The analysis of long-range optical propagation through the turbulent atmosphere is currently performed using the framework of the classical “fully developed” Kolmogorov optical turbulence theory, where the atmosphere is described by three dimensional boundless, statistically homogeneous and isotropic random fields of refractive index fluctuations (atmospheric eddies). In this idealization, the impact of boundary conditions imposed by terrain, and hydro-thermodynamic processes in the atmosphere is assumed to be “forgotten” due to a cascade of energy transfer from larger to smaller scale eddies – the process that rationalizes Kolmogorov’s assumption of statistical isotropy of fully developed turbulence. In reality, these ideal homogeneity and isotropy conditions do not exist at large scales, as they are destroyed by gravity and solar radiation induced buoyancy and friction forces. These forces lead to formation of distinct, nearly horizontally aligned atmospheric layers that are typically composed of nested sub-layers with Matryoshka doll-like fractal structures. This atmospheric stratification has been confirmed by the results of both meteorological measurements and high-performance computer simulations of atmospheric dynamics based on numerical integration of fluid dynamics (Navier-Stokes type) equations. The latter approach – commonly referred to as computational dynamical meteorology – resulted in the discovery of a rich variety of large-scale self-organized spatio-temporal coherent atmospheric structures including gravity and rotary waves, rolls, Bernard cells, jets, stratified flows, instabilities, etc. – the effects that can severely impact optical wave propagation over long distances. These large-scale (meteorological) effects cannot be described in the statistical framework of Kolmogorov’s turbulence assumptions. Complete understanding of the impact of large-scale atmosphere effects requires research focused on merging statistical (Kolmogorov turbulence based) and deterministic computational fluid dynamics approaches, combined with wave optics modeling of optical wave propagation over atmospheric paths. Merging these diverse theoretical paradigms is one of the major research objectives of this MURI program. The most serious research challenges here arise from the enormous differences in spatial and temporal scales of atmospheric processes which must properly be taken into account in analysis and computations: from tens of kilometers and several hours (the scale of regional meteorological changes), to a few millimeters and milliseconds (the characteristic scales of turbulence induced refractive index fluctuations).

Despite a number of observed violations, the classical Kolmogorov theory of fully-developed turbulence still has a significant role for analysis and predictive modeling of various atmospheric optical systems. The most important in the context of deep turbulence is that the framework of this theory can be successfully applied not only for fairly short optical paths near the ground, but also for the fully developed turbulence within atmospheric layers at heights from 9 km to 14 km. Furthermore, recent studies have shown that the general statistical approach of this theory can play a central role in understanding highly anisotropic (quasi-two- dimensional) turbulence in stratified layers with the ratio of horizontal and vertical scales of turbulent eddies on the order of 100 and higher. Accurate predictive modeling of optical wave propagation inside these atmospheric layers cannot be performed using the conventional representation of atmospheric turbulence by a set of infinitely narrow (2D) and statistically independent phase screens. In the MURI research these quasi-two-dimensional turbulent layers will be described by 3D phase distorting “pancakes” and “slabs” with pre-defined anisotropic correlation properties within the entire turbulent layer volume. The development of mathematical and computational techniques for predictive modeling of optical wave propagation in highly anisotropic turbulence layers (3D-turbulence computer simulation techniques) is an essential part of this MURI effort. These new computational techniques are urgently needed for analysis of optical systems whose performance depends on variation in optical path difference (on piston phase). Among these systems are long-range coherent imaging lidars and optical vibrometers that are envisioned for DoD space and airborne surveillance applications.

The presence of atmospheric coherent structures that are characterized by sharp mean-field refractive index gradients, especially in the vicinity of their boundaries, can result in strong optical refraction effects that in turn lead to large-scale deviations in laser beam projection trajectory, optical mirages, deep optical signal fading, and formation of optical caustics. Analysis of these effects requires departure from the existing notion of separate treatment of diffractive (wave optics) and refractive (geometrical optics) effects. The development of a theoretical framework and corresponding numerical simulation tools that merge refractive and diffractive optics approaches in the analysis of long-range propagation over the stratified atmosphere is an important part of the MURI research. Since optical refraction is driven mainly by large-scale mean-field refractive index modulation and the most severe diffraction effects are related with optical wave propagation through small-scale turbulent eddies, analysis of the combined diffraction-refraction effects will be performed in a corresponding sequence – from computational meteorology for identification of the refractive index mean-field and structure parameter to refractive optics (ray-tracing) calculations for estimation of wave propagation trajectory and, along it, generation of 2D phase screens and/or 3D phase distorting slabs with pre-calculated mean-field structure parameters, and finally wave-optics computations.

Among possible approaches in this research area, the MURI team will consider engineering of unconventional optical fields (laser beams) and optical system architectures, which are less sensitive to atmospheric distortions. This will include the generation of exotic beams in the form of multi-petal fast rotating phase patterns, stochastic beams with different polarization and/or coherence properties, and multi-aperture laser transceiver systems that use spatial diversity for mitigation of scintillations in deep turbulence conditions. Preliminary studies performed at NMSU, UM, and UD have already demonstrated significant advantages of these approaches. Yet this progress must be seen as only a first step in a new promising research direction.

For atmospheric effects mitigation in deep turbulence conditions, the MURI team will also focus on the development and utilization of unconventional adaptive beam control techniques, such as cascaded adaptive optics that have shown great promise in deep turbulence compensation experiments. This research will be further advanced by considering conformal optical systems, composed of an array of adaptive laser beam transmitters and/or imaging receivers, and thus combining the spatial diversity and adaptive optics approaches. Since the efficiency of adaptive laser beam control depends strongly upon the atmospheric models used to design the control strategy, it will be necessary to reconsider control algorithms, and re-evaluate performance once new models are developed. We anticipate that new mitigation capabilities will arise from this work that will affect directed energy and laser communication systems of the future.

The impact of extended turbulence on optical wave propagation cannot always be considered as negative. As recently demonstrated [Ref Lucky], optical wave propagation in volume turbulence can lead to the formation of high quality image regions (lucky regions) that can be utilized for imaging system performance enhancement (lucky region fusion technique). Another example is the discovery of a laser beam super-focusing effect [Ref superfocus] that can lead to the dramatic increase of projected laser beam power density on an extended remote target (even beyond the diffraction limited value in vacuum). Exploitation (instead of mitigation) of deep turbulence effects is a new exciting research topic that will be pursued by MURI team members.