Abstract
Three-wave mixing in quasi-periodic structures (QPSs) composed of nonlinear anisotropic dielectric layers, stacked in Fibonacci and Thue-Morse sequences, has been explored at illumination by a pair of pump waves with dissimilar frequencies and incidence angles. A new formulation of the nonlinear scattering problem has enabled the QPS analysis as a perturbed periodic structure with defects. The obtained solutions have revealed the effects of stack composition and constituent layer parameters, including losses, on the properties of combinatorial frequency generation (CFG). The CFG features illustrated by the simulation results are discussed. It is demonstrated that quasi-periodic stacks can achieve a higher efficiency of CFG than regular periodic multilayers.
Highlights
The recent theoretical and experimental studies of nonlinear metamaterials (MM) and photonic crystals (PhC) have demonstrated potential of their applications in functional devices operating in diverse frequency ranges, from microwaves to optics
The earlier studies of photonic crystals and periodic stacks of dielectric layers have suggested that the second-harmonic generation (SHG) and third-harmonic generation (THG) efficiency may be higher at the bandgap edges
These results demonstrate that Combinatorial frequency generation (CFG) levels in the lossy quasi-periodic structures (QPSs) are substantially decreased by dissipation of both pump waves and frequency mixing products
Summary
The recent theoretical and experimental studies of nonlinear metamaterials (MM) and photonic crystals (PhC) have demonstrated potential of their applications in functional devices operating in diverse frequency ranges, from microwaves to optics. The main distinctive features of nonlinear artificial media are usually associated with their ability to simultaneously control the dispersion and nonlinear interactions by altering both the geometry of constituent particles and their arrangements in ensembles Both periodic and quasi-periodic nonlinear structures have been studied primarily with the aim of improving harmonic generation efficiency. QPSs with additional degrees of freedom due to the higher order group symmetry are attractive for creating higher density of states that can facilitate harmonic generation [36,37,38] It has been observed in [25] that the efficiency of second-harmonic generation (SHG) in QPS is higher than in random medium, but still remains lower than in regular periodic structures.
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