Pseudo-anapole regime in terahertz metasurfaces

We present the numerical, theoretical, and experimental study of a terahertz metasurface supporting a pseudo-anapole. Pseudo-anapole effect arises when electric and toroidal dipole moments both tend to a minimum, instead of destructive interference between electric and toroidal dipole moments in conventional anapole mode. Such overlap allows resonance suppression of electric type radiation. Thus it becomes possible to study the multipoles of other families and higher order excitations. We estimate multipole contribution to the metasurface response via the multipole expansion method. The series is extended with such terms as mean-square radii and multipole interference. We also study the metasurface geometrical tunability. Via scaling, we demonstrate that it is possible to control the metasurface toroidal and electric responses independently. This in turn proves the fact that these multipoles have different physical origin. Moreover, we demonstrate that the proposed metasurface allows excitation of coherent magnetic dipole and electric quadrupole modes, which is crucial for planar cavities and lasing spasers in nanophotonics.

Figure 1

(a) Illustration of the metasurface and (b) SEM image of the metasurface fragment, where $\vec{k}$ and $\vec{E}$ denote the propagating direction and polarization of the incident THz field, respectively. (c) Current distribution in the unit cell of the metasurface at the frequency of 0.8 THz; (d) and (e) are the distributions of electric and magnetic fields at the frequency of 0.8 THz, respectively.

Figure 2

(a) Simulated plane wave (blue dashed), simulated limited area (red short dashed), and measured limited area (black solid) transmission of the material in the THz range. (b) Simulated 0.8 THz resonance $Q$ factor as a function of beam diameter.

Figure 3

Intensity of the waves generated by multipoles for the geometries vertically scaled by the factors of (a) 0.7, (b) 1, and (c) 1.3, respectively. Dipole modes are shown in dashed magenta, quadrupoles in dotted beige, and higher order multipoles in green dash-dotted curves, respectively.

Figure 4

Interference between multipoles for the geometries of (a) scale 0.7, (b) scale 1, and (c) scale 1.3, respectively.

Figure 5

Transmission, absorption, and reflection spectra for the geometries of vertical (a) scale 0.7, (b) scale 1, and (c) scale 1.3.

Figure 6

Retrieved silicon substrate properties in the THz range: (a) complex refractive index and (b) complex permittivity.