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6 February 2007 Analytical analysis of H polarized line-defect modes in two dimensional photonic crystals based on Hermite expansion of Floquet orders
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Abstract
Using polynomial expansion of electromagnetic fields has been already reported for extraction of E polarized defect modes in two-dimensional photonic crystals. This approach is now applied to straight single-line defect optical waveguides, where H polarized defect modes are analytically extracted for the first time. Electromagnetic fields are expanded in accordance with the Floquet theorem, where each Floquet order is itself expanded in terms of Hermite polynomials and finally a new set of linear ordinary differential equations with non-constant coefficients is obtained. This set of equations is handled by employing differential transfer matrix method. In this fashion, algebraic and easy to solve dispersion equations are derived, where each mode is effectively sought out in the Hilbert space spanned by Hermite polynomials. Effective index theory based on static field approximation is also presented to show the strong similarity between eigenmodes of photonic bandgap waveguides and those of slab waveguides with uniaxial anisotropic claddings.
© (2007) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Peyman Sarrafi, Amir Hossein Atabaki, Khashayar Mehrany, Sina Khorasani, Bizhan Rashidian, and Ali Adibi "Analytical analysis of H polarized line-defect modes in two dimensional photonic crystals based on Hermite expansion of Floquet orders", Proc. SPIE 6480, Photonic Crystal Materials and Devices VI, 64801D (6 February 2007); https://doi.org/10.1117/12.725950
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