Incoherent beam combination of higher-order Gaussian beam in atmospheric turbulence

In this article, an incoherent beam combination of higher-order Gaussian beams through atmospheric turbulence is studied. An analytical expression of the combined intensity and spot size of higher-order Gaussian beams such as Hermite Gaussian (HG), Laguerre Gaussian (LG), and Bessel Gaussian (BG) are derived. The performance of these higher-order Gaussian beams is analyzed in various modes including the effect of beam wander, jitter, bore-sight error, Strehl ratio, and Visibility. A series of analytical simulations shows the intensity variation of 19 higher-order combined beams. Spot size, peak, and average intensity comparisons are made between various modes of higher-order Gaussian beam combinations. It is seen that the spot size of the combined beam increases rapidly in a higher mode of HG and LG beam. We evaluate the efficiency of combining beams at different distances, noting that it increases with higher mode orders and reaches its maximum with the $H{G}_{22}$ mode. Additionally, we explore the performance of higher-order Gaussian beam combinations under varying ground turbulence conditions. We observe that higher modes such as $H{G}_{22}$ and $L{G}_{22}$ are more susceptible to strong turbulence compared to lower modes.