Coherence properties of the parametric three-wave interaction driven from an incoherent pump

Abstract

We consider the basic problem of the parametric generation process from an incoherent pump wave. The analysis of the degenerate configuration of the two-wave interaction reveals that the mutual convection (i.e., group-velocity difference) between the incoherent pump and the signal (i.e., the daughter wave) may quench their parametric interaction, so that the gain experienced by the signal may become arbitrarily small. Conversely, in the absence of convection, the incoherent pump efficiently amplifies the signal wave, although this amplification process cannot lead to the generation of a coherent signal. However, in the case of nondegenerate three-wave interaction, we show the existence of a convection-induced phase-locking mechanism in which the incoherence of the pump is absorbed by the idler wave allowing the signal wave to grow efficiently with a high degree of coherence. We calculate explicitly the autocorrelation function of the generated signal in this regime of coherent-incoherent interaction. The analysis reveals that, owing to the convection-induced averaging process that accompanies the phase-locking mechanism, the degree of coherence of the signal increases as the degree of coherence of the pump decreases. We establish the experimental conditions that would allow for the observation of the transition between the incoherent and the coherent regimes of the three-wave parametric interaction.

Temporal coherence in mirrorless optical parametric oscillators

“…As a result of the phase-locking mechanism, the transfer of phase modulation to the forward wave becomes more efficient when the group velocities of the pump and the forward parametric wave are exactly matched [8]. This was shown in Fig.…”

“…It has recently been demonstrated, both experimentally and numerically, that this spectral asymmetry occurs when the pump wave exhibits deterministic phase modulation. In accordance with the convection-induced phase-locking mechanism [7][8][9][10][11], the phase modulation in the pump is coherently transferred to the forward parametric wave, while the backward wave retains a narrow bandwidth and high coherence [12]. This mechanism has previously been verified in a MOPO pumped with relatively narrowband (1.2 THz) linearly chirped pump pulses.…”

Control of signal coherence in parametric frequency mixing with incoherent pumps: narrowband mid-infrared light generation by downconversion of broadband amplified spontaneous emission source at 1550 nm

“…Optical frequency conversion in quadratic nonlinear media using incoherent pump lasers has been studied for quite some time [1][2][3][4][5][6][7][8]; in contrast to simple intuition, such resonant phase-sensitive processes may even lead to the generation of coherent waves [5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The generation of a coherent signal from incoherent pumps may also occur through four-wave mixing in optical fibers [19].…”

“…The generation of a coherent signal from incoherent pumps may also occur through four-wave mixing in optical fibers [19]. In a quadratic medium, considering the purely one dimensional temporal problem and the limit case of small signals (i.e., no pump depletion), it has been predicted that the generation of a coherent signal may result in optical parametric generation (OPG) involving the downconversion of an incoherent pump [12][13][14]. The condition for obtaining such a coherent signal, besides the usual phase matching condition, is that the idler and pump group velocities should be locked; in this case it turns out that the signal growth is nearly independent of pump phase fluctuationsthe so-called phase-locking mechanism [12][13][14].…”

“…In a quadratic medium, considering the purely one dimensional temporal problem and the limit case of small signals (i.e., no pump depletion), it has been predicted that the generation of a coherent signal may result in optical parametric generation (OPG) involving the downconversion of an incoherent pump [12][13][14]. The condition for obtaining such a coherent signal, besides the usual phase matching condition, is that the idler and pump group velocities should be locked; in this case it turns out that the signal growth is nearly independent of pump phase fluctuationsthe so-called phase-locking mechanism [12][13][14]. Therefore, the group-velocity mismatch (GVM) of the pump and idler waves was predicted to be a key parameter that permits control of the degree of coherence of the signal beam through the phase-locking of pump and idler, i.e., the pump incoherence appears to be effectively absorbed by the generated idler wave.…”