This interdisciplinary proposal is to develop high order numerical methods to provide accurate modeling capabilities of light propagation through microphotonics. The problems of light propagation through such devices are closely related to the design of delay lines, optical buffering devices. Due to small scales of those devices and wave nature of the light signals, the accuracy of the numerical methods, especially the phase accuracy of the numerical methods, is critical in obtaining the speed and phase information of light signals through photonic devices. The development of algorithms for modeling of microphotonics such as resonant waveguides will result in advanced capabilities in solving linear and nonlinear Maxwell equations in inhomogeneous media for a wide range of engineering problems. The potential technology applications of this research will provide integration of optical elements on a single chip, to control velocity of light, to provide routing and switching functionality on a micro-scale by incorporating nonlinear optical material into the microspheres/microcylinders. These are the fundamental questions being addressed in the research communities of modern photonics. The major challenge will be the development of highly accurate and efficient numerical algorithms for the solution of linear and nonlinear Maxwell equations in layered and inhomogeneous media. The following topics will be studied: (a) Discontinuous spectral element methods for time dependent nonlinear Maxwell equations, (b) Upwinding Embedded Boundary Methods, (c) Modeling with the developed algorithms for coupled resonator optical waveguide devices. As a main goal of this proposal, we plan to find solutions to the current bottleneck problems in the designing of coupled resonator waveguides with significant impact on the development of next generation optical technologies. This includes optimization of the nanometric separation between microspheres or microcylinders to achieve a trade-off between reduced group velocity of light (desirable property for optoelectronic applications) and reduced efficiency of optical transport. This also includes understanding of the role of the size disorder existing in the presently available ensembles of microspheres and microcylinders. The results of this proposal will be directly implemented into the manufacturing of photonic devices of coupled microspheres or microcylinders in our laboratory. In addition, publicly available codes will be created for calculating of all types of optical spectra (transmission, reflection and scattering) and photonic band structures of coupled resonator waveguides. One graduate student will conduct research toward a Ph.D. degree in either optics or/and applied mathematics, and his/her participation will contribute to the educational components of the newly established Center of Optoelectronics and Optical Communications at the UNC Charlotte. Research results from this proposal, in the area of new physics and mathematical modeling tools, will be incorporated into the optics curriculum now under development at the Center, potential technology transfer of the results to the area optics industrial will be explored through the existing partnership between the Center and area optics companies. The PIs will also actively participate in the Center's technology training programs with the area high schools.
