An organizing center for optical bistability and self-pulsing

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Abstract

The problem of self-pulsing in optically bistable systems is discussed within the framework of imperfect bifurcation theory. The joint appearance of a hysteresis cycle in the cw-transmission curve and of transitions to self-pulsing is described as an interaction between steady-state and Hopf bifurcations induced by varying the incident field intensity. The bifurcation equations for the most degenerate case are shown to be determined by a corank-two and codimension-four polynomial normal form. This form can be extracted from analytical and numerical studies on the Maxwell-Bloch equations, and acts as an organizing center for bistable switching and the self-pulsing mechanism. The structurally stable unfolded bifurcation diagrams are analyzed. Besides describing correctly and in a comprehensive way all bifurcations to self-pulsing that have so far been observed, a number of new generic transitions are predicted. These include self-pulsing from the low transmission branch and transitions leading to the formation of islands with self-pulsing behavior.

Original languageEnglish (US)
Pages (from-to)157-166
Number of pages10
JournalZeitschrift für Physik B Condensed Matter
Volume53
Issue number2
DOIs
StatePublished - Jun 1983
Externally publishedYes

ASJC Scopus subject areas

  • Condensed Matter Physics

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