Relativistic optics in the lambda-cubed regime and applications to attosecond physics

Attosecond electromagnetic pulses and electron bunches, being produced efficiently, can give access to extreme field physics and coherent interaction in X-ray range. We find a path to the efficient generation of strong attosecond electromagnetic pulses and dense attosecond electron bunches in the regime of tightly focused ultrashort pulses. By focusing few-cycle laser pulses to a diffraction limited spot (the lambda-cubed regime) relativistic intensity can be achieved even with millijoule energies. If the phenomena discussed above are realized experimentally, they offer the potential for the generation of extreme fields and efficient attosecond X-ray generation