Abstract

The method of path integrals is based on the possibility of evaluating the contributions to the complex amplitude at the observation point (x′,y′,z′) due to the different path lengths of rays coming from the initial (x,y,z) to find the kernel of equation^1,2 which for weakly guiding media can be obtained as¹ Here S_g is a geometrical ray path for optical functional expanded in series up to the second order where x(τ) is a general solution for any initial conditions of the equation x″(τ) + g²(τ)x(τ) = 0, primes denoting derivatives with respect to τ, τ given by dτ/dz = n₀/n₁(z).

© 1985 Optical Society of America