General model of optical frequency conversion in homogeneous media: Application to second-harmonic generation in an ε-near-zero waveguide
AbstractTraditional optical frequency conversion model is well improved in this work. In terms of the dyadic Green's function method, a set of coupled-amplitude equations is reduced under a proposed transition layer assumption, accompanying the simultaneous integral equations. The model, as a generalization of the current frequency conversion theory, is aimed at any one-dimensional thin film or bulk nonlinear structure, allowing for arbitrary optical anisotropy and absorption without pumping and propagating limitations. The assumption reasonably simplifies the strict nonlinear boundary conditions and enables the equations to yield exact radiative field solutions. A field-enhanced phase-matching configuration is designed for second harmonic generation in a lossy ε-near-zero material. The high contrast of refractive indices between a substrate (silicon) and the material traps the harmonic wave inside and constructs a natural mirror reflection waveguide. A simulation in the lowest guided mode predicts an efficiency enhancement proportional to the relative wave impedance to the fifth power under a resonant condition.