Energy shedding during nonlinear self-focusing of laser pulses

With the development of lasers, self-trapping and self-focusing of intense light due to the intensity-dependent change in the refractive index of certain media was predicted [1]. For a medium with a sufficiently large, negative Kerr coefficient (n2), self-focusing of the incident light takes place when the power exceeds a critical value [2]. For cw and short pulse regimes (∼100fs) the phenomenon is well modelled by the Nonlinear Schrödinger equation (NLS): ∂E/∂Z = i/2 ▽2E - β/2 ∂2E/∂t2 - γf(-E-2)E (1) where E is the slowly varying envelope of the electric field, ß is the group velocity dispersion (GVD) parameter and γ is the nonlinear coefficient. f(-E-2) = -E-2 gives a cubic, and f(-E-2) = -EI2/ (1 + σ-E-2) gives a saturating nonlinearity with σ the saturation parameter. The terms on the right hand side of (1) describe respectively: diffraction, GVD and nonlinear effects. By achieving a balance between these terms, self-focusing of light takes place even beyond the diffraction limit.