Miguel A. Alonso, Ph.D. - US grants

Wave phenomena are central to physics and engineering. Modeling the propagation of waves, however, can be an analytical or computational challenge when the system, medium, or potential in which they propagate is complex. In these cases, the ray model is often used to obtain approximate solutions. For quantum mechanical wave functions, the "rays" correspond to classical particle trajectories. When ray information is used properly, it can give a very accurate description of wave propagation phenomena. While several ray-based methods for modeling the propagation of waves have been proposed, they often have problems and do not incorporate measures of their own accuracy The scientific goals of the work proposed here are to achieve a profound understanding of the validity of the ray model within wave theory, and to generate all-purpose ray-based methods that describe the propagation of waves in complex media with unprecedented accuracy and computational efficiency. This work will rely on two different and complementary frameworks. The first one, particularly suited for problems of wave propagation through inhomogeneous media for the case of small wavelengths, is based on assigning flexible, interconnected field contributions to the rays, such that their sum gives accurate field estimates that are asymptotically independent of the contributions' width. In preliminary studies, this framework has been shown to be free of the problems that plague other techniques, and to give estimates of great accuracy. Furthermore, a simple measure of the estimates' error is accessible. So far, this formalism has been applied only to test cases involving propagation of scalar waves in two-dimensional inhomogeneous media. In this project, the framework will be extended to describe realistic situations involving three (and higher) dimensional fields in complicated media presenting, for example, absorption, gain, and anisotropies. The application of the method to the solution of differential equations not related to wave phenomena will also be explored. The second framework relates to wave propagation in piecewise homogeneous media, and is particularly suited to the study of partially coherent fields. It is based on representations of wave fields that behave exactly as ray weights, obeying the free radiative transfer equation. These representations can reduce significantly the computation times needed for estimating the intensity, flux, or polarization of partially coherent fields in regions away from their sources. Analogous representations can be defined to describe waves in anisotropic, optically active, absorptive or gain media. These representations can also be used in the description of systems involving refraction and reflection at interfaces and of propagation through scattering media, although this might require some assumptions about the coherence properties of the field. The understanding of such assumptions will give insight into the applicability of the ray-based radiative transfer model.

The principal investigator and graduate students will participate in technical conferences organized by minority societies, as well as in outreach events for the promotion of science to the general public, particularly to underrepresented groups. Collaboration with national and foreign researchers in several different areas will be instrumental in the achievement of the goals of this project. These links will be strengthened not only through joint projects but also through participation in the organization of crossdisciplinary workshops and conferences.

Illumination with beams of light in unconventional polarization states departs from the usual, textbook description. Two popular examples of unconventional polarization states are radial and azimuthal polarizations (sometimes called Cylindrical Vector Beams). A wide variety of unconventional polarizations exist -- some have been well studied, while many remain unexplored. This research activity brings together three investigators that have been studying unconventional polarization states and their mathematical representation, the propagation and focusing of polarized light, and light scattering from small particles such as those found within biological cells.

This investigation makes use of a novel mathematical representation (complex-focus basis) for modeling optical focusing and scattering, the study of radial, azimuthal, and Full Poincare fields as representatives of a complex-focus basis, and the scattering of unconventional polarization states from mesoscopic particles, including cell organelles. In the process, we also address the formulation and testing of a theory of partially coherent unconventional polarization states, the coupling of unconventional polarization states to nanostructures, and develop numerically efficient theoretical models for coherent and partially coherent light propagation. We make use of the recently-introduced concept of stress- engineered optical elements to adapt an existing light scattering microscope to carry out polarization- sensitive scattering experiments. In the process, we are advancing optical physics by introducing new analytic tools for scattering analysis, a new experimental tool for rapid-acquisition pupil polarimetry, and find better ways to use polarization as a tool for improving projection imaging systems such as LCD projectors and semiconductor lithography systems.

Polarization--the vector nature of light--influences the scattering of light in profound ways, and is therefore fundamental to how we gain information about a scatterer from the scattered light. This has been used to good result in advancing cell identification for immune cell research, for example. Scattering is also important in the inspection processes that are used to guarantee high quality semiconductor circuits for computers and electronic devices. A better understanding of the physics of new polarization states will therefore have a broad impact on fields such as optical engineering and biomedical optics. The educational impact is seen annually through involvement by both undergraduates and graduate students, not merely as research assistants, but as students in training who are encouraged toward independent initiatives. Our role as educators at the Institute of Optics offers us a unique platform from which to take the results of the work, bring them into the classroom at the MS and BS levels, and to take the exciting features of polarized light with us on educational activities in area schools and science museums. Our presence at the Institute of Optics offers technology transfer to over 30 companies who are members of our Industrial Associates Program.

Polarized light (light with directional vibrations whose effects can sometimes be seen in changes in attenuation while rotating polarizing sunglasses) is everywhere--it is in the blue sky, the reflection from a pond, in light scattering from natural and manmade airborne particles, and in the display screens on our smartphones. The understanding and use of polarized light is central to both the science of light and to applications ranging from medicine to consumer electronics. For example, some of the triumphs of the computer information revolution have been built around manufacturing technologies that require almost unimaginable precision in measurements--many of which are light-based and use the polarization of light in ways that can be precisely controlled and measured. The proposed research uses the concept of an "unconventional polarization state" - a special form of light in which the polarization varies across the width of a laser beam - to explore fundamentally new ways of carrying out light-based measurements. In conjunction with some special optical devices, it is possible to use an ordinary camera to create a visual map of the polarization in a single image, something that ordinarily requires a sequence of four or more images and accompanying algorithms. These measurement methods will also spur new ways of thinking about how to execute the simultaneous measurement of sub-nanometer process errors in microelectronics manufacturing.

The multiple measurements required to characterize the polarization of an ultrafast laser pulse or individual photon require either a time-sequential operation or explicit division of the amplitude into different detector ports. While each of these has been used to good success, there is a need to truly extend polarization measurements in a way that the maximum amount of polarization information is extracted from each measured photon (in the case of low light levels) or each pulse (in the case of ultrafast pulse characterization). Because the method is extendable to the mapping of polarization over a sampled image field, it is possible to extend the concept to capture either angle- or frequency-resolved polarization information in a single image. The investigation also applies the new physics of unconventional polarization states to the now-famous physics of weak measurements by using unconventionally polarized light to measure two or more physical quantities in a single measurement. This concept will be tested by measuring nanoscale features in a microscope equipped with a liquid crystal controller that defines a field with arbitrary polarization, amplitude, and phase for focused beam scatterometry. The work is expected to impact allied areas of physics (through the introduction of new measurement methods), optical engineering (specifically, polarization engineering and image formation), biomedical optics (in medical imaging and spectroscopy), environmental science (through the use of polarimetric light scattering for aerosol characterization), and semiconductor inspection.