Soliton strings and interactions in mode-locked lasers

TL;DR

This paper introduces a modified nonlinear Schrödinger equation to model soliton strings in mode-locked lasers, revealing new interaction dynamics and stable states beyond traditional models.

Contribution

It presents a novel equation that extends the master equation, capturing soliton interactions and states in both anomalous and normal dispersion regimes.

Findings

Soliton strings form at specific pulse separations.

Anti-symmetric bi-soliton states are stable and mode-locking converges to them.

Different pulse characteristics are observed in anomalous versus normal regimes.

Abstract

Soliton strings in mode-locked lasers are obtained using a variant of the nonlinear Schrodinger equation, appropriately modified to model power (intensity) and energy saturation. This equation goes beyond the well-known master equation often used to model these systems. It admits mode-locking and soliton strings in both the constant dispersion and dispersion-managed systems in the (net) anomalous and normal regimes; the master equation is contained as a limiting case. Analysis of soliton interactions show that soliton strings can form when pulses are a certain distance apart relative to their width. Anti-symmtetric bi-soltion states are also obtained. Initial states mode-lock to these states under evolution. In the anomalous regime individual soliton pulses are well approximated by the solutions of the unperturbed nonlinear Schrodinger equation, while in the normal regime the pulses are much wider and strongly chirped.