Extended Huygens–Fresnel principle and optical waves propagation in turbulence: discussion

Extended Huygens-Fresnel principle (EHF) currently is the most common technique used in theoretical studies of the optical propagation in turbulence. A recent review paper [J. Opt. Soc. Am. A31, 2038 (2014)JOAOD60740-323210.1364/JOSAA.31.002038] cites several dozens of papers that are exclusively based on the EHF principle. We revisit the foundations of the EHF, and show that it is burdened by very restrictive assumptions that make it valid only under weak scintillation conditions. We compare the EHF to the less-restrictive Markov approximation and show that both theories deliver identical results for the second moment of the field, rendering the EHF essentially worthless. For the fourth moment of the field, the EHF principle is accurate under weak scintillation conditions, but is known to provide erroneous results for strong scintillation conditions. In addition, since the EHF does not obey the energy conservation principle, its results cannot be accurate for scintillations of partially coherent beam waves.