We study the process of x-ray second-harmonic generation (SHG) from focused ultrashort pulses. We numerically simulate and derive approximated analytical expressions for the efficiency and tolerances of the SHG process, considering the effects of temporal and spatial walk-off, and the coupling to the linear Bragg scattering. We show that for the recently observed x-ray SHG in diamond, the simultaneous Bragg diffraction of the generated second harmonic is negligible. However, spatiotemporal walk-off effects are crucial components regarding the wave propagation aspects of this process, due to the highly noncollinear phase-matching geometry. (C) 2015 Optical Society of America
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