Manifestation of $PT$ Symmetry Breaking in Polarization Space with Terahertz Metasurfaces

By utilizing the vector nature of light as well as the inherent anisotropy of artificial meta-atoms, we investigate parity time symmetry breaking in polarization space using a metasurface with anisotropic absorption, whose building blocks consist of two orthogonally orientated meta-atoms with the same resonant frequency but different loss coefficients. By varying their coupling strength, we directly observe a phase transition in the eigenpolarization states of the system, across which the long axis of the eigenpolarization ellipses experience a sudden rotation of 45°. Despite the lack of rotational symmetry of the metasurface, precisely at the phase transition, known as the exceptional point, the eigenmodes coalesce into a single circularly polarized state. The $PT$ symmetric metasurfaces are experimentally implemented at terahertz frequencies.

Figure 1

$PT$ symmetric dipole model and metasurface implementation. (a) Schematic of $PT$ symmetric metasurface with less lossy dipoles (blue) and more lossy dipoles (red). (b)–(f) Eigenstates of Eq. (2) for varying $G_{xy}$, representing the eigenpolarization states of transmission through an ideal $PT$ symmetric metasurface. (g) Photograph of $PT$ symmetric metasurface composed of 300 nm thick silver (yellow or light gray) and lead (turquoise or dark gray) SRRs on silicon substrate.

Figure 2

Full-wave simulation results for a $PT$ symmetric metasurface with variable coupling strength, controlled by changing the distance between more and less lossy SRRs between 2 and $20\mu \mathrm{m}$. (a) Polarization eigenstates for different SRR separations plotted on the Poincaré sphere with LCP at the north pole, the dashed lines represent the eigenstates of an ideal $PT$ symmetric dipole model with varying coupling coefficients and the single star occupying the southern hemisphere represents a change of sign of the coupling coefficient caused by the domination of the inductive coupling at large ring separation. Panels (b)–(f) show sampled transmission spectra for the eigenpolarization states (g)–(k) which correspond to points labeled in (a), ring separation in $\mu \mathrm{m}=2$ (b),(g), 12 (c),(h), 14.5 (d),(i), 16 (e),(j), 19 (f),(k). (l) Circular transmission spectra for SRR configuration closest to the EP (d),(i).

Figure 3

Terahertz time domain spectroscopy measurements for a $PT$ symmetric metasurface with variable coupling strength, controlled by changing the distance between lead and silver SRRs between 2 and $20\mu \mathrm{m}$. (a) Polarization eigenstates for different SRR separations plotted on the Poincaré sphere with LCP at the north pole, the dashed lines represent the eigenstates of an ideal $PT$ symmetric dipole model with varying coupling coefficients. Panels (b)–(f) show sampled transmission spectra for the eigenpolarization states (g)–(k) which correspond to points labeled in (a), nominal ring separation in $\mu \mathrm{m}=2$ (b),(g), 10 (c),(h), 11.5 (d),(i), 16 (e),(j), 20 (f),(k). (l) Circular transmission spectra for SRR configuration closest to the EP (d),(i).