The generation of ultra-strong attosecond pulses through laser-plasma interactions offers the opportunity to surpass the intensity of any known laboratory radiation source, giving rise to new experimental possibilities, such as quantum electrodynamical tests and matter probing at extremely short scales. Here we demonstrate that a laser irradiated plasma surface can act as an efficient converter from the femto- to the attosecond range, giving a dramatic rise in pulse intensity. Although seemingly similar schemes have been presented in the literature, the present setup deviates significantly from previous attempts. We present a new model describing the nonlinear process of relativistic laser-plasma interaction. This model, which is applicable to a multitude of phenomena, is shown to be in excellent agreement with particle-in-cell simulations. We provide, through our model, the necessary details for an experiment to be performed. The possibility to reach intensities above 10^26 W/cm^2, using upcoming 10 petawatt laser sources, is demonstrated.Comment: 15 pages, 5 figure
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