Abstract

We discuss, by a finite-difference time-domain method, a photonic crystal structure with two adjacent parallel line-defect waveguides to provoke highly-efficient directional emission of terahertz waves. The output field is analogous to a two-point-source interference pattern. Numerical simulations show that the maximum directional emission efficiency is up to 75%. Moreover, the efficiency is insensitive to transverse alignment error and angular alignment error. This structure is potentially important for high-efficiency coupling between freely propagated terahertz waves and Si waveguide systems.

© 2007 Optical Society of America

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  1. E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, "Enhanced transmission and beaming of light via photonic crystal surface modes," Phys. Rev. B 69, 121402 (2004).
    [CrossRef]
  2. P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, "Highly directional emission from photonic crystal waveguides of subwavelength width," Phys. Rev. Lett. 92, 113903 (2004).
    [CrossRef] [PubMed]
  3. S. K. Morrison and Y. S. Kivshar, "Engineering of directional emission from photonic-crystal waveguides," Appl. Phys. Lett. 86, 081110 (2005).
    [CrossRef]
  4. W. R. Frei, D. A. Tortorelli, and H. T. Johnson, "Topology optimization of a photonic crystal waveguide termination to maximize directional emission," Appl. Phys. Lett. 86, 111114 (2005).
    [CrossRef]
  5. I. Bulu, H. Caglayan, and E. Ozbay, "Beaming of light and enhanced transmission via surface modes of photonic crystals," Opt. Lett. 30, 3078-3080 (2005).
    [CrossRef] [PubMed]
  6. C. C. Chen, T. Pertsch, R. Iliew, F. Lederer, and A. Tünnermann, "Directional emission from photonic crystal waveguides," Opt. Express 14, 2423-2428 (2006).
    [CrossRef] [PubMed]
  7. D. Tang, L. Chen, and W. Ding, "Efficient beaming from photonic crystal waveguides via self-collimation effect," Appl. Phys. Lett. 89, 131120 (2006).
    [CrossRef]
  8. W. Y. Liang, J. W. Dong, and H. Z. Wang, "Directional emitter and beam splitter based on self-collimation effect," Opt. Express 15, 1234-1239 (2007).
    [CrossRef]
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    [CrossRef]
  10. T. Yamashita and C. J. Summers, "Evaluation of self-collimated beams in photonic crystals for optical interconnect," IEEE J. Sel. Areas Commun. 23, 1341-1347 (2005).
    [CrossRef]
  11. 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 Photon. Technol. Lett. 17, 61-63 (2005).
    [CrossRef]
  12. J. Witzens, M. Lončar, and A. Scherer, "Self-collimation in planar photonic crystals," IEEE J. Sel. Top. Quantum Electron. 8, 1246-1257 (2002).
    [CrossRef]
  13. 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]
  14. Z. Li, Y. Zhang, and B. Li, "Terahertz photonic crystal switch in silicon based on self-imaging principle," Opt. Express 14, 3887-3892 (2006).
    [CrossRef] [PubMed]
  15. Y. Zhang, Z. Li, and B. Li, "Multimode interference effect and self-imaging principle in two-dimensional silicon photonic crystal waveguides for terahertz waves," Opt. Express 14, 2679-2689 (2006).
    [CrossRef] [PubMed]
  16. K. Wang and D. M. Mittleman, "Metal wires for terahertz wave guiding," Nature 432, 376-379 (2004).
    [CrossRef] [PubMed]
  17. R. Mendis and D. Grischkowsky, "Plastic ribbon THz waveguides," J. Appl. Phys. 88, 4449-4451 (2000).
    [CrossRef]
  18. G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, "Terahertz waveguides," J. Opt. Soc. Am. B 17, 851-863 (2000).
    [CrossRef]

2007 (1)

2006 (4)

2005 (6)

S. K. Morrison and Y. S. Kivshar, "Engineering of directional emission from photonic-crystal waveguides," Appl. Phys. Lett. 86, 081110 (2005).
[CrossRef]

W. R. Frei, D. A. Tortorelli, and H. T. Johnson, "Topology optimization of a photonic crystal waveguide termination to maximize directional emission," Appl. Phys. Lett. 86, 111114 (2005).
[CrossRef]

T. Yamashita and C. J. Summers, "Evaluation of self-collimated beams in photonic crystals for optical interconnect," IEEE J. Sel. Areas Commun. 23, 1341-1347 (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 Photon. Technol. Lett. 17, 61-63 (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]

I. Bulu, H. Caglayan, and E. Ozbay, "Beaming of light and enhanced transmission via surface modes of photonic crystals," Opt. Lett. 30, 3078-3080 (2005).
[CrossRef] [PubMed]

2004 (3)

E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, "Enhanced transmission and beaming of light via photonic crystal surface modes," Phys. Rev. B 69, 121402 (2004).
[CrossRef]

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, "Highly directional emission from photonic crystal waveguides of subwavelength width," Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

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

2002 (1)

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

2000 (2)

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

G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, "Terahertz waveguides," J. Opt. Soc. Am. B 17, 851-863 (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]

Agio, M.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, "Highly directional emission from photonic crystal waveguides of subwavelength width," Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Birner, A.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, "Highly directional emission from photonic crystal waveguides of subwavelength width," Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Bulu, I.

Caglayan, H.

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 Photon. Technol. Lett. 17, 61-63 (2005).
[CrossRef]

Chen, C. C.

Chen, L.

D. Tang, L. Chen, and W. Ding, "Efficient beaming from photonic crystal waveguides via self-collimation effect," Appl. Phys. Lett. 89, 131120 (2006).
[CrossRef]

Ding, W.

D. Tang, L. Chen, and W. Ding, "Efficient beaming from photonic crystal waveguides via self-collimation effect," Appl. Phys. Lett. 89, 131120 (2006).
[CrossRef]

Dong, J. W.

Frei, W. R.

W. R. Frei, D. A. Tortorelli, and H. T. Johnson, "Topology optimization of a photonic crystal waveguide termination to maximize directional emission," Appl. Phys. Lett. 86, 111114 (2005).
[CrossRef]

Gallot, G.

García-Vidal, F. J.

E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, "Enhanced transmission and beaming of light via photonic crystal surface modes," Phys. Rev. B 69, 121402 (2004).
[CrossRef]

Gösele, U.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, "Highly directional emission from photonic crystal waveguides of subwavelength width," Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Grischkowsky, D.

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]

Iliew, R.

Jamison, S. P.

Johnson, H. T.

W. R. Frei, D. A. Tortorelli, and H. T. Johnson, "Topology optimization of a photonic crystal waveguide termination to maximize directional emission," Appl. Phys. Lett. 86, 111114 (2005).
[CrossRef]

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, 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, 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]

Kivshar, Y. S.

S. K. Morrison and Y. S. Kivshar, "Engineering of directional emission from photonic-crystal waveguides," Appl. Phys. Lett. 86, 081110 (2005).
[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, 1212-1214 (1999).
[CrossRef]

Kramper, P.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, "Highly directional emission from photonic crystal waveguides of subwavelength width," Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Lederer, F.

Lee, S. G.

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]

Li, B.

Li, Z.

Liang, W. Y.

Loncar, M.

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

Martín-Moreno, L.

E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, "Enhanced transmission and beaming of light via photonic crystal surface modes," Phys. Rev. B 69, 121402 (2004).
[CrossRef]

McGowan, R. W.

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 Photon. Technol. Lett. 17, 61-63 (2005).
[CrossRef]

Mittleman, D. M.

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

Moreno, E.

E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, "Enhanced transmission and beaming of light via photonic crystal surface modes," Phys. Rev. B 69, 121402 (2004).
[CrossRef]

Morrison, S. K.

S. K. Morrison and Y. S. Kivshar, "Engineering of directional emission from photonic-crystal waveguides," Appl. Phys. Lett. 86, 081110 (2005).
[CrossRef]

Müller, F.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, "Highly directional emission from photonic crystal waveguides of subwavelength width," Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

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]

Ozbay, E.

Park, H. Y.

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]

Pertsch, 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 Photon. Technol. Lett. 17, 61-63 (2005).
[CrossRef]

Sandoghdar, V.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, "Highly directional emission from photonic crystal waveguides of subwavelength width," Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

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. Lončar, and A. Scherer, "Self-collimation in planar photonic crystals," IEEE J. Sel. Top. Quantum Electron. 8, 1246-1257 (2002).
[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 Photon. Technol. Lett. 17, 61-63 (2005).
[CrossRef]

Soukoulis, C. M.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, "Highly directional emission from photonic crystal waveguides of subwavelength width," Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Summers, C. J.

T. Yamashita and C. J. Summers, "Evaluation of self-collimated beams in photonic crystals for optical interconnect," IEEE J. Sel. Areas Commun. 23, 1341-1347 (2005).
[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]

Tang, D.

D. Tang, L. Chen, and W. Ding, "Efficient beaming from photonic crystal waveguides via self-collimation effect," Appl. Phys. Lett. 89, 131120 (2006).
[CrossRef]

Tomita, A.

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]

Tortorelli, D. A.

W. R. Frei, D. A. Tortorelli, and H. T. Johnson, "Topology optimization of a photonic crystal waveguide termination to maximize directional emission," Appl. Phys. Lett. 86, 111114 (2005).
[CrossRef]

Tünnermann, A.

Wang, H. Z.

Wang, K.

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

Wehrspohn, R. B.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, "Highly directional emission from photonic crystal waveguides of subwavelength width," Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Witzens, J.

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

Yamashita, T.

T. Yamashita and C. J. Summers, "Evaluation of self-collimated beams in photonic crystals for optical interconnect," IEEE J. Sel. Areas Commun. 23, 1341-1347 (2005).
[CrossRef]

Zhang, Y.

Appl. Phys. Lett. (5)

S. K. Morrison and Y. S. Kivshar, "Engineering of directional emission from photonic-crystal waveguides," Appl. Phys. Lett. 86, 081110 (2005).
[CrossRef]

W. R. Frei, D. A. Tortorelli, and H. T. Johnson, "Topology optimization of a photonic crystal waveguide termination to maximize directional emission," Appl. Phys. Lett. 86, 111114 (2005).
[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, 1212-1214 (1999).
[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]

D. Tang, L. Chen, and W. Ding, "Efficient beaming from photonic crystal waveguides via self-collimation effect," Appl. Phys. Lett. 89, 131120 (2006).
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

T. Yamashita and C. J. Summers, "Evaluation of self-collimated beams in photonic crystals for optical interconnect," IEEE J. Sel. Areas Commun. 23, 1341-1347 (2005).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

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

IEEE Photon. Technol. Lett. (1)

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 Photon. Technol. Lett. 17, 61-63 (2005).
[CrossRef]

J. Appl. Phys. (1)

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

J. Opt. Soc. Am. B (1)

Nature (1)

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

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. B (1)

E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, "Enhanced transmission and beaming of light via photonic crystal surface modes," Phys. Rev. B 69, 121402 (2004).
[CrossRef]

Phys. Rev. Lett. (1)

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, "Highly directional emission from photonic crystal waveguides of subwavelength width," Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1.
Fig. 1.

Schematic diagram of the proposed structure. RQ is a measurement line of directional emission efficiency.

Fig. 2.
Fig. 2.

Equifrequency contours of the second band of the PC structure for TM-polarization modes.

Fig. 3.
Fig. 3.

Transmission versus wavelength, showing that the maximum efficiency is achieved when the wavelength is 166 µm.

Fig. 4.
Fig. 4.

Steady-state field distribution in the PC structure. The dashed rectangular region is for later analysis.

Fig. 5.
Fig. 5.

Transverse power density obtained as time average at y=11.31a. Two main peaks appear at x=±0.8a.

Fig. 6.
Fig. 6.

(a). Steady-state field distribution interfered by two point sources with 1.6a distance. (b) The dashed rectangular region in Fig. 4.

Fig. 7.
Fig. 7.

Transverse power densities obtained as time average at y=26a. (a) for transverse alignment error and (b) for angular alignment error.

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