Abstract

We studied the specular and nonspecular remittances and the absorptance of two-dimensional photonic crystals (PCs) comprising a periodic array of dielectric rods immersed in a coherent atomic gas (CAG). Illumination by obliquely incident, s-polarized plane waves was considered. Minipassbands that may include peaks of nearly complete transmission appear within the stop bands of the corresponding gas-free PCs, due to the strong frequency dispersion in the relative permittivity of the CAG. As a result, high-efficiency passbands of a gas-free PC and those arising due to the CAG can coexist. The latter can be tuned in a simpler way than by varying the constitutive parameters of the CAG, i.e., via variation of the incidence angle. In contrast with the earlier studied metallic PCs immersed in a CAG, new passbands may also appear when the CAG behaves as a medium with ultralow positive permittivity. Also, complete absorptance bands (with zero overall reflectance and overall transmittance) can be obtained, which are well correlated with the frequency-dependent characteristics of the CAG.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  38. Two such absorption bands like those in Fig. 8 can also be obtained for another choice of ω1a/c, e.g., at ω1a/c=2.625 when A peaks at almost unity for ka=2.62495 and ka=2.62504.

2011

M. Faryad and A. Lakhtakia, “Propagation of surface waves and waveguide modes guided by a dielectric slab inserted in a sculptured nematic thin film,” Phys. Rev. A 83, 013814 (2011).
[CrossRef]

2010

2009

H. Wang, Z. Zhou, H. Tian, and Y. Pei, “Tunable Goos–Hänchen shift in a prism-waveguide coupling system with a nematic liquid crystal slab,” J. Phys. D: Appl. Phys. 42, 175301 (2009).
[CrossRef]

H. Chen, C. T. Chan, S. Liu, and Z. Lin, “A simple route to a tunable electromagnetic gateway,” New J. Phys. 11, 083012 (2009).
[CrossRef]

W. Park and J.-B. Lee, “Mechanically tunable photonic crystals,” Opt. Photon. News 20(1), 40–45 (2009).
[CrossRef]

F. Wang and A. Lakhtakia, “Magnetically controllable intra-Brillouin-zone band gaps in one-dimensional helicoidal magnetophotonic crystals,” Phys. Rev. B 79, 193102 (2009).
[CrossRef]

J. Han, A. Lakhtakia, Z. Tian, X. Lu, and W. Zhang, “Magnetic and magnetothermal tunabilities of subwavelength-hole arrays in a semiconductor sheet,” Opt. Lett. 34, 1465–1467 (2009).
[CrossRef]

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

2008

2007

A. E. Serebryannikov and T. Magath, “Controlling location of opaque ranges in transmission of metallic photonic crystals,” Phys. Rev. A 76, 033828 (2007).
[CrossRef]

F. Glöckler, S. Peters, U. Lemmer, and M. Gerken, “Tunable superprism effect in photonic crystals,” Phys. Stat. Sol. A 204, 3790–3804 (2007).
[CrossRef]

J. Li, M.-H. Lu, L. Feng, X.-P. Liu, and Y.-F. Chen, “Tunable negative refraction based on the Pockels effect in two-dimensional photonic crystals composed of electro-optic crystals,” J. Appl. Phys. 101, 013516 (2007).
[CrossRef]

P. Jiang, C. Ding, X. Hu, and Q. Gong, “Tunable double-channel filter based on two-dimensional ferroelectric photonic crystals,” Phys. Lett. A 363, 332–336 (2007).
[CrossRef]

L. Kang, Q. Zhao, B. Li, J. Zhou, and H. Zhu, “Experimental verification of a tunable optical negative refraction in nematic liquid crystals,” Appl. Phys. Lett. 90, 181931 (2007).
[CrossRef]

2006

2005

J. Khurgin, “Optical buffers based on slow light in electromagnetically induced transparent media and coupled resonator structures: comparative analysis,” J. Opt. Soc. Am. B 22, 1062–1074 (2005).
[CrossRef]

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

M. Schmidt, M. Eich, U. Huebner, and R. Boucher, “Electro-optically tunable photonic crystals,” Appl. Phys. Lett. 87, 121110 (2005).
[CrossRef]

D. McPhail, M. Straub, and M. Gu, “Electrical tuning of three-dimensional photonic crystals using polymer dispersed liquid crystals,” Appl. Phys. Lett. 86, 051103 (2005).
[CrossRef]

E. P. Kosmidou, E. E. Kriezis, and T. D. Tsiboukis, “Analysis of tunable photonic crystal devices comprising liquid crystal materials as defects,” IEEE J. Quantum Electron. 41, 657–665 (2005).
[CrossRef]

2003

C. Xu, X. Hu, Z. Li, X. Liu, R. Fu, and J. Zi, “Semiconductor-based tunable photonic crystals by means of an external magnetic field,” Phys. Rev. B 68, 193201 (2003).
[CrossRef]

F. Wang, A. Lakhtakia, and R. Messier, “On piezoelectric control of the optical response of sculptured thin films,” J. Mod. Opt. 50, 239–249 (2003).
[CrossRef]

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

2001

A. Sakai, G. Hara, and T. Baba, “Propagation characteristics of ultrathin-Δ optical waveguide on silicon-on-insulator substrate,” Jpn. J. Appl. Phys. 40, L383–L385 (2001).
[CrossRef]

2000

A. V. Tarasishin, S. A. Magnitskii, V. A. Shuvaev, and A. M. Zheltikov, “Constructing a light-field distribution for the laser guiding of atoms in photonic crystals,” Opt. Commun. 184, 391–396 (2000).
[CrossRef]

1999

K. Busch and S. John, “Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum,” Phys. Rev. Lett. 83, 967–970 (1999).
[CrossRef]

1998

A. Figotin, Y. A. Godin, and I. Vitebsky, “Two-dimensional tunable photonic crystals,” Phys. Rev. B 57, 2841–2848(1998).
[CrossRef]

J. P. Marangos, “Electromagnetically induced transparency,” J. Mod. Opt. 45, 471–503 (1998).
[CrossRef]

1996

A. A. Krokhin and P. Halevi, “Influence of weak dissipation on the photonic band structure of periodic composites,” Phys. Rev. B 53, 1205–1214 (1996).
[CrossRef]

1991

K. J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef]

1990

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[CrossRef]

Alagappan, G.

Baba, T.

A. Sakai, G. Hara, and T. Baba, “Propagation characteristics of ultrathin-Δ optical waveguide on silicon-on-insulator substrate,” Jpn. J. Appl. Phys. 40, L383–L385 (2001).
[CrossRef]

Baida, F. I.

M. Roussey, M.-P. Bernal, N. Courjal, D. Van Labeke, F. I. Baida, and R. Salut, “Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons,” Appl. Phys. Lett. 89, 241110 (2006).
[CrossRef]

Bernal, M.-P.

M. Roussey, M.-P. Bernal, N. Courjal, D. Van Labeke, F. I. Baida, and R. Salut, “Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons,” Appl. Phys. Lett. 89, 241110 (2006).
[CrossRef]

Boller, K. J.

K. J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef]

Boucher, R.

M. Schmidt, M. Eich, U. Huebner, and R. Boucher, “Electro-optically tunable photonic crystals,” Appl. Phys. Lett. 87, 121110 (2005).
[CrossRef]

Busch, K.

K. Busch and S. John, “Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum,” Phys. Rev. Lett. 83, 967–970 (1999).
[CrossRef]

Chakrabarti, S.

Chan, C. T.

H. Chen, C. T. Chan, S. Liu, and Z. Lin, “A simple route to a tunable electromagnetic gateway,” New J. Phys. 11, 083012 (2009).
[CrossRef]

Chen, H.

H. Chen, C. T. Chan, S. Liu, and Z. Lin, “A simple route to a tunable electromagnetic gateway,” New J. Phys. 11, 083012 (2009).
[CrossRef]

Chen, Y.-F.

J. Li, M.-H. Lu, L. Feng, X.-P. Liu, and Y.-F. Chen, “Tunable negative refraction based on the Pockels effect in two-dimensional photonic crystals composed of electro-optic crystals,” J. Appl. Phys. 101, 013516 (2007).
[CrossRef]

Courjal, N.

M. Roussey, M.-P. Bernal, N. Courjal, D. Van Labeke, F. I. Baida, and R. Salut, “Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons,” Appl. Phys. Lett. 89, 241110 (2006).
[CrossRef]

Ding, C.

P. Jiang, C. Ding, X. Hu, and Q. Gong, “Tunable double-channel filter based on two-dimensional ferroelectric photonic crystals,” Phys. Lett. A 363, 332–336 (2007).
[CrossRef]

Doan, M. T.

Eich, M.

M. Schmidt, M. Eich, U. Huebner, and R. Boucher, “Electro-optically tunable photonic crystals,” Appl. Phys. Lett. 87, 121110 (2005).
[CrossRef]

Faryad, M.

M. Faryad and A. Lakhtakia, “Propagation of surface waves and waveguide modes guided by a dielectric slab inserted in a sculptured nematic thin film,” Phys. Rev. A 83, 013814 (2011).
[CrossRef]

Feng, L.

J. Li, M.-H. Lu, L. Feng, X.-P. Liu, and Y.-F. Chen, “Tunable negative refraction based on the Pockels effect in two-dimensional photonic crystals composed of electro-optic crystals,” J. Appl. Phys. 101, 013516 (2007).
[CrossRef]

Field, J. E.

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[CrossRef]

Figotin, A.

A. Figotin, Y. A. Godin, and I. Vitebsky, “Two-dimensional tunable photonic crystals,” Phys. Rev. B 57, 2841–2848(1998).
[CrossRef]

Fu, R.

C. Xu, X. Hu, Z. Li, X. Liu, R. Fu, and J. Zi, “Semiconductor-based tunable photonic crystals by means of an external magnetic field,” Phys. Rev. B 68, 193201 (2003).
[CrossRef]

Gao, J.

Gerken, M.

F. Glöckler, S. Peters, U. Lemmer, and M. Gerken, “Tunable superprism effect in photonic crystals,” Phys. Stat. Sol. A 204, 3790–3804 (2007).
[CrossRef]

Glöckler, F.

F. Glöckler, S. Peters, U. Lemmer, and M. Gerken, “Tunable superprism effect in photonic crystals,” Phys. Stat. Sol. A 204, 3790–3804 (2007).
[CrossRef]

Godin, Y. A.

A. Figotin, Y. A. Godin, and I. Vitebsky, “Two-dimensional tunable photonic crystals,” Phys. Rev. B 57, 2841–2848(1998).
[CrossRef]

Gong, Q.

P. Jiang, C. Ding, X. Hu, and Q. Gong, “Tunable double-channel filter based on two-dimensional ferroelectric photonic crystals,” Phys. Lett. A 363, 332–336 (2007).
[CrossRef]

Gu, M.

D. McPhail, M. Straub, and M. Gu, “Electrical tuning of three-dimensional photonic crystals using polymer dispersed liquid crystals,” Appl. Phys. Lett. 86, 051103 (2005).
[CrossRef]

Halevi, P.

A. A. Krokhin and P. Halevi, “Influence of weak dissipation on the photonic band structure of periodic composites,” Phys. Rev. B 53, 1205–1214 (1996).
[CrossRef]

Han, J.

Hara, G.

A. Sakai, G. Hara, and T. Baba, “Propagation characteristics of ultrathin-Δ optical waveguide on silicon-on-insulator substrate,” Jpn. J. Appl. Phys. 40, L383–L385 (2001).
[CrossRef]

Harris, S. E.

K. J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef]

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[CrossRef]

He, Q.

Hu, X.

P. Jiang, C. Ding, X. Hu, and Q. Gong, “Tunable double-channel filter based on two-dimensional ferroelectric photonic crystals,” Phys. Lett. A 363, 332–336 (2007).
[CrossRef]

C. Xu, X. Hu, Z. Li, X. Liu, R. Fu, and J. Zi, “Semiconductor-based tunable photonic crystals by means of an external magnetic field,” Phys. Rev. B 68, 193201 (2003).
[CrossRef]

Huebner, U.

M. Schmidt, M. Eich, U. Huebner, and R. Boucher, “Electro-optically tunable photonic crystals,” Appl. Phys. Lett. 87, 121110 (2005).
[CrossRef]

Imamoglu, A.

K. J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef]

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[CrossRef]

Jiang, P.

P. Jiang, C. Ding, X. Hu, and Q. Gong, “Tunable double-channel filter based on two-dimensional ferroelectric photonic crystals,” Phys. Lett. A 363, 332–336 (2007).
[CrossRef]

John, S.

K. Busch and S. John, “Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum,” Phys. Rev. Lett. 83, 967–970 (1999).
[CrossRef]

Kang, L.

L. Kang, Q. Zhao, B. Li, J. Zhou, and H. Zhu, “Experimental verification of a tunable optical negative refraction in nematic liquid crystals,” Appl. Phys. Lett. 90, 181931 (2007).
[CrossRef]

Khurgin, J.

Kosmidou, E. P.

E. P. Kosmidou, E. E. Kriezis, and T. D. Tsiboukis, “Analysis of tunable photonic crystal devices comprising liquid crystal materials as defects,” IEEE J. Quantum Electron. 41, 657–665 (2005).
[CrossRef]

Kriezis, E. E.

E. P. Kosmidou, E. E. Kriezis, and T. D. Tsiboukis, “Analysis of tunable photonic crystal devices comprising liquid crystal materials as defects,” IEEE J. Quantum Electron. 41, 657–665 (2005).
[CrossRef]

Krokhin, A. A.

A. A. Krokhin and P. Halevi, “Influence of weak dissipation on the photonic band structure of periodic composites,” Phys. Rev. B 53, 1205–1214 (1996).
[CrossRef]

Lakhtakia, A.

M. Faryad and A. Lakhtakia, “Propagation of surface waves and waveguide modes guided by a dielectric slab inserted in a sculptured nematic thin film,” Phys. Rev. A 83, 013814 (2011).
[CrossRef]

A. E. Serebryannikov and A. Lakhtakia, “Transmission through a metallic photonic crystal immersed in a coherent atomic gas,” J. Opt. Soc. Am. B 27, 2151–2158 (2010).
[CrossRef]

F. Wang and A. Lakhtakia, “Magnetically controllable intra-Brillouin-zone band gaps in one-dimensional helicoidal magnetophotonic crystals,” Phys. Rev. B 79, 193102 (2009).
[CrossRef]

J. Han, A. Lakhtakia, Z. Tian, X. Lu, and W. Zhang, “Magnetic and magnetothermal tunabilities of subwavelength-hole arrays in a semiconductor sheet,” Opt. Lett. 34, 1465–1467 (2009).
[CrossRef]

F. Wang, A. Lakhtakia, and R. Messier, “On piezoelectric control of the optical response of sculptured thin films,” J. Mod. Opt. 50, 239–249 (2003).
[CrossRef]

Lee, J.-B.

W. Park and J.-B. Lee, “Mechanically tunable photonic crystals,” Opt. Photon. News 20(1), 40–45 (2009).
[CrossRef]

Lemmer, U.

F. Glöckler, S. Peters, U. Lemmer, and M. Gerken, “Tunable superprism effect in photonic crystals,” Phys. Stat. Sol. A 204, 3790–3804 (2007).
[CrossRef]

Li, B.

L. Kang, Q. Zhao, B. Li, J. Zhou, and H. Zhu, “Experimental verification of a tunable optical negative refraction in nematic liquid crystals,” Appl. Phys. Lett. 90, 181931 (2007).
[CrossRef]

Li, J.

J. Li, M.-H. Lu, L. Feng, X.-P. Liu, and Y.-F. Chen, “Tunable negative refraction based on the Pockels effect in two-dimensional photonic crystals composed of electro-optic crystals,” J. Appl. Phys. 101, 013516 (2007).
[CrossRef]

Li, Z.

C. Xu, X. Hu, Z. Li, X. Liu, R. Fu, and J. Zi, “Semiconductor-based tunable photonic crystals by means of an external magnetic field,” Phys. Rev. B 68, 193201 (2003).
[CrossRef]

Lin, Z.

H. Chen, C. T. Chan, S. Liu, and Z. Lin, “A simple route to a tunable electromagnetic gateway,” New J. Phys. 11, 083012 (2009).
[CrossRef]

Liu, S.

H. Chen, C. T. Chan, S. Liu, and Z. Lin, “A simple route to a tunable electromagnetic gateway,” New J. Phys. 11, 083012 (2009).
[CrossRef]

Liu, X.

C. Xu, X. Hu, Z. Li, X. Liu, R. Fu, and J. Zi, “Semiconductor-based tunable photonic crystals by means of an external magnetic field,” Phys. Rev. B 68, 193201 (2003).
[CrossRef]

Liu, X.-P.

J. Li, M.-H. Lu, L. Feng, X.-P. Liu, and Y.-F. Chen, “Tunable negative refraction based on the Pockels effect in two-dimensional photonic crystals composed of electro-optic crystals,” J. Appl. Phys. 101, 013516 (2007).
[CrossRef]

Lu, M.-H.

J. Li, M.-H. Lu, L. Feng, X.-P. Liu, and Y.-F. Chen, “Tunable negative refraction based on the Pockels effect in two-dimensional photonic crystals composed of electro-optic crystals,” J. Appl. Phys. 101, 013516 (2007).
[CrossRef]

Lu, X.

Magath, T.

A. E. Serebryannikov and T. Magath, “Controlling location of opaque ranges in transmission of metallic photonic crystals,” Phys. Rev. A 76, 033828 (2007).
[CrossRef]

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

Magnitskii, S. A.

A. V. Tarasishin, S. A. Magnitskii, V. A. Shuvaev, and A. M. Zheltikov, “Constructing a light-field distribution for the laser guiding of atoms in photonic crystals,” Opt. Commun. 184, 391–396 (2000).
[CrossRef]

Marangos, J. P.

J. P. Marangos, “Electromagnetically induced transparency,” J. Mod. Opt. 45, 471–503 (1998).
[CrossRef]

McPhail, D.

D. McPhail, M. Straub, and M. Gu, “Electrical tuning of three-dimensional photonic crystals using polymer dispersed liquid crystals,” Appl. Phys. Lett. 86, 051103 (2005).
[CrossRef]

Messier, R.

F. Wang, A. Lakhtakia, and R. Messier, “On piezoelectric control of the optical response of sculptured thin films,” J. Mod. Opt. 50, 239–249 (2003).
[CrossRef]

Ozbay, E.

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

L. Kang, Q. Zhao, B. Li, J. Zhou, and H. Zhu, “Experimental verification of a tunable optical negative refraction in nematic liquid crystals,” Appl. Phys. Lett. 90, 181931 (2007).
[CrossRef]

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Two such absorption bands like those in Fig. 8 can also be obtained for another choice of ω1a/c, e.g., at ω1a/c=2.625 when A peaks at almost unity for ka=2.62495 and ka=2.62504.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997), Sec. 7.3.

We thank the authors of Ref. [20] for supplying us with typical data on helium used in this paper.

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Figures (13)

Fig. 1.
Fig. 1.

Schematic of the boundary-value problem considered here. The CAG-filled PC is obliquely illuminated by an s-polarized plane wave. The 2D PC comprises parallel, infinitely long dielectric rods immersed in a CAG occupying the region 0 < y < D .

Fig. 2.
Fig. 2.

Spectra of the real (purple solid curve) and imaginary (green dashed curve) parts of the relative permittivity ε h of the CAG when Ω c = 2 π × 10 10 s 1 , κ = 5 π × 10 10 s 1 , ω 1 = 5.54 π × 10 14 s 1 , Γ = 2 π × 10 9 s 1 , and ω 1 a / c = 2.58 .

Fig. 3.
Fig. 3.

Spectra of T of a CAG-free PC with P = 5 , d / a = 0.4 , and ε r = 11.4 , when (a)  θ = 0 and (b)  θ = 30 ° . The first, second, and third stop bands are denoted by “1,” “2,” and “3,” respectively. Arrows indicate the k a -regimes to which the CAG resonance regime will be matched.

Fig. 4.
Fig. 4.

Spectra of T (black solid curve), R (red dashed curve), and A (blue dotted curve) of a CAG-filled PC with P = 5 , d / a = 0.4 , and ε r = 11.4 when θ = 0 . The CAG parameters are the same as in Fig. 2. The minipassbands due to the CAG are denoted by “1” and “2.” The maxima of T in minipassband 1 are denoted by “A,” “B,” and “C.”

Fig. 5.
Fig. 5.

Spatial profiles of the electric field intensity at 0 < y < D within a period over x at the maxima of T marked “A” (left) and “B” (right) in Fig. 4.

Fig. 6.
Fig. 6.

Magnified fragment of Fig. 4 showing the second minipassband in detail.

Fig. 7.
Fig. 7.

Angular dependences of T (black solid curve), R (red dashed curve), and A (blue dotted curve) at k a = 2.579 . The remaining quantities are the same as for Figs. 2 and 4. Let us note that although Re ( ε h ) = 1.23 is not substantially different from the relative permittivity ( = 1 ) of the ambient free space, dramatic changes occur in the overall transmittance as θ is varied. The angular dependence of T × 10 2 for the corresponding CAG-free PC is shown by the orange dash-dotted curve.

Fig. 8.
Fig. 8.

Spectra of T (black solid curve), R (red dashed curve), and A (blue dotted curve) for the same parameters as for Figs. 4 and 6, except that κ = 5 π × 10 9 s 1 .

Fig. 9.
Fig. 9.

Spectra of T (black solid curve), R (red dashed curve), and A (blue dotted curve) for θ = 0 and the same parameters as in Figs. 2 and 4, except that ω 1 a / c = 5.225 .

Fig. 10.
Fig. 10.

Specular and nonspecular transmittances and reflectances as a function of θ at k a = 5.2291 when (a) the remaining parameters are the same as in Fig. 9 and (b) for the corresponding CAG-free PC. T 0 is represented by the blue solid curve, R 0 by the red dashed curve, T 1 by the green dash-dotted curve, and R 1 by the blue dotted curve; Re ( ε h ) = 0.88 for (a).

Fig. 11.
Fig. 11.

Same as Fig. 9, but for ω 1 a / c = 5.527 .

Fig. 12.
Fig. 12.

Same as Figs. 9 and 11, but for ω 1 a / c = 3.047 and θ = 30 ° .

Fig. 13.
Fig. 13.

Angular dependences of T (blue solid curve) and R (red dashed curve) at k a = 3.05015 (a) when the remaining parameters are the same as in Fig. 12 and (b) for the corresponding CAG-free PC; Re ( ε h ) = 0.913 for (a).

Equations (5)

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E ( x , y ) = exp [ i k ( x sin θ y cos θ ) ] + n = ρ n exp [ i ( α n x + η n y ) ] , y D ,
E ( x , y ) = n = τ n exp [ i ( α n x η n y ) ] , y 0 .
T = n = T n = n = | τ n | 2 Re ( η n ) / Re ( η 0 ) ,
R = n = R n = n = | ρ n | 2 Re ( η n ) / Re ( η 0 ) ,
ε h ( ω ) = 1 + κ Δ Δ 2 ( Ω c / 2 ) 2 i Γ Δ ,

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