In an atmospheric medium that shows a non-Kolmogorov turbulence behavior, the variation of the on-axis scintillation index is evaluated when higher-order laser modes are used as the excitation. The Rytov method is employed together with the equivalent structure constant, which makes our results valid in weak turbulence. In the limiting case, our solution correctly reduces to the known scintillation index of the Gaussian beam in Kolmogorov turbulence. For all the higher-order even modes, increase in the power law exponent, of the non-Kolmogorov spectrum is found to increase the scintillations. When the source size of the higher-order modes is large, higher-order even modes attain almost the same scintillation index values for all . However, for small source sizes, being valid for any realization of the non-Kolmogorov spectrum, the scintillations decrease as the mode order becomes large. The changes in the propagation distance, structure constant, and the wavelength do not vary these trends.
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