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Analytic Approach to Dielectric Optical Bent Slab Waveguides
 Optical and Quantum Electronics
, 2004
"... A rigorous classical analytic frequency domain model of confined optical wave propagation along 2D bent slab waveguides and curved dielectric interfaces is investigated, based on a piecewise ansatz for bend mode profiles in terms of Bessel and Hankel functions. This approach provides a clear pict ..."
Abstract

Cited by 16 (10 self)
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A rigorous classical analytic frequency domain model of confined optical wave propagation along 2D bent slab waveguides and curved dielectric interfaces is investigated, based on a piecewise ansatz for bend mode profiles in terms of Bessel and Hankel functions. This approach provides a clear picture of the behaviour of bend modes, concerning their decay for large radial arguments or effects of varying bend radius. Fast and accurate routines are required to evaluate Bessel functions with large complex orders and large arguments. Our implementation enabled detailed studies of bent waveguide properties, including higher order bend modes and whispering gallery modes, their interference patterns, and issues related to bend mode normalization and orthogonality properties.
2000), Numerical and asymptotic aspects of parabolic cylinder functions
 J. Comp. Appl. Math
"... Several uniform asymptotics expansions of the Weber parabolic cylinder functions are considered, one group in terms of elementary functions, another group in terms of Airy functions. Starting point for the discussion are asymptotic expansions given earlier by F.W.J. Olver. Some of his results are mo ..."
Abstract

Cited by 7 (6 self)
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Several uniform asymptotics expansions of the Weber parabolic cylinder functions are considered, one group in terms of elementary functions, another group in terms of Airy functions. Starting point for the discussion are asymptotic expansions given earlier by F.W.J. Olver. Some of his results are modified to improve the asymptotic properties and to enlarge the intervals for using the expansions in numerical algorithms. Olver’s results are obtained from the differential equation of the parabolic cylinder functions; we mention how modified expansions can be obtained from integral representations. Numerical tests are given for three expansions in terms of elementary functions. In this paper only real values of the parameters will be considered. 1991 Mathematics Subject Classification: 33C15, 41A60, 65D20.
Zeros of the Macdonald function of complex order
, 2006
"... The zzeros of the modified Bessel function of the third kind Kν(z), also known as modified Hankel function or Macdonald function, are considered for arbitrary complex values of the order ν. Approximate expressions for the zeros, applicable in the cases of very small or very large ν, are given. Th ..."
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The zzeros of the modified Bessel function of the third kind Kν(z), also known as modified Hankel function or Macdonald function, are considered for arbitrary complex values of the order ν. Approximate expressions for the zeros, applicable in the cases of very small or very large ν, are given. The behaviour of the zeros for varying ν  or arg ν, obtained numerically, is illustrated by means of some graphics. Key words: Macdonald function, modified Bessel function of the third kind, Hankel function, zeros
Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528,
, 2006
"... The zzeros of the modified Bessel function of the third kind Kν(z), also known as modified Hankel function or Macdonald function, are considered for arbitrary complex values of the order ν. Approximate expressions for the zeros, applicable in the cases of very small or very large ν, are given. Th ..."
Abstract
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The zzeros of the modified Bessel function of the third kind Kν(z), also known as modified Hankel function or Macdonald function, are considered for arbitrary complex values of the order ν. Approximate expressions for the zeros, applicable in the cases of very small or very large ν, are given. The behaviour of the zeros for varying ν  or arg ν, obtained numerically, is illustrated by means of some graphics. Key words: Macdonald function, modified Bessel function of the third kind, Hankel function, zeros
unknown title
, 2004
"... Computing solutions of the modified Bessel differential equation for imaginary orders and positive arguments ..."
Abstract
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Computing solutions of the modified Bessel differential equation for imaginary orders and positive arguments