Optical and Quantum Electronics

, Volume 36, Issue 1, pp 145-163

First online:

Applications of the finite difference mode solution method to photonic crystal structures

  • Chin-Ping YuAffiliated withGraduate Institute of Communication Engineering, National Taiwan University
  • , Hung-Chun ChangAffiliated withDepartment of Electrical Engineering, Graduate Institute of Electro-Optical Engineering, and Graduate Institute of Communication Engineering, National Taiwan University Email author 

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The finite difference waveguide mode solution method, which has been popularly employed in the study of waveguide modes on various optical and dielectric waveguides, is utilized to calculate the modal characteristics of photonic crystal fibers (PCFs) and planar photonic crystal waveguides and the band diagrams of two-dimensional photonic crystals. Vector guided modes on both PCFs based on the total internal reflection guiding mechanism ('holey fibers') and those resulting from photonic band gap effect are accurately computed, with their effective indexes and field distributions compared with other methods. Calculated dispersion of a single-core holey fiber and coupled-power behavior of a two-core holey fiber are found to agree with measured results. For applications to band diagram calculation and planar photonic crystal waveguide analysis, the finite difference scheme is modified simply by imposing suitable periodic boundary condition. Numerical results for air-column crystals and dielectric-rod crystals are both found to agree well with calculations using other methods.

finite difference method optical waveguides photonic band gap photonic crystals photonic crystal fibers photonic crystal waveguides