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Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities

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

L S Tamil, S S Mitra, R Dutta

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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.