Doubly resonant nonlinear metasurfaces enabling NIR-to-UV upconversion for reconfigurable Fourier optical processing

Abstract

Fourier optical processing underpins optical information manipulation, yet extending such operations to short wavelengths within compact platforms remains challenging. Here, we address this challenge by embedding reconfigurable Fourier-domain processing within IR-to-UV upconversion in a doubly resonant nonlinear metasurface. When coherently illuminated at the Fourier plane with an image-bearing signal and a spatially structured pump, the metasurface generates UV images via degenerate four-wave mixing. Crucially, the spatial-frequency content of these upconverted images is selectively shaped by the tailored spectrum of the pump. To boost the efficiency of this nonlinear process, the metasurface is designed to simultaneously support a toroidal dipole bound state in the continuum and a magnetic dipole resonance, providing spectrally aligned and independently enhanced field localization for signal and pump beams, respectively. Building on this architecture, we experimentally demonstrate directional and continuously tunable filtering at the upconverted UV wavelengths. These results establish nonlinear metasurfaces as a versatile platform for Fourier optics and reconfigurable all-optical image processing.

Figures (4)

• Figure 1: Principle of reconfigurable Fourier optical processing via a doubly resonant nonlinear metasurface.a Conceptual illustration of the nonlinear Fourier processing platform. An image-bearing signal beam and a spatially structured pump beam are simultaneously focused onto the metasurface at the Fourier plane. The tailored pump spectrum selectively shapes the spatial-frequency components of the signal, generating a filtered UV image via degenerate FWM. b Geometric design of the metasurface unit cell, featuring paired Si nanodisks (height $h = 220$ nm) arranged on a SiO$_2$ substrate with periods $P_{x} = 650$ nm and $P_{y} = 380$ nm. One nanodisk has a fixed radius $R = 135$ nm, while the other has a tunable radius $r$. c Energy-level diagram of the degenerate FWM process $\omega_{\text{dFWM}} = 2\omega_{\text{s}}+\omega_{\text{p}}$ coupling the signal (s) and pump (p) fields.
• Figure 2: Resonant mode analysis and linear characterization of the metasurface. a Calculated photonic band structure for a symmetric configuration ($r = R = 135$ nm). b Simulated out-of-plane electric field ($E_{z}$) distributions of Mode 1 and Mode 2 at the $\Gamma$ point, corresponding to the bands in a. c Calculated reflectance spectra under $x$-polarized incidence as a function of $r$. d Multipole decomposition of the calculated reflectance for the asymmetric configuration ($r = 125$ nm). e Experimentally measured reflectance spectrum of the fabricated sample ($r = 125$ nm). Inset: SEM image of the sample. The scale bar is 500 nm.
• Figure 3: Nonlinear optical characterization of the metasurface.a Evolution of the nonlinear emission spectra as a function of the incident signal power at a constant pump power. b Nonlinear emission intensities versus the temporal delay between the pump and signal pulses. c Polarization dependence of the degenerate FWM ($2\omega_{\text{s}}+\omega_{\text{p}}$) emission intensity. d Comparison of nonlinear emission spectra from the metasurface and an unpatterned bare Si film under identical doubly resonant excitation. e Power dependence of the degenerate FWM ($2\omega_{\text{s}}+\omega_{\text{p}}$) and THG ($3\omega_{\text{s}}$) emissions, plotted on a logarithmic scale. The solid lines indicate quadratic and cubic scaling, respectively.
• Figure 4: Reconfigurable Fourier-domain image filtering at upconverted UV wavelengths.a Experimental setup for nonlinear Fourier image processing. The signal beam encodes an object image, and the pump beam is structured by an SLM. b Examples of programmable phase patterns applied to the SLM. c Measured intensity distribution of an elongated pump beam in the Fourier plane. d Directional spatial-frequency filtering of a horizontal stripe pattern. From left to right: signal THG reference image, and degenerate FWM images obtained with circular, vertically elongated, and horizontally elongated pump beams. e Demonstration of continuously tunable filtering on a vertical stripe pattern by gradually shaping the pump beam from circular to vertically elongated. f Extracted horizontal intensity profiles corresponding to the filtered images in e. All scale bars are 1 mm.