Study On Fresnel Zone Plate Based On The Wave Vector Integral And Its Focusing Performances

Fresnel zone plate(FZP) is a kind of binary diffractive element which is frequently-used. FZP has been widely used in many research field of science and technology, because it has characteristics of a simple structure, easy preparation and wide wavelength range. Especially in the extreme ultraviolet and X-ray wavelengths, focusing and imaging technology based on the FZP has shown great advantages and potential. Circular symmetry Airy accelerate beam is a kind of new focused beam which is different from traditional converging spherical waves; Its suddenly self-focusing properties has showed potential application in many research field, such as laser medicine, optical micro manipulation, optical microscopic imaging. This paper mainly studied theories and methods based on FZP to produce a variety of new focused beam; We presented an approach, based on wave vector integral, for design of a FZP with different focusing manners.We successfully derived, for the first time to our knowledge, the analytic expressions for calculating the corresponding half-wave zones of the expected FZP; And we did quantitative analysis of FZP's focusing property with parabolic focusing trajectories, the optimum design parameter was given, etc. Main contents in this paper are as follows:1. We introduce the basic concept, background and progress of Airy beams and abruptly autofocusing beams. We also introduce the background and progress of diffraction optical element and Fresnel zone plate.2. We introduce the method based on the theory of scalar diffraction and fast Fourier transform to simulate two-dimensional diffraction light field. We put forward and studied the fast simulation method of radial symmetry of diffraction light field based on Hankel transformation, and given simulation calculation example and comparative analysis based on the Matlab.3. The design theory and method to calculate holographic diffraction optical element and Fresnel zone plate diffraction optical element was given. We study a design method to improved focus and resolving power of Fresnel zone plate, and a design example was given.4. We presented an approach for design of a Fresnel zone plates(FZPs) with different focusing manners. By re-performing the formula for calculating the half-wave zones of a conventional FZP into wave vector domain, we get a wave vector integral formula, by which the half-wave zones of a generalized FZP could be derived from the wave vector distribution of the expected focusing beams. We analyzed the situations with, respectively, a circular focusing manner and a line focusing manner, and successfully derived, for the first time to our knowledge, the analytic expressions for calculating the corresponding half-wave zones of the expected FZPs.5. According to a wave vector integral formula, we analyzed Fresnel zone plates(FZPs) with a parabolic focusing manner that produce radially symmetric Airy beams, and derived the analytic expressions for calculating the corresponding half-wave zones of the expected FZPs. We find out which factors the focusing property of the expected FZPs was associated to.