Abstract

The antiphase state is a simple periodical dynamical state that was observed recently in experiments on a three-mode solid-state laser.¹ Specifically, the antiphase state for a system of N globally coupled oscillating elements occurs when each element has the same waveform but no two oscillators have the same phase. In fact, these dynamical states–which are variously known as “splay phase states,” “discrete rotating waves,” “waltzing states,” and “ponies on a merry-go-round” in the physics and mathematics literature–have been the focus of intense study of late. As a practical matter, antiphase states necessarily occur with an extraordinarily high multiplicity: one such state implies the coexistence of some (N- 1) others! Although this property can lead to a new kind of noise sensitivity known as attractor crowding,² Otsuka has suggested³ exploiting the multiplicity to make a novel multistate optical memory element; a similar application has been proposed for superconducting Josephson-junction arrays. Any such application requires that the antiphase states be stable (i.e., attracting in phase space).

© 1993 Optical Society of America