Initially planar plasma mirrors irradiated at relativistic intensity are capable of focusing reflected light to intensities ten times higher than the incident light with focal lengths as short as 25 microns. They are useful for generating bright Compton gamma-rays from GeV laser-plasma accelerators, and for coupling plasma accelerator stages. We present laboratory experiments and PIC simulations that detail their unique optical properties.
Plasma mirrors (PMs) irradiated at sub-relativistic intensity (a0 << 1) are widely used to improve temporal contrast of ultrashort laser pulses that may subsequently be focused to relativistic intensity . Recently, new advanced accelerator applications have emerged that require a primary PM to be irradiated directly at relativistic light intensity (a0 ≥ 1). These include generation of Compton x-rays by retro-reflecting a transmitted laser-plasma accelerator (LPA) drive pulse onto trailing electrons [2,3], and coupling such a drive pulse over a short distance into the second or subsequent stage of a multi-stage LPA . Here we combine laboratory experiments with PIC simulations to elucidate the optical properties of these unique relativistic optical elements. The principal findings are:
(1) Relativistic PMs irradiated at near-normal incidence with 0.3 < a0 < 3 reflect efficiently (R > 0.6) as long as pre-pulses do not exceed 1e14 W/cm2 sooner than ~20 ps prior to the peak of the pulse. Stated equivalently, pre-plasma should have length L < 2µm as the main peak reflects.
(2) Relativistic PMs focus a significant fraction of reflected light to intensity as much as ten times the incident intensity with focal length f as short as 25 µm. This f is short enough to focus a transmitted LPA pulse onto trailing GeV electrons emerging from a bubble of radius Rb ~ 25 µm in a plasma of density ne ~ 5e17 cm-3. This in turn opens the nonlinear Compton regime, which optimizes the brightness and photon energy of Compton x (gamma)-rays. 
Experiments and simulations detailing the focusing mechanisms, their time evolution and aberrations, and methods for controlling the focus will be presented.
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