Stable aggregates of flexible elements link rays and waves

Stable superpositions of elemental ray contributions give new capabilities for the ray-based analysis of optical fields and systems. These field estimates are constructed so that the results are effectively independent of the width of the field elements associated with each ray. The elements are thus free to be, more or less arbitrarily, localized or distributed at will. Since such elements thus need not disperse under diffraction, the new scheme is not a traditional beam summation method. In fact, it is this definitive property that leads to remarkable simplifications, and to significantly more accurate ray-based wave models. With this approach, error estimates become easily accessible, and a asymptotic treatment can finally be developed for fundamental processes such as refraction and diffraction.