Airy Resonances in Photonic Crystal Superpotentials

Airy wave functions are associated with one of the simplest scenarios in wave mechanics: a quantum bouncing ball. In other words, they are the eigenstates of the time-independent Schrödinger equation with a linear potential. In the domain of optics, laser beams that are spatially shaped as Airy functions ("Airy beams") have been shown to exhibit a prominent lobe that follows a curved path, rather than propagating in a straight line, and which has self-healing properties in the presence of obstacles. Here, we observe the presence of Airy resonances in two-dimensional photonic crystals composed of a lattice of holes in a silicon slab. Analogously to electrons in a linear potential, these Airy resonances arise due to a linear spatial variation in the lattice constant of the holes. We map the electromagnetic description of the photonic crystal onto a 2D non-Hermitian Schrödinger equation with a linear potential, which we call a "superpotential." The non-Hermiticity appears in the form of a complex effective mass due to out-of-plane radiation and fundamentally alters the collective optical response of the Airy resonances.