  Two dimensional particle-in-cell simulations characterizing the interaction
of ultraintense short pulse lasers in the range 10^{18} \leq I \leq 10^{20}
W/cm^{2} with converging target geometries are presented. Seeking to examine
intensity amplification in high-power laser systems, where focal spots are
typically non-diffraction limited, we describe key dynamical features as the
injected laser intensity and convergence angle of the target are systematically
varied. We find that laser pulses are focused down to a wavelength with the
peak intensity amplified by an order of magnitude beyond its vacuum value, and
develop a simple model for how the peak location moves back towards the
injection plane over time. This performance is sustained over hundreds of
femtoseconds and scales to laser intensities beyond 10^{20} W/cm^{2} at 1 \mu m
wavelength.
