The technique of single particle Total Internal Reflection Microscopy (TIRM) has been used to study the scattering intensity from levitated microspheres. TIRM can be used to monitor the separation between microscopic spheres immersed in liquid (water in our case) and a surface with nm resolution. In the technique, microspheres scatter light when the evanescent waves are incident upon them. The intensity of the scattered light is directly related to the height above the surface and allows determination of the height. From the separation distance histograms, the interaction between the microsphere and interface may be characterized with a force resolution in the range of 0.01 picoNewtons. Such a system can be applied to the measurement of biomolecular interactions biomolecules attached to the microsphere and the surface. The intensity and scattering pattern of this light has been modeled using a modified Mie theory which accounts for the evanescent nature of the incident light. Diffusing Colloidal Probe Microscopy (DCPM) is an extension of the TIRM technique that simultaneously monitors multiple microsphere probes. The use of multiple probes introduces the issue of probe polydispersity. When measured at the surface, a variation in scattered light intensity of nearly one order of magnitude has been observed from a purchased microsphere sample. Thus the polydisperse collection of microspheres adds significant complexity to the scattered light signal. It is hypothesized that the dependence of the total scattered light intensity on microsphere size accounts for the scattered intensity distribution in a polydisperse microsphere sample. Understanding this variation in the scattered light with microsphere size will allow improved characterization of the microsphere/surface separation. Additionally, larger microspheres have the ability to resonantly confine light and produce spectrally narrow Whispering Gallery Modes (WGMs). It is hypothesized that WGMs may be excited in microspheres with the DCPM system. These modes may be used as a refractometric biosensor with high sensitivity to local refractive index changes on the surface of the microsphere. This research involves modeling scattered intensity distributions for polydispersed collections of microspheres based on modified Mie theory. The theoretical results are compared to experimentally obtained results and found to qualitatively explain the scattered light intensity distribution in a multiple probe DCPM system. This is an important result suggesting that microsphere size variation plays a major role in determining the distribution of scattered intensity in multiple microsphere probe systems. This work also suggests that it may be possible to excite such WGMs in a DCPM system. The introduction of WGMs would enable refractometric biosensing in such evanescent mode systems.

The technique of single particle Total Internal Reflection Microscopy (TIRM) has been used to study the scattering intensity from levitated microspheres. TIRM can be used to monitor the separation between microscopic spheres immersed in liquid (water in our case) and a surface with nm resolution. In the technique, microspheres scatter light when the evanescent waves are incident upon them. The intensity of the scattered light is directly related to the height above the surface and allows determination of the height. From the separation distance histograms, the interaction between the microsphere and interface may be characterized with a force resolution in the range of 0.01 picoNewtons. Such a system can be applied to the measurement of biomolecular interactions biomolecules attached to the microsphere and the surface. The intensity and scattering pattern of this light has been modeled using a modified Mie theory which accounts for the evanescent nature of the incident light. Diffusing Colloidal Probe Microscopy (DCPM) is an extension of the TIRM technique that simultaneously monitors multiple microsphere probes. The use of multiple probes introduces the issue of probe polydispersity. When measured at the surface, a variation in scattered light intensity of nearly one order of magnitude has been observed from a purchased microsphere sample. Thus the polydisperse collection of microspheres adds significant complexity to the scattered light signal. It is hypothesized that the dependence of the total scattered light intensity on microsphere size accounts for the scattered intensity distribution in a polydisperse microsphere sample. Understanding this variation in the scattered light with microsphere size will allow improved characterization of the microsphere/surface separation. Additionally, larger microspheres have the ability to resonantly confine light and produce spectrally narrow Whispering Gallery Modes (WGMs). It is hypothesized that WGMs may be excited in microspheres with the DCPM system. These modes may be used as a refractometric biosensor with high sensitivity to local refractive index changes on the surface of the microsphere. This research involves modeling scattered intensity distributions for polydispersed collections of microspheres based on modified Mie theory. The theoretical results are compared to experimentally obtained results and found to qualitatively explain the scattered light intensity distribution in a multiple probe DCPM system. This is an important result suggesting that microsphere size variation plays a major role in determining the distribution of scattered intensity in multiple microsphere probe systems. This work also suggests that it may be possible to excite such WGMs in a DCPM system. The introduction of WGMs would enable refractometric biosensing in such evanescent mode systems.

Ever-increasing interest in millimeter-wave and terahertz spectrum has prompted research and development of novel passive components working at these frequencies. Compared with the conventional planar components, non-planar dielectric devices become more attractive as frequencies increase due to their higher quality factors and dimensional tolerances. In this thesis, we present fast methods to analyze the millimeter-wave dielectric resonator and rod antenna. First, an analytical method has been developed to evaluate resonant frequencies, quality factors of the Whispering Gallery Mode (WGM) disk resonators and also the resonator-waveguide coupling. A numerical solver based on full-wave finite element method is implemented to verify the analytical result. This analytical model provides a solution for fast design and optimization of WGM resonators in filter and sensor applications. Secondly, a fast analytical approach based on local mode theory is introduced to calculate the radiation from tapered dielectric rod antenna. This efficient approximate model consumes much less computing resources and time, and demonstrates good agreements with full-wave numerical results. It supplies a quantitative way to understand the radiation mechanism and interaction between different parts of the antenna. Based on this, design criteria for the taper profile of rod antennas are given.

Ever-increasing interest in millimeter-wave and terahertz spectrum has prompted research and development of novel passive components working at these frequencies. Compared with the conventional planar components, non-planar dielectric devices become more attractive as frequencies increase due to their higher quality factors and dimensional tolerances. In this thesis, we present fast methods to analyze the millimeter-wave dielectric resonator and rod antenna. First, an analytical method has been developed to evaluate resonant frequencies, quality factors of the Whispering Gallery Mode (WGM) disk resonators and also the resonator-waveguide coupling. A numerical solver based on full-wave finite element method is implemented to verify the analytical result. This analytical model provides a solution for fast design and optimization of WGM resonators in filter and sensor applications. Secondly, a fast analytical approach based on local mode theory is introduced to calculate the radiation from tapered dielectric rod antenna. This efficient approximate model consumes much less computing resources and time, and demonstrates good agreements with full-wave numerical results. It supplies a quantitative way to understand the radiation mechanism and interaction between different parts of the antenna. Based on this, design criteria for the taper profile of rod antennas are given.

The technique of single particle Total Internal Reflection Microscopy (TIRM) has been used to study the scattering intensity from levitated microspheres. TIRM can be used to monitor the separation between microscopic spheres immersed in liquid (water in our case) and a surface with nm resolution. In the technique, microspheres scatter light when the evanescent waves are incident upon them. The intensity of the scattered light is directly related to the height above the surface and allows determination of the height. From the separation distance histograms, the interaction between the microsphere and interface may be characterized with a force resolution in the range of 0.01 picoNewtons. Such a system can be applied to the measurement of biomolecular interactions biomolecules attached to the microsphere and the surface. The intensity and scattering pattern of this light has been modeled using a modified Mie theory which accounts for the evanescent nature of the incident light. Diffusing Colloidal Probe Microscopy (DCPM) is an extension of the TIRM technique that simultaneously monitors multiple microsphere probes. The use of multiple probes introduces the issue of probe polydispersity. When measured at the surface, a variation in scattered light intensity of nearly one order of magnitude has been observed from a purchased microsphere sample. Thus the polydisperse collection of microspheres adds significant complexity to the scattered light signal. It is hypothesized that the dependence of the total scattered light intensity on microsphere size accounts for the scattered intensity distribution in a polydisperse microsphere sample. Understanding this variation in the scattered light with microsphere size will allow improved characterization of the microsphere/surface separation. Additionally, larger microspheres have the ability to resonantly confine light and produce spectrally narrow Whispering Gallery Modes (WGMs). It is hypothesized that WGMs may be excited in microspheres with the DCPM system. These modes may be used as a refractometric biosensor with high sensitivity to local refractive index changes on the surface of the microsphere. This research involves modeling scattered intensity distributions for polydispersed collections of microspheres based on modified Mie theory. The theoretical results are compared to experimentally obtained results and found to qualitatively explain the scattered light intensity distribution in a multiple probe DCPM system. This is an important result suggesting that microsphere size variation plays a major role in determining the distribution of scattered intensity in multiple microsphere probe systems. This work also suggests that it may be possible to excite such WGMs in a DCPM system. The introduction of WGMs would enable refractometric biosensing in such evanescent mode systems.

New methods of biological analyte sensing are needed for development of miniature biosensors that are highly sensitive and require minimal sample preparation. One novel technique employs optical resonances known as Whispering Gallery Modes (WGMs). These modes arise from total internal reflection of light at the internal surface of a high index microsphere within a low index medium and produce an evanescent field that extends into the surrounding medium. The WGMs produce multiple narrow spectral peaks that shift position with variations in the local index of refraction sampled by the evanescent tail of the WGMs. To excite these WGMs, we embed quantum dots (QDs) in the periphery of polystyrene microspheres to serve as local light sources. By coupling emission from the QDs to the WGMs, the sensors can be excited and interrogated remotely and, by monitoring the shift of multiple resonance modes, may provide higher sensitivity and accuracy compared with similar techniques. The high refractometric sensitivity of the WGMs offers potential for trace detection of molecules adsorbed onto or bound to the microsphere sensor elements. The sensitivity of these sensors is demonstrated by monitoring the wavelength shift of multiple resonant modes as bulk index of refraction is changed. The potential for targeted biosensing is explored through addition of a protein that adsorbs to the microsphere surface, thrombin. Microsensor response in all cases demonstrated increased sensitivity over theoretical predictions. Models based on Mie theory and continuity of the radial functions across the sphere-media interface were used to model the location, Q-factor, and sensitivity of the WGMs in microspheres by considering the embedded QDs as a high index outer layer. This model was used, along with estimates of the QD-layer index and penetration depth, to relate the locations and sensitivities of the modes to our experimental results with strong agreement between the two. In all, these microspheres demonstrate feasibility for use as remote microsensors with sensitivities rivaling current techniques.

The technique of single particle Total Internal Reflection Microscopy (TIRM) has been used to study the scattering intensity from levitated microspheres. TIRM can be used to monitor the separation between microscopic spheres immersed in liquid (water in our case) and a surface with nm resolution. In the technique, microspheres scatter light when the evanescent waves are incident upon them. The intensity of the scattered light is directly related to the height above the surface and allows determination of the height. From the separation distance histograms, the interaction between the microsphere and interface may be characterized with a force resolution in the range of 0.01 picoNewtons. Such a system can be applied to the measurement of biomolecular interactions biomolecules attached to the microsphere and the surface. The intensity and scattering pattern of this light has been modeled using a modified Mie theory which accounts for the evanescent nature of the incident light. Diffusing Colloidal Probe Microscopy (DCPM) is an extension of the TIRM technique that simultaneously monitors multiple microsphere probes. The use of multiple probes introduces the issue of probe polydispersity. When measured at the surface, a variation in scattered light intensity of nearly one order of magnitude has been observed from a purchased microsphere sample. Thus the polydisperse collection of microspheres adds significant complexity to the scattered light signal. It is hypothesized that the dependence of the total scattered light intensity on microsphere size accounts for the scattered intensity distribution in a polydisperse microsphere sample. Understanding this variation in the scattered light with microsphere size will allow improved characterization of the microsphere/surface separation. Additionally, larger microspheres have the ability to resonantly confine light and produce spectrally narrow Whispering Gallery Modes (WGMs). It is hypothesized that WGMs may be excited in microspheres with the DCPM system. These modes may be used as a refractometric biosensor with high sensitivity to local refractive index changes on the surface of the microsphere. This research involves modeling scattered intensity distributions for polydispersed collections of microspheres based on modified Mie theory. The theoretical results are compared to experimentally obtained results and found to qualitatively explain the scattered light intensity distribution in a multiple probe DCPM system. This is an important result suggesting that microsphere size variation plays a major role in determining the distribution of scattered intensity in multiple microsphere probe systems. This work also suggests that it may be possible to excite such WGMs in a DCPM system. The introduction of WGMs would enable refractometric biosensing in such evanescent mode systems.

Thesis (D. Min.)--New Orleans Baptist Theological Seminary, 2000. / Includes abstract and vita. Includes bibliographical references (leaves 69-77).

Optical whispering-gallery mode (WGM) cavities, which exhibit extraordinary spatial and temporal confinement of light, are one of the leading transducers for examining molecular recognition at low particle counts. With the advent of hybrid photonic-plasmonic and increasingly sophisticated forms of these resonators, the importance of supporting numerical methods has correspondingly become evident. In response, we adopt a full-vector finite difference approximation in order to solve for WGM's in terms of their field distributions, resonant wavelengths, and quality factors in the context of naturally discontinuous permittivity structure. A segmented Taylor series and alignment/rotation operator are utilized at such singularities in conjunction with arbitrarily spaced grid points. Simulations for microtoroids, with and without dielectric nanobeads, and plasmonic microdisks are demonstrated for short computation times and shown to be in agreement with data in the literature. Constricted surface plasmon polariton (SPP) WGM's are also featured within this document. The module of this thesis is devised as a keystone for composite WGM models that may guide experiments in the field. / Graduate

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