9 research outputs found

    Few-cycle optical rogue waves: Complex modified Korteweg-de Vries equation

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    In this paper, we consider the complex modified Korteweg–de Vries (mKdV) equation as a model of few-cycle optical pulses. Using the Lax pair, we construct a generalized Darboux transformation and systematically generate the first-, second-, and third-order rogue wave solutions and analyze the nature of evolution of higher-order rogue waves in detail. Based on detailed numerical and analytical investigations, we classify the higher-order rogue waves with respect to their intrinsic structure, namely, fundamental pattern, triangular pattern, and ring pattern. We also present several new patterns of the rogue wave according to the standard and nonstandard decomposition. The results of this paper explain the generalization of higher-order rogue waves in terms of rational solutions. We apply the contour line method to obtain the analytical formulas of the length and width of the first-order rogue wave of the complex mKdV and the nonlinear Schrödinger equations. In nonlinear optics, the higher-order rogue wave solutions found here will be very useful to generate high-power few-cycle optical pulses which will be applicable in the area of ultrashort pulse technology

    Short-lived large-amplitude pulses in the nonlinear long-wave model described by the modified Korteweg–de Vries equation

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    The appearance and disappearance of short-lived large-amplitude pulses in a nonlinear long wave model is studied in the framework of the modified Korteweg-de Vries equation. The major mechanism of such wave generation is modulational instability leading to the generation and interaction of the breathers. The properties of breathers are studied both within the modified Korteweg -de Vries equation, and also within the nonlinear Schrödinger equation derived by an asymptotic reduction from the modified Korteweg -de Vries for weakly nonlinear wave packets, The associated spectral problems (AKNS or Zakharov-Shabat) of the inverse-scattering transform technique also utilized. Wave formation due to this modulational instability is investigated for localized and for periodic disturbances. Nonlinear-dispersive focusing is identified as a possible mechanism for the formation of anomalously large pulses

    Vector optical rogue waves in mode-locked fibre lasers

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    The project consists of an experimental characterisation of optical vector rogue wave (RW) events by using three different testbed fibre laser setups. The first testbed is a long cavity fibre laser (615 m). Here, we have demonstrated for the first time, a new type of vector resonance multimode instability that inherits some features of modulation and multimode instability. This instability leads to emerging different pulse laser regimes from longitudinal modes synchronization to different types of optical RW events. Using the same testbed fibre laser, we have also shown experimentally for the first time fibre twist-based chiral symmetry breaking. This leads to versatile laser dynamics tuneable from a periodic pulse similar mode-locked regime to chaotic oscillations which are revealed as a mechanism for the emergence of RW events. The observed optical RW events have been classified as fast optical RWs or slow optical RWs depending on the autocorrelation function of the experimental data. The classified optical RWs have been studied by collecting experimental data of a 19x19 grid of polarization positions through tuning both intra-cavity and pump polarization controllers. The second testbed is a passively mode-locked fibre laser. Using this system, the control, appearance and disappearance of the soliton rain flow were demonstrated for the first time using a low range of pump power. Harmonics soliton rain, soliton fission and soliton-soliton interactions leading to the emergence of optical RWs have also been demonstrated in this experiment at a different pump power and intra-cavity birefringence. High harmonic (902 MHz) mode-locked fibre laser based on acoustic-optic effect has been realized in the same laser experiment. In the third laser testbed experiment with, a stretched mode-locked fibre laser, vector bright-dark optical RWs were observed experimentally for the first time. These bright-dark RWs have formed in the laser cavity due to modulation instability at close pump power threshold or due to the polarization instability (incoherent coupling) at higher pump power
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