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Inhomogeneous mechanical losses in micro-oscillators with high reflectivity coating
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10.1063/1.4728217
/content/aip/journal/jap/111/11/10.1063/1.4728217
http://aip.metastore.ingenta.com/content/aip/journal/jap/111/11/10.1063/1.4728217

Figures

Image of FIG. 1.
FIG. 1.

SEM image of the front (left) and the back side (right) of our typical double wheel oscillator. The diameter of the central oscillating disk is either 700 or 1000 μm, while the outer diameter of the isolation wheel is 3000 μm. The beams connecting the central mass with the wheels are either 50 or 100 μm wide, with length ranging from 300 to 450 μm, depending by the target frequency of the device. The thickness of the central disk is about 70 μm, while the thickness of the wheel is 500 μm. Here, the optical coating layer covers the whole front face of the wafer; all devices have been produced also in a version with the coating layer covering only the central disk.

Image of FIG. 2.
FIG. 2.

Design of the silicon micro-mirror. Here, the optical coating layer (in violet) covers only the central disk, but all devices have been produced also in a fully coated version. (a) Finite element domain used for finite element simulations. (b) Cross sectional view of the device.

Image of FIG. 3.
FIG. 3.

Scheme of the experimental apparatus. OI: optical isolator; FR: Faraday rotator; EOM: electro-optic modulator; H: half-wave plate; Q: quarter-wave plate; PD: photodiode; PBS: polarizing beam-splitter; MOMS: micro opto-mechanical systems. Lenses and alignment mirrors are not shown in the scheme.

Image of FIG. 4.
FIG. 4.

Upper panel: experimental displacement noise spectrum for a micro-mirror homogeneously coated (device D1). The thick solid line (red) is the fitting curve given by Eq. (3) , plus a flat background. Lower panel: displacement noise spectrum obtained from a similar oscillator, but lacking of the outer isolation wheel.

Image of FIG. 5.
FIG. 5.

Experimental spectra for a micro-mirror resonating at about 215 kHz (device D4). The curves refer to devices with FC and CC. The simulated curves are in agreement within 10% with the experimental results. The frequency shift and is due to the different contributions of the coating layer to the structure’s stiffness, as discussed in Sec. IV .

Image of FIG. 6.
FIG. 6.

Simulated noise spectra for a single device (D8 full coating) with different kinds of losses. Fit with theoretical spectra from Eq. (3) is shown only for the calibration curve with fixed loss ( ) and for the curve with both thermoelastic and structural losses.

Image of FIG. 7.
FIG. 7.

Contour plots of the energy dissipated in an oscillation cycle, plotted over the modal shape for the device D8 with full coating: (a) thermoelastic loss, (b) structural loss. In both cases, the insets show separately the dissipation in the silicon wafer and in the optical coating layer. The magenta spot in the center of the mirror gives the size of the optical waist.

Image of FIG. 8.
FIG. 8.

Contour plots of the energy dissipated in an oscillation cycle, plotted over the modal shape for the device D8 with central coating: (a) thermoelastic loss, (b) structural loss. In both cases, the insets show separately the dissipation in the silicon wafer and in the optical coating layer. The magenta spot in the center of the mirror gives the size of the optical waist.

Image of FIG. 9.
FIG. 9.

Device layer images, including the buried oxide (white region), for the central coating (left) and full coating (right) SOI samples. These images are used for the evaluation of the thickness variations.

Tables

Generic image for table
Table I.

Parameters of the different micro-mirrors as obtained by the fit of experimental thermal noise spectra with the expression ( 3 ). The experimental errors are estimated from the reproducibility of the data obtained with different samples of the same device.

Generic image for table
Table II.

Comparison between experimental and simulated Q values.

Generic image for table
Table III.

Proportionality constants describing the dependence of from the relevant parameters, according to Eq. (6) . is the sensitivity to changes of the Young modulus of the coating, to changes in the thickness of the device, and describes the effect of the mass of the coating layer covering the supporting beams. The constants are evaluated by fits on the results of FEM simulations. In the last two columns, we report the expected values of the frequency shift , and the corresponding experimental measurements . In the evaluation of , we have used , directly measured, and the best fit evaluation .

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/content/aip/journal/jap/111/11/10.1063/1.4728217
2012-06-13
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Inhomogeneous mechanical losses in micro-oscillators with high reflectivity coating
http://aip.metastore.ingenta.com/content/aip/journal/jap/111/11/10.1063/1.4728217
10.1063/1.4728217
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