No Arabic abstract
The generation of high-intensity optical fields from harmonic-wave photons, interacting via a cross-phase modulation with dark solitons both propagating in a Kerr nonlinear medium, is examined. The focus is on a pump consisting of time-entangled dark-soliton patterns, forming a periodic waveguide along the path of the harmonic-wave probe. It is shown that an increase of the strength of cross-phase modulation respective to the self-phase modulation, favors soliton-mode proliferation in the bound-state spectrum of the trapped harmonic-wave probe. The induced soliton modes, which display the structures of periodic soliton lattices, are not just rich in numbers, they also form a great diversity of population of soliton crystals with a high degree of degeneracy.
Microcomb generation with simultaneous $chi^{(2)}$ and $chi^{(3)}$ nonlinearities brings new possibilities for ultra-broadband and potentially self-referenced integrated comb sources. However, the evolution of the intracavity field involving multiple nonlinear processes shows complex dynamics that is still poorly understood. Here we report on strong soliton regulation induced by fundamental-second-harmonic (FD-SH) mode coupling. The formation of solitons from chaos is extensively investigated based on coupled Lugiato-Lefever equations. The soliton generation shows more deterministic behaviors in the presence of FD-SH mode interaction, in sharp contrast to the usual cases where the soliton number and relative locations are stochastic. Deterministic single soliton transition, soliton binding and prohibition are observed, depending on the phase matching condition and coupling coefficient between the fundamental and second-harmonic waves. Our finding provides important new insights into the soliton dynamics in microcavities with simultaneous $chi^{(2)}$ and $chi^{(3)}$ nonlinearities, and can be immediate guidance for broadband soliton comb generation with such platforms.
We show that excitability is generic in systems displaying dissipative solitons when spatial inhomogeneities and drift are present. Thus, dissipative solitons in systems which do not have oscillatory states, such as the prototypical Swift-Hohenberg equation, display oscillations and Type I and II excitability when adding inhomogeneities and drift to the system. This rich dynamical behavior arises from the interplay between the pinning to the inhomogeneity and the pulling of the drift. The scenario presented here provides a general theoretical understanding of oscillatory regimes of dissipative solitons reported in semiconductor microresonators. Our results open also the possibility to observe this phenomenon in a wide variety of physical systems.
The scattering of a linear wave on an optical event horizon, induced by a cross polarized soliton, is experimentally and numerically investigated in integrated structures. The experiments are performed in a dispersion-engineered birefringent silicon nanophotonic waveguide. In stark contrast with co-polarized waves, the large difference between the group velocity of the two cross-polarized waves enables a frequency conversion almost independent on the soliton wavelength. It is shown that the generated idler is only shifted by 10 nm around 1550 nm over a pump tuning range of 350 nm. Simulations using two coupled full vectorial nonlinear Schrodinger equations fully support the experimental results.
We derive the complex Ginzburg-Landau equation for the dynamical self-diffraction of optical waves in a nonlinear cavity. The case of the reflection geometry of wave interaction as well as a medium that possesses the cubic nonlinearity (including a local and a nonlocal nonlinear responses) and the relaxation is considered. A stable localized spatial structure in the form of a dark dissipative soliton is formed in the cavity in the steady state. The envelope of the intensity pattern, as well as of the dynamical grating amplitude, takes the shape of a $tanh$ function. The obtained complex Ginzburg-Landau equation describes the dynamics of this envelope, at the same time the evolution of this spatial structure changes the parameters of the output waves. New effects are predicted in this system due to the transformation of the dissipative soliton which takes place during the interaction of a pulse with a continuous wave, such as: retention of the pulse shape during the transmission of impulses in a long nonlinear cavity; giant amplification of a seed pulse, which takes energy due to redistribution of the pump continuous energy into the signal.
Single solitons are a special limit of more general waveforms commonly referred to as cnoidal waves or Turing rolls. We theoretically and computationally investigate the stability and accessibility of cnoidal waves in microresonators. We show that they are robust and, in contrast to single solitons, can be easily and deterministically accessed in most cases. Their bandwidth can be comparable to single solitons, in which limit they are effectively a periodic train of solitons and correspond to a frequency comb with increased power. We comprehensively explore the three-dimensional parameter space that consists of detuning, pump amplitude, and mode circumference in order to determine where stable solutions exist. To carry out this task, we use a unique set of computational tools based on dynamical system theory that allow us to rapidly and accurately determine the stable region for each cnoidal wave periodicity and to find the instability mechanisms and their time scales. Finally, we focus on the soliton limit, and we show that the stable region for single solitons almost completely overlaps the stable region for both continuous waves and several higher-periodicity cnoidal waves that are effectively multiple soliton trains. This result explains in part why it is difficult to access single solitons deterministically.