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Related Experiment Videos

Exact solution of resonant modes in a rectangular resonator.

Jiu Hui Wu1, A Q Liu

  • 1School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore.

Optics Letters
|May 12, 2006
PubMed
Summary

Researchers precisely analyzed rectangular optical resonators, simplifying resonant frequency calculations using Bessel functions. A practical rule for approximating infinite resonators is provided, aiding applications in dense wavelength-division multiplexing filters.

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Area of Science:

  • Optics and Photonics
  • Materials Science

Background:

  • Rectangular optical resonators are crucial components in photonic integrated circuits.
  • Accurate analysis of their resonant modes is essential for device design and performance.

Purpose of the Study:

  • To provide an exact analytical solution for the resonant modes of rectangular two-dimensional optical resonators.
  • To simplify the calculation of resonant frequencies for rectangular microcavities.
  • To establish criteria for approximating finite resonators as infinite in practical scenarios.

Main Methods:

  • Exact analytical solution based on the characteristics of Bessel functions.
  • Mathematical derivation of resonant frequencies.
  • Development of a criterion for resonator length approximation.

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Main Results:

  • A simplified expression for the resonant frequencies of rectangular microcavities using Bessel functions.
  • An exact analysis of resonant modes in two-dimensional rectangular optical resonators.
  • A practical rule for determining when a finite resonator can be treated as infinite.

Conclusions:

  • The presented analytical method offers a straightforward way to determine resonant frequencies.
  • The findings are applicable to the design of rectangular resonators for dense wavelength-division multiplexing (DWDM) filters.
  • The study provides valuable insights for optimizing optical resonator performance in telecommunications.