Abstract

It is demonstrated that strong asymmetry in transmission can be obtained at the Gaussian beam illumination for a single prism based on a photonic crystal (PhC) with isotropic-type dispersion, as well as for its analog made of a homogeneous material. Asymmetric transmission can be realized with the aid of refraction at a proper orientation of the interfaces and wedges of the prism, whereas neither contribution of higher diffraction orders nor anisotropic-type dispersion is required. Furthermore, incidence toward a prism wedge can be used for one of two opposite directions in order to obtain asymmetry. Thus, asymmetric transmission is a general property of the prism configurations, which can be obtained by using simple geometries and quite conventional materials. The obtained results show that strong asymmetry can be achieved in PhC prisms with (nearly) circular shape of equifrequency dispersion contours, in both cases associated with the index of refraction 0<n<1 and n>1. For the comparison purposes, results are also presented for solid uniform non-magnetic prisms made of a material with the same value of n. It is shown in zero-loss approximation that the PhC prism and the ultralow-index material prism (0<n<1) can replace each other in some cases without affecting the scenario of asymmetric transmission. Moreover, the PhC prism and the solid dielectric prism can show the same scenario at n>1. Possible contributions of scattering on the individual rods and diffraction on the wedge to the resulting mechanism are discussed. Analogs of unidirectional splitting and unidirectional deflection regimes, which are known from the studies of PhC gratings, are obtained in PhC prisms and solid uniform prisms, i.e. without higher diffraction orders.

© 2015 Optical Society of America

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References

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2014 (2)

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), doi:.
[Crossref] [PubMed]

2013 (4)

J. Shi, X. Liu, S. Yu, T. Vu, 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]

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]

D. Jalas, A. Yu. Petrov, M. Eich, W. Freude, S. Fan, Z. 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]

E. Colak, A. E. Serebryannikov, A. O. Cakmak, and E. Ozbay, “Experimental study of broadband unidirectional splitting in photonic crystal gratings with broken structural symmetry,” Appl. Phys. Lett. 102(15), 151105 (2013).
[Crossref]

2012 (9)

S. Xu, C. Qiu, and Z. Liu, “Acoustic transmission through asymmetric grating structures made of cylinders,” J. Appl. Phys. 111(9), 094505 (2012).
[Crossref]

A. E. Serebryannikov, A. O. Cakmak, and E. Ozbay, “Multichannel optical diode with unidirectional diffraction relevant total transmission,” Opt. Express 20(14), 14980–14990 (2012).
[Crossref] [PubMed]

S. Cakmakyapan, A. E. Serebryannikov, H. Caglayan, and E. Ozbay, “Spoof-plasmon relevant one-way collimation and multiplexing at beaming from a slit in metallic grating,” Opt. Express 20(24), 26636–26648 (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]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response on Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335(6064), 38 (2012).
[Crossref] [PubMed]

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

C. Wang, X. L. Zhong, and Z. Y. Li, “Linear and passive silicon optical isolator,” Sci. Rep. 2(9), 674 (2012).
[PubMed]

A. Cicek, O. A. Kaya, and B. Ulug, “Refraction-type sonic crystal junction diode,” Appl. Phys. Lett. 100(11), 111905 (2012).
[Crossref]

J. H. Oh, H. W. Kim, P. S. Ma, H. M. Seung, and Y. Y. Kim, “Inverted bi-prism photonic crystals for one-sided elastic wave transmission applications,” Appl. Phys. Lett. 100(21), 213503 (2012).
[Crossref]

2011 (6)

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]

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

M. Beruete, A. E. Serebryannikov, V. Torres, M. Navarro-Cía, 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]

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]

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]

2010 (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]

2009 (2)

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]

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

2007 (2)

2006 (2)

A. E. Serebryannikov, T. Magath, and K. Schuenemann, “Bragg transmittance of s-polarized waves through finite-thickness photonic crystals with a periodically corrugated interface,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(6), 066607 (2006).
[Crossref] [PubMed]

A. E. Serebryannikov, T. Magath, K. Schuenemann, and O. Y. Vasylchenko, “Scattering of s-polarized plane waves by finite-thickness periodic structures made of ultralow-permittivity metamaterials,” Phys. Rev. B 73(11), 115111 (2006).
[Crossref]

2005 (3)

K. Oya, T. Nakazawa, S. Kittaka, K. Tsunetomo, K. Kintaka, J. Nishii, and K. Hirao, “Ultrasmall demultiplexer by use of one-dimensional photonic crystal,” Opt. Lett. 30(2), 192–194 (2005).
[Crossref] [PubMed]

X. Ao and S. He, “Negative refraction of left-handed behavior in porous alumina with infiltrated silver at an optical wavelength,” Appl. Phys. Lett. 87(10), 101112 (2005).
[Crossref]

C. Monzon, D. W. Forester, and P. Loschialpo, “Exact solution to line source scattering by an ideal left-handed wedge,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 056606 (2005).
[Crossref] [PubMed]

2004 (2)

X. Yu and S. Fan, “Anomalous refraction at photonic crystal surfaces,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(5), 055601(R) (2004).

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004).
[Crossref] [PubMed]

2003 (3)

N. Garcia, M. Nieto-Vesperinas, E. V. Ponizovskaya, and M. Torres, “Theory for tailoring sonic devices: diffraction dominates over refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046606 (2003).
[Crossref] [PubMed]

B. T. Schwartz and R. Piestun, “Total external reflection from metamaterials with ultralow refractive index,” J. Opt. Soc. Am. B 20(12), 2448–2453 (2003).
[Crossref]

I. Bulu, H. Caglayan, and E. Ozbay, “Highly directive radiation from sources embedded inside photonic crystals,” Appl. Phys. Lett. 83(16), 3263–3265 (2003).
[Crossref]

2001 (1)

M. Bayindir, C. Kural, and E. Ozbay, “Coupled optical microcavities in one-dimensional photonic bandgap structures,” J. Opt. A, Pure Appl. Opt. 3(6), S184–S189 (2001).
[Crossref]

2000 (1)

1998 (1)

B. Temelkuran, E. Özbay, J. P. Kavanaugh, G. Tuttle, and K. M. Ho, “Resonant cavity enhanced detectors embedded in photonic crystals,” Appl. Phys. Lett. 72(19), 2376–2378 (1998).
[Crossref]

Ao, X.

X. Ao and S. He, “Negative refraction of left-handed behavior in porous alumina with infiltrated silver at an optical wavelength,” Appl. Phys. Lett. 87(10), 101112 (2005).
[Crossref]

Ayache, M.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y. F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333(6043), 729–733 (2011).
[Crossref] [PubMed]

Azad, A. K.

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]

Baets, R.

D. Jalas, A. Yu. Petrov, M. Eich, W. Freude, S. Fan, Z. 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. 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]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response on Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335(6064), 38 (2012).
[Crossref] [PubMed]

Bayindir, M.

M. Bayindir, C. Kural, and E. Ozbay, “Coupled optical microcavities in one-dimensional photonic bandgap structures,” J. Opt. A, Pure Appl. Opt. 3(6), S184–S189 (2001).
[Crossref]

Bertolotti, M.

Beruete, M.

M. Beruete, A. E. Serebryannikov, V. Torres, M. Navarro-Cía, 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]

Brinkmeyer, E.

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]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response on Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335(6064), 38 (2012).
[Crossref] [PubMed]

Bulu, I.

I. Bulu, H. Caglayan, and E. Ozbay, “Highly directive radiation from sources embedded inside photonic crystals,” Appl. Phys. Lett. 83(16), 3263–3265 (2003).
[Crossref]

Caglayan, H.

S. Cakmakyapan, A. E. Serebryannikov, H. Caglayan, and E. Ozbay, “Spoof-plasmon relevant one-way collimation and multiplexing at beaming from a slit in metallic grating,” Opt. Express 20(24), 26636–26648 (2012).
[Crossref] [PubMed]

I. Bulu, H. Caglayan, and E. Ozbay, “Highly directive radiation from sources embedded inside photonic crystals,” Appl. Phys. Lett. 83(16), 3263–3265 (2003).
[Crossref]

Cakmak, A. O.

E. Colak, A. E. Serebryannikov, A. O. Cakmak, and E. Ozbay, “Experimental study of broadband unidirectional splitting in photonic crystal gratings with broken structural symmetry,” Appl. Phys. Lett. 102(15), 151105 (2013).
[Crossref]

A. E. Serebryannikov, A. O. Cakmak, and E. Ozbay, “Multichannel optical diode with unidirectional diffraction relevant total transmission,” Opt. Express 20(14), 14980–14990 (2012).
[Crossref] [PubMed]

Cakmakyapan, S.

Chen, J.

Chen, Y. F.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y. F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333(6043), 729–733 (2011).
[Crossref] [PubMed]

Cheng, C.

Cheville, R. A.

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]

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]

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S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response on Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335(6064), 38 (2012).
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D. Jalas, A. Yu. Petrov, M. Eich, W. Freude, S. Fan, Z. 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).
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S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response on Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335(6064), 38 (2012).
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S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response on Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335(6064), 38 (2012).
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C. Lu, X. Hu, Y. Zhang, Z. Li, X. Xu, H. Yang, and Q. Gong, “Ultralow power all-optical diode in photonic crystal heterostructures with broken spatial inversion symmetry,” Appl. Phys. Lett. 99(5), 051107 (2011).
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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).
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D. Jalas, A. Yu. Petrov, M. Eich, W. Freude, S. Fan, Z. 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).
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S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response on Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335(6064), 38 (2012).
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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).
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D. Jalas, A. Yu. Petrov, M. Eich, W. Freude, S. Fan, Z. 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).
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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).
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S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response on Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335(6064), 38 (2012).
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Kavanaugh, J. P.

B. Temelkuran, E. Özbay, J. P. Kavanaugh, G. Tuttle, and K. M. Ho, “Resonant cavity enhanced detectors embedded in photonic crystals,” Appl. Phys. Lett. 72(19), 2376–2378 (1998).
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A. Cicek, O. A. Kaya, and B. Ulug, “Refraction-type sonic crystal junction diode,” Appl. Phys. Lett. 100(11), 111905 (2012).
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A. Cicek, M. B. Yucel, O. A. Kaya, and B. Ulug, “Refraction-based photonic crystal diode,” Opt. Lett. 37(14), 2937–2939 (2012).
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J. H. Oh, H. W. Kim, P. S. Ma, H. M. Seung, and Y. Y. Kim, “Inverted bi-prism photonic crystals for one-sided elastic wave transmission applications,” Appl. Phys. Lett. 100(21), 213503 (2012).
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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).
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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).
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S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response on Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335(6064), 38 (2012).
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M. Bayindir, C. Kural, and E. Ozbay, “Coupled optical microcavities in one-dimensional photonic bandgap structures,” J. Opt. A, Pure Appl. Opt. 3(6), S184–S189 (2001).
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C. Lu, X. Hu, Y. Zhang, Z. Li, X. Xu, H. Yang, and Q. Gong, “Ultralow power all-optical diode in photonic crystal heterostructures with broken spatial inversion symmetry,” Appl. Phys. Lett. 99(5), 051107 (2011).
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Li, Z. Y.

Liu, X.

J. Shi, X. Liu, S. Yu, T. Vu, 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).
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S. Xu, C. Qiu, and Z. Liu, “Acoustic transmission through asymmetric grating structures made of cylinders,” J. Appl. Phys. 111(9), 094505 (2012).
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C. Monzon, D. W. Forester, and P. Loschialpo, “Exact solution to line source scattering by an ideal left-handed wedge,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 056606 (2005).
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C. Lu, X. Hu, Y. Zhang, Z. Li, X. Xu, H. Yang, and Q. Gong, “Ultralow power all-optical diode in photonic crystal heterostructures with broken spatial inversion symmetry,” Appl. Phys. Lett. 99(5), 051107 (2011).
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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]

Lu, M.-H.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y. F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333(6043), 729–733 (2011).
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Ma, H. F.

J. Shi, X. Liu, S. Yu, T. Vu, 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).
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J. H. Oh, H. W. Kim, P. S. Ma, H. M. Seung, and Y. Y. Kim, “Inverted bi-prism photonic crystals for one-sided elastic wave transmission applications,” Appl. Phys. Lett. 100(21), 213503 (2012).
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D. Jalas, A. Yu. Petrov, M. Eich, W. Freude, S. Fan, Z. 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).
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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).
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J. H. Oh, H. W. Kim, P. S. Ma, H. M. Seung, and Y. Y. Kim, “Inverted bi-prism photonic crystals for one-sided elastic wave transmission applications,” Appl. Phys. Lett. 100(21), 213503 (2012).
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B. Temelkuran, E. Özbay, J. P. Kavanaugh, G. Tuttle, and K. M. Ho, “Resonant cavity enhanced detectors embedded in photonic crystals,” Appl. Phys. Lett. 72(19), 2376–2378 (1998).
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S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response on Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335(6064), 38 (2012).
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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).
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D. Jalas, A. Yu. Petrov, M. Eich, W. Freude, S. Fan, Z. 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).
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Plum, E.

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).
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[Crossref]

Renner, H.

D. Jalas, A. Yu. Petrov, M. Eich, W. Freude, S. Fan, Z. 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. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response on Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335(6064), 38 (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]

Rockstuhl, C.

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]

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]

Scherer, A.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y. F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333(6043), 729–733 (2011).
[Crossref] [PubMed]

Schonbrun, E.

Schuenemann, K.

A. E. Serebryannikov, T. Magath, K. Schuenemann, and O. Y. Vasylchenko, “Scattering of s-polarized plane waves by finite-thickness periodic structures made of ultralow-permittivity metamaterials,” Phys. Rev. B 73(11), 115111 (2006).
[Crossref]

A. E. Serebryannikov, T. Magath, and K. Schuenemann, “Bragg transmittance of s-polarized waves through finite-thickness photonic crystals with a periodically corrugated interface,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(6), 066607 (2006).
[Crossref] [PubMed]

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.

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]

E. Colak, A. E. Serebryannikov, A. O. Cakmak, and E. Ozbay, “Experimental study of broadband unidirectional splitting in photonic crystal gratings with broken structural symmetry,” Appl. Phys. Lett. 102(15), 151105 (2013).
[Crossref]

S. Cakmakyapan, A. E. Serebryannikov, H. Caglayan, and E. Ozbay, “Spoof-plasmon relevant one-way collimation and multiplexing at beaming from a slit in metallic grating,” Opt. Express 20(24), 26636–26648 (2012).
[Crossref] [PubMed]

A. E. Serebryannikov, A. O. Cakmak, and E. Ozbay, “Multichannel optical diode with unidirectional diffraction relevant total transmission,” Opt. Express 20(14), 14980–14990 (2012).
[Crossref] [PubMed]

M. Beruete, A. E. Serebryannikov, V. Torres, M. Navarro-Cía, 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]

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, T. Magath, K. Schuenemann, and O. Y. Vasylchenko, “Scattering of s-polarized plane waves by finite-thickness periodic structures made of ultralow-permittivity metamaterials,” Phys. Rev. B 73(11), 115111 (2006).
[Crossref]

A. E. Serebryannikov, T. Magath, and K. Schuenemann, “Bragg transmittance of s-polarized waves through finite-thickness photonic crystals with a periodically corrugated interface,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(6), 066607 (2006).
[Crossref] [PubMed]

Seung, H. M.

J. H. Oh, H. W. Kim, P. S. Ma, H. M. Seung, and Y. Y. Kim, “Inverted bi-prism photonic crystals for one-sided elastic wave transmission applications,” Appl. Phys. Lett. 100(21), 213503 (2012).
[Crossref]

Shi, J.

J. Shi, X. Liu, S. Yu, T. Vu, 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]

Sibilia, C.

Singh, R.

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]

Sorolla, M.

M. Beruete, A. E. Serebryannikov, V. Torres, M. Navarro-Cía, 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]

Stolarek, M.

Szoplik, T.

Tayeb, G.

Temelkuran, B.

B. Temelkuran, E. Özbay, J. P. Kavanaugh, G. Tuttle, and K. M. Ho, “Resonant cavity enhanced detectors embedded in photonic crystals,” Appl. Phys. Lett. 72(19), 2376–2378 (1998).
[Crossref]

Torres, M.

N. Garcia, M. Nieto-Vesperinas, E. V. Ponizovskaya, and M. Torres, “Theory for tailoring sonic devices: diffraction dominates over refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046606 (2003).
[Crossref] [PubMed]

Torres, V.

M. Beruete, A. E. Serebryannikov, V. Torres, M. Navarro-Cía, 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]

Tsunetomo, K.

Tuttle, G.

B. Temelkuran, E. Özbay, J. P. Kavanaugh, G. Tuttle, and K. M. Ho, “Resonant cavity enhanced detectors embedded in photonic crystals,” Appl. Phys. Lett. 72(19), 2376–2378 (1998).
[Crossref]

Ulug, B.

A. Cicek, O. A. Kaya, and B. Ulug, “Refraction-type sonic crystal junction diode,” Appl. Phys. Lett. 100(11), 111905 (2012).
[Crossref]

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]

Vanwolleghem, M.

D. Jalas, A. Yu. Petrov, M. Eich, W. Freude, S. Fan, Z. 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. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response on Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335(6064), 38 (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]

Vasylchenko, O. Y.

A. E. Serebryannikov, T. Magath, K. Schuenemann, and O. Y. Vasylchenko, “Scattering of s-polarized plane waves by finite-thickness periodic structures made of ultralow-permittivity metamaterials,” Phys. Rev. B 73(11), 115111 (2006).
[Crossref]

Vu, T.

J. Shi, X. Liu, S. Yu, T. Vu, 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]

Wang, C.

Wang, H.-T.

Wu, Q.

Xu, J.

Xu, S.

S. Xu, C. Qiu, and Z. Liu, “Acoustic transmission through asymmetric grating structures made of cylinders,” J. Appl. Phys. 111(9), 094505 (2012).
[Crossref]

Xu, T.

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

Xu, X.

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

Xu, Y.-L.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y. F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333(6043), 729–733 (2011).
[Crossref] [PubMed]

Yang, H.

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

Yavorskiy, D.

Yu, S.

J. Shi, X. Liu, S. Yu, T. Vu, 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]

Yu, X.

X. Yu and S. Fan, “Anomalous refraction at photonic crystal surfaces,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(5), 055601(R) (2004).

Yu, Z.

D. Jalas, A. Yu. Petrov, M. Eich, W. Freude, S. Fan, Z. 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. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response on Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335(6064), 38 (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]

Yucel, M. B.

Zapata Rodríguez, C. J.

Zhang, W.

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]

Zhang, Y.

C. Lu, X. Hu, Y. Zhang, Z. Li, X. Xu, H. Yang, and Q. 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.

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]

Zheng, Z.

Zhong, X. L.

C. Wang, X. L. Zhong, and Z. Y. Li, “Linear and passive silicon optical isolator,” Sci. Rep. 2(9), 674 (2012).
[PubMed]

Zhou, C.-Z.

Zhu, Z.

J. Shi, X. Liu, S. Yu, T. Vu, 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]

Ziolkowski, R. W.

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004).
[Crossref] [PubMed]

Appl. Phys. Lett. (9)

J. Shi, X. Liu, S. Yu, T. Vu, 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]

E. Colak, A. E. Serebryannikov, A. O. Cakmak, and E. Ozbay, “Experimental study of broadband unidirectional splitting in photonic crystal gratings with broken structural symmetry,” Appl. Phys. Lett. 102(15), 151105 (2013).
[Crossref]

M. Beruete, A. E. Serebryannikov, V. Torres, M. Navarro-Cía, 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]

I. Bulu, H. Caglayan, and E. Ozbay, “Highly directive radiation from sources embedded inside photonic crystals,” Appl. Phys. Lett. 83(16), 3263–3265 (2003).
[Crossref]

B. Temelkuran, E. Özbay, J. P. Kavanaugh, G. Tuttle, and K. M. Ho, “Resonant cavity enhanced detectors embedded in photonic crystals,” Appl. Phys. Lett. 72(19), 2376–2378 (1998).
[Crossref]

A. Cicek, O. A. Kaya, and B. Ulug, “Refraction-type sonic crystal junction diode,” Appl. Phys. Lett. 100(11), 111905 (2012).
[Crossref]

X. Ao and S. He, “Negative refraction of left-handed behavior in porous alumina with infiltrated silver at an optical wavelength,” Appl. Phys. Lett. 87(10), 101112 (2005).
[Crossref]

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

J. H. Oh, H. W. Kim, P. S. Ma, H. M. Seung, and Y. Y. Kim, “Inverted bi-prism photonic crystals for one-sided elastic wave transmission applications,” Appl. Phys. Lett. 100(21), 213503 (2012).
[Crossref]

J. Appl. Phys. (1)

S. Xu, C. Qiu, and Z. Liu, “Acoustic transmission through asymmetric grating structures made of cylinders,” J. Appl. Phys. 111(9), 094505 (2012).
[Crossref]

J. Opt. A, Pure Appl. Opt. (1)

M. Bayindir, C. Kural, and E. Ozbay, “Coupled optical microcavities in one-dimensional photonic bandgap structures,” J. Opt. A, Pure Appl. Opt. 3(6), S184–S189 (2001).
[Crossref]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (2)

Nat. Commun. (1)

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

Nat. Photonics (1)

D. Jalas, A. Yu. Petrov, M. Eich, W. Freude, S. Fan, Z. 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]

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 (5)

Opt. Lett. (5)

Phys. Rev. B (2)

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]

A. E. Serebryannikov, T. Magath, K. Schuenemann, and O. Y. Vasylchenko, “Scattering of s-polarized plane waves by finite-thickness periodic structures made of ultralow-permittivity metamaterials,” Phys. Rev. B 73(11), 115111 (2006).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (5)

A. E. Serebryannikov, T. Magath, and K. Schuenemann, “Bragg transmittance of s-polarized waves through finite-thickness photonic crystals with a periodically corrugated interface,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(6), 066607 (2006).
[Crossref] [PubMed]

N. Garcia, M. Nieto-Vesperinas, E. V. Ponizovskaya, and M. Torres, “Theory for tailoring sonic devices: diffraction dominates over refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046606 (2003).
[Crossref] [PubMed]

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004).
[Crossref] [PubMed]

C. Monzon, D. W. Forester, and P. Loschialpo, “Exact solution to line source scattering by an ideal left-handed wedge,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 056606 (2005).
[Crossref] [PubMed]

X. Yu and S. Fan, “Anomalous refraction at photonic crystal surfaces,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(5), 055601(R) (2004).

Sci. Rep. (1)

C. Wang, X. L. Zhong, and Z. Y. Li, “Linear and passive silicon optical isolator,” Sci. Rep. 2(9), 674 (2012).
[PubMed]

Science (3)

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]

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]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Response on Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335(6064), 38 (2012).
[Crossref] [PubMed]

Other (1)

E. D. Palik, ed., Handbook of optical constants of solids, Vol. I (Academic, 1985).

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Figures (6)

Fig. 1
Fig. 1 Schematics of (a) prism configuration illuminated from the lower and the upper half-space; thick and thin arrows - directions of the incident and outgoing beams, respectively; (b) coupling scenarios at the inclined interface illuminated from the prism side (forward case) and from the upper (air) half-space (backward case); circles - EFCs in ( k U , k V )-plane; straight lines – examples of construction lines: solid lines - coupling is possible, dashed lines - coupling is formally possible in the limiting case, and dotted lines - coupling is impossible.
Fig. 2
Fig. 2 Electric field distribution at 179 THz ( k a = 3.75 ): for PhC prism at (a) forward-case (here - ΓM interface) illumination and (b) backward-case (here - ΓX interface) illumination, and for non-magnetic ULIM prism with n = 0.22 at (c) forward-case (here - shorter-side) illumination and (d) backward-case (here - longer-side) illumination; yellow arrows in plots (a)-(d) show directions of beam incidence; (e) EFCs in ( k U , k V )-plane and construction lines: solid lines - EFCs for PhC at k a = 3.6 (dark-blue line), k a = 3.675 (blue line), k a = 3.75 (green line), k a = 3.825 (orange line), k a = 3.9 (brown line); dashed circle - EFC for the surrounding air at k a = 3.75 ; A and B - construction lines at k a = 3.75 for the inclined interface in forward case and backward case, respectively.
Fig. 3
Fig. 3 Electric field distribution at 179 THz ( k a = 3.75 ): for PhC prism at (a) forward-case (here - ΓM interface) illumination and (b) backward-case (wedge) illumination; for non-magnetic ULIM prism with n = 0.22 at (c) forward-case (here – longer-side) illumination and (d) backward-case (wedge) illumination; for PhC prism at (e) forward-case (ΓX - interface) illumination and backward-case (wedge) illumination; yellow arrows show directions of beam incidence.
Fig. 4
Fig. 4 Electric field distribution at f = 207 THz ( k a = 4.335 ) for PhC prism at (a) forward-case (here - ΓM interface) illumination and (b) backward-case (here - ΓX interface) illumination, and for non-magnetic ULIM prism with n = 0.59 at (c) forward-case (here – normal, shorter-side) illumination and (d) backward-case (here – inclined, longer-side) illumination; (e) EFCs in ( k U , k V )-plane and construction lines: solid lines - EFCs for PhC at k a = 4.25 (dark-blue line), k a = 4.3 (blue line), k a = 4.335 (green line), k a = 4.375 (orange line), k a = 4.425 (brown line); dashed circle - EFC for the surrounding air at k a = 4.335 ; A and B - construction lines at k a = 4.335 for the inclined interface in forward case and backward case, respectively.
Fig. 5
Fig. 5 Electric field distribution for (a) backward-case (here - wedge) illumination and (b) forward-case (here - ΓM interface) illumination for PhC prism at 207 THz ( k a = 4.335 ); (c) backward-case (here - wedge) illumination and (d) forward-case (here – normal, longer-side) illumination for non-magnetic ULIM prism with n = 0.59 at 207 THz; (e) and (f) same as (a) and (b) but at 209 THz ( k a = 4.4 ); yellow arrows show directions of beam incidence.
Fig. 6
Fig. 6 Electric field distributions at 64 THz ( k a = 1.34 ): for PhC prism at (a) forward-case (here - normal, ΓX interface) illumination and (b) backward-case (here - wedge) illumination, and for solid dielectric prism with n = 1.68 at (c) forward-case (here - normal, longer-side) illumination and (d) backward-case (here - wedge) illumination; yellow arrows show directions of beam incidence; (e) EFCs in ( k x , k y )-plane and construction lines: solid lines - EFCs for the PhC at k a = 1.1 (dark-blue line), k a = 1.225 (blue line), k a = 1.34 (green line), k a = 1.45 (orange line), k a = 1.575 (brown line); dashed circle - EFC for the surrounding air at k a = 1.34 ; A and B - construction lines at k a = 1.34 for the inclined interface in forward case and backward case; thick straight dashed line schematically shows the inclined (here - ΓM) interface at x > 0 .

Equations (2)

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S min = 2 π / [ k a ( sin γ + n ) ] .
S min = 2 π / [ k a ( 1 + n ) ] .

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