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Microwave Photonics Systems Based on Whispering-gallery-mode Resonators

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Defining cylindrical space optical resonators through supported mode properties: inverse numerical process.

Robert C Gauthier

|May 3, 2018

Summary

This study introduces an inverse numerical method to determine optical resonator properties. It uses electromagnetic field profiles to identify material and geometry, aiding in designing optical fibers and photonic crystals.

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Area of Science:

Electromagnetism
Optical Engineering
Computational Physics

Background:

Traditional methods solve electromagnetic wave equations for known material properties and geometry.
Determining material and geometric properties from field data is a challenging inverse problem.

Purpose of the Study:

To present an inverse numerical method for determining the material and geometric properties of cylindrically symmetric optical resonators.
To demonstrate a technique that solves for material and geometry using electric and magnetic field profiles.

Main Methods:

Conversion of Faraday's and Ampere's laws into matrix operator form.
Rearrangement of equations to solve for unknown relative permittivity and permeability tensors.
Application of a Fourier-Bessel numerical approach suitable for cylindrical geometries.

Main Results:

Successful determination of material and geometry for optical resonator structures.
Demonstration with non-magnetic materials and diagonal relative permittivity tensors.
Inclusion of axial field propagation to showcase design capabilities for optical and photonic crystal fibers.

Conclusions:

The presented inverse numerical process effectively determines optical resonator characteristics.
The Fourier-Bessel approach is well-suited for analyzing cylindrical optical structures.
This technique offers valuable design insights for advanced optical fiber applications.