Optical lever for broadband detection of fluid interface fluctuations

TL;DR

This work introduces a broadband optical lever–based surface fluctuation spectroscopy (SFSRS) that uses a specularly reflected laser beam to sense minute liquid–air interface fluctuations. By converting angular tilts into lateral detector signals via a dual-element photodiode, the method spans from discrete, low-frequency gravity–capillary modes to the thermal spectrum of high-frequency capillary waves, with theoretical predictions matching measurements for water and ethanol without fitting parameters. The experimental setup features a temperature-controlled sample cell to stabilize fluid properties and long acquisition times, enabling precise characterization of interfacial dynamics and boundary-condition effects. The approach offers a non-invasive, versatile tool for probing fluid interface physics across soft matter and hydrodynamic systems, bridging traditional optical interferometry and light-scattering techniques with practical interfacial measurements.

Abstract

We exploit the optical lever principle to detect minute fluctuations of a liquid-air interface. Waves propagating on the interface deflect a specularly reflected laser beam, inducing angular deviations captured by a dual-element photodiode. We implement this principle in a compact set-up that includes a temperature-controlled fluid sample. This allows us to detect deflection angle fluctuations across five orders of magnitude in frequency, from individual low-frequency surface eigenmodes to the thermal distribution of high-frequency capillary waves. In addition to demonstrating the method's versatility and broad dynamical range, we highlight practical considerations in characterising liquid interface dynamics, bridging established optical methods with their application to fluid and soft-matter systems.

Figures (13)

• Figure 1: Scheme of the experimental set-up. L, laser; HWP, half-wave plate; PBS, polarising beam splitter; BD, beam dump; QWP, quarter-wave plate; O, objective lens; S, fluid sample; DEPD, dual-element photodiode; TI, transimpedance amplifier; VA, voltage amplifier; ADC, analog-to-digital converter. Inset details the geometry of the inclined interface. A surface wave with wavelength $\lambda$ and small amplitude $\delta$ induces a local inclination angle $\theta$. Due to this inclination, the reflected beam acquires a displacement $d$ with respect to the incident beam in the objective plane. $F$ denotes the focal length of the objective lens.
• Figure 2: Temperature-controlled experimental cell. Dimensions are given in millimetres.
• Figure 3: Surface inclination spectra of chromatography water (blue line) and reagent-grade ethanol (red line), measured at $20^\circ$C using SFSRS. The dashed lines overlaying experimental data are theoretical curves of thermal noise spectra with no free parameters. Grey line, measured with a mirror placed inside the sample cell, characterises the vibrational noise floor. In this series of experiments, $\mathrm{NA} = (12.7\pm 0.3)\times 10^{-3}$.
• Figure 4: Surface inclination spectra of water at $20^\circ$C, measured for different numerical apertures, as specified in the legend. Solid lines represent experimental data, while dashed lines indicate the corresponding theoretical predictions.
• Figure 5: Surface inclination spectra measured in water, for different temperatures, as specified in the legend. The temperature is kept constant down to 5-mK fluctuations over the course of experiments (see Supplemental document for details). Consistently with previous figures, solid lines denote experimental data and dashed lines represent theoretical spectra. In this series of experiments, $\mathrm{NA} = (10.4\pm0.3)\times10^{-3}$.