Controlling photonic spin Hall effect via exceptional points

The photonic spin Hall effect (SHE), featured by a spin-dependent transverse shift of an impinging optical beam driven by its polarization handedness, has many applications including precise metrology and spin-based nanophotonic devices. It is highly desirable to control and enhance the photonic SHE. However, such a goal remains elusive, due to the weak spin-orbit interaction of light, especially for systems with optical loss. Here we reveal a flexible way to modulate the photonic SHE via exceptional points, by exploiting the transverse shift in a parity-time (PT) symmetric system with balanced gain and loss. The underlying physics is associated with the near-zero value and abrupt phase jump of the reflection coefficients at exceptional points. We find that the transverse shift is zero at exceptional points, but it is largely enhanced in their vicinity. Moreover, the transverse shift switches its sign across the exceptional point, resulting from spontaneous PT-symmetry breaking. Due to the sensitivity of transverse shift at exceptional points, our work also indicates that the photonic SHE can enable a precise way to probe the location of exceptional point in photonic systems.

Figure 1

Schematic of enhanced photonic spin Hall effect (SHE) via exceptional points. (a) Schematic illustration of photonic SHE for the reflected waves. The blue and green arrows indicate the directions of polarization vectors or the electric fields associated with each plane wave component before and after reflection. (b) Photonic SHE in a lossy system. (c) Photonic SHE in a PT-symmetric system with the balanced gain and loss distribution. Due to the photonic SHE, the reflected beam with left-handed or right-handed circular polarization (LCP or RCP) is split in the transverse or $y$ direction and has opposite transverse shifts, namely ${\delta }_{\mathrm{LCP}}=-{\delta }_{\mathrm{RCP}}$. For the reflected beam with LCP or RCP, the transverse shift near the exceptional point in PT-symmetric systems in (c) [see Fig. 2] can be much larger than that in lossy systems in (b) [see Fig. S2], i.e., $|{\delta }_{\mathrm{lossy}}|\ll |{\delta }_{\mathrm{PT}}|$. The slab with loss (gain) has a refractive index of $n_{\mathrm{loss}}=n_R+i{n}_I$ ($n_{\mathrm{gain}}=n_{\mathrm{loss}}^{*}$). The incident light is a Gaussian beam with horizontal ($p$-polarized waves) or vertical ($s$-polarized waves) polarization and has a beam waist of $30\lambda$. As a conceptual demonstration, $n_R=3$ is chosen, the two slabs with loss or gain have an identical thickness of $d=\lambda /5$.

Figure 2

Representation in parameter space of giant photonic SHE near exceptional points for the reflected beam. Here ${\delta }_{\mathrm{LCP}}$ is plotted as a function of $|\mathrm{Im}\left(n_{\mathrm{loss}/\mathrm{gain}}\right)|$ and the incident angle ${\theta }_{\mathrm{i}}$. The structural setup is the same as Fig. 1.

Figure 3

Explaining the exotic photonic SHE near/at the exceptional points from the perspective of reflection coefficients. The magnitude and phase of reflection coefficients are shown in (a)–(d) and (e)–(h), respectively.

Figure 4

Real-space demonstration of photonic SHE near/at exceptional points for the reflected beam. (a)–(f) Field distribution of the reflected beam with LCP at the interface. The $p$-polarized Gaussian beam with an incident angle of ${30}^{\circ }$ is chosen. (g), (h) Magnitudes of $|\frac{\partial r^p}{\partial {\theta }_i}|$ and $|r^s|$ near the exceptional points.