Efficient Tensor Approach For Simulating Paraxial Propagation Of Arbitrary Coherent Beams

Complicated partially coherent beams(PCBs)are useful in many applications,such as free-space optical communications,particle trapping and optical imaging,while usually it is hard to derive analytical propagation formulae for such beams,and one has to fall back on numerical methods.The conventional numerical methods have some intrinsic drawbacks.In this paper,we introduce an efficient tensor approach(ETA)for simulating paraxial propagation of arbitrary PCBs.The ETA is a direct reconstruction of the propagated PCB without aliasing and rippling problems,and the algorithm is simple and robust with a tensor/matrix multiplication as the main calculation.The validity of ETA is verified through comparing simulation results with analytical results,numerical itegration results and experimental results,respectively.The ETA provides a fast and reliable way for simulating paraxial propagation of arbitrary PCBs.The main results are as follows:(1)The theoretical model expression of the effective tensor method is deduced.Firstly,based on the theoretical analysis of the existing coherent optical numerical simulation method,a numerical simulation method is proposed,which can deal with the problem of partially coherent optical transmission called effective tensor method(ETA),and its theoretical model is deduced.Using Gaussian-model beam(GSM)in the free space transmission problem as the object,compare the analytic method,the angle spectrum method and ETA method processing the propagation of the GSM beam.Many of the traditional numerical simulation methods are based on Fourier transform(FFT),and in the case of the angle spectrum method,there are aliasing and rippling phenomenon in the analysis results,but ETA can avoid the occurrence of these phenomena.In contrast analysis,it can be seen that the speed of ETA simulation analysis is much better than analytic method and angular spectrum method.Accuracy and operation speed are the main advantages of ETA,and also the main research results of this paper.(2)By using the ETA method to simulate the propagation of different model of PCBs,and the universality of the ETA method for the simulation of different modelof PCBs is verified.Although there are a lot of coherent optical simulation methods,there are some pertinence.For a certain form of partially coherent beam,there is often only one simulation method which can be used to simulate the partial coherent beam in other forms.Through the simulation analysis of the partial coherent light,we can see the universality of the effective tensor method in the processing of partially coherent optical transmission problems.(3)The simulation results of the ETA are verified experimentally.Through the design experiment,we obtain the intensity distribution after the vortex Gauss-Schell model beam(GSMV)transmission,on the other hand,using ETA method to simulate the transmission process of the GSMV beam,the comparison between the experimental results and the simulation results fits very well,and the accuracy of the finite tensor method is further verified.(4)ETA is applied to computer-related imaging.Correlated imaging,also known as coincidence imaging and Ghost Imaging,is one of the hotspots in the field of quantum optics in recent years.The usual correlated imaging is to use the spatial correlation of incoherent light to realize the imaging method.However,the realization of pseudothermal light correlation imaging shows the possibility of partially coherent light as a light source,and the existence of partially coherent lights in nature is general.The main idea of computer correlated imaging is to draw the reference light routing computer algorithm in correlation imaging,then ETA as an accurate and fast simulation algorithm of PCB beams,which can be used in computer correlation imaging.