We propose and implement a quasi-discrete Hankel transform algorithm based on Dini series expansion （DQDHT） in this paper. By making use of the property that the zero-order Bessel function derivative J0^1（0）=0, th...We propose and implement a quasi-discrete Hankel transform algorithm based on Dini series expansion （DQDHT） in this paper. By making use of the property that the zero-order Bessel function derivative J0^1（0）=0, the DQDHT can be used to calculate the values on the symmetry axis directly. In addition, except for the truncated treatment of the input function, no other approximation is made, thus the DQDHT satisfies the discrete Parsevat theorem for energy conservation, implying that it has a high numerical accuracy. Further, we have performed several numerical tests. The test results show that the DQDHT has a very high numerical accuracy and keeps energy conservation even after thousands of times of repeating the transform either in a spatial domain or in a frequency domain. Finally, as an example, we have applied the DQDHT to the nonlinear propagation of a Gaussian beam through a Kerr medium system with cylindrical symmetry. The calculated results are found to be in excellent agreement with those based on the conventional 2D-FFT algorithm, while the simulation based on the proposed DQDHT takes much less computing time.展开更多
The bandwidth and the duration of incident pulsed beam are proved to play important roles in modifying the nonlinear image of amplitude-type scatterer. It is found that the initially positive chirp-type bandwidth can ...The bandwidth and the duration of incident pulsed beam are proved to play important roles in modifying the nonlinear image of amplitude-type scatterer. It is found that the initially positive chirp-type bandwidth can suppress the nonlinear image, while the negative one can enhance it, and that both effects are inversely proportional to the incident pulse duration. Numerical simulations further demonstrate that the location of nonlinear image is at the conjugate plane of the scatterer and that, for negatively pre-chirped pulsed beam, the nonlinear image peak intensity can be higher than that in the corresponding monochromatic case under certain conditions. Moreover the effect of group velocity dispersion on nonlinear image is found to be similar to that of chirp-type bandwidth.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos 10674045 and 60538010)the National Natural Science Foundation of Hunan Province,China (Grant No 08jj3001)
文摘We propose and implement a quasi-discrete Hankel transform algorithm based on Dini series expansion （DQDHT） in this paper. By making use of the property that the zero-order Bessel function derivative J0^1（0）=0, the DQDHT can be used to calculate the values on the symmetry axis directly. In addition, except for the truncated treatment of the input function, no other approximation is made, thus the DQDHT satisfies the discrete Parsevat theorem for energy conservation, implying that it has a high numerical accuracy. Further, we have performed several numerical tests. The test results show that the DQDHT has a very high numerical accuracy and keeps energy conservation even after thousands of times of repeating the transform either in a spatial domain or in a frequency domain. Finally, as an example, we have applied the DQDHT to the nonlinear propagation of a Gaussian beam through a Kerr medium system with cylindrical symmetry. The calculated results are found to be in excellent agreement with those based on the conventional 2D-FFT algorithm, while the simulation based on the proposed DQDHT takes much less computing time.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 60890202 and 10974049)
文摘The bandwidth and the duration of incident pulsed beam are proved to play important roles in modifying the nonlinear image of amplitude-type scatterer. It is found that the initially positive chirp-type bandwidth can suppress the nonlinear image, while the negative one can enhance it, and that both effects are inversely proportional to the incident pulse duration. Numerical simulations further demonstrate that the location of nonlinear image is at the conjugate plane of the scatterer and that, for negatively pre-chirped pulsed beam, the nonlinear image peak intensity can be higher than that in the corresponding monochromatic case under certain conditions. Moreover the effect of group velocity dispersion on nonlinear image is found to be similar to that of chirp-type bandwidth.
