ИСТИНА

Many photonics applications need devices with special spectral and dispersive properties. Generating optical signals of a given form such as ultra-short laser pulses or supercontinuum are among those tasks. Photonic crystals which spectral and dispersive properties areset by their design can be employed for that purpose. A simple model of such one-dimensional photonic crystal is a Bragg mirror, consisting of alternating dielectric layers with high and low refractive indices. This simple model enables us to understand the way of engineering optical properties. It is possible to achieve required dispersion law and to extend the bandwidth of the mirror at the same time by chirping width of the layers. The same method should be applicable for the photonic crystal. In our work we justify the applicability of a dielectric mirror model to the description of a real photonic crystal. A slab waveguide with periodically changing width is considered and it is shown that this width change can be recalculated to the effective refraction index modulation. The applicability of transfer-matrix method of transmission properties calculation was demonstrated. Two methods of deriving of the expressions for the photonic bandgap were considered and proved to be consistent, while emphasizing different aspects of the propagation process. The position and width of the bandgap as a function of waveguide’s width was investigated. Finally, modeling of one-dimensional chirped Bragg mirror was performed with respect to the material and waveguide dispersion. Numerical optimization method and analytical method were realized to calculate the chirp law for the desired dispersive characteristics.