Abstract

A novel (to our best knowledge) type of photonic crystal (PC) structure called modified annular PC (MAPC) that is composed of dielectric rods with off-centered air holes is thoroughly studied. The plane wave expansion method is applied for spectral analysis. A complete photonic bandgap region with a considerable value of gap width Δω/ω=7.06% is achieved by optimizing the structural parameters of the proposed periodic medium. By introducing geometrical asymmetry to the primitive cell of PC, we engineer the dispersion properties of the proposed photonic structure such that conventional equifrequency contours for the second band can be transformed into tilted rectangular shapes. This feature enables us to demonstrate the polarization insensitive tilted self-collimation effect. A hybrid structure composed of dielectric nanowire and MAPCs is offered to obtain a high degree of polarization independent guiding of light. The two-dimensional finite-difference time-domain method is carried out to verify the light guiding efficiencies. Polarization insensitive optical functionalities achieved by MAPC structure can be deployed in integrated optical circuits.

© 2012 Optical Society of America

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2012 (1)

2011 (8)

S. H. Kim, T. T. Kim, S. S. Oh, J. E. Kim, H. Y. Park, and C. S. Kee, “Experimental demonstration of self-collimation of spoof surface plasmons,” Phys. Rev. B 83, 165109 (2011).
[CrossRef]

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

G. Si, A. J. Danner, S. L. 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, 021205–021209 (2011).
[CrossRef]

S. Juodkazis, L. Rosa, S. Bauerdick, L. Peto, R. El-Ganainy, and S. John, “Sculpturing of photonic crystals by ion beam lithography: towards complete photonic bandgap at visible wavelengths,” Opt. Express 19, 5802–5810 (2011).
[CrossRef]

Y. F. Chau, F. L. Wu, Z. H. Jiang, and H. Y. Li, “Evolution of the complete photonic bandgap of two-dimensional photonic crystal,” Opt. Express 19, 4862–4867 (2011).
[CrossRef]

H. F. Ho, Y. F. Chau, H. Y. Yeh, and F. L. Wu, “Complete band gap arising from the effects of hollow, veins, and intersecting veins in a square lattice of square dielectric rods photonic crystal,” Appl. Phys. Lett. 98, 263115–263118 (2011).
[CrossRef]

J. Hou, D. S. Citrin, H. Wu, D. Gao, and Z. Zhou, “Enhanced bandgap in annular photonic-crystal silicon-on-insulator asymmetric slabs,” Opt. Lett. 36, 2263–2265 (2011).
[CrossRef]

T. F. Khalkhali, B. Rezaei, and M. Kalafi, “Enlargement of absolute photonic band gap in modified 2D anisotropic annular photonic crystals,” Opt. Commun. 284, 3315–3322 (2011).
[CrossRef]

2010 (5)

2009 (6)

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, 568–572 (2009).
[CrossRef]

G. G. Zheng, L. X. Shi, X. Y. Li, H. L. Wang, and J. Yuan, “Optical interconnections with photonic crystal self-collimation, directional emission and co-directional coupling mechanism,” J. Phys. D 42, 115101 (2009).
[CrossRef]

M. Wang, M. Yun, W. Kong, and C. Cui, “Beam splitter and beam bends based on self-collimation effect in two-dimensional photonic crystals,” J. Mod. Opt. 56, 1159–1162 (2009).
[CrossRef]

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

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

A. Cicek and B. Ulug, “Polarization-independent waveguiding with annular photonic crystals,” Opt. Express 17, 18381–18386(2009).
[CrossRef]

2008 (3)

2007 (4)

2005 (3)

2004 (7)

X. Wu, A. Yamilov, X. Liu, S. Li, V. P. Dravid, R. P. H. Chang, and H. Cao, “Ultraviolet photonic crystal laser,” Appl. Phys. Lett. 85, 3657–3659 (2004).
[CrossRef]

Y. F. Chau, T. J. Yang, and W. D. Lee, “Coupling technique for efficient interfacing between silica waveguides and planar photonic crystal circuits,” Appl. Opt. 43, 6656–6663 (2004).
[CrossRef]

S. Shi, A. Sharkawy, C. Chen, D. M. Pustai, and D. W. Prather, “Dispersion-based beam splitter in photonic crystals,” Opt. Lett. 29, 617–619 (2004).
[CrossRef]

D. W. Prather, S. Shi, D. M. Pustai, A. Sharkawy, C. Chen, S. Venkataraman, J. Murakowski, and G. Schneider, “Dispersion-based optical routing in photonic crystals,” Opt. Lett. 29, 50–52 (2004).
[CrossRef]

D. M. Pustai, S. Shi, C. Chen, A. Sharkawy, and D. W. Prather, “Analysis of splitters for self-collimated beams in planar photonic crystals,” Opt. Express 12, 1823–1831 (2004).
[CrossRef]

A. F. Matthews, S. F. Mingaleev, and Y. S. Kivshar, “Band-gap engineering and defect modes in photonic crystals with rotated hexagonal holes,” Laser Phys. 14, 631–634 (2004).

M. Deubel, G. V. Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[CrossRef]

2003 (2)

E. Lidorikis, M. L. Povinelli, S. G. Johnson, and J. D. Joannopoulos, “Polarization-independent linear waveguides in 3D photonic crystals,” Phys. Rev. Lett. 91, 023902 (2003).
[CrossRef]

B. S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science 300, 1537 (2003).
[CrossRef]

2002 (2)

M. Loncar, T. Yoshie, A. Scherer, P. Gogna, and Y. Qiu, “Low-threshold photonic crystal laser,” Appl. Phys. Lett. 81, 2680–2682 (2002).
[CrossRef]

J. Witzens, M. Loncar, and A. Scherer, “Self-collimation in planar photonic crystals,” IEEE J. Sel. Top. Quantum Electron. 8, 1246–1257 (2002).
[CrossRef]

2001 (3)

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, Y. H. Lee, and J. S. Kim, “Nondegenerate monopole-mode two-dimensional photonic band gap laser,” Appl. Phys. Lett. 79, 3032–3034 (2001).
[CrossRef]

W. D. Zhou, J. Sabarinathan, P. Bhattacharya, B. Kochman, E. Berg, P. C. Yu, and S. Pang, “Characteristics of a photonic bandgap single defect microcavity electroluminescent device,” IEEE J. Quantum Electron. 37, 1153–1160 (2001).
[CrossRef]

S. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[CrossRef]

2000 (3)

M. Loncar, T. Doll, J. Vuckovic, and A. Scherer, “Design and fabrication of silicon photonic crystal optical waveguides,” J. Lightwave Technol. 18, 1402–1411 (2000).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, “Three-dimensionally periodic dielectric layered structure with omnidirectional photonic band gap,” Appl. Phys. Lett. 77, 3490–3492 (2000).
[CrossRef]

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000).
[CrossRef]

1999 (1)

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, 1212–1214 (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, 2574–2577 (1998).
[CrossRef]

1996 (1)

C. M. Anderson and K. P. Giapis, “Larger two-dimensional photonic band gaps,” Phys. Rev. Lett. 77, 2949–2952 (1996).
[CrossRef]

1994 (1)

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

1993 (1)

E. Yablonovitch, “Photonic band-gap crystals,” J. Phys. 5, 2443–2460 (1993).
[CrossRef]

1992 (1)

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

1990 (2)

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

Z. Zhang and S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of the Maxwell’s equations,” Phys. Rev. Lett. 65, 2650–2653 (1990).
[CrossRef]

1987 (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef]

S. John, “Strong localization of photons in certain dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef]

1979 (1)

Anderson, C. M.

C. M. Anderson and K. P. Giapis, “Larger two-dimensional photonic band gaps,” Phys. Rev. Lett. 77, 2949–2952 (1996).
[CrossRef]

Asano, T.

B. S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science 300, 1537 (2003).
[CrossRef]

Bauerdick, S.

Berenger, J. P.

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

Berg, E.

W. D. Zhou, J. Sabarinathan, P. Bhattacharya, B. Kochman, E. Berg, P. C. Yu, and S. Pang, “Characteristics of a photonic bandgap single defect microcavity electroluminescent device,” IEEE J. Quantum Electron. 37, 1153–1160 (2001).
[CrossRef]

Bettiol, A. A.

G. Si, A. J. Danner, S. L. 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, 021205–021209 (2011).
[CrossRef]

Bhattacharya, P.

W. D. Zhou, J. Sabarinathan, P. Bhattacharya, B. Kochman, E. Berg, P. C. Yu, and S. Pang, “Characteristics of a photonic bandgap single defect microcavity electroluminescent device,” IEEE J. Quantum Electron. 37, 1153–1160 (2001).
[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, 568–572 (2009).
[CrossRef]

H. Kurt, R. Hao, Y. Chen, J. Feng, J. Blair, C. Summers, D. S. Citrin, and Z. Zhou, “Design of annular photonic crystal slabs,” Opt. Lett. 33, 1614–1616 (2008).
[CrossRef]

Boucaud, P.

Busch, K.

M. Deubel, G. V. Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[CrossRef]

Cao, H.

X. Wu, A. Yamilov, X. Liu, S. Li, V. P. Dravid, R. P. H. Chang, and H. Cao, “Ultraviolet photonic crystal laser,” Appl. Phys. Lett. 85, 3657–3659 (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, 3152–3155 (1990).
[CrossRef]

Chang, C.

Chang, R. P. H.

X. Wu, A. Yamilov, X. Liu, S. Li, V. P. Dravid, R. P. H. Chang, and H. Cao, “Ultraviolet photonic crystal laser,” Appl. Phys. Lett. 85, 3657–3659 (2004).
[CrossRef]

Chau, Y. F.

Checoury, X.

Chen, C.

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, 568–572 (2009).
[CrossRef]

H. Kurt, R. Hao, Y. Chen, J. Feng, J. Blair, C. Summers, D. S. Citrin, and Z. Zhou, “Design of annular photonic crystal slabs,” Opt. Lett. 33, 1614–1616 (2008).
[CrossRef]

H. Fu, Y. Chen, R. Chern, and C. Chang, “Connected hexagonal photonic crystals with largest full band gap,” Opt. Express 13, 7854–7860 (2005).
[CrossRef]

Chern, R.

Chutinan, A.

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H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, Y. H. Lee, and J. S. Kim, “Nondegenerate monopole-mode two-dimensional photonic band gap laser,” Appl. Phys. Lett. 79, 3032–3034 (2001).
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H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, Y. H. Lee, and J. S. Kim, “Nondegenerate monopole-mode two-dimensional photonic band gap laser,” Appl. Phys. Lett. 79, 3032–3034 (2001).
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X. Wu, A. Yamilov, X. Liu, S. Li, V. P. Dravid, R. P. H. Chang, and H. Cao, “Ultraviolet photonic crystal laser,” Appl. Phys. Lett. 85, 3657–3659 (2004).
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E. Lidorikis, M. L. Povinelli, S. G. Johnson, and J. D. Joannopoulos, “Polarization-independent linear waveguides in 3D photonic crystals,” Phys. Rev. Lett. 91, 023902 (2003).
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X. Wu, A. Yamilov, X. Liu, S. Li, V. P. Dravid, R. P. H. Chang, and H. Cao, “Ultraviolet photonic crystal laser,” Appl. Phys. Lett. 85, 3657–3659 (2004).
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W. Kuang, Z. Hou, Y. Liu, and H. Li, “The bandgap of a photonic crystal with triangular dielectric rods in a honeycomb lattice,” J. Opt. A 7, 525–528 (2005).
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M. Loncar, T. Yoshie, A. Scherer, P. Gogna, and Y. Qiu, “Low-threshold photonic crystal laser,” Appl. Phys. Lett. 81, 2680–2682 (2002).
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J. Witzens, M. Loncar, and A. Scherer, “Self-collimation in planar photonic crystals,” IEEE J. Sel. Top. Quantum Electron. 8, 1246–1257 (2002).
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M. Loncar, T. Doll, J. Vuckovic, and A. Scherer, “Design and fabrication of silicon photonic crystal optical waveguides,” J. Lightwave Technol. 18, 1402–1411 (2000).
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A. F. Matthews, S. F. Mingaleev, and Y. S. Kivshar, “Band-gap engineering and defect modes in photonic crystals with rotated hexagonal holes,” Laser Phys. 14, 631–634 (2004).

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J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, 1995).

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A. F. Matthews, S. F. Mingaleev, and Y. S. Kivshar, “Band-gap engineering and defect modes in photonic crystals with rotated hexagonal holes,” Laser Phys. 14, 631–634 (2004).

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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, 1212–1214 (1999).
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Oh, S. S.

S. H. Kim, T. T. Kim, S. S. Oh, J. E. Kim, H. Y. Park, and C. S. Kee, “Experimental demonstration of self-collimation of spoof surface plasmons,” Phys. Rev. B 83, 165109 (2011).
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H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, Y. H. Lee, and J. S. Kim, “Nondegenerate monopole-mode two-dimensional photonic band gap laser,” Appl. Phys. Lett. 79, 3032–3034 (2001).
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Park, H. Y.

Park, J. M.

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M. Deubel, G. V. Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
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E. Lidorikis, M. L. Povinelli, S. G. Johnson, and J. D. Joannopoulos, “Polarization-independent linear waveguides in 3D photonic crystals,” Phys. Rev. Lett. 91, 023902 (2003).
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M. Loncar, T. Yoshie, A. Scherer, P. Gogna, and Y. Qiu, “Low-threshold photonic crystal laser,” Appl. Phys. Lett. 81, 2680–2682 (2002).
[CrossRef]

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T. F. Khalkhali, B. Rezaei, and M. Kalafi, “Enlargement of absolute photonic band gap in modified 2D anisotropic annular photonic crystals,” Opt. Commun. 284, 3315–3322 (2011).
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B. Rezaei and M. Kalafi, “Absolute band gap properties in two-dimensional photonic crystals composed of air rings in anisotropic tellurium background,” Opt. Commun. 282, 2861–2869 (2009).
[CrossRef]

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Ryu, H. Y.

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, Y. H. Lee, and J. S. Kim, “Nondegenerate monopole-mode two-dimensional photonic band gap laser,” Appl. Phys. Lett. 79, 3032–3034 (2001).
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W. D. Zhou, J. Sabarinathan, P. Bhattacharya, B. Kochman, E. Berg, P. C. Yu, and S. Pang, “Characteristics of a photonic bandgap single defect microcavity electroluminescent device,” IEEE J. Quantum Electron. 37, 1153–1160 (2001).
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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, 1212–1214 (1999).
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M. Loncar, T. Yoshie, A. Scherer, P. Gogna, and Y. Qiu, “Low-threshold photonic crystal laser,” Appl. Phys. Lett. 81, 2680–2682 (2002).
[CrossRef]

J. Witzens, M. Loncar, and A. Scherer, “Self-collimation in planar photonic crystals,” IEEE J. Sel. Top. Quantum Electron. 8, 1246–1257 (2002).
[CrossRef]

M. Loncar, T. Doll, J. Vuckovic, and A. Scherer, “Design and fabrication of silicon photonic crystal optical waveguides,” J. Lightwave Technol. 18, 1402–1411 (2000).
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Shen, Y.

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G. G. Zheng, L. X. Shi, X. Y. Li, H. L. Wang, and J. Yuan, “Optical interconnections with photonic crystal self-collimation, directional emission and co-directional coupling mechanism,” J. Phys. D 42, 115101 (2009).
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B. S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science 300, 1537 (2003).
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M. Deubel, G. V. Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
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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, 568–572 (2009).
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A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).

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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, 1212–1214 (1999).
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G. Si, A. J. Danner, S. L. 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, 021205–021209 (2011).
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G. Si, A. J. Danner, S. L. 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, 021205–021209 (2011).
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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, 1212–1214 (1999).
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S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000).
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Wang, H. L.

G. G. Zheng, L. X. Shi, X. Y. Li, H. L. Wang, and J. Yuan, “Optical interconnections with photonic crystal self-collimation, directional emission and co-directional coupling mechanism,” J. Phys. D 42, 115101 (2009).
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M. Wang, M. Yun, W. Kong, and C. Cui, “Beam splitter and beam bends based on self-collimation effect in two-dimensional photonic crystals,” J. Mod. Opt. 56, 1159–1162 (2009).
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M. Deubel, G. V. Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
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Figures (12)

Fig. 1.
Fig. 1.

(a) Unit cell of the studied MAPC structure and its optogeometric parameters (R, r, D, θ). The structure is composed of dielectric material (Si) in air background. (b) Constituted MAPC structure and the Brillouin zone of the square lattices of the concerning structure.

Fig. 2.
Fig. 2.

3D dispersion surfaces of the designed MAPC are presented. (a), (b) Correspond to TM and TE polarizations, respectively. The colored layers in each case show the common CPBG regions.

Fig. 3.
Fig. 3.

Band structure of the TE (dotted line) and TM modes (solid line). The parameters of square-lattice MAPC are taken to be (R,r,D)=(0.360a,0.150a,0.180a) and (θ,FF1)=(45°,0.336). The shaded regions represent complete PBG.

Fig. 4.
Fig. 4.

Geometries of optimized MAPC structures for the specified rotation angles θ=(0°,20°,45°) in left column. For all the addressed geometries in the figure, the structural parameters are set to (R,r,D,FF2)=(0.485a,0.10a,0.180a,0.708). The calculated second band EFCs of the designed MAPCs are shown in the center and right columns of Figs. 4(a)4(c) for TM and TE modes, respectively. Self-collimation frequency regions for both TM and TE polarizations in Fig. 4(a) are presented by superimposing dashed boxes on the EFCs.

Fig. 5.
Fig. 5.

Spatial intensity distributions of electric field for the described MAPC structures are shown in (a)–(c) for TM polarization and (d)–(f) magnetic field intensity distributions for TE polarization. The structural parameters are set to (R,r,D)=(0.485a,0.10a,0.180a) with a filling factor of 0.708. The rotation angles, θ of the proposed structures are adjusted as shown in the figure. The operating frequency is constant at fcen1=0.283(a/λ).

Fig. 6.
Fig. 6.

Shifting angle α dependence on the variation of the rotation angle θ. The black solid-line with circle-marker represents α variation for TM mode, whereas the red solid line with square marker represents the variation for TE mode. Blue colored star shaped markers are inserted in order to show the overlapping points of α for TM and TE modes.

Fig. 7.
Fig. 7.

Dispersion plot of the hybrid type nanophotonic wire waveguide. The super cell implemented in the PWE method is given as an inset. The solid line represents TM modes, and the line with marker represents TE modes. The grayed region indicates the frequency range of interest for the polarization independent light guidance.

Fig. 8.
Fig. 8.

Steady-state field distributions of the hybrid MAPCs waveguide structure are presented. (a) Electric field (Ez) distribution for TM mode and (b) magnetic field (Hz) distribution for TE mode. The red and blue colors represent the maximum and minimum field values, respectively. (c), (d) Mode profiles of the gap-guided TM and TE modes at k=0.433(2π/a).

Fig. 9.
Fig. 9.

The normalized transmittance spectra for TM and TE modes are presented. The grayed region indicates the available frequency interval for polarization independent guiding of light.

Fig. 10.
Fig. 10.

Schematic views of polarization independent (a) self-collimated sharp bend and (b) power splitter cases. The etched area is used as a mirror. Continuous source is located at Port-0 and incident wave exits from Port-1 and Port-2. Field intensity distributions of sharp bend (c) for TM mode and (d) TE mode operation are shown. Field intensity distributions of power splitter for TM and TE polarizations are shown in (e) and (f), respectively. The optimized structural parameters are (R,r,D)=(0.360a,0.080a,0.180a) and (θ,FF3)=(0°,0.613). Common self-collimation region for both TM and TE polarizations are in the frequency range of a/λ=(0.2790.294) with a bandwidth of Δω/ω=5.24%. An appropriate operating frequency is chosen as fcen3=0.284(a/λ).

Fig. 11.
Fig. 11.

Transmission spectra for three cases of imperfections are presented. (a) The original case is provided for convenience. (b)–(d) Correspond to the inner radii of the neighboring MAPC rods that are reduced to 0.135a, 0.120a, and 0.105a, respectively.

Fig. 12.
Fig. 12.

Transmission spectra for three cases of imperfections are presented. (a) The original case is provided as a reference. (b)–(d) Correspond to outer radii of the neighboring MAPC rods that are increased to 0.365a, 0.370a, and 0.375a, respectively.

Tables (1)

Tables Icon

Table 1. Self-Collimation Region Changes with Respect to Shift Amount Parameter D

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