Abstract

We investigated the impact of the thickness of the two-dimensional triangular photonic crystal (PC) on modal propagation along a PC slab waveguide. A single line defect optical waveguide in photonic crystal slab was designed by three-dimensional finite difference time domain method, plane wave expansion and effective index methods. The thickness of the PC slab waveguide was optimized to provide modal propagation for both TE-like and TM-like polarizations within the normalized frequency band of a/λ.=0.26–0.268.

© 2007 Optical Society of America

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References

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  1. W. Bogaerts, R. Baets, P. Dumon,  et al., "Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology," J. Lightwave Technol. 23, 401-421 (2005).
    [CrossRef]
  2. B. Jalali, S. Yegnanarayanan, T. Yoon, T. Yoshimoto, I. Rendina, and F. Coppinger," Advances in silicon-on-insulator optoelectronics," IEEE J. Sel. Top. Electron. 4, 938-947 (1998).
    [CrossRef]
  3. W. Bogaerts, D. Taillaert, B. Luyssaert, P. Dumon,  et al., "Basic structures for photonic integrated circuits in Silicon-on-insulator," Opt. Express 12, 1583-1591 (2004).
    [CrossRef] [PubMed]
  4. M. Zelsmann, E. Picard, T. Charvolin, and E. Hadji, " Broadband optical characterization and modeling of photonic crystal waveguides for silicon optical interconnects," J. Appl. Phys. 95, 1606-1608 (2004).
    [CrossRef]
  5. A. Tetu, M. Kristensen, "Broadband topology-optimized crystal components for both TE and TM polarizations," Opt. Express 13, 8606-8611 (2005).
    [CrossRef] [PubMed]
  6. A. Adibi, Y. Xu, R. K. Lee, A. Yariv, and A. Scherer, "Properties of the slab modes in photonic crystal optical waveguides," J. Lightwave Technol. 18, 1554-1564 (2000).
    [CrossRef]
  7. L. C. Andreani and M. Agio, "Photonic bands and Gaps maps in a photonic crystal slab," IEEE J. Quantum Electron. 38, 891-898 (2002).
    [CrossRef]
  8. S. G. Johnson, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
    [CrossRef]
  9. A. Chutinan and S. Noda, "Waveguides and waveguide bends in two-dimensional photonic crystal slabs," Phys. Rev. B 62, 4488-4492 (2000).
    [CrossRef]
  10. T. Liu, A. R. Zakharian, M. Fallahi, J. V. Moloney, and M. Mansuripur, "Design of compact photonic crystal-based polarizing beam splitter," IEEE Photon. Technol. Lett. 17, 1435-1437 (2005).
    [CrossRef]
  11. Y. Tanaka, S. Takayama, T. Asano, and S. Noda, "Polarization mode conveter based on 2D photonic crystal slab," LEOS 2005, 339-340 (2005).
  12. A. Adibi, R. K. Lee, Y. Xu, A. Yariv and A. Scherer, "Design of photonic crystal optical waveguides with single mode propagation in the photonic band gap," Electron. Lett. 36, 1376-1378 (2000).
    [CrossRef]
  13. H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, "Optical and confinement properties of two-dimensional photonic crystals," J. Lightwave Technol. 17, 2063-2077 (1999).
    [CrossRef]
  14. H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassange, A. Beraud, and C. Jouanin, "Radiation losses of waveguide-based two-dimensional photonic crystals: Positive role of the substrate," Appl. Phys. Lett. 76, 532-534 (2000).
    [CrossRef]
  15. 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]
  16. T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, and A. Sakai, "Light propagation characterization of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate," IEEE J. Quantum Electron. 38, 1743-752 (2002).
    [CrossRef]
  17. L. C. Andreani, and M. Agio, "Intrinsic diffraction losses in photonic crystal waveguides with line defects," Appl. Phys. Lett. 82, 2011-2013 (2003).
    [CrossRef]
  18. W. Kuang, C. Kim, A. Stapleton, W. J. Kim, and J. D. O’Brien, "Calculated out-of-plane transmission loss for photonic-crystal slab waveguides," Opt. Lett. 28, 1781-1783 (2003).
    [CrossRef] [PubMed]
  19. D. Gerace, and L. C. Andreani, "Low-loss guided modes in photonic crystal waveguides," Opt. Express 13, 4939-4951 (2005).
    [CrossRef] [PubMed]
  20. A. Jafarpour, C. M. Reinke, A. Adibi, Y. Xu, and R. K. Lee, "A new method for the calculation of the dispersion of nonperiodic photonic crystal waveguides," J. Quantum Electron. 40, 1060-1067 (2004).
    [CrossRef]

2005 (5)

W. Bogaerts, R. Baets, P. Dumon,  et al., "Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology," J. Lightwave Technol. 23, 401-421 (2005).
[CrossRef]

A. Tetu, M. Kristensen, "Broadband topology-optimized crystal components for both TE and TM polarizations," Opt. Express 13, 8606-8611 (2005).
[CrossRef] [PubMed]

T. Liu, A. R. Zakharian, M. Fallahi, J. V. Moloney, and M. Mansuripur, "Design of compact photonic crystal-based polarizing beam splitter," IEEE Photon. Technol. Lett. 17, 1435-1437 (2005).
[CrossRef]

Y. Tanaka, S. Takayama, T. Asano, and S. Noda, "Polarization mode conveter based on 2D photonic crystal slab," LEOS 2005, 339-340 (2005).

D. Gerace, and L. C. Andreani, "Low-loss guided modes in photonic crystal waveguides," Opt. Express 13, 4939-4951 (2005).
[CrossRef] [PubMed]

2004 (3)

A. Jafarpour, C. M. Reinke, A. Adibi, Y. Xu, and R. K. Lee, "A new method for the calculation of the dispersion of nonperiodic photonic crystal waveguides," J. Quantum Electron. 40, 1060-1067 (2004).
[CrossRef]

W. Bogaerts, D. Taillaert, B. Luyssaert, P. Dumon,  et al., "Basic structures for photonic integrated circuits in Silicon-on-insulator," Opt. Express 12, 1583-1591 (2004).
[CrossRef] [PubMed]

M. Zelsmann, E. Picard, T. Charvolin, and E. Hadji, " Broadband optical characterization and modeling of photonic crystal waveguides for silicon optical interconnects," J. Appl. Phys. 95, 1606-1608 (2004).
[CrossRef]

2003 (2)

L. C. Andreani, and M. Agio, "Intrinsic diffraction losses in photonic crystal waveguides with line defects," Appl. Phys. Lett. 82, 2011-2013 (2003).
[CrossRef]

W. Kuang, C. Kim, A. Stapleton, W. J. Kim, and J. D. O’Brien, "Calculated out-of-plane transmission loss for photonic-crystal slab waveguides," Opt. Lett. 28, 1781-1783 (2003).
[CrossRef] [PubMed]

2002 (2)

L. C. Andreani and M. Agio, "Photonic bands and Gaps maps in a photonic crystal slab," IEEE J. Quantum Electron. 38, 891-898 (2002).
[CrossRef]

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, and A. Sakai, "Light propagation characterization of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate," IEEE J. Quantum Electron. 38, 1743-752 (2002).
[CrossRef]

2000 (5)

A. Chutinan and S. Noda, "Waveguides and waveguide bends in two-dimensional photonic crystal slabs," Phys. Rev. B 62, 4488-4492 (2000).
[CrossRef]

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassange, A. Beraud, and C. Jouanin, "Radiation losses of waveguide-based two-dimensional photonic crystals: Positive role of the substrate," Appl. Phys. Lett. 76, 532-534 (2000).
[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).
[CrossRef]

A. Adibi, R. K. Lee, Y. Xu, A. Yariv and A. Scherer, "Design of photonic crystal optical waveguides with single mode propagation in the photonic band gap," Electron. Lett. 36, 1376-1378 (2000).
[CrossRef]

A. Adibi, Y. Xu, R. K. Lee, A. Yariv, and A. Scherer, "Properties of the slab modes in photonic crystal optical waveguides," J. Lightwave Technol. 18, 1554-1564 (2000).
[CrossRef]

1999 (2)

1998 (1)

B. Jalali, S. Yegnanarayanan, T. Yoon, T. Yoshimoto, I. Rendina, and F. Coppinger," Advances in silicon-on-insulator optoelectronics," IEEE J. Sel. Top. Electron. 4, 938-947 (1998).
[CrossRef]

Appl. Phys. Lett. (2)

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassange, A. Beraud, and C. Jouanin, "Radiation losses of waveguide-based two-dimensional photonic crystals: Positive role of the substrate," Appl. Phys. Lett. 76, 532-534 (2000).
[CrossRef]

L. C. Andreani, and M. Agio, "Intrinsic diffraction losses in photonic crystal waveguides with line defects," Appl. Phys. Lett. 82, 2011-2013 (2003).
[CrossRef]

Electron. Lett. (1)

A. Adibi, R. K. Lee, Y. Xu, A. Yariv and A. Scherer, "Design of photonic crystal optical waveguides with single mode propagation in the photonic band gap," Electron. Lett. 36, 1376-1378 (2000).
[CrossRef]

IEEE J. Quantum Electron. (2)

L. C. Andreani and M. Agio, "Photonic bands and Gaps maps in a photonic crystal slab," IEEE J. Quantum Electron. 38, 891-898 (2002).
[CrossRef]

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, and A. Sakai, "Light propagation characterization of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate," IEEE J. Quantum Electron. 38, 1743-752 (2002).
[CrossRef]

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

B. Jalali, S. Yegnanarayanan, T. Yoon, T. Yoshimoto, I. Rendina, and F. Coppinger," Advances in silicon-on-insulator optoelectronics," IEEE J. Sel. Top. Electron. 4, 938-947 (1998).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

T. Liu, A. R. Zakharian, M. Fallahi, J. V. Moloney, and M. Mansuripur, "Design of compact photonic crystal-based polarizing beam splitter," IEEE Photon. Technol. Lett. 17, 1435-1437 (2005).
[CrossRef]

J. Appl. Phys. (1)

M. Zelsmann, E. Picard, T. Charvolin, and E. Hadji, " Broadband optical characterization and modeling of photonic crystal waveguides for silicon optical interconnects," J. Appl. Phys. 95, 1606-1608 (2004).
[CrossRef]

J. Lightwave Technol. (4)

J. Quantum Electron. (1)

A. Jafarpour, C. M. Reinke, A. Adibi, Y. Xu, and R. K. Lee, "A new method for the calculation of the dispersion of nonperiodic photonic crystal waveguides," J. Quantum Electron. 40, 1060-1067 (2004).
[CrossRef]

LEOS (1)

Y. Tanaka, S. Takayama, T. Asano, and S. Noda, "Polarization mode conveter based on 2D photonic crystal slab," LEOS 2005, 339-340 (2005).

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. B (2)

S. G. Johnson, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

A. Chutinan and S. Noda, "Waveguides and waveguide bends in two-dimensional photonic crystal slabs," Phys. Rev. B 62, 4488-4492 (2000).
[CrossRef]

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Figures (10)

Fig. 1.
Fig. 1.

(a). Schematic of the triangular based PC slab waveguide (b) the unit cell of the triangular based PC slab

Fig. 2.
Fig. 2.

The Gap map for the TM-like mode of the triangular based PC slab (r/a=0.3, nSi =3.48) and the PBG width versus the thickness of the PC slab.

Fig. 3.
Fig. 3.

The effective slab waveguide of the PC slab waveguide, shown in Fig. 1(a), employed for effective index method. nc , nSi , t and w 0 are the refractive index of the cladding, refractive index of the film (silicon), thickness of the slab waveguide and the width of the film layer (W 0=a).

Fig. 4.
Fig. 4.

The super-cell, depicted by the dashed line, for band calculations of the PC slab waveguide shown in Fig. 1(a). The propagation direction of the waveguide is in the x-direction.

Fig. 5.
Fig. 5.

The dispersion diagram for the TE-like polarization of the equivalent slab waveguide for three different thicknesses for r/a=0.3 (a=410 nm).

Fig. 6.
Fig. 6.

(a). Band diagrams for TM-like modes and (b) Loss as a function of the normalized frequency (a/λ) for the triangular based PC slab waveguide with t=0.5a and r/a=0.3 (a=410 nm). PBG is the band gap size for the PC slab.

Fig. 7.
Fig. 7.

(a). Band diagrams of the TM-like mode and (b) Loss as a function of the normalized frequency (a/λ) with t=0.75a and r/a=0.3 (a=410 nm). PBG is the band gap size for the PC slab.

Fig. 8.
Fig. 8.

Dispersion diagram for laterally even TE-like mode depicted by solid dotted line with t=0.75a and r/a=0.3 (a=410 nm). The solid line represents the light line. Gray region correspond to the PC slab modes.

Fig. 9.
Fig. 9.

(a). Band diagrams for TM-like modes and (b) Loss as a function of the normalized frequency (a/λ) for the triangular based PC slab waveguide with t=a and r/a=0.3 (a=410 nm). PBG is the band gap size for the PC slab.

Fig. 10.
Fig. 10.

Dispersion diagram for laterally even TE-like mode with t=a and r/a=0.3 (a=410 nm). The solid line represents the light line. Gray region correspond to the PC slab modes.

Equations (2)

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n c = π r 2 a 2 n 0 + ( 1 π r 2 a 2 ) n Si
k = κ + y ̑ k y

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