Visualizing Detection Efficiency in Optomechanical Scattering

Abstract

Many optical measurement techniques, such as light scattering from wavelength-scale particles or detecting motion from a surface with an optical lever, encode information in a complex radiation pattern. Extracting all available information is essential for many quantum-enhanced sensing protocols but is often impractical, as it requires many channels to spatially resolve the scattered signal. We present a new method to visualize how efficiently a practical measurement scheme captures the information available in the scattered light by mapping out the local contribution to the detection efficiency on the detector surface. We use this tool to experimentally optimize the free space measurement of the amplitude of motion of an optomechanical resonator with a quadrant photodiode. We show that blocking sections of the photodetector enhances sensitivity, counterintuitively yielding a significant improvement in detecting higher-order mechanical modes in the system. We also show how our method can be applied to light scattering measurements of small particles.

Figures (4)

• Figure 1: Examples of free space optomechanical scattering experiments. (a) Detection of the vibrational modes of membrane optomechanical resonator via optical lever detection. Setup includes a polarizing beam splitter (PBS), quarter wave plate ($\lambda/4$), and quadrant photodetector (QPD). (b)Detection of the location of a small particle via light scattering using high numerical aperture focusing lens (FL) and collection lens (CL). In either case information is scattered into many optical modes which are analyzed with multiple detectors which may be partially blocked assess and optimize the detection efficiency.
• Figure 2: Differential Detection Efficiency (DDE). (a,b) A thin wire is scanned in front of the QPD to locally exclude light and measure the DDE ($d\eta/dx$). Theoretical (solid curves) and Measured (data points) DDE for several membrane modes are displayed. (c,d) A beam block, diameter $B$, masks the center of the QPD, while detection efficiencies for several membrane modes (symbols are the same as in (b)) are measured. (e,f) The DDE of the partially blocked QPD (red) approaches the IRP (Black) for the (6,1) membrane mode. For all data, statical errors are smaller than the size of the symbols.
• Figure 3: Measurement Sensitivity relative to an ideal single mode interferometer. (a) Imprecision noise and efficiency for membrane modes of various $k_m$ measured with a standard QPD (Blue) or an optimally blocked QPD (Yellow), and the back action noise (Green). All values are reported relative to those of a single mode interferometer supp. Top diagrams show relative size of Gaussian beams (Red) and the mechanical wavelength (Black) (b) Thermal displacement spectrum of the (8,1) mode of the membrane measured using an standard QPD (Red) and an optimally gaped QPD (Black) where dashed horizontal lines represent the shot noise floor.
• Figure 4: Detection efficiency of the $y$ direction motion of dipolar scatterer. (a) Polar plot of the $x=0$ cross section of the far-field DDE (blue) with negative regions represented by dashed red line for $\text{NA}_\text{cl}=1$ and the IRP (black). Note, the IRP is symmetric about the $y$ axis, while the DDE is zero in the backwards directions. The full 3-D distribution is presented in the supplemental materials supp. (b) The detection efficiency $\eta_y$ as a function of the amount of blocked light, for different collection lens NA. (c) Detection efficiency $\eta_y$ as a function of the with a block angle chosen to maximize $\eta_y$.