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Real-Time Observation of Dissipative Soliton Formation in Nonlinear Polarization Rotation Mode- Locked fibre Lasers

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Real-Time Observation of Dissipative Soliton Formation in Nonlinear Polarization Rotation Mode- Locked fibre Lasers ARTICLE DOI: 10.1038/s42005-018-0022-7 OPEN Real-time observation of dissipative soliton formation in nonlinear polarization rotation mode- locked fibre lasers Junsong Peng1, Mariia Sorokina2, Srikanth Sugavanam2, Nikita Tarasov2,3, Dmitry V. Churkin3, 1234567890():,; Sergei K. Turitsyn2,3 & Heping Zeng1 Formation of coherent structures and patterns from unstable uniform state or noise is a fundamental physical phenomenon that occurs in various areas of science ranging from biology to astrophysics. Understanding of the underlying mechanisms of such processes can both improve our general interdisciplinary knowledge about complex nonlinear systems and lead to new practical engineering techniques. Modern optics with its high precision mea- surements offers excellent test-beds for studying complex nonlinear dynamics, though capturing transient rapid formation of optical solitons is technically challenging. Here we unveil the build-up of dissipative soliton in mode-locked fibre lasers using dispersive Fourier transform to measure spectral dynamics and employing autocorrelation analysis to investi- gate temporal evolution. Numerical simulations corroborate experimental observations, and indicate an underlying universality in the pulse formation. Statistical analysis identifies cor- relations and dependencies during the build-up phase. Our study may open up possibilities for real-time observation of various nonlinear structures in photonic systems. 1 State Key Laboratory of Precision Spectroscopy, East China Normal University, 200062 Shanghai, China. 2 Aston Institute of Photonic Technologies, Aston University, Aston Triangle, Birmingham B4 7ET, UK. 3 Novosibirsk State University, 1 Pirogova str., Novosibirsk 630090, Russia. Correspondence and requests for materials should be addressed to H.Z. (email: [email protected]) COMMUNICATIONS PHYSICS | (2018) 1:20 | DOI: 10.1038/s42005-018-0022-7 | www.nature.com/commsphys 1 ARTICLE COMMUNICATIONS PHYSICS | DOI: 10.1038/s42005-018-0022-7 olitons, localized wave structures formed by the balance a Ti: sapphire laser34, the origin of which remains an open Sbetween dispersion and nonlinearity, are ubiquitous in question. nature and are used both as building blocks in theoretical In this work, we unveil the build-up of dissipative solitons in concepts and in various practical applications in many fields of mode-locked fibre lasers by means of the TS-DFT technique. We science and engineering, including optics, Bose–Einstein con- observe two different types of dynamics during dissipative soliton densates (BEC), hydrodynamics, plasmas, field theory and many build-up, depending on the length of the laser cavity. In a long – others1 7. In addition to fascinating feature of maintaining its cavity, multiple processes are involved in the build-up phase, shape during propagation, the continuous interest in soliton is including modulation instability (Benjamin–Feir instability), also stimulated by their unique properties upon interaction; that mode locking, self-phase modulation (SPM)-induced instability, is, they behave like particles exerting forces on each other. dissipative soliton splitting and partial annihilation. In a short Interactions between solitons give rise to rich soliton physics, cavity, only modulation instability and mode locking are including phenomena such as soliton fusion8, fission9, full10 and responsible for dissipative soliton formation. A long-standing partial annihilation11, soliton turbulence and many others. issue in the build-up of mode locking refers to the role of noise The problem of the soliton formation mechanisms is of a involved: a randomly strong noise spike was assumed to evolve to fundamental physical interest. The soliton formation processes be a mode-locked pulse37. Here we show that the role of noise is are rather different in integrable and non-integrable nonlinear to stimulate modulation instability in nonlinear polarization models12. In the integrable systems, for instance, the rotation (NPR) mode-locked fibre lasers. We employ advanced Korteweg–de Vries equation, soliton formation process can be statistical analysis to quantify the dependency and correlation periodic (repetitive) when the process is coherently self-seeded between the signals at various stages of dissipative soliton build- and refers to the well-known Fermi–Pasta–Ulam recurrence up. We show that in complex non-stationary systems correlation phenomenon13. Such repetitive process can be readily observed in and dependency may differ from each other. Thus, their simul- experiments. For instance, periodic pulse collision leading to taneous application reveal underlying physical processes that can soliton generation was observed experimentally in a passive fibre be missed when a simplified analysis is used. Our work shows – ring oscillator14. In contrast, typical soliton formation dynamics significant difference to other works34 36. First, modulation in non-integrable systems is non-repetitive and exhibit complex instability is firstly unveiled in the initial phase of dissipative behaviour before a stationary soliton settles down15. In contrast soliton formation in our work, in analogy with soliton formation to the large number of theoretical studies, experimental obser- in BEC4; second, we observe interference patterns on the tran- vations of soliton build-up dynamics are relatively rare. This is sient spectra, evidencing two critical phases: dissipative soliton due to the technical difficulties encountered in practice to record splitting and interactions of double solitons. These two phases such rapid non-repetitive evolution, especially in the realm of were not observed in other works34,35, as the cavities were short. ultrafast optical systems, as most of measurement tools only give Soliton interactions were observed in another work36; however, time-averaged data that washes out these transient dynamics. no soliton survived after such interactions, while our work shows Recently, through real-time imaging technique, the formation that a soliton survives after interactions. The multiple solitons process of matter-wave solitons was captured in BEC4. The role of emerged from noisy field36, while double solitons are generated the modulation instability in the solitons formation was eluci- from splitting of a large soliton in our work. It is worth to note dated. It is of particular interest to know whether the same that full field measurements of the dissipative solitons are realized mechanism accounts for soliton formation in optics. Formation in Ref 36. Finally, to the best of our knowledge, we firstly present a of extreme optical waves through modulation instability in fibre- numerical study on the build-up phase of dissipative soliton in a optic systems have been studied in Refs 16,17. laser, and show how our numerical study qualitatively agrees with The term soliton is often used to refer to localized coherent the experiments. structures in a wide range of nonlinear systems, varying from the integrable (where the term was initially invented) and Hamilto- nian systems to non-integrable and non-conservative ones. Many Results real-world nonlinear systems are non-integrable, meaning the Principle. As a test-bed system, we build a typical dissipative strict mathematic definition of soliton as it was proposed for the soliton fibre laser as shown in Fig. 1a (see Supplementary Note 1 integrable systems is rarely met in practice. Therefore, a term for details). Since fibre lasers are known to exhibit rich nonlinear 'dissipative soliton' is often used to refer to localized coherent dynamics purely by extension of their cavity lengths, the build-up structures in systems with a balance of both conservatives effects dynamics of dissipative solitons in them are also expected to be (e.g. dispersion and nonlinearity) and dissipative ones (gain and different. Hence, the laser cavity length is varied three times – loss)18 20. For example, a pulse generated from mode-locked during the experiment for a systematic study (see Supplementary lasers is a dissipative soliton since a laser is intrinsically a dis- Fig. 1 for details). The detection system is shown in Fig. 1b. As sipative system. Mode-locked lasers provide a flexible platform shown, the output of the laser is split into two ports by an output for studying dissipative soliton dynamics. Recently, by virtue of coupler. One port (undispersed) is used for measuring the evo- the emerging real-time measurement technologies such as the lution of the instantaneous intensity I(t), over many cavity round- time-stretch dispersive Fourier transform (TS-DFT) trip (RT) numbers N, in order to produce a two-dimensional – technique21 23 and ‘time microscope24,25, some important spatio-temporal intensity profile I(t, N). The signal from the other dynamics of mode-locked lasers have been unveiled. These stu- port is fed into a long dispersive fibre segment (~11 km here) to dies can be divided into two categories. One relates to repetitive stretch the pulses and thus yield spectra measurements (TS-DFT). (periodic) processes such as internal motion of soliton mole- Two identical photodetectors (PD1, PD2) with 50-GHz band- cules26,27 and spectral modulation of a single pulse28. The other width are used, and the signals are captured by a real-time refers to non-repetitive events such as rogue wave oscilloscope with bandwidth of 32 GHz (Agilent). It is important – generation29 31, soliton explosions32,33 and the build-up of a to point out that by measuring the temporal delay between the – dissipative
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