Dynamics and selective temporal focusing of a time truncated Airy pulse in varying dispersive media

Abstract

We theoretically and numerically investigate the dynamics of a time truncated finite energy Airy pulse (FEAP) under longitudinally varying group velocity dispersion (GVD), which significantly influences the Airy dynamics. Realistic waveguide geometries are proposed that offer linear and oscillating GVD profiles through which one can efficiently control the ballistic Airy trajectory. We observe that a linear spatial variation of GVD may lead to a quasi-linear trajectory of the accelerating Airy pulse with modulated peak power. The impact of the periodic GVD on Airy dynamics is found to be interesting, where FEAP exhibits an oscillatory trajectory with a periodic modulation of peak power. Exploiting the transcendental relation between the modulation strength and period of GVD, we theoretically estimate an optimized length of the waveguide that delivers maximum power at the output. The effect of oscillatory third-order dispersion is dramatic for an Airy pulse, where it experiences successive singularities during its propagation. At singularity, the Airy pulse undergoes a temporal inversion after reaching a focal point. The rich dynamics of FEAP near the singularity point is theoretically investigated by solving the propagation equation. We provide detailed theoretical analyses to achieve selective temporal focusing of FEAP, which may be useful for practical applications. Theoretical results derived in this paper are verified numerically with satisfactory agreements.