Universal phase relation between longitudinal and transverse fields observed in focused terahertz beams

Abstract

We directly observe longitudinal electromagnetic fields in focused freely propagating terahertz (THz) beams of radial and linear polarization. Employing electro-optic detection, which is phase sensitive, allows one to selectively detect longitudinal and transverse field components. A phase shift of π /2 between the transverse and longitudinal field components is revealed. This phase shift is of universal nature, as it does not depend on the mode, frequency and focusing conditions. We show that the universal phase relation is a direct consequence of the divergence-free nature of electromagnetic waves in vacuum. In the experiments, we observe the phase shift of π /2 for all frequency components of single-cycle THz radiation pulses of both radial and linear polarization. Additionally, we show that the longitudinal field of a radially polarized THz beam has a smaller spot size as compared with the transverse field of a linearly polarized beam that is focused under the same conditions. For field-sensitive measurements this property can be exploited even for moderate focusing conditions. Furthermore, the phase-sensitive detection of longitudinal electromagnetic fields opens up new possibilities to study their interaction with electronic excitations in semiconductor nanostructures.