  We present an analytical model that describes the response of companion stars
after being impacted by a supernova in a close binary system. This model
captures key properties of the luminosity evolution obtained from 1D stellar
evolution calculations fairly well: a high-luminosity plateau phase and a
decaying tail phase. It can be used to constrain the pre-supernova binary
properties from the observed photometry of the companion star several years
after the explosion in a relatively simple manner. The derived binary
parameters are useful in constraining the evolutionary scenario for the
progenitors and the physics of binary interactions. We apply our model to some
known stripped-envelope supernova companions (SN1993J, SN2001ig, SN2006jc,
SN2011dh, SN2013ge). Combined with other observational constraints such as the
pre-supernova progenitor photometry, we find that SN1993J and SN2011dh likely
had relatively massive companions on wide orbits, while SN2006jc may have had a
relatively low-mass companion on a tight orbit. This trend suggests that type
IIb supernova progenitors evolved from stable mass transfer channels and type
Ibc progenitors may have formed from common-envelope channels. The constraints
on orbital separation helps us probe the highly uncertain common-envelope
physics for massive stars, especially with multiple epochs of companion
observations. We also highlight possible limitations of our model due to the
assumptions made in the underlying 1D models.
