Delay-differential-equation model for mode-locked lasers based on nonlinear optical and amplifying loop mirrors

Delay differential equation model of a NOLM-NALM mode-locked laser is developed that takes into account finite relaxation rate the gain medium and asymmetric beam splitting at entrance nonlinear mirror loop. Asymptotic linear stability analysis continuous wave solutions performed in limit large delay indicates class-B flip instability leading to period doubling cascade development square-wave patterns can be suppressed by short wavelength modulational instability. Numerically it shown demonstrate windows regular fundamental harmonic regimes with single multiple pulses per cavity round trip time separated domains irregular pulsing.