A nonlinear response of a laser-diode-pumped microchip LiNdP(4)O(12) (LNP) multimode laser that is subjected to multiple-frequency modulations is investigated. Clustering and breathing motions featuring intermode parametric resonances are demonstrated when the LNP laser was modulated by rational frequencies chosen to be nearly resonant to multiple relaxation-oscillation frequencies inherent in multimode lasers. A simple correspondence between the modulation signal patterns and the total-output power-spectrum patterns is demonstrated.

We determine numerically the response of a multimode laser with intracavity second-harmonic generation to a periodic modulation of the gain in the linear and nonlinear regimes. We show that resonances can appear either at the relaxation oscillation frequency or the low internal frequency and at its first subharmonic. Instabilities leading to period doubling occur at the low internal frequency and at its first harmonic.

In a multimode laser operating near steady state, we determine analytically relations which connect the power spectrum density of each modal intensity and of the total intensity at the same frequency. We prove that, if the laser is in an antiphase regime, these relations become independent of the initial condition. This property rests on the existence of widely different time scales for the oscillation frequencies and their damping. Numerical simulations indicate that these relations remain true when a small amplitude modulation is applied to the control parameter.

The emergence of local chaotic antiphase states and self-induced switching among the ruins of local chaotic antiphase attractors (i.e. chaotic itinerancy) leading to fully developed global chaos have been demonstrated by numerical simulations in a model of intracavity second-harmonic generation in multimode lasers. Dynamical characterization of chaotic itinerancy has been carried out using circulation analysis.

We analyse the problem of intracavity second harmonic generation to determine properties of the antiphased states that have been observed in this system. We study the time-periodic solutions by means of a perturbation expansion in powers of a small parameter which is the ratio of the cavity lifetime to the population inversion relaxation time. We prove that each mode intensity is characterized by two oscillation frequencies though the total intensity oscillates with only one of these frequencies. In first approximation, we find that the bifurcation from the steady state to the periodic state remains vertical. We resolve this singularity by a complementary numerical analysis. We show that there are at least four distinct types of antiphase dynamics, including partial clustering of the oscillating modes into subsets of antiphasing states. Finally, we analyse the scaling exponent of the oscillation amplitudes near the bifurcation point and determine that the generic 1/2 exponent is the rule for only two of four types of antiphasing. The exponents of the other two cases depend on the mode number and partition.

We analyze theoretically a case of antiphase dynamics in the self-pulsing regime involving two orthogonal polarizations in intracavity second-harmonic generation. We show that, for this model, antiphase dynamics may lead to a nonreciprocal independence of the two polarizations as a result of partial overlap between the pulses. In the case in which two modes oscillate with one polarization and a single mode oscillates with orthogonal polarization, we find that the two modes can display chaos while the orthogonal mode remains periodic, despite coupling among all the modes.

Antiphase periodic states in a passive Q-switching regime of multimode intracavity second-harmonic generation are investigated theoretically, paying special attention to nonlinear interaction between orthogonally polarized modes and the destruction process of antiphase periodic states involving large oscillating modes. A nonreciprocal gain flow among the two polarizations, clustering into antiphase periodic modes and chaotic modes, and chaotic itenerancy among attractor ruins of destabilized clustered states are found in numerical simulations.