The two-century struggle to measure chiroptical properties of organized, anisotropic media leaves an enormous hole in the science of molecular and materials chirality. What little has been learned during the past three decades has come haltingly. In order to unravel averaged, pseudo-scalar solution chiroptical effects into quantities that can be compared with electronic structures of real molecules, a database of molecular crystal tensors is required. They must be measured using a methodology that is robust, can be easily adopted, and can generate the quantity of data that enables comparison, analysis, and understanding. Mueller matrix imaging polarimetry is the solution because all linear optical properties can be determined simultaneously, it can assay depolarization in imperfect samples, and is suited to the treatment of non-normal incidence analytically. A fast device without moving optical components will require the synchronous operation of four photoelastic modulators. This has never been achieved but will be carried out with Hinds Instruments of Hillsboro, Oregon, a leading developer of photoelastic modulators and polarimeters, through collaboration of postdoctoral researchers in Oregon and New York. The need for a commercial, turnkey polarimeter for oriented materials is essential because chiroptical anisotropy is a chasm too large for one group to bridge. With this device, the optical rotation of isomorphous molecular crystals that lend themselves to the interpretation of small structural perturbations will be measured. To avoid complications associated with excitonic interactions in resonance, the anisotropy of circular dichroism of "oriented gases" of dyes in host crystals will be studied. Mueller matrix microscopes and polarimeters are also applicable to meso-structured materials such as cholesteric liquid crystals and chiral sculpted meta-materials.
NON TECHNICAL Exactly two hundred years ago (1811) François Arago first observed the rotation of the plane of light polarization passing through a crystal of quartz along the direction of highest symmetry. It is been said that no phenomenon "has had so profound an effect on chemical thought as that of natural optical rotatory power" (Liehr, 1954. Unfortunately, since that time it has been almost impossible to measure optical rotation in organized media like crystals along general directions because the electromagnetic field of light suffers greater perturbations in low-symmetry environments that mask the phenomenon of interest. Thus, we remain ignorant about the orientation dependence of optical rotation in molecules, a fundamental light-matter interaction. Our project is aimed at developing an instrument for measuring the polarization state of light in any medium quickly and accurately enough so that we can derive the essential quantities. The device is based on photoelastic modulators that can change the polarization state of light at a rate of ~50,000 times per second. Using four such modulators, built by our GOALI partner, Hinds instruments, we can generate a complex signal that can be treated by the mathematical techniques of one of Arago's colleagues', Fourier. We have established a relationship with the Bronx Academy of Science and Technology, an underserved public high school with 98% native Spanish speakers. We provide, in addition to research opportunities in our lab during the summer and academic year, SAT tutoring, an advantage commonly exercised in wealthy school districts. We are convinced that creating scientists, especially those from underrepresented groups, requires first developing within students, one-by-one, scientific identities, and ensuring that the basics are attended.
tellectual Merits. In 2010, we proposed to put an end to our two-century struggle to measure chiroptical properties of organized, anisotropic media. Here we refer to the differential optical responses of left and right helically polarized light that occur in materials that also show distinct properties of different directions. The coexistence of anisotropy, a comparatively large effect, with optical activity, a comparatively small effect, has presented severe technical challenges related to characterizing the latter, thus leaving an enormous hole in the science of molecular and materials chirality. In order to make the requisite measurements we proposed a new methodology that required building a new kind of instrument, an optical polarimeter capable of delivering the entire so-called Mueller matrix without any moving parts. The Mueller matrix is the operator that transforms the input polarization state into the output polarization state. Mueller matrix imaging polarimetry is the solution because all linear optical properties can be determined simultaneously, it can assay depolarization in imperfect samples, and is suited to the treatment of non-normal incidence analytically. For this device to operate without moving optical components we synchronously run of four photoelastic modulators of different frequency. Photoelastic modulators sinusoidally change the polarization state of light rapidly. Our polarimeter was designed and constructred with our GOALI partner, Hinds Instruments of Hillsboro Oregon, a leading developer of photoelastic modulators and polarimeters. Our device, the so-called "4-PEM" was awarded a Research and Development 100 Award in 2013. My PhD student, supported as a postdoc through the GOALI project, is now a permanent and critical staff scientist at Hinds which is currently selling 4-PEM devices. We continue to work with Hinds to develop solutions for imaging with photoelastic modulators, a long standing challenge in polarimetry. With our 4-PEM polarimeter we measured the anisotropy of optical rotation in quartz and AgGaS2, the electric field induced optical activity in quartz, developed a strategy for measuring the Mueller matrix in fluorescence, measured the circular dichroism anisotropy for oriented, isolated dye molecules, evaluated depolarization, and analyzed the problem of optical activity in "two dimensional" nanohole arrays. Our instrument is sensitive and versatile. Broader Impacts. Outreach: Each summer for the past five summers, including the three during which this award was active we hosted one or two students in the lab from an underserved Bronx high school, the Academy of Language and Technology. In total we hosted seven students. We work with these students during the academic year, providing SAT tutoring, an advantage commonly exercised in wealthy school districts. We mentored two others from the Ellis Academy, an unequally underserved Bronx public high school with a population dominated by new immigrants. We are convinced that creating scientists, especially those from underrepresented groups, requires first developing within students, one-by-one, scientific identities. Pedagogy: We aspired to change the presentation of chiroptics in textbooks. Standard works mistake the necessary condition for optical rotation as enantiomorphism, and fail to interpret optical rotation on the basis of electronic structure. We succeeded in appealing to Brent Iverson and Eric Anslyn of the University of Texas, the authors of Organic Chemistry by Brown, Iverson, Anslyn, and Foote. I wrote a section on the Optical Activity of Achiral Compounds which appears in their 2013 edition. History: Analysis of the roots of crystallography continued with a translation from Russian, with Dr. A. Shtukenberg, of Shafronovsky’s History of Crystallography, the most comprehensive work of its kind. Lastly, we prepared an essay about the greatest work of François Arago, the abolition of slavery throughout the French Empire, a fitting tribute on the 200th anniversary of his discovery of optical rotation. Additionally, we wrote a biography of Hans Mueller, the beloved MIT physics professor who invented the Mueller matrix.
