Finite difference solution for graded-index cylindrical dielectric waveguides: a scalar wave approximation

Area of Science:

• Photonics and Optical Communications
• Computational Electromagnetics
• Numerical Analysis

Background:

• The scalar wave equation is fundamental for analyzing light propagation in optical fibers.
• Existing numerical methods may face limitations with complex refractive index profiles.
• Accurate computation of propagation constants is crucial for fiber design and performance.

Purpose of the Study:

• To present a simple and accurate numerical method for solving the scalar wave equation in optical fibers.
• To demonstrate the method's capability in analyzing fibers with arbitrary refractive index profiles.
• To assess the accuracy and limitations of the proposed numerical approach.

Main Methods:

• A finite difference numerical method is employed.
• The Ricatti transformation is applied to the scalar wave equation.
• The method is designed to handle arbitrary refractive index profiles.

Main Results:

• The numerical method achieves high accuracy, with errors as low as 0.005% for propagation constants of lower-order modes.
• The method is capable of analyzing optical fibers with diverse and complex refractive index profiles.
• An observed increase in error occurs for frequencies approaching the cutoff frequency.

Conclusions:

• The presented finite difference method offers a simple yet effective tool for analyzing optical fibers.
• The Ricatti transformation enhances the method's applicability to complex fiber structures.
• Further investigation may be needed to address error behavior near cutoff frequencies for improved accuracy.