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SEM image of a “low-deformation mirror” device resonating at . (a) Front side with the elastic structure etched in the device layer and the circular mirror deposited over the central disk. (b) Back side with the circular frame etched in the handle layer.
Modal shape of the fundamental mechanical mode of two devices. The central circle indicates the area covered with the reflective coating. The contour plot shows the vertical displacement of the structure, from 0 (blue) to a maximum arbitrary value (red). The amplitude of the displacement has been exaggerated for clarity. (a) “Low-deformation mirror” design: the vertical displacement of the mirror is almost uniform over the coated area, thanks to the structure made of alternated torsional and flexural springs. (b) Standard design (see Ref. 16): the mirror is supported by radial flexural springs and the bending of the flexural members induces a significant bending also in the disk.
Filtering effect of the suspended frame. The isolation wheel weights and its resonant frequency is fixed at 30 kHz. The effective mass of the mirror is and its resonant frequency is fixed at . (a) Section of the modal shape of a typical wafer vibration at 130 kHz and schematic model used to evaluate the effective quality factor of the resonator mode. The wafer is supported at its circumference and the detail shows that the resulting displacement of the resonator is much reduced by the isolation frame. The equivalent mass of a typical wafer mode at 100 kHz is . (b) Simulated loss factor of the main resonator mode with the isolation wheel. For each mode, elastic constants K are obtained by the values of resonant frequency and equivalent mass. Even if a loss angle as low as is assigned to the resonator and the suspended frame, the resulting total loss factor of the resonator mode can just worsen by less than one order of magnitude, depending on the frequency and the loss of the wafer mode. (c) Simulated loss factor of the main resonator mode without the isolation wheel. In this case, the resulting loss factor is strongly correlated to the loss of the wafer mode.
FEM simulations showing the effect of the laser beam power absorption. (a) Temperature mapping (K) with the background at liquid helium temperature, when the absorbed power is 1 mW. (b) Temperature mapping (K) with the background at 300 mK and an absorbed power of 0.1 mW. In both cases, the total laser power is applied on a circular surface of diameter 0.1 mm at the center of the mirror.
Experimental and simulated parameters of the devices. D0 =standard oscillator. D1 = low-deformation mirror oscillator. is the frequency of the main mode of the resonator and its effective mass, estimated from thermal noise measurements at room temperature.a
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