Effective radius of curvature of partially coherent Hermite–Gaussian beams propagating through non-Kolmogorov turbulence

Abstract

Based on the extended Huygens–Fresnel principle and non-Kolmogorov spectrum, the analytical expression for the effective radius of curvature of partially coherent Hermite–Gaussian (PCHG) beams propagating through non-Kolmogorov turbulence is derived, and the relative effective radius of curvature is used to describe the effect of turbulence on the effective radius of curvature. It is shown that the effective radius of curvature of PCHG beams depends on the beam and non-Kolmogorov turbulence parameters and on the propagation distance. The variation of relative effective radius of curvature with increasing generalized exponent parameter α of non-Kolmogorov turbulence is non-monotonic. The longer the propagation distance is, the larger the effect of turbulence on the effective radius of curvature of PCHG beams is. The effective radius of curvature of PCHG beams with shorter wavelength, smaller beam order, larger beam waist width or better spatial coherence is more affected by the non-Kolmogorov turbulence. The results are interpreted physically.

Keywords:

• non-Kolmogorov turbulence
• relative effective radius of curvature
• partially coherent Hermite–Gaussian (PCHG) beam

Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant No. 61275203, the Science Foundation of Sichuan Provincial Education Department under Grant No. 12ZA203, the Natural Science Foundation of Yibin University under Grant No. 2010B14, and National Natural Science Foundation of China and Civil Aviation Administration of China under Grant No. 61079023.