  Following optical pulses ($\lambda=405~\text{nm}$) on titanium nitride (TiN)
Microwave Kinetic Inductance Detectors (MKIDs) cooled down at temperatures $T
\le T_c / 20$ ($T_c \simeq 4.6~\text{K}$), we observe a large phase-response
highlighting two different modes simultaneously that are nevertheless related.
The first corresponds to the well-known transition of cooper-pair breaking into
quasi-particles which produces a known phase response. This is immediately
followed by a large inverse response lasting several hundreds of microseconds
to several milliseconds depending on the temperature. We propose to model this
inverse pulse as the thermal perturbation of the superconductor and interaction
with two level system (TLS) that reduces the dielectric constant which in turns
modify the capacitance and therefore the resonance frequency. The ratio of the
TLS responding to the illumination is on the order of that of the area of the
inductor to the whole resonator
