Evaluating Beam Smoothing Techniques in Laser-Driven Inertial Confinement Fusion Using Spatial-Frequency Power Spectral Density of Focal-Spot-Intensity Relative Deviation

We propose an evaluation approach based on spatial-frequency power spectral density of focal-spot-intensity relative deviation (PSDFRD), which corresponds to the spatial frequency distribution of squared focal-spot-intensity contrast, to quantify the effectiveness of beam smoothing techniques in laser-driven inertial confinement fusion (ICF). This approach enables assessment of smoothing effects that cannot be adequately distinguished by conventional metrics like contrast and fractional power above intensity (FOPAI). Beam smoothing techniques employed in this work include continuous phase plate (CPP), smoothing by spectral dispersion (SSD), and polarization smoothing (PS) with two implementations: birefringent wedge (BW) and spatially-random polarization control plate (SRPCP)). Focal spot intensity distributions were characterized for six beam smoothing configurations (CPP only, CPP+BW, CPP+SRPCP, CPP+SSD, CPP+BW+SSD, and CPP+SRPCP+SSD), with uniformity analyzed using the proposed method. CPP+PS (BW or SRPCP) configurations enhance intensity distribution and improve uniformity in the low-frequency range (0-0.002 μm^-1), but introduce increased intensity and non-uniformity at high frequencies (0.050-0.070 μm^-1). Compared to the one-dimensionally periodic smoothing characteristics of CPP+BW across spatial frequencies, CPP+SRPCP demonstrates superior smoothing uniformity across all spatial frequency domains. CPP+SSD reduces intensity distribution and improves uniformity across most frequencies, but it significantly increases both intensity and non-uniformity in the low-frequency region (0-0.001 μm^-1). The CPP+PS (BW or SRPCP) +SSD not only mitigates elevated high-frequency intensity and non-uniformity inherent to the CPP+PS (BW or SRPCP) but also reduces low-frequency non-uniformity characteristic of CPP+SSD. Therefore, the combination of CPP, PS, and SSD exhibits a complementary smoothing effect.