Xifeng Xiao

Wave optics simulation approach for partial spatially coherent beams

A numerical wave optics approach for simulating a partial spatially coherent beam is presented. The approach involves the application of a sequence of random phase screens to an initial beam field and the summation of the intensity results after propagation. The relationship between the screen parameters and the spatial coherence function for the beam is developed and the approach is verified by comparing results with analytic formulations for a Gaussian Schell-model beam. The approach can be used for modeling applications such as free space optical laser links that utilize partially coherent beams.

On-axis probability density function and fade behavior of partially coherent beams propagating through turbulence

We examine the gamma-gamma and lognormal distributions as they apply to the irradiance at a point detector produced by partially coherent beams propagating horizontally through atmospheric turbulence. Our investigation compares the probability density functions and probability of fade predicted by the distributions with results from a wave-optics simulation developed for partially coherent beam propagation. For a partially coherent beam that is not too far removed from a coherent beam, we find the wave-optics results tend to the gamma-gamma model for the weak fluctuation regime and the results are closer to the lognormal model for the strong fluctuation regime. We observe that increasing the initial beam size/Fried parameter ratio (w(0)/r(0)) or shortening the coherence length (l(c)) tends to narrow the probability density profile produced by the simulation.

Experimentally generating any desired partially coherent Schell-model source using phase-only control

A technique is presented to produce any desired partially coherent Schell-model source using a single phase-only liquid-crystal spatial light modulator (SLM). Existing methods use SLMs in combination with amplitude filters to manipulate the phase and amplitude of an initially coherent source. The technique presented here controls both the phase and amplitude using a single SLM, thereby making the amplitude filters unnecessary. This simplifies the optical setup and significantly increases the utility and flexibility of the resulting system. The analytical development of the technique is presented and discussed. To validate the proposed approach, experimental results of three partially coherent Schell-model sources are presented and analyzed. A brief discussion of possible applications is provided in closing.

Metric for optimizing spatially partially coherent beams for propagation through turbulence

A performance metric Δ is described that can be used to determine the parameters of a partially coherent beam for near-optimal performance of a free-space optical link. The metric is defined as the mean received irradiance minus the standard deviation of the irradiance, and maximizing Δ balances the effects of beam spread and scintillation. An analytic form of Δ is developed for a Gaussian Schell-model beam, where the optimization parameter is the transverse coherence length. Comparisons of the metric performance are made with the more conventional probability-of-fade metric. The metric Δ is applied to determine the characteristics of the optimized coherence length as a function of a variety of link parameters and scenarios. In general, the optimized coherence length tends to decrease with increasing turbulence strength and propagation distance but increases with wavelength, although the behavior of specific scenarios can vary.

Producing any desired far-field mean irradiance pattern using a partially-coherent Schell-model source

A new technique is presented to produce any desired mean far-field irradiance pattern using a partially-coherent Schell-model source. The new method differs from similar approaches in the literature by requiring only phase control. This permits the proposed approach to be easily implemented in the laboratory using a single spatial light modulator. The analytical development of the phase-only method is presented and discussed. Simulation and experimental results are presented to validate the proposed method. Applications for the new technique include free-space optical communications, material processing/manufacture, and particle trapping.

Numerical modeling of Schell-model beams with arbitrary far-field patterns

An approach is described for creating random complex screens to be used in computer simulations of arbitrary Schell-model beams with a prescribed far-field intensity distribution. Simulation examples including beam profiles with reflection symmetry and rotational symmetry, flat-top, and pyramidal shapes are presented to verify the proposed approach. A more general scenario with a nonsymmetric far-field beam shape is illustrated to demonstrate the evolution in the free-space propagation from the source plane to the far zone.

SLM-based laboratory simulations of Kolmogorov and non-Kolmogorov anisotropic turbulence

In this paper, we present a laboratory setup to simulate anisotropic, non-Kolmogorov turbulence. A sequence of numerical phase screens that incorporate the turbulence characteristics were applied to a spatial light modulator placed in the path of a laser beam with a Gaussian intensity profile and the resulting far-field intensity patterns were recorded by a CCD camera. The values of scintillation at the position of the maximum intensity were extracted from the images and compared with theoretical values. Our experimental results show a trend that is in agreement with known theoretical expressions; however, the turbulence rescaling due to anisotropy shows some discrepancy with theory and requires more investigation.

Computational approaches for generating electromagnetic Gaussian Schell-model sources

Two different methodologies for generating an electromagnetic Gaussian-Schell model source are discussed. One approach uses a sequence of random phase screens at the source plane and the other uses a sequence of random complex transmittance screens. The relationships between the screen parameters and the desired electromagnetic Gaussian-Schell model source parameters are derived. The approaches are verified by comparing numerical simulation results with published theory. This work enables one to design an electromagnetic Gaussian-Schell model source with pre-defined characteristics for wave optics simulations or laboratory experiments.

Scintillation analysis of truncated Bessel beams via numerical turbulence propagation simulation

Scintillation aspects of truncated Bessel beams propagated through atmospheric turbulence are investigated using a numerical wave optics random phase screen simulation method. On-axis, aperture averaged scintillation and scintillation relative to a classical Gaussian beam of equal source power and scintillation per unit received power are evaluated. It is found that in almost all circumstances studied, the zeroth-order Bessel beam will deliver the lowest scintillation. Low aperture averaged scintillation levels are also observed for the fourth-order Bessel beam truncated by a narrower source window. When assessed relative to the scintillation of a Gaussian beam of equal source power, Bessel beams generally have less scintillation, particularly at small receiver aperture sizes and small beam orders. Upon including in this relative performance measure the criteria of per unit received power, this advantageous position of Bessel beams mostly disappears, but zeroth- and first-order Bessel beams continue to offer some advantage for relatively smaller aperture sizes, larger source powers, larger source plane dimensions, and intermediate propagation lengths.

Beam wander analysis for focused partially coherent beams propagating in turbulence

We extend the theory of beam wander for propagation through atmospheric turbulence to the case of a focused partially coherent beam (PCB). In addition to investigating the beam wander expression, we restate expressions for the beam size, long- and short-time average beam intensity profile, and the on-axis scintillation index of tracked and untracked beams. A wave optics simulation is implemented and the numerical results are compared with corresponding analytic results. The cases examined involve turbulence strengths ranging from Cn2 = 10−16 to 10−14  m−2/3 and for various horizontal paths ranging from 1 to 10 km. Although the extended analytic theory stems from a study of coherent beams, the simulation results show good agreement with the analytical results for PCBs in fluctuation regimes ranging from weak to intermediate.