Angle-Multiplexed Metasurfaces: Encoding Independent Wavefronts in a Single Metasurface under Different Illumination Angles

The angular response of thin diffractive optical elements is highly correlated. For example, the angles of incidence and diffraction of a grating are locked through the grating momentum determined by the grating period. Other diffractive devices, including conventional metasurfaces, have a similar angular behavior due to the fixed locations of the Fresnel zone boundaries and the weak angular sensitivity of the meta-atoms. To alter this fundamental property, we introduce angle-multiplexed metasurfaces, composed of reflective high-contrast dielectric U-shaped meta-atoms, whose response under illumination from different angles can be controlled independently. This enables flat optical devices that impose different and independent optical transformations when illuminated from different directions, a capability not previously available in diffractive optics.

Popular Summary

Diffractive optical elements such as lenses, gratings, and holograms are used in several applications, including compact cameras, heads-up displays, holographic scanners, and printers. All of these devices must contend with a general law of optics known as the “angular optical memory effect,” wherein the response of the diffracted light is highly correlated over various incident angles. For example, a thin diffractive hologram projects an image when illuminated under a fixed angle, while illumination from a different angle results in the same image but with distortions. Breaking this correlation could lead to a wide variety of compact, complex, multifunctional optical applications. We designed and tested a new type of device called an angle-multiplexed metasurface, whose response to illumination from different angles can be controlled independently.

Optical metasurfaces are two-dimensional arrangements of a large number of discrete meta-atoms—in our case, U-shaped silicon nanostructures—that enable precise control of optical wave fronts with subwavelength resolution. These U-shaped meta-atoms support symmetric and antisymmetric resonances, which allow us to independently control the phases imparted onto light impinging from two directions. This enables dramatically different embedded optical functions in a single metasurface, separately accessible under different illumination angles. As a proof of concept, we demonstrate a metasurface device that encodes and projects different holographic images under different illumination angles.

This concept opens the way toward new categories of ultracompact multifunctional optical elements that multiplex several functions into a single diffractive surface. We envision applications in head-mounted 3D projectors with the capability of tweaking various parts of the 3D image depending on illumination angle, or holograms with more secure antifraud protection.

Figure 1

Angle-multiplexed metasurface concept. (a) Schematic illustration of diffraction of light by a grating. A grating adds a fixed linear momentum ($\hslash k_g$) to the incident light, independent of the illumination angle. If the illumination angle deviates from the designated incident angle, light is deflected to a different angle, which is dictated by the grating period. (b) Illustration of the angle-multiplexed metasurface platform. This platform provides different responses according to the illumination angle. For instance, two gratings with different deflection angles (different grating momenta) can be multiplexed such that different illumination angles acquire different momenta. (c) Illustration of a typical hologram that creates one specific image (Caltech logo) under one illumination angle (left). The same hologram will be translated laterally (and distorted) by tilting the illumination angle (right). (d) Schematic illustration of an angle-multiplexed hologram. Different images are created under different illumination angles. For ease of illustration, the devices are shown in transmission, while the actual fabricated devices are designed to operate in reflection mode.

Figure 2

The meta-atom structure and the design graphs. (a) Schematic drawing of various views of a uniform array of U-shaped cross-section $\alpha$-Si meta-atoms arranged in a square lattice resting on a thin ${\mathrm{SiO}}_2$ spacer layer on a reflective surface (i.e., a metallic mirror). The array provides angle-dependent response such that TE-polarized light at 0° and 30° illumination angles undergoes different phase shifts as it reflects from the array. (b) Simulated values of the U meta-atom dimensions ($D_x$, $D_y$, $D_{x\mathrm{in}}$, and $D_{y\mathrm{in}}$) for achieving full $2\pi$ phase shifts for TE-polarized light at 0° and 30° illumination angles, respectively. From (b), one can find the dimensions of a meta-atom that imposes ${\varphi }_1$ and ${\varphi }_2$ phase shifts under 0° and 30° illuminations, respectively. (c) Electric energy density inside a single unit cell in a periodic uniform lattice for a typical meta-atom [shown in (b) with a star symbol] at 0° and 30° illumination angles, plotted in three cross sections. Blue arrows indicate in-plane electric field distributions excited at each illumination angle. Different field distributions at normal and 30° incidence are an indication of excitation of different resonant modes under different incident angles. In all parts of the figure, the meta-atoms are 500 nm tall. The silicon dioxide and aluminum layers are 125 nm and 100 nm thick, respectively, the lattice constant is 450 nm, and all simulations are performed at a wavelength of 915 nm. ($\alpha \text{−}\mathrm{Si}$: amorphous silicon, ${\mathrm{SiO}}_2$: silicon dioxide.)

Figure 3

Angle-multiplexed grating. (a) Simplified schematic of the measurement setup (left) and measured reflectance of the angle-multiplexed grating under normal illumination of TE-polarized light as a function of the observation angle ${\theta }_0$ (right). The grating deflects 0° and 30° TE-polarized incident light to $-1.85°$ and $+33.2°$, respectively. Orange dashed lines indicate the designed deflection angles ($-1.85°$ and $+33.2°$ under 0° and 30° incidence, respectively) and the deflection angles corresponding to regular gratings with fixed grating periods (2.7° under normal and 27.88° under 30° illumination angles assuming grating periods of $21\lambda$ and $31\lambda$, respectively). See Appendix B and Ref. [63] (Fig. 2) for measurement details. (b) Optical image of the angle-multiplexed grating. The inset shows a scanning electron micrograph of the top view of meta-atoms composing the metasurface. See Appendix pp2 for fabrication details. BS is for beam splitter.

Figure 4

Angle-multiplexed hologram. (a) Simplified drawing of the measurement setups under normal and 30° illumination angles (left). The angle-multiplexed hologram is designed to create two different images under different incident angles (Caltech and LMI logos under 0° and 30°, respectively). Simulated and measured reflected images captured under 915-nm TE-polarized light at 0° and 30° illumination angles are shown on the right. See Appendix pp2 and Ref. [63] (Fig. 3) for measurement details. (b) Optical image of a portion of the angle-multiplexed hologram. The inset shows a scanning electron micrograph under oblique view of meta-atoms composing the metasurface. See Appendix pp2 for fabrication details.