Weierstrass Institute, Germany

Multisection ring and edge-emitting semiconductor lasers (SLs) are useful devices for different purposes. The small size and the high frequency of the optical field intensity modulation make these devices interesting for optical data communications and their application in photonic integrated circuits. Modeling, simulations and analysis are crucial for optimizing of existing SLs as well as for designing new devices with a particular dynamical behavior. For simulations and analysis of SLs, we use the traveling wave (TW) model, which is a 1+1 dimensional system of PDEs for counterpropagating, slowly varying optical fields coupled to the linear system of ODEs for polarization functions and ODEs for a carrier density. In this talk, we shall present a method that allows computing and analyzing longitudinal optical modes in SLs governed by the TW model. The concept of optical modes plays a significant role for understanding laser dynamics in general. They represent the natural oscillations of the electromagnetic field and determine the optical frequency and the lifetime of the photons contained in the given laser cavity. The instantaneous longitudinal optical modes are pairs of eigenvalues and eigenvectors of the spectral problem which is defined by the linear system of the field equations obtained after freezing the instantaneous distribution of the carrier density.The imaginary and the real parts of the complex eigenvalues are mainly determining the angular frequency and the damping of the corresponding mode. Thus, eigenvectors of modes with vanishing damping are defining (stable or unstable) stationary (continuous wave) states with optical frequencies given by the real parts of the same eigenvalues. Finally, we shall demonstrate how our mode analysis can be used for locating of all stationary states of the laser, for explaining the interactions between different modes, for decomposing of the simulated optical fields into modal components, and for reduction of the original PDE model to the low-dimensional system of ODEs.