Anomalous Spontaneous Emission Enhancement by Non-Hermitian Momentum-Space Bound States in the Continuum

Abstract

Conventional Purcell theory emphasizes high quality factors (Q) for spontaneous emission (SE) enhancement in cavities, but overlooks collective Bloch mode effects in periodic nanostructures like photonic crystal slabs. We introduce a unified temporal coupled-mode framework to compute Purcell and photoluminescence factors through momentum-space integration, revealing anomalous SE enhancement by non-Hermitian momentum-space bound states in the continuum (BICs). In silicon gratings with comparable effective mode volumes, this yields substantial SE enhancement in low-Q regimes--defying the traditional high-Q paradigm and inversely correlated with system Q--while emission rates are stably twice the photoluminescence, eliminating critical coupling requirements. Unique spectral profiles, contradicting Lorentzian/Fano assumptions, arise from collective mode interactions. Full-wave simulations confirm these challenges to conventional wisdom, with non-Hermitian BICs outperforming high-Q designs across broad numerical apertures. This establishes a novel paradigm leveraging non-Hermiticity and topological protection for robust, bright emitters, redefining nanophotonic applications in lasers and light-emitting diodes

Figures (4)

• Figure 1: Schematic of SE enhancement in local and nonlocal metasurfaces. (a) Local metasurface with absorbing boundaries (e.g., PML), where dipoles couple to discrete modes. (b) Nonlocal metasurface with periodic boundaries, supporting orthogonal Bloch modes labeled by in-plane wavevector $\mathbf{k}$. (c) Continuous band structure in momentum space, where a dipole excites all modes at a given frequency. (d) PL collected from the radiative power $P_{\rm rad}$ within a limited NA in momentum space.
• Figure 2: (a) Schematic of the ternary folded grating. (b) Grating structural parameters. (c) TE mode field profiles of QGM and BIC at the $\Gamma$ point. (d) Radiation spectra under BIC excitation near the eigenfrequency of BIC: simulations (left) and analytical model (right), comparing LDOS ($P_\text{tot}$, up) and PL ($P_\text{rad}$, bottom). (e) Mode $Q$ factor versus folding strength $S$. (f) QGM excitation: total emission (gray) and PL (colored) under different folding strength $S$ in consistent with (e). The colored background represents analytical model.
• Figure 3: (a) Grating with weak refractive index contrast. (b) Supported TM-BIC mode magnetic field distribution. (c) Momentum-space band structure, with linewidth and color determined by the imaginary part of eigenfrequencies. (d) Momentum-space far-field PL spectra. (e-h) Results for a silicon grating with strong non-Hermiticity, exhibiting low radiation $Q$ factors yet retaining a flat-BIC.
• Figure 4: (a) Purcell factor for flat-BIC (black line), conventional BIC (red line), and QGM (blue line). (b,c) Analytical fit between numerical and theoretical spectrum, corresponding to the dashed boxes in (a), respectively. (d,f) Purcell (gray solid) and PL (colored solid) factors for BIC and QGM under varying low-index value, $\Re[n_\text{low}]$. (e) Peak values of $F_p$ and $F_\text{PL}$ from (d) versus $\Re[n_\text{low}]$. (g) PL enhancement under different NA collections. Black: flat-BIC. Red: conventional BIC. Blue: conventional QGM.