Multi-orbital photonic lattices

Photonic lattices are such a fertile experimental platform that tests different physical properties emerging from geometry, surfaces, and interactions, with well-defined band spectra. The theoretical research is mainly supported by coupled mode theory in a weak coupling regime, which agrees perfectly with the well-known tight-binding approximation from solid-state physics. This has allowed photonics to demonstrate several old and new predicted phenomena, with the main advantage of directly imaging the wavefunctions in space. However, almost all the progress has been developed under a single-mode approach, which is the simpler and more robust limit in a discrete theory. However, during the past years, the increment on degrees of freedom has emerged as an important route for more complex research, where, for example, a multi-mode photonic regime allows the excitation of several optical modes that can be directly mapped to orbitals in quantum mechanics. In this tutorial, we will describe our recent research on multi-orbital photonics and show the phenomena emerging on different lattice geometries when considering the interaction experienced in between otherwise orthogonal orbital states.