Transmissive Ultrathin Pancharatnam-Berry Metasurfaces with nearly 100% Efficiency

Pancharatnam-Berry (PB) metasurfaces exhibit strong abilities to control spin-polarized light, but transmission-mode PB functional devices exhibiting simultaneously nearly 100% efficiencies and ultrathin thicknesses are rarely seen. Here, we show that 100%-efficiency photonic spin Hall effect (PSHE) can be realized in ultrathin PB metasurfaces exhibiting both electric and magnetic responses satisfying certain criteria, and then we design and fabricate a microwave transmissive PB metasurface with thickness of approximately $\lambda /8$ yet exhibiting a maximum PSHE efficiency of approximately 91% in experiments (approximately 94% in full-wave simulations). Our results can stimulate the realizations of high-performance PB metadevices with diversified functionalities at different frequencies. As an example, we fabricate several vortex-beam generators and demonstrate that they not only exhibit ultrahigh working efficiencies but also are immune from normal-mode background interferences.

Figure 1

(a) Schematics of a $\varphi$-oriented meta-atom with transmission and reflection characteristics described by two Jones matrices $\mathbf{T}$ and $\mathbf{R}$, and the $E$ fields radiated from the electric and magnetic currents (${\overrightarrow{J}}^e$ and ${\overrightarrow{J}}^m$) generated on the meta-atom. (b) Anomalous and normal transmissions and reflections (with efficiencies of $T_a$, $R_a$, $T_n$, $R_n$) generated by a generic PB metasurface consisting of meta-atoms with spatially varying orientation angles $(0,\varphi ,2\varphi ,3\varphi \dots )$ under illumination of a linearly polarized incident beam. (c) Schematics of the 100%-efficiency PSHE achieved by a PB metasurface satisfying Eq. (2), with $|x⟩$, $|+⟩$, $|-⟩$ representing beams with linear polarization, left circular polarization, and right circular polarization, respectively.

Figure 2

(a) Transmission amplitude and two equal-transmission-phase lines in the ${ϵ}_A-{ϵ}_B$ diagram for the $ABA$ model (see inset) with the thicknesses of two layers as $d_A/\lambda =0.063$ and $d_B/\lambda =0.014$ calculated by the transfer-matrix method (TMM) at wavelength $\lambda$. Evolutions of the (b) amplitude and (c) phase of the electric field inside the model $ABA$ structure (with ${ϵ}_A^u=6.2$, ${ϵ}_B^u=-48$, ${ϵ}_A^v=15.5$, ${ϵ}_B^v=240$) and the realistic $ABA$ structure (see the Fig. 3 caption details) illuminated by normally incident EM waves polarized along two principle axes at 10.5 GHz calculated by the TMM (for the model) and FDTD simulations (for the realistic structure). Field integrations over the $x\text{−}y$ plane within a unit cell are performed to obtain the FDTD results. We set $d_A=1.8\mathrm{mm}$ and $d_B=0.4\mathrm{mm}$ in the model $ABA$ structure.

Figure 3

(a) Schematics of the $ABA$ meta-atom and individual $A$ structure and $B$ structure. Dielectric spacers with thickness $h=2\mathrm{mm}$ and $ϵ=4.6$ are adopted to separate three metallic structures to form the final $ABA$ meta-atom. (b) Pictures of the fabricated layer $A$ (left) and layer $B$ (right). Measured and FDTD simulated spectra of transmission (c) amplitude and (e) phase for a metasurface consisting of a periodic array of $ABA$ meta-atoms (with periodicity $7\times 7{\mathrm{mm}}^2$). Efficiencies of (d) anomalous or normal transmissions and (f) anomalous or normal reflections for a PB metasurface constructed with the $ABA$ meta-atoms studied in (c),(e) calculated with Eq. (1) based on measured or simulated, transmission or reflection characteristics of the meta-atom. Here, $a=5.8\mathrm{mm}$, $w=1.1\mathrm{mm}$, $d=6.5\mathrm{mm}$.

Figure 4

Spectra of (a) amplitudes and (b) phases of the electric and magnetic susceptibilities of our meta-atom obtained by integrating FDTD-simulated electric or magnetic current distributions inside the structure illuminated by normally incident plane waves with polarizations along the $\widehat{u}$ and $\widehat{v}$ axes.

Figure 5

(a) Picture of fabricated PB metasurface formed by the $ABA$ meta-atoms studied in Fig. 3. Measured scattered-field intensities (color map) in the (b),(c) transmission and (e),(f) reflection sides versus the frequency and the detecting angle for the PB metasurface illuminated by normally incident LP beams. The receivers are circularly polarized antennas with polarization (b),(f) LCP and (c),(e) RCP, respectively. (d) Absolute efficiencies of the four modes versus frequency for the PB metasurface obtained by integrations over the appropriate angle regions of different modes based on the experimental data in (b),(c),(e),(f). Blue stars in (b),(c),(e),(f) represent the results obtained based on the generalized Snell’s law.

Figure 6

FDTD-simulated scattered-field intensities (color map) in the (b),(c) transmission and (e),(f) reflection regions versus the frequency and detecting angle for the PB metasurface illuminated by the normally incident LP beams. Simulated absolute efficiencies of the four modes in the cases where the metasurfaces are illuminated by (a) RCP and (d) LCP beams. The maximum value of $T_a$ is 94% at 10.5 GHz.

Figure 7

Pictures of fabricated vortex-beam generators with topological charge (a) $q=1$, (d) $q=2$, and (g) $q=3$ constructed with the $ABA$ meta-atom studied in Fig. 3. Measured $\mathrm{Re}(E_x)$ distributions on an $x\text{−}y$ plane 50 cm below two metasurfaces, which are shined by normally incident RCP waves at (b),(e),(h) 10.5 GHz and (c),(f),(i) 14.5 GHz.