[CrossRef]

Vitebskiy, I.

A. Figotin and I. Vitebskiy, “Electromagnetic unidirectionality and frozen modes in magnetic photonic crystals,” J. Magn. Magn. Mater. 300(1), 117–121 (2006).
[CrossRef]

Wan, W.-W.

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett. 96(11), 111111 (2010).
[CrossRef]

Wang, Z.

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljacić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100(1), 013905 (2008).
[CrossRef] [PubMed]

Wei, T.

K. Xiu-Bao, T. Wei, W. Zhan-Shan, W. Zhi-Guo, and C. Hong, “High efficiency one-way transmission by one-dimensional photonic crystals with graings on one side,” Chin. Phys. Lett. 27(7), 074204 (2010).
[CrossRef]

Xiu-Bao, K.

K. Xiu-Bao, T. Wei, W. Zhan-Shan, W. Zhi-Guo, and C. Hong, “High efficiency one-way transmission by one-dimensional photonic crystals with graings on one side,” Chin. Phys. Lett. 27(7), 074204 (2010).
[CrossRef]

Yang, H.

Yin, R.-C.

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett. 96(11), 111111 (2010).
[CrossRef]

Youngs, I.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
[CrossRef] [PubMed]

Yu, Z.

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3(2), 91–94 (2009).
[CrossRef]

Zhang, H.

S. K. Ibrahim, S. Bhandare, D. Sandel, H. Zhang, and R. Noe, “Non-magnetic 30dB integrated opical isolator in III/Vmaterial,” Electron. Lett. 40(20), 1293–1294 (2004).
[CrossRef]

Zhang, L.

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis, “Negative refraction and superlens behavior in a two-dimensional photonic crystal,” Phys. Rev. B 71(8), 085106 (2005).
[CrossRef]

Zhan-Shan, W.

K. Xiu-Bao, T. Wei, W. Zhan-Shan, W. Zhi-Guo, and C. Hong, “High efficiency one-way transmission by one-dimensional photonic crystals with graings on one side,” Chin. Phys. Lett. 27(7), 074204 (2010).
[CrossRef]

Zhi-Guo, W.

K. Xiu-Bao, T. Wei, W. Zhan-Shan, W. Zhi-Guo, and C. Hong, “High efficiency one-way transmission by one-dimensional photonic crystals with graings on one side,” Chin. Phys. Lett. 27(7), 074204 (2010).
[CrossRef]

Appl. Phys. Lett. (6)

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett. 96(11), 111111 (2010).
[CrossRef]

G. Shvets, “Optical polarizer/isolator based on rectangular waveguide with helical grooves,” Appl. Phys. Lett. 89(14), 141127 (2006).
[CrossRef]

M. Beruete, A. E. Serebryannikov, V. Torres, M. Navarro-Cia, and M. Sorolla, “Toward compact millimeter-wave diode in thin stacked hole array assisted by a dielectric grating,” Appl. Phys. Lett. 99(15), 154101 (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]

A. E. Serebryannikov, A. Y. Petrov, and E. Ozbay, “Toward photonic crystal based spatial filters with wide angle ranges of total transmission,” Appl. Phys. Lett. 94(18), 181101 (2009).
[CrossRef]

D. Schurig and D. R. Smith, “Spatial filtering using media with indefinite permittivity and permeability tensors,” Appl. Phys. Lett. 82(14), 2215–2217 (2003).
[CrossRef]

Chin. Phys. Lett. (1)

K. Xiu-Bao, T. Wei, W. Zhan-Shan, W. Zhi-Guo, and C. Hong, “High efficiency one-way transmission by one-dimensional photonic crystals with graings on one side,” Chin. Phys. Lett. 27(7), 074204 (2010).
[CrossRef]

Electron. Lett. (1)

S. K. Ibrahim, S. Bhandare, D. Sandel, H. Zhang, and R. Noe, “Non-magnetic 30dB integrated opical isolator in III/Vmaterial,” Electron. Lett. 40(20), 1293–1294 (2004).
[CrossRef]

J. Appl. Phys. (1)

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76(4), 2023–2025 (1994).
[CrossRef]

J. Magn. Magn. Mater. (1)

A. Figotin and I. Vitebskiy, “Electromagnetic unidirectionality and frozen modes in magnetic photonic crystals,” J. Magn. Magn. Mater. 300(1), 117–121 (2006).
[CrossRef]

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

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

Nat. Photonics (1)

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3(2), 91–94 (2009).
[CrossRef]

Nat. Phys. (1)

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. B (3)

A. E. Serebryannikov, “One-way diffraction effects in photonic crystal gratings made of isotropic materials,” Phys. Rev. B 80(15), 155117 (2009).
[CrossRef]

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis, “Negative refraction and superlens behavior in a two-dimensional photonic crystal,” Phys. Rev. B 71(8), 085106 (2005).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65(20), 201104 (2002).
[CrossRef]

Phys. Rev. Lett. (5)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
[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]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljacić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100(1), 013905 (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]

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

Other (3)

K. Inoue and K. Ohtaka, Eds., Photonic Crystals. Physics, Fabrication, and Applications (Springer, Berlin, 2004).

J. A. Kong, Electromagnetic Wave Theory (EMW Publishing, Cambridge, MA, USA, 2005).

See, www.cst.com .

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Figures (7)

Fig. 1
Fig. 1

Coupling scenarios, at which the unidirectional transmission can be obtained: green solid line – IFC of PC; blue dashed circle – IFC in air; dotted lines – construction lines; “0”, “-1” and “+1” denote n; “+” and “−“ at the plot top indicate that the corresponding order that propagates in air is coupled or not coupled to a FB wave, if the corrugated side is illuminated; “−“ and “X” at the plot bottom indicate that the corresponding order may propagate in air but is not coupled or evanescent, if the noncorrugated side is illuminated; IFCs of PC are located around (a) Γ point, (b) X point, (c) M point, and (d) Γ and M points.

Fig. 2
Fig. 2

Diffraction scenarios corresponding to unidirectional transmission in nonsymmetric PC gratings: (a) deflection and (b) splitting in the direct (forward) transmission regime, and (c) splitting in the inverse (backward) transmission regime.

Fig. 3
Fig. 3

Transmittance t 0 = t 0 = t 0 (a), t 1 (b), and t 1 (c) at P=12 , ε r =11.4 , and d/a=0.4 ; t 0 = t 0 = t 0 (d), t 1 (e), and t 1 (f) at P=12 , ε r =9.61 , d/a=0.45 , and benchmark corrugations, direct regime.

Fig. 4
Fig. 4

Same as Fig. 3 but for another range of θ variation, inverse regime.

Fig. 5
Fig. 5

Transmittances t n and T (a,d,g), t n and T (b,e,h), and reflectances r n and R (c,f) at P=12 and benchmark corrugations; (a)-(c): ε r =11.4 , d/a=0.4 , and θ= 43 o ; (d)-(f): ε r =9.61 , d/a=0.45 , and θ= 47 o ; (g,h): ε r =9.61 , d/a=0.45 , and θ= 17.3 o ; blue solid line – n=0 , red dashed line – n=1 , cyan dotted line – T (a,d,g), T (b,e,h), and R (c,f); asterisk denotes the cases of T =1 (a,d) and T =1 (h).

Fig. 6
Fig. 6

Diffraction scenario with the two beams that are simultaneously incident from the corrugated and noncorrugated sides in the opposite directions; fw and bw stand for the forward and backward cases, respectively.

Fig. 7
Fig. 7

Transmittances t n and T [plots (a),(b)], and t n and T [plot (c)] for the PC grating with corrugations obtained by removing every second rod from all of the eight layers (a) and one layer (b) that are adjacent to the corrugated (here - illuminated) interface, and (c) from all of the four layers that are adjacent to the corrugated (here - exit) interface, L=2a ; ε r =5.8 , P=12 , θ=0 , (a,c) d/a=0.4 , (b) d/a=0.31 ; blue solid line – n=0 , red dashed line – n=1 , cyan dotted line – T [plots (a),(b)] and T [plot (c)]; asterisk denotes (a) max T >0.9 , (b) T =1 , and (c) T =1 .

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

k x (n) =(ω/c)sinθ+2πn/L,
ϕ n = sin 1 [sin θ +2πn/kL].

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