Renormalization group interpretation of the Born and Rytov approximations.
In this paper the method of renormalization group (RG) [Phys. Rev. E54, 376 (1996)] is related to the well-known approximations of Rytov and Born used in wave propagation in deterministic and random media. Certain problems in linear and nonlinear media are examined from the viewpoint of RG and compared with the literature on Born and Rytov approximations. It is found that the Rytov approximation forms a special case of the asymptotic expansion generated by the RG, and as such it gives a superior approximation to the exact solution compared with its Born counterpart. Analogous conclusions are reached for nonlinear equations with an intensity-dependent index of refraction where the RG recovers the exact solution.
Kirkinis
Eleftherios
E
Applied Mathematics, University of Washington, Seattle, WA 98195, USA. kirkinis@amath.washington.edu