  Neurons and other excitable systems can release energy suddenly given a small
stimulus. Excitability has recently drawn increasing interest in optics, as it
is key to realize all-optical artificial neurons enabling speed-of-light
information processing. However, the realization of all-optical excitable units
and networks remains challenging. Here we demonstrate how laser-driven optical
cavities with memory in their nonlinear response can sustain excitability
beyond the constraints of memoryless systems. First we demonstrate different
classes of excitability and spiking, and their control in a single cavity with
memory. This single-cavity excitability is limited to a narrow range of memory
times commensurate with the linear dissipation time. To overcome this
limitation, we explore coupled cavities with memory. We demonstrate that this
system can exhibit excitability for arbitrarily long memory times, even when
the inter-cavity coupling rate is smaller than the dissipation rate. Our
coupled-cavity system also sustains spike trains -- a hallmark of neurons --
that spontaneously break mirror symmetry. Our predictions can be readily tested
in thermo-optical cavities, where thermal dynamics effectively give memory to
the nonlinear optical response. The huge separation between thermal and optical
time scales in such cavities is promising for the realization of artificial
neurons that can self-organize to the edge of a phase transition, like many
biological systems do.
