Compound Metaoptics for Amplitude and Phase Control of Wave Fronts

Metasurfaces allow tailored control of electromagnetic wave fronts. However, due to local conservation of power flow, passive, lossless, and reflectionless metasurfaces have been limited to imparting phase discontinuities—and not power density discontinuities—onto a wave front. Here, we show how the phase and amplitude profiles of a wave front can be independently controlled using two closely spaced phase-discontinuous metasurfaces. The two metasurfaces, each designed to exhibit spatially varying refractive properties, are separated by a wavelength-scale distance and together form a compound metaoptic. A method of designing the compound metaoptic is presented, which enables transformation between arbitrary complex-valued field distributions without reflection, absorption, polarization loss, or active components. Such compound metaoptics may find applications in the optical trapping of particles, displaying three-dimensional holographic images, shrinking the size of optical systems, or producing custom (shaped and steered) far-field radiation patterns.

Figure 1

Two metasurfaces form the compound metaoptic, establishing three regions. The phase-discontinuous metasurfaces reshape the amplitude and phase profiles of an incident beam, as demonstrated by the wave front behavior. The inset plots display the amplitude and phase profiles of the electric field before and after each metasurface. Local power flux through each metasurface is conserved, eliminating reflections.

Figure 2

The unit cell of a bianisotropic Huygens metasurface is shown in (a), in which three sheet impedances $Z_s$ are separated by a distance $d$. TE wave impedance on either side of the metasurface is denoted as ${\eta }^i$ for the incident field and ${\eta }^t$ for the transmitted field. The unit cell is modeled by the transmission line circuit shown in (b), in which transmission lines separate three shunt impedances.

Figure 3

A compound metaoptic reshapes an incident Gaussian beam to produce a Dolph-Chebyshev far-field pattern pointed towards 40 deg. The metaoptic performance is shown in (a) as the transmitted electric field amplitude $\lambda /3$ from the metaoptic, (b) as the far-field radiation pattern, and (c) as the real part of the simulated electric field.

Figure 4

A compound metaoptic produces the field scattered by three line scatterers arranged as shown in (a). The simulated electric field is compared to the line scatterer interference pattern at a distance of $11.5\lambda$ from the metaoptic in (b) as the field amplitude and (c) as the phase. The far-field radiation pattern is shown in (d) for the simulated field distribution and the scatterer interference pattern.