The closed-form expression for the mean-squared beam width of partially coherent Hermite-Gaussian (H-G) beams propagating through atmospheric turbulence is derived. The influence of turbulence on the spreading of partially coherent H-G beams is studied quantitatively by examining the mean-squared beam width. It is found that the smaller the coherence length sigma(0) of the source is, and the larger the beam order m and the wavelength lambda are, the less partially coherent H-G beams are affected by the turbulence, although the beams with smaller sigma(0), larger m, and larger lambda have greater spreading in free space. In addition, it is shown that two partially coherent H-G beams may generate the same angular spread and that there exist equivalent partially coherent H-G beams that may have the same directionality as a fully coherent Gaussian beam in free space and also in turbulence. The results are illustrated by examples, and a comparison with previous work is also made.
The analytical expression for the spectral degree of coherence of partially coherent flat-topped beams propagating through the turbulent atmosphere is derived, and the spatial correlation properties are studied in detail. In particular, we find that the oscillatory behavior and phase singularities of the spectral degree of coherence may appear when partially coherent flat-topped beams propagate through the turbulent atmosphere; this behavior is very different from the behavior of Gaussian Schell-model beams. But the oscillatory behavior becomes weaker with increasing turbulence and even disappears when the turbulence is strong enough. The width of the spectral degree of coherence is always smaller than that of the spectral density in the far field when the turbulence is strong enough, whereas the width of the spectral degree of coherence in free space can be either larger or smaller than that of the spectral density in the far field.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.