Lecture 4

statistical description

stochastic equation is a random function

Parabolic (paraxial) approximation < > < > Small Perturbations; Local Perturbations; Smooth Perturbations; Path Integral Feynman diagrams Fokker-Plank Equation Random Matrix Theory Supersymmetry Parabolic (paraxial) approximation

propagator

< > < > < > < > < >

1 2 3

single scattering (first Born) approximation

random function < > < >

in the far zone

far zone

resonant Bragg scattering

V energy flux density Differential SCS

Total SCS

INVERSE PROBLEM

energy conservation

energy conservation ?

Extinction Length energy conservation !

small perturbation, weak total scattering (Energy of the scattered field) (Energy of the incident field)

smooth perturbations is not necessarily small new small parameter

Parabolic Approximation

Parabolic Equation

forward scattering backscattering

small angle of scattering

Geometrical Optics

eikonal amplitude

Phase fluctuations

Amplitude fluctuations

Multiple scattering! Compare to the result of the first Born approximation (single scattering) Gaussian random function

Transverse Ray Deflection Optical Magnus effect Transverse Ray Deflection POLARIZATION helicity

there is neither no polarization in the equations of rays helicity

Transverse Ray Deflection linear polarization

Limits of validity of GO approximation rays, no diffraction

Multiple scattering

<….……………………………… >

odd even Gaussian