高斯光束经环形光栅的衍射特性分析

Diffraction Characteristics of Gaussian Beam Limited by Circular Grating

基于傅里叶-贝塞尔变换计算高斯光束垂直入射环形光栅时的衍射远场分布,分析了其衍射远场光强分布的一般规律,并与平面波入射时的情况进行了比较.计算结果表明:当光栅半径为1.5倍高斯光束束腰半径时,随着光栅环数的增加,中央亮斑半值全宽先减小后增大、中央亮斑所包含的功率占总功率的比值减小、中央主极大光强值减小,三者的变化趋势与平面波入射时的趋势一致;中央亮斑半径、次极大光强值变化趋势与平面波入射时的变化趋势不同.当环数小于5时,高斯光束经过环形光栅的衍射场光强变化无规律;当环数大于10后两种情况下衍射场光强变化都不明显;当环数趋于无穷时中央亮斑半径、中央亮斑半值全宽、次极大光强值趋于圆孔衍射(环数等于1)时的值,中央亮斑所包含的功率占总功率的比值约等于圆孔衍射时的1/2,中央主极大光强值约等于圆孔衍射时的1/4.

Based on Fourier-Bessel transformation,diffraction field distribution of Gaussian beam limited by the circular grating is calculated and analyzed.Compared with plane wave,the results show that,if the circular grating radius is 1.5 times of the incident light spot radius,with number of rings increasing,the variation of FWHM decreasing first and then increasing,power ratio of the central spot decreasing,the intensity of central principal maximum decreasing,which are accordance with these of plane wave.But the variation of central spots radius and secondary maximum intensity are different with these of plane wave.If number of rings is less than 5,diffraction field distribution of Gaussian beam limited by the circular grating change irregular.If number of rings is more than 10,diffraction field distribution change unobvious.If number of rings tends to infinite,the central spots radius,FWHM and secondary maximum intensity tend to these of Gaussian beam diffraction limited by circular aperture,power ratio of the central spot is equal to 1/2 of that Gaussian beam diffraction limited by circular aperture,and central Maximum light intensity is equivalent to 1/4 of that of Gaussian beam diffraction limited by circular aperture.