  We theoretically predict a new working principle for optical amplification,
based on Weyl semimetals: when a Weyl semimetal is suitably irradiated at two
frequencies, electrons close to the Weyl points convert energy between the
frequencies through the mechanism of topological frequency conversion from
[Martin et al, PRX 7 041008 (2017)]. Each electron converts energy at a
quantized rate given by an integer multiple of Planck's constant multiplied by
the product of the two frequencies. In simulations, we show that optimal, but
feasible band structures can support topological frequency conversion in the
"THz gap" at intensities down to $ 2{\rm W}/{\rm mm^2}$; the gain from the
effect can exceed the dissipative loss when the frequencies are larger than the
relaxation time of the system. Topological frequency conversion provides a new
paradigm for optical amplification, and further extends Weyl semimetals'
promise for technological applications.
