Nonlinear Exceptional Points with a Complete Basis in Dynamics

Dynamic gain and frequency comb formation in exceptional-point lasers

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.

Arbitrarily Configurable Nonlinear Topological Modes

Topological modes (TMs) are typically localized at boundaries, interfaces and dislocations, and exponentially decay into the bulk of a large enough lattice. Recently, the non-Hermitian skin effect has been leveraged to delocalize the wave functions of TMs from the boundary and thus to increase the capacity of TMs dramatically. Here, we explore the capability of nonlinearity in designing and configuring the wave functions of TMs. With growing intensity, wave functions of these in-gap nonlinear TMs undergo an initial deviation from exponential decay, gradually merge into arbitrarily designable plateaus, then encompass the entire nonlinear domain, and eventually concentrate at the nonlinear boundary. Intriguingly, such extended nonlinear TMs are still robust against defects and disorders, and stable in dynamics under external excitation. Advancing the conceptual understanding of the nonlinear TMs, our results open new avenues for increasing the capacity of TMs and developing compact and configurable topological devices.

Synchronization under saturable nonlinearity

In this theoretical work, we introduce a nonlinear gain saturation law representative of the experimentally observed properties manifested by phenomena ranging from aeroacoustic shear layers in self-sustained cavity oscillations to flame heat release rate in thermoacoustic instabilities. Furthermore, this type of saturable gain may be relevant for a wider class of physical systems, such as active laser media in photonics. The nonlinearity discussed herein governs the fullscale behavior of a self-oscillator exhibiting linear loss under large amplitude perturbations, in contrast to the cubic damping and linear gain of the Van der Pol model. A distinctive characteristic of the proposed equation is the simple, well behaved gain term in the slow timescale dynamics.

Observation of Nonlinear Exceptional Points with a Complete Basis in Dynamics

The exotic physics associated with exceptional points (EPs) is always under the scrutiny of theoretical and experimental science. Recently, considerable effort has been invested in the combination of nonlinearity and non-Hermiticity. The concept of nonlinear EPs (NEPs) has been introduced, which can avoid the loss of completeness of the eigenbasis in dynamics while retaining the key features of linear EPs. Here, we present the first direct experimental demonstration of a NEP based on two non-Hermition coupled circuit resonators combined with a nonlinear saturable gain. At the NEP, the response of the eigenfrequency to perturbations demonstrates a third-order root law and the eigenbasis of the Hamiltonian governing the system dynamics is still complete. Our results bring this counterintuitive aspect of the NEP to light and possibly open new avenues for applications.