Dark Temporal Cavity Soliton Pairs in Fabry-Pérot Resonators with Normal Dispersion and Orthogonal Polarizations

Temporal cavity solitons have attracted significant interest for optical frequency comb generation with a large number of applications including precision spectroscopy, LIDAR, and channel generation for telecom systems [1]. Here we introduce dark and dark-bright vectorial temporal cavity soliton pairs in a Fabry-Pérot (FP) resonator with normal dispersion and two orthogonal polarizations. A FP resonator with highly reflective mirrors, Fig. 1a, which contains a normally dispersive Kerr medium and driven by an input field with two orthogonal polarizations can be modeled [2] with the following system of two integro-partial differential equations \begin{equation*} \partial_{t}\psi_{\pm}=S-(1+i\Theta)\psi_{\pm}-i\partial_{\zeta}^{2}\psi_{\pm}+i\frac{2}{3}(\vert \psi_{\pm}\vert ^{2}+2\{\vert \psi_{\pm}\vert ^{2}\rangle+2\vert \psi_{\mp}\vert ^{2}+2\{\vert \psi_{\mp}\vert ^{2}\rangle)\psi_{\pm}+i\frac{4}{3}\{\psi\pm\psi_{\mp}^{*}\}\psi_{\mp} \tag{1} \end{equation*} where
$\psi_{\pm}$
are the fields of left and right handed circular polarization with input fields
$S$
and detuning to the nearest cavity resonance
$\theta$
. Here
$t, \zeta$
are the slow time and fast time variables describing the evolution over many round trips and single round trip
$t_{\mathrm{R}}$
respectively. Integral terms correspond to angled brackets and take the form of global averages in the fast time over a round trip of the resonator. They arise due to the counterpropagation of the fields inherent in a FP configuration or in bidirectionaly pumped ring resonators [3].