Optimal efficiency for passively coupling partially coherent light intomode-limited optical waveguides

In this paper, we examine the problem of coupling partially coherent light from a telescope into an optical fiber within the framework of phase space optics using Wigner distributions. Specifically, we consider optimization of the coupling efficiency for passive optical systems under constraints in the number of spatial modes guided by the optical fiber, as are often imposed by the limitations of fiber devices or detectors employed later in the optical chain. As our primary example, we consider in detail the case of monochromatic plane wave optical fields distorted by random phase perturbations caused by propagation through atmospheric turbulence. By analyzing the Wigner distribution function for a plane wave in atmospheric turbulence, we develop an expression for the coupling efficiency as a function of the number of fiber modes and the ratio of the telescope diameter to Fried’s atmospheric coherence diameter.