Single-mode and multimode instabilities in lasers and related optical systems

Under conditions that are properly detailed in the text, we demonstrate the existence of a deep and useful link between single-mode and multimode instabilities in lasers, and laser-related optical systems. We exhibit this connection explicitly for a homogeneously broadened single-mode and multimode laser model, with the possible inclusion of a driving external field; we also provide the necessary arguments to justify the validity of our conclusions for inhomogeneously broadened lasers, lasers with a nonuniform transverse intensity profile, lasers with saturable absorbers, laser systems in a Fabry-Perot cavity, and lasers whose dynamics is governed by the rate equations. Our main conclusion is that in all these systems, the existence of a single-mode instability implies necessarily a corresponding multimode instability in the ``good-cavity'' limit and, conversely, the existence of a multimode instability in the good-cavity limit implies, under an appropriate additional condition, the existence of a single-mode instability for a sufficiently ``bad'' cavity. We provide numerous examples to illustrate this correspondence, and provide evidence of its usefulness by making specific predictions on a new type of unstable behavior.