An analytical method for band structure calculations of photonic crystal fibers with liquid crystal infiltrations is presented. The scalar eigenvalue equation is extended to treat both isotropic and anisotropic materials by introducing a coefficient to describe the index contrast between the extraordinary and ordinary refractive index of the liquid crystal. The simple model provides a fast insight into bandgap formation in photonic crystal fibers filled with anisotropic material such as liquid crystal, which would be useful to aid the design based on such fibers.
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Hu et al. (2008) studied this question.