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Exceptional points (EPs)--singularities in the parameter space ofnon-Hermitian systems where two nearby eigenmodes coalesce--feature uniqueproperties with applications for microcavity lasers such as sensitivityenhancement and chiral emission. Present EP lasers operate with staticpopulations in the gain medium. Here, we show theoretically that a laseroperating sufficiently close to an EP will spontaneously induce amulti-spectral multi-modal instability that creates an oscillating populationinversion and generates a frequency comb. The comb formation is enhanced by thenon-orthogonality of modes via the Petermann factor. Such an "EP comb" featuresan ultra-compact size and a widely tunable repetition rate, without requiringexternal modulators or a continuous-wave pump. We develop an exact ab initiodynamic solution of the space-dependent Maxwell-Bloch equations, describing allsteady-state properties of the EP comb. We illustrate this phenomenon in arealistic parity-time-symmetric 5-{\mu}m-long AlGaAs cavity and validate ourprediction with finite-difference time-domain simulations. This work revealsthe rich physics that connect non-Hermitian degeneracies and the nonlineardynamics of gain media to fundamentally alter the laser behavior.

Dynamic gain and frequency comb formation in exceptional-point lasers