We analyse condensing lightpipes of the form often used to couple an infrared detector to a relatively slow optical system. The response in a given direction is expressed in terms of the radiation patterns of the different waveguide modes propagating in the lightpipe and throat section. Such lightpipes are seen to be just a generalization of the electromagnetic horn antennas often used to illuminate radiotelescopes and other reflector antennas. The results of our analysis are compared with ray-tracing results for horns operating in the short wavelength geometrical optics limit: excellent agreement is obtained. This new analysis is equally valid in the long wavelength case pertaining for most FIR and submm detector systems, where only a few spatial modes propagate and the radiation pattern cannot be adequately determined by any other means.