Propagation in planar waveguides and the effects of wall roughness

doi:10.1364/OE.9.000461

Optics Express

Editor: J. H. Eberly
Vol. 9, Iss. 9 — Oct. 22, 2001
pp: 461–475

Propagation in planar waveguides and the effects of wall roughness

J. Merle Elson »View Author Affiliations

Optics Express, Vol. 9, Issue 9, pp. 461-475 (2001)
http://dx.doi.org/10.1364/OE.9.000461

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Abstract

We consider the propagation of guided waves in a planar waveguide that has smooth walls except for a finite length segment that has random roughness. Maxwell’s equations are solved in the frequency domain for both TE and TM polarization in 2-D by using modal expansion methods. Obtaining numerical solutions is facilitated by using perfectly matched boundary layers and the R-matrix propagator.Varying lengths of roughness segments are considered and numerical results are obtained for guided wave propagation losses due to roughness induced scattering. The roughness on each waveguide boundary is numerically generated from an assumed Gaussian power spectrum. The guided waves are excited by a Gaussian beam incident on the waveguide aperture. Considerable numerical effort is given to determine the stability of the algorithm.

[Optical Society of America ]

OCIS Codes
(230.7390) Optical devices : Waveguides, planar
(290.5880) Scattering : Scattering, rough surfaces

ToC Category:
Research Papers

History
Original Manuscript: September 28, 2001
Published: October 22, 2001

Citation
J. Merle Elson, "Propagation in planar waveguides and the effects of wall roughness," Opt. Express 9, 461-475 (2001)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-9-9-461

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References

J. M. Elson and P. Tran, "R-matrix propagator with perfectly matched layers for the study of integrated optical components," J. Opt. Soc. Am. A 16, 2983-2989 (1999). [CrossRef]
J. M. Elson and P. Tran, "Coupled-mode calculation with the R-matrix propagator for the dispersion of surface waves on a truncated photonic crystal," Phys. Rev. B 54, 1711-1715 (1996). [CrossRef]
J. M. Elson and P. Tran, "Band structure and transmission of photonic media: a real-space finite-difference calculation with the R-matrix propagator," NATO ASI Series E: Applied Sciences on Photonic Band Gap Materials Vol. 315 341-354 Crete, Greece June 15-29 (1995).
L. Li, "Multilayer modal method for diffraction gratings of arbitrary profile, depth, and permittivity," J. Opt. Soc. Am. A 11, 2816-2828 (1993). [CrossRef]
L. Li, "Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings," J. Opt. Soc. Am. 13, 1024-1035 (1996). [CrossRef]
J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comp. Phys. 114, 185-200 (1995). [CrossRef]
J. P. Berenger, "Three-dimensional perfectly matched layer for the absorption of electromagnetic waves," J. Comp. Phys. 127, 363-379 (1996). [CrossRef]
D. Marcuse, "Mode conversion caused by surface imperfections in a dielectric slab waveguide," Bell Sys. Tech. J. 48, 3187-3215 (1969).
D. Marcuse, "Radiation losses of dielectric waveguides in terms of the power spectrum of the wall distortion function," Bell Sys. Tech. J. 48, 3233-3242 (1969).
F. P. Payne and J. P. R. Lacey, "A theoretical analysis of scattering loss from planar optical waveguides," Opt. and Quantum Elec. 26, 977-986 (1994). [CrossRef]
J. P. R. Lacey and F. P. Payne, "Radiation loss from planar waveguides with random wall imperfections," IEEE Proc. J. 137, 282-288 (1990).
K. K. Lee, D. R. Lim, H. Luan, A. Agarwal, J. Foresi and L. Kimerling, "Effect of size and roughness on light transmission on a Si/SiO2 waveguide: Experiment and model," Appl. Phys. Lett. 77, 1617-1619 (2000). [CrossRef]
F. Ladouceur, J. D. Love and T. J. Senden, "Effect of side wall roughness in buried channel waveguides," IEEE Proc.-Optoelectron. 141, 242-248 (1994). [CrossRef]
F. Ladouceur, J. D. Love and T. J. Senden, "Measurement of surface roughness in buried channel waveguides," Electron. Lett. 28, 1321-1322 (1992). [CrossRef]
J. Rodrguez, R. D. Crespo, S. Fernandez, J. Pandavenes, J. Olivares, S. Carrasco, I. Ibanez, J. Virgos, "Radiation losses on discontinuities in integrated optical waveguides," Opt. Engr. 38, 1896-1906 (1999). [CrossRef]
P. Lalanne and G. Morris, "Highly improved convergence of the coupled-wave method for TM polarization," J. Opt. Soc. Am. 13, 779-784 (1996). [CrossRef]
L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. 13, 1870-1876 (1996). [CrossRef]
A. A. Maradudin, T. Michel, A. R. McGurn, and E. Mendez, "Enhanced backscattering of light from a random grating," Annals of Physics 203, 225-307 (1990). [CrossRef]

Other

J. M. Elson and P. Tran, "R-matrix propagator with perfectly matched layers for the study of integrated optical components," J. Opt. Soc. Am. A 16, 2983-2989 (1999). [CrossRef]
J. M. Elson and P. Tran, "Coupled-mode calculation with the R-matrix propagator for the dispersion of surface waves on a truncated photonic crystal," Phys. Rev. B 54, 1711-1715 (1996). [CrossRef]
J. M. Elson and P. Tran, "Band structure and transmission of photonic media: a real-space finite-difference calculation with the R-matrix propagator," NATO ASI Series E: Applied Sciences on Photonic Band Gap Materials Vol. 315 341-354 Crete, Greece June 15-29 (1995).
L. Li, "Multilayer modal method for diffraction gratings of arbitrary profile, depth, and permittivity," J. Opt. Soc. Am. A 11, 2816-2828 (1993). [CrossRef]
L. Li, "Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings," J. Opt. Soc. Am. 13, 1024-1035 (1996). [CrossRef]
J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comp. Phys. 114, 185-200 (1995). [CrossRef]
J. P. Berenger, "Three-dimensional perfectly matched layer for the absorption of electromagnetic waves," J. Comp. Phys. 127, 363-379 (1996). [CrossRef]
D. Marcuse, "Mode conversion caused by surface imperfections in a dielectric slab waveguide," Bell Sys. Tech. J. 48, 3187-3215 (1969).
D. Marcuse, "Radiation losses of dielectric waveguides in terms of the power spectrum of the wall distortion function," Bell Sys. Tech. J. 48, 3233-3242 (1969).
F. P. Payne and J. P. R. Lacey, "A theoretical analysis of scattering loss from planar optical waveguides," Opt. and Quantum Elec. 26, 977-986 (1994). [CrossRef]
J. P. R. Lacey and F. P. Payne, "Radiation loss from planar waveguides with random wall imperfections," IEEE Proc. J. 137, 282-288 (1990).
K. K. Lee, D. R. Lim, H. Luan, A. Agarwal, J. Foresi and L. Kimerling, "Effect of size and roughness on light transmission on a Si/SiO2 waveguide: Experiment and model," Appl. Phys. Lett. 77, 1617-1619 (2000). [CrossRef]
F. Ladouceur, J. D. Love and T. J. Senden, "Effect of side wall roughness in buried channel waveguides," IEEE Proc.-Optoelectron. 141, 242-248 (1994). [CrossRef]
F. Ladouceur, J. D. Love and T. J. Senden, "Measurement of surface roughness in buried channel waveguides," Electron. Lett. 28, 1321-1322 (1992). [CrossRef]
J. Rodrguez, R. D. Crespo, S. Fernandez, J. Pandavenes, J. Olivares, S. Carrasco, I. Ibanez, J. Virgos, "Radiation losses on discontinuities in integrated optical waveguides," Opt. Engr. 38, 1896-1906 (1999). [CrossRef]
P. Lalanne and G. Morris, "Highly improved convergence of the coupled-wave method for TM polarization," J. Opt. Soc. Am. 13, 779-784 (1996). [CrossRef]
L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. 13, 1870-1876 (1996). [CrossRef]
A. A. Maradudin, T. Michel, A. R. McGurn, and E. Mendez, "Enhanced backscattering of light from a random grating," Annals of Physics 203, 225-307 (1990). [CrossRef]

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