Verification of the Common Plane-wave Model by Band-limiting the Far Field of a Highly Localized Source

Abstract

The common plane-wave model of the electromagnetic field is shown to predict anomalous intensity modulations on and close to the axis in the band-limited far field of a localized source. This prediction, which has not yet been widely realized, is at variance with the expected asymptotic behaviour of the field of such a source. We propose an experiment to test this prediction. The predicted anomalous intensity modulations have high contrast and a readily measurable spatial frequency if the experimental conditions are such that the product of the source diameter and the upper bandlimit is of the order of one or less. The predicted anomalous intensity modulations are likely to be little affected by diffraction and aberrations in the experimental system. A positive verification by experiment of these anomalous intensity modulations would confirm the validity of the common plane-wave model, even for highly localized field sources; some modifications in the expected asymptotic behaviour of such a field would then have to be made. On the other hand, the absence of anomalous intensity modulations in the band-limited far field of a highly localized source would confirm the expected asymptotic behaviour of such a field, but would bring the validity of the common plane-wave model into question. Absence of anomalous intensity modulations on axis in the band-limited far field of a highly localized source could be explained by using an alternative plane-wave model, which employs non-uniform plane waves that propagate on axis.