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A delay differential eqution NOLM-NALM mode-locked laser model

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