2012/08/31 by Pavel M. Lushnikov, Sergey A. Dyachenko, Natalia Vladimirova · 21 citations
Mathematics · Physics and Astronomy · #Advanced Fiber Laser Technologies #Amplitude #Approx #Geometry #Laser #Laser beams #Laser-Matter Interactions and Applications #Logarithm #Mathematical analysis #Mathematics #Nonlinear Photonic Systems #Nonlinear system #Order (exchange) #Perturbation theory (quantum mechanics) #Physics #Pulse (music) #Quantum mechanics #Scaling #Scaling law #Self-focusing #Statistical physics #math.AP #nlin.PS #physics.optics
paper · pdf · doi:10.1103/physreva.88.013845
published in Physical Review A 88(1) (American Physical Society) · 9 pages, 5 figures; extended text compare with previous version
arxiv created 2013/02/19 · openalex publication_date 2013/07/29 · arxiv updated 2013/07/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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\ensuremath-z)1/2 scaling law with the well-known leading-order modification of loglog type \ensuremath∝(ln|ln(zc\ensuremath-z)|)^\ensuremath-1/2. We show that the validity of the loglog modification requires double-exponentially large amplitudes of the solution \ensuremath∼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 (\ensuremath\lesssim1.2) the critical power of self-focusing, the scaling agrees with numerical simulations beginning with amplitudes around only three times above the initial pulse.