Since 1970, there have been many analytic theories studying waveguide modes in optical fibers. As the years progressed, the structure of optical fiber and its characteristics have undergone many changes. In recent years, the methods of analysis have also evolved into a more numerical style, such as the finite element and finite difference approach. In this thesis, we propose a semi-analytic, coupled Ez and Hz method for solving a multiple layered piecewise constant cylindrical dielectric waveguides. In our mathematical model, we are able to handle any arbitrary layered structure, in particular, the step-index fiber, W-type fiber, and dielectric tubes. Within each layer, we express the azimuthal field components in terms of Bessel functions whose coefficients are determined by two pairs of Ez and Hz components that define the layer. By equating the transverse fields (above) on either side of each layer interface the coupled field equations are derived. The field components are either real, or purely imaginary, this allows us to formulate our matrix in real arithmetic. Further simplification is possible by using the Wronskians of the Bessel functions. The resulting matrices are both real and symmetric, which is consistent with the reciprocity principle. Compared to the traditional formulation from the early 1970s, we have reduced the variables by half and extended the formulation to include any arbitrary number of layers. Numerous numerical results are presented in this thesis for all three types of fiber previously mentioned. Both lower-order modes as well as higher-order modes including TE, TM, HE, and EH modes are presented and discussed. Our formulations are compared to that of textbook formulas for the simple two-layered step index fiber, and are found to be identical.

In this study, an investigation was undertaken to research the use of holographic phase masks (HPMs) in photo-thermo-refractive (PTR) glass as mode converters for linearly polarized (LP) fiber modes. A Spatial Light Modulator (SLM) was used to generate higher-order transverse fiber modes LPm,n. Under proper incidence condition on the holographic device, LPm,n modes are diffracted and simultaneously converted into higher order or lower order LP modes. The process was analyzed by imaging the far field on a CCD camera. It is demonstrated that using this novel method of converting transverse fiber modes several combinations of LP modes can be converted to each other with mode conversion efficiencies up to 70%. Mode purities were found to be around 85% for up conversion and around 90% for down conversion, respectively. It is noticed that this approach has several promising applications such as mode multiplexing, beam cleaning and power scaling of higher-order mode fiber lasers and amplifiers by combining mode conversion and beam combining.

Since aggressive cancers are frequently hypermetabolic with angiogenic vessels, quantification of blood flow (BF) can be vital for cancer diagnosis. Our laboratory has developed a noncontact diffuse correlation tomography (ncDCT) system for 3-D imaging of BF distribution in deep tissues (up to centimeters). The ncDCT system employs two sets of optical lenses to project source and detector fibers respectively onto the tissue surface, and applies finite element framework to model light transportation in complex tissue geometries. This thesis reports our first step to adapt the ncDCT system for 3-D imaging of BF contrasts in human breast tumors. A commercial 3-D camera was used to obtain breast surface geometry which was then converted to a solid volume mesh. An ncDCT probe scanned over a region of interest on the breast mesh surface and the measured boundary data were used for 3-D image reconstruction of BF distribution. This technique was tested with computer simulations and in 28 patients with breast tumors. Results from computer simulations suggest that relatively high accuracy can be achieved when the entire tumor was within the sensitive region of diffuse light. Image reconstruction with a priori knowledge of the tumor volume and location can significantly improve the accuracy in recovery of tumor BF contrasts. In vivo ncDCT imaging results from the majority of breast tumors showed higher BF contrasts in the tumor regions compared to the surrounding tissues. Reconstructed tumor depths and dimensions matched ultrasound imaging results when the tumors were within the sensitive region of light propagation. The results demonstrate that ncDCT system has the potential to image BF distributions in soft and vulnerable tissues without distorting tissue hemodynamics. In addition to this primary study, detector fibers with different modes (i.e., single-mode, few-mode, multimode) for photon collection were experimentally explored to improve the signal-to-noise ratio of diffuse correlation spectroscopy flow-oximeter measurements.