Optical readout of displacements of nanowires along two mutually perpendicular directions

Nanowires are good force transducers due to their low mass. The singleness of the direction of the motion detection in a certain system is an existing limitation, and to overcome the limitation is the key point in this article. Optical methods, such as polarized light interferometry and light scattering, are generally used for detecting the displacement of nanowires. Typically, either light interference or light scattering is considered when relating the displacement of a nanowire with the photodetector’s measurements. In this work, we consider both the light interference along the optical axis and light scattering perpendicular to the optical axis of a micro-lens fiber optic interferometer. Identifying the displacement along the two directions and the corresponding vibration conversion efficiency coefficients for the nanowire is a significant part of our study. Our analysis shows that the optimal working point of the micro-lens fiber optic interferometer can realize the detection of displacement along the optical axis without the disturbance coming from the motion perpendicular to the optical axis, and vice versa. We use Mie scattering theory to calculate the scattering light for the reason that the size of the nanowire is comparable to the wavelength of light. Our results could provide a guide for optical readout experiments of the displacement of nanowires.