Impact of FM-AM conversion on smoothing by spectral dispersion

In order to set the shape of the focal spot, high power lasers for inertial confinement fusion have a phase plate at the end of the chain. This produces hot spots that can be avoided by the use of optical smoothing. Smoothing consists either in reducing the number of high-energy hot spots by splitting the focal spot energy on two orthogonal states of polarization or in moving the speckle pattern sufficiently fast so that the focal spot seems more homogeneous over time. In the latter case, the spectrum is broadened by a temporal phase modulation and dispersed with a grating. However, because of propagation impairments (filtering functions, chromatic dispersion, frequency conversion,...), part of the frequency modulation is converted into detrimental amplitude modulation. This is called FM-AM conversion. Its impact on smoothing performance is considered here. Three main parameters may be affected: Power fluctuations of the focal spot, size of the speckle hot spots (autocorrelation function) and dynamic of the evolution of the spatial contrast of the focal spot versus time. We show that depending on the features of the FM-AM conversion (frequency content of AM, type of filtering function) either one or more of these parameters may be affected. As a matter of fact, a low frequency AM induces power fluctuations while higher frequency AM induces variation of the autocorrelation function. Moreover, as opposed to an amplitude-filtering function, chromatic dispersion will not change the power spectral density of the pulse and thus the dynamic of the contrast.