Abstract

We present a three-dimensional (3-D) analysis of scattering losses due to sidewall roughness in rectangular dielectric waveguides valid for any refractive-index contrast and field polarization. The analysis is based on the volume current method and uses array factors to introduce significant mathematical simplifications to better understand the influence of individual waveguide parameters on scattering losses. We show that the typical two-dimensional (2-D) analyses can substantially overestimate scattering losses in small waveguides and that scattering losses exhibit considerable polarization dependence. We produce scattering-loss estimates for a wide variety of waveguides and provide guidelines for design of waveguide cross sections that are less sensitive to sidewall roughness.

© 2005 IEEE

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  1. D. Marcuse, "Mode conversion caused by surface imperfections of a dielectric slab waveguide", Bell Syst. Tech. J., vol. 48, pp. 3187-3215, Dec. 1969.
  2. D. Marcuse, "Radiation losses of dielectric waveguides in terms of the power spectrum of the wall distortion function", Bell Syst. Tech. J., vol. 48, pp. 3233-3244, Dec. 1969.
  3. D. G. Hall, "Comparison of two approaches to the waveguide scattering problem", Appl. Opt., vol. 19, no. 11, pp. 1732-1734, 1980.
  4. R. W. Gruhlke and D. G. Hall, "Comparison of two approaches to the waveguide scattering problem: TM polarization", Appl. Opt., vol. 23, no. 1, pp. 127-133, Jan. 1984.
  5. J. P. R. Lacey and F. P. Payne, "Radiation loss from planar wave-guides with random wall imperfections", Proc. Inst. Elect. Eng. J., vol. 137, no. 4, pp. 282-288, Aug. 1990.
  6. F. P. Payne and J. P. R. Lacey, "A theoretical analysis of scattering loss from planar optical waveguides", Opt. Quantum. Electron, vol. 26, no. 10, pp. 977-986, Oct. 1994.
  7. F. Ladouceur, J. D. Love and T. J. Senden, "Effect of side wall roughness in buried channel waveguides", Proc. Inst. Elect. Eng. Optoelectron., vol. 141, no. 4, pp. 242-248, Aug. 1994.
  8. K. S. Chiang, C. H. Kwan and K. M. Lo, "Effective-index method with built-in perturbation correction for the vector modes of rectangular-core optical waveguides", J. Lightw. Technol., vol. 17, no. 4, pp. 716-722, Apr. 1999.
  9. K. K. Lee, D. R. Lim, H. C. Luan, A. Agarwal, J. Foresi and L. C. Kimerling, "Effect of size and roughness on light transmission in a Si/SiO2 waveguide: Experiments and model", Appl. Phys. Lett., vol. 77, no. 11, pp. 1617-1619, Sep. 2000.
  10. H. A. Haus, , private communication, Jan. 2002
  11. T. Barwicz, H. A. Haus and H. I. Smith, "A three-dimensional analysis of scattering losses due to sidewall roughness in integrated optical waveguides", presented at the Conf. Lasers and Electo-Optics/Int. Quantum Electronics Conf. (CLEO/QELS), Baltimore, MD, Jun. 2003.
  12. T. Barwicz, "3D analysis of scattering losses due to sidewall roughness in microphotonic waveguides: High-index contrast", presented at the Conf. Lasers and Electo-Optics/Int. Quantum Electronics Conf. (CLEO/QELS), Baltimore, MD, May 2005.
  13. T. Barwicz and H. I. Smith, "Evolution of line-edge-roughness during fabrication of high index-contrast microphotonic devices", J. Vac. Sci. Technol. B, vol. 21, no. 6, pp. 2892-2896, Nov./Dec. 2003.
  14. N. E. Nahi, Estimation Theory and Applications, New York: Wiley, 1969.
  15. M. Kuznetsov and H. A. Haus, "Radiation loss in dielectric waveguide structures by the volume current method", IEEE J. Quantum Electron., vol. QE-19, no. 10, pp. 1505-1514, Oct. 1983.
  16. J. A. Kong, Electromagnetic Wave Theory, Cambridge, MA: EMW Pub., 2000.
  17. W. C. Chew, Waves and Fields in Inhomogeneous Media, New York: IEEE Press, 1995.
  18. W. C. Chew and S. Y. Chen, "Response of a point source embedded in a layered medium", IEEE Antennas Wireless Propag. Lett., vol. 2, no. 16, pp. 254-258, 2003.
  19. J. C. Cooke, "Stationary phase in two dimensions", IMA J. Appl. Math., vol. 29, no. 1, pp. 25-37, 1982.
  20. W. Gander and W. Gautschi, "Adaptive quadrature-Revisited", B.I.T., vol. 40, no. 1, pp. 84-101, Mar. 2000.
  21. S. J. Spector, M. W. Geis, D. M. Lennon, R. C. Williamson and T. M. Lyszczarz, "Hybrid multi-mode/single-mode waveguides for low loss", presented at the Integrated Photonics Research Topical Meeting, San Francisco, CA, Jun. 27-Jul. 2, 2004.
  22. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Boston, MA: Artech House, 2000.

Other (22)

D. Marcuse, "Mode conversion caused by surface imperfections of a dielectric slab waveguide", Bell Syst. Tech. J., vol. 48, pp. 3187-3215, Dec. 1969.

D. Marcuse, "Radiation losses of dielectric waveguides in terms of the power spectrum of the wall distortion function", Bell Syst. Tech. J., vol. 48, pp. 3233-3244, Dec. 1969.

D. G. Hall, "Comparison of two approaches to the waveguide scattering problem", Appl. Opt., vol. 19, no. 11, pp. 1732-1734, 1980.

R. W. Gruhlke and D. G. Hall, "Comparison of two approaches to the waveguide scattering problem: TM polarization", Appl. Opt., vol. 23, no. 1, pp. 127-133, Jan. 1984.

J. P. R. Lacey and F. P. Payne, "Radiation loss from planar wave-guides with random wall imperfections", Proc. Inst. Elect. Eng. J., vol. 137, no. 4, pp. 282-288, Aug. 1990.

F. P. Payne and J. P. R. Lacey, "A theoretical analysis of scattering loss from planar optical waveguides", Opt. Quantum. Electron, vol. 26, no. 10, pp. 977-986, Oct. 1994.

F. Ladouceur, J. D. Love and T. J. Senden, "Effect of side wall roughness in buried channel waveguides", Proc. Inst. Elect. Eng. Optoelectron., vol. 141, no. 4, pp. 242-248, Aug. 1994.

K. S. Chiang, C. H. Kwan and K. M. Lo, "Effective-index method with built-in perturbation correction for the vector modes of rectangular-core optical waveguides", J. Lightw. Technol., vol. 17, no. 4, pp. 716-722, Apr. 1999.

K. K. Lee, D. R. Lim, H. C. Luan, A. Agarwal, J. Foresi and L. C. Kimerling, "Effect of size and roughness on light transmission in a Si/SiO2 waveguide: Experiments and model", Appl. Phys. Lett., vol. 77, no. 11, pp. 1617-1619, Sep. 2000.

H. A. Haus, , private communication, Jan. 2002

T. Barwicz, H. A. Haus and H. I. Smith, "A three-dimensional analysis of scattering losses due to sidewall roughness in integrated optical waveguides", presented at the Conf. Lasers and Electo-Optics/Int. Quantum Electronics Conf. (CLEO/QELS), Baltimore, MD, Jun. 2003.

T. Barwicz, "3D analysis of scattering losses due to sidewall roughness in microphotonic waveguides: High-index contrast", presented at the Conf. Lasers and Electo-Optics/Int. Quantum Electronics Conf. (CLEO/QELS), Baltimore, MD, May 2005.

T. Barwicz and H. I. Smith, "Evolution of line-edge-roughness during fabrication of high index-contrast microphotonic devices", J. Vac. Sci. Technol. B, vol. 21, no. 6, pp. 2892-2896, Nov./Dec. 2003.

N. E. Nahi, Estimation Theory and Applications, New York: Wiley, 1969.

M. Kuznetsov and H. A. Haus, "Radiation loss in dielectric waveguide structures by the volume current method", IEEE J. Quantum Electron., vol. QE-19, no. 10, pp. 1505-1514, Oct. 1983.

J. A. Kong, Electromagnetic Wave Theory, Cambridge, MA: EMW Pub., 2000.

W. C. Chew, Waves and Fields in Inhomogeneous Media, New York: IEEE Press, 1995.

W. C. Chew and S. Y. Chen, "Response of a point source embedded in a layered medium", IEEE Antennas Wireless Propag. Lett., vol. 2, no. 16, pp. 254-258, 2003.

J. C. Cooke, "Stationary phase in two dimensions", IMA J. Appl. Math., vol. 29, no. 1, pp. 25-37, 1982.

W. Gander and W. Gautschi, "Adaptive quadrature-Revisited", B.I.T., vol. 40, no. 1, pp. 84-101, Mar. 2000.

S. J. Spector, M. W. Geis, D. M. Lennon, R. C. Williamson and T. M. Lyszczarz, "Hybrid multi-mode/single-mode waveguides for low loss", presented at the Integrated Photonics Research Topical Meeting, San Francisco, CA, Jun. 27-Jul. 2, 2004.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Boston, MA: Artech House, 2000.

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