  Nonlinear transmission lines (NLTLs) are nonlinear electronic circuits
commonly used for parametric amplification and pulse generation. It has
previously been shown that harmonic generation can be enhanced, and shock waves
suppressed, in so-called "left-handed" NLTLs, a manifestation of the unique
properties of left-handed media. Here, 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.
