Patterns of the lightwave propagation in a layered medium with a change in optical properties along a parabolic graded-index film

Model of theoretical description of a change in optical properties in near-surface layers due lightwave propagation along a parabolic graded-index film waveguide structure is proposed. Exact analytical solution of the value boundary problem formulated, which describe the stationary eigenmodes of the waveguide structure, are found. The modes correspond to a discrete spectrum of values of the effective refractive index determined by the optical and geometrical parameters of the waveguide system. The field amplitude enlarges and the penetration depth of the field decreases with an increase in the longitudinal wave numbed. The intensity of the light flux in thicker films in the center of the film is higher than near its surfaces. The equation is derived, the use of which makes it possible to establish the adequacy of the choice of a parabolic profile for real semiconductor crystals for a given film thickness and wavelength. Analytical expressions of the total power flow of the lightwave along the waveguide structure are obtained. The total power flow enlarges with an increase in the film thickness for modes of all orders. The minimum of dependence of the flow on the wave number is observed. The value of the power flow minimum decreases with increasing order of the mode and goes into saturation. Possibility to choose a thickness of the parabolic graded-index film is shown, at which the power of the transferred light flux will be concentrated in a certain region of the waveguide structure.