A Study On Astigmatic And Partially Coherent Spiral Bessel Beam

In this thesis,we mainly research on astigmatic Bessel beam and the construction and optical properties of partially coherent spiral Bessel beam.In the first part,the influence of machining error and astigmatism on the quality of Bessel beam are studied respectively in this paper.We focus on the influence of astigmatism on high order Bessel beam and a method for detecting the topological charge number of vortex beam based on astigmatic principle is proposed.In the second part,the formation and propagation properties of partially coherent spiral Bessel beam are studied and the influence of light field regulation on the beam is also discussed.The main contents of this research are:1.A machining error structure of an axicon is proposed.The transmittance function of the axicon with vertex off axis machining error has been derived theoretically.Based on Huygens-Fresnel diffraction integral theory and stationary phase method,we derive the expression of diffraction field and analyze the influence of the vertex off axis machining error in an axicon on the Bessel beams.The expression of diffraction field behind the axicon is simulated numerically.Results show that if the axicon is ideal manufactured,the field distribution behind the axicon is approximately an ideal Bessel beam.If the machining error existed,the diffraction beam pattern will split in half.2.High order Bessel beam can be generated by using spiral phase plate(SPP)-axicon system.Based on Kirchhoff diffraction integral theory,the expression of diffraction field after the axicon that illuminated by an oblique vortex beam is derived.The influence of astigmatism introduced by oblique illumination on high order Bessel beam is analyzed in detail.Results show that when a small oblique incidence angle occurs,the center bright ring of high order Bessel beam become elliptical.The ellipticity of center bright ring increases with the increasing of oblique incidence angle.Continue to increase the oblique incidence angle,the bright ring will split one by one from inside to outside,and ultimately it will evolve into caustics beam with point array structure.In the evolution process above,a phenomenon of dark core splitting can be found easily.Experiments are designed to verify above researches.Experimental results are in good agreement with theoretical predictions and numerical simulation.3.Based on Kirchhoff diffraction integral theory,the expression of diffraction field after the axicon or convex lens that illuminated by an oblique vortex beam is derived.A simple and feasible method for detecting topological charge number by using an axicon is proposed.We compare this method with the method of using convex lens,results show that there is no need to fix detection point strictly by using an axicon.In practice,this method shows more flexibility and applicability.Experiments are designed to verify above researches.Experimental results are in good agreement with theoretical predictions and numerical simulation.4.The principle of generating the spiral Bessel beam was theoretically analyzed.Based on the cross-spectral density function of Gaussian Shell-Model and the theory of cross-spectral density propagation,the expression of partially coherent spiral Bessel beam was derived.The propagation characteristics of partially coherent spiral Bessel beam and the influence of coherence on its transmission characteristics were studied.The results show that with the increase of transmission distance,the contrast ratio of beam intensity distribution decreases,and the distribution of light field changes from the Bessel type to the Gauss type.However,the beam still maintains the selfacceleration property.For the high-order beam,a phenomenon of dark core fading can be found easily and the fading distance of the dark core increases with the increasing of the beam order.With the decreasing of the coherence length,the distribution of Bessel light field decreases gradually,and the non-diffraction distance of the beam is shortened.Moreover,the influence of light field regulation on the beam is also discussed,which includes the parameter setting of the hologram and the adjustment of the coherence of the light field.