Collocation method has been developed as a method which can treat the modal field computation as well as the total field propagation with equal ease and efficiency. The method, based on the orthogonal collocation principle, converts the Helmholtz equation into a matrix ordinary differential equation. This equation termed as the collocation equation can be solved either by using direct numerical techniques or by special techniques based on the matrix operator algebra. In the present paper, we outline the basic principle of the method and the implementation of the perfectly matched layer technique to overcome the reflections from the edge of the numerical window. In addition, we discuss its applications to Bragg waveguides and to soliton propagation which ave lately assumed great significance.

Date Published: 25 September 2001
PDF: 7 pages
Proc. SPIE 4417, Photonics 2000: International Conference on Fiber Optics and Photonics, (25 September 2001); doi: 10.1117/12.441281

Published in SPIE Proceedings Vol. 4417:
Photonics 2000: International Conference on Fiber Optics and Photonics
S. K. Lahiri; Ranjan Gangopadhyay; Asit K. Datta; Samit K. Ray; B. K. Mathur; S. Das, Editor(s)