Abstract

We present optical properties of crescent-shaped dielectric nano-rods that comprise a square lattice periodic structure named as crescent-shaped photonic crystals (CPC). The circular symmetry of individual cells of periodic dielectric structures is broken by replacing each unit cell with a reduced symmetry crescent shaped structure. The created configuration is assumed to be formed by the intersection of circular dielectric and air rods. The degree of freedom to manipulate the light propagation arises due to the rotational sensitivity of the CPC. The interesting dispersion property of designed CPC occurs due to the anisotropic nature of the iso-frequency contours that yield tilted self-collimated wave guiding. Furthermore, this feature allows focusing, routing, splitting and deflecting light beams along certain routes which are independent of the lattice symmetry directions of regular PCs. The propagation direction of light can be tuned by means of the opening angle of the crescent shape. Finally, the property of being all-dielectric structure ensures the absence of optical absorption losses that are reminiscent of employed metallic nano-particles.

© 2012 OSA

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]

2011 (6)

H. F. Ho, Y. F. Chau, H. Y. Yeh, and F. L. Wu, “Complete bandgap arising from the effects of hollow, veins, and intersecting veins in a square lattice of square dielectric rods photonic crystal,” Appl. Phys. Lett. 98(26), 263115 (2011).
[CrossRef]

H. Wu, L. Y. Jiang, W. Jia, and X. Y. Li, “Imaging properties of an annular photonic crystal slab for both TM-polarization and TE-polarization,” J. Opt. 13(9), 095103 (2011).
[CrossRef]

C. Tan, T. Niemi, C. Peng, and M. Pessa, “Focusing effect of a graded index photonic crystal lens,” Opt. Commun. 284(12), 3140–3143 (2011).
[CrossRef]

B. Vasić and R. Gajić, “Self-focusing media using graded photonic crystals: Focusing, Fourier transforming and imaging, directive emission, and directional cloaking,” J. Appl. Phys. 110(5), 053103 (2011).
[CrossRef]

G. Si, A. J. Danner, S. Lang Teo, E. J. Teo, J. Teng, and A. A. Bettiol, “Photonic crystal structures with ultrahigh aspect ratio in lithium niobate fabricated by focused ion beam milling,” J. Vac. Sci. Technol. B 29(2), 021205–021209 (2011).
[CrossRef]

H. Kurt, I. H. Giden, and K. Ustun, “Highly efficient and broadband light transmission in 90° nanophotonic wire waveguide bends,” J. Opt. Soc. Am. B 28(3), 495–501 (2011).
[CrossRef]

2010 (3)

B. Vasić, G. Isić, R. Gajić, and K. Hingerl, “Controlling electromagnetic fields with graded photonic crystals in metamaterial regime,” Opt. Express 18(19), 20321–20333 (2010).
[CrossRef] [PubMed]

M. Lu, B. K. Juluri, S.-C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, “Beam Aperture Modification and Beam Deflection Using Gradient-Index Photonic Crystals,” J. Appl. Phys. 108(10), 103505 (2010).
[CrossRef]

Y. Zhang, L. Kong, Z. Feng, and Z. Zheng, “PBG structures of novel two-dimensional annular photonic crystals with triangular lattice,” Optoelectron. Lett. 6(4), 281–283 (2010).
[CrossRef]

2009 (5)

J. Hou, D. Gao, H. Wu, and Z. Zhou, “Polarization insensitive self-collimation waveguide in square lattice annular photonic crystals,” Opt. Commun. 282(15), 3172–3176 (2009).
[CrossRef]

B. Rezaei, T. Fathollahi Khalkhali, A. Soltani Vala, and M. Kalafi, “Absolute band gap properties in two-dimensional photonic crystals composed of air rings in anisotropic tellurium background,” Opt. Commun. 282(14), 2861–2869 (2009).
[CrossRef]

B. Rezaei and M. Kalafi, “Tunable full band gap in two-dimensional anisotropic photonic crystals infiltrated with liquid crystals,” Opt. Commun. 282(8), 1584–1588 (2009).
[CrossRef]

J. Feng, Y. Chen, J. Blair, H. Kurt, R. Hao, D. S. Citrin, C. J. Summers, and Z. Zhou, “Fabrication of annular photonic crystals by atomic layer deposition and sacrificial etching,” J. Vac. Sci. Technol. B 27(2), 568–572 (2009).
[CrossRef]

H. Xie and Y. Y. Lu, “Modeling two-dimensional anisotropic photonic crystals by Dirichlet-to-Neumann maps,” J. Opt. Soc. Am. A 26(7), 1606–1614 (2009).
[CrossRef] [PubMed]

2008 (6)

D. Gao, Z. Zhou, and D. S. Citrin, “Self-collimated waveguide bends and partial bandgap reflection of photonic crystals with parallelogram lattice,” J. Opt. Soc. Am. A 25(3), 791–795 (2008).
[CrossRef] [PubMed]

R. Proietti Zaccaria, P. Verma, S. Kawaguchi, S. Shoji, and S. Kawata, “Manipulating full photonic band gaps in two dimensional birefringent photonic crystals,” Opt. Express 16(19), 14812–14820 (2008).
[CrossRef] [PubMed]

Y. Xu, X. J. Chen, S. Lan, Q. Guo, W. Hu, and L. J. Wu, “The all-angle self-collimating phenomenon in photonic crystals with rectangular symmetry,” J. Opt. A, Pure Appl. Opt. 10(8), 085201 (2008).
[CrossRef]

I. Khromova and L. Melnikov, “Anisotropic photonic crystals: generalized plane wave method and dispersion symmetry properties,” Opt. Commun. 281(21), 5458–5466 (2008).
[CrossRef]

H. Kurt, E. Colak, O. Cakmak, H. Caglayan, and E. Ozbay, “The focusing effect of graded index photonic crystals,” Appl. Phys. Lett. 93(17), 171108 (2008).
[CrossRef]

X. Zhu, Y. Zhang, D. Chandra, S. C. Cheng, J. M. Kikkawa, and S. Yang, “Two-dimensional photonic crystals with anisotropic unit cells imprinted from poly (dimethylsiloxane) membranes under elastic deformation,” Appl. Phys. Lett. 93(16), 161911 (2008).
[CrossRef]

2007 (2)

H. Kurt and D. S. Citrin, “A novel optical coupler design with graded-index photonic crystals,” IEEE Photon. Technol. Lett. 19(19), 1532–1534 (2007).
[CrossRef]

H. Kurt and D. S. Citrin, “Graded index photonic crystals,” Opt. Express 15(3), 1240–1253 (2007).
[CrossRef] [PubMed]

2006 (1)

E. Centeno, D. Cassagne, and J. P. Albert, “Mirage and superbending effect in two-dimensional graded photonic crystals,” Phys. Rev. B 73(23), 235119 (2006).
[CrossRef]

2005 (3)

F. Guan, Z. Lin, and J. Zi, “Opening up complete photonic bandgaps by tuning the orientation of birefringent dielectric spheres in three-dimensional photonic crystals,” J. Phys. Condens. Matter 17(33), L343– L349 (2005).
[CrossRef]

H. Kurt and D. S. Citrin, “Annular photonic crystals,” Opt. Express 13(25), 10316–10326 (2005).
[CrossRef] [PubMed]

Y. Ogawa, Y. Omura, and Y. Iida, “Study on Self-collimated light-focusing device using the 2-D Photonic Crystal with a Parallelogram Lattice,” J. Lightwave Technol. 23(12), 4374–4381 (2005).
[CrossRef]

2004 (4)

P. Borel, A. Harpøth, L. Frandsen, M. Kristensen, P. Shi, J. Jensen, and O. Sigmund, “Topology optimization and fabrication of photonic crystal structures,” Opt. Express 12(9), 1996–2001 (2004).
[CrossRef] [PubMed]

A. I. Cabuz, E. Centeno, and D. Cassagne, “Superprism effect in bidimensional rectangular photonic crystals,” Appl. Phys. Lett. 84(12), 2031–2033 (2004).
[CrossRef]

T. Trifonov, L. F. Marsal, A. Rodríguez, J. Pallarès, and R. Alcubilla, “Effects of symmetry reduction in two dimensional square and triangular lattices,” Phys. Rev. B 69(23), 235112 (2004).
[CrossRef]

R. R. Panepucci, H. B. Kim, R. V. Almeida, and M. D. Jones, “Photonic crystals in polymers by direct electron-beam lithography presenting a photonic band gap,” J. Vac. Sci. Technol. B 22(6), 3348–3351 (2004).
[CrossRef]

2003 (3)

C. S. Kee, K. Kim, and H. Lim, “Tuning of anisotropic optical properties of two-dimensional dielectric photonic crystals,” Physica B 338(1-4), 153–158 (2003).
[CrossRef]

S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67(23), 235107 (2003).
[CrossRef]

D. Chigrin, S. Enoch, C. Sotomayor Torres, and G. Tayeb, “Self-guiding in two-dimensional photonic crystals,” Opt. Express 11(10), 1203–1211 (2003).
[CrossRef] [PubMed]

2001 (2)

2000 (2)

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62(12), 8212–8222 (2000).
[CrossRef]

S. W. Leonard, J. P. Mondia, H. M. van Driel, O. Toader, S. John, K. Busch, A. Birner, U. Gösele, and V. Lehmann, “Tunable two-dimensional photonic crystals using liquid-crystal infiltration,” Phys. Rev. B 61(4), R2389– R2392 (2000).
[CrossRef]

1999 (2)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering,” Appl. Phys. Lett. 74(10), 1370–1372 (1999).
[CrossRef]

1998 (1)

Z. Y. Li, B. Y. Gu, and G. Z. Yang, “Large absolute band gap in 2D anisotropic photonic crystals,” Phys. Rev. Lett. 81(12), 2574–2577 (1998).
[CrossRef]

1994 (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[CrossRef]

1993 (1)

1992 (1)

P. R. Villeneuve and M. Piche, “Photonic band gaps in two-dimensional square and hexagonal lattices,” Phys. Rev. B Condens. Matter 46(8), 4969–4972 (1992).
[CrossRef] [PubMed]

1990 (1)

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[CrossRef] [PubMed]

1982 (1)

D. E. Aspnes, “Local-Field Effects and Effective-Medium Theory: A microscopic perspective,” Am. J. Phys. 50(8), 704–709 (1982).
[CrossRef]

1979 (1)

Albert, J. P.

E. Centeno, D. Cassagne, and J. P. Albert, “Mirage and superbending effect in two-dimensional graded photonic crystals,” Phys. Rev. B 73(23), 235119 (2006).
[CrossRef]

Alcubilla, R.

T. Trifonov, L. F. Marsal, A. Rodríguez, J. Pallarès, and R. Alcubilla, “Effects of symmetry reduction in two dimensional square and triangular lattices,” Phys. Rev. B 69(23), 235112 (2004).
[CrossRef]

Almeida, R. V.

R. R. Panepucci, H. B. Kim, R. V. Almeida, and M. D. Jones, “Photonic crystals in polymers by direct electron-beam lithography presenting a photonic band gap,” J. Vac. Sci. Technol. B 22(6), 3348–3351 (2004).
[CrossRef]

Aspnes, D. E.

D. E. Aspnes, “Local-Field Effects and Effective-Medium Theory: A microscopic perspective,” Am. J. Phys. 50(8), 704–709 (1982).
[CrossRef]

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[CrossRef]

Bettiol, A. A.

G. Si, A. J. Danner, S. Lang Teo, E. J. Teo, J. Teng, and A. A. Bettiol, “Photonic crystal structures with ultrahigh aspect ratio in lithium niobate fabricated by focused ion beam milling,” J. Vac. Sci. Technol. B 29(2), 021205–021209 (2011).
[CrossRef]

Birner, A.

S. W. Leonard, J. P. Mondia, H. M. van Driel, O. Toader, S. John, K. Busch, A. Birner, U. Gösele, and V. Lehmann, “Tunable two-dimensional photonic crystals using liquid-crystal infiltration,” Phys. Rev. B 61(4), R2389– R2392 (2000).
[CrossRef]

Blair, J.

J. Feng, Y. Chen, J. Blair, H. Kurt, R. Hao, D. S. Citrin, C. J. Summers, and Z. Zhou, “Fabrication of annular photonic crystals by atomic layer deposition and sacrificial etching,” J. Vac. Sci. Technol. B 27(2), 568–572 (2009).
[CrossRef]

Borel, P.

Busch, K.

S. W. Leonard, J. P. Mondia, H. M. van Driel, O. Toader, S. John, K. Busch, A. Birner, U. Gösele, and V. Lehmann, “Tunable two-dimensional photonic crystals using liquid-crystal infiltration,” Phys. Rev. B 61(4), R2389– R2392 (2000).
[CrossRef]

Cabuz, A. I.

A. I. Cabuz, E. Centeno, and D. Cassagne, “Superprism effect in bidimensional rectangular photonic crystals,” Appl. Phys. Lett. 84(12), 2031–2033 (2004).
[CrossRef]

Caglayan, H.

H. Kurt, E. Colak, O. Cakmak, H. Caglayan, and E. Ozbay, “The focusing effect of graded index photonic crystals,” Appl. Phys. Lett. 93(17), 171108 (2008).
[CrossRef]

Cakmak, O.

H. Kurt, E. Colak, O. Cakmak, H. Caglayan, and E. Ozbay, “The focusing effect of graded index photonic crystals,” Appl. Phys. Lett. 93(17), 171108 (2008).
[CrossRef]

Cassagne, D.

E. Centeno, D. Cassagne, and J. P. Albert, “Mirage and superbending effect in two-dimensional graded photonic crystals,” Phys. Rev. B 73(23), 235119 (2006).
[CrossRef]

A. I. Cabuz, E. Centeno, and D. Cassagne, “Superprism effect in bidimensional rectangular photonic crystals,” Appl. Phys. Lett. 84(12), 2031–2033 (2004).
[CrossRef]

Centeno, E.

E. Centeno, D. Cassagne, and J. P. Albert, “Mirage and superbending effect in two-dimensional graded photonic crystals,” Phys. Rev. B 73(23), 235119 (2006).
[CrossRef]

A. I. Cabuz, E. Centeno, and D. Cassagne, “Superprism effect in bidimensional rectangular photonic crystals,” Appl. Phys. Lett. 84(12), 2031–2033 (2004).
[CrossRef]

Chan, C. T.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[CrossRef] [PubMed]

Chandra, D.

X. Zhu, Y. Zhang, D. Chandra, S. C. Cheng, J. M. Kikkawa, and S. Yang, “Two-dimensional photonic crystals with anisotropic unit cells imprinted from poly (dimethylsiloxane) membranes under elastic deformation,” Appl. Phys. Lett. 93(16), 161911 (2008).
[CrossRef]

Chau, Y. F.

H. F. Ho, Y. F. Chau, H. Y. Yeh, and F. L. Wu, “Complete bandgap arising from the effects of hollow, veins, and intersecting veins in a square lattice of square dielectric rods photonic crystal,” Appl. Phys. Lett. 98(26), 263115 (2011).
[CrossRef]

Chen, X. J.

Y. Xu, X. J. Chen, S. Lan, Q. Guo, W. Hu, and L. J. Wu, “The all-angle self-collimating phenomenon in photonic crystals with rectangular symmetry,” J. Opt. A, Pure Appl. Opt. 10(8), 085201 (2008).
[CrossRef]

Chen, Y.

J. Feng, Y. Chen, J. Blair, H. Kurt, R. Hao, D. S. Citrin, C. J. Summers, and Z. Zhou, “Fabrication of annular photonic crystals by atomic layer deposition and sacrificial etching,” J. Vac. Sci. Technol. B 27(2), 568–572 (2009).
[CrossRef]

Cheng, S. C.

X. Zhu, Y. Zhang, D. Chandra, S. C. Cheng, J. M. Kikkawa, and S. Yang, “Two-dimensional photonic crystals with anisotropic unit cells imprinted from poly (dimethylsiloxane) membranes under elastic deformation,” Appl. Phys. Lett. 93(16), 161911 (2008).
[CrossRef]

Chigrin, D.

Citrin, D. S.

J. Feng, Y. Chen, J. Blair, H. Kurt, R. Hao, D. S. Citrin, C. J. Summers, and Z. Zhou, “Fabrication of annular photonic crystals by atomic layer deposition and sacrificial etching,” J. Vac. Sci. Technol. B 27(2), 568–572 (2009).
[CrossRef]

D. Gao, Z. Zhou, and D. S. Citrin, “Self-collimated waveguide bends and partial bandgap reflection of photonic crystals with parallelogram lattice,” J. Opt. Soc. Am. A 25(3), 791–795 (2008).
[CrossRef] [PubMed]

H. Kurt and D. S. Citrin, “Graded index photonic crystals,” Opt. Express 15(3), 1240–1253 (2007).
[CrossRef] [PubMed]

H. Kurt and D. S. Citrin, “A novel optical coupler design with graded-index photonic crystals,” IEEE Photon. Technol. Lett. 19(19), 1532–1534 (2007).
[CrossRef]

H. Kurt and D. S. Citrin, “Annular photonic crystals,” Opt. Express 13(25), 10316–10326 (2005).
[CrossRef] [PubMed]

Colak, E.

H. Kurt, E. Colak, O. Cakmak, H. Caglayan, and E. Ozbay, “The focusing effect of graded index photonic crystals,” Appl. Phys. Lett. 93(17), 171108 (2008).
[CrossRef]

Danner, A. J.

G. Si, A. J. Danner, S. Lang Teo, E. J. Teo, J. Teng, and A. A. Bettiol, “Photonic crystal structures with ultrahigh aspect ratio in lithium niobate fabricated by focused ion beam milling,” J. Vac. Sci. Technol. B 29(2), 021205–021209 (2011).
[CrossRef]

Enoch, S.

Fan, S.

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62(12), 8212–8222 (2000).
[CrossRef]

Fathollahi Khalkhali, T.

B. Rezaei, T. Fathollahi Khalkhali, A. Soltani Vala, and M. Kalafi, “Absolute band gap properties in two-dimensional photonic crystals composed of air rings in anisotropic tellurium background,” Opt. Commun. 282(14), 2861–2869 (2009).
[CrossRef]

Feng, J.

J. Feng, Y. Chen, J. Blair, H. Kurt, R. Hao, D. S. Citrin, C. J. Summers, and Z. Zhou, “Fabrication of annular photonic crystals by atomic layer deposition and sacrificial etching,” J. Vac. Sci. Technol. B 27(2), 568–572 (2009).
[CrossRef]

Feng, Z.

Y. Zhang, L. Kong, Z. Feng, and Z. Zheng, “PBG structures of novel two-dimensional annular photonic crystals with triangular lattice,” Optoelectron. Lett. 6(4), 281–283 (2010).
[CrossRef]

Foteinopoulou, S.

S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67(23), 235107 (2003).
[CrossRef]

Frandsen, L.

Gajic, R.

B. Vasić and R. Gajić, “Self-focusing media using graded photonic crystals: Focusing, Fourier transforming and imaging, directive emission, and directional cloaking,” J. Appl. Phys. 110(5), 053103 (2011).
[CrossRef]

B. Vasić, G. Isić, R. Gajić, and K. Hingerl, “Controlling electromagnetic fields with graded photonic crystals in metamaterial regime,” Opt. Express 18(19), 20321–20333 (2010).
[CrossRef] [PubMed]

Gao, D.

J. Hou, D. Gao, H. Wu, and Z. Zhou, “Polarization insensitive self-collimation waveguide in square lattice annular photonic crystals,” Opt. Commun. 282(15), 3172–3176 (2009).
[CrossRef]

D. Gao, Z. Zhou, and D. S. Citrin, “Self-collimated waveguide bends and partial bandgap reflection of photonic crystals with parallelogram lattice,” J. Opt. Soc. Am. A 25(3), 791–795 (2008).
[CrossRef] [PubMed]

Gao, T.

M. Lu, B. K. Juluri, S.-C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, “Beam Aperture Modification and Beam Deflection Using Gradient-Index Photonic Crystals,” J. Appl. Phys. 108(10), 103505 (2010).
[CrossRef]

Giden, I. H.

Gösele, U.

S. W. Leonard, J. P. Mondia, H. M. van Driel, O. Toader, S. John, K. Busch, A. Birner, U. Gösele, and V. Lehmann, “Tunable two-dimensional photonic crystals using liquid-crystal infiltration,” Phys. Rev. B 61(4), R2389– R2392 (2000).
[CrossRef]

Gu, B. Y.

Z. Y. Li, B. Y. Gu, and G. Z. Yang, “Large absolute band gap in 2D anisotropic photonic crystals,” Phys. Rev. Lett. 81(12), 2574–2577 (1998).
[CrossRef]

Guan, F.

F. Guan, Z. Lin, and J. Zi, “Opening up complete photonic bandgaps by tuning the orientation of birefringent dielectric spheres in three-dimensional photonic crystals,” J. Phys. Condens. Matter 17(33), L343– L349 (2005).
[CrossRef]

Guo, Q.

Y. Xu, X. J. Chen, S. Lan, Q. Guo, W. Hu, and L. J. Wu, “The all-angle self-collimating phenomenon in photonic crystals with rectangular symmetry,” J. Opt. A, Pure Appl. Opt. 10(8), 085201 (2008).
[CrossRef]

Hao, R.

J. Feng, Y. Chen, J. Blair, H. Kurt, R. Hao, D. S. Citrin, C. J. Summers, and Z. Zhou, “Fabrication of annular photonic crystals by atomic layer deposition and sacrificial etching,” J. Vac. Sci. Technol. B 27(2), 568–572 (2009).
[CrossRef]

Harpøth, A.

Hingerl, K.

Ho, H. F.

H. F. Ho, Y. F. Chau, H. Y. Yeh, and F. L. Wu, “Complete bandgap arising from the effects of hollow, veins, and intersecting veins in a square lattice of square dielectric rods photonic crystal,” Appl. Phys. Lett. 98(26), 263115 (2011).
[CrossRef]

Ho, K. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[CrossRef] [PubMed]

Hou, J.

J. Hou, D. Gao, H. Wu, and Z. Zhou, “Polarization insensitive self-collimation waveguide in square lattice annular photonic crystals,” Opt. Commun. 282(15), 3172–3176 (2009).
[CrossRef]

Hu, W.

Y. Xu, X. J. Chen, S. Lan, Q. Guo, W. Hu, and L. J. Wu, “The all-angle self-collimating phenomenon in photonic crystals with rectangular symmetry,” J. Opt. A, Pure Appl. Opt. 10(8), 085201 (2008).
[CrossRef]

Huang, T. J.

M. Lu, B. K. Juluri, S.-C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, “Beam Aperture Modification and Beam Deflection Using Gradient-Index Photonic Crystals,” J. Appl. Phys. 108(10), 103505 (2010).
[CrossRef]

Iida, Y.

Isic, G.

Jensen, J.

Jia, W.

H. Wu, L. Y. Jiang, W. Jia, and X. Y. Li, “Imaging properties of an annular photonic crystal slab for both TM-polarization and TE-polarization,” J. Opt. 13(9), 095103 (2011).
[CrossRef]

Jiang, L. Y.

H. Wu, L. Y. Jiang, W. Jia, and X. Y. Li, “Imaging properties of an annular photonic crystal slab for both TM-polarization and TE-polarization,” J. Opt. 13(9), 095103 (2011).
[CrossRef]

Joannopoulos, J.

Joannopoulos, J. D.

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62(12), 8212–8222 (2000).
[CrossRef]

John, S.

S. W. Leonard, J. P. Mondia, H. M. van Driel, O. Toader, S. John, K. Busch, A. Birner, U. Gösele, and V. Lehmann, “Tunable two-dimensional photonic crystals using liquid-crystal infiltration,” Phys. Rev. B 61(4), R2389– R2392 (2000).
[CrossRef]

Johnson, S.

Johnson, S. G.

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62(12), 8212–8222 (2000).
[CrossRef]

Jones, M. D.

R. R. Panepucci, H. B. Kim, R. V. Almeida, and M. D. Jones, “Photonic crystals in polymers by direct electron-beam lithography presenting a photonic band gap,” J. Vac. Sci. Technol. B 22(6), 3348–3351 (2004).
[CrossRef]

Juluri, B. K.

M. Lu, B. K. Juluri, S.-C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, “Beam Aperture Modification and Beam Deflection Using Gradient-Index Photonic Crystals,” J. Appl. Phys. 108(10), 103505 (2010).
[CrossRef]

Kalafi, M.

B. Rezaei, T. Fathollahi Khalkhali, A. Soltani Vala, and M. Kalafi, “Absolute band gap properties in two-dimensional photonic crystals composed of air rings in anisotropic tellurium background,” Opt. Commun. 282(14), 2861–2869 (2009).
[CrossRef]

B. Rezaei and M. Kalafi, “Tunable full band gap in two-dimensional anisotropic photonic crystals infiltrated with liquid crystals,” Opt. Commun. 282(8), 1584–1588 (2009).
[CrossRef]

Kawaguchi, S.

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering,” Appl. Phys. Lett. 74(10), 1370–1372 (1999).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering,” Appl. Phys. Lett. 74(10), 1370–1372 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[CrossRef]

Kawata, S.

Kee, C. S.

C. S. Kee, K. Kim, and H. Lim, “Tuning of anisotropic optical properties of two-dimensional dielectric photonic crystals,” Physica B 338(1-4), 153–158 (2003).
[CrossRef]

Khromova, I.

I. Khromova and L. Melnikov, “Anisotropic photonic crystals: generalized plane wave method and dispersion symmetry properties,” Opt. Commun. 281(21), 5458–5466 (2008).
[CrossRef]

Kikkawa, J. M.

X. Zhu, Y. Zhang, D. Chandra, S. C. Cheng, J. M. Kikkawa, and S. Yang, “Two-dimensional photonic crystals with anisotropic unit cells imprinted from poly (dimethylsiloxane) membranes under elastic deformation,” Appl. Phys. Lett. 93(16), 161911 (2008).
[CrossRef]

Kim, H. B.

R. R. Panepucci, H. B. Kim, R. V. Almeida, and M. D. Jones, “Photonic crystals in polymers by direct electron-beam lithography presenting a photonic band gap,” J. Vac. Sci. Technol. B 22(6), 3348–3351 (2004).
[CrossRef]

Kim, K.

C. S. Kee, K. Kim, and H. Lim, “Tuning of anisotropic optical properties of two-dimensional dielectric photonic crystals,” Physica B 338(1-4), 153–158 (2003).
[CrossRef]

Kiraly, B.

M. Lu, B. K. Juluri, S.-C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, “Beam Aperture Modification and Beam Deflection Using Gradient-Index Photonic Crystals,” J. Appl. Phys. 108(10), 103505 (2010).
[CrossRef]

Kong, L.

Y. Zhang, L. Kong, Z. Feng, and Z. Zheng, “PBG structures of novel two-dimensional annular photonic crystals with triangular lattice,” Optoelectron. Lett. 6(4), 281–283 (2010).
[CrossRef]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering,” Appl. Phys. Lett. 74(10), 1370–1372 (1999).
[CrossRef]

Kristensen, M.

Kurt, H.

H. Kurt, I. H. Giden, and K. Ustun, “Highly efficient and broadband light transmission in 90° nanophotonic wire waveguide bends,” J. Opt. Soc. Am. B 28(3), 495–501 (2011).
[CrossRef]

J. Feng, Y. Chen, J. Blair, H. Kurt, R. Hao, D. S. Citrin, C. J. Summers, and Z. Zhou, “Fabrication of annular photonic crystals by atomic layer deposition and sacrificial etching,” J. Vac. Sci. Technol. B 27(2), 568–572 (2009).
[CrossRef]

H. Kurt, E. Colak, O. Cakmak, H. Caglayan, and E. Ozbay, “The focusing effect of graded index photonic crystals,” Appl. Phys. Lett. 93(17), 171108 (2008).
[CrossRef]

H. Kurt and D. S. Citrin, “A novel optical coupler design with graded-index photonic crystals,” IEEE Photon. Technol. Lett. 19(19), 1532–1534 (2007).
[CrossRef]

H. Kurt and D. S. Citrin, “Graded index photonic crystals,” Opt. Express 15(3), 1240–1253 (2007).
[CrossRef] [PubMed]

H. Kurt and D. S. Citrin, “Annular photonic crystals,” Opt. Express 13(25), 10316–10326 (2005).
[CrossRef] [PubMed]

Lan, S.

Y. Xu, X. J. Chen, S. Lan, Q. Guo, W. Hu, and L. J. Wu, “The all-angle self-collimating phenomenon in photonic crystals with rectangular symmetry,” J. Opt. A, Pure Appl. Opt. 10(8), 085201 (2008).
[CrossRef]

Lang Teo, S.

G. Si, A. J. Danner, S. Lang Teo, E. J. Teo, J. Teng, and A. A. Bettiol, “Photonic crystal structures with ultrahigh aspect ratio in lithium niobate fabricated by focused ion beam milling,” J. Vac. Sci. Technol. B 29(2), 021205–021209 (2011).
[CrossRef]

Lehmann, V.

S. W. Leonard, J. P. Mondia, H. M. van Driel, O. Toader, S. John, K. Busch, A. Birner, U. Gösele, and V. Lehmann, “Tunable two-dimensional photonic crystals using liquid-crystal infiltration,” Phys. Rev. B 61(4), R2389– R2392 (2000).
[CrossRef]

Leonard, S. W.

S. W. Leonard, J. P. Mondia, H. M. van Driel, O. Toader, S. John, K. Busch, A. Birner, U. Gösele, and V. Lehmann, “Tunable two-dimensional photonic crystals using liquid-crystal infiltration,” Phys. Rev. B 61(4), R2389– R2392 (2000).
[CrossRef]

Li, X. Y.

H. Wu, L. Y. Jiang, W. Jia, and X. Y. Li, “Imaging properties of an annular photonic crystal slab for both TM-polarization and TE-polarization,” J. Opt. 13(9), 095103 (2011).
[CrossRef]

Li, Z. Y.

Z. Y. Li, B. Y. Gu, and G. Z. Yang, “Large absolute band gap in 2D anisotropic photonic crystals,” Phys. Rev. Lett. 81(12), 2574–2577 (1998).
[CrossRef]

Lim, H.

C. S. Kee, K. Kim, and H. Lim, “Tuning of anisotropic optical properties of two-dimensional dielectric photonic crystals,” Physica B 338(1-4), 153–158 (2003).
[CrossRef]

Lin, S.-C. S.

M. Lu, B. K. Juluri, S.-C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, “Beam Aperture Modification and Beam Deflection Using Gradient-Index Photonic Crystals,” J. Appl. Phys. 108(10), 103505 (2010).
[CrossRef]

Lin, Z.

F. Guan, Z. Lin, and J. Zi, “Opening up complete photonic bandgaps by tuning the orientation of birefringent dielectric spheres in three-dimensional photonic crystals,” J. Phys. Condens. Matter 17(33), L343– L349 (2005).
[CrossRef]

Loncar, M.

Lu, M.

M. Lu, B. K. Juluri, S.-C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, “Beam Aperture Modification and Beam Deflection Using Gradient-Index Photonic Crystals,” J. Appl. Phys. 108(10), 103505 (2010).
[CrossRef]

Lu, Y. Y.

Marsal, L. F.

T. Trifonov, L. F. Marsal, A. Rodríguez, J. Pallarès, and R. Alcubilla, “Effects of symmetry reduction in two dimensional square and triangular lattices,” Phys. Rev. B 69(23), 235112 (2004).
[CrossRef]

Melnikov, L.

I. Khromova and L. Melnikov, “Anisotropic photonic crystals: generalized plane wave method and dispersion symmetry properties,” Opt. Commun. 281(21), 5458–5466 (2008).
[CrossRef]

Mondia, J. P.

S. W. Leonard, J. P. Mondia, H. M. van Driel, O. Toader, S. John, K. Busch, A. Birner, U. Gösele, and V. Lehmann, “Tunable two-dimensional photonic crystals using liquid-crystal infiltration,” Phys. Rev. B 61(4), R2389– R2392 (2000).
[CrossRef]

Niemi, T.

C. Tan, T. Niemi, C. Peng, and M. Pessa, “Focusing effect of a graded index photonic crystal lens,” Opt. Commun. 284(12), 3140–3143 (2011).
[CrossRef]

Notomi, M.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering,” Appl. Phys. Lett. 74(10), 1370–1372 (1999).
[CrossRef]

Ogawa, Y.

Omura, Y.

Ozbay, E.

H. Kurt, E. Colak, O. Cakmak, H. Caglayan, and E. Ozbay, “The focusing effect of graded index photonic crystals,” Appl. Phys. Lett. 93(17), 171108 (2008).
[CrossRef]

Pallarès, J.

T. Trifonov, L. F. Marsal, A. Rodríguez, J. Pallarès, and R. Alcubilla, “Effects of symmetry reduction in two dimensional square and triangular lattices,” Phys. Rev. B 69(23), 235112 (2004).
[CrossRef]

Panepucci, R. R.

R. R. Panepucci, H. B. Kim, R. V. Almeida, and M. D. Jones, “Photonic crystals in polymers by direct electron-beam lithography presenting a photonic band gap,” J. Vac. Sci. Technol. B 22(6), 3348–3351 (2004).
[CrossRef]

Peng, C.

C. Tan, T. Niemi, C. Peng, and M. Pessa, “Focusing effect of a graded index photonic crystal lens,” Opt. Commun. 284(12), 3140–3143 (2011).
[CrossRef]

Pessa, M.

C. Tan, T. Niemi, C. Peng, and M. Pessa, “Focusing effect of a graded index photonic crystal lens,” Opt. Commun. 284(12), 3140–3143 (2011).
[CrossRef]

Piche, M.

P. R. Villeneuve and M. Piche, “Photonic band gaps in two-dimensional square and hexagonal lattices,” Phys. Rev. B Condens. Matter 46(8), 4969–4972 (1992).
[CrossRef] [PubMed]

Proietti Zaccaria, R.

Rezaei, B.

B. Rezaei and M. Kalafi, “Tunable full band gap in two-dimensional anisotropic photonic crystals infiltrated with liquid crystals,” Opt. Commun. 282(8), 1584–1588 (2009).
[CrossRef]

B. Rezaei, T. Fathollahi Khalkhali, A. Soltani Vala, and M. Kalafi, “Absolute band gap properties in two-dimensional photonic crystals composed of air rings in anisotropic tellurium background,” Opt. Commun. 282(14), 2861–2869 (2009).
[CrossRef]

Rodríguez, A.

T. Trifonov, L. F. Marsal, A. Rodríguez, J. Pallarès, and R. Alcubilla, “Effects of symmetry reduction in two dimensional square and triangular lattices,” Phys. Rev. B 69(23), 235112 (2004).
[CrossRef]

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering,” Appl. Phys. Lett. 74(10), 1370–1372 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[CrossRef]

Scherer, A.

Shi, P.

Shoji, S.

Si, G.

G. Si, A. J. Danner, S. Lang Teo, E. J. Teo, J. Teng, and A. A. Bettiol, “Photonic crystal structures with ultrahigh aspect ratio in lithium niobate fabricated by focused ion beam milling,” J. Vac. Sci. Technol. B 29(2), 021205–021209 (2011).
[CrossRef]

Sigmund, O.

Soltani Vala, A.

B. Rezaei, T. Fathollahi Khalkhali, A. Soltani Vala, and M. Kalafi, “Absolute band gap properties in two-dimensional photonic crystals composed of air rings in anisotropic tellurium background,” Opt. Commun. 282(14), 2861–2869 (2009).
[CrossRef]

Sotomayor Torres, C.

Soukoulis, C. M.

S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67(23), 235107 (2003).
[CrossRef]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[CrossRef] [PubMed]

Summers, C. J.

J. Feng, Y. Chen, J. Blair, H. Kurt, R. Hao, D. S. Citrin, C. J. Summers, and Z. Zhou, “Fabrication of annular photonic crystals by atomic layer deposition and sacrificial etching,” J. Vac. Sci. Technol. B 27(2), 568–572 (2009).
[CrossRef]

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering,” Appl. Phys. Lett. 74(10), 1370–1372 (1999).
[CrossRef]

Tan, C.

C. Tan, T. Niemi, C. Peng, and M. Pessa, “Focusing effect of a graded index photonic crystal lens,” Opt. Commun. 284(12), 3140–3143 (2011).
[CrossRef]

Tayeb, G.

Teng, J.

G. Si, A. J. Danner, S. Lang Teo, E. J. Teo, J. Teng, and A. A. Bettiol, “Photonic crystal structures with ultrahigh aspect ratio in lithium niobate fabricated by focused ion beam milling,” J. Vac. Sci. Technol. B 29(2), 021205–021209 (2011).
[CrossRef]

Teo, E. J.

G. Si, A. J. Danner, S. Lang Teo, E. J. Teo, J. Teng, and A. A. Bettiol, “Photonic crystal structures with ultrahigh aspect ratio in lithium niobate fabricated by focused ion beam milling,” J. Vac. Sci. Technol. B 29(2), 021205–021209 (2011).
[CrossRef]

Toader, O.

S. W. Leonard, J. P. Mondia, H. M. van Driel, O. Toader, S. John, K. Busch, A. Birner, U. Gösele, and V. Lehmann, “Tunable two-dimensional photonic crystals using liquid-crystal infiltration,” Phys. Rev. B 61(4), R2389– R2392 (2000).
[CrossRef]

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering,” Appl. Phys. Lett. 74(10), 1370–1372 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[CrossRef]

Trifonov, T.

T. Trifonov, L. F. Marsal, A. Rodríguez, J. Pallarès, and R. Alcubilla, “Effects of symmetry reduction in two dimensional square and triangular lattices,” Phys. Rev. B 69(23), 235112 (2004).
[CrossRef]

Ustun, K.

van Driel, H. M.

S. W. Leonard, J. P. Mondia, H. M. van Driel, O. Toader, S. John, K. Busch, A. Birner, U. Gösele, and V. Lehmann, “Tunable two-dimensional photonic crystals using liquid-crystal infiltration,” Phys. Rev. B 61(4), R2389– R2392 (2000).
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Supplementary Material (2)

» Media 1: MOV (2311 KB)     
» Media 2: MOV (2236 KB)     

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Figures (8)

Fig. 1
Fig. 1

(a) The designed crescent-shaped PC (CPC). The refractive index of the dielectric rod is n = 3.13 and the radii of two rods are R1 = R2 = 0.30a The distance between the circles is D = R1 = R2 (b) Finite size square lattice CPC structure is created. (c) Brillouin zone of the structure.

Fig. 2
Fig. 2

The operating frequency contours of the different crescent open-angle, θ . The operating frequencies are a / λ = 0.416 in (a) a / λ = 0.39 in (b) and a / λ = 0.412 in (c). The media file presents IFCs of different crescent open angle that varies from 0° to 90° (Media 1).

Fig. 3
Fig. 3

The steady state e-field intensity distribution of CPC structure is shown. (a) θ = 30 0 (b) θ = + 30 0 and (c) θ = 0 0 . (d) The schematic view of the locations of focal points and the output angle α variations for different θ values.

Fig. 4
Fig. 4

The dependency of α to θ parameter is sketched. There are three operational frequencies used for each region. The different colors designate the three regions.

Fig. 5
Fig. 5

(a) Iso-frequency contours corresponding to the second band of the CPC with a crescent open angle θ = 30 0 The observed tilted self collimation characteristics along different propagation directions are presented in (b) and (c). The yellow boxes in (b) and (c) show the location of CPC. The normalized frequency is taken to be 0.416.

Fig. 6
Fig. 6

The representation of the construction methods of CPCs for various application areas: (a) the design of beam-splitting and (b) beam-deflectors and routers.

Fig. 7
Fig. 7

A composite CPC set up and steady-state electric field distribution. The cascade structure is obtained by combining two-block of CPC, one is negative θ and the second part has positive θ . The blue and red colors correspond to minimum and maximum values of e-field’s amplitude. Black arrow shows the location of source and the dashed-white one demonstrates the path of the propagation

Fig. 8
Fig. 8

Beam splitter configuration. The upper and lower parts of the CPC have opposite angle θ = ± 20 0 . (a) The steady-state intensity distribution of electric field throughout the structure (Media 2). (b) The transverse intensity profile at the end of the structure.

Equations (1)

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v g ( x , y ) = k ω ( k = ( k x , k y ) ) = ω k x x ^ + ω k y y ^ ,

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