Abstract
Making use of the effective medium theory, we reduce the two-dimensional photonic crystals to an effective one-dimensional model. This one-dimensional model not only predicts correctly the dispersion in the long-wavelength limit (where the wavelength is much larger than the period of material) but also gives a good approximation for shorter wavelength. We further use the perturbation theory to improve the calculation of dispersion up to medium wavelength (which is of the order of space period of the material). Our work gives an insight into the modes of electromagnetic field propagating in photonic crystals.
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