Three-dimensional particle-in-cell simulations show that the periodic
solid-state structures irradiated by intense (∼1019 W/cm2) laser
pulses can generate collimated electron bunches with energies up to 30 MeV (and
acceleration gradient of 11.5 GeV/cm), if the microstructure period is equal
to the laser wavelength. A one-dimensional model of piecewise acceleration in
the microstructure is proposed and it is in a good agreement with the results
of numerical simulations. It shows that the acceleration process for
relativistic electrons can be theoretically infinite. In the simulations, the
optimal target parameters (the width of the microstructure elements and the
microstructure period) are determined. The explored parameters can be used for
proof-of-principle experiments demonstrating an ultrahigh gradient acceleration
by a number of identical and mutually coherent laser pulses [A. Pukhov et al.,
Eur. Phys. J. Spec. Top. 223, 1197 (2014)]