Focusing Properties Of Laser Beams In Dual-Focus System With Zone Plate And Thin Lens

In this thesis, the focusing properties of plane waves, Gaussian beams and Laguerre-Gaussian beams passing through a dual-focus optical system consisted of a Fresnel zone plate and thin lens have been investigated. The axial intensity distribution and focal switch of beams have been discussed based on the theoretical of the general Huygens-Fresnel diffraction integral formula. And then the effect of optical system parameters and beam parameters on the focusing properties has been obtained. The main studies are in the following:Firstly, the equation for the axial intensity distribution of plan waves passing through a dual-focus system is derived based on the general Huygens-Fresnel diffraction integral formula. The numerical results show that:a) as the number of the half-period zones is increased, the axial intensity increases, and the extreme points of weak light intensity between two major intensity peaks also increase; b) when the half-period zones number is even, the focal switch occurs only once as the number of Fresnel zones decrease; c) the half-period zone number is more and the critical Fresnel number is less; d) for the odd half-period zone number, both of focal shift and focal switch do not occur and at the geometrical focus, the intensity of major peak is extremely strong and some very weak side lobe maximums exist around it. The analysis formula for the axial intensity distribution of converging spherical waves passing through a Fresnel zone plate is derived accoding to the general Huygens-Fresnel diffraction integral formula again. The same closed formula with reference [17] is obtained, but some numerical mistakes in reference [17] are corrected.The analysis formulas for the output field and the axial intensity distribution of Gaussian beams passing through a dual-focus system are derived. The influences from Fresnel number, truncation parameter and the half-period zone number on focal switch are given. The focal switch occurs only once with the decreasing of Fresnel number or truncation parameter for the beams. For less Fresnel number of the beams, the critical truncation parameter is more and vice versa. In addition, truncation parameter has an upper limit while Fresnel number has a lower one, and if they exceed respective limits, the focal switch will not take place. As the half-period zone number goes up, all the values of the axial intensity increase and the space between the two major intensity peaks goes up too. Moreover, the value of the axial intensity for the even half-period zone number is smaller than that for the odd one and as the half-period zone number rises; Both critical Fresnel number and critical truncation parameter increase with the increasing of half-period zone number Furthermore, critical Fresnel number for the even half-period zone number is more than that for the odd one, whereas the case of critical truncation parameter is just opposite.The focusing properties of the Laguerre-Gaussian beams passing through a dual-focus system are investigated, the axial intensity distribution formula is derived and the relationships between focal switch and Fresnel number, radial mode number, truncation parameter and Fresnel half-period zone number are studied. It is found that as Fresnel number and truncation parameter of the beams decrease, focal switch also appears only once in this system, which is analogous to the previous results. In addition to the increasing of radial mode number for Laguerre-Gaussian beams, the increasing of the Fresnel half-period zone number or the decreasing of truncation parameter will lead to the rising of axial intensity peak number. Besides, the half-period zone number has a great influence on the axial irradiance distribution. When the half-period zone number is odd, the major peak is at the geometrical focus and its intensity is much stronger than those near it. However, in the case of the even one, the major peak lies nearby the geometrical focus and the intensity difference between the major and secondary peaks is very small. As the half-period zone number increases, both of the critical Fresnel number and the amplitude of focal switch are enhanced and the critical Fresnel number for the even half-period zone number is more than that for the odd one. Furthermore, the critical truncation parameter as a function of Fresnel number decreases monotonously but the change of the critical Fresnel number is not monotonous with the truncation parameter.