Femtosecond laser inscriptions in Kerr nonlinear transparent media: dynamics in the presence of K-photon absorptions, radiative recombinations and electron diffusions

Abstract

Femtosecond lasers interacting with Kerr nonlinear optical materials, propagate in form of filaments due to the balance of beam diffraction by self-focusing induced by the Kerr nonlinearity. Femtosecond laser filamentation is a universal phenomenon that belongs to a general class of processes proper to ultrashort lasers processing systems, associated with the competition between nonlinearity and dispersion also known to promote optical solitons. The present work considers a model describing femtosecond laser inscriptions in a transparent medium with Kerr nonlinearity. Upon inscription, the laser stores energy in the optical material which induces an electron plasma. The model consists of a cubic complex Ginzburg-Landau equation, in which an additional K-order nonlinear term takes into account K-photon absorption processes. The complex Ginzburg-Landau equation is coupled to a time first-order nonlinear ordinary differential equation, accounting for time evolution of the plasma density. The main objective of the study is to examine effects of the competition between multi-photon absorptions, radiative recombination and electron diffusion processes, on temporal profiles of the laser amplitude as well as of the plasma density. From numerical simulations, it is found that when the photon number (i.e. K) contributing to multiphoton ionization is large enough, taking the electron diffusion processes into account favours periodic structures in temporal profiles both of the laser and the plasma density. The pulse repetition rate in the optical soliton train is increased with increase of the electron diffusion coefficient, while the plasma density is a train of multi-periodic anharmonic wave patterns.

Keywords:

• Femtosecond laser inscription
• Kerr nonlinear materials
• complex Ginzburg-Landau equation
• optical solitons
• electron–hole radiative recombinations
• multiphoton absorptions

Acknowledgments

E. O. Akeweje wishes to thank AIMS-Ghana for the opportunity of visit, and E. Opoku Gyasi for enriching discussions during his stay at AIMS Ghana. The authors thank the reviewer for suggesting some references.

Disclosure statement

No potential conflict of interest was reported by the author(s).