This project intends to design, fabricate and study advanced III-V semiconductor nanostructures-based devices for the generation of coherent optical frequency combs (OFCs) with controllable transverse patterns dynamics. Our approach consists in an optically-injected vertical-emission Kerr Gires-Tournois Interferometer (KGTI) integrated in a compact free-space cavity. The KGTI shall consist in a (Al)GaAs/InGaAs metasurface-based VCSEL, with controlled light confinement and phase dispersion, to enhance fast nonlinear light-matter interaction. The coupled-cavity system will be designed to reach the bistable regime and achieve coherent light states with properties overcoming current limitations for telecom and imaging applications. This new experimental framework will be complemented by the development and bifurcation analysis of a hybrid time-delayed, partial differential equations 3D theoretical model, that includes both transverse 2D diffraction and on-axis temporal dynamics. The external cavity design will allow to pass from a single transverse mode to a highly transverse degenerate (self-imaging) system. In that latter case, we envision the possibility to generate multiple, spatially independent, OFCs. We expect this project to yield as a final product, a first experimental demonstrator of vertically-emitted 1D and 3D OFCs in a mature planar III-V semiconductor based platform. Our vertical KGTI will allow to produce combs with high coherence, low power consumption, GHz repetition rates, and containing hundreds of lines in the near infrared spectral domain, with, thanks to the planar vertical architecture, potentially 10 × 10 transversally multiplexed and reconfigurable beams.These results will have groundbreaking applications for instance in massively parallel comb generation or for double comb sensing application and it will help to overcome several limitations for telecom applications. On the technological and experimental sides, the technical barriers to be lifted consists in developing a microcavity containing a nonlinear material having a very high value of the Kerr nonlinear coefficient. For this objective we plan on using the almost untapped potential of AlGaAs-based semiconductor materials operated below their band-gap. The nonlinear interaction will benefit from the strong light confinement in the microcavity. The microcavity design shall find a compromise between the width of the frequency comb targeted as well as the value of the optical power one wishes to inject into the KGTI system. Critical power threshold for the formation of Kerr combs can be controlled via the external cavity reflectivity and imaging configuration, and detuning of the optical pumping with respect to the microcavity resonance; the sign of the latter allowing also to explore both anomalous and normal dispersion regimes. On the theoretical side, the modeling of the system we wish to realize necessitates using Delay Algebraic Equations (DAEs). While the latter have a great potential for the modeling of dispersive phenomena in photonic systems, their studies is comparatively less developed than those of partial differential equations (PDEs). In addition, if DAEs are the natural choice for studying temporal dispersive dynamics, the diffractive propagation of light in the transverse plane of the cavity as well as field curvature effects induced by lenses and mirrors require using PDEs. As such, a full 3D model shall consists of a hybrid DAE-PDE system whose analysis is way beyond the state of the art and represents an exciting and challenging endeavor. The theoretical aspects of KOGIT will also significantly advance the study of spatio-temporal phenomena in nonlinear media. The proposed experimental framework will be complemented by the development of bifurcation analysis method of a hybrid DAE-PDE system that will constitute a qualitative jump in the state of the art.