Body-of-revolution finite-difference time-domain modeling of space-time focusing by a three-dimensional lens

We introduce a body-of-revolution finite-difference time-domain simulation capability that can be applied to rotationally symmetric linear-optics problems. This simulator allows us to reduce a computationally intractable, three-dimensional problem to a numerically solvable two-dimensional one. It is used to model the propagation of a pulsed Gaussian beam through a thin dielectric lens and the focusing of the resulting pulsed beam. Analytic results for such a lens-focused, pulsed Gaussian beam are also derived. It is shown that, for the same input energy, one can design ultrawide-bandwidth driving signals to achieve a significantly larger intensity enhancement than is possible with equivalent many-cycle, monochromatic signals. Several specially engineered (designer) pulses are introduced that illustrate how one can achieve these intensity enhancements. The simulation results confirm that intensity enhancements can be realized with properly designed ultrawide-bandwidth pulses.