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A laser-boosted relativistic solid-density paraboloidal foil is known toefficiently reflect and focus a counterpropagating laser pulse. Here we showthat in the case of an ultrarelativistic counterpropagating pulse, ahigh-energy and ultrahigh intensity reflected pulse can be more effectivelygenerated by a relatively slow and heavy foil than by a fast and light one.This counterintuitive result is explained with the larger reflectivity of aheavy foil, which compensates for its lower relativistic Doppler factor.Moreover, since the counterpropagating pulse is ultrarelativistic, the foil isabruptly dispersed and only the first few cycles of the counterpropagatingpulse are reflected. Our multi-dimensional particle-in-cell simulations showthat even few-cycle counterpropagating laser pulses can be further shortened(both temporally and in the number of laser cycles) with pulse amplification. Asingle few-cycle, multi-petawatt laser pulse with several joule of energy andwith peak intensity exceeding 10^23 W/cm^2 can be generated already employingnext-generation high-power laser systems. In addition, the carrier-envelopephase of the generated few-cycle pulse can be tuned provided that thecarrier-envelope phase of the initial counterpropagating pulse is controlled.

Plasma-Based Generation and Control of a Single Few-Cycle High-Energy Ultrahigh-Intensity Laser Pulse