Numerical solution to modal field equation with a finite difference beam propagation method: application to Bragg fiber

Rihab Chatta; Mehdi Ammar; Mourad Zghal; Rabah Attia

doi:10.1117/12.481183

4 September 2002 Numerical solution to modal field equation with a finite difference beam propagation method: application to Bragg fiber

Rihab Chatta, Mehdi Ammar, Mourad Zghal, Rabah Attia

Author Affiliations +

Proceedings Volume 4769, Optical Design and Analysis Software II; (2002) https://doi.org/10.1117/12.481183
Event: International Symposium on Optical Science and Technology, 2002, Seattle, WA, United States

Abstract

The Beam Propagation Method (BPM) is the most widely used tool for the investigation of complex photonic structures. Since the original BPM was introduced, many improvements and extensions have been proposed. We have developed a computer program based on the Finite Difference BPM for modeling propagation in optical waveguides. This method has been successfully applied for several 3D problems such as propagation on Bragg Fiber. The main drawback of this method is its complexity and long computation time using a personal computer. In this paper, a simple efficient numerical solution method, we called double 2D-BPM, is proposed. This technique is based on the decomposition of the 3D field propagation equation onto two 2D equations related to transverse plans. Propagation along the x and y axes is computed separately in two steps. Using a similar technique, a finite difference approximation for each propagation step involves the solution of two equations and the complete problem splits into two independent 2D problems. We performed propagation tests in elementary 3D problems but also on Bragg fiber. The numerical results of 3D-BPM and double 2D-BPM have been compared. The propagation step along the propagation axis has been experimentally determined. Parameters that affect the accuracy and the stability of this method were discussed. Losses induced by propagation on Bragg fiber were also considered. We have established that the global effect of the double 2D-BPM is equivalent to 3D-BPM technique. Comparison with exact results obtained from analytical expressions also shows excellent agreement.

Citation Download Citation

Rihab Chatta, Mehdi Ammar, Mourad Zghal, and Rabah Attia "Numerical solution to modal field equation with a finite difference beam propagation method: application to Bragg fiber", Proc. SPIE 4769, Optical Design and Analysis Software II, (4 September 2002); https://doi.org/10.1117/12.481183

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