Loading...

Basis functions for solution of non-homogeneous wave equation

Khorasani, S ; Sharif University of Technology | 2013

831 Viewed
  1. Type of Document: Article
  2. DOI: 10.1117/12.2019539
  3. Publisher: 2013
  4. Abstract:
  5. 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
  6. Keywords:
  7. Differential transfer matrix method ; Optics ; Quantum mechanics ; Wave equation ; Differential transfer matrix methods ; Divergent behaviors ; Initial conditions ; Linear ordinary differential equations ; Matrix exponentials ; Non-homogeneous ; Real and imaginary ; System of equations ; Linear transformations ; Optoelectronic devices ; Ordinary differential equations ; Quantum theory ; Wave equations ; Functions
  8. Source: Proceedings of SPIE - The International Society for Optical Engineering ; Volume 8619 , February , 2013 ; 0277786X (ISSN); 9780819493880 (ISBN)
  9. URL: http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=1668445