Wave optics simulation of spatially partially coherent beams: Applications to free space laser communications

One of the main drawbacks that prevent the extensive application of free space laser communications is the atmospheric turbulence through which the beam must propagate. For the past four decades, much attention has been devoted to finding different methods to overcome this difficulty. A partially coherent beam (PCB) has been recognized as an effective approach to improve the performance of an atmospheric link. It has been examined carefully with most analyses considering the Gaussian Schell-model (GSM) beam. However, practical PCBs may not follow GSM theory and are better examined through some numerical simulation approach such as a wave optics simulation. Consequently, an approach for modeling the spatially PCB in wave optics simulation is presented here. 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 (GSM) beam.

A variety of simulation studies were performed for this dissertation. The propagation through turbulence of a coherent beam and a particular version of a PCB, a pseudo-partially coherent beam (PPCB), is analyzed. The beam is created with a sequence of several Gaussian random phase screens for each atmospheric realization. The average intensity profiles, the scintillation index and aperture averaging factor for a horizontal propagation scenario are examined. Comparisons between these results and their corresponding analytic results for the well-known GSM beam are also made. Cumulative probability density functions for the received irradiance are initially investigated.

Following the general simulation investigations, a performance metric is proposed as a general measure for optimizing the transverse coherence length of a partial spatially coherent beam for a given communication scenario. The expression is essentially the mean intensity minus the standard deviation of the intensity and we seek to maximize this quantity. This measure is preliminarily verified through a comparison with the probability of fade assuming the log-normal distribution model under the weak turbulence condition. The measure is also examined as a function of coherence length using wave optics simulations and these results are compared with relationships predicted by analytic theory under weak to medium-strong turbulence conditions. These results indicate there exists a unique coherence length that can optimize the receiver beam quality. Moreover, by taking the derivative of this quantity with respect to the atmospheric transverse coherence length and setting the result to zero, a result is obtained that indicates the near-optimal partially coherent beam for a given lasercom system.

Finally, the analytical theory of the probability density function of the received irradiance and the probability of fade for the log-normal and Gamma- Gamma distributions was extended for partially coherent beams propagating through arbitrary atmospheric turbulence. In addition, wave optics simulations were carried out for horizontal propagations of Gaussian Schell-model beams for a variety of typical link parameters. The simulated irradiance values at the center of the received beam are used to estimate the probability density of the irradiance. The probability of fade was examined using the accumulative probability density from zero to a threshold level. The results derived from the simulation compare favorably with the corresponding analytical theory. The comparisons reveal that the Gamma-Gamma and log-normal distributions of probability density functions provide a good fit to the wave optics simulation results under weak and moderate-to-strong turbulence regimes, respectively. Yet, for the probability of fade, the wave optics simulation results show a transition from the Gamma-Gamma to log-normal distribution under weak to strong turbulence.