Abstract

Unidirectional transmission is studied theoretically and experimentally for the gratings with one-side corrugations (non-symmetric gratings), which are based on two-dimensional photonic crystals composed of alumina rods. The unidirectional transmission appears at a fixed angle of incidence as a combined effect of the peculiar dispersion features of the photonic crystal and the properly designed corrugations. It is shown that the basic unidirectional transmission characteristics, which are observed at a plane-wave illumination, are preserved at Gaussian-beam and horn antenna illuminations. The main attention is paid to the single-beam unidirectional regime, which is associated with the strong directional selectivity arising due to the first negative diffraction order. An additional degree of freedom for controlling the transmission of the electromagnetic waves is obtained by making use of the asymmetric corrugations at the photonic crystal interface.

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2010 (2)

2009 (4)

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]

2007 (2)

Z. Yu, Z. Wang, and S. Fan, “One-way total reflection with one-dimensional magneto-optical photonic crystals,” Appl. Phys. Lett. 90(12), 121133 (2007).
[CrossRef]

N. Bonod, E. Popov, L. Li, and B. Chernov, “Unidirectional excitation of surface plasmons by slanted gratings,” Opt. Express 15(18), 11427–11432 (2007).
[CrossRef] [PubMed]

2006 (2)

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

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

2005 (1)

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]

2003 (2)

A. Figotin and I. Vitebskiy, “Electromagnetic unidirectionality in magnetic photonic crystals,” Phys. Rev. B 67(16), 165210 (2003).
[CrossRef]

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

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]

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 (1994).
[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 (1994).
[CrossRef]

Boltasseva, A.

Bonod, N.

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 (1994).
[CrossRef]

Bozhevolnyi, S. I.

Brucoli, G.

Caglayan, H.

Cakmakyapan, S.

Chernov, B.

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]

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 (1994).
[CrossRef]

Fan, S.

Z. Yu, Z. Wang, and S. Fan, “One-way total reflection with one-dimensional magneto-optical photonic crystals,” Appl. Phys. Lett. 90(12), 121133 (2007).
[CrossRef]

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]

A. Figotin and I. Vitebskiy, “Electromagnetic unidirectionality in magnetic photonic crystals,” Phys. Rev. B 67(16), 165210 (2003).
[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]

García-Vidal, F. J.

Guo, C.-C.

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]

Hibbins, A. P.

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

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]

Li, L.

Lockyear, M. J.

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

Luo, C.

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]

Martín-Moreno, L.

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]

Ozbay, E.

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]

Piestun, R.

Popov, E.

Radko, I. P.

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]

Sambles, J. R.

M. J. Lockyear, A. P. Hibbins, K. R. White, and J. R. Sambles, “One-way diffraction grating,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(5), 056611 (2006).
[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 (1994).
[CrossRef]

Schwartz, B. T.

Serebryannikov, A. E.

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]

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]

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]

A. Figotin and I. Vitebskiy, “Electromagnetic unidirectionality in magnetic photonic crystals,” Phys. Rev. B 67(16), 165210 (2003).
[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]

Z. Yu, Z. Wang, and S. Fan, “One-way total reflection with one-dimensional magneto-optical photonic crystals,” Appl. Phys. Lett. 90(12), 121133 (2007).
[CrossRef]

White, K. R.

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

Ye, W.-M.

Yu, Z.

Z. Yu, Z. Wang, and S. Fan, “One-way total reflection with one-dimensional magneto-optical photonic crystals,” Appl. Phys. Lett. 90(12), 121133 (2007).
[CrossRef]

Yuan, X.-D.

Zen, C.

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]

Appl. Phys. Lett. (1)

Z. Yu, Z. Wang, and S. Fan, “One-way total reflection with one-dimensional magneto-optical photonic crystals,” Appl. Phys. Lett. 90(12), 121133 (2007).
[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 (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. B (1)

Opt. Express (5)

Opt. Lett. (1)

Phys. Rev. B (4)

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]

A. Figotin and I. Vitebskiy, “Electromagnetic unidirectionality in magnetic photonic crystals,” Phys. Rev. B 67(16), 165210 (2003).
[CrossRef]

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

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

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

Phys. Rev. Lett. (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]

Other (1)

R. Petit, Electromagnetic theory of gratings (Springer, Berlin, 1980).

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Figures (16)

Fig. 1
Fig. 1

The geometry of the PC grating under study (two lateral periods are shown) – illustrations (a)-(d) and the schematic of the experimental setup – illustration (e). NA stands for the Network Analyzer, W represents the aperture size of the horn antenna.

Fig. 2
Fig. 2

The transmittance for the cases shown in Fig. 1(a) – plot (a) and Fig. 1(b) – plot (b); solid blue line – zero order, dashed thicker red line – first negative order, dotted green line – second negative order, solid wine-colored line – first positive order; θ = 30ο.

Fig. 3
Fig. 3

Same as in Fig. 2 but for the cases shown in Fig. 1(c) – plot (a), and Fig. 1(d) – plot (b).

Fig. 4
Fig. 4

IFCs of the PC on the (kx ,ky )-plane in the vicinity of kL = 8.3 – plot (a), and in the vicinity of kL = 11.4 – plot (b). The numbers of the PC bands (Floquet-Bloch wave numbers start from 0) are shown in the boxes. Thin arrows show the possible directions of the gradients that indicate the directions of the group velocity, v g. The air IFCs (green circles), the construction lines (vertical dashed lines), the wave vectors of the diffraction orders, k0 and k-1 (intermediately thick arrows) and the directions of v g (thick arrows) correspond to kL = 8.13 in plot (a) and kL = 11.03 in plot (b). The vectors k0 and k-1 and the directions of v g are shown here at θ = 30° and at the illumination direction depicted in Figs. 1(a) and 1(c). The dotted lines show the ranges of k0, where the unidirectional transmission is expected to appear.

Fig. 13
Fig. 13

The integral transmittance in the kL range, which includes the range C: plot (a) corresponds to Figs. 1(a) and 1(b), plot (b) corresponds to Figs. 1(c) and 1(d); R i = 25cm.

Fig. 7
Fig. 7

Angular dependence of the transmittance at a frequency value from the range A: plot (a) corresponds to Figs. 1(a) and 1(b), plot (b) corresponds to Figs. 1(c) and 1(d); blue line – the non-corrugated interface is illuminated, red line – the corrugated interface is illuminated; R i = 20cm; θ = 30ο.

Fig. 5
Fig. 5

The integral transmittance at the Gaussian-beam illumination: left plot corresponds to Figs. 1(a) and 1(b), right plot corresponds to Figs. 1(c) and 1(d); solid blue line - the illumination is from the non-corrugated interface (Lower), red line – the illumination is from the corrugated interface (Upper); θ = 30°.

Fig. 6
Fig. 6

Transmittance (in logarithmic scale) at the Gaussian-beam illumination on (kL,Φ)-plane: plots (a), (b), (c) and (d) correspond to Figs. 1(a), 1(b), 1(c) and 1(d), respectively; θ = 30ο.

Fig. 8
Fig. 8

Same as Fig. 7 but for a frequency value taken from the range C.

Fig. 9
Fig. 9

Same as Fig. 7 but for a frequency value taken from the range B.

Fig. 10
Fig. 10

The measured transmittance (in arbitrary units, in logarithmic scale) on the (kL,Φ)-plane for the range A in the upper case as in Fig. 1(a) – plot (a), for the range A in the lower case in Fig. 1(b) – plot (b), for the range C in the upper case as in Fig. 1(a) – plot (c), and for the range C in the lower case as in Fig. 1(b) – plot (d); R i = 25cm.

Fig. 11
Fig. 11

The measured transmittance (in arbitrary units, in logarithmic scale) on the (kL,Φ)-plane for the range C in the upper case as in Fig. 1(c) – plot (a), and for the range C in the lower case as in Fig. 1(d) – plot (b); R i = 25cm.

Fig. 12
Fig. 12

Same as Fig. 10 but for R i = 60cm.

Fig. 14
Fig. 14

The measured angular distribution of the transmittance for a kL value taken from the range C: plot (a) corresponds to Figs. 1(a) and 1(b), plot (b) corresponds to Figs. 1(c) and 1(d); R i = 25cm.

Fig. 15
Fig. 15

Same as Fig. 14 but for R i = 60cm.

Fig. 16
Fig. 16

The measured angular distribution of the transmittance for kL values taken from the range A – plot (a), and range B – plot (b); plot (a) and left panel of plot (b) correspond to Figs. 1(a) and 1(b), right panel in plot (b) corresponds to Figs. 1(c) and 1(d); R i = 60cm.

Equations (4)

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

T = M N t n ,
k min ( 2 ) > k > k max ( 1 ) ,
τ = 1 π 0 π T ( Φ ) d Φ ,   and   τ = 1 π 0 π T ( Φ ) d Φ .
ϕ n = sin 1 ( sin θ + 2 π n / k L ) .

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