Two laws of Spatially Coherent Superposition of Eigenmodes

Unlike conventional light sources, lasers possess unique characteristics such as coherence and focused nature. Consequently, numerous applications of laser beams can be enhanced according to their spatial distribution characteristics. This paper presents two patterns of change in the intensity distributions of Hermite Gaussian beams regarding the impact of variables, including relative phase, intensity coefficient, and order of indexes. By conducting simulations in Matlab, we generate various patterns of Hermite Gaussian beams by adjusting parameters such as order indexes, relative phase, and intensity coefficients. The superposition principle is then applied to calculate the spatial intensity distribution of the combined laser beams. Our results indicate that as the order of indexes increases, the complexity of spatial distributions also increases. We analyze the symmetry and rotational properties of the Hermite Gaussian modes, revealing reflection and central symmetries, as well as rotational changes concerning the relative phase. Our discussions focus on exploring the potential for generating complex optical fields and theoretically validating experimental feasibility. We provide a schematic representation of the generation process for complex structured optical fields.