Microwave characterization of nanomechanical resonator

We suggest a new method for microwave diagnostics of nanomechanical resonators. The system under consideration is a microwave coplanar line (MWCL), interacting through a capacitive load with nanomehanichal resonator (NAMR). The input is a superposition of two signals with close frequencies, one of which coincides with the fundamental frequency of the MWCL. Thus NAMR is excited by a difference frequency, which leads to a modulation of the output signal at this frequency. The modulation amplitudes of the output signal has the characteristic peaks at the resonant frequency of the NAMR, which allows the determination of the position of the NAMR resonance and its quality factor. The paper presents a theoretical calculation of the modulation amplitudes. It is shown that their frequency dependence has a characteristic Lorentzian structure with the position of the peak and the width being determined by NAMR resonance characteristics.