Nonlinear Propagations Of Weak-Light And Their Applications

Nonlinear propagation of weak-light is a very important research area in modern optics. Conventional nonlinear propagations of weak-light mainly refer to the nonlinear interactions of weak-light with matter, which cause the nonlinear propagation of the beams via nonlinearity-induced phase modulation, i.e. nonlinear effects of weak-light. However, recently, scientists find that weak-light can propagate in free space by a nonlinear way through the interference by itself, which is realized by the special phase modulation in the generation of light. The beams corresponding to this non-traditional nonlinear propagation are called "self-accelerating beams". The emergence of self-accelerating beams greatly enriches the concept of nonlinear propagations of weak-light. Investigations on nonlinear propagations of weak-light, including nonlinear effects of weak-light and self-accelerating beams, make people look at the physics world of the interactions of light with matter from a different view. Nonlinear propagations of weak-light bring about many applications on optical localization, optical control, optical-signal transmission and photonics devices, which will show important practical significance for information, biotechnology, energy and national security and so on.In this dissertation, we study some fundamental phenomena arising from nonlinear propagations of weak-light. The thesis is structured as follows:In chapter one, we give a summary on the progress of nonlinear propagations of weak-light, including nonlinear effects of weak-light and self-accelerating beams, which make us have a new understanding on nonlinear propagations of weak-light and find the significance of our work on nonlinear propagations of weak-light and their application. Indeed, nonlinear propagations of weak light have opened the door of many important applications and have made remarkable achievements in theories and experiments. They have entered the stage of rapid development.In chapter two, firstly, we review several theoretical approaches of incoherent nonlinear optics, such as the mutual coherence function approach, the coherent density method, the self-consistent multimode theory, the Wigner’s transform approach, the ray-optics approach, and the thermokinetic approach. We compare the advantages and disadvantages of these approaches, and discuss recent advances in this area. Next, we introduce in detail the features and relative experiments of modulation instability of incoherent light. Especially, we focus on modulation instability of incoherent light with different phase relationships, in addition to discussion of prior work on Bump-on-Tail instability like photonic plasma and modulation instability of a coherent and incoherent mixture. At last, we investigate the application of modulation instability of incoherent light on optical-signal extraction, namely nonlinear imaging of incoherent light via dynamical stochastic resonance. In this study, we find the ratios between the coherent signal and incoherent background noise affect the imaging via dynamical stochastic resonance. Our results provide a new method to optimize the imaging via dynamical stochastic resonance.In chapter three, we study the propagations of spatially incoherent Airy beams in free space and nonlinear media. We successfully measure the coherence length of spatially incoherent Airy beams and find that the propagation features of the beams are governed by the spatial coherence:in free space, our results suggest that spatial coherence affects the exponential truncation factor and self-healing property of Airy beams but has little effect on their self-acceleration trajectories; In the nonlinear media, we find that incoherent Airy beam initially driven by a self-defocusing nonlinearity experiences anomalous diffraction and can maintain its shape in subsequent propagation, but its intensity pattern and acceleration cannot persist when driven by a self-focusing nonlinearity. Note that spatial incoherence can reduce the nonlinear effect and Airy beams could keep their shape better.In chapter four, firstly, we study the generation and propagation of three-Airy beam. Such beams represent a two-dimensional field that is a product (rather than superposition) of three Airy beams. Our results show that, in contrast to conventional Airy beams, this new family of Airy beams can be realized even without the use of truncation by finite apertures. In addition, it is found that a three-Airy beam linearly diffracts into a super-Gaussian-like beam or a Laguerre-Gaussian-like beam, while in the nonlinear medium it either breaks up with a self-defocusing nonlinearity or evolves into a self-trapped channel with a self-focusing nonlinearity. Secondly, we investigate the acceleration feature and propagation dynamics of2D Airy beams with arbitrary initial angles between their two wings using geometrical-optics method and optical catastrophe theory. Our results show that, as a result of "Hyperbolic umbilic" catastrophe, these deformed beams cannot keep non-diffracting and their propagation cannot be simply described by the vector superposition principle, yet the beam acceleration still follows along the parabolic trajectories in spite of the deviation and deformation in their intensity profiles. It is found that there are two parabolic trajectories describing the beam propagation:one describes the acceleration of the main lobe, while the other describes the acceleration of the peak intensity.In chapter five, we discuss the applications of Airy beams. After a brief introduction of prior related demonstrations (such as particle micromanipulation, curved plasma channels, accelerating Plasmon, spatio-temporal bullets, laser micromachining, self-bending electron beams, and super-resolution imaging), we investigate the application of Airy beams on image signal transmission. Our results show that we can encode image information onto the Airy beams which preserves during propagation even in turbulent or disordered media.Finally, we summarize the contents of this dissertation. We emphasize the significance of our research on nonlinear propagations of weak-light and their applications, and discuss future directions in these areas.Above all, we have studied the nonlinear propagations of weak-light and their application. We obtain a series of research results, which will be the foundation for further research on this area for us.