Dissipative soliton combs with spectral filtering

The paradigmatic Lugiato-Lefever model describes the electric field envelope in a ring cavity filled with a Kerr medium and driven by a coherent injected laser beam. This model is applied to the formation of frequency combs associated with localized structures in micro and macroresonators. Including temporal filtering, we derive a generalized Lugiato-Lefever equation. This equation includes diffusion, linear, and nonlinear convection, and third-order dispersion with purely imaginary coefficients. Multiscale analysis enables us to disregard higher-order terms, such as nonlinear convection and third-order dispersion. We investigate the formation of periodic and localized structures resulting from the combined action of temporal spectral filtering effect together with Kerr nonlinearity, pumping, dissipation, and frequency detuning. We show that spectral filtering reduces the intensity of the output field and increases the period of traveling solutions. Similarly, the maximum intensity of moving localized structures, often called dissipative solitons, is reduced. In addition, we show that the threshold associated with breathers is shifted toward large input intensities and that the associated domain of existence is significatively reduced. We show that, when the drift is absent, dissipative solitons exhibit a homoclinic snaking bifurcation. Increasing the strength of the temporal filter reduces the pinning range. The presence of the drift breaks the homoclinic snaking and transforms it into isolas of solutions.