Abstract

The TM propagation properties of planar 12-fold photonic quasi-crystal patterns are theoretically examined using FDTD. The patterns examined can be produced using a dual beam multiple exposure technique. Simulated transmission plots are shown for various fill factors, dielectric contrast and propagation direction. It is shown that low index waveguides can be produced using the quasi-crystal photonic crystal pattern.

© 2005 Optical Society of America

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  1. P. I. Borel, L. H. Frandsen, A. Harpøth, J. B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, “Bandwidth engineering of photonic crystal waveguide bends,” Electron. Lett. 401263–1264 (2004)
    [CrossRef]
  2. H. Park, J. Hwang, J. Huh, H. Ryu, S. Kim, J. Kim, and Y. Lee, “Characteristics of Modified Single-Defect Two-Dimensional Photonic Crystal Lasers,” Quantum Electron. 381353–1365 (2002)
    [CrossRef]
  3. S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Rate-equation analysis of output efficiency and modulation rate of photonic-crystal light-emitting diodes,” Quantum Electron. 36, 1123–1130 (2000)
    [CrossRef]
  4. N. Hitoshi, Y. Sugimoto, K. Kanamoto, N. Ikeda, Y. Tanaka, Y. Nakamura, S. Ohkouchi, Y. Watanabe, K. Inoue, H. Ishikawa, and K. Asakawa, “Ultra-fast photonic crystal/quantum dot alloptical switch for future photonic networks,” Opt. Express 12, 6606–6614 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-26-6606
    [CrossRef] [PubMed]
  5. M. E. Potter and R. W. Ziolkowski, “Two compact structures for perpendicular coupling of optical signals between dielectric and photonic crystal waveguides,” Opt. Express 10, 691–698 (2002). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-15-691
    [PubMed]
  6. L. B. Shaw, J. S. Sanghera, I. D. Aggarwal, and F. H. Hung, “As-S and As-Se based photonic band gap fiber for IR laser transmission,” Opt. Express 11, 3455–3460 (2003) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-25-3455
    [CrossRef] [PubMed]
  7. Y. Roh, S. Yoon, H. Jeon, S. Han, and Q. Park, “Two-dimensional photonic crystal waveguides with multiple sharp bends,” Proc. SPIE Int. Soc. Opt. Eng. 5360, 199–201 (2004)
  8. T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B 50, 4220–4223 (1994)
    [CrossRef]
  9. C. Sibilia, I. S. Nefedov, M. Scalora, and M. Bertolotti, “Electromagnetic mode density for finite quasi-periodic structures,” J. Opt. Soc. Am. B 15, 1947–1952 (1998)
    [CrossRef]
  10. M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. M. De La Rue, and P Millar, “Two-dimensional Penrose-tiled photonic quasicrystals: diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771–1778 (2000)
  11. M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. M. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals: From diffraction to band structure,” Nanotechnology 11274–280 (2000)
    [CrossRef]
  12. C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, D. J. Zhang, S. Z. Ban, and B. Sun, “Band gap and wave guiding effect in a quasiperiodic photonic crystal,” App. Phys. Lett. 75, 1848–50 (1999)
    [CrossRef]
  13. C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, and D. J. Zhang, “Two-dimensional dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region,” Phys. Rev. B 61, 10762 (2000)
    [CrossRef]
  14. X. Zhang, Z.-Q. Zhang, and C. T. Chan, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B 63, 081105 (2001)
    [CrossRef]
  15. Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic Band Gaps in Two Dimensional Photonic Quasicrystals,” Phys. Rev. Lett. 80, 956–959 (1998)
    [CrossRef]
  16. S. S. M. Cheng, L.-M. Li, C. T. Chan, and Z. Q. Zhang, “Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems,” Phys. Rev. B 59, 4091–4099 (1999)
    [CrossRef]
  17. M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, P. Millar, and R. De La Rue, “Diffraction and transmission of light in low refractive index Penrose-tiled quasicrystals,” J. Phys2.: Condens. Matter 1310459–10470 (2001)
    [CrossRef]
  18. M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P Millar, “The design of two-dimensional photonic quasicrystals by means of a Fourier transform method,” J. Mod. Opt. 48, 9–14 (2001)
  19. R. C. Gauthier and K. W. Mnaymneh, “Design of photonic band gap structures through a dual-beam multiple exposure technique,” Opt. Laser Tech. 36, 625–633 (2004)
    [CrossRef]
  20. K. W. Mnaymneh, Department of Electronics, Carleton University, Ottawa, Ontario, Canada, K1S-5B6 and R. C. Gauthier are preparing a manuscript to be called “Multiple exposure and direct-write electron-beam photonic quasicrystal pattern generation”
  21. R. C. Gauthier and A. Ivanov, “Production of quasi-crystal template patterns using a dual beam multiple exposure technique,” Opt. Express 12, 990–1003 (2004) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-990
    [CrossRef] [PubMed]
  22. W. Bogaerts, V. Wiaux, D. Taillaert, S. Beckx, B. Luyssaert, P. Bienstman, and R. Baets, “Fabrication of Photonic Crystals in Silicon-on-Insulator Using 248-nm Deep UV Lithography,” IEEE Select. Quantum. Electron.,  8, 928–934 (2003)
    [CrossRef]
  23. K. Sakoda, Optical Properties of Photonic Crystals (Springer2001), Chap. 2.
  24. 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) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173
    [CrossRef] [PubMed]
  25. D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (Wiley-IEEE Press, New York, 2000)
    [CrossRef]
  26. S. Harada and Y. Iida, “Waveguide Bandpass Filter and FDTD Analysis,” Electron. Comm. Japan, Part 2  86, 12–19 (2003)

2004 (5)

P. I. Borel, L. H. Frandsen, A. Harpøth, J. B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, “Bandwidth engineering of photonic crystal waveguide bends,” Electron. Lett. 401263–1264 (2004)
[CrossRef]

N. Hitoshi, Y. Sugimoto, K. Kanamoto, N. Ikeda, Y. Tanaka, Y. Nakamura, S. Ohkouchi, Y. Watanabe, K. Inoue, H. Ishikawa, and K. Asakawa, “Ultra-fast photonic crystal/quantum dot alloptical switch for future photonic networks,” Opt. Express 12, 6606–6614 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-26-6606
[CrossRef] [PubMed]

Y. Roh, S. Yoon, H. Jeon, S. Han, and Q. Park, “Two-dimensional photonic crystal waveguides with multiple sharp bends,” Proc. SPIE Int. Soc. Opt. Eng. 5360, 199–201 (2004)

R. C. Gauthier and K. W. Mnaymneh, “Design of photonic band gap structures through a dual-beam multiple exposure technique,” Opt. Laser Tech. 36, 625–633 (2004)
[CrossRef]

R. C. Gauthier and A. Ivanov, “Production of quasi-crystal template patterns using a dual beam multiple exposure technique,” Opt. Express 12, 990–1003 (2004) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-990
[CrossRef] [PubMed]

2003 (3)

W. Bogaerts, V. Wiaux, D. Taillaert, S. Beckx, B. Luyssaert, P. Bienstman, and R. Baets, “Fabrication of Photonic Crystals in Silicon-on-Insulator Using 248-nm Deep UV Lithography,” IEEE Select. Quantum. Electron.,  8, 928–934 (2003)
[CrossRef]

S. Harada and Y. Iida, “Waveguide Bandpass Filter and FDTD Analysis,” Electron. Comm. Japan, Part 2  86, 12–19 (2003)

L. B. Shaw, J. S. Sanghera, I. D. Aggarwal, and F. H. Hung, “As-S and As-Se based photonic band gap fiber for IR laser transmission,” Opt. Express 11, 3455–3460 (2003) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-25-3455
[CrossRef] [PubMed]

2002 (2)

M. E. Potter and R. W. Ziolkowski, “Two compact structures for perpendicular coupling of optical signals between dielectric and photonic crystal waveguides,” Opt. Express 10, 691–698 (2002). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-15-691
[PubMed]

H. Park, J. Hwang, J. Huh, H. Ryu, S. Kim, J. Kim, and Y. Lee, “Characteristics of Modified Single-Defect Two-Dimensional Photonic Crystal Lasers,” Quantum Electron. 381353–1365 (2002)
[CrossRef]

2001 (4)

X. Zhang, Z.-Q. Zhang, and C. T. Chan, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B 63, 081105 (2001)
[CrossRef]

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, P. Millar, and R. De La Rue, “Diffraction and transmission of light in low refractive index Penrose-tiled quasicrystals,” J. Phys2.: Condens. Matter 1310459–10470 (2001)
[CrossRef]

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P Millar, “The design of two-dimensional photonic quasicrystals by means of a Fourier transform method,” J. Mod. Opt. 48, 9–14 (2001)

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) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173
[CrossRef] [PubMed]

2000 (4)

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, and D. J. Zhang, “Two-dimensional dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region,” Phys. Rev. B 61, 10762 (2000)
[CrossRef]

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. M. De La Rue, and P Millar, “Two-dimensional Penrose-tiled photonic quasicrystals: diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771–1778 (2000)

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. M. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals: From diffraction to band structure,” Nanotechnology 11274–280 (2000)
[CrossRef]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Rate-equation analysis of output efficiency and modulation rate of photonic-crystal light-emitting diodes,” Quantum Electron. 36, 1123–1130 (2000)
[CrossRef]

1999 (2)

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, D. J. Zhang, S. Z. Ban, and B. Sun, “Band gap and wave guiding effect in a quasiperiodic photonic crystal,” App. Phys. Lett. 75, 1848–50 (1999)
[CrossRef]

S. S. M. Cheng, L.-M. Li, C. T. Chan, and Z. Q. Zhang, “Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems,” Phys. Rev. B 59, 4091–4099 (1999)
[CrossRef]

1998 (2)

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic Band Gaps in Two Dimensional Photonic Quasicrystals,” Phys. Rev. Lett. 80, 956–959 (1998)
[CrossRef]

C. Sibilia, I. S. Nefedov, M. Scalora, and M. Bertolotti, “Electromagnetic mode density for finite quasi-periodic structures,” J. Opt. Soc. Am. B 15, 1947–1952 (1998)
[CrossRef]

1994 (1)

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B 50, 4220–4223 (1994)
[CrossRef]

Abram, R. A.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, P. Millar, and R. De La Rue, “Diffraction and transmission of light in low refractive index Penrose-tiled quasicrystals,” J. Phys2.: Condens. Matter 1310459–10470 (2001)
[CrossRef]

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P Millar, “The design of two-dimensional photonic quasicrystals by means of a Fourier transform method,” J. Mod. Opt. 48, 9–14 (2001)

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. M. De La Rue, and P Millar, “Two-dimensional Penrose-tiled photonic quasicrystals: diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771–1778 (2000)

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. M. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals: From diffraction to band structure,” Nanotechnology 11274–280 (2000)
[CrossRef]

Aggarwal, I. D.

Asakawa, K.

Baets, R.

P. I. Borel, L. H. Frandsen, A. Harpøth, J. B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, “Bandwidth engineering of photonic crystal waveguide bends,” Electron. Lett. 401263–1264 (2004)
[CrossRef]

W. Bogaerts, V. Wiaux, D. Taillaert, S. Beckx, B. Luyssaert, P. Bienstman, and R. Baets, “Fabrication of Photonic Crystals in Silicon-on-Insulator Using 248-nm Deep UV Lithography,” IEEE Select. Quantum. Electron.,  8, 928–934 (2003)
[CrossRef]

Ban, S. Z.

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, D. J. Zhang, S. Z. Ban, and B. Sun, “Band gap and wave guiding effect in a quasiperiodic photonic crystal,” App. Phys. Lett. 75, 1848–50 (1999)
[CrossRef]

Beckx, S.

P. I. Borel, L. H. Frandsen, A. Harpøth, J. B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, “Bandwidth engineering of photonic crystal waveguide bends,” Electron. Lett. 401263–1264 (2004)
[CrossRef]

W. Bogaerts, V. Wiaux, D. Taillaert, S. Beckx, B. Luyssaert, P. Bienstman, and R. Baets, “Fabrication of Photonic Crystals in Silicon-on-Insulator Using 248-nm Deep UV Lithography,” IEEE Select. Quantum. Electron.,  8, 928–934 (2003)
[CrossRef]

Bertolotti, M.

Bienstman, P.

W. Bogaerts, V. Wiaux, D. Taillaert, S. Beckx, B. Luyssaert, P. Bienstman, and R. Baets, “Fabrication of Photonic Crystals in Silicon-on-Insulator Using 248-nm Deep UV Lithography,” IEEE Select. Quantum. Electron.,  8, 928–934 (2003)
[CrossRef]

Bogaerts, W.

P. I. Borel, L. H. Frandsen, A. Harpøth, J. B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, “Bandwidth engineering of photonic crystal waveguide bends,” Electron. Lett. 401263–1264 (2004)
[CrossRef]

W. Bogaerts, V. Wiaux, D. Taillaert, S. Beckx, B. Luyssaert, P. Bienstman, and R. Baets, “Fabrication of Photonic Crystals in Silicon-on-Insulator Using 248-nm Deep UV Lithography,” IEEE Select. Quantum. Electron.,  8, 928–934 (2003)
[CrossRef]

Borel, P. I.

P. I. Borel, L. H. Frandsen, A. Harpøth, J. B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, “Bandwidth engineering of photonic crystal waveguide bends,” Electron. Lett. 401263–1264 (2004)
[CrossRef]

Brand, S.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, P. Millar, and R. De La Rue, “Diffraction and transmission of light in low refractive index Penrose-tiled quasicrystals,” J. Phys2.: Condens. Matter 1310459–10470 (2001)
[CrossRef]

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P Millar, “The design of two-dimensional photonic quasicrystals by means of a Fourier transform method,” J. Mod. Opt. 48, 9–14 (2001)

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. M. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals: From diffraction to band structure,” Nanotechnology 11274–280 (2000)
[CrossRef]

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. M. De La Rue, and P Millar, “Two-dimensional Penrose-tiled photonic quasicrystals: diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771–1778 (2000)

Chan, C. T.

X. Zhang, Z.-Q. Zhang, and C. T. Chan, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B 63, 081105 (2001)
[CrossRef]

S. S. M. Cheng, L.-M. Li, C. T. Chan, and Z. Q. Zhang, “Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems,” Phys. Rev. B 59, 4091–4099 (1999)
[CrossRef]

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic Band Gaps in Two Dimensional Photonic Quasicrystals,” Phys. Rev. Lett. 80, 956–959 (1998)
[CrossRef]

Chan, Y. S.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic Band Gaps in Two Dimensional Photonic Quasicrystals,” Phys. Rev. Lett. 80, 956–959 (1998)
[CrossRef]

Cheng, B. Y.

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, and D. J. Zhang, “Two-dimensional dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region,” Phys. Rev. B 61, 10762 (2000)
[CrossRef]

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, D. J. Zhang, S. Z. Ban, and B. Sun, “Band gap and wave guiding effect in a quasiperiodic photonic crystal,” App. Phys. Lett. 75, 1848–50 (1999)
[CrossRef]

Cheng, S. S. M.

S. S. M. Cheng, L.-M. Li, C. T. Chan, and Z. Q. Zhang, “Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems,” Phys. Rev. B 59, 4091–4099 (1999)
[CrossRef]

De La Rue, R.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P Millar, “The design of two-dimensional photonic quasicrystals by means of a Fourier transform method,” J. Mod. Opt. 48, 9–14 (2001)

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, P. Millar, and R. De La Rue, “Diffraction and transmission of light in low refractive index Penrose-tiled quasicrystals,” J. Phys2.: Condens. Matter 1310459–10470 (2001)
[CrossRef]

De La Rue, R. M.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. M. De La Rue, and P Millar, “Two-dimensional Penrose-tiled photonic quasicrystals: diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771–1778 (2000)

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. M. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals: From diffraction to band structure,” Nanotechnology 11274–280 (2000)
[CrossRef]

Dumon, P.

P. I. Borel, L. H. Frandsen, A. Harpøth, J. B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, “Bandwidth engineering of photonic crystal waveguide bends,” Electron. Lett. 401263–1264 (2004)
[CrossRef]

Fan, S.

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Rate-equation analysis of output efficiency and modulation rate of photonic-crystal light-emitting diodes,” Quantum Electron. 36, 1123–1130 (2000)
[CrossRef]

Frandsen, L. H.

P. I. Borel, L. H. Frandsen, A. Harpøth, J. B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, “Bandwidth engineering of photonic crystal waveguide bends,” Electron. Lett. 401263–1264 (2004)
[CrossRef]

Gauthier, R. C.

R. C. Gauthier and K. W. Mnaymneh, “Design of photonic band gap structures through a dual-beam multiple exposure technique,” Opt. Laser Tech. 36, 625–633 (2004)
[CrossRef]

R. C. Gauthier and A. Ivanov, “Production of quasi-crystal template patterns using a dual beam multiple exposure technique,” Opt. Express 12, 990–1003 (2004) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-990
[CrossRef] [PubMed]

Han, S.

Y. Roh, S. Yoon, H. Jeon, S. Han, and Q. Park, “Two-dimensional photonic crystal waveguides with multiple sharp bends,” Proc. SPIE Int. Soc. Opt. Eng. 5360, 199–201 (2004)

Harada, S.

S. Harada and Y. Iida, “Waveguide Bandpass Filter and FDTD Analysis,” Electron. Comm. Japan, Part 2  86, 12–19 (2003)

Harpøth, A.

P. I. Borel, L. H. Frandsen, A. Harpøth, J. B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, “Bandwidth engineering of photonic crystal waveguide bends,” Electron. Lett. 401263–1264 (2004)
[CrossRef]

Hattori, T.

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B 50, 4220–4223 (1994)
[CrossRef]

Hitoshi, N.

Huh, J.

H. Park, J. Hwang, J. Huh, H. Ryu, S. Kim, J. Kim, and Y. Lee, “Characteristics of Modified Single-Defect Two-Dimensional Photonic Crystal Lasers,” Quantum Electron. 381353–1365 (2002)
[CrossRef]

Hung, F. H.

Hwang, J.

H. Park, J. Hwang, J. Huh, H. Ryu, S. Kim, J. Kim, and Y. Lee, “Characteristics of Modified Single-Defect Two-Dimensional Photonic Crystal Lasers,” Quantum Electron. 381353–1365 (2002)
[CrossRef]

Iida, Y.

S. Harada and Y. Iida, “Waveguide Bandpass Filter and FDTD Analysis,” Electron. Comm. Japan, Part 2  86, 12–19 (2003)

Ikeda, N.

Inoue, K.

Ishikawa, H.

Ivanov, A.

Jeon, H.

Y. Roh, S. Yoon, H. Jeon, S. Han, and Q. Park, “Two-dimensional photonic crystal waveguides with multiple sharp bends,” Proc. SPIE Int. Soc. Opt. Eng. 5360, 199–201 (2004)

Jin, C. J.

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, and D. J. Zhang, “Two-dimensional dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region,” Phys. Rev. B 61, 10762 (2000)
[CrossRef]

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, D. J. Zhang, S. Z. Ban, and B. Sun, “Band gap and wave guiding effect in a quasiperiodic photonic crystal,” App. Phys. Lett. 75, 1848–50 (1999)
[CrossRef]

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) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173
[CrossRef] [PubMed]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Rate-equation analysis of output efficiency and modulation rate of photonic-crystal light-emitting diodes,” Quantum Electron. 36, 1123–1130 (2000)
[CrossRef]

Johnson, S. G.

Kaliteevski, M. A.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P Millar, “The design of two-dimensional photonic quasicrystals by means of a Fourier transform method,” J. Mod. Opt. 48, 9–14 (2001)

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, P. Millar, and R. De La Rue, “Diffraction and transmission of light in low refractive index Penrose-tiled quasicrystals,” J. Phys2.: Condens. Matter 1310459–10470 (2001)
[CrossRef]

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. M. De La Rue, and P Millar, “Two-dimensional Penrose-tiled photonic quasicrystals: diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771–1778 (2000)

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. M. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals: From diffraction to band structure,” Nanotechnology 11274–280 (2000)
[CrossRef]

Kanamoto, K.

Kawato, S.

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B 50, 4220–4223 (1994)
[CrossRef]

Kim, J.

H. Park, J. Hwang, J. Huh, H. Ryu, S. Kim, J. Kim, and Y. Lee, “Characteristics of Modified Single-Defect Two-Dimensional Photonic Crystal Lasers,” Quantum Electron. 381353–1365 (2002)
[CrossRef]

Kim, S.

H. Park, J. Hwang, J. Huh, H. Ryu, S. Kim, J. Kim, and Y. Lee, “Characteristics of Modified Single-Defect Two-Dimensional Photonic Crystal Lasers,” Quantum Electron. 381353–1365 (2002)
[CrossRef]

Krauss, T. F.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, P. Millar, and R. De La Rue, “Diffraction and transmission of light in low refractive index Penrose-tiled quasicrystals,” J. Phys2.: Condens. Matter 1310459–10470 (2001)
[CrossRef]

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P Millar, “The design of two-dimensional photonic quasicrystals by means of a Fourier transform method,” J. Mod. Opt. 48, 9–14 (2001)

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. M. De La Rue, and P Millar, “Two-dimensional Penrose-tiled photonic quasicrystals: diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771–1778 (2000)

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. M. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals: From diffraction to band structure,” Nanotechnology 11274–280 (2000)
[CrossRef]

Kristensen, M.

P. I. Borel, L. H. Frandsen, A. Harpøth, J. B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, “Bandwidth engineering of photonic crystal waveguide bends,” Electron. Lett. 401263–1264 (2004)
[CrossRef]

Lee, Y.

H. Park, J. Hwang, J. Huh, H. Ryu, S. Kim, J. Kim, and Y. Lee, “Characteristics of Modified Single-Defect Two-Dimensional Photonic Crystal Lasers,” Quantum Electron. 381353–1365 (2002)
[CrossRef]

Leon, J. B.

P. I. Borel, L. H. Frandsen, A. Harpøth, J. B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, “Bandwidth engineering of photonic crystal waveguide bends,” Electron. Lett. 401263–1264 (2004)
[CrossRef]

Li, L.-M.

S. S. M. Cheng, L.-M. Li, C. T. Chan, and Z. Q. Zhang, “Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems,” Phys. Rev. B 59, 4091–4099 (1999)
[CrossRef]

Li, Z. L.

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, and D. J. Zhang, “Two-dimensional dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region,” Phys. Rev. B 61, 10762 (2000)
[CrossRef]

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, D. J. Zhang, S. Z. Ban, and B. Sun, “Band gap and wave guiding effect in a quasiperiodic photonic crystal,” App. Phys. Lett. 75, 1848–50 (1999)
[CrossRef]

Liu, H.

P. I. Borel, L. H. Frandsen, A. Harpøth, J. B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, “Bandwidth engineering of photonic crystal waveguide bends,” Electron. Lett. 401263–1264 (2004)
[CrossRef]

Liu, Z. Y.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic Band Gaps in Two Dimensional Photonic Quasicrystals,” Phys. Rev. Lett. 80, 956–959 (1998)
[CrossRef]

Luyssaert, B.

W. Bogaerts, V. Wiaux, D. Taillaert, S. Beckx, B. Luyssaert, P. Bienstman, and R. Baets, “Fabrication of Photonic Crystals in Silicon-on-Insulator Using 248-nm Deep UV Lithography,” IEEE Select. Quantum. Electron.,  8, 928–934 (2003)
[CrossRef]

Man, B. Y.

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, and D. J. Zhang, “Two-dimensional dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region,” Phys. Rev. B 61, 10762 (2000)
[CrossRef]

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, D. J. Zhang, S. Z. Ban, and B. Sun, “Band gap and wave guiding effect in a quasiperiodic photonic crystal,” App. Phys. Lett. 75, 1848–50 (1999)
[CrossRef]

Millar, P

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P Millar, “The design of two-dimensional photonic quasicrystals by means of a Fourier transform method,” J. Mod. Opt. 48, 9–14 (2001)

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. M. De La Rue, and P Millar, “Two-dimensional Penrose-tiled photonic quasicrystals: diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771–1778 (2000)

Millar, P.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, P. Millar, and R. De La Rue, “Diffraction and transmission of light in low refractive index Penrose-tiled quasicrystals,” J. Phys2.: Condens. Matter 1310459–10470 (2001)
[CrossRef]

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. M. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals: From diffraction to band structure,” Nanotechnology 11274–280 (2000)
[CrossRef]

Mnaymneh, K. W.

R. C. Gauthier and K. W. Mnaymneh, “Design of photonic band gap structures through a dual-beam multiple exposure technique,” Opt. Laser Tech. 36, 625–633 (2004)
[CrossRef]

K. W. Mnaymneh, Department of Electronics, Carleton University, Ottawa, Ontario, Canada, K1S-5B6 and R. C. Gauthier are preparing a manuscript to be called “Multiple exposure and direct-write electron-beam photonic quasicrystal pattern generation”

Nakamura, Y.

Nakatsuka, H.

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B 50, 4220–4223 (1994)
[CrossRef]

Nefedov, I. S.

Ohkouchi, S.

Park, H.

H. Park, J. Hwang, J. Huh, H. Ryu, S. Kim, J. Kim, and Y. Lee, “Characteristics of Modified Single-Defect Two-Dimensional Photonic Crystal Lasers,” Quantum Electron. 381353–1365 (2002)
[CrossRef]

Park, Q.

Y. Roh, S. Yoon, H. Jeon, S. Han, and Q. Park, “Two-dimensional photonic crystal waveguides with multiple sharp bends,” Proc. SPIE Int. Soc. Opt. Eng. 5360, 199–201 (2004)

Potter, M. E.

Roh, Y.

Y. Roh, S. Yoon, H. Jeon, S. Han, and Q. Park, “Two-dimensional photonic crystal waveguides with multiple sharp bends,” Proc. SPIE Int. Soc. Opt. Eng. 5360, 199–201 (2004)

Ryu, H.

H. Park, J. Hwang, J. Huh, H. Ryu, S. Kim, J. Kim, and Y. Lee, “Characteristics of Modified Single-Defect Two-Dimensional Photonic Crystal Lasers,” Quantum Electron. 381353–1365 (2002)
[CrossRef]

Sakoda, K.

K. Sakoda, Optical Properties of Photonic Crystals (Springer2001), Chap. 2.

Sanghera, J. S.

Scalora, M.

Shaw, L. B.

Sibilia, C.

Sugimoto, Y.

Sullivan, D. M.

D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (Wiley-IEEE Press, New York, 2000)
[CrossRef]

Sun, B.

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, D. J. Zhang, S. Z. Ban, and B. Sun, “Band gap and wave guiding effect in a quasiperiodic photonic crystal,” App. Phys. Lett. 75, 1848–50 (1999)
[CrossRef]

Taillaert, D.

W. Bogaerts, V. Wiaux, D. Taillaert, S. Beckx, B. Luyssaert, P. Bienstman, and R. Baets, “Fabrication of Photonic Crystals in Silicon-on-Insulator Using 248-nm Deep UV Lithography,” IEEE Select. Quantum. Electron.,  8, 928–934 (2003)
[CrossRef]

Tanaka, Y.

Tsurumachi, N.

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B 50, 4220–4223 (1994)
[CrossRef]

Villeneuve, P. R.

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Rate-equation analysis of output efficiency and modulation rate of photonic-crystal light-emitting diodes,” Quantum Electron. 36, 1123–1130 (2000)
[CrossRef]

Watanabe, Y.

Wiaux, V.

P. I. Borel, L. H. Frandsen, A. Harpøth, J. B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, “Bandwidth engineering of photonic crystal waveguide bends,” Electron. Lett. 401263–1264 (2004)
[CrossRef]

W. Bogaerts, V. Wiaux, D. Taillaert, S. Beckx, B. Luyssaert, P. Bienstman, and R. Baets, “Fabrication of Photonic Crystals in Silicon-on-Insulator Using 248-nm Deep UV Lithography,” IEEE Select. Quantum. Electron.,  8, 928–934 (2003)
[CrossRef]

Wouters, J.

P. I. Borel, L. H. Frandsen, A. Harpøth, J. B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, “Bandwidth engineering of photonic crystal waveguide bends,” Electron. Lett. 401263–1264 (2004)
[CrossRef]

Yoon, S.

Y. Roh, S. Yoon, H. Jeon, S. Han, and Q. Park, “Two-dimensional photonic crystal waveguides with multiple sharp bends,” Proc. SPIE Int. Soc. Opt. Eng. 5360, 199–201 (2004)

Zhang, D. J.

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, and D. J. Zhang, “Two-dimensional dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region,” Phys. Rev. B 61, 10762 (2000)
[CrossRef]

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, D. J. Zhang, S. Z. Ban, and B. Sun, “Band gap and wave guiding effect in a quasiperiodic photonic crystal,” App. Phys. Lett. 75, 1848–50 (1999)
[CrossRef]

Zhang, X.

X. Zhang, Z.-Q. Zhang, and C. T. Chan, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B 63, 081105 (2001)
[CrossRef]

Zhang, Z. Q.

S. S. M. Cheng, L.-M. Li, C. T. Chan, and Z. Q. Zhang, “Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems,” Phys. Rev. B 59, 4091–4099 (1999)
[CrossRef]

Zhang, Z.-Q.

X. Zhang, Z.-Q. Zhang, and C. T. Chan, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B 63, 081105 (2001)
[CrossRef]

Ziolkowski, R. W.

App. Phys. Lett. (1)

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, D. J. Zhang, S. Z. Ban, and B. Sun, “Band gap and wave guiding effect in a quasiperiodic photonic crystal,” App. Phys. Lett. 75, 1848–50 (1999)
[CrossRef]

Electron. Comm. Japan (1)

S. Harada and Y. Iida, “Waveguide Bandpass Filter and FDTD Analysis,” Electron. Comm. Japan, Part 2  86, 12–19 (2003)

Electron. Lett. (1)

P. I. Borel, L. H. Frandsen, A. Harpøth, J. B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, “Bandwidth engineering of photonic crystal waveguide bends,” Electron. Lett. 401263–1264 (2004)
[CrossRef]

IEEE Select. Quantum. Electron. (1)

W. Bogaerts, V. Wiaux, D. Taillaert, S. Beckx, B. Luyssaert, P. Bienstman, and R. Baets, “Fabrication of Photonic Crystals in Silicon-on-Insulator Using 248-nm Deep UV Lithography,” IEEE Select. Quantum. Electron.,  8, 928–934 (2003)
[CrossRef]

J. Mod. Opt. (2)

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P Millar, “The design of two-dimensional photonic quasicrystals by means of a Fourier transform method,” J. Mod. Opt. 48, 9–14 (2001)

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. M. De La Rue, and P Millar, “Two-dimensional Penrose-tiled photonic quasicrystals: diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771–1778 (2000)

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

J. Phys2.: Condens. Matter (1)

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, P. Millar, and R. De La Rue, “Diffraction and transmission of light in low refractive index Penrose-tiled quasicrystals,” J. Phys2.: Condens. Matter 1310459–10470 (2001)
[CrossRef]

Nanotechnology (1)

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. M. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals: From diffraction to band structure,” Nanotechnology 11274–280 (2000)
[CrossRef]

Opt. Express (5)

Opt. Laser Tech. (1)

R. C. Gauthier and K. W. Mnaymneh, “Design of photonic band gap structures through a dual-beam multiple exposure technique,” Opt. Laser Tech. 36, 625–633 (2004)
[CrossRef]

Phys. Rev. B (4)

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B 50, 4220–4223 (1994)
[CrossRef]

S. S. M. Cheng, L.-M. Li, C. T. Chan, and Z. Q. Zhang, “Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems,” Phys. Rev. B 59, 4091–4099 (1999)
[CrossRef]

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, and D. J. Zhang, “Two-dimensional dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region,” Phys. Rev. B 61, 10762 (2000)
[CrossRef]

X. Zhang, Z.-Q. Zhang, and C. T. Chan, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B 63, 081105 (2001)
[CrossRef]

Phys. Rev. Lett. (1)

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic Band Gaps in Two Dimensional Photonic Quasicrystals,” Phys. Rev. Lett. 80, 956–959 (1998)
[CrossRef]

Proc. SPIE Int. Soc. Opt. Eng. (1)

Y. Roh, S. Yoon, H. Jeon, S. Han, and Q. Park, “Two-dimensional photonic crystal waveguides with multiple sharp bends,” Proc. SPIE Int. Soc. Opt. Eng. 5360, 199–201 (2004)

Quantum Electron. (2)

H. Park, J. Hwang, J. Huh, H. Ryu, S. Kim, J. Kim, and Y. Lee, “Characteristics of Modified Single-Defect Two-Dimensional Photonic Crystal Lasers,” Quantum Electron. 381353–1365 (2002)
[CrossRef]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Rate-equation analysis of output efficiency and modulation rate of photonic-crystal light-emitting diodes,” Quantum Electron. 36, 1123–1130 (2000)
[CrossRef]

Other (3)

K. W. Mnaymneh, Department of Electronics, Carleton University, Ottawa, Ontario, Canada, K1S-5B6 and R. C. Gauthier are preparing a manuscript to be called “Multiple exposure and direct-write electron-beam photonic quasicrystal pattern generation”

K. Sakoda, Optical Properties of Photonic Crystals (Springer2001), Chap. 2.

D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (Wiley-IEEE Press, New York, 2000)
[CrossRef]

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Figures (14)

Fig. 1.
Fig. 1.

12-fold quasi-crystal patterns produced using different threshold levels for exposure. Dark regions correspond to unexposed resist and thus the high dielectric. (a) Threshold of 12 out of a maximum of 24 produces 50 % fill. (b) 9/24 giving 80% fill. (c) 15/24 giving 20 % fill. (d) 13.5/24 giving 33.3% fill.

Fig. 2.
Fig. 2.

Curve A plots the high dielectric fill factor versus exposure threshold level used in the production of 12-fold quasi-crystal patterns. Curve B shows the change in the fill factor versus a threshold change of 0.5. Curve C shows the reverse sensitivity regions and is obtained by inverting the polarity of the photoresist.

Fig. 3.
Fig. 3.

Photonic quasi-crystal (6 by 10 µm) located in the (6 by 13 µm) discretization grid. Black regions indicate high dielectric. Solid line across point 1 indicates location of the plane wave soft source. Solid colored circles indicate points where time domain data is retained and FFT transmission plots computed.

Fig. 4.
Fig. 4.

TE polarization (Hz component) transmission spectrum for a 10 µm length 12-fold quasi-crystal of 50% fill factor. A band gap is present between the wavelengths of 1.05 µm and 1.28 µm and contains two defect states within.

Fig. 5.
Fig. 5.

TM polarization (Ez component) transmission spectrum for a 10 µm length 12-fold quasi-crystal of 50% fill factor. Several band gap regions are present over the wavelength range displayed. Due to the rich nature of the band gaps for the TM polarization we explore in detail the optical properties of the 12-fold quasi-crystal for this polarization state of light.

Fig. 6.
Fig. 6.

Line plot of the transmission spectrum for the Ez component of the TM polarization plotted versus wavelength and dielectric fill factor. The larger of the band gaps is located in the flat zone about the 1.5 µm wavelength value. A second large band gap is located in the 1.0 µm wavelength range.

Fig. 7.
Fig. 7.

Line plot of the transmission spectrum for the Ez component of the TM polarization plotted versus wavelength and 0° to 15° propagation angle in 2.5° increments. Through rotational symmetry, other propagation angle outside 15o range can be rotated into the 0-15° range displayed. The quasi-crystal displays a uniform transmission spectrum over propagation angle.

Fig. 8.
Fig. 8.

High band gap region plotted versus dielectric fill factor. This large band gap exists down to a dielectric contrast of 2:1 but is considerably narrower than for high dielectric contrasts. The information displayed in Fig. 6Fig. 8 indicates that the design of a band gap in the 1.55 um range can be achieved through a large selection in the fill factor, dielectric contrast and propagation angle.

Fig. 9.
Fig. 9.

Plot of the Poynting vector magnitude versus wavelength and Fourier transform point location in the center of a 1.50 µm wide waveguide centered on the quasi-crystal. The top trace indicates that the low dielectric waveguide transmits strongly in the band gap range of the quasi-crystal and leaks light in those wavelength ranges which correspond to the transmission bands of the quasi-crystal.

Fig. 10.
Fig. 10.

Plot of the TM Ez component versus wavelength and Fourier transform point location in the waveguide for a 1.50 µm wide waveguide centered on the quasi-crystal. The top trace indicates that the low dielectric waveguide transmits strongly in the band gap range of the quasi-crystal and leaks light in those wavelength ranges which correspond to the transmission bands of the quasi-crystal.

Fig, 11.
Fig, 11.

Transmission profile of the 1.5 µm wavelength through a 1.50 µm low index waveguide centered on the photonic quasi-crystal. The dimensions of the quasi-crystal is 6 µm across and 17 µm long. High transmission is observed for this wavelength.

Fig. 12.
Fig. 12.

Transmission profile (b) of the 1.55 µm wavelength through a 1.50 µm low index waveguide centered on the photonic quasi-crystal (a). The dimensions of the quasi-crystal structure is 6 µm across and 17 µm long. The waveguide transmits an attenuated light for this particular wavelength.

Fig. 13.
Fig. 13.

Transmission profile (b) of the 1.65 µm wavelength through a 1.50 µm low index waveguide centered on the photonic quasi-crystal (a). The dimensions of the quasi-crystal is 6 µm across and 17 µm long. The waveguide displays a resonant back coupling of the light with only a small transmitted contribution.

Fig. 14.
Fig. 14.

Transmission profile of the 1.50 µm wavelength through a Y splitter fabricated from low index 1.50 µm waveguides positioned in the photonic quasi-crystal. Quasi-crystal 6 µm across and 17 µm long. The splitter divides the power and excites the two output ports evenly. The Y junction also generates a small backwards propagating component which exits the input waveguide. No attempts were made to optimize the Y branches splitting properties.

Equations (1)

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I j = E j 1 2 + E j 2 2 + 2 E j 1 E j 2 cos ( θ j 12 ) cos ( [ k j 1 k j 2 ] r + φ oj 1 + φ oj 2 )

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