  We show that a temporal soliton can induce resonant radiation by three-wave
mixing nonlinearities. This constitutes a new class of resonant radiation whose
spectral positions are parametrically tunable. The experimental verification is
done in a periodically poled lithium niobate crystal, where a femtosecond
near-IR soliton is excited and resonant radiation waves are observed exactly at
the calculated soliton phase-matching wavelengths via the sum- and
difference-frequency generation nonlinearities. This extends the supercontinuum
bandwidth well into the mid-IR to span 550-5000 nm and the mid-IR edge is
parametrically tunable over 1000 nm by changing the three-wave mixing
phase-matching condition. The results are important for bright and broadband
supercontinuum generation and for frequency comb generation in quadratic
nonlinear microresonators.
