Related Experiment Video
Updated: Sep 13, 2025

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior
Published on: April 13, 2016
Geometric parametric instabilities induced by beatings of two modes
None:
The phenomenon of geometric parametric instabilities (GPI) has been initially introduced and studied within the context of multiple modes' beating dynamics in graded-index fibers. The large numbers of participating modes, supported by the specific structure of graded-index fibers, enhance the amplitude of the resulting modulation, and therefore lead to pronounced instabilities. However, this is not a necessary condition for the emergence of GPI. Furthermore, the complex multi-mode nonlinear dynamics hinder theoretical analysis of GPI. In this work, we demonstrate that even two modes beating is sufficient to trigger GPI. As such, the phenomenon of GPI is generic and can be observed in a large class of optical systems. We provide a detailed theoretical analysis of GPI induced by two modes' beatings and derive the generalized phase-matching conditions, which reveal the fundamental physical mechanisms behind the multi-peak structure of such parametric resonances.
Related Concept Videos
Modes of Standing Waves - I
Forced Oscillations
Modes of Standing Waves: II
For a tube open at one end and closed at the other filled with air, the modes are such that there is always an antinode at the open end and a node at the closed end....
Damped Oscillations
Although friction and other non-conservative...
Beats
Pole and System Stability
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's...

