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Photonic band structures solved by a plane-wave-based transfer-matrix method.

Zhi-Yuan Li1, Lan-Lan Lin

  • 1Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 6, 2003
PubMed
Summary
This summary is machine-generated.

This study extends transfer-matrix methods to compute photonic band structures for 2D and 3D photonic crystals. The approach demonstrates superior convergence for complex photonic crystals compared to conventional methods.

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Area of Science:

  • Computational Physics
  • Materials Science
  • Optics and Photonics

Background:

  • Transfer-matrix methods (TMM) with plane-wave basis are standard for electromagnetic wave scattering in multilayer gratings and photonic crystal slabs.
  • Calculating photonic band structures is crucial for understanding and designing photonic crystals.

Purpose of the Study:

  • To extend TMM combined with Bloch's theorem for solving photonic band structures in 2D and 3D photonic crystals.
  • To present and discuss three eigensolution schemes for band diagram computation along high-symmetry lines.

Main Methods:

  • Combines transfer-matrix methods with Bloch's theorem.
  • Employs optimal Fourier expansion rules for dielectric functions and electromagnetic fields, addressing discontinuities.
  • Utilizes three distinct eigensolution schemes for band structure analysis.

Main Results:

  • Successfully extends TMM to compute photonic band structures for 2D and 3D photonic crystals.
  • Demonstrates accelerated convergence through optimized Fourier expansion rules.
  • Shows superior convergence for 3D layer-by-layer photonic crystals compared to conventional plane-wave expansion.

Conclusions:

  • The extended TMM offers an efficient and accurate method for photonic band structure calculations.
  • The approach provides a robust alternative for analyzing complex photonic crystal designs.
  • Optimized numerical techniques significantly enhance computational efficiency and accuracy.