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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 15, Iss. 5 — May. 1, 1998
  • pp: 1401–1410

Polarization characteristics of optical waveguides with separable symmetric refractive-index profiles

Hagen Renner  »View Author Affiliations

JOSA A, Vol. 15, Issue 5, pp. 1401-1410 (1998)

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In contrast with scalar modes, the vector modes of two-dimensional waveguides with separable refractive-index profiles cannot be calculated by a simple product ansatz for the fields. It is shown that a separation of the dominant field component into two factors, with each depending on only one of the two Cartesian coordinates, is accurately possible up to first order in the small relative refractive-index difference Δ for symmetric separable profiles. This allows us to calculate the modal propagation constants by decomposing the problem into two independent TE and TM planar wave equations. Birefringence is thereby included to an accuracy of first order in Δ. The minor field component can be separated to first order in Δ, if one of the two factors constituting the major field component is the fundamental mode of the parabolic profile, but cannot be separated in general. The longitudinal field components are separable to their lowest order Δ1/2 for all separable profiles.

© 1998 Optical Society of America

OCIS Codes
(130.0130) Integrated optics : Integrated optics
(130.2790) Integrated optics : Guided waves
(130.3120) Integrated optics : Integrated optics devices
(230.7370) Optical devices : Waveguides
(230.7380) Optical devices : Waveguides, channeled
(230.7390) Optical devices : Waveguides, planar

Hagen Renner, "Polarization characteristics of optical waveguides with separable symmetric refractive-index profiles," J. Opt. Soc. Am. A 15, 1401-1410 (1998)

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  1. A. Ankiewicz, “Ray theory of graded non-circular optical fibres,” Opt. Quantum Electron. 11, 197–203 (1979).
  2. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).
  3. A. Sharma, E. Khular, K. Thyagarajan, and A. K. Ghatak, “Coupling of two parallel multimode parabolic index waveguides: an exact analysis in the weakly guiding approximation,” Opt. Commun. 30, 166–169 (1979).
  4. E. A. J. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell Syst. Tech. J. 48, 2071–2102 (1969).
  5. H. Renner, “Far-from-core field of bound modes on non-circular weakly guiding optical waveguides,” J. Mod. Opt. 39, 1–7 (1992).
  6. H. Renner, “Asymptotic coupling coefficients of well-separated single-mode optical waveguides,” J. Mod. Opt. 39, 907–915 (1992).
  7. P. Yeh and H. F. Taylor, “Contradirectional frequency-selective couplers for guided-wave optics,” Appl. Opt. 19, 2848–2855 (1980).
  8. A. Kumar, K. Thyagarajan, and A. K. Ghatak, “Analysis of rectangular-core dielectric waveguides: an accurate perturbation analysis,” Opt. Lett. 8, 63–65 (1983).
  9. K. Hayata, K. Miura, and M. Koshiba, “Full vectorial finite element formalism for lossy anisotropic waveguides,” IEEE Trans. Microwave Theory Tech. 37, 875–883 (1989).
  10. F. A. Fernandez and Y. Lu, “A variational finite element formulation for dielectric waveguides in terms of transverse magnetic fields,” IEEE Trans. Magn. 27, 3864–3867 (1991).
  11. Y. Lu and F. A. Fernandez, “An efficient finite element solution of inhomogeneous anisotropic and lossy dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 41, 1215–1223 (1993).
  12. G. D. Maxwell and B. J. Ainslie, “Demonstration of directly written directional coupler using UV-induced photosensitivity in a planar silica waveguide,” Electron. Lett. 31, 95–96 (1995).
  13. P. Baldi, P. Aschieri, S. Nouh, M. De Micheli, D. B. Ostrowski, D. Delacourt, and M. Papuchon, “Modeling and experimental observation of parametric fluorescence in periodically poled lithium niobate waveguides,” IEEE J. Quantum Electron. 31, 997–1008 (1995).
  14. C. F. Kaue and R. R. Krchnayet, “Benzocyclobutene optical waveguides,” IEEE Photonics Technol. Lett. 7, 535–537 (1995).
  15. I. Faderl, P. Labeye, P. Gidon, and P. Mottier, “Integration of an electrooptic polymer in an integrated optics circuit on silicon,” J. Lightwave Technol. 13, 2020–2026 (1995).
  16. E. R. Hedin and F. J. Goetz, “Experimental studies of electro-optic polymer modulators and waveguides,” Appl. Opt. 34, 1554–1561 (1995).
  17. A. L. Sala, M. G. Mirkov, B. G. Bagley, and R. T. Deick, “Derivation of dimensional and material requirements for propagation and processing of temporal optical solitons in planar geometry channel waveguides,” Appl. Opt. 36, 7846–7852 (1997).
  18. P. K. Sinha, “Coupling characteristics of 4×4 elliptical core optical waveguide coupler,” Fiber Integr. Opt. 15, 125–133 (1996).
  19. C. K. Madsen and J. H. Zhao, “A general planar waveguide autoregressive optical filter,” J. Lightwave Technol. 14, 437–447 (1996).
  20. D. Rafizadeh, J. P. Zhang, S. C. Hagness, A. Taflove, K. A. Stair, S. T. Ho, and R. C. Tiberio, “Waveguide-coupled AlGaAs/GaAs microcavity ring and disk resonators with high finesse and 1.6-nm free spectral range,” Opt. Lett. 22, 1244–1246 (1997).
  21. T. Isoshima and K. Tada, “Local normal-mode analysis of second-harmonic generation in a periodic waveguide,” IEEE J. Quantum Electron. 33, 164–175 (1997).
  22. A. Kumar, R. K. Varshney, and K. Thyagarajan, “Birefringence calculations in elliptical-core optical fibres,” Electron. Lett. 20, 112–113 (1984).
  23. R. K. Varshney and A. Kumar, “Effect of depressed inner cladding on the polarization characteristics of elliptical-core fibers,” Opt. Lett. 9, 522–524 (1984).
  24. A. Kumar, A. N. Kaul, and A. K. Ghatak, “Prediction of coupling length in a rectangular-core directional coupler: an accurate analysis,” Opt. Lett. 10, 86–88 (1985).
  25. R. K. Varshney and A. Kumar, “Birefringence calculations in side-tunnel optical fibers: a rectangular-core waveguide model,” Opt. Lett. 11, 45–47 (1986).
  26. I. Yokohama, K. Okamoto, and J. Noda, “Analysis of fiber-optic polarizing beam splitters consisting of fused-taper couplers,” J. Lightwave Technol. LT-4, 1352–1359 (1986).
  27. A. Kumar, U. K. Das, R. K. Varshney, and I. C. Goyal, “Design of a mode filter consisting of two dual-mode highly elliptical core fibers,” J. Lightwave Technol. 8, 34–38 (1990).
  28. K. S. Chiang, “Analysis of the effective-index method for the vector modes of rectangular-core dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 44, 692–700 (1996).
  29. A. W. Snyder and W. R. Young, “Modes of optical waveguides,” J. Opt. Soc. Am. 68, 297–309 (1978).
  30. Ph. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).
  31. M. Svalgaard, C. V. Poulsen, A. Bjarklev, and O. Poulsen, “Direct UV writing of buried singlemode channel waveguides in Ge-doped silica films,” Electron. Lett. 30, 1401–1403 (1994).
  32. D. Johlen, P. Klose, and E. Brinkmeyer, “UV-written directional couplers in silica on silicon,” in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 279–280.

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