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Dispersion implementation in optical filter design by the Fourier transform method using correction factors.

Stéphane Larouche1, Ludvik Martinu

  • 1Regroupement québécois sur les matériaux de pointe and Department of Engineering Physics, Ecole polytechnique de Montréal, Québec, Canada. stephane.larouche@polymtl.ca

Applied Optics
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Summary

This study introduces an improved Fourier transform method for designing graded-index optical filters. The enhanced technique accurately accounts for refractive index dispersion, leading to superior filter performance using SiO2/TiO2 mixtures.

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Area of Science:

  • Optics and Materials Science
  • Photonics and Optical Engineering

Background:

  • Traditional Fourier transform methods for graded-index optical filter design utilize approximate Q functions and neglect refractive index dispersion.
  • These limitations often necessitate iterative correction processes to achieve desired filter performance.

Purpose of the Study:

  • To address the drawback of neglecting refractive index dispersion in Fourier transform-based optical filter design.
  • To propose and validate an enhanced method for designing graded-index optical filters with improved accuracy.

Main Methods:

  • Modified the Fourier transform method by scaling the wavelength with the filter's optical thickness.
  • Incorporated a wavelength-dependent correction factor into the Q function to account for dispersion.
  • Designed and evaluated optical filters using SiO2/TiO2 mixtures with the enhanced method.

Main Results:

  • The proposed method effectively accounts for the dispersion of the index of refraction.
  • Optical filters designed with the correction factors demonstrated high performance.
  • Validation was achieved using the optical properties of SiO2/TiO2 mixtures.

Conclusions:

  • The enhanced Fourier transform method provides a more accurate approach to designing graded-index optical filters.
  • This method overcomes the limitations of previous techniques by incorporating refractive index dispersion.
  • The demonstrated effectiveness with SiO2/TiO2 mixtures highlights its practical applicability.