Phase Matching Free Sensing with Undetected Light Using a Nonlinear Thin-Film Metasurface

TL;DR

This work addresses phase matching free sensing with undetected light using a thin-film nonlinear source. It demonstrates stimulated four-wave mixing in a resonant plasmonic metasurface within a folded Michelson interferometer and derives a visibility model $V = \frac{2\sqrt{\kappa T T_f}(\eta + \sqrt{T_f R_f})}{R_f T_f + (\eta^2 + T_f)(1 + \kappa T)}$, with $\kappa = T_p^2 T_s$ and $\eta = \frac{\sigma_-}{\sigma_+}$. Experimentally, a maximum visibility greater than 50% is observed while sensing through a 240 μm silicon window, and phase information is retrieved despite reduced visibility, demonstrating undetected-light sensing. Spectroscopic dispersion measurements show ultrafast, spectrally resolved sensing capabilities and indicate potential extension to deeper mid-IR wavelengths, where metasurface resonances define the operating bands.

Abstract

In this article, we report classical sensing with undetected light using octave spanning stimulated four-wave mixing from a plasmonic metasurface. The bidirectional nonlinear scattering due to inherent reflections from such thin nonlinear materials modifies their operation within a nonlinear interferometer. The theoretical model for visibility accounting for such bidirectionality as well as pulsed illumination accurately predicts visibility in the system as a function of transmission in the near-infrared seed (idler) arm. Spectrally resolving the visible signal emission evaluates the total dispersion within the interferometer, highlighting the prospect of ultrafast sensing with undetected photons.

Figures (4)

• Figure 1: The interferometer system, metasurface and interference (a) The Michelson interferometer setup operating in the far field. The 835 nm pump (red) and 1500 nm seed (idler, magenta) pulsed lasers stimulate 580 nm FWM (signal, yellow). (b) SEM image the nonlinear metasurface comprised of two gold discs and a gold bar antenna per unit cell. The scale bar is 500 nm. (c, d) Graphical illustration of the bidirectional FWM (signal) emission at the first and second pass, respectively. The optical axes have been angularly displaced for clarity and do not indicate amplitude. (e) Temporal positions of FWM (signal) pulses created at each pass. The dashed lines represent $E_{f1+}$ and $E_{f2-}$. Distance $d$ is from the metasurface to curved mirror 1. (f, g, h) Intensity of FWM (signal) at the camera with no beam blocks in the interferometer arms, when beams are blocked at curved mirror 1, and when the seed (idler) is blocked at curved mirror 2, respectively. Scale bars are 2 mm. (i) Intensity at the camera along the dashed lines on (f, g, h).
• Figure 2: Visibility and phase of the FWM (signal) interference, centred at 580 nm, with and without a 240 µ m silicon window in the seed (idler) arm of the interferometer. Experimental visibility at the camera with no additional material in the seed (idler) path (a) and with the silicon window (b). The corresponding phase of interference, without (c), and with (d), the silicon window in the seed (idler) arm.
• Figure 3: Visibility as functions of the optical properties of the metasurface and transmission in the seed (idler) arm. Theoretical dependence of visibility on (a) $\eta$, (b) T$_f$ and (c) $\kappa$. The experimentally measured and theoretically optimised metasurface parameters are marked by the solid and dashed vertical lines, respectively. Constant parameters are held at the values in Table SI of the SI. (d) Dependence of visibility on seed (idler) transmission, $T$, for the experimental measured (solid curve) and theoretically optimised (dashed curve) metasurface parameters. (e) Experimental average visibility measured at knife edge positions that reduce seed (idler) transmission. The knife edge is brought along the horizontal axis of the object plane and visibility is averaged across three rows of pixels. (f) Experimental visibility as the knife edge is introduced, averaged across all pixels and normalised to the unobstructed visibility. The theoretical curve uses the experimentally measured optical properties.
• Figure 4: 2D FWM interference spectrograms for wavelength against pump-seed delay position. (a) Intensity of the FWM (signal) DC component indicating the chirp of spectral components. (b) Spectrally resolved FWM (signal) visibility as a function of pump-seed delay, measured by scanning the interferometer idler mirror at each delay position. (c) The spectrally resolved accumulative phase from all beams as a function of pump-seed delay showing the small intrinsic dispersion of the interferometer. For (b) and (c), data points extracted with a coefficient of determination, R$^2< 0.7$, have been removed.