This work presents a hybrid modeling technique to simulate extended cavity semiconductor mode-locked lasers, using a combination of traveling wave equations with the nonlinear Schrödinger equation. The simulations are compared to and show correspondence with experimental results from a III-V-on-silicon mode-locked laser. I. Introduction and modeling descriptionSemiconductor passively mode-locked (ML) lasers are promising tools for the generation of optical combs on a photonic chip. It has been demonstrated that they can be used for dual-comb spectroscopy (DCS) purposes [1]. The smaller repetition frequency and relatively large comb power are the main reasons behind the popularity of ML lasers. Of particular interest is the usage of extended cavities, which has been proven to be beneficial in reducing the optical linewidth of the individual comb lines [2]. Therefore, this recent type of semiconductor ML laser can be of importance for high-precision measurements. To consider different laser topologies and settings, accurate modeling tools are indispensable.Considerable work has been performed on this topic. The fundamentals behind ML were written down by Haus a few decades ago, resulting in the so-called master equation [3]. Different extensions have built upon this essential model, coexisting with other representations such as the delay differential equations (DDEs) as introduced by Vladimirov [4]. Although those simplified models provide valuable insights into the principles behind ML, they fail to capture the more detailed physics that determines the behavior of practical ML lasers. Therefore, different numerical solvers rely on the traveling wave model (TWM) equations to include the mechanisms of interest. PHIsim © is an example of such an open-source code developed by E. Bente et al. at the Eindhoven University of Technology [5]. The code allows for the simulation of ML lasers with short round-trip times. However, the implementation of extended cavities poses a considerable computational challenge since the spatial step size in the TWM is extremely short compared to the cavity length. Hence, this work attempts to alleviate that problem by building further upon the results of [6,7]. The report presents a novel hybrid modeling technique that combines a TWM description of the active segments with the nonlinear Schrödinger equation (NLSE) to account for the propagation in the passive cavity. To this end, the NLSE is solved by means of the split-step Fourier (SSF) algorithm. However, previous work made use of a simple TWM as a proof of concept. In this work, the PHIsim © package is leveraged to increase physical accuracy and computational performance of the hybrid model. Furthermore, it improves upon the PHIsim © equations by leveraging an additional update equation to account for gain dispersion [8]. Within this framework, a Lorentzian gain profile is assumed.To elaborate on the operation of the hybrid modeling concept, the model is applied to a recently demonstrated III-V-on-Si heterogeneous mode-locked laser [9]...