Tunnelling escape of waves

Applications of waves in communications, information processing and sensing need a clear understanding of how many strongly coupled channels or degrees of freedom exist in and out of volumes of space and how the coupling falls off for larger numbers. Numerical results are possible, and some heuristics exist, but there has been no simple physical picture and explanation for arbitrary volumes. By considering waves from a bounding spherical volume, we show a clear onset of a tunnelling escape of waves that both defines a limiting number of well-coupled channels for any volume and explains the subsequent rapid fall-off of coupling strengths. The approach works over all size scales, from nanophotonics and small radiofrequency antennas up to imaging optics. It gives a unified view from the multipole expansions common for antennas and small objects to the limiting plane and evanescent waves of large optics, showing that all such waves can escape to propagation to some degree, by tunnelling if necessary, and gives a precise diffraction limit.