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Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities

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Published on: November 30, 2012

Approximate solution to the scalar wave equation for optical waveguides.

I C Goyal, R L Gallawa, A K Ghatak

|August 14, 2010

Summary

This study presents an accurate approximate solution for optical waveguides, outperforming the WKB method by working even at turning points. The method is applicable to arbitrary refractive-index profiles and waveguide geometries.

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Area of Science:

Optics and Photonics
Computational Electromagnetics

Background:

Optical waveguides are crucial in modern photonics.
Existing approximate methods like the WKB approximation have limitations, particularly at turning points.

Purpose of the Study:

To introduce and validate an accurate approximate solution for the wave equation in optical waveguides.
To provide a method applicable to arbitrary refractive-index profiles and waveguide geometries (2D/3D).

Main Methods:

Developed an approximate solution to the wave equation.
Applied the method to circular and planar waveguide geometries.
Calculated fields and propagation constants for lowest-order modes.

Main Results:

The proposed approximate solution is valid even at turning points, unlike the WKB method.
Calculated results for two specific profiles show excellent agreement with exact solutions.
Demonstrated applicability to arbitrary refractive-index profiles and waveguide geometries.

Conclusions:

The presented approximate solution offers superior accuracy and utility compared to the WKB method for optical waveguides.
This method, though not novel, is largely unknown and underutilized within the optics community.
Recommends wider adoption of this effective technique for waveguide analysis.