Complete reconstruction of the space-time dynamics in a Kerr-lens mode-locked laser

TL;DR

This paper provides a comprehensive numerical analysis of Kerr-lens mode-locking in lasers, capturing the full space-time dynamics across all relevant time scales to better understand and optimize ultrashort pulse generation.

Contribution

It introduces a novel numerical tool that simulates the complete spatio-temporal evolution of KLM in lasers, incorporating all key nonlinear effects and validating against experimental pulse formation.

Findings

Reproduces pulse evolution from noise to steady state

Shows the interplay of gain, dispersion, and SPM affects pulse characteristics

Enables analysis of nonlinear space-time phenomena in KLM

Abstract

We present a complete numerical analysis and simulation of the full spatio-temporal dynamics of Kerr-lens mode-locking (KLM) in a laser on all time-scales. The KLM dynamics, which is the workhorse mechanism for generating ultrashort pulses, relies on the intricate coupling between the spatial nonlinear evolution due to self focusing and the temporal nonlinear compression due to self-phase modulation (SPM) and dispersion. Our numerical tool emulates the dynamical evolution of the optical field in the cavity on all time scales: the fast time scale of the pulse envelope within a single round trip, and the slow time-scale between one round-trip to the next. We employ a nonlinear ABCD formalism that fully handles all relevant effects in the laser, namely - self focusing and diffraction, dispersion and SPM, space-dependent loss and gain saturation. We confirm the validity of our model by reproducing the pulse-formation in KLM in all aspects: The evolution of the pulse energy, duration, and gain is observed during the entire cavity buildup (from spontaneous noise to steady state), demonstrating the nonlinear mode competition in full, as well as the dependence of the final pulse in steady state on the interplay between gain bandwidth, dispersion and self-phase modulation. The direct observation of the nonlinear space-time evolution of the pulse is a key enabler to analyse and optimize the KLM operation, as well as to explore new nonlinear space-time phenomena.