Teixeira Raul Celistrino
Opt Express. 2020 Mar 30;28(7):9541-9551. doi: 10.1364/OE.390126.
We present a new numerical method to calculate the optimum lens transformation to implement on a monochromatic laser beam path, in order to maximize its coupling to the fundamental Gaussian mode of a resonator or to a single-mode optical fiber whose mode can be described as Gaussian to a good approximation. This method relies on a useful mathematical relation on Laguerre-Gauss modes of different waists and reduces in the end to numerically maximizing a polynomial that is a function of the state of the beam in a finite interval, thus being numerically very efficient. We show with a simple example that this method is particularly efficient against other common methods used in the laboratory when it comes to laser beams composed of a coherent superposition of higher-order Laguerre-Gauss modes, as it is the case for instance for beams traversing optical elements suffering from spherical aberration.
我们提出了一种新的数值方法，用于计算在单色激光束路径上实施的最佳透镜变换，以便最大限度地提高其与谐振器的基模高斯模式或单模光纤的耦合，该单模光纤的模式在良好近似下可描述为高斯模式。该方法依赖于不同束腰的拉盖尔 - 高斯模式之间的一个有用数学关系，最终简化为在有限区间内对作为光束状态函数的多项式进行数值最大化，因此在数值上非常高效。我们通过一个简单示例表明，当涉及由高阶拉盖尔 - 高斯模式的相干叠加组成的激光束时，该方法相对于实验室中使用的其他常用方法特别有效，例如对于穿过存在球差的光学元件的光束就是这种情况。
