Abstract

Asymmetric wave transmission is a Lorentz reciprocal phenomenon, which can appear in the structures with broken symmetry. It may enable high forward-to-backward transmittance contrast, while transmission for one of the two opposite incidence directions is blocked. In this paper, it is demonstrated that ultrawideband, high-contrast asymmetric wave transmission can be obtained at terahertz frequencies in the topologically simple, i.e., one- or two-layer nonsymmetric gratings, which are entirely or partially made of a polar dielectric working in the ultralow-ε regime inspired by phonon-photon coupling. A variety of polar dielectrics with different characteristics can be used that gives one a big freedom concerning design. Simple criteria for estimating possible usefulness of a certain polar dielectric are suggested. Contrasts exceeding 80dB can be easily achieved without a special parameter adjustment. Stacking a high-ε corrugated layer with a noncorrugated layer made of a polar dielectric, one can enhance transmission in the unidirectional regime. At large and intermediate angles of incidence, a better performance can be obtained owing to the common effect of nonsymmetric diffractions and directional selectivity, which is connected with the dispersion of the ultralow-ε material. At normal incidence, strong asymmetry in transmission may occur in the studied structures as a purely diffraction effect.

© 2014 Optical Society of America

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2013

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

A. E. Serebryannikov, E. Ozbay, “One-way Rayleigh-Wood anomalies and tunable narrowband transmission in photonic crystal gratings with broken structural symmetry,” Phys. Rev. A 87(5), 053804 (2013).
[CrossRef]

M. Mutlu, S. Cakmakyapan, A. E. Serebryannikov, E. Ozbay, “One-way reciprocal spoof surface plasmons and relevant reversible diodelike beaming,” Phys. Rev. B 87(20), 205123 (2013).
[CrossRef]

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

P. Rodríguez-Ulibarri, M. Beruete, M. Navarro-Cia, A. E. Serebryannikov, “Wideband unidirectional transmission with tunable sign-switchable refraction and deflection in nonsymmetric structures,” Phys. Rev. B 88(16), 165137 (2013).
[CrossRef]

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

2012

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

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

S. Cakmakyapan, A. E. Serebryannikov, H. Caglayan, 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, E. Colak, A. O. Cakmak, E. Ozbay, “Dispersion irrelevant wideband asymmetric transmission in dielectric photonic crystal gratings,” Opt. Lett. 37(23), 4844–4846 (2012).
[CrossRef] [PubMed]

V. Liu, D. A. B. Miller, 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]

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

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

A. E. Serebryannikov, K. B. Alici, T. Magath, A. O. Cakmak, E. Ozbay, “Asymmetric Fabry-Perot-type transmission in photonic-crystal gratings with one-sided corrugations at a two-way coupling,” Phys. Rev. A 86(5), 053835 (2012).
[CrossRef]

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

2011

M. Beruete, A. E. Serebryannikov, V. Torres, M. Navarro-Cia, 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. Foteinopoulou, M. Kafesaki, E. N. Economou, C. M. Soukoulis, “Two-dimensional polaritonic photonic crystals as terahertz uniaxial metamaterials,” Phys. Rev. B 84(3), 035128 (2011).
[CrossRef]

2010

X.-B. Kang, W. Tan, Z.-S. Wang, Z.-G. Wang, H. Cheng, “High-efficiency one-way transmission by one-dimensional photonic crystal with gratings on one side,” Chin. Phys. Lett. 27(7), 074204 (2010).
[CrossRef]

W.-M. Ye, X.-D. Yuan, C. C. Guo, C. Zen, “Unidirectional transmission in non-symmetric gratings made of isotropic material,” Opt. Express 18(8), 7590–7595 (2010).
[CrossRef] [PubMed]

2009

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

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

2007

A. Alù, M. G. Silveirinha, A. Salandrino, N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[CrossRef]

P. B. Catrysse, S. Fan, “Near-complete transmission through subwavelength hole arrays in phonon-polaritonic thin films,” Phys. Rev. B 75(7), 075422 (2007).
[CrossRef]

2006

M. J. Lockyear, A. P. Hibbins, K. R. White, J. R. Sambles, “One-way diffraction grating,” Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 74(5), 056611 (2006).
[CrossRef] [PubMed]

A. E. Serebryannikov, T. Magath, K. Schuenemann, 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]

M. V. Erementchouk, L. I. Deych, A. A. Lisyansky, “Spectral properties of exciton polaritons in one-dimensional resonant photonic crystals,” Phys. Rev. B 73(11), 115321 (2006).
[CrossRef]

2005

T. Magath, 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]

A. Rung, C. G. Ribbing, M. Qiu, “Gap maps for triangular photonic crystals with a dispersive and absorbing component,” Phys. Rev. B 72(20), 205120 (2005).
[CrossRef]

2004

K. C. Huang, M. L. Povinelli, J. D. Joannopoulos, “Negative effective permeability in polaritonic photonic crystals,” Appl. Phys. Lett. 85(4), 543–545 (2004).
[CrossRef]

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

2003

2001

A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, S. G. Tikhodeev, T. Fujita, T. Ishihara, “Polariton effect in distributed feedback microcavities,” J. Phys. Soc. Jpn. 70(4), 1137–1144 (2001).
[CrossRef]

2000

S. Nojima, “Photonic-crystal laser mediated by polaritons,” Phys. Rev. B 61(15), 9940–9943 (2000).
[CrossRef]

1999

S. Nojima, “Optical response of excitonic polaritons in photonic crystals,” Phys. Rev. B 59(8), 5662–5677 (1999).
[CrossRef]

1998

S. Nojima, “Excitonic polaritons in one-dimensional photonic crystals,” Phys. Rev. B 57(4), R2057–R2060 (1998).
[CrossRef]

1994

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, K. M. Ho, “Electromagnetic-wave propagation through dispersive and absorptive photonic-band-gap materials,” Phys. Rev. B Condens. Matter 49(16), 11080–11087 (1994).
[CrossRef] [PubMed]

Alici, K. B.

A. E. Serebryannikov, K. B. Alici, T. Magath, A. O. Cakmak, E. Ozbay, “Asymmetric Fabry-Perot-type transmission in photonic-crystal gratings with one-sided corrugations at a two-way coupling,” Phys. Rev. A 86(5), 053835 (2012).
[CrossRef]

Alù, A.

A. Alù, M. G. Silveirinha, A. Salandrino, N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[CrossRef]

Azad, A. K.

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

Baets, R.

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

Beruete, M.

P. Rodríguez-Ulibarri, M. Beruete, M. Navarro-Cia, A. E. Serebryannikov, “Wideband unidirectional transmission with tunable sign-switchable refraction and deflection in nonsymmetric structures,” Phys. Rev. B 88(16), 165137 (2013).
[CrossRef]

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

Caglayan, H.

Cakmak, A. O.

E. Colak, A. E. Serebryannikov, A. O. Cakmak, 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, K. B. Alici, T. Magath, A. O. Cakmak, E. Ozbay, “Asymmetric Fabry-Perot-type transmission in photonic-crystal gratings with one-sided corrugations at a two-way coupling,” Phys. Rev. A 86(5), 053835 (2012).
[CrossRef]

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

A. E. Serebryannikov, E. Colak, A. O. Cakmak, E. Ozbay, “Dispersion irrelevant wideband asymmetric transmission in dielectric photonic crystal gratings,” Opt. Lett. 37(23), 4844–4846 (2012).
[CrossRef] [PubMed]

Cakmakyapan, S.

M. Mutlu, S. Cakmakyapan, A. E. Serebryannikov, E. Ozbay, “One-way reciprocal spoof surface plasmons and relevant reversible diodelike beaming,” Phys. Rev. B 87(20), 205123 (2013).
[CrossRef]

S. Cakmakyapan, A. E. Serebryannikov, H. Caglayan, 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]

Catrysse, P. B.

P. B. Catrysse, S. Fan, “Near-complete transmission through subwavelength hole arrays in phonon-polaritonic thin films,” Phys. Rev. B 75(7), 075422 (2007).
[CrossRef]

Chan, C. T.

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, K. M. Ho, “Electromagnetic-wave propagation through dispersive and absorptive photonic-band-gap materials,” Phys. Rev. B Condens. Matter 49(16), 11080–11087 (1994).
[CrossRef] [PubMed]

Cheng, H.

X.-B. Kang, W. Tan, Z.-S. Wang, Z.-G. Wang, H. Cheng, “High-efficiency one-way transmission by one-dimensional photonic crystal with gratings on one side,” Chin. Phys. Lett. 27(7), 074204 (2010).
[CrossRef]

Cheville, R. A.

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

Cicek, A.

Colak, E.

E. Colak, A. E. Serebryannikov, A. O. Cakmak, 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, E. Colak, A. O. Cakmak, E. Ozbay, “Dispersion irrelevant wideband asymmetric transmission in dielectric photonic crystal gratings,” Opt. Lett. 37(23), 4844–4846 (2012).
[CrossRef] [PubMed]

Deych, L. I.

M. V. Erementchouk, L. I. Deych, A. A. Lisyansky, “Spectral properties of exciton polaritons in one-dimensional resonant photonic crystals,” Phys. Rev. B 73(11), 115321 (2006).
[CrossRef]

Doerr, C. R.

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

Economou, E. N.

S. Foteinopoulou, M. Kafesaki, E. N. Economou, C. M. Soukoulis, “Two-dimensional polaritonic photonic crystals as terahertz uniaxial metamaterials,” Phys. Rev. B 84(3), 035128 (2011).
[CrossRef]

Eich, M.

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

Engheta, N.

A. Alù, M. G. Silveirinha, A. Salandrino, N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[CrossRef]

Erementchouk, M. V.

M. V. Erementchouk, L. I. Deych, A. A. Lisyansky, “Spectral properties of exciton polaritons in one-dimensional resonant photonic crystals,” Phys. Rev. B 73(11), 115321 (2006).
[CrossRef]

Fan, S.

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

V. Liu, D. A. B. Miller, 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]

P. B. Catrysse, S. Fan, “Near-complete transmission through subwavelength hole arrays in phonon-polaritonic thin films,” Phys. Rev. B 75(7), 075422 (2007).
[CrossRef]

Foteinopoulou, S.

S. Foteinopoulou, M. Kafesaki, E. N. Economou, C. M. Soukoulis, “Two-dimensional polaritonic photonic crystals as terahertz uniaxial metamaterials,” Phys. Rev. B 84(3), 035128 (2011).
[CrossRef]

Freude, W.

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

Fujita, T.

A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, S. G. Tikhodeev, T. Fujita, T. Ishihara, “Polariton effect in distributed feedback microcavities,” J. Phys. Soc. Jpn. 70(4), 1137–1144 (2001).
[CrossRef]

Gippius, N. A.

A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, S. G. Tikhodeev, T. Fujita, T. Ishihara, “Polariton effect in distributed feedback microcavities,” J. Phys. Soc. Jpn. 70(4), 1137–1144 (2001).
[CrossRef]

Guo, C. C.

Hibbins, A. P.

M. J. Lockyear, A. P. Hibbins, K. R. White, J. R. Sambles, “One-way diffraction grating,” Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 74(5), 056611 (2006).
[CrossRef] [PubMed]

Ho, K. M.

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, K. M. Ho, “Electromagnetic-wave propagation through dispersive and absorptive photonic-band-gap materials,” Phys. Rev. B Condens. Matter 49(16), 11080–11087 (1994).
[CrossRef] [PubMed]

Huang, K. C.

K. C. Huang, M. L. Povinelli, J. D. Joannopoulos, “Negative effective permeability in polaritonic photonic crystals,” Appl. Phys. Lett. 85(4), 543–545 (2004).
[CrossRef]

Ishihara, T.

A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, S. G. Tikhodeev, T. Fujita, T. Ishihara, “Polariton effect in distributed feedback microcavities,” J. Phys. Soc. Jpn. 70(4), 1137–1144 (2001).
[CrossRef]

Jalas, D.

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

Joannopoulos, J. D.

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

K. C. Huang, M. L. Povinelli, J. D. Joannopoulos, “Negative effective permeability in polaritonic photonic crystals,” Appl. Phys. Lett. 85(4), 543–545 (2004).
[CrossRef]

Kafesaki, M.

S. Foteinopoulou, M. Kafesaki, E. N. Economou, C. M. Soukoulis, “Two-dimensional polaritonic photonic crystals as terahertz uniaxial metamaterials,” Phys. Rev. B 84(3), 035128 (2011).
[CrossRef]

Kang, X.-B.

X.-B. Kang, W. Tan, Z.-S. Wang, Z.-G. Wang, H. Cheng, “High-efficiency one-way transmission by one-dimensional photonic crystal with gratings on one side,” Chin. Phys. Lett. 27(7), 074204 (2010).
[CrossRef]

Kaya, O. A.

Kim, H. W.

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

Kim, Y. Y.

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

Kotynski, R.

Lederer, F.

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

Li, Z.-Y.

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

Lisyansky, A. A.

M. V. Erementchouk, L. I. Deych, A. A. Lisyansky, “Spectral properties of exciton polaritons in one-dimensional resonant photonic crystals,” Phys. Rev. B 73(11), 115321 (2006).
[CrossRef]

Liu, V.

Liu, Z.

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

Lockyear, M. J.

M. J. Lockyear, A. P. Hibbins, K. R. White, J. R. Sambles, “One-way diffraction grating,” Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 74(5), 056611 (2006).
[CrossRef] [PubMed]

Lusakowski, J.

Ma, P. S.

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

Magath, T.

A. E. Serebryannikov, K. B. Alici, T. Magath, A. O. Cakmak, E. Ozbay, “Asymmetric Fabry-Perot-type transmission in photonic-crystal gratings with one-sided corrugations at a two-way coupling,” Phys. Rev. A 86(5), 053835 (2012).
[CrossRef]

A. E. Serebryannikov, T. Magath, K. Schuenemann, 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]

T. Magath, 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]

Melloni, A.

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

Menzel, C.

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

Miller, D. A. B.

Muljarov, E. A.

A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, S. G. Tikhodeev, T. Fujita, T. Ishihara, “Polariton effect in distributed feedback microcavities,” J. Phys. Soc. Jpn. 70(4), 1137–1144 (2001).
[CrossRef]

Mutlu, M.

M. Mutlu, S. Cakmakyapan, A. E. Serebryannikov, E. Ozbay, “One-way reciprocal spoof surface plasmons and relevant reversible diodelike beaming,” Phys. Rev. B 87(20), 205123 (2013).
[CrossRef]

Navarro-Cia, M.

P. Rodríguez-Ulibarri, M. Beruete, M. Navarro-Cia, A. E. Serebryannikov, “Wideband unidirectional transmission with tunable sign-switchable refraction and deflection in nonsymmetric structures,” Phys. Rev. B 88(16), 165137 (2013).
[CrossRef]

M. Beruete, A. E. Serebryannikov, V. Torres, M. Navarro-Cia, M. Sorolla, “Toward compact millimeter-wave diode in thin stacked-hole array assisted by a dielectric grating,” Appl. Phys. Lett. 99(15), 154101 (2011).
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S. Nojima, “Photonic-crystal laser mediated by polaritons,” Phys. Rev. B 61(15), 9940–9943 (2000).
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S. Nojima, “Optical response of excitonic polaritons in photonic crystals,” Phys. Rev. B 59(8), 5662–5677 (1999).
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S. Nojima, “Excitonic polaritons in one-dimensional photonic crystals,” Phys. Rev. B 57(4), R2057–R2060 (1998).
[CrossRef]

Oh, J. H.

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

Ozbay, E.

A. E. Serebryannikov, E. Ozbay, “One-way Rayleigh-Wood anomalies and tunable narrowband transmission in photonic crystal gratings with broken structural symmetry,” Phys. Rev. A 87(5), 053804 (2013).
[CrossRef]

E. Colak, A. E. Serebryannikov, A. O. Cakmak, 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. Mutlu, S. Cakmakyapan, A. E. Serebryannikov, E. Ozbay, “One-way reciprocal spoof surface plasmons and relevant reversible diodelike beaming,” Phys. Rev. B 87(20), 205123 (2013).
[CrossRef]

A. E. Serebryannikov, K. B. Alici, T. Magath, A. O. Cakmak, E. Ozbay, “Asymmetric Fabry-Perot-type transmission in photonic-crystal gratings with one-sided corrugations at a two-way coupling,” Phys. Rev. A 86(5), 053835 (2012).
[CrossRef]

S. Cakmakyapan, A. E. Serebryannikov, H. Caglayan, 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, E. Colak, A. O. Cakmak, E. Ozbay, “Dispersion irrelevant wideband asymmetric transmission in dielectric photonic crystal gratings,” Opt. Lett. 37(23), 4844–4846 (2012).
[CrossRef] [PubMed]

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

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

Petrov, A.

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

Piestun, R.

Plum, E.

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

Popovic, M.

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

Povinelli, M. L.

K. C. Huang, M. L. Povinelli, J. D. Joannopoulos, “Negative effective permeability in polaritonic photonic crystals,” Appl. Phys. Lett. 85(4), 543–545 (2004).
[CrossRef]

Qiu, C.

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

Qiu, M.

A. Rung, C. G. Ribbing, M. Qiu, “Gap maps for triangular photonic crystals with a dispersive and absorbing component,” Phys. Rev. B 72(20), 205120 (2005).
[CrossRef]

Renner, H.

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

Ribbing, C. G.

A. Rung, C. G. Ribbing, M. Qiu, “Gap maps for triangular photonic crystals with a dispersive and absorbing component,” Phys. Rev. B 72(20), 205120 (2005).
[CrossRef]

Rockstuhl, C.

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

Rodríguez-Ulibarri, P.

P. Rodríguez-Ulibarri, M. Beruete, M. Navarro-Cia, A. E. Serebryannikov, “Wideband unidirectional transmission with tunable sign-switchable refraction and deflection in nonsymmetric structures,” Phys. Rev. B 88(16), 165137 (2013).
[CrossRef]

Rung, A.

A. Rung, C. G. Ribbing, M. Qiu, “Gap maps for triangular photonic crystals with a dispersive and absorbing component,” Phys. Rev. B 72(20), 205120 (2005).
[CrossRef]

Salandrino, A.

A. Alù, M. G. Silveirinha, A. Salandrino, N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[CrossRef]

Sambles, J. R.

M. J. Lockyear, A. P. Hibbins, K. R. White, J. R. Sambles, “One-way diffraction grating,” Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 74(5), 056611 (2006).
[CrossRef] [PubMed]

Schuenemann, K.

A. E. Serebryannikov, T. Magath, K. Schuenemann, 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]

Schwartz, B. T.

Serebryannikov, A. E.

M. Mutlu, S. Cakmakyapan, A. E. Serebryannikov, E. Ozbay, “One-way reciprocal spoof surface plasmons and relevant reversible diodelike beaming,” Phys. Rev. B 87(20), 205123 (2013).
[CrossRef]

P. Rodríguez-Ulibarri, M. Beruete, M. Navarro-Cia, A. E. Serebryannikov, “Wideband unidirectional transmission with tunable sign-switchable refraction and deflection in nonsymmetric structures,” Phys. Rev. B 88(16), 165137 (2013).
[CrossRef]

E. Colak, A. E. Serebryannikov, A. O. Cakmak, 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, E. Ozbay, “One-way Rayleigh-Wood anomalies and tunable narrowband transmission in photonic crystal gratings with broken structural symmetry,” Phys. Rev. A 87(5), 053804 (2013).
[CrossRef]

S. Cakmakyapan, A. E. Serebryannikov, H. Caglayan, 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, E. Ozbay, “Multichannel optical diode with unidirectional diffraction relevant total transmission,” Opt. Express 20(14), 14980–14990 (2012).
[CrossRef] [PubMed]

A. E. Serebryannikov, E. Colak, A. O. Cakmak, E. Ozbay, “Dispersion irrelevant wideband asymmetric transmission in dielectric photonic crystal gratings,” Opt. Lett. 37(23), 4844–4846 (2012).
[CrossRef] [PubMed]

A. E. Serebryannikov, K. B. Alici, T. Magath, A. O. Cakmak, E. Ozbay, “Asymmetric Fabry-Perot-type transmission in photonic-crystal gratings with one-sided corrugations at a two-way coupling,” Phys. Rev. A 86(5), 053835 (2012).
[CrossRef]

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

T. Magath, 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]

Seung, H. M.

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

Sigalas, M. M.

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, K. M. Ho, “Electromagnetic-wave propagation through dispersive and absorptive photonic-band-gap materials,” Phys. Rev. B Condens. Matter 49(16), 11080–11087 (1994).
[CrossRef] [PubMed]

Silveirinha, M. G.

A. Alù, M. G. Silveirinha, A. Salandrino, N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[CrossRef]

Singh, R.

R. Singh, E. Plum, C. Menzel, C. Rockstuhl, A. K. Azad, R. A. Cheville, F. Lederer, W. Zhang, 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-Cia, 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.

S. Foteinopoulou, M. Kafesaki, E. N. Economou, C. M. Soukoulis, “Two-dimensional polaritonic photonic crystals as terahertz uniaxial metamaterials,” Phys. Rev. B 84(3), 035128 (2011).
[CrossRef]

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, K. M. Ho, “Electromagnetic-wave propagation through dispersive and absorptive photonic-band-gap materials,” Phys. Rev. B Condens. Matter 49(16), 11080–11087 (1994).
[CrossRef] [PubMed]

Stolarek, M.

Szoplik, T.

Tan, W.

X.-B. Kang, W. Tan, Z.-S. Wang, Z.-G. Wang, H. Cheng, “High-efficiency one-way transmission by one-dimensional photonic crystal with gratings on one side,” Chin. Phys. Lett. 27(7), 074204 (2010).
[CrossRef]

Tikhodeev, S. G.

A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, S. G. Tikhodeev, T. Fujita, T. Ishihara, “Polariton effect in distributed feedback microcavities,” J. Phys. Soc. Jpn. 70(4), 1137–1144 (2001).
[CrossRef]

Torres, V.

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

Ulug, B.

Vanwolleghem, M.

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

Vasylchenko, O. Y.

A. E. Serebryannikov, T. Magath, K. Schuenemann, 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]

Wang, C.

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

Wang, Z.-G.

X.-B. Kang, W. Tan, Z.-S. Wang, Z.-G. Wang, H. Cheng, “High-efficiency one-way transmission by one-dimensional photonic crystal with gratings on one side,” Chin. Phys. Lett. 27(7), 074204 (2010).
[CrossRef]

Wang, Z.-S.

X.-B. Kang, W. Tan, Z.-S. Wang, Z.-G. Wang, H. Cheng, “High-efficiency one-way transmission by one-dimensional photonic crystal with gratings on one side,” Chin. Phys. Lett. 27(7), 074204 (2010).
[CrossRef]

White, K. R.

M. J. Lockyear, A. P. Hibbins, K. R. White, J. R. Sambles, “One-way diffraction grating,” Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 74(5), 056611 (2006).
[CrossRef] [PubMed]

Xu, S.

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

Yablonskii, A. L.

A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, S. G. Tikhodeev, T. Fujita, T. Ishihara, “Polariton effect in distributed feedback microcavities,” J. Phys. Soc. Jpn. 70(4), 1137–1144 (2001).
[CrossRef]

Yavorskiy, D.

Ye, W.-M.

Yu, Z.

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

Yuan, X.-D.

Yucel, M. B.

Zapata Rodríguez, C. J.

Zen, C.

Zhang, W.

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

Zheludev, N. I.

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

Zhong, X.-L.

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

Ziolkowski, R. W.

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

Appl. Phys. Lett.

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

K. C. Huang, M. L. Povinelli, J. D. Joannopoulos, “Negative effective permeability in polaritonic photonic crystals,” Appl. Phys. Lett. 85(4), 543–545 (2004).
[CrossRef]

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

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

Chin. Phys. Lett.

X.-B. Kang, W. Tan, Z.-S. Wang, Z.-G. Wang, H. Cheng, “High-efficiency one-way transmission by one-dimensional photonic crystal with gratings on one side,” Chin. Phys. Lett. 27(7), 074204 (2010).
[CrossRef]

J. Appl. Phys.

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

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

J. Phys. Soc. Jpn.

A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, S. G. Tikhodeev, T. Fujita, T. Ishihara, “Polariton effect in distributed feedback microcavities,” J. Phys. Soc. Jpn. 70(4), 1137–1144 (2001).
[CrossRef]

Nat. Photonics

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

Opt. Express

Opt. Lett.

Phys. Rev. A

A. E. Serebryannikov, E. Ozbay, “One-way Rayleigh-Wood anomalies and tunable narrowband transmission in photonic crystal gratings with broken structural symmetry,” Phys. Rev. A 87(5), 053804 (2013).
[CrossRef]

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Phys. Rev. B

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Figures (12)

Fig. 1
Fig. 1

(a) Typical frequency dependence of permittivity of a polar dielectric ε P at γ = 0 and schematics of (b) two-layer and (c) single-layer nonsymmetric gratings containing polar dielectrics; for two- and single-layer gratings, D is the maximal thickness and L is grating period; for two-layer grating, h is thickness of the non-dispersive dielectric layer.

Fig. 2
Fig. 2

T and t m vs k L for configurations (a) A and (b) B, and (c) C T vs k L , at ω T L / c = 1.5 π and θ = 60 ° ; (a) and (b): t m at m = 1 - red dashed line, m = 2 - green dotted line, m = 3 - blue dash-dotted line, m = 4 - black dashed line, and T - cyan dotted line; (c): C T for configurations A and B is shown by dark-green solid line and violet dashed line, respectively; gray rectangles - locations of the unidirectional transmission ranges.

Fig. 3
Fig. 3

T and t m vs k L for configurations (a,d) A and (b,e) B, and (c,f) C T vs k L , at ω T L / c = 1.5 π , (a-c) θ = 47 ° and (d-f) θ = 40 ° ; (a), (b), (d), (e): t m at m = 0 - gray solid line, m = 1 - red dashed line, m = 2 - green dotted line, m = 3 - blue dash-dotted line, m = 4 - black dashed line, and T - cyan dotted line; (c,f): C T for configurations A and B is shown by dark-green solid line and violet dashed line, respectively; gray rectangles - unidirectional transmission ranges.

Fig. 4
Fig. 4

T and t m vs k L for configurations (a) A and (b) B at ω T L / c = 1.1 π and θ = 60 ° ; t m at m = 0 - gray solid line, m = 1 - red dashed line, m = 2 - green dotted line, m = 3 - blue dash-dotted line, m = 4 - black dashed line, and T - cyan dotted line; gray rectangles - unidirectional transmission ranges.

Fig. 5
Fig. 5

T and t m for configurations (a) A and (b) B, and (c) T and t m for configuration B at ω T L / c = 1.1 π and θ = 40 ° ; t m and t m at m = 0 - gray solid line, m = 1 - red dashed line, m = 2 - green dotted line, m = 3 - blue dash-dotted line, m = 4 - black dashed line, T and T - cyan dotted line; gray rectangles - unidirectional transmission ranges.

Fig. 6
Fig. 6

Same as Fig. 2 but for ω T L / c = 0.7 π ; (a,b) gray solid line - t 0 .

Fig. 7
Fig. 7

T and t m for configuration (a) A at θ = 40 ° , (b) configuration B at θ = 40 ° , and (c) configuration A at θ = 47 ° , when ω T L / c = 0.7 π ; t m at m = 0 - gray solid line, m = 1 - red dashed line, m = 2 - green dotted line, m = 3 - blue dash-dotted line, and T - cyan dotted line; gray rectangles - unidirectional transmission ranges.

Fig. 8
Fig. 8

R and r m (a) and R and r m (b) vs k L for configuration B at ω T L / c = 0.7 π and θ = 40 ° ; r m and r m at m = 0 - gray solid line, m = 1 - red dashed line, m = 2 - green dotted line, m = 3 - blue dash-dotted line, R and R - cyan dotted line; (b): t 0 and T are shown by thin gray solid line and thin cyan dotted line, respectively.

Fig. 9
Fig. 9

T and t m (a) and T and t m (b) for configuration A at ω T L / c = 0.4 π and θ = 60 ° , and same other parameters and notations as in Fig. 5.

Fig. 10
Fig. 10

T and t m (a) and T and t m (b) vs k L for a similar configuration as A but with the ultralow- ε layer made of NaCl, at ω T L / c = 2 π and θ = 60 ° ; t m and t m at m = 0 - gray solid line, m = 1 - red dashed line, m = 2 - green dotted line, m = 3 - blue dash-dotted line, m = 4 - black dashed line; T and T - cyan dotted line; gray rectangle - unidirectional transmission range.

Fig. 11
Fig. 11

T and t m vs k L for configuration A (a), T and t m for configuration A (b), and C T for configurations A and B (c), at ω T L / c = 1.5 π and θ = 0 ; (a) and (b): t m and t m at m = 0 - gray solid line, m = ± 1 - red dashed line, m = ± 2 - green dotted line, m = ± 3 - blue dash-dotted line, and T and T - cyan dotted line; (c): C T for configurations A and B is shown by dark-green solid line and violet dashed line, respectively; asterisks indicate the cases of C T < 20 d B .

Fig. 12
Fig. 12

T and t m (a), T and t m (b), and C T (c) vs k L , for configuration that is similar to B but made of GaAs, at ω T L / c = 2 π and θ = 0 ; (a) and (b): t m and t m at m = 0 - gray solid line, m = ± 1 - red dashed line, and T and T - cyan dotted line; (c): asterisk indicates the case of C T < 20 d B .

Tables (1)

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Table 1 Comparison of Various Polar Dielectrics in Terms of Characteristics Responsible for the Relative Width of Unidirectional Transmission Range

Equations (7)

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ε P ( ω ) = ε + ( ε 0 ε ) ω T 2 / ( ω T 2 ω 2 i γ ω ) ,
ω L 2 / ω T 2 = ε 0 / ε .
ω u 2 =( A ε ω L 2 ω T 2 )/( A ε 1 ).
Δω= ω u ω L .
ζ = Δ ω / ω L = [ ( A ε ω T 2 / ω L 2 ) / ( A ε 1 ) ] 1 / 2 1.
ε P 1/2 +1>2π/(kL),
k L = k m L = 2 π | m | / ( 1 sgn m sin θ ) .

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