We show that a photoconductive crystal, placed in a rapidly alternating ac
field and exposed to nonuniform light, exhibits singularities of the induce
d space charge and discontinuities of the corresponding space-charge field.
The singularities appear at the local intensity maxima when the curvature
of the intensity profile exceeds a certain (often very low) threshold value
. We analyze the characteristic features of the singular ac response and co
nsider its possible optical manifestations.