Winner-takes-all dynamics and antiphase states in modulated multimode lasers

(N-1)! coexisting antiphase states are predicted to appear in an N-mode laser when the pump power drops below the threshold during part of the modulation cycle. The total output exhibits the so-called spiking mode pulsations at a frequency ${\mathrm{\omega }}_{\mathit{s}}$. However, each longitudinal-mode output shows pulses at a frequency ${\mathrm{\omega }}_{\mathit{s}}$/N, with each oscillator shifted by 2π/${\mathrm{\omega }}_{\mathit{s}}$ from its neighbor, resulting from a ‘‘winner-takes-all’’ dynamics. The assignment to antiphase states embedded in a high-dimensional phase space by injection seeding is shown. Applicability to a rewritable memory of (N-1)! different ‘‘dynamical patterns’’ is demonstrated on the basis of numerical simulations.