Self-Phase Modulation

In the non-stationary process of doubling the frequency of high-power laser radiation in metamaterials, the effects of self-and cross-phase modulation, related to the cubic nonlinearity of the medium, are considered. It is assumed that the pump wave propagates in a region with negative refraction. It is shown that in the case of a nonlinear optical process of frequency doubling of an intense light wave in a metamaterial, it is important to take into account the influence of a powerful pump wave. It is shown that the frequency shift of the maximum of the harmonic spectrum in the metamaterial is related to the cubic nonlinearity of the medium. It is shown how the width of the spectrum of the second-harmonic depends on the pump intensity, linear and nonlinear phase detuning. In addition, analytical expressions are obtained for the optimal values of frequency detuning and group velocities on which the maximum of the harmonic spectrum is obtained for non-stationary generation in a metamaterial. Estimations of the quasistatic interaction lengths and the frequency shift of the second-harmonic spectrum are given. By varying the linear phase detuning or the pump intensity, it is possible to manipulate the frequency shift of the maximum of the harmonic spectrum, and from here one can realize a smooth rearrangement of the central frequency of the harmonic spectrum.

An overview of optical solitons was presented in this project. Starting from the nonlinear effects on the refractive index and the wave equation, the Nonlinear Schrodinger Equation (NLSE) was developed. The NLSE is capable of describing both temporal and spatial solitons of both the bright and dark types. The solutions to these NLSE were also given, and their physical properties were explored. The crux of soliton theory is that the 𝛽2 linear dispersive effects (GVD or diffraction) can be balanced by intensity dependent nonlinear effects, creating a field that does not change in shape as it propagates. This places a defining condition between the pulse width and amplitude. Simulation results of soliton propagation through a dispersive fiber were presented, and it was found that the exact initial conditions of a soliton do not have to be matched, since solitons are self-adjusting. The implementation of optical solitons for fiber optic communications were studied, and the relations between bit-rate, transmission distance, and pulse widths in a typical setup were determined. There are several challenges in the implementation, the most important is power loss in the fiber, which causes an exponential broadening of pulse width during propagation. Finally, a brief description of previous experimental results on soliton transmission in fiber optic communications was presented.

This thesis presents an experimental study of hydrodynamical phenomena of a laser propagating nonlinearly. For a medium presenting an intensity-dependent refractive index, and in the frame of the paraxial approximation, the intensity of the laser beam is equivalent to a density of a fluid, the propagation direction is seen as a time evolution of the fluid as well as the phase gradient of the laser beam defines a flow velocity and the nonlinear refractive index change allows defining a sound velocity of the fluid. Under this analogy, we call the propagating laser beam a fluid of light. In this thesis, we provide a study of the superfluidity concept of a fluid of light in a self-defocusing regime of the nonlinearity. It is defined as the absence of diffraction when the fluid of light encounters an obstacle. The parameters which control the superfluid transition are: the flow velocity as well as the sound velocity. They are monitored respectively through the wave vector and the intensity of the laser beam. In the frame of this analogy, we also present in this manuscript a study of vortex shedding regime as a result of the interaction between the fluid of light and the obstacle. Here, the obstacle is considered being strong. When twice the flow velocity at the poles of the obstacle is larger than the sound velocity, pairs of vortex/anti-vortex are emitted demonstrating a hydrodynamical behaviour of the fluid of light. In order to underline the nonlinear refractive index change, we also report in this thesis a study of the photorefractive nonlinearity using the self-phase modulation effect.

In this paper we propose the operation of an all-optical logical gate based in a symmetric nonlinear directional coupler (NLDC) operating with a pulse position modulation (PPM). The performance of a symmetric NLDC realizing two-input AND/OR logical functions, which can be applied in transmission and processing of signals in all-optical form in TDM systems, is examined. This integrated symmetric NLDC logical gate operates with two ultrashort soliton light pulses (2 ps), which are modulated in agreement with the technique of pulse position modulation (PPM). Initially, we evaluate the effect resulting of an increment in the PPM coding parameter offset (ɛ), for the temporal position of the output pulse, considering the anomalous group-velocity dispersion (GVD), nonlinear self phase modulation (SPM) and without loss propagation regime of input pulses, in the cores 1 and 2 of the NLDC. In this situation, we analyze the four possible situations for the two-input logical gate, modulating the 1 and 2 input pulses through temporal displacement and allowing a variation in the coding parameter offset. We can conclude that is possible to get AND/OR logical operations for the cores 1 or 2, without to insert PPM error, since a phase control (Δϕ) exists applied in agreement with the logical level of the input pulse in the core 1. Finally we define the truth table, considering the adequate phase difference and coding parameter offset for the stable operation of the AND/OR logical gate based in the symmetric NLDC.

We investigate the properties of localized waves in systems governed by nonlocal nonlinear Schrodinger type equations. We prove rigorously by bounding the Hamiltonian that nonlocality of the nonlinearity prevents collapse in, e.g., Bose-Einstein condensates and optical Kerr media in all physical dimensions. The nonlocal nonlinear response must be symmetric, but can be of completely arbitrary shape. We use variational techniques to find the soliton solutions and illustrate the stabilizing effect of nonlocality.

The propagation in water of nanosecond focused laser pulses having power densities up to terra watts / cm2 and wavelength of 532+/-2nm, has been investigated extensively by our group. Fast imaging as well as time resolved photography of the nonlinear optical processes, revealed the formation of running spherical foci as well as luminous cavitation bubbles along the direction of the propagating beam. Associated mechanical effect of shock pressure was measured at the exit window as soon as the bubbles collapsed, using piezoelectric silicon gauge. The lifetime of the luminous cavitation bubbles and running spherical foci were found to vary between 160 to 50 ps. Their propagation velocities were estimated to be of the order of 106 m/s. The results are discussed and could be explained partially according to the Moving Focus Model, the self-phase Modulation Model and other associated processes.

By integrating the full Maxwell's equations we predict the existence of gap solitons in a quadratic, Fabry-Perot negative index cavity. An intense, fundamental pump pulse shifts the band structure that forms when magnetic and electric plasma frequencies are different so that a weak, second harmonic pulse initially tuned inside the gap is almost entirely transmitted. The process is due cascading, which occurs far from phase matching conditions, and causes pulse compression. A nonlinear polarization spawns a dark soliton, while a nonlinear magnetization produces a bright soliton.