The application of complex Pade approximants to reflection at optical waveguide facets

Numerical Investigation of a Kretschmann-Type Surface Plasmon Resonance Waveguide Sensor

“…To suppress the instabilities that are caused by the use of a small ∆z, we resort to the complex Padé approximant [10]- [12]. The complex reference refractive index approach [12], which is equivalent to the branch-cut rotation method [11], is adopted, in which the reference refractive index is changed into a complex value, i.e., n 0 =n 0 e iρ , wheren 0 is the original real reference refractive index, and ρ is a phase factor.…”

Three-Dimensional Numerical Investigation of an Improved Surface Plasmon Resonance Waveguide Sensor

“…To remove numerical instability often encountered in the vicinity of metal, we adopt the complex reference refractive index approach [8] equivalent to the branch-cut rotation method [9]. In particular, we apply the complex reference index only to the metal region where the reference index in the coefficient of the first derivative in the Fresnel equation is changed into a complex value, while in the phase variation term is kept real [10] ( is the free space wavenumber and is the refractive index of the structure).…”

New method for nonparaxial beam propagation

“…[1][2][3][4][5][6][7][8][9][10][11][12][13] In general, this non-paraxial propagation would involve solving directly the wave equation, which contains a second order partial derivative with z (the general direction of propagation) as against the first order partial derivative in the paraxial wave equation. All the methods for non-paraxial beam propagation discussed in the literature approach this problem iteratively, in which a numerical effort equivalent to solving the paraxial equation several times is involved.…”

“…[1][2][3][4][5][6][7][8][9][10][11] We have recently shown that a direct numerical solution (DNS) of the scalar wave equation gives very good accuracy and is also numerically efficient. 14 The method is non-paraxial and hence, is applicable to wide-angle as well as to bi-directional propagation.…”

“…Many of these methods neglect the backward propagating components and solve the one-way wave equation; but even methods that deal with bi-directional propagation employ special techniques either to suppress or to model evanescent modes, which are a source of instability in these methods. [8][9][10] In all these methods, the square root of the propagation operator involved in the wave equation is approximated in various ways.…”