Phase-Matching Controlled Nonlinear Frequency Conversion Of Orbital Angular Momentum

Orbital angular momentum(OAM)beams have important application prospects in many fields such as optical conmmunication,quantum technology and optical micro-manipulation because of their unique helical wavefront distribution.The generation and control of OAM beams can be achieved by both linear and non-linear means.By means of non-linear frequency conversion,the working band range of this kind of beam can be further expanded.Meanwhile,the OAM of fndamental frequency wave will be transferred to harmonic wave through non-linear interaction.In previous studies,it is generally believed that OAM follows the conservation law in the process of non-linear frequency conversion.Our research shows that the OAM transfer law of the non-linear process is regulated by the phase matching mechanism.In this paper,we study the transfer law of OAM in one-dimensional optical superlattices,including several non-collinear second harmonic generation(SHG)processes and SHG in angular polarized superlattices,both theoretically and experimentally.1.The introduction mainly reviews the research and development of orbital angular momentum beams and nonlinear optics.The basic properties of vortex light and the basic principle of quasi-phase matching technology are introduced.The transfer law of orbital angular momentum of beams carrying OAM in the process of nonlinear frequency conversion is also introduced.2.In Chapter 2,the mathematical form of Laguerre-Gaussian(LG)beams is introduced firstly,and the optical field characteristics of beams with OAM,as well as the methods of linear generation and modulation are described.Then,starting from the coupled wave equation,it is described that the beam carrying OAM must not only follow the conservation of energy and momentum,but also the conservation of orbital angular momentum in the process of nonlinearity.In addition,the measurement method of topological charge of beams carrying OAM is also introduced.3.In Chapter3,the orbital angular momentum transfer of beams carrying OAM in the process of non-collinear frequency doubling is introduced.By solving the Green's function,a theoretical processing method for the non-collinear SHG of beams with OAM is established.In experiments,based on several important phase matching mechanisms(colinear second harmonic generation,non-linear Bragg diffraction,non-linear Raman-Nath diffraction,etc.)in one-dimensional periodically polarized optical superlattices,we have studied the mechanism of phase matching regulating the transfer of OAM.The experimental results are consistent with the theoretical expectations.4.In Chapter 4,the transfer law of orbital angular momentum in our team's nonlinear angular dffraction is preliminarily studied.By analogy with linear angular gratings,we study the OAM spectrum distribution of frequency doubled light in angular modulated nonlinear phase gratings with second-order nonlinear coefficient x2.Preliminary theoretical and experimental studies show that the OAM spectrum of SHG diffaction field is not only related to the orbital angular momentum of incident light,but also to the angular polarization period of x2.