TM-modes in a planar optical waveguide with a graded index of the symmetric Epstein type

C.A. van Duin, J. Boersma, F.W. Sluijter

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Samenvatting

The eigenvalue problem for the TM-modes in a planar optical waveguide is rigorously solved by analytical and numerical methods in the case of a symmetric Epstein-type variation of the dielectric permittivity. It is shown that there exists a finite number of guided TM-modes. The TM-modal fields are expressed in terms of Heun functions and the corresponding eigenvalues (or propagation coefficients) are numerically determined from the minimal solution of a three-term recurrence relation. Upper and lower bounds are established for the difference between corresponding eigenvalues of the TE- and TM-modes.
Originele taal-2Engels
Pagina's (van-tot)175-190
Aantal pagina's16
TijdschriftWave Motion
Volume8
Nummer van het tijdschrift2
DOI's
StatusGepubliceerd - 1986

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