Abstract

We present two types of antireflection structures for two-dimensional photonic crystals of square lattice air holes in silicon, which are embedded in homogeneous background media. One type consists of rows of air holes, and the other consists of air slots that are introduced into the photonic crystal interfaces. The finite-difference time-domain simulations show that the terahertz waves couple efficiently into and out of the self-collimating photonic crystals with the designed antireflection structures applied. The proposed antireflection structures can bring significant improvements in coupling efficiency for compact terahertz devices based on self-collimating photonic crystals.

© 2009 Optical Society of America

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    [CrossRef]
  2. K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432, 376-379 (2004).
    [CrossRef] [PubMed]
  3. H. Kurt and D. S. Citrin, “Photonic crystals for biochemical sensing in the terahertz region,” Appl. Phys. Lett. 87, 041108 (2005).
    [CrossRef]
  4. G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, “Terahertz waveguides,” J. Opt. Soc. Am. B 17, 851-863 (2000).
    [CrossRef]
  5. R. Mendis and D. Grischkowsky, “Plastic ribbon THz waveguides,” J. Appl. Phys. 88, 4449-4451 (2000).
    [CrossRef]
  6. Y. Zhao and D. Grischkowsky, “Terahertz demonstrations of effectively two dimensional photonic bandgap structures,” Opt. Lett. 31, 1534-1536 (2006).
    [CrossRef] [PubMed]
  7. T. Prasad, V. L. Colvin, Z. Jian, and D. M. Mittleman, “Superprism effect in a metal-clad terahertz photonic crystal slab,” Opt. Lett. 32, 683-685 (2007).
    [CrossRef] [PubMed]
  8. H. Liu, J. Yao, D. Xu, and P. Wang, “Propagation characteristics of two-dimensional photonic crystals in the terahertz range,” Appl. Phys. B 87, 57-63 (2007).
    [CrossRef]
  9. Y. Zhang, Y. Zhang, and B. Li, “Highly-efficient directional emission from photonic crystal waveguides for coupling of freely propagated terahertz waves into Si slab waveguides,” Opt. Express 15, 9281-9286 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
  12. J. Witzens, M. Loncar, and A. Scherer, “Self-collimation in planar photonic crystals,” IEEE J. Sel. Top. Quantum Electron. 8, 1246-1257 (2002).
    [CrossRef]
  13. X. Yu and S. Fan, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett. 83, 3251-3253 (2003).
    [CrossRef]
  14. 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] [PubMed]
  15. S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 87, 181106 (2005).
    [CrossRef]
  16. B. Miao, C. Chen, S. Shi, and D. W. Prather, “A high-efficiency in-plane splitting coupler for planar photonic crystal self-collimation devices,” IEEE Photonics Technol. Lett. 17, 61-63 (2005).
    [CrossRef]
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  18. J.-M. Park, S.-G. Lee, H. Y. Park, and J.-E. Kim, “Efficient beaming of self-collimated light from photonic crystals,” Opt. Express 16, 20354-20367 (2008).
    [CrossRef] [PubMed]
  19. T. Baba and D. Ohsaki, “Interfaces of photonic crystals for high efficiency light transmission,” Jpn. J. Appl. Phys. 40, 5920-5924 (2001).
    [CrossRef]
  20. F. J. Lawrence, L. C. Botten, K. B. Dossou, and C. Martijn de Sterke, “Antireflection coatings for two-dimensional photonic crystals using a rigorous impedance definition,” Appl. Phys. Lett. 93, 121114 (2008).
    [CrossRef]
  21. T. P. White, C. Martijn de Sterke, R. C. McPhedran, and L. C. Botten, “Highly efficient wide-angle transmission into uniform rod-type photonic crystals,” Appl. Phys. Lett. 87, 111107 (2005).
    [CrossRef]
  22. Z. Li, E. Ozbay, H. Chen, J. Chen, F. Yang, and H. Zheng, “Resonant cavity based compact efficient antireflection structures for photonic crystals,” J. Phys. D 40, 5873-5877 (2007).
    [CrossRef]
  23. J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Sherer, “Mode matching interface for efficient coupling of light into planar photonic crystals,” Phys. Rev. E 69, 046609 (2004).
    [CrossRef]
  24. B. Momeni and A. Adibi, “Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystal,” Appl. Phys. Lett. 87, 171104 (2005).
    [CrossRef]
  25. J. Ushida, M. Tokushima, M. Shirane, and H. Yamada, “Systematic design of antireflection coating for semi-infinite one-dimensional photonic crystals using Bloch wave expansion,” Appl. Phys. Lett. 82, 7-9 (2003).
    [CrossRef]
  26. S.-G. Lee, J.-S. Choi, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Reflection minimization at two-dimensional photonic crystal interfaces,” Opt. Express 16, 4270-4277 (2008).
    [CrossRef] [PubMed]
  27. S.-G. Lee, M. Yi, J. Ahn, J.-E. Kim, and H. Y. Park, “Optimization of photonic crystal interfaces for high efficient coupling of terahertz waves,” in International Conference on Infrared and Millimeter Waves/THz Electronics (IRMMW-THZ 2008) (IEEE, 2008), pp. 1-2
  28. K. S. Yee, “Numerical solution of initial boundary problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302-307 (1966).
  29. S. G. 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] [PubMed]
  30. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185-200 (1994).
    [CrossRef]
  31. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge Univ. Press, 1999), pp. 63-74.
  32. H. A. Macleod, Thin Film Optical Filters, 3rd ed. (Institute of Physics, 2001), Chaps. 2 and 3.
    [CrossRef]

2008

2007

T. Prasad, V. L. Colvin, Z. Jian, and D. M. Mittleman, “Superprism effect in a metal-clad terahertz photonic crystal slab,” Opt. Lett. 32, 683-685 (2007).
[CrossRef] [PubMed]

Y. Zhang, Y. Zhang, and B. Li, “Highly-efficient directional emission from photonic crystal waveguides for coupling of freely propagated terahertz waves into Si slab waveguides,” Opt. Express 15, 9281-9286 (2007).
[CrossRef] [PubMed]

Z. Li, E. Ozbay, H. Chen, J. Chen, F. Yang, and H. Zheng, “Resonant cavity based compact efficient antireflection structures for photonic crystals,” J. Phys. D 40, 5873-5877 (2007).
[CrossRef]

H. Liu, J. Yao, D. Xu, and P. Wang, “Propagation characteristics of two-dimensional photonic crystals in the terahertz range,” Appl. Phys. B 87, 57-63 (2007).
[CrossRef]

2006

2005

H. Kurt and D. S. Citrin, “Photonic crystals for biochemical sensing in the terahertz region,” Appl. Phys. Lett. 87, 041108 (2005).
[CrossRef]

B. Momeni and A. Adibi, “Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystal,” Appl. Phys. Lett. 87, 171104 (2005).
[CrossRef]

T. P. White, C. Martijn de Sterke, R. C. McPhedran, and L. C. Botten, “Highly efficient wide-angle transmission into uniform rod-type photonic crystals,” Appl. Phys. Lett. 87, 111107 (2005).
[CrossRef]

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 87, 181106 (2005).
[CrossRef]

B. Miao, C. Chen, S. Shi, and D. W. Prather, “A high-efficiency in-plane splitting coupler for planar photonic crystal self-collimation devices,” IEEE Photonics Technol. Lett. 17, 61-63 (2005).
[CrossRef]

2004

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Sherer, “Mode matching interface for efficient coupling of light into planar photonic crystals,” Phys. Rev. E 69, 046609 (2004).
[CrossRef]

K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432, 376-379 (2004).
[CrossRef] [PubMed]

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] [PubMed]

2003

X. Yu and S. Fan, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett. 83, 3251-3253 (2003).
[CrossRef]

J. Ushida, M. Tokushima, M. Shirane, and H. Yamada, “Systematic design of antireflection coating for semi-infinite one-dimensional photonic crystals using Bloch wave expansion,” Appl. Phys. Lett. 82, 7-9 (2003).
[CrossRef]

2002

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

P. H. Siegel, “Terahertz technology,” IEEE Trans. Microwave Theory Tech. 50, 910-928 (2002).
[CrossRef]

2001

T. Baba and D. Ohsaki, “Interfaces of photonic crystals for high efficiency light transmission,” Jpn. J. Appl. Phys. 40, 5920-5924 (2001).
[CrossRef]

S. G. 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] [PubMed]

2000

G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, “Terahertz waveguides,” J. Opt. Soc. Am. B 17, 851-863 (2000).
[CrossRef]

R. Mendis and D. Grischkowsky, “Plastic ribbon THz waveguides,” J. Appl. Phys. 88, 4449-4451 (2000).
[CrossRef]

1999

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]

1994

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

1966

K. S. Yee, “Numerical solution of initial boundary problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302-307 (1966).

Adibi, A.

B. Momeni and A. Adibi, “Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystal,” Appl. Phys. Lett. 87, 171104 (2005).
[CrossRef]

Ahn, J.

S.-G. Lee, M. Yi, J. Ahn, J.-E. Kim, and H. Y. Park, “Optimization of photonic crystal interfaces for high efficient coupling of terahertz waves,” in International Conference on Infrared and Millimeter Waves/THz Electronics (IRMMW-THZ 2008) (IEEE, 2008), pp. 1-2

Baba, T.

T. Baba and D. Ohsaki, “Interfaces of photonic crystals for high efficiency light transmission,” Jpn. J. Appl. Phys. 40, 5920-5924 (2001).
[CrossRef]

Baehr-Jones, T.

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Sherer, “Mode matching interface for efficient coupling of light into planar photonic crystals,” Phys. Rev. E 69, 046609 (2004).
[CrossRef]

Berenger, J. P.

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

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge Univ. Press, 1999), pp. 63-74.

Botten, L. C.

F. J. Lawrence, L. C. Botten, K. B. Dossou, and C. Martijn de Sterke, “Antireflection coatings for two-dimensional photonic crystals using a rigorous impedance definition,” Appl. Phys. Lett. 93, 121114 (2008).
[CrossRef]

T. P. White, C. Martijn de Sterke, R. C. McPhedran, and L. C. Botten, “Highly efficient wide-angle transmission into uniform rod-type photonic crystals,” Appl. Phys. Lett. 87, 111107 (2005).
[CrossRef]

Chen, C.

B. Miao, C. Chen, S. Shi, and D. W. Prather, “A high-efficiency in-plane splitting coupler for planar photonic crystal self-collimation devices,” IEEE Photonics Technol. Lett. 17, 61-63 (2005).
[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] [PubMed]

Chen, H.

Z. Li, E. Ozbay, H. Chen, J. Chen, F. Yang, and H. Zheng, “Resonant cavity based compact efficient antireflection structures for photonic crystals,” J. Phys. D 40, 5873-5877 (2007).
[CrossRef]

Chen, J.

Z. Li, E. Ozbay, H. Chen, J. Chen, F. Yang, and H. Zheng, “Resonant cavity based compact efficient antireflection structures for photonic crystals,” J. Phys. D 40, 5873-5877 (2007).
[CrossRef]

Choi, J.-S.

Citrin, D. S.

H. Kurt and D. S. Citrin, “Photonic crystals for biochemical sensing in the terahertz region,” Appl. Phys. Lett. 87, 041108 (2005).
[CrossRef]

Colvin, V. L.

Dossou, K. B.

F. J. Lawrence, L. C. Botten, K. B. Dossou, and C. Martijn de Sterke, “Antireflection coatings for two-dimensional photonic crystals using a rigorous impedance definition,” Appl. Phys. Lett. 93, 121114 (2008).
[CrossRef]

Fan, S.

X. Yu and S. Fan, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett. 83, 3251-3253 (2003).
[CrossRef]

Gallot, G.

Ghattan, Z.

Grischkowsky, D.

Hasek, T.

Hochberg, M.

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Sherer, “Mode matching interface for efficient coupling of light into planar photonic crystals,” Phys. Rev. E 69, 046609 (2004).
[CrossRef]

Jamison, S. P.

Jian, Z.

Joannopoulos, J. D.

S. G. 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] [PubMed]

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

Johnson, S. G.

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, 1212-1214 (1999).
[CrossRef]

Kawashima, 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, 1212-1214 (1999).
[CrossRef]

Kee, C.-S.

S.-G. Lee, J.-S. Choi, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Reflection minimization at two-dimensional photonic crystal interfaces,” Opt. Express 16, 4270-4277 (2008).
[CrossRef] [PubMed]

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 87, 181106 (2005).
[CrossRef]

Kim, J.-E.

S.-G. Lee, J.-S. Choi, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Reflection minimization at two-dimensional photonic crystal interfaces,” Opt. Express 16, 4270-4277 (2008).
[CrossRef] [PubMed]

J.-M. Park, S.-G. Lee, H. Y. Park, and J.-E. Kim, “Efficient beaming of self-collimated light from photonic crystals,” Opt. Express 16, 20354-20367 (2008).
[CrossRef] [PubMed]

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 87, 181106 (2005).
[CrossRef]

S.-G. Lee, M. Yi, J. Ahn, J.-E. Kim, and H. Y. Park, “Optimization of photonic crystal interfaces for high efficient coupling of terahertz waves,” in International Conference on Infrared and Millimeter Waves/THz Electronics (IRMMW-THZ 2008) (IEEE, 2008), pp. 1-2

Koch, M.

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, 1212-1214 (1999).
[CrossRef]

Kurt, H.

H. Kurt and D. S. Citrin, “Photonic crystals for biochemical sensing in the terahertz region,” Appl. Phys. Lett. 87, 041108 (2005).
[CrossRef]

Lawrence, F. J.

F. J. Lawrence, L. C. Botten, K. B. Dossou, and C. Martijn de Sterke, “Antireflection coatings for two-dimensional photonic crystals using a rigorous impedance definition,” Appl. Phys. Lett. 93, 121114 (2008).
[CrossRef]

Lee, S.-G.

J.-M. Park, S.-G. Lee, H. Y. Park, and J.-E. Kim, “Efficient beaming of self-collimated light from photonic crystals,” Opt. Express 16, 20354-20367 (2008).
[CrossRef] [PubMed]

S.-G. Lee, J.-S. Choi, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Reflection minimization at two-dimensional photonic crystal interfaces,” Opt. Express 16, 4270-4277 (2008).
[CrossRef] [PubMed]

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 87, 181106 (2005).
[CrossRef]

S.-G. Lee, M. Yi, J. Ahn, J.-E. Kim, and H. Y. Park, “Optimization of photonic crystal interfaces for high efficient coupling of terahertz waves,” in International Conference on Infrared and Millimeter Waves/THz Electronics (IRMMW-THZ 2008) (IEEE, 2008), pp. 1-2

Li, B.

Li, Z.

Z. Li, E. Ozbay, H. Chen, J. Chen, F. Yang, and H. Zheng, “Resonant cavity based compact efficient antireflection structures for photonic crystals,” J. Phys. D 40, 5873-5877 (2007).
[CrossRef]

Liu, H.

H. Liu, J. Yao, D. Xu, and P. Wang, “Propagation characteristics of two-dimensional photonic crystals in the terahertz range,” Appl. Phys. B 87, 57-63 (2007).
[CrossRef]

Loncar, M.

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

Macleod, H. A.

H. A. Macleod, Thin Film Optical Filters, 3rd ed. (Institute of Physics, 2001), Chaps. 2 and 3.
[CrossRef]

Martijn de Sterke, C.

F. J. Lawrence, L. C. Botten, K. B. Dossou, and C. Martijn de Sterke, “Antireflection coatings for two-dimensional photonic crystals using a rigorous impedance definition,” Appl. Phys. Lett. 93, 121114 (2008).
[CrossRef]

T. P. White, C. Martijn de Sterke, R. C. McPhedran, and L. C. Botten, “Highly efficient wide-angle transmission into uniform rod-type photonic crystals,” Appl. Phys. Lett. 87, 111107 (2005).
[CrossRef]

McGowan, R. W.

McPhedran, R. C.

T. P. White, C. Martijn de Sterke, R. C. McPhedran, and L. C. Botten, “Highly efficient wide-angle transmission into uniform rod-type photonic crystals,” Appl. Phys. Lett. 87, 111107 (2005).
[CrossRef]

Meade, R. D.

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

Mendis, R.

R. Mendis and D. Grischkowsky, “Plastic ribbon THz waveguides,” J. Appl. Phys. 88, 4449-4451 (2000).
[CrossRef]

Miao, B.

B. Miao, C. Chen, S. Shi, and D. W. Prather, “A high-efficiency in-plane splitting coupler for planar photonic crystal self-collimation devices,” IEEE Photonics Technol. Lett. 17, 61-63 (2005).
[CrossRef]

Mittleman, D. M.

Momeni, B.

B. Momeni and A. Adibi, “Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystal,” Appl. Phys. Lett. 87, 171104 (2005).
[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, 1212-1214 (1999).
[CrossRef]

Oh, S. S.

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 87, 181106 (2005).
[CrossRef]

Ohsaki, D.

T. Baba and D. Ohsaki, “Interfaces of photonic crystals for high efficiency light transmission,” Jpn. J. Appl. Phys. 40, 5920-5924 (2001).
[CrossRef]

Ozbay, E.

Z. Li, E. Ozbay, H. Chen, J. Chen, F. Yang, and H. Zheng, “Resonant cavity based compact efficient antireflection structures for photonic crystals,” J. Phys. D 40, 5873-5877 (2007).
[CrossRef]

Park, H. Y.

S.-G. Lee, J.-S. Choi, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Reflection minimization at two-dimensional photonic crystal interfaces,” Opt. Express 16, 4270-4277 (2008).
[CrossRef] [PubMed]

J.-M. Park, S.-G. Lee, H. Y. Park, and J.-E. Kim, “Efficient beaming of self-collimated light from photonic crystals,” Opt. Express 16, 20354-20367 (2008).
[CrossRef] [PubMed]

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 87, 181106 (2005).
[CrossRef]

S.-G. Lee, M. Yi, J. Ahn, J.-E. Kim, and H. Y. Park, “Optimization of photonic crystal interfaces for high efficient coupling of terahertz waves,” in International Conference on Infrared and Millimeter Waves/THz Electronics (IRMMW-THZ 2008) (IEEE, 2008), pp. 1-2

Park, J.-M.

Prasad, T.

Prather, D. W.

B. Miao, C. Chen, S. Shi, and D. W. Prather, “A high-efficiency in-plane splitting coupler for planar photonic crystal self-collimation devices,” IEEE Photonics Technol. Lett. 17, 61-63 (2005).
[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] [PubMed]

Pustai, D. M.

Sato, 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, 1212-1214 (1999).
[CrossRef]

Scherer, A.

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

Shahabadi, M.

Sharkawy, A.

Sherer, A.

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Sherer, “Mode matching interface for efficient coupling of light into planar photonic crystals,” Phys. Rev. E 69, 046609 (2004).
[CrossRef]

Shi, S.

B. Miao, C. Chen, S. Shi, and D. W. Prather, “A high-efficiency in-plane splitting coupler for planar photonic crystal self-collimation devices,” IEEE Photonics Technol. Lett. 17, 61-63 (2005).
[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] [PubMed]

Shirane, M.

J. Ushida, M. Tokushima, M. Shirane, and H. Yamada, “Systematic design of antireflection coating for semi-infinite one-dimensional photonic crystals using Bloch wave expansion,” Appl. Phys. Lett. 82, 7-9 (2003).
[CrossRef]

Siegel, P. H.

P. H. Siegel, “Terahertz technology,” IEEE Trans. Microwave Theory Tech. 50, 910-928 (2002).
[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, 1212-1214 (1999).
[CrossRef]

Tokushima, M.

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H. Liu, J. Yao, D. Xu, and P. Wang, “Propagation characteristics of two-dimensional photonic crystals in the terahertz range,” Appl. Phys. B 87, 57-63 (2007).
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T. P. White, C. Martijn de Sterke, R. C. McPhedran, and L. C. Botten, “Highly efficient wide-angle transmission into uniform rod-type photonic crystals,” Appl. Phys. Lett. 87, 111107 (2005).
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J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 1995).

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J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Sherer, “Mode matching interface for efficient coupling of light into planar photonic crystals,” Phys. Rev. E 69, 046609 (2004).
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H. Liu, J. Yao, D. Xu, and P. Wang, “Propagation characteristics of two-dimensional photonic crystals in the terahertz range,” Appl. Phys. B 87, 57-63 (2007).
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J. Ushida, M. Tokushima, M. Shirane, and H. Yamada, “Systematic design of antireflection coating for semi-infinite one-dimensional photonic crystals using Bloch wave expansion,” Appl. Phys. Lett. 82, 7-9 (2003).
[CrossRef]

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Z. Li, E. Ozbay, H. Chen, J. Chen, F. Yang, and H. Zheng, “Resonant cavity based compact efficient antireflection structures for photonic crystals,” J. Phys. D 40, 5873-5877 (2007).
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X. Yu and S. Fan, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett. 83, 3251-3253 (2003).
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Z. Li, E. Ozbay, H. Chen, J. Chen, F. Yang, and H. Zheng, “Resonant cavity based compact efficient antireflection structures for photonic crystals,” J. Phys. D 40, 5873-5877 (2007).
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Figures (9)

Fig. 1
Fig. 1

(a) Schematic of the ARC structure for a semi-infinite 2D square lattice PC consisting of rods (or holes) in a homogeneous background medium, which is enclosed by the gray rectangle (orange online). (b) Schematic of a light beam incident normally from homogeneous Si background to a semi-infinite 2D hole-type PC. (c) Schematic of the hole-type ARC structure, ARC A H for a semi-infinite 2D hole-type PC in Si background, which is enclosed by a rectangle. (d) Schematic of the slot-type ARC structure, ARC A S for a semi-infinite 2D hole-type PC in Si background, which is enclosed by a rectangle . In (b)–(d), the thick and thin gray arrows (red online) indicate the incident and reflected beams, respectively.

Fig. 2
Fig. 2

(a) Reflection spectra of the semi-infinite 2D hole-type PC in homogeneous Si background for the cases without the ARC, with the ARC A H , and with the ARC A S structures [see Figs. 1b, 1c, 1d, respectively]. (b) Transmission spectra of a finite PC sample of size 21 2 a = 1782 μ m in Si background for the cases without the ARC, with the ARC A H , and with the ARC A S applied at both the input and output ends. The dark gray dashed and gray dotted curves indicate the transmission spectra of the intermediate structures, in which only at the input end, either the ARC A H or the ARC A S is applied. In (a) and (b), the vertical dotted lines indicate the SC frequency f = 0.191 c a = 0.955 THz .

Fig. 3
Fig. 3

(a) Schematic of a light beam incident normally from air to a semi-infinite 2D square lattice PC consisting of air holes in Si without any ARC structure. (b) Reflection at the interface between air and the semi-infinite 2D hole-type PC for the light of SC frequency f = 0.955 THz , as a function of the distance d cut between the first layer of holes and the PC–air interface when no ARC structure is applied. (c) Schematic of the ARC B H for the semi-infinite 2D hole-type PC in air background, which is enclosed by a rectangle. The ARC parameters are the distances H 1 h , H 2 h , and the radius r of air holes. (d) Schematic of the ARC B S for the semi-infinite 2D hole-type PC in air background, which is enclosed by a rectangle. The ARC parameters are the distances H 1 s , H 2 s , and the thickness t air of air slot. In (a), (c), and (d), the thick and thin gray arrows (red online) indicate the incident and reflected beams, respectively.

Fig. 4
Fig. 4

(a) Reflection spectra of the semi-infinite 2D hole-type PC in air for the cases without the ARC, with the ARC B H , and with the ARC B S structures [see Figs. 3a, 3c, 3d, respectively]. The distance d cut between the first layer of holes of the PC and the PC–air interface for the case without the ARC structure is set to 0.39 a = 23.4 μ m [see Fig. 3b]. (b) Transmission spectra of a 2D hole-type Si PC sample of size 21 2 a in air for the cases without the ARC, with the ARC B H , and with the ARC B S . The dark gray dashed lines and gray dotted lines indicate the intermediate structures; only at the input ends of the PC sample, either the ARC B H or the ARC B S is attached. In (a) and (b), the vertical dotted lines indicate the SC frequency f = 0.191 c a = 0.955 THz .

Fig. 5
Fig. 5

(a) Schematic of the designed ARC C H for semi-infinite 2D Si in air, which is composed of two rows of holes and enclosed by a rectangle. (b) r 23 is the reflection coefficient of the second row of the ARC C H with the hole radius r arc when the light is incident upon it from Si, and r 12 is that of the first layer of the ARC C H with the hole radius r and H 1 h when the light is incident upon it from air. H 1 h is the distance of the first hole layer of the ARC C H from the Si–air interface. (c) Schematic of the designed ARC C S for semi-infinite 2D Si in air, which is composed of two parallel air slots and enclosed by a rectangle. (d) r 23 is the reflection coefficient of the second slot of the ARC C S with the thickness t Si when the light is incident upon it from Si, and r 12 is that of the first slot of the ARC C S with the thickness t air and H 1 s when the light is incident upon it from air. H 1 s is the distance of the first air slot of the ARC C S from the Si–air interface. In (a)–(d), the thick and thin gray arrows (red online) indicate the incident and reflected beams, respectively.

Fig. 6
Fig. 6

(a) Reflection spectra of semi-infinite 2D Si in air for the cases without the ARC, with the ARC C H [see Fig. 5a], and with the ARC C S [see Fig. 5c] structures. (b) Transmission spectra of a Si sample of size 21 2 a = 1782 μ m in air for the cases without the ARC, with the ARC C H , and with the ARC C S . The dark gray dashed curves and gray dotted curves indicate the intermediate structures; only the input end has either the ARC C H or the ARC C S . In (a) and (b), the vertical dotted lines indicate the SC frequency f = 0.191 c a = 0.955 THz .

Fig. 7
Fig. 7

Schematics of the designed structures, (a) PCW d cut , (b) PCW B A H , and (c) PCW B A S . Two PCWs in the PC are introduced by removing three rows of air holes with six holes in a row at both sides of the center air holes starting from the interface of the PC and the 2D Si along the x direction (the ΓM direction) in a finite PC structure, which is composed of 19 and 29 layers of air holes in Si in the x and y directions, respectively. The combined structure of PC and PCWs is sandwiched between air and Si. The thick arrows indicate the incident beams. In (b) and (c), the large and small rectangles denote the ARC B H ( S ) and the ARC A H ( S ) structures, respectively.

Fig. 8
Fig. 8

Magnetic-field amplitude distributions at steady states for the corresponding structures depicted in Figs. 7a, 7b, 7c, 5a, 5c, and the bare 2D Si in air without any ARC structure, which are displayed in that order. The SC frequency and width of the incident Gaussian beam are f = 0.191 c a = 0.955 THz and 4 a, respectively. The Gaussian TM mode light source denoted by the short gray line (red online) is launched at the distance of 2 a before the center (i.e., y = 0) of the input surface layer of all the structures described above and propagates along the x direction in the plane at y = 0, where x = 0 is positioned at the input surface layer of the 2D Si. The other short lines (yellow online) denote the detector positions to measure the power transmitted along the x direction. The detectors have the width of 4 a and are positioned at x = 11.0 a and x = 22.7 a, at which the angular spread is 20° and 10°, respectively. In (b) and (c), the ARC B H ( S ) is applied at the input side interface of air and the PC, and the ARC A H ( S ) at the output side interface between the PC and the PCWs, which are enclosed by the large (red) and the small (green) rectangles, respectively. In (d) and (e), the dark (blue) rectangles denote the ARC C H and the ARC C S structures, respectively.

Fig. 9
Fig. 9

Transmission spectra for the corresponding beaming structures shown in Fig. 8 within the angles of (a) 20° and (b) 10°. The vertical dotted lines indicate the SC frequency f = 0.191 c a = 0.955 THz .

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