ABSTRACT
In this case, equation (7.151) for (; can be simplified. Let us introduce the spherical coordinates K, v and f{J of the vector K. Here, v is the angle between the vectors K and R - Ro, and !fJ is the angle characterizing the direction of projection of the vector R on the plane perpendicular to the vector R - Ro. Taking into account the fact that D(K) depends only on the modulus of the vector K and calculating the integrals over v and !fJ in equation (7.151), one obtains
- 1 foo dK KeiK /R-Ro/ G(IR - RoD = i4:rr21R _ Rol -00 k2 - K2 - D(/Ki) . (7.153)
residues of the integrand at its poles located in the upper half-plane. These poles are determined by the dispersion equation
(7.154) Assume that IDI « k2• Note that this assumption is valid in the Bourret
approximation [238]. Then, Kn ~ ±k, so that D(IKnD in equation (7.154) can be replaced by D(k). In this case, the solution of equation (7.154) for Kn is given by Kn = ±kNeff, where
Neff = 1 - D(k)/2e . (7.155) It will be shown below that 1m D(k) < O. Therefore, there is only one pole in the upper half-space, located at the point Kn = kNeff. Calculating the residue at this pole, one obtains the final formula for the mean Green's function,
G(IR _ RoD = _ exp(ikNefflR - RoD . 4rriR - Rol (7.156)
In this formula, Neff can be treated as the effective refractive index of a moving random medium. The introduction of the effective refractive index allows one to express G(IR - RoD in the same form as the Green's function Go(R - Ro) in a motionless homogeneous medium, the refractive index of which is equal to Neff.
