  We study the dynamics of active Janus particles that self-propel in solution
by light-activated catalytic decomposition of chemical "fuel." We develop an
analytical model of a photo-active self-phoretic particle that accounts for
"self-shadowing" of the light by the opaque catalytic face of the particle. We
find that self-shadowing can drive "phototaxis" (rotation of the catalytic cap
towards the light source) or "anti-phototaxis," depending on the properties of
the particle. Incorporating the effect of thermal noise, we show that the
distribution of particle orientations is captured by a Boltzmann distribution
with a nonequilibrium effective potential. Furthermore, the mean vertical
velocity of phototactic (anti-phototactic) particles exhibits a superlinear
(sublinear) dependence on intensity. Overall, our findings show that
photo-active particles exhibit a rich "tactic" response to light, which could
be harnessed to program complex three-dimensional trajectories.
