Study On The Generation,Propagation And Detection Of Canonical Vortex To Non-canonical Vortex Beams

Vortex beams have a helical phase structure.Studies have shown that vortex beams have phase singularities,and photons in the beams carry orbital angular momentum.Such beams have an important role in classical and quantum fields.The potential applications of such beams in information processing,optical micro-manipulation,optical measurement,super-resolution imaging and other fields have attracted continuous attention of scientific researchers.This makes the study of vortex beams an important research area in modern optics.Canonical vortex beams include Laguerre-Gaussian beams,Bessel beams,Gaussian vortex beams,etc.In recent years,some non-canonical vortex beams have also attracted more and more researchers'attention,including fractional vortex beams,Mathieu vortex beam,power-exponent-phase vortex beam,etc.The study of vortex beams extends from canonical vortex to non-canonical vortex,which has important theoretical and practical significance,and can provide a theoretical basis for the manipulation of optical vortex and its application in engineering field.Based on the above research background,this thesis studies the generation,propagation and detection of vortex beams,and the research object extends from canonical vortex to non-canonical vortex.The specific chapters of this thesis are arranged as follows:The first chapter introduces the background of vortex beams and optical propagation theory,combs the research status and development trends of vortex beams,and points out the research purpose and significance of this thesis.Then it introduces the theoretical basis and research methods involved in this thesis,including:generalized diffraction integral formula,Fourier optical propagation method,deep learning and image recognition method,and introduces experimental methods of vortex beam generation.The second chapter proposes a method based on a twisting phase to detect the orbital angular momentum of Gaussian vortex beams.By utilizing the Fourier optical propagation method,the beam propagation characteristics of the Gaussian vortex beam after the twisting phase are numerically simulated.The parameters of the phase are used to study the influence of parameter changes on the detection of orbital angular momentum.Finally,the design experiment verifies the theoretical simulation.The third chapter introduces the mode conversion of Laguerre-Gaussian and Hermite-Gaussian beams,and proposes a new type of mode conversion device.Based on the generalized Fresnel diffraction integral formula,the analytical expressions of the two types of beams after passing through the new mode conversion device are derived.The theory indicates that the two types of beams can be converted to each other after passing through the new mode conversion device,and the theoretical results are verified by experiments.The fourth chapter studies a class of non-canonical vortex beams.Based on the generalized Fresnel integral formula and series expansion method,the propagation formula of a new kind of power-exponent-phase vortex beam is derived,and the analytical solution is obtained.At the same time,the results were compared and verified by Fourier propagation method.After that,experiments were performed to verify the theoretical simulation results.The experimental results are highly consistent with the theoretical simulations.Finally,the orbital angular momentum of the new power-exponent-phase vortex beam is studied and calculated.The fifth chapter introduces the application of deep learning in the field of optics,and proposes a method based on deep learning to detect the topological charge and power exponent parameters of a new type of power exponential vortex beam,which is combined with optical experiments through neural network model building.The model was verified,and the results show that this method is feasible in detecting new vortex beams.The sixth chapter summarizes the main work and innovations of this thesis,and puts forward the outlook for future work.