Beyond leading-order logarithmic scaling in the catastrophic self-focusing of a laser beam in Kerr media
Abstract
We study the catastrophic stationary self-focusing (collapse) of a laser beam in nonlinear Kerr media. The width of self-similar solutions near the collapse distance z=zc obeys the (zc-z)1/2 scaling law with the well-known leading-order modification of loglog type ∝(ln|ln(zc-z)|)-1/2. We show that the validity of the loglog modification requires double-exponentially large amplitudes of the solution ∼1010100, which is unrealistic to achieve in either physical experiments or numerical simulations. We derive an equation for the adiabatically slow parameter which determines the system self-focusing across a large range of solution amplitudes. Based on this equation we develop a perturbation theory for scaling modifications beyond the leading loglog. We show that, for the initial pulse with the optical power moderately above (≲1.2) the critical power of self-focusing, the scaling agrees with numerical simulations beginning with amplitudes around only three times above the initial pulse.
- Publication:
-
Physical Review A
- Pub Date:
- July 2013
- DOI:
- 10.1103/PhysRevA.88.013845
- arXiv:
- arXiv:1208.4425
- Bibcode:
- 2013PhRvA..88a3845L
- Keywords:
-
- 42.65.Jx;
- 52.38.Hb;
- Beam trapping self-focusing and defocusing;
- self-phase modulation;
- Self-focussing channeling and filamentation in plasmas;
- Nonlinear Sciences - Pattern Formation and Solitons;
- Mathematics - Analysis of PDEs;
- Physics - Optics
- E-Print:
- 9 pages, 5 figures