  We demonstrate the use of a low power near-infrared laser illuminating the
front facet of a quantum cascade laser (QCL) as an optical actuator for the
coherent control of a mid-infrared frequency comb. We show that by appropriate
current control of the QCL comb and intensity modulation of the near-infrared
laser, a tight phase lock of a comb line to a distributed feedback laser is
possible with 2 MHz of locking bandwidth and 200 mrad of residual phase noise.
A characterization of the whole scheme is provided showing the limits of the
electrical actuation which we bypassed using the optical actuation. Both comb
degrees of freedom can be locked by performing electrical injection locking of
the repetition rate in parallel. However, we show that the QCL acts as a fast
near-infrared light detector such that injection locking can also be achieved
through modulation of the near-infrared light. These results on the coherent
control of a quantum cascade laser frequency comb are particularly interesting
for coherent averaging in dual-comb spectroscopy and for mid-infrared frequency
comb applications requiring high spectral purity.
