  Wave effects in lensing form a rich phenomenon at the intersection of
classical caustic singularities and quantum interference, yet are notoriously
difficult to model. A large number of recently observed pulsars and fast radio
bursts in radio astronomy and the prospected increase in sensitivity of
gravitational wave detectors suggest that wave effects will likely be observed
in the near future. The interference fringes are sensitive to physical
parameters which cannot be inferred from geometric optics. In particular, for
multi-plane lensing, the pattern depends on the redshifts of the lens planes. I
present a new method to define and efficiently evaluate multi-plane lensing of
coherent electromagnetic waves by plasmas and gravitational lenses in
polynomial time. This method will allow the use of radio and gravitational wave
sources to probe our universe in novel ways.
