Research On Optimization Of Numerical Method For Diffraction Beam Propagation In Free Space

Fast and accuate numerical method for the diffraction propagation in the free space is meaningful for the optical system simulation whose performance largely depends on the diffraction. These kinds of systems include the laser resonator and the beam shaping apparatus. The optimized numerical method for diffraction beam propagation in free space is explored in this thesis. The main contents are classified as follows:(1) It is proposed that a method which can be used to the laser resonator with an apherecial tail mirror and gain saturation. This method is based on the fast Fourier transform. The gain saturation is treated as several gain sheets between resonator mirrors and the apherecial mirror is considered as a phase element. Simulation results show that the pan-like mirror resonator would support a ring-mode laser output, which is consistent with the experiment result. In the experiment, a laser beam with M2factor of6.16is got. Meanwhile, the Fourier-based method is compared with the conventional Gaussian integral method.(2) The conventional Fourier-based method only permits the different sampling window size and the sampling interval must be maintained to be the same in the input and output calculation window. The widely used two-step Fresnel method is only valid for the propagation in the Fresnel region. It is proposed that a method which permit the different sampling window size and sampling interval in the input and out sampling window. It is a Fourier-based method and can be used for the propagation out of the Fresnel region because the angular diffraction method is strict for the near and far field calculation.(3) A novel method is proposed for simulating free-space diffraction propagation. This method is an improvement of the angular spectrum method (AS) and the band-limited angular method (BLAS). Due to the sampling problem about the transfer function, AS is not suited for the long-distance propagation. For the proposed method, the calculation window size is chosen to make sure all the sampling points in the frequency domain are effective at the sense of Nyquist theorem. The calculation complexity is independent of the calculation window size, because of the use of the linear convolution. The linear convolution can be evaluated effectively by fast Fourier transform and the calculation complexity is comparable with AS and BLAS. This method can get the simulation result with high accuracy for far and near field propagation.(4) The method, based on the rotation of the angular spectrum in the frequency domain, is generally used for the diffraction between the tilted planes. Due to the rotation of the angular spectrum, the interval of the sampling points in the Fourier domain is not even. In the conventional method a spectrum interpolation is needed to get the approximate sampling value on the equidistant sampling points. However, the calculation error caused by the interpolation on the Fourier spectrum cannot be estimated and controlled, especially for the large angle rotation. Here, the diffraction propagation between the tilted planes is transformed into a problem about Fourier transform on the uneven sampling points, which can be evaluated effectively through nonuniform fast Fourier transform. The most important advantage of this method is that the conventional interpolation is avoided and the calculation accuracy is completely under control. Simulation example shows that this method is a safe and effective method for any rotation angle. Its calculation burden is comparable with that of the conventional method.(5) Based on the equivalent circuit model of RF discharge and the plasma discharge parameters obtained in the experiment, it is analysed that the effect of discharge voltage, discharge current, working pressure, the discharge spacing and discharge frequency on the plasma equivalent circuit model in the practical laser system. Using this equivalent circuit model, the optimized number and the positon of the resonant inductances and excitation ports are got. The calculation results show that the self-excited oscillation frequency of the RF power, the discharge electrode spacing and the number and the position of resonant inductor would greatly impact the voltage distribution on the discharge slab and needed to be precisely controlled in the practical laser. The calculated results also show that the multi-feed port is an effective way to improve the uniformity of the voltage distribution on the discharge slab.