Normal Dispersion Kerr Cavity Solitons: Beyond the Mean Field Limit

Optical frequency comb generation using Kerr resonators has attracted a lot of interest in recent years. In the regime where the intracavity power is relatively low and the overall cavity detuning remains small during propagation, the mean field approximation can be employed and the formation of OFCs in Kerr resonators is well-described by the Lugiato-Lefever Equation (LLE). However, mean field models are not always able to account for the complete range of complex dynamics observed and alternative approaches based on e.g., extended LLE equations or Ikeda map models are used. Recently, an alternative method for the generation of phase-locked OFCs in optically-injected vertical-emission Kerr Gires-Tournois Interferometers (KGTI) was proposed. This setup consist in a micro-cavity containing a Kerr medium coupled to a long external cavity of size <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\tau$</tex> which is closed by a feedback mirror and which is subject to injection using a continuous wave laser of amplitude <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$Y_{0}$</tex> and frequency ωo (cf. Fig. (1)). While it was demonstrated that in the weakly dissipative limit, the KGTI can successfully be modeled by the LLE [1], in general, the model can be used to study the dynamics beyond these limitations which is the subject of this contribution [2]. We demonstrate the existence of a novel type of temporal localized structure (TLS). These bright pulses exist in the normal dispersion regime, yet they do not correspond to the usual scenario of domain wall locking that induces complex shape multi-stability, weak stability as well as a reduced domain of existence. Their shape is uniquely defined, with peak intensities beyond that of the upper steady state, and they are stable over a broad range of the injection field, highlighting their potential for optical frequency comb generation. The underlying model is derived from first principles and relies on delay algebraic equations (DAEs). That is, the slowly evolving micro-cavity field <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$E$</tex> is governed by an ordinary differential equation while the external cavity field <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$Y$</tex> needs to fulfill a delay algebraic constraint: