Twisted light from topological chiral exceptional points in a nanolaser array

TL;DR

This work addresses deterministic nanoscale OAM generation by leveraging non-Hermitian topology in a compact four-cavity ring that realizes a Rice-Mele-like lattice with complex detunings. The authors identify a symmetry-protected non-Hermitian zero mode from non-Hermitian particle-hole symmetry, enforcing a $\pm\frac{\pi}{2}$ phase progression between neighboring cavities and yielding a chiral exceptional point at $\Delta = \pm i (t_1 - t_2)$ that enables unidirectional energy flow and OAM emission. Experimentally, four InP photonic-crystal nanolasers demonstrate a CEP with robust phase winding, confirmed via Sagnac interferometry and phase-resolved imaging, and nonlinear gain saturation preserves the OAM over a range of pump imbalances. The element-wise design principle introduced here offers a scalable route to compact, phase-locked OAM lasers and broadens the potential for structured light generation in integrated photonics, with implications for higher-order OAM states and other resonator platforms.

Abstract

We propose and experimentally demonstrate an orbital angular momentum (OAM) nanolaser array arranged in a ring geometry on an InP-based photonic crystal membrane. The device realizes a non-Hermitian extension of the Rice-Mele model, featuring alternating coupling strengths and imaginary on-site detunings. This configuration supports a symmetry-protected zero mode stabilized by non-Hermitian particle-hole symmetry, which enforces a uniform $π/2$ phase shift between adjacent nanolasers, establishing a coherent phase winding around the array. By adjusting the gain/loss contrast in a parity-time (PT)-like pumping scheme, the system can be tuned to a chiral exceptional point, where energy flows unidirectionally between nanocavities despite their reciprocal coupling. This symmetry-enforced, directional tunneling leads to far-field emission carrying non-zero OAM, providing a direct signature of the phase-structured lasing mode. Our results demonstrate a robust and scalable strategy for engineering compact, phase-locked laser arrays with controllable angular momentum output, and open new avenues for structured light generation in integrated photonic platforms.

Figures (5)

• Figure 1: (a) Schematic diagram of our nanolaser array. The unit cell is a dimer with sufficient gain (loss) in the left cavity, and with the lattice momentum $q=\pi$ between two unit cells, a CCW (CW) non-Hermitian zero mode is achieved (indicated by the arrow and the phase of the complex amplitude in each cavity). Dashed line in the middle shows the mirror symmetry between these two configurations. (b) Band structure of the lattices in (a). Three cases are shown: $\Delta = 0$ (dotted line), $\Delta=it_1$ (solid line), $\Delta=i(t_1-t_2)$ (dashed line). At $q=\pi$, they have 0, 2 (red dots), and 1 non-Hermitian zero mode (black dot; a CEP). Red and black dots overlap in the left panel. $t_1=5$, $t_2=2$ are used.
• Figure 2: (a) PhC nanolaser array design consisting of four coupled cavities in a ring configuration. Arrows indicate the couplings $t_1\neq t_2$ due to the hole radius change (red dots), and false colors indicate the two sublattices A (cavities 1,3) and B (cavities 2,4) with detuning $\pm\Delta$. (b) Schematic of two chiral modes operating at CEPs in our coupled nanolaser array, with arrows indicating the Poynting vector. (c) COMSOL numerical simulations (circles), eigenvalue calculations with unsaturated gain [dashed blue line, from Eq. (\ref{['eq:L']})] and nonlinear results including gain saturation (solid red line) showing a CW CEP at $r=0.53$. Here $t_1-t_2=1.2, \alpha=3, \Delta_0=\alpha(t_1-t_2)$ and the total pump power for the linear case is $P_\text{tot}=2.9P_0$, for the nonlinear calculation, $P_\text{tot}=4.9P_0$, where $P_0$ is the threshold for a single cavity.
• Figure 3: Experimental (left column) and simulation results (right column) of the lasing spectrum. The CEP is below the laser threshold in (a,c) and above in (b,d). Bottom panels f show the field profiles of the chiral mode, with the nodal line(s) added in the far fields of the experimental data. In the nonlinear stochastic simulations, we take $t_1-t_2=0.5$, other parameters can be found in the Supplementary Note 5. The near fields are measured by imaging at the sample plane, whereas the far fields are obtained by imaging at the back focal plane of the objective.
• Figure 4: (a) Schematics of the Sagnac interferometer, enabling robust interferometric measurements with spatially shifted patterns. (b) Near-field interference pattern near the EP (left). The circles mark the positions of the cavities, and a fork-shaped feature appears at the center of the structure. The lower panel shows the corresponding phase distribution, revealing a clear phase singularity. The right panel presents the corresponding simulation results.
• Figure 5: Topological regions characterized by an $\mathbb{Z}_2$ index in the complex $\Delta$ plane. $t_{1},t_2$ are $5,\,2$ in panel (a) and $5-0.32i,\,2+0.1i$ in panel (b). Open circles mark the CEPs, and false colors show the identical OAM $\langle L_z\rangle$ of the two chiral modes in a single quartet [see Eq. (\ref{['eq:Lz']})].