Signal processing is of critical importance for various science and technology fields. Analog optical processing can provide an effective solution to perform large-scale and real-time data processing, superior to its digital counterparts, which have the disadvantages of low operation speed and large energy consumption. As an important branch of modern optics, Fourier optics exhibits great potential for analog optical image processing, for instance for edge detection. While these operations have been commonly explored to manipulate the spatial content of an image, mathematical operations that act directly over the angular spectrum of an image have not been pursued. Here, we demonstrate manipulation of the angular spectrum of an image, and in particular its differentiation, using dielectric metasurfaces operating across the whole visible spectrum. We experimentally show that this technique can be used to enhance desired portions of the angular spectrum of an image. Our approach can be extended to develop more general angular spectrum analog meta-processors, and may open opportunities for optical analog data processing and biological imaging.

Metasurfaces have provided a promising approach to enhance the nonlinearity at subwavelength scale, but usually suffer from a narrow bandwidth as imposed by sharp resonant features. Here, we counterintuitively report a broadband, enhanced second-harmonic generation, in nanopatterned hyperbolic metamaterials. The nanopatterning allows the direct access of the mode with large momentum, rendering the rainbow light trapping, i.e. slow light in a broad frequency, and thus enhancing the local field intensity for boosted nonlinear light-matter interactions. For a proof-of-concept demonstration, we fabricated a nanostructured Au/ZnO multilayer, and enhanced second harmonic generation can be observed within the visible wavelength range (400-650 nm). The enhancement factor is over 50 within the wavelength range of 470-650 nm, and a maximum conversion efficiency of 1.13×10⁻⁶ is obtained with a pump power of only 8.80 mW. Our results herein offer an effective and robust approach towards the broadband metasurface-based nonlinear devices for various important technologies.

Dynamically encircling exceptional points (EPs) can lead to chiral mode switching as the system parameters are varied along a path that encircles EP. However, conventional encircling protocols result in low transmittance due to path-dependent losses. Here, we present a paradigm to encircle EPs that includes fast Hamiltonian variations on the parameter boundaries, termed Hamiltonian hopping, enabling ultrahigh-efficiency chiral mode switching. This protocol avoids path-dependent loss and allows us to experimentally demonstrate nearly 90% efficiency at 1550 nm in the clockwise direction, overcoming a long-standing challenge of non-Hermitian optical systems and powering up new opportunities for EP physics.

Exceptional points (EPs) are degeneracies at which two or more eigenvalues and eigenstates of a physical system coalesce. Dynamically encircling EPs by varying the parameters of a non-Hermitian system enables chiral mode switching, that is, the final state of the system upon a closed loop in parameter space depends on the encircling handedness. In conventional schemes, the parametric evolution during the encircling process has to be sufficiently slow to ensure adiabaticity. Here, we show that fast parametric evolution along the parameter space boundary of the system Hamiltonian can relax this constraint. The proposed scheme enables highly efficient transmission and more compact footprint for asymmetric mode converters. We experimentally demonstrate these principles in a 57 μm-long double-coupled silicon waveguide system, enabling chiral mode switching with near-unity transmission efficiency at 1550 nm. This demonstration paves the way towards high-efficiency and highly integrated chiral mode switching for a wide range of practical applications.