1. Benson, T. M., Integrated optical components produced in GaAs and InP epitaxial layers using the photo-elastic egect, Ph.D. Thesis, Dept. of Electronic and Electrical Engineering, University of Sheffield, UK, 1982.

2. Schweig, E. and W. B. Bridges, "Computer analysis of dielectric waveguides --- A finite difference method," IEEE Trans. MTT, Vol. 32, 531-541, 1984.
doi:10.1109/TMTT.1984.1132717        Google Scholar

3. Robertson, M. J., S. Ritchie, and P. Dayan, "Semiconductor waveguides: Analysis of optical propagation in single rib structures and directional couplers," IEE Proc. J, Vol. 132, 336-342, 1985.        Google Scholar

4. Lagu, R. K. and R. V. Ramaswamy, "A variational finite difference method for analysing channel waveguides with arbitrary index profiles," IEEE J. Quantum Electron., Vol. 22, 968-976, 1986.
doi:10.1109/JQE.1986.1073033        Google Scholar

5. Schulz, N., K. Bierwirth, and F. Arndt, "Finite difference analysis of integrated optical waveguides without spurious mode solutions," Electron. Lett., Vol. 22, 963-965, 1986.
doi:10.1049/el:19860657        Google Scholar

6. Bierwirth, K., N. Schulz, and F. Arndt, "Finite difference analysis of rectangular dielectric waveguide structures," IEEE Trans. MTT, Vol. 34, 1104-1114, 1986.
doi:10.1109/TMTT.1986.1133506        Google Scholar

7. Stern, M. S., "Semivectorial polarised finite difference method for optical waveguides with arbitrary index profiles," IEE Proc. J, Vol. 135, 56-63, 1988.        Google Scholar

8. Stern, M. S., "Semivectorial polarised H-field solutions for dielectric waveguides with arbitrary index profiles," IEE Proc. J, Vol. 135, 333-338, 1988.
doi:10.1049/ip-d.1988.0049        Google Scholar

9. Benson, T. M., P. C. Kendall, M. S. Stern, and D. A. Quinney, "New results for rib waveguide propagation constants," IEE Proc. J, No. 136, 97-102, 1989.        Google Scholar

10. Working Group 1, COST-216 "Comparison of different modeling techniques for longitudinauy invariant integrated optical waveguides," IEE Proc. J, Vol. 136, 273-280, 1989.        Google Scholar

11. Kim, C. M. and R. V. Ramaswamy, "Modeling of graded index channel waveguides using non-uniform finite difference method," IEEE J. Lightwave Technol., Vol. 7, 1581-1589, 1989.
doi:10.1109/50.39101        Google Scholar

12. Schulz, N., K. Bierwirth, F. Arndt, and U. Koster, "Finite difference method without spurious solutions for the hybrid-mode analysis of diffused channel waveguides," IEEE Trans. MTT, Vol. 38, 722-729, 1990.
doi:10.1109/22.130966        Google Scholar

13. Seki, S., T. Yamanaka, and K. Yokoyama, "Two-dimensional analysis of optical waveguides with a non-uniform finite difference method," IEE Proc. J, Vol. 138, 123-127, 1991.        Google Scholar

14. Stern, M. S., "Rayleigh quotient solution of semi-vectorial field problems for optical waveguides with arbitrary index profiles," IEE Proc. J, Vol. 138, 185-190, 1991.        Google Scholar

15. Schulz, N., K. Bierwirth, F. Arndt, and U. Koster, "Rigorous finite difference analysis of coupled channel waveguides with arbitrarily varying index profile," IEEE J. Lightwave Technol., Vol. 9, 1244-1253, 1991.
doi:10.1109/50.90922        Google Scholar

16. Vassallo, C., Optical Waveguide Concepts, Elsevier, 1991.

17. Vassallo, C., "Improvement of finite difference methods for stepindex optical waveguides," IEE Proc. J, Vol. 139, 137-142, 1992.        Google Scholar

18. Matin, M. A., T. M. Benson, P. C. Kendall, and M. S. Stern, "New technique for finite difference analysis of optical waveguide problems," International J. Numerical Modeling: Electronic Networks, Devices and Fields, Vol. 7, 25-33, 1994.
doi:10.1002/jnm.1660070104        Google Scholar

19. Adams, M. J., An Introduction to Optical Waveguides, John Wiley, 1981.

20. Owyang, G. H., Foundations of Optical Waveguide, Edward Arnold, 1981.

21. Marcuse, D., Theory of Dielectric Optical Waveguides, Academic Press, 1974.

22. Ghatak, A. K. and K. Thyagarajan, Optical Electronics, Cambridge University Press, 1989.
doi:10.1017/CBO9781139167857

23. Kendall, P. C., M. J. Adarns, S. Ritchie, and M. J. Robertson, "Theory for calculating approximate values of the propagation constants of an optical rib waveguide by weighting the refractive indices," IEE Proc. A, Vol. 134, 699-702, 1987.        Google Scholar

24. Robertson, M. J., P. C. Kendall, S. Ritchie, P. W. A. McIlroy, and M. J. Adarns, "The weighted index method: A new technique for analysing planar optical waveguides," IEEE J. Lightwave Technol., Vol. 7, 2105-2111, 1989.
doi:10.1109/50.41636        Google Scholar

25. Kendall, P. C., M. J. Robertson, P. W. A. McIlroy, S. Ritchie, and M. J. Adams, "Advances in rib waveguide analysis using the weighted index method or the method of moments," IEE Proc. J, Vol. 137, 27-29, 1990.        Google Scholar

26. Robson, P. N. and P. C. Kendall (Eds.), Rib Waveguide Theory by the Spectral Index Method, Research Studies Press (Taunton) and John Wiley (Chichester), 1990.

27. Kendall, P. C., P. W. A. McIlroy, and M. S. Stern, "Analysis of semiconductor rib waveguides: Spectral index method," Proc. IEE Colloquium on Integrated Optics, IEE Digest No. 1989193, 13/1-13/4, 1989.        Google Scholar

28. McIlroy, P. W. A., M. S. Stern, and P. C. Kendall, "Fast and accurate method for calculation of polarised modes in semiconductor rib waveguides," Electron Lett., Vol. 25, 1586-1587, 1989.
doi:10.1049/el:19891065        Google Scholar

29. McIlroy, P. W. A., M. S. Stern, and P. C. Kendall, "Spectral index method for polarized modes in semiconductor rib waveguides," IEEE J. Lightwave Technol., Vol. 8, 113-117, 1990.
doi:10.1109/50.45937        Google Scholar

30. Stern, M. S., P. C. Kendall, and P. W. A. McIlroy, "Analysis of the spectral index method for vector modes of rib waveguides," IEE Proc. J, Vol. 137, 21-26, 1990.        Google Scholar

31. Kendall, P. C., M. S. Stern, and P. N. Robson, "Discrete spectral index method for rib waveguide analysis," Optical and Quantum Electron., Vol. 22, 555-560, 1990.
doi:10.1007/BF02189505        Google Scholar

32. Koshiba, M., K. Hayata, and M. Suzuki, "Finite element formulation in terms of the electric field vector for electromagnetic waveguide problems," IEEE Trans. MTT, Vol. 33, 900-905, 1985.
doi:10.1109/TMTT.1985.1133148        Google Scholar

33. Rahman, B. M. A. and J. B. Davies, "Finite element analysis of optical and microwave waveguide problems," IEEE Trans. MTT, Vol. 32, 20-28, 1984.
doi:10.1109/TMTT.1984.1132606        Google Scholar

34. Rahman, B. M. A. and J. B. Davies, "Finite element solution of optical waveguides," IEEE J. Lightwave Technol., Vol. 2, 682-688, 1984.
doi:10.1109/JLT.1984.1073669        Google Scholar

35. Rahman, B. M. A. and J. B. Davies, "Penalty function improvement of waveguide solution by finite elements," IEEE Trans. MTT, Vol. 32, 922-928, 1984.
doi:10.1109/TMTT.1984.1132789        Google Scholar

36. Rahman, B. M. A. and J. B. Davies, "Vector-H finite element solution of GaAsIGaAlAs rib waveguides," IEE Proc. J, Vol. 132, 349-353, 1985.        Google Scholar

37. Koshiba, M., K. Hayata, and M. Suzuki, "Improved finite element formulation in terms of the magnetic field vector for dielectric waveguides," IEEE Trans. MTT, Vol. 33, 227-233, 1985.
doi:10.1109/TMTT.1985.1132985        Google Scholar

38. Young, T. P. and P. Smith, "Finite element modeling of integrated optical waveguides," GEC J. Research, Vol. 4, 249-255, 1986.        Google Scholar

39. Young, T. P., "Design of integrated optical circuits using finite elements," IEE Proc. A, Vol. 135, 135-144, 1988.        Google Scholar

40. Fernandez, F. A. and Y. Lu, "Variational finite element analysis of dielectric waveguides with no spurious modes," Electron. Lett., Vol. 26, 2125-2126, 1990.
doi:10.1049/el:19901367        Google Scholar

41. Fernandez, F. A. and Y. Lu, "A variational finite element formulation for dielectric waveguides in terms of transverse magnetic fields," IEEE Trans. Magnetics, Vol. 27, 3864-3867, 1991.
doi:10.1109/20.104946        Google Scholar

42. Lu, Y., F. A. Fernandez, S. Zhu, and J. B. Davies, "A new variational finite element analysis of microwave and optical waveguides without spurious solutions," Proc. IEE International Conf. on Computation in Electromagnetics, IEE Conf. Publ. No. 350, 160-163, 1991.        Google Scholar

43. Courant, R., Diflerential and Integral Calculus, 97-99, Blackie and Son, 1959.

44. Lennox, S. C. and M. Chadwick, Mathematics for Engineers and Applied Scientists, 20-22, Heinemann, 1977.

45. Fox, L., An Introduction to Numerical Linear Algebra, Clarendon Press, 1964.

46. Wilkinson, J. H., The Algebraic Eigenvalue Problem, Clarendon Press, 1964.

47. Johnson, L. W. and R. D. Riess, Numerical Analysis, Addison-Wesley, 1977.

48. Atkinson, L. V., P. J. Harley, and J. D. Hudson, Numerical Methods with FORTRAN-77, Addison-Wesley, 1989.

49. Benson, T. M., P. C. Kendall, M. A. Matin, and M. S. Stern, "Polarization correction applied to scalar analysis of semiconductor rib waveguides," IEE Proc. J, Vol. 139, 39-41, 1992.        Google Scholar

50. Fox, L., (Ed.), Numerical Solution of Ordinary and Partial Diflerentlal Equations, Pergamon Press, 1962.

51. Srnith, G. D., Numerical Solution of Partial Diflerential Equations, Oxford University Press, 1965, 1978, 1985.

52. Quinney, D. A., An Introduction to the Numerical Solution of Differential Equations, Research Studies Press (Taunton) and John Wiley (Chichester), 1985.

53. Huang, W. P. and H. A. Haus, "A simple variational approach to optical rib waveguides," IEEE J. Lightwave Technol., Vol. 9, 56-61, 1991.
doi:10.1109/50.64923        Google Scholar

54. Koshiba, M., H. Saitoh, M. Eguchi, and K. Hirayama, "Simple scalar finite element approach to optical rib waveguides," IEE Proc. J, Vol. 139, 166-171, 1992.        Google Scholar

55. Liu, P. L. and B. J. Li, "Semi-vectorial beam propagation method for analyzing polarised modes of rib waveguides," IEEE J. Quantum Electron., Vol. 28, 778-782, 1992.
doi:10.1109/3.135193        Google Scholar

56. Liu, P. L. and B. J. Li, "Semi-vectorial Helmholtz beam propagation by Lanczos reduction," IEEE J. Qzlantum Electron., Vol. 29, 2385-2389, 1993.
doi:10.1109/3.245570        Google Scholar

57. Austin, M. W., "Theoretical and experimental investigation of GaAslGaAlAs and nn GaAs rib waveguides," IEEE J. Lightwave Technol., Vol. 2, 688-694, 1984.
doi:10.1109/JLT.1984.1073682        Google Scholar

58. Austin, M. W., "GaAs/GaAlAs curved rib waveguides," IEEE J. Qzlantum Electron., Vol. 18, 795-800, 1982.
doi:10.1109/JQE.1982.1071580        Google Scholar

59. Huang, W. P. and H. A. Haus, "Simple variational approach to optical rib waveguides," IEEEIOSA Topical Meeting on Integmted Photonics Research, Hilton Head USA, Tech. Digest Series, Vol. 5, 85-86, 1990.        Google Scholar

60. Kendall, P. C., M. S. Stern, and P. N. Robson, "A Huygens-type formula for curvature loss from dlelectric waveguides in optoelectronics," Electron. Lett., Vol. 23, 850-851, 1987.
doi:10.1049/el:19870601        Google Scholar

61. Stern, M. S., P. C. Kendall, and P. N. Robson, "Estimation of rib waveguide radiation losses," Electron. Lett., Vol. 24, 17-19, 1988.
doi:10.1049/el:19880012        Google Scholar

62. Kendall, P. C., M. S. Stern, and P. N. Robson, "A new cufvature loss formula of Huygens-type for rib waveguides," IEE Proc. J, Vol. 135, 11-16, 1988.        Google Scholar

63. Stern, M. S., P. C. Kendall, R. C. Hewson-Browne, P. N. Robson, and D. A. Quinney, "Scattering loss from rough sidewalls in semiconductor rib waveguides," Electron. Lett., Vol. 25, 1231-1232, 1989.
doi:10.1049/el:19890825        Google Scholar

64. Stern, M. S., "Comparison of spectral index, semi-vectorial finite difference and vector finite element methods for the modal analysis of semiconductor optical rib waveguides," Proc. IEE International Conf. on Computation in Electromagnetics, IEE Conf. Publ. NO. 350, 18-21, 1991.        Google Scholar

65. Benson, T. M., P. C. Kendall, and M. A. Matin, "Simple variational approach to optical rib waveguide analysis," Electron. Lett., Vol. 28, 1897-1898, 1992.
doi:10.1049/el:19921214        Google Scholar

66. Benson, T. M., P. C. Kendall, M. A. Matin, and M. S. Stern, "Polarised modes of semiconductor rib waveguides," Electron. Lett., Vol. 27, 1488-1489, 1991.
doi:10.1049/el:19910931        Google Scholar

67. Mao, Z. and W. P. Huang, "Analysis of opticd rib waveguides and couplers with buried guiding layer," IEEE J. Quantum Electron., Vol. 28, 176-183, 1992.
doi:10.1109/3.119512        Google Scholar

68. Burke, S. V., "Spectral index method applied to coupled rib waveguides," Electron. Lett., Vol. 25, 605-606, 1989.
doi:10.1049/el:19890411        Google Scholar

69. Burke, S. V., "Spectral index method applied to rib and strip loaded directional coupler," IEE Proc. J, Vol. 137, 7-10, 1990.        Google Scholar

70. Benson, T. M., P. C. Kenddl, and M. S. Stern, "Microwave simulation of optoelectronic bending loss in the presence of a dielectric discontinuity," IEE Proc. J, Vol. 135, 325-331, 1988.        Google Scholar