Critical power for self-focusing of optical beam in absorbing media

Abstract

Self-focusing effects are of central importance for most nonlinear optical effects. The critical power for self-focusing is commonly investigated theoretically without considering a material's absorption. Although this is practicable for various materials, investigating the critical power for self-focusing in media with non-negligible absorption is also necessary, because this is the situation usually met in practice. In this paper, the simple analytical expressions describing the relationships among incident power, absorption coefficient and focal position are provided by a simple physical model based on the Fermat principle. Expressions for the absorption dependent critical power are also derived; these can play important roles in experimental and applied research on self-focusing-related nonlinear optical phenomena in absorbing media. Numerical results, based on the nonlinear wave equation-and which can predict experimental results perfectly-are also presented, and agree quantitatively with the analytical results proposed in this paper.

Sensing with Femtosecond Laser Filamentation

“…As depicted in Figure 2d, the collimated laser pulse with a transverse Gaussian distribution can be regarded as a series of successive slices in the temporal domain. The pulse slices will lead to an intensity-dependent Kerr nonlinear index ∆n k , and converge to the focal point providing the power is high enough to ensure that the self-focusing "lens" overcomes diffraction, that is, exceeds the critical power P cr [27]. The self-focusing distance is:…”