Quasinormal modes (QNMs) are essential for understanding the stability and
resonances of open systems, with increasing prominence in black hole physics.
We present here the first study of QNMs of optical potentials. We show that
solitons can support QNMs, deriving a soliton perturbation equation and giving
exact analytical expressions for the QNMs of fiber solitons. We discuss the
boundary conditions in this intrinsically dispersive system and identify novel
signatures of dispersion. From here, we discover a new analogy with
astrophysical black holes and describe a regime in which the soliton is a
robust black hole simulator for light-ring phenomena. Our results invite a
range of applications, from the description of optical pulse propagation with
QNMs to the use of state-of-the-art technology from fiber optics to address
questions in black hole physics, such as QNM spectral instabilities and the
role of nonlinearities in ringdown.Comment: 5 pages, 3 figure