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In this dissertation, a hybrid method combing both the analytical and the numerical solutions is developed for full-wave simulations of vegetation. A realistic field setup is introduced to consider the plant structures and gaps within the vegetation canopy. The scattering of the whole vegetation field is then decomposed and solved in the following two steps. In the first step, the numerical solver is utilized to perform full-wave simulations of one single plant, from which the corresponding T-matrix is extracted based on the near-field using the Huygens principle and vector cylindrical wave (VCW) expansions. The full-wave based T-matrix characterizes the scattering of one single plant and captures the multiple scattering effects caused by the plant structure. In the second step, the T-matrix is combined with Foldy-Lax (FL) multiple scattering equations to consider the interactions among different plants within the vegetation field. The resulting closed-form equations are solved analytically using the VCW expansions and the translational addition theorem. The convergence and the accuracy of the hybrid method are verified with the High Frequency Structure Simulator (HFSS) by comparing the solutions of scatterings from four wheat plants. After that, the hybrid method is applied to investigate the frequency dependence of the vegetation effects by performing full-wave simulations of wheat fields at L-, S-, and C-band. A physical-iterative approach is implemented together with Message Passing Interface (MPI) parallel computing to facilitate the Monte Carlo simulations. The results obtained from the hybrid method are compared with those of the classical radiative transfer equation (RTE) model to illustrate the importance of full-wave simulations. In the second part, the full-wave simulation of forest is realized using the hybrid method after two critical issues are successfully resolved. To overcome the challenge in calculating the tree T-matrix, the general relation between the T-matrix and the scattered field coefficient is first revealed and a far-field based T-matrix extraction method applicable for plants of arbitrary size and structure is thus developed. Second, the memory challenge of hybrid method is eliminated by adopting the iterative solutions for solving the FL equations. The proposed methods are validated with FEKO by comparing the field solutions of scattering from three eight meters tall trees. The full-wave Monte Carlo simulations of forest are performed to investigate the tree effects on microwave propagation and the potential of using L-band signal to retrieve soil moisture over the forested area.

Kinetic equations have played a significant role in optics since the introduction of the radiative transport equation (RTE) by Schuster in the early 20th century. Now they are applied in many scientific fields such as atmospheric physics and biomedical imaging to understand how light interacts with a complex medium. In this thesis we investigate how these equations arise in: 1. models of classical optics in an inhomogeneous disordered scattering medium 2. in fully quantum real space models with a random distribution of atoms In certain spatial and temporal regimes it has been empirically observed that light interacting with a highly disordered scattering medium may be described by a radiative transport equation with a constant scattering coefficient. One way to derive such equations from microscopic principles is to model the medium as a random field which is statistically homogeneous. We show that in a quasi-homogeneous media, where statistical correlations vary rapidly on small length scales and slowly on large length scales, light obeys a radiative transport equation with variable scattering coefficient. In the second part of this thesis we introduce a new model in quantum optics which allows us to treat a quantized electromagnetic field coupled to a medium of two level atoms, both in real space. The rest of the chapter focuses on the interaction of atoms with a field consisting of at most one photon. First we recover a classical result due to Wigner and Weisskopf on the rate of single atom spontaneous emission. Next we show that in a statistically homogeneous distribution of two level atoms the field and atomic amplitude satisfy linear kinetic equations. Finally we show that at sufficiently long times and large distances these amplitudes are asymptotically governed by diffusion equations which may be solved analytically. In the final chapter we use the previous model to analyze a system in which there can be at most two photons. This allows us to study the time evolution of states that initially contain two entangled photons, a phenomenon which has no classical analogue. We show that the various probability amplitudes satisfy linear two particle kinetic equations which again may be asymptotically evaluated at large distances and long times.

Wavefront shaping provides an increasingly appealing avenue for imaging and other applications that require controlling electromagnetic waves passing through complex and disordered media. Indeed, these techniques allow researchers and engineers to exploit the properties of high-frequency waves, particularly optical ones, as they interact with these media to obtain nearly perfect transmission and a high degree of focusing. Here, we simulate the process of wave propagation in 3D random media using full-wave, integral equation-based computational electromagnetics schemes. We replicate many experimental observations relating to the existence of so-called open channels in non-absorbing random media and the distribution of their transmission coefficients. In addition, we develop new schemes for manipulating these waves, e.g. by focusing them onto one or multiple spots in the output plane. Furthermore, we leverage the computational methods to develop new schemes for characterizing random media, e.g. by computing their scattering and transmission matrices under a variety of conditions. Finally, we study the transmission properties of absorbing media and find a universal fluctuant pattern of their maximal transmission coefficients.

The objective of my research is two-fold: to study wave scattering phenomena in dense volumetric random media and in periodic wave functional materials. For the first part, the goal is to use the microwave remote sensing technique to monitor water resources and global climate change. Towards this goal, I study the microwave scattering behavior of snow and ice sheet. For snowpack scattering, I have extended the traditional dense media radiative transfer (DMRT) approach to include cyclical corrections that give rise to backscattering enhancements, enabling the theory to model combined active and passive observations of snowpack using the same set of physical parameters. Besides DMRT, a fully coherent approach is also developed by solving Maxwell’s equations directly over the entire snowpack including a bottom half space. This revolutionary new approach produces consistent scattering and emission results, and demonstrates backscattering enhancements and coherent layer effects. The birefringence in anisotropic snow layers is also analyzed by numerically solving Maxwell’s equation directly. The effects of rapid density fluctuations in polar ice sheet emission in the 0.5~2.0 GHz spectrum are examined using both fully coherent and partially coherent layered media emission theories that agree with each other and distinct from incoherent approaches. For the second part, the goal is to develop integral equation based methods to solve wave scattering in periodic structures such as photonic crystals and metamaterials that can be used for broadband simulations. Set upon the concept of modal expansion of the periodic Green’s function, we have developed the method of broadband Green’s function with low wavenumber extraction (BBGFL), where a low wavenumber component is extracted and results a non-singular and fast-converging remaining part with simple wavenumber dependence. We’ve applied the technique to simulate band diagrams and modal solutions of periodic structures, and to construct broadband Green’s functions including periodic scatterers.

The objective of my research is two-fold: to study wave scattering phenomena in dense volumetric random media and in periodic wave functional materials. For the first part, the goal is to use the microwave remote sensing technique to monitor water resources and global climate change. Towards this goal, I study the microwave scattering behavior of snow and ice sheet. For snowpack scattering, I have extended the traditional dense media radiative transfer (DMRT) approach to include cyclical corrections that give rise to backscattering enhancements, enabling the theory to model combined active and passive observations of snowpack using the same set of physical parameters. Besides DMRT, a fully coherent approach is also developed by solving Maxwell’s equations directly over the entire snowpack including a bottom half space. This revolutionary new approach produces consistent scattering and emission results, and demonstrates backscattering enhancements and coherent layer effects. The birefringence in anisotropic snow layers is also analyzed by numerically solving Maxwell’s equation directly. The effects of rapid density fluctuations in polar ice sheet emission in the 0.5~2.0 GHz spectrum are examined using both fully coherent and partially coherent layered media emission theories that agree with each other and distinct from incoherent approaches. For the second part, the goal is to develop integral equation based methods to solve wave scattering in periodic structures such as photonic crystals and metamaterials that can be used for broadband simulations. Set upon the concept of modal expansion of the periodic Green’s function, we have developed the method of broadband Green’s function with low wavenumber extraction (BBGFL), where a low wavenumber component is extracted and results a non-singular and fast-converging remaining part with simple wavenumber dependence. We’ve applied the technique to simulate band diagrams and modal solutions of periodic structures, and to construct broadband Green’s functions including periodic scatterers.

The Models of Random Motions in Random Media (RMRM) have been shown to have fruitful applications in various scientific areas such as polymer physics, statistical mechanics, oceanography, etc. In this dissertation, we consider a special model of RMRM: the Ornstein-Uhlenbeck process in a Poisson random medium and investigate the long time evolution of its random energy. We give complete answers to the long time asymptotics of the exponential moments of the random energy with both positive and negative coefficients, under both quenched and annealed regimes. Through these results, we find out a dramatic difference between the long time behavior of the Brownian motion dynamics and the Ornstein-Uhlenbeck dynamics in the Poisson random medium.

Mesoscale optical phenomena occur when light interacts with a number of different types of materials, such as biological and chemical systems and fabricated nanostructures. As a framework, mesoscale optics unifies the interpretations of the interaction of light with complex media when the outcome depends significantly upon the scale of the interaction. Most importantly, it guides the process of designing an optical sensing technique by focusing on the nature and amount of information that can be extracted from a measurement. Different aspects of mesoscale optics are addressed in this dissertation which led to the solution of a number of problems in complex media. Dynamical and structural information from complex fluids—such as colloidal suspensions and biological fluids—was obtained by controlling the size of the interaction volume with low coherence interferometry. With this information, material properties such as particle sizes, optical transport coefficients, and viscoelastic characteristics of polymer solutions and blood were determined in natural, realistic conditions that are inaccessible to conventional techniques. The same framework also enabled the development of new, scale-dependent models for several important physical and biological systems. These models were then used to explain the results of some unique measurements. For example, the transport of light in disordered photonic lattices was interpreted as a scale-dependent, diffusive process to explain the anomalous behavior of photon path length distributions through these complex structures. In addition, it was demonstrated how specialized optical measurements and models at the mesoscale enable solutions to fundamental problems in cell biology. Specifically, it was found for the first time that the nature of cell motility changes markedly with the curvature of the substrate that the cells iv move on. This particular work addresses increasingly important questions concerning the nature of cellular responses to external forces and the mechanical properties of their local environment. Besides sensing of properties and modeling behaviors of complex systems, mesoscale optics encompasses the control of material systems as a result of the light-matter interaction. Specific modifications to a material’s structure can occur due to not only an exchange of energy between radiation and a material, but also due to a transfer of momentum. Based on the mechanical action of multiply scattered light on colloidal particles, an optically-controlled active medium that did not require specially tailored particles was demonstrated for the first time. The coupling between the particles and the random electromagnetic field affords new possibilities for controlling mesoscale systems and observing nonequilibrium thermodynamic phenomena.

An ultrawide band (UWB) time domain (TD) radar has been developed for Time Reversal (TR) synthetic inverse scattering. This work describes the fabrication and test of a time domain TR “mirror” (TRM), which is the system that transmits, receives, and processes TR signals. Time reversal electromagnetics is a family of signal processing techniques that exploit the time reversal invariance of Maxwell equations, and allow focusing of waves in space and time with “super resolution”, i.e. beyond the classical resolution limit. In a typical TR experiment, first a pulsed signal is emitted and scattered by a target, which then acts as a weak emitter “source” toward the TRM. Then the TRM senses and records the weak scattered signal. Next, the recorded signals are time-reversed for their subsequent normalization and reradiation into the medium. The result is a signal that focuses in time and space where the target originally was, permitting localization and identification applications.A 12 mW low power short range experimental verification of the above process in the microwave domain is demonstrated in this work. The developed system exhibits a 40 GHz useful bandwidth such as to be able to follow 12 ps transition duration signals without distortion. An antenna system was designed and fabricated to satisfy the above bandwidth specification. The backward propagation in the TR process is executed synthetically on account of the current state of the required technology to recreate ultra-fast signals of arbitrary shape.Owing to its intrinsic TD nature, the finite difference time-domain (FDTD) method was applied as the numerical engine to simulate the electromagnetic fields in the TR process, facilitating the link between acquired data and its interpretation. The system designed showed capable of recreating in TD, with this extended bandwidth, the standard TR experiment as predicted by the theory. Hence, from real measurements the system was able to recreate synthetically space and time focusing. This kind of system could have application in subsurface target detection, trough-wall imaging and novel wireless communications. Additionally, in this work a numerical study introducing a novel technique to estimate the (mean) effective permittivity of a random media applying TR techniques is presented, and for which high performance computing was required to process the data. The results showed that TR can be applied to determine effective permittivity of random media difficult to otherwise model deterministically.

The propagation symmetry of electromagnetic fields is affected by encounters with material systems. The effects of such interactions, for example, modifications of intensity, phase, polarization, angular spectrum, frequency, etc. can be used to obtain information about the material system. However, the propagation of electromagnetic waves imposes a fundamental limit to the length scales over which the material properties can be observed. In the realm of near-field optics, this limitation is overcome only through a secondary interaction that couples the high-spatial-frequency (but non-propagating) field components to propagating waves that can be detected. The available information depends intrinsically on this secondary interaction, which constitutes the topic of this study. Quantitative measurements of material properties can be performed only by controlling the subtle characteristics of these processes. This dissertation discusses situations where the effects of near-field interactions can be (i) neglected in certain passive testing techniques, (ii) exploited for active probing of static or dynamic systems, or (iii) statistically isolated when considering optically inhomogeneous materials. This dissertation presents novel theoretical developments, experimental measurements, and numerical results that elucidate the vectorial aspects of the interaction between light and nano-structured material for use in sensing applications.

Time reversal is a general technique in wave propagation in inhomogeneous media when a signal is recorded at points of a device called time reversal mirror, gets time reversed and radiated back in the medium. The resulting field has a property of refocusing. Time reversal in acoustics has been extensively studied both experimentally and theoretically. In this thesis we consider the problem of time reversal of electromagnetic waves in inhomogeneous layered media. We use Markov process model for the medium parameters which allows us to exploit diffusion approximation theorem. We show that the field generated by the time reversal mirror focuses at a point of initial source inside of the medium. The size of the focusing spot is of the kind that it is smaller than the one that would be obtained if the medium were homogeneous meaning that the super resolution phenomenon is observed.

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 × 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.

Next generation photonics-based technologies will ultimately rely on novel materials and devices. For this purpose, phenomena at subwavelength scales are being studied to advance both fundamental knowledge and experimental capabilities. In this dissertation, concepts specific to near-field optics and experimental capabilities specific to near-field microscopy are used to investigate various aspects of the statistical properties of random electromagnetic fields in the vicinity of optically inhomogeneous media which emit or scatter radiation. The properties of such fields are being characterized within the frame of the coherence theory. While successful in describing the far-field properties of optical fields, the fundamental results of the conventional coherence theory disregard the contribution of short-range evanescent waves. Nonetheless, the specific features of random fields at subwavelength distances from interfaces of real media are influenced by the presence of evanescent waves because, in this case, both propagating and nonpropagating components contribute to the detectable properties of the radiation. In our studies, we have fully accounted for both contributions and, as a result, different surface and subsurface characteristics of inhomogeneous media could be explored. We investigated different properties of random optical near-fields which exhibit either Gaussian or non-Gaussian statistics. We have demonstrated that characteristics of optical radiation such as first- and second-order statistics of intensity and the spectral density in the vicinity of random media are all determined by both evanescent waves contribution and the statistical properties of the physical interface. For instance, we quantified the subtle differences which exist between the near- and far-field spectra of radiation and we brought the first experimental evidence that, contrary to the predictions of the conventional coherence theory, the values of coherence length in the near field depend on the distance from the interface and, moreover, they can be smaller than the wavelength of light. The results included in this dissertation demonstrate that the statistical properties of the electromagnetic fields which exist in the close proximity of inhomogeneous media can be used to extract structural information. They also suggest the possibility to adjust the coherence properties of the emitted radiation by modifying the statistical properties of the interfaces. Understanding the random interference phenomena in the near-field could also lead to new possibilities for surface and subsurface diagnostics of inhomogeneous media. In addition, controlling the statistical properties of radiation at subwavelength scales should be of paramount importance in the design of miniaturized optical sources, detectors and sensors.