Resonant excitation and all-optical switching of femtosecond soliton molecules

Abstract

The emergence of confined structures and pattern formation are exceptional manifestations of concurring nonlinear interactions found in a variety of physical, chemical and biological systems 1 . Optical solitons are a hallmark of extreme spatial or temporal confinement enabled by a variety of nonlinearities. Such particle-like structures can assemble in complex stable arrangements, forming "soliton molecules" 2,3 . Recent works revealed oscillatory internal motions of these bound states, akin to molecular vibrations 4-8 . These observations beg the question as to how far the "molecular" analogy reaches, whether further concepts from molecular spectroscopy apply in this scenario, and if such intra-molecular dynamics can be externally driven or manipulated. Here, we probe and control such ultrashort bound-states in an optical oscillator, utilizing real-time spectroscopy and time-dependent external perturbations. We introduce two-dimensional spectroscopy of the linear and nonlinear bound-state response and resolve anharmonicities in the soliton interaction leading to overtone and sub-harmonic generation. Employing a non-perturbative interaction, we demonstrate all-optical switching between distinct states with different binding separation, opening up novel schemes of ultrafast spectroscopy, optical logic operations and all-optical memory.Mirroring the hierarchy of the atomic and molecular composition of matter, fundamental solitons constitute stable entities which can aggregate to form structures of increased complexity. Such condensation manifests in soliton fluids, molecules and crystals, as observed in diverse physical systems 2,9,10 . The underlying forces are responsible for various emergent phenomena, such as self-organization of Bose-Einstein condensates, soliton crystallization in micro-cavities, soliton fission in supercontinua or rogue waves in optical fiber [10][11][12][13][14][15] . It is wellknown that ultrashort solitons can form highly-stable bound-states, and these optical soliton molecules arise from balanced forces during propagation in passive fibers and in dissipative laser resonators [2][3][4][5]8,[16][17][18][19][20][21] . Recent real-time studies have revealed rapid transients, internal vibrations and even chaotic dynamics 6,7,[22][23][24] .In this study, we transfer the concepts of optical spectroscopy to the case of ultrafast soliton molecules by driving them with an external perturbation and monitoring their response in real time. We discover a resonance in the response of soliton molecules to external perturbation and probe the associated anharmonic binding potential (Fig. 1a, approach I). Applying stronger, non-perturbative stimuli, we also demonstrate reliable and reversible all-optical switching between two different bound states (Fig. 1a, approach II)suggesting applications in fast optical sampling and pulse control.

Collective synthesis and dissociation of soliton molecules in parallel optical-soliton reactors

“…Compared with other platforms commonly used in the study of soliton dynamics, such as microresonators 8,9,13,29 , passive bre loops 31,38 , and solid-state mode-locked lasers 11,12 , optoacoustically mode-locked bre lasers 14 offer several advantages, including high exibility and simple con guration with no need of external driving or feedback control. The long bre cavity dissected by the self-organized optomechanical lattice not only accommodate large number of solitons (with possibility of further expansion using longer cavity), but also tolerate the group velocity discrepancies between different solitonic elements, leading to well-isolated and fully-manipulated parallel soliton reactions for the rst time.…”

“…Soliton interactions within selected reactors can be controlled by launching a sequence of precisely timed optical pulses into the laser cavity (Fig. 1a) 12,14,31 , permitting individual solitonic elements to be edited by XPM (see Methods and SI Section VII). To demonstrate this, we rst prepared a soliton supramolecule in which a mixture of long-range double-solitons and phase-locked soliton-pairs exist in the time-slots.…”

“…The studies on soliton interactions continue to date and are currently experiencing a vibrant renaissance, partly due to developments of the timestretched dispersive Fourier transform (DFT) method 6 which facilitates resolving of transient soliton dynamics, as well as due to trending focuses on soliton microresonators [7][8][9] which, as novel platforms, advance rapidly toward chip-scale integration. In parallel, many light-matter analogies have been suggested for multi-soliton complexes bound by soliton interactions [10][11][12][13][14][15][16] , epitomized by the "soliton molecules" 17,18 which refers to closely bound solitons through direct interactions [19][20][21][22] . Reminiscent of chemical molecules synthesized from single atoms, optical soliton molecules behave like a single entity while displaying complex internal dynamics 11,12,23−26 , and have attracted considerable interest both in fundamental nonlinear physics and refreshed application promises such as ultrafast lasers 10,27,28 , spectroscopy 29 ,optical communications 2,30 and all-optical information processing 3,12,14,31 .…”

“…These solitons are actually results of double balances, with gain and loss in addition to nonlinearity and dispersion, known as dissipative solitons 10 . To understand the stochasticity of their complex interactions 24,32,35−37 in the nonlinear dissipative system from a collective level, large numbers of solitons and soliton complexes with controllable interactions are demanded, which, however, has long been challenging in the experiments 12,14,15 . In particular, as analogous with chemical reactions between atoms, the synthesis of soliton-molecules from single solitons, and their dissociation into single solitons 10 has not yet been experimentally demonstrated in a fully controlled manner so far.…”

“…We found that soliton motions during these two processes follow similar random-walk-like trajectories, accompanied with occasional radical repulsions and metastable states. While the statistical analysis on these processes reveals that the reaction rates of optical solitons follow classical theory of chemical kinetics, the rst demonstration of fully-controlled switching between different multi-soliton states in parallel optical-soliton reactors suggests many potential applications in information storage, data processing and logical operations using optical-soliton bits 12,14,30,31 .…”