Far-field propagation of partially coherent laser light in random mediums.

The irradiance of a partially coherent light propagated under the influence of multiple random effects is shown to be the convolution of the irradiance propagated in a vacuum with the system's point spread function representing the random effects. This is true regardless of whether the propagation is far-field or not. We also show that the far-field irradiance of any laser system, regardless of complexity, can be expressed in terms of three basic parameters; laser power, field area, and a pupil factor. A general analytical formula for the far-field irradiance distribution for partially coherent laser sources of any complexity is derived. The formula includes multiple random effects including strong turbulence, random beam jitter, partial coherence, in addition to laser system pupil effects. An efficient matrix based numerical solution is also developed to verify the accuracy of the formula. Applications to the propagation of clipped Gaussian or flat-top beams with an obscuration, both as a single beam or an array of beams, are shown to give accurate results over the whole range of weak to strong turbulence as compared to numerical modeling.

Far-field propagation of partially coherent laser light in random mediums: erratum.

We present a correction to a typographical error in Eq. (27) and Eq. (28) in our article of [Opt. Express 26, 15609 (2018)].

Generation of anisotropy in turbulent flows subjected to rapid distortion.

A computational tool for the anisotropic time-evolution of the spectral velocity correlation tensor is presented. We operate in the linear, rapid distortion limit of the mean-field-coupled equations. Each term of the equations is written in the form of an expansion to arbitrary order in the basis of irreducible representations of the SO(3) symmetry group. The computational algorithm for this calculation solves a system of coupled equations for the scalar weights of each generated anisotropic mode. The analysis demonstrates that rapid distortion rapidly but systematically generates higher-order anisotropic modes. To maintain a tractable computation, the maximum number of rotational modes to be used in a given calculation is specified a priori. The computed Reynolds stress converges to the theoretical result derived by Batchelor and Proudman [Quart. J. Mech. Appl. Math. 7, 83 (1954)QJMMAV0033-561410.1093/qjmam/7.1.83] if a sufficiently large maximum number of rotational modes is utilized; more modes are required to recover the solution at later times. The emergence and evolution of the underlying multidimensional space of functions is presented here using a 64-mode calculation. Alternative implications for modeling strategies are discussed.

Self-similarity of two flows induced by instabilities.

The implications of full self-similarity of the Rayleigh-Taylor mixing layer and the Kelvin-Helmholtz shear layer are examined using a simplified group-theoretic analysis. The constraints on the behavior and evolution of these layers imposed by rigorous self-similarity are identified, and equations are constructed for the growth rate of these layers based on a total energy balance. This analysis does not prove that such flows will become self-similar. Rather, the analysis demonstrates the behaviors that would arise if these flows were to become fully self-similar.