Time Domain Analysis of Electromagnetic Scattering From Multiple Cavities Embedded in a Ground Plane

This work examines the scattered fields produced when a transient wave is reflected from an infinite perfect electric conductor (PEC) ground plane with multiple embedded cavities. Incident and reflected waves will be decomposed into transverse magnetic to the z direction (TMz) and transverse electric to the z direction (TEz) polarizations, with primary focus given to the TMz. Cavities may be unfilled, partially filled, or fully filled with non-magnetic dielectric material and no assumptions are made regarding similarity, regularity, or periodicity. The Newmark method is used to discretize time and a variational formulation is presented for each time step. The principle outcome is to show that the variational formulation of the scalar problem is well posed. Additionally, the variational formulation is applied in a stable numerical model using the finite element-boundary integral (FE-BI) method. Interior fields are approximated using the finite element method (FEM) for each time step, then the boundary integral is applied using the appropriate Green’s function to approximate exterior scattered fields. The exterior fields for one time step provide the boundary conditions for the interior problem at the next time step. In this way, the numerical model marches through time. Various numerical experiments are run to examine the effect of coupling on aperture and external fields. Of particular interest are the differences between single-cavity and multiple-cavity solutions

Fully quantum mechanical dynamic analysis of single-photon transport in a single-mode waveguide coupled to a traveling-wave resonator

We analyze the dynamics of single photon transport in a single-mode waveguide coupled to a micro-optical resonator using a fully quantum mechanical model. We examine the propagation of a single-photon Gaussian packet through the system under various coupling conditions. We review the theory of single photon transport phenomena as applied to the system and we develop a discussion on the numerical technique we used to solve for dynamical behavior of the quantized field. To demonstrate our method and to establish robust single photon results, we study the process of adiabatically lowering or raising the energy of a single photon trapped in an optical resonator under active tuning of the resonator. We show that our fully quantum mechanical approach reproduces the semi-classical result in the appropriate limit and that the adiabatic invariant has the same form in each case. Finally, we explore the trapping of a single photon in a system of dynamically tuned, coupled optical cavities.Comment: 24 pages, 10 figure

The physics of extreme sensitivity in whispering gallery mode optical biosensors

Whispering gallery mode (WGM) optical biosensors are capable of extraordinarily sensitive specific and nonspecific detection of species suspended in a gas or fluid. Recent experimental results suggest that these devices may attain single-molecule sensitivity to protein solutions in the form of stepwise shifts in their resonance wavelength, λ_R, but present sensor models predict much smaller steps than were reported. This study examines the physical interaction between a WGM sensor and a molecule adsorbed to its surface, exploring assumptions made in previous efforts to model WGM sensor behavior, and describing computational schemes that model the experiments for which single protein sensitivity was reported. The resulting model is used to simulate sensor performance, within constraints imposed by the limited material property data. On this basis, we conclude that nonlinear optical effects would be needed to attain the reported sensitivity, and that, in the experiments for which extreme sensitivity was reported, a bound protein experiences optical energy fluxes too high for such effects to be ignored