Starting from the infinite-dimensional Ikeda map, we derive an extended temporal Lugiato-Lefever equation that may account for the effects of the conjugate electromagnetic fields (also called 'negative frequency fields'). In the presence of nonlinearity in a ring cavity, these fields lead to new forms of modulational instability and resonant radiations. Numerical simulations based on the new extended Lugiato-Lefever model show that the negative-frequency resonant radiations emitted by ultrashort cavity solitons can impact Kerr frequency comb formation in externally pumped temporal optical cavities of small size. Our theory is very general, is not based on the slowly-varying envelope approximation, and the predictions are relevant to all kinds of resonators, such as fiber loops, microrings and microtoroids.

We study the influence of third-harmonic generation (THG) and negative-frequency polarization terms in the self-phase modulation (SPM) of short and intense pulses in Kerr media. We find that THG induces additional symmetric lobes in the SPM process. The amplitude of these new sidebands are greatly enhanced by the contributions of the negative-frequency Kerr (NFK) term and the shock operator. We compare our theoretical predictions based on the analytical nonlinear phase with simulations carried out by using the full unidirectional pulse propagation equation (UPPE).

Solitons propagating in media with higher order dispersion will shed radiation known as dispersive wave or resonant radiation, with applications in frequency broadening, deep UV sources for spectroscopy or simply fundamental studies of soliton physics. Starting from a recently proposed equation that models the behaviour of ultrashort optical pulses in nonlinear materials using the analytic signal, we find that the resonant radiation associated with the third-harmonic generation term of the equation is parametrically stimulated with an unprecedented gain. Resonant radiation levels, typically only a small fraction of the soliton, are now as intense as the soliton itself. The mechanism is quite universal and works also in normal dispersion and with harmonics higher than the third. We report experimental hints of this super-resonant radiation stimulated by the fifth harmonic in diamond.

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