602 Opt.Soc.Am.A/Vol.2,No.4/April 1985 L.M.Walpita reading of the manuscript.The author also wishes to thank 6.T.Miyamoto and M.Momoda,"Propagation characteristics of J.B.Davis and C.W.Pitt of University College,London,for a multilayered thin film optical waveguide with buffer layer,"J. initial discussions.This work was initially carried out at 0pt.Soc.Am.72,1163-1166(1982). University College,London,and continued at the University 7.J.R.Wait,Electromagnetic Waves in Stratified Media (Perga- mon,London,1970),pp.8-21. of California,San Diego. 8.E.F.Kuester and D.C.Chang,"Propagation,attenuation,and dispersion characteristics of inhomogeneous dielectric slab waveguides,"IEEE Trans.Microwave Theory Tech.MTT-23, REFERENCES 98-106(1975). 9.M.Born andE.Wolf,Principles of Optics(Pergamon,London, 1.P.K.Tien,"Light waves in thin films and integrated optics," 1980),pp.665-718. Appl.0pt.10,2395-2413(1971). 10.V.Ramaswamy,"Ray model of energy and power flow in aniso- 2.D.P.Gia Russo and J.H.Harris,"Wave propagation in aniso- tropic film waveguides,"J.Opt.Soc.Am.64,1313-1320 tropic thin film optical waveguides,"J.Opt.Soc.Am.63,138-145 (1974). (1973). 11.E.C.Jordon and K.G.Balman,Electromagnetic Waves and 3.M.O.Vassell,"Structure of optical guided modes in planar Radiating Systems (Prentice-Hall,Englewood Cliffs,N.J.,1968), multilayers of optically anisotropic materials,"J.Opt.Soc.Am. pp.100-111. 64,166-173(1974). 12.The computer-time differential depends on the size of the prob- 4.Y.Yamato,T.Kamiya,and H.Yanai,"Characteristics of optical lem under investigation.As an example,in obtaining the nor guided modes in multilayer metal-clad planar optical guide with malized propagation constant of a 10-layer structure,the zero- low index dielectric buffer layer,"IEEE J.Quantum Electron element method takes less than 5%of the computation time that QE-11,729-736(1975). Vassell's method requires. 5.G.B.Hocker and W.K.Burns,"Modes in diffused optical 13.T.Findakly and C.L.Chen,"Diffused optical waveguides with waveguides of arbitrary index profile,"IEEE J.Quantum Elec- exponential profiles:effect of metal-clad and dielectric overlay," tron.QE-11,270-276(1975). Appl.0pt.17,469-474(1978).602 Opt. Soc. Am. A/Vol. 2, No. 4/April 1985 reading of the manuscript. The author also wishes to thank J. B. Davis and C. W. Pitt of University College, London, for initial discussions. This work was initially carried out at University College, London, and continued at the University of California, San Diego. REFERENCES 1. P. K. Tien, "Light waves in thin films and integrated optics," Appl. Opt. 10, 2395-2413 (1971). 2. D. P. Gia Russo and J. H. Harris, "Wave propagation in aniso￾tropic thin film optical waveguides," J. Opt. Soc. Am. 63, 138-145 (1973). 3. M. 0. Vassell, "Structure of optical guided modes in planar multilayers of optically anisotropic materials," J. Opt. Soc. Am. 64, 166-173 (1974). 4. Y. Yamato, T. Kamiya, and H. Yanai, "Characteristics of optical guided modes in multilayer metal-clad planar optical guide with low index dielectric buffer layer," IEEE J. Quantum Electron. QE-lI, 729-736 (1975). 5. G. B. Hocker and W. K. Burns, "Modes in diffused optical waveguides of arbitrary index profile," IEEE J. Quantum Elec￾tron. QE-lI, 270-276 (1975). 6. T. Miyamoto and M. Momoda, "Propagation characteristics of a multilayered thin film optical waveguide with buffer layer," J. Opt. Soc. Am. 72, 1163-1166 (1982). 7. J. R. Wait, Electromagnetic Waves in Stratified Media (Perga￾mon, London, 1970), pp. 8-21. 8. E. F. Kuester and D. C. Chang, "Propagation, attenuation, and dispersion characteristics of inhomogeneous dielectric slab waveguides," IEEE Trans. Microwave Theory Tech. MTT-23, 98-106 (1975). 9. M. Born and E. Wolf, Principles of Optics (Pergamon, London, 1980), pp. 665-718. 10. V. Ramaswamy, "Ray model of energy and power flow in aniso￾tropic film waveguides," J. Opt. Soc. Am. 64, 1313-1320 (1974). 11. E. C. Jordon and K. G. Balman, Electromagnetic Waves and Radiating Systems (Prentice-Hall, Englewood Cliffs, N.J., 1968), pp. 100-111. 12. The computer-time differential depends on the size of the prob￾lem under investigation. As an example, in obtaining the nor- malized propagation constant of a 10-layer structure, the zero- element method takes less than 5% of the computation time that Vassell's method requires. 13. T. Findakly and C. L. Chen, "Diffused optical waveguides with exponential profiles: effect of metal-clad and dielectric overlay," Appl. Opt. 17, 469-474 (1978). L. M. Walpita