Scintillation index for N Gaussian laser beams with different wavelengths in weak atmospheric turbulence

We study the scintillation index of N partially overlapping lowest order Gaussian laser beams with different wavelengths in weak atmospheric turbulence. Assuming a Von Karman turbulence spectrum and slow detector response and using the Rytov approximation we calculate the longitudinal and radial components of the scintillation index for typical free-space laser communication setups. We find the initial beam separation that minimizes the longitudinal scintillation and corresponds to the optimal beam configuration. Further reduction of the longitudinal scintillation is obtained by optimizing with respect to both initial beam separation and initial spot size. The longitudinal scintillation of the optimal N-beam configurations is inversely proportional to N, resulting in a 92% reduction for a 9-beam system compared with the single beam value. The existence of the minimum of longitudinal scintillation is not very sensitive to the form of the turbulence spectrum. Moreover, the radial scintillation values for the optimal N-beam configurations are found to be significantly smaller than the corresponding single beam values, and this reduction effect also grows with increasing N.