Dynamics of interacting cavity solitons

TL;DR

This paper develops a theoretical framework for understanding the interactions of Kerr cavity solitons, explaining how their tail overlap influences their dynamics and stability, with implications for soliton molecule formation.

Contribution

It introduces a new effective interaction model for Kerr solitons based on tail overlap and global variables, validated by numerical simulations.

Findings

Interaction can be purely repulsive or alternating between attraction and repulsion.

Stable soliton molecules correspond to fixed points in the effective dynamical system.

Exponential decay of interaction may hinder molecule formation in experiments.

Abstract

We derive the equations governing the motion of Kerr solitons in pair waveforms. Recent experiments in microresonators have studied a variety of interaction effects in multisoliton waveforms, including collisions and formation of soliton molecules and crystals. Here we analyze the effective interaction that arises from the coupling of soliton-tail overlap nonlinearity with global soliton variables associated with the breaking of translation symmetry. The interaction is either purely repulsive, or alternates between attraction and repulsion, according to whether the decay of soliton tails is monotone or oscillatory. In the latter case, stable fixed points of the effective dynamical system signify stable soliton molecule configuration, but the exponential weakening of the interaction with increasing inter-soliton separation may prevent the molecule from forming in experimentally accessible time scales. Our theory becomes asymptotically exact in the large-separation limit, and we verify the theoretical calculations using soliton trajectories extracted from direct numerical solutions of the wave equation.