Wave modes induced by cross-phase reshaping of a probe photon in the guiding structure of a periodic train of temporal pulses are investigated theoretically with emphasis on exact solutions to the wave equation for the probe. The study has direct connection with recent advances on the issue of light control by light, the focus being on the trapping of a low-power probe by a temporal sequence of periodically matched high-power pulses of a dispersion-managed optical fiber. The problem is formulated in terms of the nonlinear optical fiber equation with averaged dispersion, coupled to a linear equation for the probe including a cross-phase modulation term. Shape-preserving modes which are robust against the dispersion are shown to be induced in the probe, they form a family of mutually orthogonal solitons the characteristic features of which are determined by the competition between the self-phase and cross-phase effects. Considering a specific context of this competition, the theory predicts two degenerate modes representing a train of bright signals and one mode which describes a train of dark signals. When the walk-off between the pump and probe is taken into consideration, these modes have finite-momentum envelopes and none of them is totally transparent vis-à-vis the optical pump soliton.

The performance of optical devices manufactured via laser micromachining on nonlinear transparent materials usually relies on three main factors, which are the characteristic laser parameters (i.e. the laser power, pulse duration and pulse repetition rate), the characteristic properties of host materials (e.g. their chromatic dispersions, optical nonlinearities or self-focusing features) and the relative importance of physical processes such as the avalanche impact ionization, multiphoton ionization and electron–hole radiative recombination processes. These factors act in conjunction to impose the regime of laser operation; in particular, their competition determines the appropriate laser operation regime. In this work a theoretical study is proposed to explore the effects of the competition between multiphoton absorption, plasma ionization and electron–hole radiative recombination processes on the laser dynamics in transparent materials with Kerr nonlinearity. The study rests on a model consisting of a K-order nonlinear complex Ginzburg–Landau equation, coupled to a first-order equation describing time variation of the electron plasma density. An analysis of the stability of continuous waves, following the modulational instability approach, reveals that the combination of multiphoton absorption and electron–hole radiative recombination processes can be detrimental or favorable to continuous-wave operation, depending on the group-velocity dispersion of the host medium. Numerical simulations of the model equations in the fully nonlinear regime reveal the existence of pulse trains, the amplitudes of which are enhanced by the radiative recombination processes. Numerical results for the density of the induced electron plasma feature two distinct regimes of time evolution, depending on the strength of the electron–hole radiative recombination processes.

Thermo-optical effects cause a bifocusing of incoming beams in optical media, due to the birefringence created by a thermal lens that can resolve the incoming beams into two-component signals of different polarizations. We propose a non-perturbative theoretical description of the process of formation of double-pulse solitons in Kerr optical media with a thermally-induced birefringence, based on solving simultaneously the heat equation and the propagation equation for a beam in a one-dimensional medium with uniform heat flux load. By means of a non-isospectral Inverse Scattering Transform assuming an initial solution with a pulse shape, a one-soliton solution to the wave equation is obtained that represents a double-pulse beam which characteristic properties depend strongly on the profile of heat spatial distribution. PACS numbers: 42.65.Tg, 42.70.Gi, 44.10.+i In dielectric media with thermo-optical effects, the modulations of incoming beams can lead to a wavefront distortion [1-3] reflecting their instability. Generally this instability gives rise to a depolarization of a highpower field [4-9] due to a thermally-induced birefringence which is attributed [10-12] to a change in the refractive index of the medium. It has been established [1] that this change in the refractive index originates from heat deposition in the propagation medium, resulting in a space-dependent temperature gradient (so-called thermal lensing) [1,4,13]. For media with linear indices, the thermal lens leads to a drastic change in the irradiance along the beam axis so that the resulting depolarization can strongly degrade the beam quality requiring thermal lensing compensation. However in nonlinear media such as Kerr media, the nonlinearity can be a relevant self-compensaton factor [14] stabilizing multi-wave modes generated by the thermal birefringence. While several materials exhibiting thermo-optical effects are known in the literature [1], a most investigated one is the solid-state laser Nd:YAG [1,4,13,15]. This material is represented as a rod crystal with a cylindrical geometry, where the change in temperature induces thermal distortion of incoming laser beams [9]. For this particular material, several theoretical attempts have been made to formulate the spatial profile of the temperature gradient along the rod exploiting available experimental data. In particular, in refs. [1,13,15] it was found that in the cylindrical rod configuration where the heat is generated at a constant rate [9, 13], a quadratic spatial distribution gives a very good description of the experimentally observed birefringence and the resulting beam bifocusing [9,16]. But thermo-optical processes are actually common to a broad class of materials, not just solid-state lasers. Indeed, photonic crystals and optical fibers (including laser fibers) displaying nonlocal thermal and photothermal properties have been considered in the recent past, from both experimental and theoretical points of view [17,18]. These materials share in common the fact that heat re-sulting f...

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The influence of thermo-optic effects on shape profiles of soliton crystals in optical Kerr microresonators is investigated. The study rests on a model that consists of the Lugiato-Lefever equation, coupled to the one-dimensional heat diffusion equation with a source term proportional to the average power of the optical field. Using appropriate variable changes the model equations are transformed into a set of coupled first-order nonlinear ordinary differential equations. These equations are solved numerically with emphasis on the influence of thermo-optic effects on the amplitude and instantaneous frequency of the optical field, as well as on the temperature profile in the microresonator cavity. It is found that thermo-optic effects do not prevent soliton crytals from forming in optical Kerr microresonators, however a strong thermal detuning will decrease the soliton-crystal amplitude. The model predicts a temperature profile in the microresonator cavity which is insensitive to the specific spatio-temporal profile of the soliton crystal propagating in the microresonator, a feature peculiar to the model.