Abstract
A numerical method for obtaining mode cutoffs for planar waveguides with arbitrary index profiles is developed. The method is based on the Galerkin method in which the wave equation for modes at cutoff is converted to a matrix eigenvalue equation using a set of orthogonal basis functions. Due to different boundary conditions, we have identified two separate cases; one, in which the cover and the substrate indices are identical leading to same behavior of the field at cutoff in these two regions and, the other, in which the two indices are different and hence, the field behaves differently. We have accordingly chosen different basis functions for the two cases. The method results in a generalized matrix eigenvalue problem which has been converted to a standard symmetric matrix eigenvalue analytically. The method has been used to obtain mode cutoffs for waveguides with a variety of index profiles. Comparisons with available exact results show that very good accuracies can be obtained with moderate matrix sizes.
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References
Adams, M.J. An Introduction to Optical Waveguides, Wiley, Chichester, 1981.
Boucouvalas, A.C. In Proceedings of Performance Engineering of Computer and telecommunication Systems of UKPEW 95, ed. M. Merabti, Liverpool John Moores University, UK, 5-6 September 1995.
Boucouvalas, A.C. and C.D. Papageorgiou. IEEE J. Quantum Electron. QE-18 2027, 1982.
Cea, P. and 1048, 1982.
Chiang, K.S. Opt. Lett. 16 714, 1991.
Espinosa-ortiz, N., Yu.V. Kolesnichenko and V.V. Shevchenko. J. Commun. Technol. Electron. 38 82, 1993.
Gambling, W.A., D.N. Payne and H. Matsumura. Electron. Lett. 13 139, 1977.
Hocker, G.B. and W.K. Burns. Appl. Opt. 16 113, 1977.
Hosain, S.I. and J.P. Meunier. IEEE Photon. Technol. Lett. 3 801, 1991.
Kaul, A.N., S.I. Hosain and K. Thyagarajan. IEEE Trans. Microwave Theory Tech. MTT-34 288, 1986.
Kokubun, Y. and K. Iga. J. Opt. Soc. Am. 70 36, 1980.
Kumar, A., R. Chandra, R.A. Sammut and A.K. Ghatak. Electron. Lett. 14 676, 1978.
Lamouche, G. and S.I. Najafi. Can. J. Phys. 68 1251, 1990.
Love, J.D. Opt. Quantum Electron. 17 139, 1985.
Meliga, M., S. Morasca, B. Sordo and C. De Bernardi. Proc. SPIE 835 251, 1988.
Meunier, J.P., J. Pigeon and J.N. Massot. Electron. Lett. 16 27, 1980.
Meunier, J.P., J. Pigeon and J.N. Massot. J. Lightwave Technol. 2 171, 1984.
Mishra, P.K. and A. Sharma. J. Lightwave Technol. 4 204, 1986.
Papageorgiou, C.D. and A.C. Boucouvalas. Optica Acta 31 555, 1984.
Renner, H. IEEE J. Quantum Electron. QE-33 724, 1997.
Sharma, A. Opt. Quantum Electron. 21 517, 1989.
Sharma, A. and P. Bindal. Opt. Quantum Electron. 24 1359, 1992.
Sharma, A. and A.K. Ghatak. IEEE Trans. Microwave Theory Tech. vol. MTT-29 607, 1981. Comments, Reply and Errata: vol. MTT-30 108, 1982.
Sharma, E.K., I.C. Goyal and A.K. Ghatak. IEEE J. Quantum Electron. QE-13 71, 1981.
Torner, L., F. Canal and J. Hernandez-Marco. Opt. Quantum Electron. 21 451, 1989.
Yata, A. and H. Ikuno. Electron. Lett. 17 9, 1981.
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Sharma, A., Meunier, JP. Cutoff frequencies in planar optical waveguides with arbitrary index profiles: An efficient numerical method. Optical and Quantum Electronics 34, 377–392 (2002). https://doi.org/10.1023/A:1015072710209
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DOI: https://doi.org/10.1023/A:1015072710209