  Asymmetric superconducting tunnel junctions with gaps $\Delta_1>\Delta_2$
have been proven to show a peculiar nonlinear bipolar thermoelectric effect.
This arises due to the spontaneous breaking of electron-hole symmetry in the
system, and it is maximized at the matching-peak bias
$|V|=V_p=(\Delta_1-\Delta_2)/e$. In this paper, we investigate the interplay of
photon-assisted tunneling (PAT) and bipolar thermoelectric generation. In
particular, we show how thermoelectricity, at the matching peak, is supported
by photon absorption/emission processes at the frequency-shifted sidebands
$V=\pm V_p+n\hbar\omega$, $n \in \mathbb{Z}$. This represents a sort of
microwave-assisted thermoelectricity. We show the existence of multiple stable
solutions, being associated with different photon sidebands, when a load is
connected to the junction. Finally, we discuss how the nonlinear cooling
effects are modified by the PAT. The proposed device can detect millimeter
wavelength signals by converting a temperature gradient into a thermoelectric
current or voltage.
