Log-amplitude and phase correlations of general-type beams are formulated in atmospheric turbulence. A general beam is described as the superposition of many sets of multimode contents, each mode being off-axis Hermite–Gaussian. Since the Rytov solution is utilized, the formulas are valid in the weakly turbulent regime. The results are presented in integral forms that should be numerically evaluated for the specific beam type of interest. Our general beam results correctly reduce to the existing solutions for the correlations of limiting-case beams such as higher-order single-mode, multimode, off-axis Hermite–Gaussian, Hermite–sinusoidal-Gaussian, higher-order-annular, flat-topped-Gaussian, and thus naturally fundamental mode, plane, and spherical waves. Scintillation index and phase fluctuations in atmospheric optical links employing such special beams will be examined in future using the results reported here.
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