Topologically Enhanced Harmonic Generation in a Nonlinear Transmission Line Metamaterial*

We demonstrate that harmonic generation in a left-handed NLTL can be greatly increased by the presence of a topological edge state. Our NLTL is a nonlinear analogue of the Su-Schrieffer-Heeger (SSH) lattice. Recent studies of nonlinear SSH circuits have investigated the solitonic and self-focusing behaviors of modes at the fundamental harmonic. We find, however, that frequency-mixing processes in an SSH NLTL have important effects that have previously been neglected. The presence of a topological edge mode at the first harmonic can produce strong higher-harmonic signals that propagate into the lattice, acting as an effectively nonlocal cross-phase nonlinearity. We observe maximum third-harmonic signal intensities that are 5 times that of a comparable left-handed NLTL of a conventional design, and a 250-fold intensity contrast between the topologically nontrivial and trivial lattice configurations. Our work may have applications for compact electronic frequency generators, as well as for advancing the fundamental understanding of the effects of nonlinearities on topological states.