Multi-plane lensing in wave optics

Wave effects in lensing form a rich phenomenon at the intersection of classical caustic singularities and quantum interference, yet are notoriously difficult to model. Due to a large number of recently observed pulsars and fast radio bursts in radio astronomy and the prospected increase in sensitivity of gravitational wave detectors, wave effects have already been observed in plasma lensing and will be observed in gravitational lensing in the near future. The interference fringes are sensitive to physical parameters, which cannot be inferred from geometric optics. In particular, for multiplane lensing, the pattern depends on the redshifts of the lens planes. I present a new method to define and efficiently evaluate multiplane 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.