Vallone Giuseppe
Opt Lett. 2017 Mar 15;42(6):1097-1100. doi: 10.1364/OL.42.001097.
Laguerre-Gauss (LG) modes represent an orthonormal basis set of solutions of the paraxial wave equation. LG modes are characterized by two integer parameters n and ℓ that are related to the radial and azimuthal profile of the beam. The physical dimension of the mode is instead determined by the beam waist parameter w: only LG modes with the same w satisfy the orthogonality relation. Here, we derive the scalar product between two LG modes with different beam waists and show how this result can be exploited to derive different expansions of a generic beam in terms of LG modes. In particular, we apply our results to the recently introduced circular beams by deriving a previously unknown expansion. We finally show how the waist parameter must be chosen in order to optimize such expansion.
拉盖尔 - 高斯（LG）模式代表了傍轴波动方程解的一组正交归一基。LG模式由两个整数参数n和ℓ表征，它们与光束的径向和方位角分布有关。模式的物理尺寸反而由束腰参数w决定：只有具有相同w的LG模式满足正交关系。在此，我们推导了具有不同束腰的两个LG模式之间的标量积，并展示了如何利用这个结果来推导一般光束关于LG模式的不同展开式。特别地，我们通过推导一个先前未知的展开式，将我们的结果应用于最近引入的圆形光束。我们最终展示了为了优化这种展开式必须如何选择束腰参数。
