Abstract

The 3-D finite difference time domain (FDTD) cut-back method is used to study losses in nondisordered photonic crystal silicon membrane waveguides. Losses above the light-line have been shown to be in good agreement with other methods. Below the light-line, however, FDTD is predicting a rapid increase in losses. This paper studies the possible causes for this effect, including meshing effects, back reflections, and finite thickness sidewalls. It is found that since below the light-line the group index becomes very high and the loss becomes very low, strong Fabry–Perot oscillations dominate the cut-back results. The paper also discusses the impact of operating near to the cut-off wavelength of the photonic crystal waveguide Bloch mode and the implications this has for loss calculation.

© 2009 IEEE

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  1. E. Dulkeith, S. J. McNab, Y. A. Vlasov, "Mapping the optical properties of slab-type two-dimensional photonic crystal waveguides," Phys. Rev. B 72, 115102 (2005).
  2. Y. Sugimoto, Y. Tanaka, N. Ikeda, Y. Nakamura, K. Asakawa, K. Inoue, "Low propagation loss of 0.76 dB/mm in GaAs-based single-line-defect two-dimensional photonic crystal slab waveguides up to 1 cm in length," Opt. Exp. 12, 1090-1096 (2004).
  3. S. Hughes, L. Ramunno, J. F. Young, J. E. Sipe, "Extrinsic optical scattering loss in photonic cristal waveguides: Role of fabrication disorder and photon group velocity," Phys. Rev. Lett. 94, 033903 (2005).
  4. L. C. Andreani, D. Gerace, "Light-matter interaction in photonic crystal slabs," Phys. Stat. Sol. (B) 244, 3528-3539 (2007).
  5. J.-M. Brosi, J. Leuthold, W. Freude, "Microwave-frequency experiments validate optical simulation tools and demonstrate novel dispersion-tailored photonic crystal waveguides," IEEE J. Lightw. Technol. 25, (2007).
  6. L. O'Faolain, T. P. White, D. O'Brien, X. Yuan, M. D. Settle, T. F. Krauss, "Dependence of extrinsic loss on group velocity in photonic crystal waveguides," Opt. Exp. 15, 13129-13138 (2007).
  7. P. Lalanne, "Electromagnetic analysis of photonic crystal waveguides operating above the light cone," IEEE J. Quant. Electron. 38, 800-804 (2002).
  8. C. Sauvan, P. Lalanne, "Accurate modeling of line-defect photonic cristal waveguides," IEEE Photon. Technol. Lett. 15, 1243-1245 (2003).
  9. S. Boscolo, M. Midrio, "3D multiple-scattering technique for the analysis of photonic crystal Slabs," J. Lightw. Technol. (2004).
  10. M. J. Cryan, I. J. Craddock, C. J. Railton, "FDTD modelling of losses and group velocity below the light-line in PhC Slabs," Photonic and Electromagnetic Crystals Conf., PECS VI CreteGreece (2006).
  11. Y. Tanaka, Y. Sugimoto, N. Ikeda, H. Nakamura, K. Asakawa, K. Inoue, S. G. Johnson, "Group velocity dependence of propagation losses in single-line-defect photonic crystal waveguides on GaAs membranes," Electron. Lett. 40, (2004).
  12. M. J. Cryan, D. C. L. Wong, I. J. Craddock, S. Yu, J. Rorison, C. J. Railton, "Calculation of losses in 2D photonic crystal membrane waveguides using the 3D FDTD method," IEEE Photon. Technol. Lett. 17, 58-60 (2005).
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  15. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001).
  16. A. Sugitatsu, S. Noda, "Room temperature operation of 2D photonic crystal slab defect-waveguide laser with optical pump," Electron. Lett. 39, (2003).
  17. Z.-Y. Li, K.-M. Ho, "Anomalous propagation loss in photonic crystal waveguides," Phys. Rev. Lett. 92, 063904 (2004).
  18. C. Sauvan, P. Lalanne, "Anomalous propagation loss in photonic crystal waveguides," Phys. Rev. Lett. 95, 229401 (2005).
  19. R. S. Jacobsen, A. V. Lavrinenko, L. H. Frandsen, C. Peucheret, B. Zsigri, G. Moulin, J. Fage-Pedersen, P. I. Borel, "Direct experimental and numerical determination of extremely high group indices in photonic crystal waveguides," Opt. Exp. 13, 7861-7871 (2005).

2007 (3)

L. C. Andreani, D. Gerace, "Light-matter interaction in photonic crystal slabs," Phys. Stat. Sol. (B) 244, 3528-3539 (2007).

J.-M. Brosi, J. Leuthold, W. Freude, "Microwave-frequency experiments validate optical simulation tools and demonstrate novel dispersion-tailored photonic crystal waveguides," IEEE J. Lightw. Technol. 25, (2007).

L. O'Faolain, T. P. White, D. O'Brien, X. Yuan, M. D. Settle, T. F. Krauss, "Dependence of extrinsic loss on group velocity in photonic crystal waveguides," Opt. Exp. 15, 13129-13138 (2007).

2005 (5)

E. Dulkeith, S. J. McNab, Y. A. Vlasov, "Mapping the optical properties of slab-type two-dimensional photonic crystal waveguides," Phys. Rev. B 72, 115102 (2005).

S. Hughes, L. Ramunno, J. F. Young, J. E. Sipe, "Extrinsic optical scattering loss in photonic cristal waveguides: Role of fabrication disorder and photon group velocity," Phys. Rev. Lett. 94, 033903 (2005).

M. J. Cryan, D. C. L. Wong, I. J. Craddock, S. Yu, J. Rorison, C. J. Railton, "Calculation of losses in 2D photonic crystal membrane waveguides using the 3D FDTD method," IEEE Photon. Technol. Lett. 17, 58-60 (2005).

C. Sauvan, P. Lalanne, "Anomalous propagation loss in photonic crystal waveguides," Phys. Rev. Lett. 95, 229401 (2005).

R. S. Jacobsen, A. V. Lavrinenko, L. H. Frandsen, C. Peucheret, B. Zsigri, G. Moulin, J. Fage-Pedersen, P. I. Borel, "Direct experimental and numerical determination of extremely high group indices in photonic crystal waveguides," Opt. Exp. 13, 7861-7871 (2005).

2004 (4)

Z.-Y. Li, K.-M. Ho, "Anomalous propagation loss in photonic crystal waveguides," Phys. Rev. Lett. 92, 063904 (2004).

S. Boscolo, M. Midrio, "3D multiple-scattering technique for the analysis of photonic crystal Slabs," J. Lightw. Technol. (2004).

Y. Tanaka, Y. Sugimoto, N. Ikeda, H. Nakamura, K. Asakawa, K. Inoue, S. G. Johnson, "Group velocity dependence of propagation losses in single-line-defect photonic crystal waveguides on GaAs membranes," Electron. Lett. 40, (2004).

Y. Sugimoto, Y. Tanaka, N. Ikeda, Y. Nakamura, K. Asakawa, K. Inoue, "Low propagation loss of 0.76 dB/mm in GaAs-based single-line-defect two-dimensional photonic crystal slab waveguides up to 1 cm in length," Opt. Exp. 12, 1090-1096 (2004).

2003 (3)

C. Sauvan, P. Lalanne, "Accurate modeling of line-defect photonic cristal waveguides," IEEE Photon. Technol. Lett. 15, 1243-1245 (2003).

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

A. Sugitatsu, S. Noda, "Room temperature operation of 2D photonic crystal slab defect-waveguide laser with optical pump," Electron. Lett. 39, (2003).

2002 (1)

P. Lalanne, "Electromagnetic analysis of photonic crystal waveguides operating above the light cone," IEEE J. Quant. Electron. 38, 800-804 (2002).

2001 (1)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001).

J. Lightw. Technol. (1)

S. Boscolo, M. Midrio, "3D multiple-scattering technique for the analysis of photonic crystal Slabs," J. Lightw. Technol. (2004).

Electron. Lett. (2)

Y. Tanaka, Y. Sugimoto, N. Ikeda, H. Nakamura, K. Asakawa, K. Inoue, S. G. Johnson, "Group velocity dependence of propagation losses in single-line-defect photonic crystal waveguides on GaAs membranes," Electron. Lett. 40, (2004).

A. Sugitatsu, S. Noda, "Room temperature operation of 2D photonic crystal slab defect-waveguide laser with optical pump," Electron. Lett. 39, (2003).

IEEE J. Lightw. Technol. (1)

J.-M. Brosi, J. Leuthold, W. Freude, "Microwave-frequency experiments validate optical simulation tools and demonstrate novel dispersion-tailored photonic crystal waveguides," IEEE J. Lightw. Technol. 25, (2007).

IEEE J. Quant. Electron. (1)

P. Lalanne, "Electromagnetic analysis of photonic crystal waveguides operating above the light cone," IEEE J. Quant. Electron. 38, 800-804 (2002).

IEEE Photon. Technol. Lett. (2)

C. Sauvan, P. Lalanne, "Accurate modeling of line-defect photonic cristal waveguides," IEEE Photon. Technol. Lett. 15, 1243-1245 (2003).

M. J. Cryan, D. C. L. Wong, I. J. Craddock, S. Yu, J. Rorison, C. J. Railton, "Calculation of losses in 2D photonic crystal membrane waveguides using the 3D FDTD method," IEEE Photon. Technol. Lett. 17, 58-60 (2005).

Opt. Exp. (3)

R. S. Jacobsen, A. V. Lavrinenko, L. H. Frandsen, C. Peucheret, B. Zsigri, G. Moulin, J. Fage-Pedersen, P. I. Borel, "Direct experimental and numerical determination of extremely high group indices in photonic crystal waveguides," Opt. Exp. 13, 7861-7871 (2005).

L. O'Faolain, T. P. White, D. O'Brien, X. Yuan, M. D. Settle, T. F. Krauss, "Dependence of extrinsic loss on group velocity in photonic crystal waveguides," Opt. Exp. 15, 13129-13138 (2007).

Y. Sugimoto, Y. Tanaka, N. Ikeda, Y. Nakamura, K. Asakawa, K. Inoue, "Low propagation loss of 0.76 dB/mm in GaAs-based single-line-defect two-dimensional photonic crystal slab waveguides up to 1 cm in length," Opt. Exp. 12, 1090-1096 (2004).

Opt. Lett. (1)

Phys. Rev. B (1)

E. Dulkeith, S. J. McNab, Y. A. Vlasov, "Mapping the optical properties of slab-type two-dimensional photonic crystal waveguides," Phys. Rev. B 72, 115102 (2005).

Phys. Rev. Lett. (4)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001).

Z.-Y. Li, K.-M. Ho, "Anomalous propagation loss in photonic crystal waveguides," Phys. Rev. Lett. 92, 063904 (2004).

C. Sauvan, P. Lalanne, "Anomalous propagation loss in photonic crystal waveguides," Phys. Rev. Lett. 95, 229401 (2005).

S. Hughes, L. Ramunno, J. F. Young, J. E. Sipe, "Extrinsic optical scattering loss in photonic cristal waveguides: Role of fabrication disorder and photon group velocity," Phys. Rev. Lett. 94, 033903 (2005).

Phys. Stat. Sol. (B) (1)

L. C. Andreani, D. Gerace, "Light-matter interaction in photonic crystal slabs," Phys. Stat. Sol. (B) 244, 3528-3539 (2007).

Other (2)

M. J. Cryan, I. J. Craddock, C. J. Railton, "FDTD modelling of losses and group velocity below the light-line in PhC Slabs," Photonic and Electromagnetic Crystals Conf., PECS VI CreteGreece (2006).

COST P11: The Physics of Linear, Non-linear and Active PhCs http://w3.uniroma1.it/energetica/copy.htm, http://w3.uniroma1.it/energetica/WG2.htm.

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