Scattering of a scalar field at dielectric surfaces by Born series expansion

A method for the calculation of the transmitted and reflected scalar fields at arbitrary dielectric surfaces is presented. The method is based on an evaluation of the Born series expansion and is of high accuracy as multiple reflections and refractions are taken into account. We show by comparison with Fresnel formulas that with the algorithm the ratio of transmitted and reflected field amplitudes can be calculated exactly. Results obtained by our algorithm are compared with results from rigorous diffraction calculations for a dielectric cylinder. We also demonstrate the application of the method to a more complicated surface geometry. Furthermore, advantages and restrictions of this algorithm are identified.

[1]  James E. Harvey,et al.  Fourier treatment of near‐field scalar diffraction theory , 1979 .

[2]  É. Lalor,et al.  Conditions for the Validity of the Angular Spectrum of Plane Waves , 1968 .

[3]  M Totzeck,et al.  Interference microscopy of sub-λ structures: A rigorous computation method and measurements , 1997 .

[4]  Paul Lagasse,et al.  Beam-propagation method: analysis and assessment , 1981 .

[5]  Peter Török,et al.  Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: an integral representation , 1995 .

[6]  René Dändliker,et al.  Scattering of an off-axis Gaussian beam by a dielectric cylinder compared with a rigorous electromagnetic approach , 1995 .

[7]  E. Wolf,et al.  Exact Solution of the Equations of Molecular Optics for Refraction and Reflection of an Electromagnetic Wave on a Semi-Infinite Dielectric* , 1972 .

[8]  Wolfgang Freude,et al.  Rayleigh-Sommerfeld and Helmholtz-Kirchhoff integrals: application to the scalar and vectorial theory of wave propagation and diffraction , 1995 .

[9]  Martial Geiser,et al.  Laser-based refractive-index detection for capillary electrophoresis: ray-tracing interference theory. , 1993, Applied optics.

[10]  H. Weyl,et al.  Ausbreitung elektromagnetischer Wellen über einem ebenen Leiter , 1919 .

[11]  M. Totzeck.  Validity of the scalar Kirchhoff and Rayleigh–Sommerfeld diffraction theories in the near field of small phase objects , 1991 .

[12]  K. Brenner,et al.  Light propagation through microlenses: a new simulation method. , 1993, Applied optics.

[13]  John A. DeSanto,et al.  Reconstruction of rough-surface profiles with the Kirchhoff approximation , 1991 .

[14]  G. Arfken.  Mathematical Methods for Physicists , 1967 .

[15]  Christoph Cremer,et al.  Development of a two-parameter slit-scan flow cytometer for screening of normal and aberrant chromosomes: application to a karyotype of Sus scrofa domestica (pig) , 1992 .

[16]  Karl-Heinz Brenner,et al.  Transition of the scalar field at a refracting surface in the generalized Kirchhoff diffraction theory , 1995 .