Antiphase dynamics in pump-modulated multimode intracavity second-harmonic generation

Abstract

Abstract. We determine numerically the response of a multimode laser with intracavity secondharmonic 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.Multimode lasers have been shown to display diverse behaviours, regular and irregular. Because there can be a large number of modes that are coupled globally, these lasers may exhibit collective self-organization. One such self-organization is antiphase dynamics (AD). In its simplest form, AD is characterized by a cyclic periodic pulsing of the individual mode intensities. As a result, the N -mode laser is in a periodic state, with each mode having the same waveform but shifted from its neighbour by 1/N of the period. AD appears as a manifestation of the coherence properties associated with the phase of the mode intensities rather than with usual phase of the mode fields. The first experimental confirmation of AD in lasers was reported in [1] for a Nd:YAG laser cavity containing a KTP frequency doubling crystal. The theoretical analysis of this problem and an explanation of the mathematical mechanism through which antiphased solutions occur in this system was reported in [2] and [3]. More complex periodic AD states were found and analysed in [3] and [4]. Another example of AD is the 'winner-takes-all' dynamics in deeply modulated Fabry-Pérot lasers [5]. AD has also been reported in spontaneous self-pulsing [6,7], in the presence of an external modulation [8], in the noise spectrum at steady state [9], in the transient relaxation to steady state [10][11][12], in the chaotic regime [13][14][15][16] and in the routes to chaos [17]. If the dynamics is limited to the relaxation towards a steady state, AD implies that each modal intensity is characterized by a number of frequencies (smaller or equal to the mode number) while the total intensity is characterized by only one frequency, the largest of the modal intensity frequencies, the so-called relaxation oscillation frequency. In the chaotic domain, AD has the same characteristics as in the relaxation to steady state: each mode displays a number of frequencies with broadened peaks whereas the total intensity displays broad peaks around the largest of the modal intensity frequencies. In the present letter, we shall focus on multimode intracavity second-harmonic generation in the region of parameters where there is a stable steady state. Our primary aim is to study the influence of †

Elimination of Chaos in Multimode, Intracavity-Doubled Lasers in the Presence of Spatial Hole-Burning

“…3. As it can be seen, for small nonlinearity, ǫ < 0.8 × 10 −4 , there is a rather good agreement between theoretically [Wang & Mandel, 1993] and numerically obtained results. However, when nonlinearity increases, 0.8 × 10 −4 < ǫ < 1.0 × 10 −4 , the minimal number of modes obtained in numerial simulations 5 is larger than the number predicted theoretically.…”

“…The results presented in [James et al, 1990b, Magni et al, 1993, where the crosssaturation coefficient was assummed to be constant for all modes, are compared with the numerical data. It is shown that the theoretically obtained [Wang & Mandel, 1993] linear dependence of the minimal number of modes necassary for stabilization the laser output on the strength of nonlinearity agrees with the numerical solutions only in the case of sufficiently small nonlinearity. For larger values of nonlinearity, due to the cancellation of modes during the evolution, the minimal number of modes obtained by the numerical simulations is larger than the number which follows from the theoretical predictions.…”

Antiphased modulation of a laser array

“…When the pump-modulation frequency is far from 2 1 (not 2 ) the response is linear in the sense that the laser is tied to the pump modulation and displays inphased P1 solutions. The nonlinear response is observed near 2 1 . Within the range limited by the points labelled 1 and 2, the lasers oscillate at half the modulation frequency (i.e.…”

“…In a recent paper [1], we analysed numerically the response of a multimode laser, with intracavity second harmonic generation (ISHG), to a periodic modulation of the gain in the linear and nonlinear regimes. We found that, depending on the relative phase of the modal gain modulation, the resonance which is expected at the relaxation oscillation frequency can appear to be or can be shifted to the lower internal frequency.…”

“…We note that 2 / 1 ∼ = 1 + γ , which means that the system has a single relaxation frequency if the coupling coefficient γ → 0. Along the lines of the analysis made in [5], one can prove analytically that the N modes relax to the steady state in phase at 2 and in antiphase at 1 . In the following sections, we set N = 3 and choose to vary the modulation frequency .…”