Airy Pulsed Beams

The Airy beams (AiB's) have attracted a lot of attention recently because of their intriguing features, the most distinctive one is the propagation along curved trajectories in free-space. These beams are also weakly diffractive along their trajectories, i.e., they retain their structure and remain essentially diffraction-free for distances that are much longer than Gaussian beams with the same width. We have previously shown that the AiB is in fact a caustic of rays that radiate from the periphery of the aperture. In the present paper we derive ultra wideband (UWB) Airy Pulsed Beams (AiPB's), which are the extension of the AiB's into the time domain. We introduce a frequency scaling of the initial aperture field that renders the ray skeleton of the field, including the caustic, frequency independent, thus ensuring that all the frequency components propagate along the same curved trajectory, so that the AiPB does not disperse due to the wide frequency band. The resulting AiPB's preserve the intriguing features of the time-harmonic AiB's discussed above. Closed form solutions for the AiPB's are derived using the Spectral Theory of Transients (STT). The STT solution also explains how the strong pulsed field is formed in regions near the caustic, including its shadow side.