Symmetry properties and coexistence of the mode-locked states in semiconductor lasers

Coexistence of multiple dynamical states of operation is known in multimode lasers. In this work, we examine the symmetry properties of various laser models based on the delay differential equation (DDE) approach [1], and explain a vast class of experimental observations in mode-locked semiconductor lasers. In these models, the complex electric field amplitude E(t) is presented by the equation having the form: (equation presented) where dot means differentiation with respect to time, γ is the width of a Lorentzian bandwidth limiting element (such as a filter or gain profile); ϕ = ΩT is the term accounting the frequency detuning Ω between one of the cavity modes and the transmittance peak of the filter; T is the cold cavity round trip time; R(t − T ) is a function describing gain, saturable losses or/and nonlinearity.