Coexistence of stable ECM solutions in the Lang-Kobayashi system (Q611890)

The authors consider a system of equations with a delay modeling the behaviour of external cavity semiconductor lasers. It reads \[ \begin{aligned} (d{\mathbf E}/dt)&=(1+i\alpha)N{\mathbf E}+\eta e^{-i\omega_0\tau}{\mathbf E}(t-\tau),\\ T (dN/dt)&=P-N-(1+2N)|{\mathbf E}|^2,\end{aligned} \] where \({\mathbf E}=E_x(t)+iE_y(t)\) is the complex electric field, and \(N(t)\) is the carrier number density of the laser. The authors study the bifurcations and stability of external cavity modes, solutions having the form \({\mathbf E}=E_se^{i\phi_st}\), \(N=N_s\) where \(E_s\), \(\phi_s\) and \(N_s\) are constants.