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Related Experiment Videos

Photonic band structure calculations using scattering matrices.

L C Botten1, N A Nicorovici, R C McPhedran

  • 1School of Mathematical Sciences, University of Technology, Sydney, New South Wales 2007, Australia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 3, 2001
PubMed
Summary

This study presents a new method for calculating the band structure of two-dimensional photonic crystals using scattering matrices of one-dimensional gratings. This approach simplifies calculations and provides insights into band gaps and effective dielectric constants.

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Area of Science:

  • Condensed matter physics
  • Photonics
  • Materials science

Background:

  • Photonic crystals are artificial materials with unique optical properties.
  • Calculating their band structure is crucial for designing optical devices.
  • Existing methods can be computationally intensive.

Purpose of the Study:

  • To develop an efficient method for calculating the band structure of 2D photonic crystals.
  • To simplify the analysis of photonic crystals by treating them as stacks of gratings.
  • To derive new expressions for band gaps and effective dielectric constants.

Main Methods:

  • Utilizing plane wave scattering matrices of 1D gratings.
  • Applying Bloch's theorem to solve an eigenvalue problem.

Related Experiment Videos

  • Deriving simplifications for symmetric lattices and analyzing eigenvalue spectrum.

    • Main Results:

    • Established a method to determine photonic crystal band structure from grating scattering matrices.
    • Derived simplified eigenvalue problems for symmetric lattices.
    • Obtained closed-form expressions for scattering matrices of finite and infinite grating stacks.
    • Deduced expressions for band gaps and effective dielectric constants in the long-wavelength limit.

    Conclusions:

    • The scattering matrix method offers an efficient approach for photonic crystal band structure calculations.
    • This method provides a deeper understanding of band gap formation and effective medium properties.
    • The derived expressions are valuable for the design and analysis of photonic devices.