The influence of the geometrical and physical parameters on the photonic band-gap of GaAs and AlGaAs 2D photonic
crystals has been investigated. As a result the gap-maps for geometrical parameters appropriate for operation at around
the λ = 1.5μm wavelength have been obtained, i.e. the wavelength region most widely used in current fibre-optic
telecommunications. Using these gap-maps, it is possible to find the PhC parameters for which the PhC exhibits a PBG
within the telecommunication range.
The photonic crystal (PC) coupler and planar photonic band gap (PBG) coupler were theoretically investigated. Also the conventional step-index coupler was investigated for comparison with these couplers. The PC-coupler is a structure formed by the gradual tapering of the photonic-crystal holey fiber and the conventional step-index coupler -- by the gradual tapering of the conventional fiber. The planar PBG-coupler is a planar PC waveguide, in which defect region has taper-like geometry. The photonic crystal couplers are characterized by alternation of the material refractive index along the wave propagation direction, i. e. along the optical axis of the taper. In our investigation an effective refractive index model for two-dimensional photonic crystal was used. This model allows to analyze the waveguide structures, which work on the effective index waveguiding in a defect of the photonic crystal. The optical field in photonic crystal couplers, PBG couplers and conventional couplers was investigated. Also losses and mode shape distortion of all types of the couplers were calculated.
In the present paper the modified effective-index model of photonic-crystal waveguide is proved and presented. This model allows to reduce the three-dimensional numerical analysis to the two-dimensional consideration of the waveguiding due to representing of the waveguide as its step-index analog with the cladding region described by the effective refractive index of two-dimensional photonic crystal (PC) and the effective core size. The effective core size allowing equivalent description of waveguiding properties in the PC waveguide using the modified effective-index model and its numerical approximation are numerically defined. The obtained data have been used for numerical investigation of waveguide couplers formed by tapered photonic crystal fiber (PCF). It was shown that the couplers have smaller loss in comparison with couplers made by tapered step-index fiber.
At the present paper the photonic crystal coupler of an optical fiber, which has been made by the adiabatic tapering of the optical fiber based on the photonic crystal is presented. These couplers are characterizing by material refractive index changing in a spatial direction along of the wave propagation direction. In our investigation an effective refractive index model of two-dimensional photonic crystal was used. This model allows analyzing the waveguide structures, which work on the effective index waveguiding in a defect of the photonic crystal. Also this model allows reducing the investigation time by reducing the three-dimensional numerical analysis of the coupler to the two-dimensional consideration. The effective refractive indexes of such couplers were numerically found. Using this model the field distribution in these couplers were investigated and were calculated its losses. It was shown that the couplers with smaller input diameter and the fixed output diameter have smaller losses.
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