1. Fleck, Jr., J. A., J. R. Morris, and M. D. Feit, "Time-dependent propagation of high energy laser beams through the atmosphere," Appl. Phys., Vol. 10, 129-160, 1976.
doi:10.1007/BF00896333 Google Scholar
2. Feit, M. D., J. A. Fleck, and Jr., "Light propagation in graded-index optical fibers," Appl. Opt., Vol. 17, 3990-3998, 1978.
doi:10.1364/AO.17.003990 Google Scholar
3. Feit, M. D., J. A. Fleck, and Jr., "Calculation of dispersion in graded-index multimode fibers by a propagating beam method," Appl. Opt., Vol. 18, 2843-2851, 1979.
doi:10.1364/AO.18.002843 Google Scholar
4. Feit, M. D., J. A. Fleck, and Jr., "Computation of mode properties in optical fiber waveguides by a propagating beam method," Appl. Opt., Vol. 19, 1154-1166, 1980.
doi:10.1364/AO.19.001154 Google Scholar
5. Feit, M. D., J. A. Fleck, and Jr., "Computation of mode eigenfunctions in graded-index optical fibers by the propagating beam method," Appl. Opt., Vol. 19, 2240-2246, 1980.
doi:10.1364/AO.19.002240 Google Scholar
6. Feit, M. D., J. A. Fleck, and Jr., "Mode properties of optical fibers with lossy components by the propagating beam method," Appl. Opt., Vol. 20, 848-856, 1981.
doi:10.1364/AO.20.000848 Google Scholar
7. Feit, M. D., J. A. Fleck, and Jr., "Analysis of rib waveguides and couplers by the propagating beam method," J. Opt. Soc. Am. A, Vol. 7, 73-79, 1990.
doi:10.1364/JOSAA.7.000073 Google Scholar
8. Sharma, A. and S. Banerjee, "Method for propagation of total fields or beams through optical waveguides," Opt. Lett., Vol. 14, 94-96, 1989.
doi:10.1364/OL.14.000096 Google Scholar
9. Banerjee, S. and A. Sharma, "Propagation characteristics of optical waveguiding structures by direct solution of the Helmholtz equation for total fields," J. Opt. Soc. Am. A, Vol. 6, 1884-1894, 1989; Errata: Vol. 7, 2156, 1990.
doi:10.1364/JOSAA.6.001884 Google Scholar
10. Sharma, A. and A. Taneja, "Unconditionally stable formulation of the collocation method," Integrated Photonics Research Meeting of the Optical Society of America, Paper # W 4, Monterey (Califofia, USA), April 9-11, 1991. Google Scholar
11. Sharma, A. and A. Taneja, "Unconditionally stable procedure to propagate beams through optical waveguides using the collocation method," Opt. Lett., Vol. 16, 1162-1164, 1991.
doi:10.1364/OL.16.001162 Google Scholar
12. Sharma, A. and A. Taneja, "Variable-transformed collocation method for field propagat ion through waveguiding structures," Opt. Lett., Vol. 17, 804-806, 1992.
doi:10.1364/OL.17.000804 Google Scholar
13. Sharma, A. and A. Taneja, "Collocation method for field propagation through optical waveguides: A simple variable transformation to improve accuracy," Proc. International Conference from Galileo's "Occhialino" to Optoelectronics, 916-921, (Ed. P. Mazzoldi), Singapore World Scientific, 1993. Google Scholar
14. Taneja, A. and A. Sharma, "Propagation of beams through optical waveguiding structures: Comparison of the beam propagation method (BPM) and the collocation method," J. Opt. Soc. Am. A, Vol. 10, 1739-1745, 1993.
doi:10.1364/JOSAA.10.001739 Google Scholar
15. Sharma, A. and S. Banerjee, "A numerical method for solving the generalized equation for nonlinear pulse propagation through optical fibers," Proc. Conference on Emerging Optoelectronic Technologies, 366-369, New Delhi Tata McGraw-Hill, 1992. Google Scholar
16. Deb, S. and A. Sharma, "Nonlinear pulse propagation through optical fibers: An efficient numerical method," Opt. Eng., Vol. 32, 695-699, 1993; Errata: Vol. 32, 2986, 1993.
doi:10.1117/12.61283 Google Scholar
17. Deb, S., A. Taneja, and A. Sharma, "Wave propagation through a randomly perturbed waveguide using the collocation method,", (to be published).
doi:10.1117/12.61283 Google Scholar
18. Frazer, R. A., W. P. Jones, and S. W. Skan, "Approximations to functions and to the solution of differential equations," Gt. Brit. Aero. Res. Council Rept. and Memo., 1799; Reprinted in Gt. Brit. Air Ministry Aero. Res. Comm. Tech. Rept., Vol. 1, 517-549, 1937. Google Scholar
19. Lanczos, C., "Trignometric interpolation of empirical and analytical functions," J. Math. Phys., Vol. 17, 123-199, 1938.
doi:10.1002/sapm1938171123 Google Scholar
20. Lanczos, C., Applied Analysis, Englewood Cliffs (NJ) Prentice, 1956.
21. Finlayson, B. A. and L. E. Scriven, "The method of weighted residuals --- A review," Appl. Mech. Rev., Vol. 19, 735-748, 1966. Google Scholar
22. Villadsen, J. V. and W. E. Stewart, "Solution of boundary value problems by orthogonal collocation," Chem. Engg. Sci., Vol. 22, 1483-1501, 1967.
doi:10.1016/0009-2509(67)80074-5 Google Scholar
23. Fletcher, C. A. J., Computational Galerkin Methods, Springer, 1984.
doi:10.1007/978-3-642-85949-6
24. Finlayson, B. A., "Method of Weighted Residuals and Variational Principles with Applications to Fluid Mechanics, Heat and Mass Transfer," New York Academic, 1972. Google Scholar
25. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, New York Dover, 1964.
26. Stroud, A. H. and D. Secrest, Gaussian Quadrature Formulas, Englewood Cliffs (NJ) Prentice Hall, 1966.
27. Scarborough, J. B., Numerical Mathematical Analysis, London Oxford University Press, 1966.
28. Adams, M. J., An Introduction to Optical Waveguides, Chichester Wiley, 1981.
29. Yevick, D. and B. Hermansson, "New approach to perturbed optical waveguides," Opt. Lett., Vol. 11, 103-105, 1986.
doi:10.1364/OL.11.000103 Google Scholar
30. Gear, C. W., Numerical Initial Value Problems in Ordinary Differential Equations, Englewood Cliffs (NJ) Prentice-Hall, 1971.
31. Aitken, R. C., (ed.), Stiff Computations, New York Oxford Press, 1985.
32. Hall, G. and J. M. Watt, Modern Numerical Methods for Ordinary Differential Equation, Oxford Clarendon, 1976.
33. Rahman, B. M. A. and J. B. Davies, "Finite-element analysis of optical and microwave waveguide problems," IEEE Trans. Microwave Theory Tech., Vol. 32, 20-28, 1984.
doi:10.1109/TMTT.1984.1132606 Google Scholar
34. Scarmozzino, R., R. M. Osgood, and Jr., "Comparison of finite-difference and Fourier-transform solutions of the parabolic wave equation with emphasis on integrated optic applications," J. Opt. Soc. Am. A, Vol. 8, 724-731, 1991.
doi:10.1364/JOSAA.8.000724 Google Scholar
35. Knox, R. M. and P. P. Toulis, "Integrated circuits for millimeter through optical frequency range," Symp. Submillimeter Waves, Broohlyn Polytechnic Institute, 1970. Google Scholar
36. Hocker, G. B. and W. K. Burns, "Mode dispersion in diffused channel waveguides by the effective index method," Appl. Opt., Vol. 16, 113-118, 1977.
doi:10.1364/AO.16.000113 Google Scholar
37. Sharma, A., "On approximate theories of single mode rectangular waveguides," Opt. Quantum Electron., Vol. 21, 517-520, 1989.
doi:10.1007/BF02189133 Google Scholar
38. Sharma, A., "A method for obtaining optimum equivalent 1-D index profiles for 2-D index profiles of optical waveguides," Optics in Complex Systems, Proc. SPIE, Vol. 1319, 118, F.Lanzl, H.-J. Preuss, G. Weigelt, eds., 1990.
doi:10.1117/12.22218 Google Scholar
39. Mevenkemp, W. and E. Voges, "Modeling and beam propagation analysis of integrated electro-optic devices," AEU, Vol. 40, 289-296, 1986. Google Scholar
40. Marcatili, E. A. J. and A. A. Hardy, "The azimuthal effective index method," IEEE J. Quantum Electron., Vol. 24, 766-774, 1988.
doi:10.1109/3.192 Google Scholar
41. Komori, K., S. Arai, Y. Suematsu, I. Arima, and M. Aoki, "Single mode properties of distributed reflector lasers," IEEE J. Quantum Electron., Vol. 25, 1235-1244, 1989.
doi:10.1109/3.29254 Google Scholar
42. Wang, S., "Principles of distributed feedback and distributed Bragg reflector lasers," IEEE J.Quantum Electron., Vol. 10, 413-427, 1974.
doi:10.1109/JQE.1974.1068152 Google Scholar
43. Hadjicostas, G., J. K. Butler, G. A. Evans, N. W. Carlson, and R. Amantea, "A numerical investigation of wave interactions in dielectric waveguides with periodic surface corrugations," IEEE J. Quantum Electron., Vol. 26, 893-902, 1990.
doi:10.1109/3.55531 Google Scholar
44. Kogelnik, H. and C. V. Shank, "Coupled wave theory of distributed feedback lasers," J. Appl. Phys., Vol. 43, 2327-2335, 1972.
doi:10.1063/1.1661499 Google Scholar
45. Jaggard, D. L. and C. Elachi, "Floquet and coupled wave analysis of higher order Bragg coupling in a periodic medium," J. Opt. Soc. Am., Vol. 66, 537-539, 1975. Google Scholar
46. Sharma, A. and S. Deb, "Wave propagation through peiodic waveguides: A numerical simulation method," Linear and Nonlinear Integrated Optics Confemnce in International Symposium on Integrated Optics, Lindau (Germany), April 11-15, 1994 (to appear in Proc. SPIE, Vol. 2212). Google Scholar
47. Ballman, R., Introduction to Matrix Analysis, New York McGraw Hill, 1960.
48. Agrawal, G. P. and A. H. Bobeck, "Modeling of distributed feed-back semiconductor lasers with axially-varying parameters," IEEE J. Quantum Electron., Vol. 24, 2407-2414, 1988.
doi:10.1109/3.14370 Google Scholar
49. Haus, H. A., Waves and Fields in Optoelectronics, Englewood Cliffs Prentice-Hall, 1984.
50. Uscinski, B. J., Elements of Wave Propagation in Random Media, London McGraw-Hill, 1977.
51. Tatarskii, V. I., The Effects of the Turbulent Atmosphere on Wave Propagation, Springfield National Technical Information Service, 1971.
52. Ishimaru, A., Wave Propagation and Scattering in Random Media, New York Academic, 1978.
53. Prokhorov, A. M., F. V. Bunkin, K. S. Gochelashvily, and V. I. Shishov, "Laser irradiance propagation in turbulent media," Proc. IEEE, Vol. 63, 790-811, 1975.
doi:10.1109/PROC.1975.9828 Google Scholar
54. Fante, R. L., "Electromagnetic beam propagation in turbulent media: An update," Proc. IEEE, Vol. 68, 1424-1444, 1980.
doi:10.1109/PROC.1980.11882 Google Scholar
55. Brown, VV. P., Jr., "Fourth moment of a wave propagating in a random medium," J. Opt. Soc. Am., Vol. 62, 966-971, 1972.
doi:10.1364/JOSA.62.000966 Google Scholar
56. Tur, M. and M. J. Beran, "Propagation of a finite beam through a random medium," Opt. Lett., Vol. 5, 306-308, 1982.
doi:10.1364/OL.5.000306 Google Scholar
57. Gozani, J., "Numerical solution for the fourth order coherence function of a plane wave propagating in a two-dimensional Kolmogorovian medium," J. Opt. Soc. Am. A, Vol. 2, 2144-2151, 1985.
doi:10.1364/JOSAA.2.002144 Google Scholar
58. Flatte, S. M. and F. D. Tappert, "Calculation of the effect of internal waves on oceanic sound transmission," J. Acoust. Soc. Am., Vol. 58, 1151-1159, 1975.
doi:10.1121/1.380798 Google Scholar
59. Goyal, I. C., M. S. Sodha, and A. K. Ghatak, "Propagation of electromagnetic waves in a medium with random radial dielectric-constant gradient," J. Opt. Soc. Am., Vol. 63, 940-943, 1973.
doi:10.1364/JOSA.63.000940 Google Scholar
60. Sharma, A., I. C. Goyal, N. K. Bansal, and A. K. Ghatak, "Propagation of Gaussian beams through parabolic-index optical waveguides with random dielectric constant gradient," Fiber Integrated Optics, Vol. 2, 299-314, 1979.
doi:10.1080/01468037908202108 Google Scholar
61. Papanicolaou, G. C., D. McLaughlin, and R. Burridge, "A stochastic gaussian beam," J. Math. Phys., Vol. 14, 84-87, 1973.
doi:10.1063/1.1666177 Google Scholar
62. Crosignani, B., B. Daino, and P. D. Porto, "Statistical coupled equations in lossless optical fibers," IEEE Trans. Microwave Theory Tech., Vol. 23, 416-420, 1975.
doi:10.1109/TMTT.1975.1128583 Google Scholar
63. Hasegawa, A. and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers, 1. Anomalous dispersion," Appl. Phys. Lett., Vol. 142, 142-144, 1973.
doi:10.1063/1.1654836 Google Scholar
64. Mollenauer, L. F., R. H. Stolen, and J. P. Gordon, "Experimental observation of picosecond pulse narrowing and solitons in optical fibers," Phys. Rev. Lett., Vol. 45, 1095-1098, 1980.
doi:10.1103/PhysRevLett.45.1095 Google Scholar
65. Agrawal, G. P., Nonlinear Fiber Optics, Boston Academic, 1989.
66. Kurnar, A., "Soliton dynamics in a monomode optical fiber," Physics Reports, Vol. 187, 63-108, 1990.
doi:10.1016/0370-1573(90)90097-L Google Scholar
67. Satsurna, J. and N. Yajima, "Initial value problems of one dimensional self-modulation of nonlinear waves in dispersive media," Prog. Theor. Phys. Suppl., Vol. 55, 284-306, 1973. Google Scholar
68. Schubert, M. and B. Wilhelmi, Nonlinear Optics and Quantum Electronics, New York John Wiley, 1986.
69. Fisher, R. A. and W. K. Bischel, "The role of linear dispersion in plane-wave self phase modulation," Appl. Phys. Lett., Vol. 23, 661-663, 1973.
doi:10.1063/1.1654782 Google Scholar
70. Hermansson, B. and D. Yevick, "Generalized propagation techniques --- Application to semiconductor rib waveguide Y-junctions," Photon. Technol. Lett., Vol. 2, 738-740, 1990.
doi:10.1109/68.60776 Google Scholar
71. Glasner, M., D. Yevick, and B. Hermansson, "High-order generalized propagation techniques," J. Opt. Soc. Am. B, Vol. 8, 413-415, 1991.
doi:10.1364/JOSAB.8.000413 Google Scholar
72. Hermansson, B. and D. Yevick, "Generalized propagation techniques," Opt. Lett., Vol. 16, 354-356, 1991.
doi:10.1364/OL.16.000354 Google Scholar