| This work is concerned with the problem of light propagation in a diaphanous medium, in which the index of refraction changes rapidly transverse to the direction of propagation. The medium is considered diaphanous because it possesses small variation of the index of refraction in range, but with a very high gradient, which characterizes what is called a shock wave profile medium.;This problem was modeled considering three approaches: The proposed parabolic approximation, which is independent of the wave number k, the diaphanous or phase object approximation, and the geometrical optics field. The diaphanous approximation was used here to validate the results obtained with the parabolic approximation. The high order of the frequencies involved in this problem lends to the accuracy of the geometrical optical field representation, as long as diffraction phenomena are not present. This approximation was also used with the purpose of corroborating the parabolic approximation results.;The parabolic equation in the present approximation is arrived at through the asymptotic expansion of a multiple scaled reduced wave equation, and its solution represents the leading term solution in the expansion. The conditions for the validity of the proposed equation are investigated and details of its derivation are also presented.;An important aspect to point out is that the computation of the derived parabolic equation is independent of the wave number k. Thus this method overcomes the difficulty posed by the propagation over large optical distances, with insignificant computational effort. Furthermore, the method retains all the diffraction effects associated with the specific geometry of the problem under study; being particularly suitable for media with index of refraction with small variations in range, such as the case considered here. |
