Abstract
The transfer matrix of a dielectric slab under propagation of a Gaussian beam was formulated. The derived matrix was applied for a one-dimensional photonic crystal (1DPC) structure and the transmittance spectrum and photonic bandgap (PBG) properties were investigated. An r-dependent (r is the radial coordinate of the Gaussian beam) PBG was obtained. With the increase of r, a redshift and a decrease in the PBG are observed. Higher PBGs experience more shift. Also properties of the photonic crystal (PC) structure with defect layer were investigated and displacement to red and decrease of the defect mode peak height, with an increase of r, were observed. The extra optical path that the outer rays travel due to the oblique propagation compared to the central ray in a Gaussian beam is responsible for these effects. For long Rayleigh ranges our results for the Gaussian beam were the same as that for plane wave.
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