  Electronic frequency mixers are fundamental building blocks of electronic
systems. Harmonic frequency mixing in particular enables broadband
electromagnetic signal analysis across octaves of spectrum using a single local
oscillator. However, conventional harmonic frequency mixers do not operate
beyond hundreds of GHz to a few THz. If extended to the petahertz scale in a
compact and scalable form, harmonic mixers would enable field-resolved optical
signal analysis spanning octaves of spectra in a monolithic device without the
need for frequency conversion using nonlinear crystals. Here we demonstrate
lightwave-electronic harmonic frequency mixing beyond 0.350 PHz using plasmonic
nanoantennas. We demonstrate that the mixing process enables complete,
field-resolved detection of spectral content far outside that of the local
oscillator, greatly extending the range of detectable frequencies compared to
conventional heterodyning techniques. Our work has important implications for
applications where optical signals of interest exhibit coherent
femtosecond-scale dynamics spanning multiple harmonics.
