Observation of Geometric Parametric Instability Induced by the Periodic Spatial Self-Imaging of Multimode Waves

Spatiotemporal mode coupling in highly multimode physical systems permits new routes for exploring
complex instabilities and forming coherent wave structures. We present here the first experimental
demonstration of multiple geometric parametric instability sidebands, generated in the frequency domain
through resonant space-time coupling, owing to the natural periodic spatial self-imaging of a multimode
quasi-continuous-wave beam in a standard graded-index multimode fiber. The input beam was launched in
the fiber by means of an amplified microchip laser emitting sub-ns pulses at 1064 nm. The experimentally
observed frequency spacing among sidebands agrees well with analytical predictions and numerical
simulations. The first-order peaks are located at the considerably large detuning of 123.5 THz from the
pump. These results open the remarkable possibility to convert a near-infrared laser directly into a broad
spectral range spanning visible and infrared wavelengths, by means of a single resonant parametric
nonlinear effect occurring in the normal dispersion regime. As further evidence of our strong space-time
coupling regime, we observed the striking effect that all of the different sideband peaks were carried by a
well-defined and stable bell-shaped spatial profile.
DOI: 10.1103/PhysRevLett.116.183901
Pattern formation as the result of parametric instability
(PI) is a universal phenomenon that is widely encountered
in many branches of physics [1]. PIs emerge in wave
propagation thanks to the interplay between nonlinearity
and the dispersion of the medium, when one of the medium
parameters is periodically modulated along the longitudinal
direction. In the case of externally forced systems, PI is
commonly referred to as the Faraday instability, following
its initial observation in hydrodynamics under the external
modulation of the vertical position of an open fluid tank [2].
Besides fluid mechanics, Faraday-like patterns were subsequently
reported in a variety of physical contexts such as
crystallization dynamics, chemical systems, or laser physics
[3–7]. In addition to parametrically forced systems,
many physical systems naturally exhibit collective oscillations
that may lead to a so-called geometric-type of
parametric instability