矢量衍射理论的比较研究及标量近似的有效性

光束束腰与波长相比拟时,标量近似已不再成立.以高斯光束的微小圆孔衍射为例,对矢量衍射场的级数解、非傍轴近似解以及精确解进行了详细的数值计算和比较研究.结果表明,对受硬边光阑限制的非傍轴光束,级数展开法适用于处理光束在近场区域的传播,而非傍轴近似解则适用于处理非近场区域光束的传播,具有一定的互补性.讨论了高斯光束圆孔衍射标量近似的有效性,当高斯光束的束腰半径、衍射孔孔径大于几个光波波长时,标量衍射理论是精确、有效的.

A comparative study of vectorial diffraction theories and the validity of scalar approximation

It is well known that the scalar approximation is no longer valid for the beams with small spot size comparable with the wavelength.Detailed numerical calculations for the series expansion solution,non-paraxial approximation solution and exact solution of vectorial Gaussian beams diffracted at a small circular aperture are performed and compared;It is shown that the series expansion solution is valid in the near-field region,and the non-paraxial approximation solution is valid in the non-near-field region for the propagation of a non- paraxial beam diffracted by a small hard-edge aperture,and they are compensated mutually. The validity of the scalar approximation of Gaussian beams diffracted at a circular aperture is discussed;the scalar diffraction theory is rigorous and valid when the waist width of a Gaussian beam and the aperture size is larger than several wavelengths.