  We theoretically study first and second-order optical responses in a
transition metal dichalcogenide monolayer with distinct trivial, nodal, and
time-reversal invariant topological superconducting (TRITOPS) phases. We show
that the second-order DC response, also known as the photogalvanic response,
contains signatures for differentiating these phases while the first-order
optical response does not. We find that the high-frequency photogalvanic
response is insensitive to the phase of the system, while the low-frequency
response exhibits features distinguishing the three phases. At zero doping,
corresponding to an electron filling in which the Fermi level lies at nodal
points, there are opposite sign zero-frequency divergences in the response when
approaching the nodal phase boundaries from the trivial and the TRITOPS phases.
In the trivial phase, both the high-frequency and low-frequency response of the
system are negative, but in the TRITOPS phase, the low-frequency response
becomes positive while the high-frequency response remains negative.
Furthermore, since phase transitions are controlled by the Rashba spin-orbit
coupling and the ratio of intra-orbital and inter-orbital paring amplitudes,
our results not only help distinguish the phases but can also provide an
estimate of the pairing amplitudes based on the photogalvanic response of the
system.
