Nonlinear parameter retrieval from three- and four-wave mixing in metamaterials

We present a generalized nonlinear susceptibility retrieval method for metamaterials based on transfer matrices and valid in the nondepleted pump approximation. We construct a general formalism to describe the transfer matrix method for nonlinear media and apply it to the processes of three- and four-wave mixing. The accuracy of this approach is verified via finite element simulations. The method is then reversed to give a set of equations for retrieving the nonlinear susceptibility. Finally, we apply the proposed retrieval operation to a three-wave mixing transmission experiment performed on a varactor loaded split ring resonator metamaterial sample and find quantitative agreement with an analytical effective medium theory model. © 2010 The American Physical Society.

Control of radiative processes using tunable plasmonic nanopatch antennas.

The radiative processes associated with fluorophores and other radiating systems can be profoundly modified by their interaction with nanoplasmonic structures. Extreme electromagnetic environments can be created in plasmonic nanostructures or nanocavities, such as within the nanoscale gap region between two plasmonic nanoparticles, where the illuminating optical fields and the density of radiating modes are dramatically enhanced relative to vacuum. Unraveling the various mechanisms present in such coupled systems, and their impact on spontaneous emission and other radiative phenomena, however, requires a suitably reliable and precise means of tuning the plasmon resonance of the nanostructure while simultaneously preserving the electromagnetic characteristics of the enhancement region. Here, we achieve this control using a plasmonic platform consisting of colloidally synthesized nanocubes electromagnetically coupled to a metallic film. Each nanocube resembles a nanoscale patch antenna (or nanopatch) whose plasmon resonance can be changed independent of its local field enhancement. By varying the size of the nanopatch, we tune the plasmonic resonance by ∼ 200 nm, encompassing the excitation, absorption, and emission spectra corresponding to Cy5 fluorophores embedded within the gap region between nanopatch and film. By sweeping the plasmon resonance but keeping the field enhancements roughly fixed, we demonstrate fluorescence enhancements exceeding a factor of 30,000 with detector-limited enhancements of the spontaneous emission rate by a factor of 74. The experiments are supported by finite-element simulations that reveal design rules for optimized fluorescence enhancement or large Purcell factors.

Application of Numerical Methods to Study Arrangement and Fracture of Lithium-Ion Microstructure

The focus of this work is to develop and employ numerical methods that provide characterization of granular microstructures, dynamic fragmentation of brittle materials, and dynamic fracture of three-dimensional bodies.

We first propose the fabric tensor formalism to describe the structure and evolution of lithium-ion electrode microstructure during the calendaring process. Fabric tensors are directional measures of particulate assemblies based on inter-particle connectivity, relating to the structural and transport properties of the electrode. Applying this technique to X-ray computed tomography of cathode microstructure, we show that fabric tensors capture the evolution of the inter-particle contact distribution and are therefore good measures for the internal state of and electronic transport within the electrode.

We then shift focus to the development and analysis of fracture models within finite element simulations. A difficult problem to characterize in the realm of fracture modeling is that of fragmentation, wherein brittle materials subjected to a uniform tensile loading break apart into a large number of smaller pieces. We explore the effect of numerical precision in the results of dynamic fragmentation simulations using the cohesive element approach on a one-dimensional domain. By introducing random and non-random field variations, we discern that round-off error plays a significant role in establishing a mesh-convergent solution for uniform fragmentation problems. Further, by using differing magnitudes of randomized material properties and mesh discretizations, we find that employing randomness can improve convergence behavior and provide a computational savings.

The Thick Level-Set model is implemented to describe brittle media undergoing dynamic fragmentation as an alternative to the cohesive element approach. This non-local damage model features a level-set function that defines the extent and severity of degradation and uses a length scale to limit the damage gradient. In terms of energy dissipated by fracture and mean fragment size, we find that the proposed model reproduces the rate-dependent observations of analytical approaches, cohesive element simulations, and experimental studies.

Lastly, the Thick Level-Set model is implemented in three dimensions to describe the dynamic failure of brittle media, such as the active material particles in the battery cathode during manufacturing. The proposed model matches expected behavior from physical experiments, analytical approaches, and numerical models, and mesh convergence is established. We find that the use of an asymmetrical damage model to represent tensile damage is important to producing the expected results for brittle fracture problems.

The impact of this work is that designers of lithium-ion battery components can employ the numerical methods presented herein to analyze the evolving electrode microstructure during manufacturing, operational, and extraordinary loadings. This allows for enhanced designs and manufacturing methods that advance the state of battery technology. Further, these numerical tools have applicability in a broad range of fields, from geotechnical analysis to ice-sheet modeling to armor design to hydraulic fracturing.