标量衍射理论的级数解及其有效性

当光束具有较大的发散角或光束束腰可与波长相比拟时,傍轴近似不再成立;文章在标量衍射理论角谱表示的基础上,以平面波圆孔衍射为例,给出了衍射场的级数解,分析了级数解的有效性;级数解的适用范围与光束的束腰宽度、传输距离以及所使用的级数解的阶次有关;对受硬边光阑限制的光束,由于高频分量的贡献,当传输距离z较大时,高阶级数解的修正效果不好,甚至失效,级数解的有效范围将受到很大限制。

Series expansion solution of the scalar diffraction theory and its validity

As the paraxial approximation is no longer valid for the beams with large divergence angles or small spot size comparable with the wavelength,a rigorous non-paraxial treatment becomes necessary.In this paper,on the basis of the scalar diffraction theory of the angular spectrum representation and by taking the circular aperture diffraction as an example,power-series expansion corrections to the paraxial approximation are derived.It is shown that the applicable range of the series expansion approach depends on the waist width and propagation distance of the beam and the order of the series expansion.For the aperture diffractions,the high-order series expansion corrections are not very useful if the propagation distance z is relatively long,because contributions due to the high-frequency components cannot be neglected.Therefore its applicable range is quite limited.