Third Order Dispersion in Optical Time Delayed Systems: The Case of Mode-Locked Vertical External-Cavity Surface-Emitting Lasers

Delayed dynamical systems (DDSs) describe a large number of phenomena in nature and they exhibit a wealth of dynamical regimes such as localized structures (LSs) [1], fronts and chimera states. A fertile perspective lies in their interpretation as spatially extended diffusive systems which holds in the limit of long delays [2]. A strong limitation of DDSs for this aim comes from the difficulty of taking into consideration chromatic dispersion. As such, DDSs description of wave propagation is limited to low dispersive media and/or narrow-spectrum signals. Nevertheless, chromatic dispersion plays a leading role in many phenomena occurring during wave evolution [3]. Beyond second order dispersion (SOD), third order dispersion (TOD) is the lowest order non-trivial parity symmetry breaking effect, which leads to convective instabilities [4] and drifts.