Nonlinear Manipulation And Modal Analysis Of Laguerre-gaussian Beams

The vortex beam possesses orbital angular momentum due to its special spiral wavefront phase distribution.In recent years,with the gradual clarification of researchers' understanding of vortex beams and the maturation of the theoretical system of nonlinear optics,the research on the nonlinear transition of vortex beams has been further developed.Laguerre-Gaussian beam is one of the most typical vortex beams,which not only carry topological charge and radial quantum number,but also meet the spatial orthogonality among different topological states.Therefore,it is widely used in various researches.In this thesis,the nonlinear transformation of Laguerre-Gaussian beam and the modal analysis of multimode Laguerre-Gaussian beam are studied based on the popular artificial intelligence technology.The innovations and main contents of the thesis are as follows:(1)The second harmonic of Laguerre-Gaussian beam generated by traditional quasi-phase matching method includes Laguerre-Gaussian beam with different radial quantum number.In order to generate a second harmonic carrying a target radial quantum number,we propose a nearly quasi-phase matching structure.By introducing two degrees of freedom,phase oscillation period and crystal length,the LaguerreGaussian second harmonic with target radial quantum number can be generated in the nonlinear process,and the nonlinear optical conversion efficiency can also be improved.As the two degrees of freedom of the structure,the oscillation period and the crystal length can be used to increase the proportion of the target mode and ensure a high nonlinear optical conversion efficiency.Through our analysis,calculation and discussion,we predict the appropriate value range of the two parameters.To reduce the intensity of the interference mode,the value of the crystal length should be similar to the value of the oscillation period.To increase the intensity of the target mode,the oscillation period must be long enough.Therefore,when the value of the oscillation period is equivalent to the value of the Rayleigh length,the characteristics of the Gouy phase shift can be well utilized to ensure the high purity and high intensity of the second harmonic.By designing the structure of different parameters,each major mode in the second harmonic can be isolated and generated as the target mode,with the purity up to 95%.These single-mode second harmonics generated by the structure can be modulated separately in the subsequent modulation process and used as input signals in the mode division multiplexing system.(2)A scheme for predicting the coefficients of each mode in a multimode Laguerre-Gaussian beam using deep learning is proposed.The eigenmodes of all Laguerre-Gaussian beams are composed of a standard orthogonal basis,so the field distribution of any Laguerre-Gaussian beam can be superposed by its eigenmodes.The intensity picture of multi-mode Laguerre-Gaussian beam is simulated by MATLAB,and the convolution neural network is trained.The results show that the trained network has a good generalization ability for intensity coefficient and phase information even in normal noisy environment.Moreover,in the highly noisy environment,the network trained with noiseless data still has a low error in predicting the phase of intensity images with noise.In addition,the phase information is predicted with the networks trained separately with strong and noiseless data.The results show that the performance of the network remains almost the same under both conditions.The prediction time for each image is less than 3 milliseconds.This work not only lays a foundation for the simple,fast and economical Laguerre-Gaussian beam mode division multiplexing technology,but also provides a new way to find phase information from intensity images.