Research On The Adaptive Algorithm For The Focused Optical Beam Propagating In Nonlinear Media

The most important components of optical imaging and data processing systemsare converging lenses, which have been widely used in diverse fields such asmanufactured optical instrument, radio astronomy, radar systems, and lens antenna. Apossible modern application is the use of relatively large converging lenses andself-focusing effect to concentrate solar energy on relatively small photovoltaic cells.While the rapidly varying quadratic phase factor from converging lens may increasethe sampling rate of the optical field by the sampling theorem, it will lead to the poorefficiency of the existing direct sampling numerical methods. Thus it is necessary todevelop high-efficiency numerical methods for the focused beam. On the basis of thisidea, we modified (CA) the conventional method based on the Fast Fourier TransformAlgorithm (FFT) for linear propagation and Beam Propagation Method (BPM) forself-focusing propagation, and then proposed the adaptive method (AM) and adaptiveBPM (ABPM) which are suitable to linear propagation and self-focusing propagation,respectively.Firstly, we proposed the AM based on the CM and proved its feasibility. Thenumerical results demonstrated that it needed only (f-z)/f(propagation distance z,focal length f, z <f) number of samples that of the CM to obtain the identical results.Specifically, motivated by the idea of the slowly varying envelope approximation(SVEA) and lower sampling requirements for the unfocused beam, we transformed thepropagation of focused beams into the propagation of the unfocused beam so as toobtain the envelope of focused beam indirectly under the unfocused beam’s lowsampling requirements. Then we verified the correctness of MA analytically bypropagating of focused Gaussian beam and numerically by that of focused Gaussianbeam in linear media, respectively. Numerical simulations of strongly Super-Gaussianbeam based on MA were also in good agreement with those of CM.Secondly, based on the linear AM and BPM, we proposed the ABPM which wasadaptive for the self-focusing propagation. It still needed only (f-z)/fnumber ofsamples that of the BPM to obtain the same results as the BPM. As the propagationdistance was closer the focus position, the BPM’s samples were increasing while thenumber of the ABPM maintained a small value. In details, the linear part of ABPMadopted the AM, and the trapezoidal rule and approximate integral were used forcalculating the nonlinear part to improve the computational accuracy. Then the correctness of ABPM were demonstrated numerically by propagating of focusedGaussian beam and Super-Gaussian beam in Kerr media, respectively. Compared tothe linear propagation by only one step calculation, the ABPM requiring multi-stepcalculation economized more computing resources and was more efficient.