Nonlinear transverse modes of large-aspect-ratio homogeneously broadened lasers: II. Pattern analysis near and beyond threshold.

摘要: Complex order-parameter equation descriptions of pattern evolution in large-aspect-ratio two-level and Raman lasers are derived systematically as solvability conditions a multiple-scales asymptotic expansion the original Maxwell-Bloch laser equations powers small parameter. These amplitude equations, although strictly valid near threshold for lasing, shown to capture essential features instability well beyond lasing threshold. A technical difficulty that can arise laser, namely, subcriticality bifurcation critical wave number, is not addressed present paper only when this situation does arise. Analytical expressions long-wavelength phase instabilities underlying traveling-wave pattern, which appears natural nonlinear mode detuning from gain peak positive, obtained coefficients Cross-Newell equation. Phase boundaries, computed via complex equation, be consistent all cases studied with exception case subcritical approaches number ${\mathit{k}}_{\mathit{c}}$.