Mechanisms of Spatiotemporal Mode-Locking

TL;DR

This paper introduces a theoretical framework called attractor dissection to understand three-dimensional spatiotemporal mode-locking in lasers, revealing new coherent light phases with potential for novel applications.

Contribution

It develops a minimal reduced model approach for 3D mode-locking, identifying and explaining new phases of coherent laser light not seen in 1D.

Findings

Identification of distinct 3D STML phases

Experimental validation with over 10^7 cavity modes

Insight into intracavity effects responsible for stability

Abstract

Mode-locking is a process in which different modes of an optical resonator establish, through nonlinear interactions, stable synchronization. This self-organization underlies light sources that enable many modern scientific applications, such as ultrafast and high-field optics and frequency combs. Despite this, mode-locking has almost exclusively referred to self-organization of light in a single dimension - time. Here we present a theoretical approach, attractor dissection, for understanding three-dimensional (3D) spatiotemporal mode-locking (STML). The key idea is to find, for each distinct type of 3D pulse, a specific, minimal reduced model, and thus to identify the important intracavity effects responsible for its formation and stability. An intuition for the results follows from the 'minimum loss principle,' the idea that a laser strives to find the configuration of intracavity light that minimizes loss (maximizes gain extraction). Through this approach, we identify and explain several distinct forms of STML. These novel phases of coherent laser light have no analogues in 1D and are supported by experimental measurements of the three-dimensional field, revealing STML states comprising more than $10^7$ cavity modes. Our results should facilitate the discovery and understanding of new higher-dimensional forms of coherent light which, in turn, may enable new applications.