Gouy phase shift of a tightly focused, radially polarized beam

Radially polarized beams represent an important member of the family of vector beams, in particular due to the possibility of using them to create strong and tightly focused longitudinal fields, a fundamental property that has been exploited by applications ranging from microscopy to particle acceleration. Since the properties of such a focused beam are intimately related to the Gouy phase shift, proper knowledge of its behavior is crucial. Terahertz microscopic imaging is used to extract the Gouy phase shift of the transverse and longitudinal field components of a tightly focused, radially polarized beam. Since the applied terahertz time-domain approach is capable of mapping the amplitude and phase of an electromagnetic wave in space, we are able to directly trace the evolution of the geometric phase as the wave propagates through the focus. We observe a Gouy phase shift of 2π for the transverse and of π for the longitudinal component. Our experimental procedure is universal and may be applied to determine the geometric phase of other vector beams, such as optical vortices, or even arbitrarily shaped and polarized propagating waves.