RUI: Casimir Forces From Scattering Theory

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This award funds the research activities of Professor Noah Graham at Middlebury College. Microelectromechanical devices --- tiny machines that can be embedded within an integrated circuit chip --- can trigger car airbags in a collision, detect the movement of a video-game controller or the orientation of a smartphone, sense low air pressure in a car tire, and provide the feedback necessary to stabilize car suspensions and flying drones. As these devices shrink toward sizes of a micron or smaller, a special quantum-mechanical force called the Casimir force will begin to play an important role in their design and function. In contrast to the more familiar electric attraction and repulsion between opposite and like charges, the Casimir force arises from quantum-mechanical fluctuations inherent in Heisenberg's Uncertainty Principle. While the physical mechanism underlying the Casimir force has been well understood for many years, until recently precise calculations were only possible for the most elementary examples. New techniques, in which the Casimir force is expressed in terms of information about the reflection of light from each individual object on which the force is acting, have greatly expanded the range of potential applications. The research supported by this grant will formulate and implement numerical calculations of this scattering data, making it possible to calculate Casimir forces in a broad range of systems relevant to experimental physics and nanotechnology. These general-purpose computational tools will also be applicable to other problems in science and engineering. Research in this area thus advances the national interest by promoting the progress of science with many potential technological implications. And because this approach is centered around fundamental concepts in quantum mechanics and electromagnetism, it will be possible for undergraduate students to make meaningful contributions to this research at the same time as they build scientific and computational skills that will serve them well in graduate or professional work, both within physics and across a wide range of fields in science and engineering.The technical approach to this problem will be based on the variable phase method, which this research program is applying for the first time to electromagnetic scattering. High-performance parallel computation will make it possible to go beyond objects with a high degree of symmetry to calculate full T-matrices in multichannel scattering, for materials with position- and frequency-dependent dielectric response. These tools will then be applied to calculations of Casimir forces in cases of current experimental interest, such as dielectric gratings with deep corrugations, for which existing techniques based on the Rayleigh expansion are insufficient.