Laser Mode Competition
Two-mode rate equations · Gain saturation · Winner-take-all bistability
Rate equations: dI₁/dt = (g₁N − κ − g₁I₁ − βg₂I₂)I₁, dI₂/dt = (g₂N − κ − g₂I₂ − βg₁I₁)I₂, dN/dt = R − γN − (g₁I₁ + g₂I₂)N.
Self-saturation limits each mode; cross-saturation (β) creates competition. When β < 1: coexistence is possible. When β > 1: winner-take-all — the stronger mode suppresses the weaker.
Bistability: for intermediate β and symmetric gains, both single-mode solutions are stable (hysteresis). Q-switching analog: periodic gain modulation causes pulsed emission.