Neuromorphic Functions of Light in Parity‐Time‐Symmetric Systems

Abstract

As an elementary processor of neural networks, a neuron performs exotic dynamic functions, such as bifurcation, repetitive firing, and oscillation quenching. To achieve ultrafast neuromorphic signal processing, the realization of photonic equivalents to neuronal dynamic functions has attracted considerable attention. However, despite the nonconservative nature of neurons due to energy exchange between intra‐ and extra‐cellular regions through ion channels, the critical role of non‐Hermitian physics in the photonic analogy of a neuron has been neglected. Here, a neuromorphic non‐Hermitian photonic system ruled by parity‐time symmetry is presented. For a photonic platform that induces the competition between saturable gain and loss channels, dynamical phases are classified with respect to parity‐time symmetry and stability. In each phase, unique oscillation quenching functions and nonreciprocal oscillations of light fields are revealed as photonic equivalents of neuronal dynamic functions. The proposed photonic system for neuronal functionalities will become a fundamental building block for light‐based neural signal processing.

Topologically Protected All‐Optical Memory

“…[ 16 ] In handling dynamical systems, we focus on the topological properties of the “trajectories” of optical states, which have been widely employed in dynamical theory. [ 13 ] In previous works on non‐Hermitian and nonlinear photonic molecules, [ 17,18 ] we demonstrated the topological classification of the dynamical trajectories of optical “intensity” distributions, also showing the critical role of PT symmetry in the form of the dynamical trajectories. Because of the nature of topology, the deliberate design of the photonic molecules allows for the existence of topologically protected stable states—oscillation quenching states [ 17,18 ] —which preserve their convergent dynamical trajectories, and therefore, provide subsequent noise immunity.…”

“…Although such topologically protected quenching states provide robustness to any type of defect as long as the defect preserves dynamical trajectories, the oscillation quenching states in previous platforms [17,18] cannot provide the all-optical memory functions necessary for in-memory processors. It is due to the lack of coexisting multiple stable states-at least ON and OFF states are necessary for binary-level memory, which should also be tunable with all-optical modulation.…”

“…Therefore, the previous approaches can be applied only to single-channel applications or externally modulated multichannel devices such as laser stabilization, signal regeneration, or electro-optical rectification. [17,18] To realize multiple oscillation quenching states in a given system and achieve an all-optical transition between these states, we investigate a triatomic PT-symmetric photonic molecule composed of one Hermitian and linear resonator and two non-Hermitian and nonlinear resonators (Figure 1). In the linear regime, the triatomic PT-symmetric system has been widely studied to utilize higher-order exceptional points (EPs) [12,[21][22][23][24][25] for enhanced sensitivity, [12] mechanical cooling, [21] cavity magnonics systems, [23] successive state conversion, [24] and wireless power transfer.…”

“…To explore the oscillation quenching states that result in stable field intensities inside resonators, [17,18] we examine the dynamics of the real-valued field intensities I G,N,L obtained from the separation of amplitudes and phases in the complexvalued field ψ G,N,L = (I G,N,L ) 1/2 exp(iθ G,N,L ). [29] Notably, because the applied optical nonlinearities in Equation ( 1) are dependent only on the field intensity, the equation for I G,N,L describes well the stability and transition condition of optical states, as described in later sections.…”

“…[20,31] We also emphasize that the coexisting phases C U1-U2 and C U1-BR inherently include two stable states at a given set of system parameters, in sharp contrast to previous approaches that support only a unique stable state with the fixed PT-symmetric phase. [17,18] For a given set of system parameters, each coexisting phase supports multiple stable equilibria, which are protected by the topology of the state trajectories in the wave quantity space: the 3D parameter space of Ι G -Ι N -Ι L . Therefore, we can envisage the realization of robust all-optical memory by using these equilibria as "topologically protected memory states".…”