Geometric representation of higher-order optical modes

Abstract

An octant representation of higher-order optical modes that includes Laguerre-Gaussian and Hermite-Gaussian modes is presented. The octant picture captures the high-dimensional nature of three-state optical systems and beyond, with standard Poincaré spheres for orbital angular momentum forming subspaces of the entire state space. This representation enables intuitive manipulation of both classical modes and optical qudits and provides a framework for extending Berry phases and topological invariants to high dimensions.

Figures (3)

• Figure 1: Octant representation of second order HG modes. Intensity modulated phase distributions are provided for a set of states. The inset shows the torus structure above (i).
• Figure 2: Octant representation of second order LG modes. Intensity modulated phase distributions are provided for a set of states. The inset shows the torus structure above (ii).
• Figure 3: Phase profile of second-order LG modes, with and without intensity modulation, for increasing $\theta$ and fixed $\phi$ (in all cases $\chi_1=\chi_2=0$).