The dielectric waveguide is an important component used in the optical communication system. In this thesis, we conduct basic research on the propagation constant and the characteristic of the dielectric waveguide. We develop a method to expand 2-D rectangular dielectric waveguide modes with simple orthogonal bases. Furthermore, we improve the convergent rate by expanding waveguide modes with tensor product of properly chosen guiding-mode bases. We first derive the coupled differential equations of the two transverse magnetic field components which satisfy the continuous boundary conditions across all material interfaces. Then we investigate and verify the accuracy of this method on 1-D rectangular waveguide so that we can apply the technique to 2-D rectangular waveguides. By means of linear combination of simple 2-D orthogonal bases, we expand the mode of rectangular dielectric waveguide. Through rigorous mathematical closed-form integration, we obtain the equivalent matrix whose eigenvalues and associated eigenvectors become the mode propagation constants and mode field distribution functions of the underlying 2-D dielectric waveguide. Whenever symmetry exists we can reduce the size of the problem by choosing appropriate boundary conditions in accordance to particular mode polarization desired. This method provides at least four significant digits of propagation constant and detailed field description of the rectangular dielectric waveguide. We believe that it is an effective method for modal analysis of 2-D complex dielectric-waveguides.

Photonic crystals (PCs) are structures with spatially periodic variations in dielectric constants. The prime property of PCs is the existence of the photonic band gaps (PBGs) which could prohibit the propagation of light within a certain frequency range. Once the PC structures are fabricated, it is hard to tune their optical properties for the fixed geometries. Thus, it is important to develop tunable PC waveguide devices for the applications in the photonic integrated circuits. We utilize the mode-gap effect to design two-dimensional (2-D) tunable Y-shaped PC waveguides with the polyaniline type electrorheological (ER) fluids. The propagation of light on the Y-shaped waveguide can be controlled by applying the electric field in specific regions. Besides, we also propose a tunable multi-channel PC waveguide with the polyaniline type ER fluids. We then investigate the tunable propagation characteristics of a 2-D single line-defect PC waveguide with liquid crystals (LCs) by varying the direction of LCs and the hole sizes. We also simulate the tunable optical properties of a 2-D Y-shaped PC waveguide utilizing LCs. Finally, we consider a 3-D Y-shaped PC slab waveguide with LCs. The effects of the direction of LCs and the slab thickness are discussed.

Surface plasmons are of interest for various applications, including optical interconnects and devices, light sources, nanolithography, biosensors, solar cells, and negative-refraction prisms or superlenses. Some of the most important applications are SP-based optical interconnects and devices, which offer the potential of realizing integrated optical nanocircuitry due to the subwavelength confinement and the slow-wave nature of SPs. The fundamental building element of these applications is the plasmonic waveguide. Among the family of various plasmonic waveguides, the metal-insulator-metal waveguide has superior lateral confinement because of the relatively shallow field penetration into the metal claddings (about a skin depth -- usually tens of nanometers). Such subwavelength confinement cannot be achieved by conventional dielectric optical waveguides. However, the loss in the MIM waveguide is substantial due to the strong absorption of metal in the visible or near-infrared spectrum. Therefore, the design, simulation, and measurement of the loss in the MIM waveguide are critically important in the development of SP-based nanocircuitry. Surface plasmons (SPs) are of interest for various applications, including optical interconnects and devices, light sources, nanolithography, biosensors, solar cells, and negative-refraction prisms or superlenses. Some of the most important applications are SP-based optical interconnects and devices, which offer the potential of realizing integrated optical nanocircuitry due to the subwavelength confinement and the slow-wave nature of SPs. The fundamental building element of these applications is the plasmonic waveguide. Among the family of various plasmonic waveguides, the metal-insulator-metal (MIM) waveguide has superior lateral confinement because of the relatively shallow field penetration into the metal claddings (about a skin depth -- usually tens of nanometers). Such subwavelength confinement cannot be achieved by conventional dielectric optical waveguides. However, the loss in the MIM waveguide is substantial due to the strong absorption of metal in the visible or near-infrared spectrum. Therefore, the design, simulation, and measurement of the loss in the MIM waveguide are critically important in the development of SP-based nanocircuitry. Owing to the subwavelength sizes of MIM waveguides, the excitation of an MIM plasmonic mode typically requires end-fire coupling with tapered fibers or waveguides. Further, the conventional loss measurements require the usage of a near-field scanning optical microscopy (NSOM) or multiple waveguide samples with various length scales; however, the two aforementioned techniques are both complicated and have issues of sensitivity to uncontrollable environmental factors or variations in coupling strength, respectively. These experimental challenges have been a primary reason for the slow experimental development of the MIM waveguide and device. The research in this thesis focuses on the development of the transverse transmission/reflection (TTR) method, which is a more reliable, accurate, and straightforward method of characterizing the plasmonic modes in the MIM waveguide. The theory of the TTR method, which incorporates an attenuated total reflection (ATR) configuration, is developed based on the transmission matrix formulation. A methodology for obtaining the propagation constant and attenuation coefficient of a plasmonic mode in an MIM waveguide is illustrated. Using the Metricon Prism Coupler, the TTR method is experimentally applied to planar, single-mode MIM (Au-SiO$_2$-Au) waveguides with various core thicknesses at $lambda=1550$ nm. The experimental results are in very good agreement with the theoretical results. It is also shown experimentally that the TTR method is robust against difficult-to-quantify parameters such as the metal cladding thickness and the air gap thickness between the prism and the waveguide. As a result, the TTR method can be readily applied by using other similar ATR or prism-coupler configurations, without concern for the sensitivity issues caused by the subtle differences between various configurations. Moreover, the TTR method is also experimentally applied to planar, multimode MIM waveguides. Multimode MIM waveguides, which have larger core sizes, may be of interest for applications in low-loss interconnects or tapered end-couplers. Thanks to the superior angular selectivity of the ATR configuration, the TTR method is capable of detecting the propagation constant and attenuation coefficient of each mode. To the best of the author's knowledge, this is the first time the propagation constant of each mode in a multimode MIM waveguide has been individually measured. Also, to the best of the author's knowledge, this is the first time the attenuation coefficient of each mode in a multimode MIM waveguide has been individually measured. The TTR method is proved to be a reliable, accurate, and straightforward approach to characterize plasmonic modes in MIM waveguides. Future research will target the extension of the TTR method to 2D MIM waveguides, asymmetric MIM waveguides, and inclusion of scattering loss. Taking full advantage of the TTR method, the development of plasmonic devices can be potentially accelerated. The theory of the TTR method, which incorporates an attenuated total reflection (ATR) configuration, is developed based on the transmission matrix formulation. A methodology for obtaining the propagation constant and attenuation coefficient of a plasmonic mode in an MIM waveguide is illustrated. Using the Metricon Prism Coupler, the TTR method is experimentally applied to planar, single-mode MIM (Au-SiO$_2$-Au) waveguides with various core thicknesses at $lambda=1550$ nm. The experimental results are in very good agreement with the theoretical results. It is also shown experimentally that the TTR method is robust against difficult-to-quantify parameters such as the metal cladding thickness and the air gap thickness between the prism and the waveguide. As a result, the TTR method can be readily applied by using other similar ATR or prism-coupler configurations, without concern for the sensitivity issues caused by the subtle differences between various configurations. Moreover, the TTR method is also experimentally applied to planar, multimode MIM waveguides. Multimode MIM waveguides, which have larger core sizes, may be of interest for applications in low-loss interconnects or tapered end-couplers. Thanks to the superior angular selectivity of the ATR configuration, the TTR method is capable of detecting the propagation constant and attenuation coefficient of each mode. To the best of the author's knowledge, this is the first time the propagation constant of each mode in a multimode MIM waveguide has been individually measured. Also, to the best of the author's knowledge, this is the first time the attenuation coefficient of each mode in a multimode MIM waveguide has been individually measured. The TTR method is proved to be a reliable, accurate, and straightforward approach to characterize plasmonic modes in MIM waveguides. Future research will target the extension of the TTR method to 2D MIM waveguides, asymmetric MIM waveguides, and inclusion of scattering loss. Taking full advantage of the TTR method, the development of plasmonic devices can be potentially accelerated.

Recently, there is strong interest in the through-wall sensing capabilities of radar for use in law enforcement, search and rescue, and urban military operations. Due to the high attenuation of walls, through-wall radar typically operates in the low GHz frequency region, where resolution is limited. It is worthwhile to explore other means of propagating radar waves into and back out of a building’s interior for sensing applications. One possibility is through duct-like structures that are commonly found in a building, such as metal pipes used for plumbing or air conditioning ducts. The objective of this dissertation is to investigate techniques to acquire radar images of targets through a pipe. First, using the pipe as an electromagnetic propagation channel is studied. A modal approach previously developed for computing the radar cross-section of a circular duct is modified to compute the transmission through a pipe. This modal approach for transmission is validated against measured data. It is also shown that a pipe is a high-pass propagation channel. The modal analysis is then extended to two-way, through-pipe propagation for backscattering analysis. The backscattering from a target is observed through a pipe in simulation and measurement. Next, methods to form two-dimensional radar images from backscattering data collected through a pipe are explored. Four different methods previously developed for free-space imaging are applied to the problem of imaging through a pipe: beamforming, matched filter processing, MUSIC, and compressed sensing. In all four methods it is necessary to take into account the propagation through the pipe in order to properly generate a focused radar image. Each method is demonstrated using simulation and validated against measurement data. The beamforming and matched filter methods are found to suffer from poor cross-range resolution. To improve resolution, the MUSIC algorithm is applied and shown to give superior resolution at the expense of more complicated data collection. The final method, compressed sensing, is shown to achieve good cross-range resolution with simpler data collection. A comparison of the tradeoffs between the four methods is summarized and discussed. Two additional extensions are studied. First, a method for computing the transmission through an arbitrary pipe network using the generalized scattering matrix approach is proposed and implemented. Second, a new method for computing joint time-frequency distributions based on compressed sensing is applied to analyze the backscattering phenomenology from a pipe. / text

A comprehensive and rigorous description of instantaneous balance of electromagnetic power defined as the derivative of energy with respect to time is offered by the Poynting's theorem. Such theorem is expressed as the sum of a series of volume integrals representing the volume densities of densities of different components of electromagnetic power and the power flow through the general surface surrounding the entire domain in which the Poynting's vector expresses the instantaneous power leaving the domain (the positive normal is the outward normal to the enclosing surface). The original feature of the present approach is the introduction in the electromagnetic power balance and conservation of the electromechanical energy conversion by the use of the flux derivatives of the fields [D with vector arrow] and [B with vector arrow]. For the moving points (rotors) involved in electromechanical energy conversion, the surface of integration is driven together with them and [permittivity] and [permeatility] remain substantially constant--(a point in movement maintains its properties as [formula]). Then the balance of energy (and power) can be written at each infinitesimal time interval for the electromagnetic energy in which case the elementary mechanical work is produced by mechanical forces of electromagnetic origin. The thermal energy accounts for the Joule (and hysteresis) losses in the system. A treatment of the flow of electromagnetic energy is given for a complete of illustrative relationship in time and frequency domain. / text

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The scope of the present doctoral thesis has been the conception of a novel and efficient method for decelerating, over a range of frequencies, and completely 'stopping' light (zero group velocity, vg = 0) inside solid-state materials, at room temperature. To this end, we analytically show that an adiabatically tapered waveguide having a core of a lossless negative refractive index (NRI) metamaterial (MM) and claddings made of normal dielectrics can 'trap' a light pulse in such a way that each individual frequency component of the pulse is stopped at a different point along the waveguide, forming what we have called a 'trapped rainbow'. Crucially, it is shown that light can efficiently be in-coupled inside such a waveguide heterostructure from a normal dielectric waveguide, since with a suitable design one can achieve simultaneous thickness-, mode- and characteristic-impedance-matching between the two waveguides. A pertinent analysis reveals that the optical path length of a 'trapped' light ray (associated with a particular frequency component of the pulse), as well as the corresponding effective thickness of the NRI waveguide itself, become exactly zero. The ray circulates at the point where it is trapped in such a way that its trajectory forms what we have called (in view of its characteristic hourglass form) an 'optical clepsydra'. Furthermore, we introduce a novel methodology that allows for obtaining ultra- low- or zero-loss magnetic metamaterials over a continuous range of frequencies. We analytically prove that a higher-degrees-of-freedom MM design methodology based on equivalent electrical circuits with more than one mesh leads to metamaterial magnetism with either ultra-high figures-of-merit or with perfectly lossless performance over a broad range of frequencies. The so-obtained lossless metamaterial magnetism has a truly intrinsic character, and as such is scalable and can be implemented at any frequency regime, from the radio up to the optical domain.