  In the standard gravitational lensing scenario, rays from a background source
are bent in the direction of a foreground lensing mass distribution. Diverging
lens behaviour produces deflections in the opposite sense to gravitational
lensing, and is also of astrophysical interest. In fact, diverging lensing due
to compact distributions of plasma has been proposed as an explanation for the
extreme scattering events (ESEs) that produce frequency-dependent dimming of
extra-galactic radio sources, and may also be related to the refractive
radio-wave phenomena observed to affect the flux density of pulsars. In this
work we study the behaviour of two families of astrophysical diverging lenses
in the geometric optics limit, the power-law and the exponential plasma lenses.
Generally, the members of these model families show distinct behaviour in terms
of image formation and magnification, however the inclusion of a finite core
for certain power-law lenses can produce a caustic and critical curve
morphology that is similar to the well-studied Gaussian plasma lens. Both model
families can produce dual radial critical curves, a novel distinction from the
tangential distortion usually produced by gravitational (converging) lenses.
The deflection angle and magnification of a plasma lens varies with the
observational frequency, producing wavelength-dependent magnifications that
alter the amplitudes and the shape of the light curves. Thus, multi-wavelength
observations can be used to physically constrain the distribution of the
electron density in such lenses.
