  We present an extensive study of the electric, magnetic and elastic responses
of tetragonal ferroelectrics under illumination, using a new theory
intertwining material and wave symmetries. Optical rectification,
photomagnetic, photovoltaic and phototoroidal vector responses are worked out
as functions of the wave vector and wave polarization directions. Second-order
response tensors associated with photoelastic, photomagnetoelectric,
photorefractive effects and photoconductivity are described. We discuss in
detail the photo-Hall and a new non-linear optical effect in tungsten bronzes.
Finally, we compare the properties of tetragonal materials with those of
hexagonal, orthorhombic and trigonal ferroelectrics previously reported in the
literature.
