1. Lecture 4

2. statistical description

3. stochastic equation
is a random function

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

5. propagator

8. < > < >
< > < >
< >

11. 1 2 3

12. single scattering (first Born) approximation

13. random function
< >
< >

15. in the far zone

16. far zone

17. resonant Bragg scattering

18. V
energy flux density
Differential SCS

19. Total SCS

21. INVERSE PROBLEM

22. energy conservation

23. energy conservation ?

25. Extinction Length
energy conservation !

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

27. smooth perturbations
is not necessarily small
new small parameter

28. Parabolic Approximation

31. Parabolic Equation

32. forward scattering
backscattering

33. small angle of scattering

34. Geometrical Optics

35. eikonal
amplitude

36. Phase fluctuations

37. Amplitude fluctuations

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

39. Transverse Ray Deflection
Optical Magnus effect
Transverse Ray Deflection
POLARIZATION
helicity

40. there is neither no polarization in the equations of rays
helicity

41. Transverse Ray Deflection
linear polarization

42. Limits of validity of GO approximation
rays, no diffraction

44. Multiple scattering

47. <….……………………………… >

48. odd
even
Gaussian