Photonic crystals have allowed unprecedented control of light and have allowed bringing new functionalities on chip. Photonic crystal waveguides (PCWs), which are linear defects in a photonic crystal, have unique features that distinguish these waveguides from other waveguides. The unique features include very large dispersion, existence of slow light, and the possibility of tailoring the dispersion properties for guiding light. In my research, I have overcome some of the challenges in using slow light in PCWs. In this work, I have demonstrated (i) high efficiency coupling of light into slow group velocity modes of a PCW, (ii) large bandwidth high transmission and low dispersion bends in PCWs, (iii) accurate modeling of pulse propagation in PCWs, (iv) high efficiency absorbing boundary conditions for dispersive slow group velocity modes of PCWs. To demonstrate the utility of slow light in designing high efficiency devices, I have demonstrated refractive index sensors using slow light in PCWs. In the end, a few high efficiency devices based on slow light in PCWs are mentioned. The remaining issues in the widespread use of PCW are also discussed in the last chapter.

Thesis (M.S. in Applied Science (Signal Processing))--Naval Postgraduate School, June 2004. / Thesis advisor(s): Lawrence J. Ziomek. Includes bibliographical references (p. 47). Also available online.

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We numerically investigate electron transport properties in an electron waveguide which can be constructed in 2DEG of the heterostructure of GaAs and AlGaAs. We apply R-matrix theory to solve a Schrödinger equation and construct a S-matrix, and we then calculate conductance of an electron waveguide. We study single impurity scattering in a waveguide. A [delta]-function model as a single impurity is very attractive, but it has been known that [delta]-function potential does not give a convergent result in two or higher space dimensions. However, we find that it can be used as a single impurity in a waveguide with the truncation of the number of modes. We also compute conductance for a finite size impurity by using R-matrix theory. We propose an appropriate criteria for determining the cut-off mode for a [delta]-function impurity that reproduces the conductance of a waveguide when a finite impurity presents. We find quantum scattering echoes in a ripple waveguide. A ripple waveguide (or cavity) is widely used for quantum chaos studies because it is easy to control a particle's dynamics. Moreover we can obtain an exact expression of Hamiltonian matrix with for the waveguide using a simple coordinate transformation. Having an exact Hamiltonian matrix reduces computation time significantly. It saves a lot of computational needs. We identify three families of resonance which correspond to three different classical phase space structures. Quasi bound states of one of those resonances reside on a hetero-clinic tangle formed by unstable manifolds and stable manifolds in the phase space of a corresponding classical system. Resonances due to these states appear in the conductance in a nearly periodic manner as a function of energy. Period from energy frequency gives a good agreement with a prediction of the classical theory. We also demonstrate wavepacket dynamics in a ripple waveguide. We find quantum echoes in the transmitted probability of a wavepacket. The period of echoes also agrees with the classical predictions. We also compute the electron transmission probability through a multi-ripple electron waveguide. We find an effect analogous to the Dicke effect in the multi-ripple electron waveguide. We show that one of the S-matrix poles, that of the super-radiant resonance state, withdraws further from the real axis as each ripple is added. The lifetime of the super-radiant state, for N quantum dots, decreases as [1/N] . This behavior of the lifetime of the super-radiant state is a signature of the Dicke effect. / text

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Numerical analysis of the electromagnetic fields in large, complex structures is very challenging due to the high computational overhead. Recently, it has been shown that a new method called Trefftz-FLAME ( Flexible Local Approximation MEthod) is suitable for problems where there exist a large number of similar structures. / This thesis develops Trefftz-FLAME in two areas. First, a novel 2D Trefftz-FLAME method incorporates the modal analysis and port boundary condition that are essential to an accurate calculation of reflection and transmission coefficients for photonic crystal devices. The new technique outperforms existing methods in both accuracy and computational cost. / The second area pertains to the 3D, vector problem of electromagnetic wave scattering by aggregates of identical dielectric particles. A methodology for the development of local basis functions is introduced, applicable to particles of any shape and composition. Boundary conditions on the surface of the finite FLAME domain are described, capable of representing the incident wave and absorbing the outgoing radiation. A series of problems involving dielectric spheres is solved to validate the new method. Comparison with exact solutions is possible in some cases and shows that the method is able to produce accurate near-field results even when the computational grid spacing is equal to the radius of the spheres.

Planar optical waveguides fabricated by K$ sp+$-Na$ sp+$ ion-exchange in soda-lime glass substrates are investigated. / Experimental characterizations of planar waveguide with respect to a wide range of fabrication conditions have been carried out, including detailed measurements of the refractive index anisotropy resulting from the large induced surface stresses. / Parallel to this, the non-linear diffusion process of ion-exchange was simulated numerically to provide, along with the results of the characterizations, a complete description of the refractive index profile from any set of fabrication conditions. / The magnitude of the maximum surface index change observed was shown theoretically to be almost entirely due to the induced stress at the surface of the substrate, arising from the presence of the larger potassium ions. / Finally, a novel class of single-mode channel waveguides, made by a "two-step" ion-exchange was analyzed. A simple model for these waveguides was developed and used in the design of two directional coupler structures which were fabricated and measured. / The two-step process was conceived because it relaxes waveguides' dimensional control, yielding single-mode guides of larger size, better suited for low-loss connections to optical fibers. It also provides an additional degree of freedom to adjust device properties.

This dissertation reports a metal-transfer-molding (MTM) technique for simultaneous implementation of air-lifted RF passive components, as well as coplanar waveguide (CPW) structures, in a high performance and potentially cost-effective fashion. A metal transfer mechanism is introduced into the conventional micro-molding process to realize polymer-core RF passive components and integration. A system-on-package (SOP) integration scheme of front-end RF components can be realized by this process. Several air-lifted RF components based on MTM technology have been presented with excellent performance. As an integration application of the MTM technology, a novel wireless passive airflow sensor based on the RF evanescent-mode cavity resonators has been also presented. The sensor makes use of RF technology to measure wind velocity through changes in the resonant frequency with applied airflow. Compared with reported wireless sensors based on conventional RF cavity resonator, this design has advantages such as compact size and greatly improved sensitivity. Wireless interrogating has also been demonstrated for the passive sensor. Overall, the RF components developed in this thesis illustrate the great potential of MTM technology in both wireless communication and sensor areas.

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