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Proceedings Paper

Basis functions for solution of non-homogeneous wave equation
Author(s): Sina Khorasani; Farhad Karimi
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Paper Abstract

In this note we extend the Differential Transfer Matrix Method (DTMM) for a second-order linear ordinary differential equation to the complex plane. This is achieved by separation of real and imaginary parts, and then forming a system of equations having a rank twice the size of the real-valued problem. The method discussed in this paper also successfully removes the problem of dealing with essential singularities, which was present in the earlier formulations. Then we simplify the result for real-valued problems and obtain a new set of basis functions, which may be used instead of the WKB solutions. These basis functions not only satisfy the initial conditions perfectly, but also, may approach the turning points without the divergent behavior, which is observed in WKB solutions. Finally, an analytical transformation in the form of a matrix exponential is presented for improving the accuracy of solutions.

Paper Details

Date Published: 14 March 2013
PDF: 12 pages
Proc. SPIE 8619, Physics and Simulation of Optoelectronic Devices XXI, 86192B (14 March 2013); doi: 10.1117/12.2019539
Show Author Affiliations
Sina Khorasani, Sharif Univ. of Technology (Iran, Islamic Republic of)
Farhad Karimi, The Univ. of Wisconsin-Madison (United States)


Published in SPIE Proceedings Vol. 8619:
Physics and Simulation of Optoelectronic Devices XXI
Bernd Witzigmann; Marek Osinski; Fritz Henneberger; Yasuhiko Arakawa, Editor(s)

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