Modeling the effects of high-energy-laser beam quality using scalar Schell-model sources

At the system level, poor beam quality often leads to significant performance degradations. For instance, if a high-energy laser (HEL) source has poor beam quality, then the effectiveness of a beam-control system becomes compromised. This outcome is the result of non-common path phase errors in the HEL beam that are not sensed by the beam-control system. Therefore, phase-compensation performance becomes degraded, because if the phase errors that degrade performance cannot be sensed, then their effects cannot be corrected. To help quantity these system-level performance degradations, we need a reliable and accurate way to model the effects of poor beam quality. As such, this paper develops a statistical approach using scalar Schell-model sources. Applying the work of Santarsiero et al. [J. Opt. Soc. Am. A 16, 106 (1999)], we show that we can quantify the effects of poor beam quality statistically in terms of the M² parameter. Then, we develop Monte Carlo wave-optics simulations which specify the field correlation coefficient in terms of M² for modeling HEL phase errors. The results show that we obtain convergence to the desired M² parameter thus properly modeling the phase errors. In addition, we investigate the statistics of the »instantaneous» M² parameter. We find, quite interestingly, that the instantaneous M₂ is very nearly lognormal. This information will be useful in HEL beam-control system design.