Observation of Light-Driven Levitation Near Epsilon-Near-Zero Surfaces

Abstract

Optical manipulation of micro- and nanoparticles near surfaces is fundamental for applications in sensing and microfluidics, yet controlling particle-surface interactions remains challenging. Here we experimentally investigate light-induced forces on dielectric particles near epsilon-near-zero (ENZ) metamaterial surfaces using photonic force microscopy. By illuminating trapped particles with tunable visible light, we observe a wavelength-dependent repulsive force unique to ENZ surfaces, contrasting with the attractive forces near dielectric or metallic substrates. This repulsion peaks near the ENZ frequency and may be attributed to combined optical ENZ effects and thermophoretic forces. Our findings demonstrate that ENZ metamaterials can induce stable levitation of particles via light-driven forces, offering a novel mechanism for contactless manipulation in microfluidic environments. This work advances understanding of light-matter interactions at ENZ interfaces and suggests potential for ENZ-based optical control of micro- and nanoscale objects, with potential applications in micro- and nanofluidic environments.

Figures (12)

• Figure 1: Epsilon-near-zero sample structure and experimental setup. (A) A typical epsilon-near-zero (ENZ) sample structure consists of 5 trilayers of Al$_2$O$_3$ and Ag with a thin Ge layer ensuring surface wetting (see Methods). The stacks are deposited on a glass substrate. A polystyrene probe particle is trapped near the surface and excited with tunable visible light to measure the resulting axial force. (B) Optical properties of the ENZ sample structure. The multilayer is deposited by electron beam evaporation and designed to exhibit an ENZ frequency with low loss, with a nominal complex permittivity $\epsilon_s = 0.51 i$. The real and imaginary parts of the effective permittivity are obtained from spectroscopic ellipsometry combined with transfer-matrix modeling, showing that the ENZ condition, ${\rm Re} (\epsilon_s) = 0$, occurs at a wavelength of about 547 nm. (C) Sketch of the experimental setup. A laser diode provides the trapping beam at 830 nm. After passing through a 4:1 telescope, a $p$-polarizing beam splitter (PBS) and a quarter waveplate, it is reflected by a dichroic mirror (D) towards the back aperture of a NA=1.3 objective, which focuses the trapping beam to the diffraction limit near the surface inside the sample chamber (see inset, not to scale). A piezostage with nanometric resolution is used for positioning and motion control. The backscattering from the trapped particle is back-collected by the same objective, passes through the quarter waveplate and its $s$-polarized component is delivered to the detector, a quadrant photodiode (QPD). A long-pass edge filter prevents light at wavelengths $<$ 633 nm to reach the detector. A white light laser is used as a tunable polarizing beam (PB) by selecting its wavelength in the visible. The light is sent through a fiber and focused so that the beam waist at the sample is $w_0=2.8\pm0.2$$\mu$m (larger than the particle radius). The PB is chopped at 8 Hz and sent through an optical fibre on the trapped particle. A photodiode (PD), collecting a small portion of the PB, is used to synchronize the tracking signal measurements with the laser pulses. The signals from QPD and photodiode are acquired by a data acquisition board and stored in a computer for the analysis.
• Figure 2: Calibrated optical force measurements near sample surfaces. (A) Calibrated axial tracking signals under pulsed polarizing light from the PB source. The polystyrene particle is trapped in front of glass (red curve, $P_{trap}\sim$13 mW) or in front of ENZ (blue curve, $P_{trap}\sim$2 mW) surface. The polarizing white light beam is chopped with a frequency of 8 Hz. The trap equilibrium positions when PB illumination is on (red dashed line, glass, $\lambda_{\rm PB}=620$ nm, $P=2.6$ mW; blue dashed line, ENZ, $\lambda_{\rm PB}=500$ nm, $P=1.77$ mW) or off (black dashed line) are shown. Negative/positive shifts correspond to axial motion towards/away from the surface. The inset shows the average speed of the particle repelled by the ENZ surface, $\sim 96\ \mu$m/s (see Suppl. Mater.). (B) Axial force distributions (red, glass surface; blue, ENZ surface) corresponding to the tracking signals in (A). These are obtained from the optical trap calibration through the power spectrum density analysis of the particle thermal fluctuations (see Suppl. Mater.).
• Figure 3: Total force versus wavelength for particles over different surfaces. Total normalized axial force $F_z / P$ under pulsed polarizing beam illumination of incident power $P$ as a function of the polarizing beam wavelength $\lambda_{\rm PB}$. The top three curves are for a particle over an ENZ at three different edge-to-edge heights $h$ above the surface, all showing net repulsion ($F_z > 0$). In contrast, the bottom two curves are over Ag (gray, $h = 0.8$$\mu$m) and glass (pink, $h= 8$$\mu$m), showing net attraction ($F_z < 0$). The three configurations are shown schematically on the right. The ENZ surface has an ENZ point at 547 nm, and the region shaded in blue shows the range of wavelengths where the optical force is predicted to be strongly repulsive. This range was approximately calculated as the full-width half-maximum of the $F_z > 0$ region from a simplified theory assuming a point dipole close to the surface, with the ENZ modeled via an anisotropic effective medium rodriguez2016repulsion. For the ENZ curves the force is dramatically enhanced in this region, and for $h= 0.8$$\mu$m it becomes sufficiently strong to push the bead out of the trap, preventing force measurements between $\lambda_{\rm PB} = 500-540$ nm.
• Figure 4: Spectrum of the polarizing pulses (bottom) and corresponding polarizing power (top) at each wavelength used. Linewidth is 10 nm, except for the line at 480 nm, having bandwidth 20 nm.
• Figure 5: a) Drag force method. A trapped particle is subjected to a sinusoidal oscillation of known amplitude ($A_s$) in a direction ($y$) parallel to the surface (a). The peak (b) in power spectral density of the corresponding signal is used to calculate the diffusion coefficient $D_{\|}$ as a function of the distance $d$ of the beam focus from the surface.