Tailor the Functionalities of Metasurfaces Based on a Complete Phase Diagram

Metasurfaces in a metal-insulator-metal configuration have been widely used in photonics, with applications ranging from perfect absorption to phase modulation, but why and when such structures can realize what functionalities are not yet fully understood. Here, we establish a complete phase diagram in which the optical properties of such systems are fully controlled by two simple parameters (i.e., the intrinsic and radiation losses), which are, in turn, dictated by the geometrical or material properties of the underlying structures. Such a phase diagram can greatly facilitate the design of appropriate metasurfaces with tailored functionalities demonstrated by our experiments and simulations in the terahertz regime. In particular, our experiments show that, through appropriate structural or material tuning, the device can be switched across the phase boundaries yielding dramatic changes in optical responses. Our discoveries lay a solid basis for realizing functional and tunable photonic devices with such structures.

Figure 1

Schematics of (a) the MIM system and (b) the single-port resonator model in CMT. Phase diagrams of (c) the on-resonance absorption $A$ and (d) the span of reflection phase $\mathrm{\Delta }\varphi$ versus $Q_r$ and $Q_a$ calculated with CMT for the single-port model shown in (b).

Figure 2

(a) $Q_r$ and $Q_a$ for a series of metasurfaces (see inset for system geometry) with varying $h$ obtained by analytical calculations (lines) based on Eqs. (2) and (3) or retrieved from FDTD-simulated spectra (open symbols) and from experimental results (solid symbols). Other geometrical parameters of these metasurfaces are fixed as $a=20\mu \mathrm{m}$, $d=100\mu \mathrm{m}$, $h_m=0.05\mu \mathrm{m}$. (b) Replot of the results displayed in (a) into a $Q_a-Q_r$ phase diagram, where the $Q_r=Q_a$ line separates the overdamped region (blue) and the underdamped region (orange). Inset shows an optical image of the sample with $h=8\mu \mathrm{m}$. Spectra of (c) reflectance and (d) reflection phase of four typical samples with $h$ given in the legend of (c) obtained by THz TDS measurements (symbols) and FDTD simulations (lines).

Figure 3

(a) $Q_r$ and $Q_a$ for a series of metasurfaces with varying slit width $a$ obtained by analytical calculations (lines) based on Eqs. (2) and (3) or retrieved from FDTD-simulated spectra (open symbols) and experimental results (solid symbols). Other geometrical parameters of these metasurfaces are fixed as $h=8\mu \mathrm{m}$, $d=100\mu \mathrm{m}$, $h_m=0.05\mu \mathrm{m}$. (b) Replot of the results displayed in (a) in a $Q_a-Q_r$ diagram. Spectra of (c) reflectance and (d) reflection phase of four typical samples with $a$ given in the legend of (c) obtained by THz TDS measurements (symbols) and FDTD simulations (lines).

Figure 4

(a) $Q_r$ and $Q_a$ for a series of metasurfaces with ${\sigma }_d$ varying from 8 to $50\mathrm{S}/\mathrm{m}$ and with metal assumed lossless obtained by analytical calculations (circles) based on Eqs. (2) and (3) or retrieved from FDTD-simulated spectra (squares). (b) $Q_r$ and $Q_a$ for a series of metasurfaces with ${\sigma }_m$ varying from $5\times {10}^4$ to $2\times {10}^6\mathrm{S}/\mathrm{m}$ and with ${\sigma }_d$ fixed as $0\mathrm{S}/\mathrm{m}$ obtained by analytical calculations (circles) based on Eqs. (2) and (3) or retrieved from FDTD-simulated spectra (squares). Other parameters are fixed as $h=8\mu \mathrm{m}$, $a=20\mu \mathrm{m}$, $d=100\mu \mathrm{m}$, $h_m=0.05\mu \mathrm{m}$.

Figure 5

(a) Optical images of three fabricated metallic cross-shaped samples (labeled as $S1$, $S2$, and $S3$) with geometrical parameters given in units of $\mu \mathrm{m}$. Bright colored areas are occupied by Au. (b) $Q_r$ and $Q_a$ for three metasurfaces retrieved from FDTD-simulated spectra (open squares) and retrieved from experimental results (solid symbols). Spectra of (c) reflectance and (d) reflection phase of three samples obtained by THz TDS measurements (symbols) and FDTD simulations (lines).