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(a) Setup for measuring the optical response of the piezoelectrically actuated AlN optomechanical resonator. EDFA: erbium-doped fiber amplifier. PR: photoreceiver. FPC: fiber polarization controller. TDL: tunable diode laser. The RF voltage from a network analyzer is applied to the electrode placed directly above the center of the wheel resonator. The silicon substrate is grounded and the electric field lines are shown in dotted purple lines. (b) The equivalent circuit of the air gap–AlN–air gap resonator stack modeled as three capacitors in series. Rm , Lm , and Cm are the motional resistance, inductor, and capacitance of the mechanical resonator, respectively. C 1 is the physical capacitance between the electrode and the wheel's upper surface, C 2 is the physical capacitance between the wheel's lower surface and the ground, and C p is the dielectric capacitance of the AlN device layer. (c) Typical optical transmission of an AlN wheel optomechanical resonator with the inner radius Ri = 32.6 μm and outer radius Ro = 37.6 μm. The left inset is a scanning electron micrograph of the AlN wheel resonator and the right inset is the zoom-in of a resonance near 1544.85 nm with a loaded optical Q factor of 125 000.
Spectrum of magnitude (a) and phase (b) of the S 21 measurement from 0 to 4 GHz showing three distinct modes around 47.3 MHz, 1.04 GHz, and 3.12 GHz. The asymmetric line-shape of the magnitude spectrum around the resonances can be modeled as a Fano-like resonance as a result of interference between the mechanical resonances and Pockels modulation. The blue line around 1.04 GHz is a Fano-like line-shape fitting to Eq. (5) with the following fitted parameters: ω r/2π = 1.04 GHz, Q m = 2470, and q/2π = 130 MHz.
(a) Zoomed-in displacement amplitude and phase spectrum of the mechanical resonance around 47.3 MHz. (b) Zoomed-in spectrum of the mechanical resonance around 1.04 GHz under various driving power levels from −30 dBm to 0 dBm. The plot in the right inset shows a linear dependence of the displacement on the driving voltage. (c) Zoomed-in spectrum of the mechanical resonance around 3.12 GHz. The numerically calculated cross-sectional displacement mode profiles in the radial direction are shown in the left inset, respectively, for each mechanical mode.
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