  Visible or near infra-red light can be manipulated to produce bursts of
coherent extreme ultraviolet (XUV) or X-rays via the relativistic high-order
harmonic generation process when a laser irradiates a solid plasma target. The
intensity of the spectral components of the reflected signal decays with
increase of harmonic order and the efficiency of this non-linear process
largely hinges on how prompt this decay is. This is governed by the conditions
of the laser-plasma interaction for which various models have been proposed. At
relativistic intensities, a spectrum exhibiting a power-law decay with an
exponent of 8/3 or 4/3 is often stated. Here, we analyse the dependence of this
exponent on interaction parameters including the angle of incidence, the
carrier envelope phase, intensity of the laser and the pre-plasma length, and
discuss opportunities for optimization. Our simulations show that, rather than
there being one universal exponent, the spectral decay is a continuous function
of the laser-plasma interaction parameters.
