## Keywords

propagation, detection, random media, polarization, coherence

## Abstract

Most of the physically realizable optical sources are radiating in a random manner given the random nature of the radiation of a large number of atoms that constitute the source. Besides, a lot of natural and synthetic materials are fluctuating randomly. Hence, the optical fields that one encounters, in most of the applications are fluctuating and must be treated using random or stochastic functions. Within the framework of the scalar-coherence theory, one can describe changes of the properties of any stochastic field such as the spectral density and the spectral degree of coherence on propagation in any linear medium, deterministic or random. One of the frequently encountered random media is the atmospheric turbulence, where the fluctuating refractive index of such medium severely degrades any signal propagating through it; especially it causes intensity fades of the signal. The usage of stochastic beams at the transmitter instead of deterministic ones has been suggested sometime ago to suppress the severe effects of intensity fluctuations caused by the atmospheric turbulence. In this dissertation, we study the usage of partially coherent beams in long path propagation schemes through turbulent atmosphere such as one frequently encounters in remote sensing, in the use of communication systems, and in guiding. Also the used detection scheme at the receiver is important to quantify the received signal efficiently, hence we compare the performance of incoherent (direct) detection versus coherent (heterodyne) detection upon the use of either one of them at the receiver of the communication system of beams propagating in turbulent atmosphere and namely we evaluate the signal-to-noise-ratio (SNR) for each case. The scalar-coherence theory ignored the vector nature of stochastic fields, which should be taken into account for some applications such as the ones that depend on the change of the polarization of the field. Recently generalization for the scalar-coherence theory including the vector aspects of the stochastic beams has been formulated and it is well-known as the unified theory of coherence and polarization of stochastic beams. The use of the unified theory of coherence and polarization makes it possible to study both the coherence properties and the polarization properties of stochastic electromagnetic beams on propagation in any linear media. The central quantity in this theory is a 2 Ã— 2 matrix that describes the statistical ensemble of any stochastic electromagnetic beam in the space-frequency domain or its Fourier transform in the space-time domain. In this dissertation we derive the conditions that the cross-spectral density matrix of a so-called planar, secondary, electromagnetic Gaussian Schell-model source has to satisfy in order to generate a beam propagating in vacuum. Also based on the unified-theory of coherence and polarization we investigate the subtle relationship between coherence and polarization under general circumstances. Besides we show the effects of turbulent atmosphere on the degree of polarization and the polarization state of a partially coherent electromagnetic beam, which propagates through it and we compare with the propagation in vacuum. The detection of the optical signals is important; hence it affects the fidelity of the communication system. In this dissertation we present a general analysis for the optical heterodyne detection of stochastic electromagnetic beams. We derive an expression for the SNR when two stochastic electromagnetic beams are mixed coherently on a detector surface in terms of the space-time domain representation of the beams, the beam coherence polarization matrices. We evaluate also the heterodyne efficiency of a heterodyne detection system for stochastic beams propagating in vacuum and we discuss the dependence of the heterodyne efficiency of the detection process on the changes in the beam parameters as the beam propagates in free space.

## Notes

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## Graduation Date

2007

## Semester

Fall

## Advisor

Rolland, Jannick

## Degree

Doctor of Philosophy (Ph.D.)

## College

College of Optics and Photonics

## Department

Optics and Photonics

## Degree Program

Optics

## Format

application/pdf

## Identifier

CFE0001932

## URL

http://purl.fcla.edu/fcla/etd/CFE0001932

## Language

English

## Length of Campus-only Access

None

## Access Status

Doctoral Dissertation (Open Access)

## STARS Citation

Salem, Mohamed Fouad, "Effects Of Polarization And Coherence On The Propagation And The Detection Of Stochastic Electromagnetic Beams" (2007). *Electronic Theses and Dissertations*. 3328.

https://stars.library.ucf.edu/etd/3328