Studies On The Propagation And Scattering Of The Vector Or Scalar Light Beams Through The Complicated Optical Systems And Media

Until recently, the propagation properties of light beams have been investigated largely on the basis of the scalar theory, whereas polarization requires a vector treatment. It is actually a generalization of the study from scalar fields to electromagnetic vector fields. In the year 2003, Wolf indicated in his unified theory of coherence and polarization that the coherence and polarization of light are two closely related aspects in statistical optics. Many features of fluctuating electromagnetic fields can be fully understood only in this theoretical framework. It has not only enriched the theory of optics, but also brought new insights into many aspects in statistical optics. The development has important applications, such as tracking, remote sensing, and optical communication. Other applications will undoubtedly emerge in coming years. In this dissertation, we study the statistical optical properties of the stochastic electromagnetic beams propagating in turbulent atmosphere and optical systems by using the vector theory. We consider the complicated conditions of apertured, focusing, imaging, and the optical Hartley transform. Using the scalar theory, we study the scattering of a plane wave by anisotropic media or collections of anisotropic particles. The propagation of the elliptical Gaussian beam, which is truncated by elliptical apertures, the elliptical cosh-Gaussian beam, and the elliptical Hermite-cosh-Gaussian beam are also studied.In Chapter 1, we introduce the research background of this dissertation in three parts: the unified theory of coherence and polarization of stochastic electromagnetic beams; the coherence effect in scattering of light; laser beam models and their propagations. After analyzing the situation and trend at home and abroad, we emphasize the motivation and significance of this dissertation. Then we introduce the fundamental method and the theoretical basis used in our work:the cross-spectral density matrix of the stochastic electromagnetic beams; scattering theory of partially coherent beams; matrix optics and the generalized form of the diffraction integral.In Chapter 2, analytical expressions for the elements of the cross-spectral density matrix of the anisotropic stochastic electromagnetic beams propagating through the turbulent atmosphere are obtained. The changes in the spectral density, the spectral degree of coherence, and the spectral degree of polarization are calculated by use of the derived expressions. Numerical examples show that the spectral degree of polarization of the anisotropic stochastic electromagnetic beams does not return to its value in the source plane after propagating a sufficiently large distance in the turbulent atmosphere. Furthermore, analytical expressions are derived for the elements of the cross-spectral density matrix of a stochastic electromagnetic beam truncated by a slit aperture and passing through the turbulent atmosphere. The formula can be used in the study of the modulation in the spectral degree of polarization of the electromagnetic Gaussian Schell-model beam on propagation. We find that the spectral degree of polarization at the output plane can be directly controlled by the width of the slit aperture. The effect of polarization shaping is also illustrated. We find out the criterion for keeping completely unpolarized or completely polarized stochastic electromagnetic beams on propagation in free space or through the turbulent atmosphere.In Chapter 3, the formula for the propagation of the stochastic electromagnetic beam through the axially nonsymmetrical ABCD optical system is written in tensor form. The analytical expressions for the elements of the cross-spectral density matrix of electromagnetic Gaussian Schell-model beams through axially nonsymmetrical optical systems are obtained. The changes in the spectral degree of polarization, the spectral degree of coherence, and the spectral density are calculated. Analytical formulas for the elements of the cross-spectral density matrix of the stochastic electromagnetic Gaussian Schell-model beam truncated by rectangular apertures with different sizes and passing through the axially nonsymmetrical optical system are derived. Numerical examples relating to the changes in the spectral degree of polarization of the truncated beams passing through free space, focal system and dual-focus system are illustrated. A parametric study is performed in investigating the uniformly polarized electromagnetic Gaussian Schell-model beam passing through ABCD optical systems. The general imaging formula of the stochastic electromagnetic beam is derived. Numerical calculations are also presented to verify the theoretical analysis results.In Chapter 4, the optical Hartley transform is expressed in tensor form. Analytical formulas are obtained for describing the propagation of the off-axial elliptical Gaussian beam and the off-axial electromagnetic Gaussian Schell-model beam passing through the optical Hartley transform system. Numerical examples indicate that the information about the displacement magnitude and direction of the source can be represented in the form of fringes with different space frequencies and oscillating orientations at the output plane of the optical Hartley transform system. This phenomenon can be observed when calculating the intensity, the spectral density, and the spectral degree of polarization. The information about the displacement of the source can be exhibited by the distribution of the spectral degree of polarization, it may indicate a new technique for information recording, which means that one can record the information about the source in the form of distributions of spectral degree of polarization by use of an optical Hartley transform system and stochastic electromagnetic beams with different states of coherence.In Chapter 5, we analyze the general case when the light beam is scattered by Gaussian-correlated, quasi-homogeneous, anisotropic media. The analytical expression for the cross-spectral density function of the scattered field is derived, which provides an effective and convenient way to investigate the scattering of the polychromatic plane wave by Gaussian-correlated, quasi-homogeneous, anisotropic media. Numerical examples are given to illustrate the spectral density and the spectral degree of coherence of the scattered field. Furthermore, we study the scattering of the polychromatic plane wave by the system of anisotropic particles with deterministic locations and obtain the analytical expression for the cross-spectral density function of the scattered field. Numerical examples show the interference effect arising from the coherence of the fields scattered by each of the particles. Our results indicate that the information about the number, shape and relative position of the particles may be obtained from measurements of the scattered field.In Chapter 6, the elliptical aperture is described approximately by a tensor form, which can be expanded as a finite sum of complex Gaussian functions. The analytical expression for an off-axial elliptical Gaussian beam truncated by an elliptical aperture and passing through an axially nonsymmetrical ABCD optical system is obtained. Numerical calculations are presented buy use of the derived formula. The results are compared with the numerically integral ones. It is shown that our method can significantly improve the efficiency of numerical calculation. The elliptical annular aperture function is expressed as the subtraction of two elliptical aperture functions. The analytical expression for an elliptical Gaussian beam modulated by an elliptical annular aperture and passing through an axially nonsymmetrical optical system is obtained. Numerical examples are illustrated for the propagation of the beam in free space with an elliptical annular aperture, an elliptical screen, or an elliptical aperture. The fractional Fourier transform of the truncated elliptical Gaussian beam is investigated. The focal shift and focal switch of the truncated elliptical Gaussian beam are shown. Necessary physical explanations are given for the phenomena.In Chapter 7, a new kind of light beam named the elliptical cosh-Gaussian beam is introduced by use of tensor method. The analytical expression for the elliptical cosh-Gaussian beam passing through axially nonsymmetrical ABCD optical systems is derived. Numerical examples are illustrated for the propagation properties of the beam in free space and the focal system. The off-axial elliptical Hermite-cosh-Gaussian beam is introduced by use of tensor method. The analytical expression for the fractional Fourier transform of the elliptical Hermite-cosh-Gaussian beam is obtained and numerical calculations are presented. The method used in this chapter can be extended to the analyses of other kinds of elliptical sinusoidal-Gaussian beams or off-axial elliptical sinusoidal-Gaussian beams, elliptical Hermite-sinusoidal-Gaussian beams or off-axial elliptical Hermite-sinusoidal-Gaussian beams.In Chapter 8, we outline main conclusions and discuss plans for future work.