1. SOLITONS in space

2. BEAM PROPAGATION MAXWELL Townes Soliton: solution of an eigenvalue equation (dimensionless form): 2D NONLINEAR SCHROEDINGER EQUATION Normalization: and

3. Scaling parameters: Such that critical power SOLUTION: TOWNES SOLITON (Gaeta) Radius: o Peak Field: o o o 2 2 TOWNES SOLITON AS A “BEAM CLEANER”

4. Simulations with Elliptical Input Beam 4X 3.5 P cr x y z = 0 z = 0.8 z = 1.8 Alexander L. Gaeta Cornell University

5. K. D. Moll, G. Fibich, and A. L. Gaeta, Phys. Rev. Lett. 90, 203902 (2003). Experiments performed in glass aberrated input output input power position intensity

7. Some properties of filaments “Conical Emission” Intensity clamp: always the same energy in a filament “Ideal filter”: a distorted beam produces a nice round filament Pattern of filaments – not always random – often in a circle. Very broad spectrum ? ? ? ? ? ?

8. The filaments appear in circle for P > 10 P cr and “super Gaussian” beams Too complicated! SIMPLIFY! Approximation: neglect diffraction Solution: Gaussian Super-Gaussian

9. SIMULATION OF GAETA Data of Olivier Chalus