This paper is a review of the theory-of laser beams and resonators. It is meant to be tutorial in nature and useful in scope. No attempt is made to be exhaustive in the treatment. Rather, emphasis is placed on formulations and derivations which lead to basic understanding and on results which bear practical significance.

Laser Beams and Resonators

Optical wireless communication (OWC) refers to transmission in unguided propagation media through the use of optical carriers, i.e., visible, infrared (IR), and ultraviolet (UV) bands. In this survey, we focus on outdoor terrestrial OWC links which operate in near IR band. These are widely referred to as free space optical (FSO) communication in the literature. FSO systems are used for high rate communication between two fixed points over distances up to several kilometers. In comparison to radio-frequency (RF) counterparts, FSO links have a very high optical bandwidth available, allowing much higher data rates. They are appealing for a wide range of applications such as metropolitan area network (MAN) extension, local area network (LAN)-to-LAN connectivity, fiber back-up, backhaul for wireless cellular networks, disaster recovery, high definition TV and medical image/video transmission, wireless video surveillance/monitoring, and quantum key distribution among others. Despite the major advantages of FSO technology and variety of its application areas, its widespread use has been hampered by its rather disappointing link reliability particularly in long ranges due to atmospheric turbulence-induced fading and sensitivity to weather conditions. In the last five years or so, there has been a surge of interest in FSO research to address these major technical challenges. Several innovative physical layer concepts, originally introduced in the context of RF systems, such as multiple-input multiple-output communication, cooperative diversity, and adaptive transmission have been recently explored for the design of next generation FSO systems. In this paper, we present an up-to-date survey on FSO communication systems. The first part describes FSO channel models and transmitter/receiver structures. In the second part, we provide details on information theoretical limits of FSO channels and algorithmic-level system design research activities to approach these limits. Specific topics include advances in modulation, channel coding, spatial/cooperative diversity techniques, adaptive transmission, and hybrid RF/FSO systems.

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Survey on Free Space Optical Communication: A Communication Theory Perspective

This paper is a review of the theory of laser beams and resonators. It is meant to be tutorial in nature and useful in scope. No attempt is made to be exhaustive in the treatment. Rather, emphasis is placed on formulations and derivations which lead to basic understanding and on results which bear practical significance.

/pdf/laser-beams-and-resonators-3z6ox0w31g.pdf

Laser beams and resonators

We develop a model for the probability density function (pdf) of the irradiance fluctuations of an optical wave propagating through a turbulent medium. The model is a two-parameter distribution that is based on a doubly stochastic theory of scintillation that assumes that small-scale irradiance fluctuations are modulated by large-scale irradi- ance fluctuations of the propagating wave, both governed by indepen- dent gamma distributions. The resulting irradiance pdf takes the form of a generalized K distribution that we term the gamma-gamma distribution. The two parameters of the gamma-gamma pdf are determined using a recently published theory of scintillation, using only values of the refractive-index structure parameter C n (or Rytov variance) and inner scale l 0 provided with the simulation data. This enables us to directly calculate various log-irradiance moments that are necessary in the scaled plots. We make a number of comparisons with published plane wave and spherical wave simulation data over a wide range of turbu- lence conditions (weak to strong) that includes inner scale effects. The gamma-gamma pdf is found to generally provide a good fit to the simu- lation data in nearly all cases tested. © 2001 Society of Photo-Optical Instrumen-

/pdf/mathematical-model-for-the-irradiance-probability-density-12lphyjf63.pdf

Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media

The theoretical basis of antenna tolerance theory is reviewed. Formulas are presented for the axial loss of gain and the pattern degradation as a function of the reflector surface rms error and the surface spatial correlation. Methods of determining these quantities by astronomical or ground-based electrical measurements are described. Correlation between the theoretical predictions and the performance of actual large antenna structures is presented.

Antenna tolerance theory&#8212;A review

Laser beam propagation in the atmosphere

Experimental results are described of measurements of irradiance fluctuations of laser radiation through atmospheric turbulence Simultaneous measurements of irradiance fluctuations, inner scale, and structure parameter were made in conditions of homogeneous turbulence during a number of summer days, from very early in the morning, before sunrise, until approximately noon During the measurements the turbulence strength varied continuously, spanning very low as well as intermediate and very high levels We used the data collected in selected intervals, during which turbulence was stationary, to obtain plots of irradiance variance versus the structure parameter for fixed ranges of values of the inner scale The results clearly show the effect of the inner scale For a given value of the structure parameter larger inner scales result in larger values of irradiance variance in the regime of strong scintillation

Inner-scale effect on irradiance variance measured for weak-to-strong atmospheric scintillation

In order to determine the characteristic parameters of the atmospheric turbulence, the mutual dancing of two parallel narrow laser beams propagating through a turbulent atmosphere has been investigated theoretically and experimentally. The experiments have been carried out with a He-Ne laser on a 130-m path, one meter from the ground. The method allowed the determination of the variance of the refractive index fluctuations, as well as the values of scale of the turbulence in the vertical and horizontal planes.

Investigation of atmospheric turbulence by narrow laser beams.

Measuring inner scale of atmospheric turbulence by angle of arrival and scintillation

An eigenvalue analysis of the noise-prone image leads to (a) an analysis of the eigenfunctions and eigenvalues of the sin2(x)/x2 kernel; and (b) an expression relating an effective number Neff of degrees of freedom directly to the signal-to-noise ratio σ0/σv. The latter are the variances of object and noise, respectively. For the particular case of incoherent, diffraction-limited imagery, Neff is found to be reduced from its noise-free value, the Shannon number, by the factor (1 − σv/σ0). A maximum number Nmax of degrees of freedom is also defined. Comparing one-dimensional objects illuminated alternatively by coherent and incoherent light, we find they have the same number Nmax of degrees of freedom. However, for the corresponding two-dimensional case, the incoherent value for Nmax is double that of the coherent value.

Anna Consortini

Papers

Laser beam propagation in the atmosphere

Inner-scale effect on irradiance variance measured for weak-to-strong atmospheric scintillation

Investigation of atmospheric turbulence by narrow laser beams.

Measuring inner scale of atmospheric turbulence by angle of arrival and scintillation

Degrees of freedom, and eigenfunctions, for the noisy image