Optical interferometric displacement detection techniques have recently found use in the study of nanoelectromechanical systems (NEMS). Here, we study the effectiveness of these techniques as the relevant NEMS dimensions are reduced beyond the optical wavelength used. We first demonstrate that optical cavities formed in the sacrificial gaps of subwavelength NEMS enable enhanced displacement detection sensitivity. In a second set of measurements, we show that the displacement sensitivity of conventional path-stabilized Michelson interferometry degrades rapidly beyond the diffraction limit. Both experiments are consistent with numerical models.
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Optical interferometry has found recent use in the detection of nanometer scale displacements of nanoelectromechanical systems ͑NEMS͒. At the reduced length scale of NEMS, these measurements are strongly affected by the diffraction of light. Here, we present a rigorous numerical model of optical interferometric displacement detection in NEMS. Our model combines finite element methods with Fourier optics to determine the electromagnetic field in the near-field region of the NEMS and to propagate this field to a detector in the far field. The noise analysis based upon this model allows us to elucidate the displacement sensitivity limits of optical interferometry as a function of device dimensions as well as important optical parameters. Our results may provide benefits for the design of next generation, improved optical NEMS.
We present transport and tunneling measurements of Pb-Ag bilayers with thicknesses, d(Pb) and d(Ag), that are much less than the superconducting coherence length. The transition temperature, T(c), and energy gap, Delta, in the tunneling density of states (DOS) decrease exponentially with d(Ag) at fixed d(Pb). Simultaneously, a DOS that increases linearly from the Fermi energy grows and introduces states within the gap. The integrated subgap DOS approaches 40% of the normal state value in the lowest T(c) film investigated (T(c) approximately 0.1 T(Pb)(c,bulk)). This behavior suggests that a growing fraction of quasiparticles decouple from the superconductor as T(c)-->0. The linear dependence is consistent with the quasiparticles becoming trapped on integrable trajectories in the metal layer.
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