Abstract
We investigate the Laplace transform of the reduced radial Helmholtz equation for the electromagnetic fields in weakly guiding optical fibres. In the Laplace transform space we derive an integral condition for the cutoff frequencies of the LP modes. We apply our equation to several refractive index profiles of practical interest.
Similar content being viewed by others
References
Anderssen, R.S., F.R. de Hoog and J.D. Love. Opt. Quantum Electron. 13 217, 1981.
Bélanger, P.-A. Optical Fiber Theory, World Scientific, Singapore, 1993.
Doetsch, G. Handbuch der Laplace-Transformationen, Vol. 2, pp. 142–155, Birkhäuser, Basel, 1955.
Gambling, W.A. and H. Matsumura. Opt. Quantum Electron. 10 31, 1978.
Gambling, W.A., H. Matsumura and C.M. Ragdale. Opt. Quantum Electron. 10 301, 1978.
Gambling, W.A., D.N. Payne and H. Matsumura. Electron. Lett. 13 139, 1977.
Lachance, R.L. and P.-A. Bélanger. J. Lightwave Technol. 9 1425, 1991.
Love, J.D. Opt. Quantum Electron. 11 464, 1979.
Love, J.D. Opt. Quantum Electron. 17 139, 1985.
Lukowski, T.I. and F.P. Kapron. J. Opt. Soc. Am. 67 1185, 1977.
Marcuse, D. J. Opt. Soc. Am. 68 103, 1978.
Marcuse, D. Light Transmission Optics, Van Nostrand Reinhold Company, New York, 1982.
Neumann, E.-G. Single-Mode Fibers, Springer, Berlin, New York, 1988.
Paiano, G. Nuovo Cimento B 111 701, 1996 ibid. 1539 (Erratum).
Paiano, G. and P. Cea. Nuovo Cimento B 114 163, 1999.
Sneddon, I.N. Special Functions of Mathematical Physics and Chemistry, Oliver and Boyd, Edinburgh and London, 1961.
Snyder, A.W. and R. Sammut, Electron. Lett. 15 269, 1979.
Watson, G.N. A Treatise on the Theory of Bessel Functions, University Press, Cambridge, 1962.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Cea, P., Paiano, G. Determining the cutoff frequencies of weakly guiding optical fibres by the Laplace transform. Optical and Quantum Electronics 32, 77–95 (2000). https://doi.org/10.1023/A:1007084902281
Issue Date:
DOI: https://doi.org/10.1023/A:1007084902281