2D Self-Similar Profile for Laser Beam Propagation in Medium with Saturating Multi-Photon Absorption

Abstract

We study a self-similar mode of 2D laser beam propagation in media with multiphoton absorption (MA) taking into account a resonant nonlinearity and nonlinear absorption saturating. An analytical solution of the corresponding equations describing the problems under consideration is derived using an eigenvalue problem method generalization for solitonlike solution finding. The developed solution is used as incident beam profile and phase front for computer simulation of the 2D laser beam propagation. In particular, we demonstrate numerically that the laser beam propagation in a self-similar mode occurs within a certain distance, which depends on medium properties. Under certain relations between the nonlinear absorption and resonant nonlinearity, and cubic nonlinear response, we observe the super long distance of the beam propagation without any beam profile distributions.

Superluminality phenomenon at a femtosecond laser pulse propagation in a medium containing nanorods

“…As mentioned earlier, we derived self-similar solutions for laser pulse propagation in the media with nonlinear MPA. 39,40 Their pulse phase distributions are described by the third term in Eq. (27) with the constant coefficient at this term (hðzÞ ¼ const along the z-coordinate).…”

“…(40). Taking into account that the sign of this coefficient coincides with the sign of the chirp h, which is given by Eq.…”

“…Earlier, we investigated the self-similar mode of laser pulse propagation in homogeneous media with TPA or multiphoton absorption (MPA) and showed that the appropriate initial frequency chirp is crucial for the self-similar mode realization. 39,40 In Ref. 38, we also discussed, in detail, the pulse chirp role and described a nonlinear chirp formation due to the light energy absorption and the positive phase-amplitude grating in the media with nanorods.…”