An alternative interpretation of the Zeeman and Faraday laser

In this paper we present a summary of the experimental observations of the polarization behavior of a Zeeman and Faraday laser and discuss difficulties with the usual interpretation in terms of two circularly polarized modes. To illustrate a single-mode view we solve analytically the problem of a laser with a weak dichroism and a weak Faraday rotation. The theory explains essentially all of the experimental observations. Equally important, we show that circularly polarized modes by themselves do not satisfy the accepted laser equations and consequently that a two-mode interpretation is not tenable. Our treatment is couched in the language of nonlinear dynamics. The transition from a fixed-point solution to a periodic solution that occurs at a critical field is identified as a saddle-point instability. In three separate appendixes, we consider: a polarization propagation picture that gives us physical insight into the behavior of a dichroic Zeeman or Faraday laser, possible extensions of our calculations to cavities with large anisotropies, and we discuss the merits of ``bare cavity'' laser models. {} 1996 The American Physical Society.