Mixed-Hybrid Formulation of Multidimensional Fracture Flow

We shall study Darcy flow on the heterogeneous system of 3D, 2D, and 1D domains and we present four models for coupling of the flow. For one of these models, we describe in detail its mixed-hybrid formulation. Finally, we show that Schur complements are suitable for solution of the linear system resulting form the lowest order approximation of the mixed-hybrid formulation

Random Raman Lasing

The propagation of light in turbid media is something that is experienced by everyone, everywhere, everyday. These dynamics play an essential role in everything from the color of a material, to the multitude of colors present during a sunset. Considering the central role of these dynamics, there are still a great deal of outstanding questions that remain to be answered. Nonlinear light propagation in turbid media is one such question, with far ranging applications in biomedical imaging where it has potential to elucidate many biological processes label-free and in vivo. Conventional wisdom suggests that nonlinear effects, such as stimulated Raman scattering (SRS), should not play a significant role in the propagation of light through random media. The diffusive nature of elastic scattering restricts the interaction distance by limiting the depth at which high intensities can be delivered, thus reducing the efficiency of nonlinear optical effects. However, light scattering can dramatically increase the interaction length by multiply scattering the photons in a random walk type motion, making the overall outcome somewhat hard to predict. Random Raman lasing uses SRS as the primary gain mechanism for a lasing process that receives feedback through multiple elastic scattering in the material. This is a fundamentally new optical system that pushes the boundaries of the understanding of light propagation in turbid media. The discovery of this lasing system will be presented along with several fundamental measurements of the process, some of which contrast with classical light transport theory and point towards exciting new physics. Furthermore, random Raman lasing opens the door to many exciting applications ranging from remote chemical identification at unprecedented range, in a single laser pulse, to a revolutionary new light source for imaging microscopy 10,000 times brighter than conventional sources while maintaining the low spatial coherence required for speckle-free imaging

Enhanced Optical Coupling and Raman Scattering via Microscopic Interface Engineering

Spontaneous Raman scattering is an extremely powerful tool for the remote detection and identification of various chemical materials. However, when those materials are contained within strongly scattering or turbid media, as is the case in many biological and security related systems, the sensitivity and range of Raman signal generation and detection is severely limited. Here, we demonstrate that through microscopic engineering of the optical interface, the optical coupling of light into a turbid material can be substantially enhanced. This improved coupling facilitates the enhancement of the Raman scattering signal generated by molecules within the medium. In particular, we detect at least two-orders of magnitude more spontaneous Raman scattering from a sample when the pump laser light is focused into a microscopic hole in the surface of the sample. Because this approach enhances both the interaction time and interaction region of the laser light within the material, its use will greatly improve the range and sensitivity of many spectroscopic techniques, including Raman scattering and fluorescence emission detection, inside highly scattering environments

Enhanced Coupling of Light into a Turbid Medium through Microscopic Interface Engineering

There are many optical detection and sensing methods used today that provide powerful ways to diagnose, characterize, and study materials. For example, the measurement of spontaneous Raman scattering allows for remote detection and identification of chemicals. Many other optical techniques provide unique solutions to learn about biological, chemical, and even structural systems. However, when these systems exist in a highly scattering or turbid medium, the optical scattering effects reduce the effectiveness of these methods. In this article, we demonstrate a method to engineer the geometry of the optical interface of a turbid medium, thereby drastically enhancing the coupling efficiency of light into the material. This enhanced optical coupling means that light incident on the material will penetrate deeper into (and through) the medium. It also means that light thus injected into the material will have an enhanced interaction time with particles contained within the material. These results show that, by using the multiple scattering of light in a turbid medium, enhanced light-matter interaction can be achieved; this has a direct impact on spectroscopic methods such as Raman scattering and fluorescence detection in highly scattering regimes. Furthermore, the enhanced penetration depth achieved by this method will directly impact optical techniques that have previously been limited by the inability to deposit sufficient amounts of optical energy below or through highly scattering layers