Diffraction Characteristics Of Non-diffracting Beams In Special Optical Elements

In this thesis, the diffraction characteristics of non-diffracting beams in special optical elements have been investigated. The research content mainly includes the following points:1. Base on Fresnel diffraction theory, complex Gaussian function expansion and stationary phase method of hard-edged aperture, the non-diffracting optical fields’ formula of Gauss plane wave propagating through the axicon were deduced, the transverse intensity distribution of the beam in difference propagation distances was numerical simulated and the experimental verify was also carried out. The intensity distribution in difference propagation distances was captured by a CCD camera. The results of the experiment and simulation all suggest that the plane wave passing through an optical system with an axicon and elliptical aperture system can obtain the qausi-non-diffracting beam which have similar characteristics to Mathieu beam. This result has guiding function in the application of optical nondestructive testing and barcode scanning.2. Base on Fresnel diffraction theory and complex Gaussian function expansion of hard-edged aperture, the optical fields’ formula of Bessel beam propagating through the elliptical annular aperture was deduced, the transverse intensity distribution of the beam was numerical simulated.The change of the optical field and the propagation process of Bessel beam passing through elliptical annular aperture was studied. In the experiment for the first time, the non-diffracting beam through an elliptical annular aperture that generate by axicon. The optical intensity distribution in difference propagation distances was captured by a CCD camera. The theoretical analysis and experimental results both show that Bessel beam passing through elliptical annular aperture can generate hollow beam. The research result will have important application value in micromanipulation and trapping particle.3. Studying the influence of the bifocal lens on the focusing properties of Bessel beam. Based on the generalized Huygens Fresnel diffraction integral, a more general expression of the light intensity distribution of nonsymmetrical optical system which described by 4x4 matrix is deduced. The optical field distribution of Bessel beam passing through bifocal lens is given, and simulated numerically. The influence of the focal length of the bifocal lens on Bessel beam was analyzed in detail. The generalized expression of the light intensity distribution can involve ordinary lens, bifocal lens and cylindrical lens three cases. The greater of astigmatic, the poorer of bottle beam quality. The ability of imprisoned microscopic particles was decreased.4. Based on the Mathieu-Hankel wave’s theory, the focusing characteristics of Mathieu beam propagating through axicon was analyzed.By Fresnel diffraction theory and the method of stationary phase, the optical fields’ formula of Mathieu beam propagating through the axicon was deduced, the transverse intensity distribution in difference propagation distances was numerical simulated. The theoretical analysis and numerical simulation both show that the Mathieu beam passing through axicon can generate periodic Mathieu beam. This result has provided a theoretical basis in application of Mathieu beam.