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Register a new userDissipative optical solitons in asymmetric Rosen-Morse potential
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We investigate the existence and stability of dissipative soliton solution in a system described by complex Ginzburg-Landau (CGL) equation with asymmetric complex potential, which is obtained from original parity reflection - time reversal ($mathcal{PT}$) symmetric Rosen-Morse potential. In this study, stability of solution is examined by numerical analysis to show that solitons are stable for some parameter ranges for both self-focusing and self-defocusing nonlinear modes. Dynamical properties such as evolution and transverse energy flow for both modes are also analyzed. Obtained results are useful for experimental designs and applications in related fields.
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An unstable particle in quantum mechanics can be stabilized by frequent measurements, known as the quantum Zeno effect. A soliton with dissipation behaves like an unstable particle. Similar to the quantum Zeno effect, here we show that the soliton can be stabilized by modulating periodically dispersion, nonlinearity, or the external harmonic potential available in BEC. This can be obtained by analyzing a Painleve integrability condition, which results from the rigorous Painleve analysis of the generalized nonautonomous nonlinear Schrodinger equation. The result has a profound implication to the optical soliton transmission and the matter-wave soliton dynamics.
We present the results of asymptotic and numerical analysis of dissipative Kerr solitons in whispering gallery mode microresonators influenced by higher order dispersive terms leading to the appearance of a dispersive wave (Cherenkov radiation). Combining direct perturbation method with the method of moments we find expressions for the frequency, strength, spectral width of the dispersive wave and soliton velocity. Mutual influence of the soliton and dispersive wave was studied. The formation of the dispersive wave leads to a shift of the soliton spectrum maximum from the pump frequency (spectral recoil), while the soliton displaces the dispersive wave spectral peak from the zero dispersion point.
We report the existence of vectorial dark dissipative solitons in optical cavities subject to a coherently injected beam. We assume that the resonator is operating in a normal dispersion regime far from any modulational instability. We show that the vectorial front locking mechanism allows for the stabilisation of dark dissipative structures. These structures differ by their temporal duration and their state of polarization. We characterize them by constructing their heteroclinic snaking bifurcation diagram showing evidence of multistability within a finite range of the control parameter.
Mode-locked fiber lasers provide a versatile playground to study dissipative soliton (DS) dynamics. The corresponding studies not only give insights into soliton dynamics in dissipative systems, but also contribute to femtosecond fiber laser design. Recently, Mamyshev oscillators (MOs), which rely upon a pair of narrow filters with offset passing frequencies, have emerged as a promising candidate for high power, ultrabroad bandwidth pulse generation. To date, only stable mode-locking states in MOs have been reported. Here, we present a comprehensive experimental and numerical investigation of pulsating DSs in an ytterbium MO. By reducing the filter separation down to 4 nm, we observe pulsation in a single pulse state as well as a soliton molecule state. In the single pulse state, the output pulse energy can vary as large as 40 times in our MO. Single-shot spectra measured by the dispersive Fourier transform (DFT) method reveal the spectral bandwidth breathing during pulsation and enables the observation of soliton explosion in a pulsation state. In addition, pulsation with a period lasting 9 round trips and even a chaotic pulsation state are also observed. Numerical simulations based on a lumped model qualitatively agree with our observation. Our results enrich DS dynamics in MOs and show the impact of filter separation on the stability of MOs.
In 1995, C. I. Christov and M. G. Velarde introduced the concept of a dissipative soliton in a long-wave thin-film equation [Physica D 86, 323--347]. In the 25 years since, the subject has blossomed to include many related phenomena. The focus of this short note is to survey the conceptual influence of the concept of a production-dissipation (input-output) energy balance that they identified. Our recent results on nonlinear periodic waves as dissipative solitons (in a model equation for a ferrofluid interface in a parallel-flow rectangular geometry subject to an inhomogeneous magnetic field) have shown that the classical concept also applies to nonlocalized (specifically, spatially periodic) nonlinear coherent structures. Thus, we revisit the so-called KdV-KSV equation studied by C. I. Christov and M. G. Velarde to demonstrate that it also possesses spatially periodic dissipative soliton solutions. These coherent structures arise when the linearly unstable flat film state evolves to sufficiently large amplitude. The linear instability is then arrested when the nonlinearity saturates, leading to permanent traveling waves. Although the two model equations considered in this short note feature the same prototypical linear long-wave instability mechanism, along with similar linear dispersion, their nonlinearities are fundamentally different. These nonlinear terms set the shape and eventual dynamics of the nonlinear periodic waves. Intriguingly, the nonintegrable equations discussed in this note also exhibit multiperiodic nonlinear wave solutions, akin to the polycnoidal waves discussed by J. P. Boyd in the context of the completely integrable KdV equation.
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