7 N ov 2 00 8 Measurement of superluminal phase and group velocities of Bessel beams in free space

We report on an interferometry-based measurement of the phase and group velocities of optical Bessel beams, providing confirmation of their superluminal character in the non-diffractive region. The measurements were performed in free space with a continuous wave laser and femtosecond pulses for phase and group velocities respectively. The Bessel beams were produced using a conical mirror. Einstein's special theory of relativity prohibits communicating at a speed faster than light. Nevertheless, su-perluminal phase and group velocities of electromagnetic waves have been observed in a variety of settings [1–5]. While, for different reasons, the observed behavior of optical waves cannot be used for superluminal signalling, these studies captured significant attention both within and outside the optics community and lead to a more precise understanding of the notion of signal velocity. Among the many arrangements where light exhibits quasi-superluminal properties, a special place belongs to laser beams whose radial profile is given by the zeroth-order Bessel function (Bessel beams). Discovered by Durnin in 1987 [6], the Bessel beam [Fig. 1(a)] is a coherent superposition of an equal-phase set of infinite plane waves that propagate at the cone angle θ relative to a fixed axis (which we define as z). The component waves interfere to produce a wavefront which is invariant in the propagation direction, and is thus " diffraction-free " , al-beit over a limited propagation range of R/ tan θ, where R is the radius of the optical element used to generate the beam. In the first realization, Bessel beams were produced using a circular slit and a lens [7], but subsequently a refracting axicon [8] became the most common approach, and recently a conical mirror scheme has been proposed [9]. While each component mode of the Bessel wave propagates at speed c, the wavevector of the Bessel wavefront is equal to the z-projection of each component's wavevec-tor, i.e. k = (ω/c) cos θ, where ω is the optical frequency. Accordingly, the phase and group velocities of the Bessel wavefront are v = ω/k = c/ cos θ, exceeding the speed of light in vacuum. In contrast to Refs. [1–5], the su-perluminal property of Bessel beams is not related to absorption/dispersion anomalies in the spectrum of the propagation medium but arises due to unusual interference between the plane wave components of the beam. As a result, superluminal propagation is observed in a wide spectral range. As in the case of dispersive media, …