To date, there exists no complete, computationally efficient, physics-based model to compute the radar backscatter from forest canopies. Several models attempt to predict the backscatter coefficient for random forest canopies by using the Vector Radiative Transfer (VRT) Theory with success, however, these models often rely on purely time-harmonic formulations and approximations to integrals. Forms of VRT models have recently been developed which account for a Gaussian pulse incident waveform, however, these models often rely heavily on very specific and obfuscated approximations to solve the associated integrals. This thesis attempts to resolve this problem by outlining a method by which existing, proven, time harmonic solutions to the VRT equation can be modified to account for arbitrary pulse waveforms through simple path delay method. These techniques lend physical insight into the actual scattering mechanisms behind the returned waveform, as well as offer explanations for why approximations of previous authors' break down in certain regions. Furthermore, these radiative transfer solutions can be reformulated into a convolutional model which is capable of quickly and accurately predicting the radar return of random volumes. A brief overview of radiative transfer theory as it applies to remote sensing is also given. / Master of Science

High frequency solid-state switches are critical elements in communication systems, radio frequency (RF) systems and instrumentation. Key parameters to an RF switch include insertion loss while on and off-state isolation. Power handling and linearity are important to consider for a cost-effective construction. This becomes a design challenge into K-band frequencies as components required need to be small, dielectric losses and transmission lines need to be physically matched for proper isolative and through states. This thesis presents a novel single pole eight throw (SP8T) hybrid design composed of commercially available surface mount technology solutions to achieve high isolation and low insertion loss from 2-20GHz. A range of PIN diode solutions were surveyed against key design requirements for the SP8T hybrid switch. There were no commercially available solutions for a SP8T switch using surface mount components. A SP2T switch is combined with two SP4T to make the hybrid model. A wide range of RF switch topologies were simulated and designed into a printed circuit board panel that includes 15 test structures. This board is fabricated on a low loss dielectric material with a 4-layer stack that is operational up to 20 GHz and beyond. An onboard calibration structure including STOL standards are tested through a vector network analyzer to determine losses and reflection. Each switch design is on its own board to better determine the performance of the SP8T hybrid. High frequency coplanar waveguide to 2.4mm coaxial connectors are used to evaluate each board. This design is characterized against individual MMIC and PIN diode boards through switched states in decibels (dB). Second harmonic content is also measured at a target frequency at 2.4GHz for all configurations to determine the magnitude of undesirable spectral content with input power no greater than 10dBm. Results display acceptable loss in the lower half of the frequency band and narrow resonance nearer to 20 GHz due to board loss and reflections. This design has been successful in its design and operation at broadband RF frequencies. Performance characteristics are given in the summary section. Details of the design process and measurement methodology are given in the body of this thesis.

Monitoring biological systems is crucial in healthcare, driving the need for reliable and noninvasive solutions. The proliferation of unverified drugs in the market necessitates reliable methods for their detection and identification, especially amidst advancements in pharmaceuticals. Plasmonic biosensors emerge as a great platform for ultra-sensitive detection, identification, and manipulation of biomolecular systems. This dissertation report addresses the critical need for precise detection and monitoring of biomolecules and drugs, presenting innovative solutions through the design of a plasmonic biosensor to tackle challenges in sensitivity, selectivity, and label-free detection and identification. We introduce a robust and tunable, cavity-integrated plasmonic nanopatterned sensor that exhibits superchiral light in the infrared domain for ultrasensitive detection of chiral molecular concentrations and enantiomeric excesses. The multispectral capability of this system is further harnessed to generate unique chiral fingerprint-based barcodes for the identification of diverse chiral drugs and biomolecules. We further discuss and demonstrate results for a surface-modified plasmonic biosensor operating in the visible-near-infrared realm in detecting viral biomarkers and neurotransmitters directly from complex physiological environments. The system, on coupling with a microfluidic flow setup allows sensitive, selective and rapid detection without requiring complex pre-processing or sample preparation steps. We discuss additional applications of the unique plasmonic sensor, utilizing the property of tunable superchirality to create a dynamic chirality tracking system operating in the near infrared for real-time monitoring of protein dynamics. These techniques aim to revolutionize bio-detection, chiral differentiation, and sorting processes, having extensive applications in medical research and pharmaceutical industries.

Semiconductor lasers are considered essential for the advancement in the field of photonics where compact and energy-efficient lasers are necessary. Advancements in integrated photonic technologies will help push the performance of semiconductor lasers in the coming years and expand the technology to several other applications. Semiconductor lasers offer several key features such as high energy efficiency, mass production, availability at a myriad of wavelengths, and high integration capabilities. However, limitations in noise performance, pulse energy, and duration hold back semiconductor lasers from being utilized to their full potential. This dissertation reviews the utilization and development of external techniques that enable semiconductor mode-locked lasers to be used in multi-photon imaging and microwave photonic applications. We first review a two-color external cavity mode-locked laser system operating at wavelengths 834 nm and 974 nm that can generate synchronized picosecond pulses with peak powers exceeding 80 W and 100 W respectively. We verify the feasibility of this system to induce non-linear processes by demonstrating two-photon excitation in commercially available dyes. Next, we introduce the concepts of optical injection locking and discuss the development of a multi-tone optical self-injection locking technique to improve the noise performance and optical linewidth of a chip-scale InP based mode-locked laser. We utilize a Fabry-Perot etalon as the optical comb filter, which also serves to suppress the super-mode noise that arises from external cavity feedback. In addition to this, we also implement a coupled opto-electronic loop and reference it to an external RF source demonstrating exceptional timing stability. This approach along with the usage of fully integrated and ultra-compact components in subsequent versions has the potential to realize compact frequency comb lasers for microwave photonic and other practical applications.

The finite element method (FEM) is a widely-used numerical tool in the fields of structural dynamics, acoustics and electromagnetics. In this work, our goal is to develop robust FEM strategies for solving problems in the areas of acoustics, structures and electromagnetics, and then extend these strategies to solve multi-physics problems such as magnetohydrodynamics and structural acoustics. We now briefly describe the finite element strategies developed in each of the above domains. In the structural domain, we show that the trapezoidal rule, which is a special case of the Newmark family of algorithms, conserves linear and angular momenta and energy in the case of undamped linear elastodynamics problems, and an ‘energy-like measure’ in the case of undamped acoustic problems. These conservation properties, thus, provide a rational basis for using this algorithm. In linear elastodynamics variants of the trapezoidal rule that incorporate ‘high-frequency’ dissipation are often used, since the higher frequencies, which are not approximated properly by the standard displacement-based approach, often result in unphysical behavior. Instead of modifying the trapezoidal algorithm, we propose using a hybrid FEM framework for constructing the stiffness matrix. Hybrid finite elements, which are based on a two-field variational formulation involving displacement and stresses, are known to approximate the eigenvalues much more accurately than the standard displacement-based approach, thereby either bypassing or reducing the need for high-frequency dissipation. We show this by means of several examples, where we compare the numerical solutions obtained using the displacementbased and hybrid approaches against analytical solutions. We also present a monolithic formulation for the solution of structural acoustic problems based on the hybrid finite element approach. In the area of electromagnetics, since our goal is to ultimately couple the electromagnetic analysis with structural or fluid variables in a ‘monolithic’ framework, we focus on developing nodal finite elements rather than using ‘edge elements’. It is well-known that conventional nodal finite elements can give rise to spurious solutions, and that they cannot capture singularities when the domains are nonconvex and have sharp corners. The commonly used remedies of either adding a penalty term or using a potential formulation are unable to address these problems satisfactorily. In order to overcome this problem, we first develop several mixed finite elements in two and three dimensions which predict the eigenfrequencies (including their multiplicities) accurately, even for non-convex domains. In this proposed formulation, no ad-hoc terms are added as in the penalty formulation, and the improvement is achieved purely by an appropriate choice of the finite element spaces for the different variables. For inhomogeneous domains, ‘double noding’ is used to enforce the appropriate continuity conditions at an interface. Although the developed mixed FEM works very accurately for all 2D geometries and regular Cartesian 3D geometries, it has so far not yielded success for curved 3D geometries. Therefore, for 3D harmonic and transient analysis problems, we propose and use a modified form of the potential formulation that overcomes the disadvantages of the standard potential method, especially on non-convex domains. Electromagnetic radiation and scattering in an exterior domain traditionally involved imposing a suitable absorbing boundary condition (ABC) on the truncation boundary of the numerical domain to inhibit reflection from it. In this work, based on the Wilcox asymptotic expansion of the electric far-field, we propose an amplitude formulation within the framework of the nodal FEM, whereby the highly oscillatory radial part of the field is separated out a-priori so that the standard Lagrange interpolation functions have to capture a relatively gently varying function. Since these elements can be used in the immediate vicinity of the radiator or scatterer (with few exceptions which we enumerate), it is more effective compared to methods of imposing ABCs, especially for high-frequency problems. We show the effectiveness of the proposed formulation on a wide variety of radiation and scattering problems involving both conducting and dielectric bodies, and involving both convex and non-convex domains with sharp corners. The Time Domain Finite Element Method (TDFEM) has been used extensively to solve transient electromagnetic radiation and scattering problems. Although conservation of energy in electromagnetics is well-known, we show in this work that there are additional quantities that are also conserved in the absence of loading. We then show that the developed time-stepping strategy (which is closely related to the trapezoidal rule) mimics these continuum conservation properties either exactly or to a very good approximation. Thus, the developed numerical strategy can be said to be ‘unconditionally stable’ (from an energy perspective) allowing the use of arbitrarily large time-steps. We demonstrate the high accuracy and robustness of the developed method for solving both interior and exterior domain radiation problems, and for finding the scattered field from conducting and dielectric bodies. In the field of magneto-hydrodynamics, we develop a monolithic strategy based on a continuous velocity-pressure formulation that is known to satisfy the Babuska-Brezzi (BB) conditions. The magnetic field is interpolated in the same way as the velocity field, and the entire formulation is within a nodal finite element framework. Both transient and steady-state formulations are developed for two- and three-dimensional geometries. An exact linearization of the monolithic strategy ensures that rapid (quadratic) convergence is achieved within each time (or load) step, while the stable nature of the interpolations used ensure that no instabilities arise in the solution. Good agreement with analytical solutions, even with the use of very coarse meshes, shows the efficacy of the developed formulation.

With the rapid increase in available compute power and memory, and bolstered by the advent of efficient formulations and algorithms, the role of 3D full-wave computational methods for accurate modelling of complex electromagnetic (EM) structures has gained in significance. The range of problems includes Radar Cross Section (RCS) computation, analysis and design of antennas and passive microwave circuits, bio-medical non-invasive detection and therapeutics, energy harvesting etc. Further, with the rapid advances in technology trends like System-in-Package (SiP) and System-on-Chip (SoC), the fidelity of chip-to-chip communication and package-board electrical performance parameters like signal integrity (SI), power integrity (PI), electromagnetic interference (EMI) are becoming increasingly critical. Rising pin-counts to satisfy functionality requirements and decreasing layer-counts to maintain cost-effectiveness necessitates 3D full wave electromagnetic solution for accurate system modelling. Method of Moments (MoM) is one such widely used computational technique to solve a 3D electromagnetic problem with full-wave accuracy. Due to lesser number of mesh elements or discretization on the geometry, MoM has an advantage of a smaller matrix size. However, due to Green's Function interactions, the MoM matrix is dense and its solution presents a time and memory challenge. The thesis focuses on formulation and development of novel techniques that aid in fast MoM based electromagnetic solutions. With the recent paradigm shift in computer hardware architectures transitioning from single-core microprocessors to multi-core systems, it is of prime importance to parallelize the serial electromagnetic formulations in order to leverage maximum computational benefits. Therefore, the thesis explores the possibilities to expedite an electromagnetic simulation by scalable parallelization of near-linear complexity algorithms like Fast Multipole Method (FMM) on a multi-core platform. Secondly, with the best of parallelization strategies in place and near-linear complexity algorithms in use, the solution time of a complex EM problem can still be exceedingly large due to over-meshing of the geometry to achieve a desired level of accuracy. Hence, the thesis focuses on judicious placement of mesh elements on the geometry to capture the physics of the problem without compromising on accuracy- a technique called Adaptive Mesh Refinement. This facilitates a reduction in the number of solution variables or degrees of freedom in the system and hence the solution time. For multi-scale structures as encountered in chip-package-board systems, the MoM formulation breaks down for parts of the geometry having dimensions much smaller as compared to the operating wavelength. This phenomenon is popularly known as low-frequency breakdown or low-frequency instability. It results in an ill-conditioned MoM system matrix, and hence higher iteration count to converge when solved using an iterative solver framework. This consequently increases the solution time of simulation. The thesis thus proposes novel formulations to improve the spectral properties of the system matrix for real-world complex conductor and dielectric structures and hence form well-conditioned systems. This reduces the iteration count considerably for convergence and thus results in faster solution. Finally, minor changes in the geometrical design layouts can adversely affect the time-to-market of a commodity or a product. This is because the intermediate design variants, in spite of having similarities between them are treated as separate entities and therefore have to follow the conventional model-mesh-solve workflow for their analysis. This is a missed opportunity especially for design variant problems involving near-identical characteristics when the information from the previous design variant could have been used to expedite the simulation of the present design iteration. A similar problem occurs in the broadband simulation of an electromagnetic structure. The solution at a particular frequency can be expedited manifold if the matrix information from a frequency in its neighbourhood is used, provided the electrical characteristics remain nearly similar. The thesis introduces methods to re-use the subspace or Eigen-space information of a matrix from a previous design or frequency to solve the next incremental problem faster.

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<p>The fiber-to-the-x (FTTX) has been widely investigated as a leading access technology to meet the ever growing demand for bandwidth in the last mile. The passive optical network (PON) provides a cost-effective and durable solution. In this thesis, we investigate different aspects of the PON, in the search for cost-effective and high-performance designs of link system and devices.</p> <p>In Chapter 2, we propose a novel upstream link scheme for optical orthogonal frequency division multiplexing (OOFDM)-PON. The colorless laser diodes are used at the optical network units (ONUs), and the overlapped channel spectrum of orthogonal subcarrier multiplexing provides high spectral efficiency. At the optical line terminal (OLT), optical switch and all optical fast Fourier transform (OFFT) are adopted for high speed demultiplexing. The deterioration caused by the laser perturbation is also investigated.</p> <p>In Chapter 3, we design a novel polarization beam splitter (PBS), which is one of the most important components in polarization-controlled optical systems, e.g. the next-generation PON utilizing polarization multiplexing. Our PBS is built on a slab waveguide platform where the light is vertically confined. Planar lenses are formed to collimate and refocus light beam by converting the phase front of the beam. A planar subwavelength grating of a wedge shape induces the form birefringence, where the transverse electric (TE) and transverse magnetic (TM) waves have different effective refractive indices, and are steered to distinct directions. This design provides low insertion loss (< 0.9 dB) and low crosstalk (< -30 dB) for a bandwidth of 100 nm in a compact size, and can be realized by different material systems for easy fabrication and/or monolithic integration with other optical components.</p> <p>In Chapter 4, we study the mode partition noise (MPN) characteristics of the Fabry-Perot (FP) laser diode using the time-domain simulation of noise-driven multi-mode laser rate equation. FP laser is cheaper than the widely used distributed feedback (DFB) laser diode in PON, but its MPN is the major limiting factor in an optical transmission system. We calculate the probability density functions for each longitudinal mode. We also investigate the k-factor, which is a simple yet important measure of MPN. The sources of the k-factor are studied with simulation, including the intrinsic source of the laser Langevin noise, and the extrinsic source of the bit pattern.</p> / Doctor of Philosophy (PhD)

<p>In this study, we developed and improved the numerical mode matching (NMM) method which has previously been shown to be a fast and robust semi-analytical solver to investigate the propagation of electromagnetic (EM) waves in an isotropic layered medium. The applicable models, such as cylindrical waveguide, optical fiber, and borehole with earth geological formation, are generally modeled as an axisymmetric structure which is an orthogonal-plano-cylindrically layered (OPCL) medium consisting of materials stratified planarly and layered concentrically in the orthogonal directions.</p><p>In this report, several important improvements have been made to extend applications of this efficient solver to the anisotropic OCPL medium. The formulas for anisotropic media with three different diagonal elements in the cylindrical coordinate system are deduced to expand its application to more general materials. The perfectly matched layer (PML) is incorporated along the radial direction as an absorbing boundary condition (ABC) to make the NMM method more accurate and efficient for wave diffusion problems in unbounded media and applicable to scattering problems with lossless media. We manipulate the weak form of Maxwell's equations and impose the correct boundary conditions at the cylindrical axis to solve the singularity problem which is ignored by all previous researchers. The spectral element method (SEM) is introduced to more efficiently compute the eigenmodes of higher accuracy with less unknowns, achieving a faster mode matching procedure between different horizontal layers. We also prove the relationship of the field between opposite mode indices for different types of excitations, which can reduce the computational time by half. The formulas for computing EM fields excited by an electric or magnetic dipole located at any position with an arbitrary orientation are deduced. And the excitation are generalized to line and surface current sources which can extend the application of NMM to the simulations of controlled source electromagnetic techniques. Numerical simulations have demonstrated the efficiency and accuracy of this method.</p><p>Finally, the improved numerical mode matching (NMM) method is introduced to efficiently compute the electromagnetic response of the induction tool from orthogonal transverse hydraulic fractures in open or cased boreholes in hydrocarbon exploration. The hydraulic fracture is modeled as a slim circular disk which is symmetric with respect to the borehole axis and filled with electrically conductive or magnetic proppant. The NMM solver is first validated by comparing the normalized secondary field with experimental measurements and a commercial software. Then we analyze quantitatively the induction response sensitivity of the fracture with different parameters, such as length, conductivity and permeability of the filled proppant, to evaluate the effectiveness of the induction logging tool for fracture detection and mapping. Casings with different thicknesses, conductivities and permeabilities are modeled together with the fractures in boreholes to investigate their effects for fracture detection. It reveals that the normalized secondary field will not be weakened at low frequencies, ensuring the induction tool is still applicable for fracture detection, though the attenuation of electromagnetic field through the casing is significant. A hybrid approach combining the NMM method and BCGS-FFT solver based integral equation has been proposed to efficiently simulate the open or cased borehole with tilted fractures which is a non-axisymmetric model.</p> / Dissertation