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Abstract Exceptional points (EPs)—singularities in the parameter space of non-Hermitian systems where two nearby eigenmodes coalesce—feature unique properties with applications such as sensitivity enhancement and chiral emission. Existing realizations of EP lasers operate with static populations in the gain medium. By analyzing the full-wave Maxwell–Bloch equations, here we show that in a laser operating sufficiently close to an EP, the nonlinear gain will spontaneously induce a multi-spectral multi-modal instability above a pump threshold, which initiates an oscillating population inversion and generates a frequency comb. The efficiency of comb generation is enhanced by both the spectral degeneracy and the spatial coalescence of modes near an EP. Such an “EP comb” has a widely tunable repetition rate, self-starts without external modulators or a continuous-wave pump, and can be realized with an ultra-compact footprint. We develop an exact solution of the Maxwell–Bloch equations with an oscillating inversion, describing all spatiotemporal properties of the EP comb as a limit cycle. We numerically illustrate this phenomenon in a 5-μm-long gain-loss coupled AlGaAs cavity and adjust the EP comb repetition rate from 20 to 27 GHz. This work provides a rigorous spatiotemporal description of the rich laser behaviors that arise from the interplay between the non-Hermiticity, nonlinearity, and dynamics of a gain medium. 

Theoretical bounds are commonly used to assess the limitations of photonic design. Here we introduce a more active way to use theoretical bounds, integrating them into part of the design process and identifying optimal system parameters that maximize the efficiency limit itself. As an example, we consider wide-field-of-view high-numerical-aperture metalenses, which can be used for high-resolution imaging in microscopy and endoscopy, but no existing design has achieved a high efficiency. By choosing aperture sizes to maximize an efficiency bound, setting the thickness according to a thickness bound, and then performing inverse design, we come up with high-numerical-aperture (NA=0.9) metalens designs with, to our knowledge, record-high 98% transmission efficiency and 92% Strehl ratio across all incident angles within a 60° field of view, reaching the maximized bound. This maximizing-efficiency-limit approach applies to any multi-channel system and can help a wide range of optical devices reach their highest possible performance.