高斯-谢尔模型光束在有色差的分数傅里叶变换系统中的光谱特性

Spectrum Properties of Gaussian-Shell Mode Beam in the Chromatics Aberrated Fractional Fourier Transforms System

基于柯林斯(Collins)积分公式,导出了高斯-谢尔模型(GSM)光束在有色差的分数傅里叶变换(FRFT)系统中的光谱传输表达式,并以Lohmann Ⅱ型系统为例,通过数值计算与分析,研究了色差大小、分数傅里叶变换阶数、以及相对横向坐标对输出面归一化光谱和相对谱移动的影响。研究表明,相对谱移动随FRFT阶数的变化而改变,色差的大小会影响相对谱移动的大小、光谱跃变发生的位置以及光谱跃变量的大小;相对谱移动随色差的变化而改变,在不同阶数的FRFT系统中,相对谱移动随色差的变化规律各不相同。此外,归一化的光谱和相对谱移动还随相对横坐标的变化而改变。

Based on the Collins integral formula,the analytical spectral equations of the propagation of Gaussian-Shell mode（GSM） beam through a chromatics aberrated fractional Fourier transform（FRFT） system are derived.By giving the example of Lohmann II system,the effect of chromatic aberration coefficient,FRFT order and the relative transverse coordinate on the normalized intensity distributions and relative spectral shift on exporting surface are analyzed numerically.It is shown that the relative spectral shift changes with the FRFT order.The value of chromatic aberration can affect the value of the relative spectrum shifting,the critical FRFT order,at which the spectral switch taking place,and the magnitude of the spectral jumping.The relative spectrum shift changes with FRFT,and there are differences of changing rules of that in systems with different FRFT order.In addition the normalized specteum and relative spectral shift change with the chromatic aberration coefficient and relative transverse coordinate as well.