Study On Non-diffracting Beam Based On Fourier Transform

The paper mainly studies the generation and propagation characteristics of nondiffracting beams by Fourier transform.Firstly,the diffraction properties of the partially coherent non-diffracting beams through the hard-edged aperture are studied;Secondly,based on the Fourier transform,the Bottle beam is obtained by axcion-lens system;Finally,two kinds of optical systems are designed to generate completely coherent and partially coherent non-diffracting Mathieu beams.The main contents of the paper include the following four aspects:1.Propagation properties of partially coherent Bessel beam passing through an annular aperture were studied.Based on Gaussian-Schell model and method of the cross spectral density,the optical intensity formula of partially coherent Bessel beam passing through an annular aperture is derived theoretically.Simulating its optical intensity formula numerically by MathCAD software and the cross-sectional light spot diagram of different propagation distance were derived.The results show that partially coherent Bessel beam passing through an annular aperture can generate a hollow beam.In experiment,green LED is used as the light source to obtain partially coherent Bessel beam focused by axicon,and an annular aperture is placed in its nondiffracting distance.A stereo microscope camera system are used to shoot the diffraction light spot diagram of partially coherent Bessel beam passing through the annular aperture,and the results agree with the simulation results.The conclusion has a great reference value for the study of propagation properties of partially coherent non-diffracted beam.2.Discrete Fourier method is used to describe the light intensity distribution of the Bottle beam generated by the monochromatic plane wave.The multi-wavelength LED light source is also applicable by using the method of weighted stack.The discrete Fourier method is used to derive the discrete formula of the Bottle beam generating by the LED light source,then appropriate sampling parameters are selected and simulating into MATLAB to simulate the intensity graphs of different positions.Finally,the corresponding experiment is designed and found that the experimental results coincide with the simulated light intensity graphs,which indicates that the LED through the axicon-lens system can produce partial coherent Bottle beam and the veracity of Fourier method analyzing partial coherent Bottle beam.What's more it is more concise and faster than the traditional scalar diffraction theory,and it is a new and reliable method to study Bottle beam.3.Mathieu beam is one kind of non-diffracting beams,which has the characteristic of diffraction-free when propagating.A noval and simple optical element has been designed,beam transforms into diffraction-free Mathieu beam after passing through the diffraction element and focusing by a lens.Furthermore,Mathieu beams with different q values are obtained when changing the parameters of the diffractive element.Discrete Fourier methods are theoretically used to derive the Mathieu beam expressions producing by this optical system,the beam spot intensity diagrams are simulated by using MATLAB.Finally,experiment is designed to verify the result,the non-diffracting Mathieu beam with three different q values are obtained by using different parameters of the diffractive element,and numerical simulation as well as experimental results all indicate that this diffractive element can produce diffraction-free Mathieu beam.4.The blue LED is used as the light source,which generate partially coherent elliptical Gaussian beam through the elliptical aperture,and the partially coherent non-diffracting Mathieu beam is obtained after focusing by the axcion.We use the Fresnel diffraction integral in Fourier transform to derive the expression of the light field after the monochromatic elliptical Gaussian beam passing through the axcion.For the multi-wavelength LED light source,the different wavelengths are superposed to obtain the LED light source generating partially coherent non-diffracting Mathieu beam expression and substitute it into MATLAB to simulate.Finally,we experimentally verify the correctness of this optical system to produce partially coherent non-diffracting Mathieu beam.