四、高阶高斯光束(Higher-order Gaussianmodes)·厄米特-高斯光束(方形孔径的共焦腔或稳定球面腔)·其横向场分布由高斯函数和厄米特多项式(Hermite polynomial)的乘积决定，沿x方向有m条节线，沿y方向有n条节线H0The Hermite-gaussian beam functions alternate betweeneven and odd symmetry alternating index n. The n-th orderfunction has n nulls and n+1 peaks
四、高阶高斯光束 (Higher-order Gaussian modes) • 厄米特-高斯光束 (方形孔径的共焦腔或稳定球面腔) • 其横向场分布由高斯函数和厄米特多项式 (Hermite polynomial)的乘积决定，沿x方向有m 条节线，沿y方向有n条节线 − e H x H y m n r 2 2 2 2 The Hermite-gaussian beam functions alternate between even and odd symmetry alternating index n. The n-th order function has n nulls and n+1 peaks
Agmn =(m+ n +1)arctg·附加相移+0m =(2m+1)0·x方向和y方向的光腰尺寸0, =(2n+1)·在z处的光斑尺寸0(z) =(2m+1)α2(z)の,(z)=(2n+1)*(z)20m(z)222m+100.D= lim在x方向和y方向mZ->80z元0的远场发散角2120,(2)=/2n+1002n+]= lim1Z>80Z元0
• 附加相移 • x方向和y方向的光腰尺寸 • 在z处的光斑尺寸 2 0 2 2 0 2 (2 1) (2 1) = + = + n m n m ( ) (2 1) ( ) ( ) (2 1) ( ) 2 2 2 2 z n z z m z n m = + = + 0 0 0 0 2 1 2 2 1 2 ( ) lim 2 1 2 2 1 2 ( ) lim = = + = + = = + = + → → n n z z m m z z n z n m z m f z mn = (m + n +1)arctg 在x方向和y方向 的远场发散角
·拉盖尔-高斯光束(柱对称稳定腔、圆形孔径共焦腔)·柱对称系统中的高阶高斯光束的横向场分布由下列函数描述，沿半径r方向有n个节线圆沿辐角β方向有m根节线cosm0sin m@The higher-order Laguerre-gaussian modepatterns are characterized by azimuthal andradial symmetry
• 拉盖尔-高斯光束(柱对称稳定腔、圆形孔径共焦 腔) • 柱对称系统中的高阶高斯光束的横向场分布 由下列函数描述，沿半径r方向有n个节线圆， 沿辐角方向有m根节线 − m m e r L r m n sin cos (2 ) 2 2 2 2 The higher-order Laguerre-gaussian mode patterns are characterized by azimuthal and radial symmetry