Abstract

Ultrashort optical pulses propagating in a dissipative nonlinear system can interact and bind stably, forming optical soliton molecules. Soliton molecules in ultrafast lasers are under intense research focus and present striking analogies with their matter molecules counterparts. The recent development of real-time spectral measurements allows probing the internal dynamics of an optical soliton molecule, mapping the dynamics of the pulses’ relative separations and phases that constitute the relevant internal degrees of freedom of the molecule. The soliton-pair molecule, which consists of two strongly bound optical solitons, has been the most studied multi-soliton structure. We here demonstrate that two soliton-pair molecules can bind subsequently to form a stable molecular complex and highlight the important differences between the intra-molecular and inter-molecular bonds. The dynamics of the experimentally observed soliton molecular complexes are discussed with the help of fitting models and numerical simulations, showing the universality of these multi-soliton optical patterns.

Highlights

  • Ultrashort optical pulses propagating in a dissipative nonlinear system can interact and bind stably, forming optical soliton molecules

  • By employing an ultrafast fibre laser setup whose output is spectrally analysed on a real-time shot-to-shot basis, we demonstrate that two basic molecules, each made up of a pair of solitons, can bind stably so as to form what we define here as a “2 + 2 soliton molecular complex” (SMC), i.e., an entity in which the bond between the basic molecules may differ by its nature and its dynamics from the bond between the two solitons of each basic molecule

  • We show that the experimental dynamics of a 2 + 2 SMC can be interpreted thanks to a simple analytical description and reproduced with the help of numerical simulations

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Summary

Introduction

Ultrashort optical pulses propagating in a dissipative nonlinear system can interact and bind stably, forming optical soliton molecules. Once formed, stable optical soliton molecules will propagate almost indefinitely around a mode-locked laser cavity[6,7] In other scenarios, they can evolve under mutual collisions, resulting in possible dissociations or in the synthesis of new molecules[16,17], form various “isomers”[18], and even “polymerise” into macromolecules and soliton crystals[19], comprising up to thousands of bound soliton pulses[20]. The onset of vibrating and oscillating soliton molecules typically follows a Hopf-type bifurcation[3] Aware of these fundamental differences, the salient question that naturally arises is to guess how far the analogy between optical soliton bound states and matter molecules can go, considering their structures, as well as their dynamics[27]. The 2 + 2 SMC reveals a new aspect of the universality of optical soliton molecules, because it appears as the optics version of the well-known molecular complexes in condensed-matter physics

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