Based on Fresnel diffraction theory and complex Gaussian function expansion of hard-edged aperture, the optical field formula of Bessel beam propagating through an elliptical annular aperture is derived, and the transverse intensity distribution of the beam is numerically simulated. The changes of the optical field and the propagation process of the diffracted beam behind the elliptical annular aperture are studied. In the experiment for the first time, a quasi non-diffracting beam is generated by an axicon and the patterns that are due to the beam diffraction by an elliptical annular aperture at different propagation distances are observed with a charge-coupled device camera. The theoretical analysis and experimental results both show that Bessel beam passing through an elliptical annular aperture can generate a hollow beam.
Self-reconstruction properties of the Mathieu beam are studied theoretically and experimentally. By means of the Mathieu-Hankel wave's theory, the self-reconstruction mechanism of Mathieu beam is analyzed. Based on the Fresnel diffraction theory, an analytical expression for the optical field of a Mathieu beam partially blocked by a circular opaque obstacle is derived, and the self-reconstruction process of Mathieu beam is simulated based on the analytical expression. Using a cylindrical lens and an axicon system to generate Mathieu beam, the self-reconstruction properties of the Mathieu beam partially blocked by a circular opaque obstacle on axis and off axis are verified. Experimental results agree well with the theoretical analysis.
In this paper, we study 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 is described by 4×4 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 is analyzed in detail. The generalized expression of the light intensity distribution can involve three cases, i.e., ordinary lens, bifocal lens and cylindrical lens. The greater the astigmation, the poorer the bottle beam quality will be. The ability to imprison microscopic particles decreases.
A novel method of generating zero order non-diffracting Mathieu beam with an axicon is proposed. To create quasi non-diffracting Mahtieu beam, an axicon is used to focus a plane wave modulated by elliptical Gaussian amplitude. Based on the formula of diffraction integral of a plane wave modulated by elliptical Gaussian amplitude propagating through the axicon, the intensity of quasi non-diffracting beam is simulated numerically. The maximum propagation distance of the quasi-non-diffracting Mathieu beam is calculated according to a geometrical optical model. To verify the results of the theory, an experimental setup is designed.Using a cylindrical lens and a collimating and expanding system, a circular Gaussian beam can be converted in to a plane wave modulated by elliptical Gaussian amplitude. Focusing the plane wave using an axicon, a qausi-non-diffracting Mathieu beam can be generated. The exoerimental results are consistent with theoretical calcuations and numerical simulations.
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