Influence of speckles on laser intensity profile near turning points

Ray-tracing codes have difficulty simulating beams near caustics (eg. turning or focal points) due to the wavelength-scale features that develop in the laser-spot intensity profile. Compounding the issue is the propensity for caustic-driven intensity amplification to trigger deleterious parametric instabilities such as cross-beam energy transfer between incident and reflected components of the wavefield (sometimes called `self-CBET'). Such instabilities can limit fusion yields in laser-driven fusion schemes by reducing the drive symmetry or increasing energy losses, so their accurate prediction is paramount. At the National Ignition Facility (NIF), phase plates are used to condition the laser spot at best focus, giving it a well-characterized profile. A byproduct of this process is the introduction of fine-scale intensity modulations called speckles, which further complicate the modeling of caustics. Here, we present a new analytical model for the behavior of a speckled laser beam near a turning point that illustrates how speckles modify the typically assumed Airy function profile. We discuss the limits in which the model reduces to Airy behavior in terms of practical constraints on system parameters, such as the f-number of the laser aperture. Finally, we present numerical simulations to verify the new analytical model. The findings from this study will be used to inform future reduced modeling efforts of speckled laser beams.