Influence Of Elliptical Gauss Beam On The Characteristics Of Non-diffracting Optical Transmission

The graduation thesis studies the effect of elliptical Gaussian beams on the transmission characteristics of non-diffraction beams.In this paper,the elliptical Gaussian beam is mainly obtained by using a cylindrical lens or a film with an elliptical hole.We have done some studies on the transmission characteristics of non-diffraction beams with the axicon,the important optical elements in non-diffraction beams studies.Firstly,under the coherent light condition,the influence of the cylindrical lens on the high-order Bessel beam is studied based on the Fresnel diffraction theory,and a new system to improve the transmission quality of the Mathieu beam is designed.Secondly,it was confirmed that partially coherent light can also produce high-quality Mathieu beams based on the diffraction theory in the Fourier transform.The main contents of the paper include the following three parts:1.The light field distribution characteristics of high-order Bessel beams passing through a cylindrical lens were studied.Based on the generalized Huygens-Fresnel diffraction integral theory,the expression of the distribution of the diffracted light field after the high-order Bessel beam is derived.And we simulate the distribution at different distances with MATLAB and MATHCAD.In experiment,the different order Bessel beams were generated by axicon and spiral phase plates.And passing the higher-order Bessel beams through the cylindrical lens,the diffraction light fields at different distances were recorded by CCD.The research results show that the high-order Bessel beam forms a lip-shaped caustic beam through a cylindrical lens.There are many applications about caustic beam such as large depth of field imaging.Meanwhile,it also has some reference value for the transmission of high-order Bessel beams in asymmetric optical systems.2.A new optical system was designed and numerically simulated to increase the diffraction-free distance of the Mathieu beams.According to the traditional method,Mathieu beams were produced with axicon focusing the elliptical Gaussian beams.Due to the divergent properties of the concave lens,it is placed in front of the axicon to increases the diffraction-free distance of the Mathieu beam.We can draw conclusions by comparing the new system with traditional methods.Mathieu beam with high diffraction-free distance and high quality can be obtained by using the concave lens system.Compared to other methods for improving the Mathieu beam,the new system is simple and efficient.There is good prospect in practical life applications.3.The Mathieu beam produced by partially coherent light is studied theoretically and experimentally,based on Fresnel diffraction theory and Fourier transform.With the LED as the light,partially coherent elliptical Gaussian beam is obtained by an elliptical aperture.So we can get the Mathieu beam through the axicon.The intensity expression of the Mathieu beam is derived with sampling theory and dispersion formula.The section intensity distribution of the Mathieu beam at different propagation distances is simulated.And the experiment is designed to verify the simulation results.We would choose multi-wavelength blue LED as the light source in the the experiment.The Mathieu beam would be obtained using an axicon and a film with an elliptical aperture.Both simulated and experimental results show that partially coherent light can produce Mathieu beams.The results provide a theory evidence for extending the application range of Mathieu beam.