Dynamics of multimode semiconductor lasers

We analyze multi-longitudinal-mode semiconductor lasers experimentally. We show that the intensity of each mode displays large amplitude oscillations but obeys a highly organized antiphase dynamics leading to an almost constant total intensity output. For each mode, regular switching is observed in the megahertz range, while the optical frequency as a function of time follows a well defined sequence from blue to red. Using a multimode theoretical model, we identify that four-wave mixing is the dominant mechanism at the origin of the observed dynamics. The asymmetry of the susceptibility function of semiconductor materials allows us to explain the optical frequency sequence.

Figure 1

Experimental setup: LD, laser diode; C, collimator; OI, optical isolator; BS, beam splitter; L, lens; APD, avalanche photodiode $2\mathrm{GHz}$; FP, Fabry-Pérot interferometer; D, detector; S, oscilloscope; DS, digital oscilloscope; SA, spectrum analyzer.

Figure 2

Modal intensity behavior. The modes $a–f$ detected are shown from the bluest to the reddest (from bottom to top) and can be related to the labels in the optical spectrum of Fig. 3. At the top we plot the total intensity output (gray line). We have displaced vertically the intensity traces of modes $b–f$ by opportune offset ($15\mathrm{mV}$ for $b$, $30\mathrm{mV}$ for $c$, and so on, by multiples of $15\mathrm{mV}$) to avoid overlapping the five traces. The total intensity has been displaced by an offset of $80\mathrm{mV}$. The laser pump is about 60% over the threshold and the temperature is 19 °C.

Figure 3

Left: Optical spectrum of the laser emission relative to Fig. 2. Frequency increases from right to left. Right: Power spectra of the total intensity output (gray line) and of the modal intensity labeled $c$ in Fig. 2. We used a microwave amplifier of $20\mathrm{dB}$ at the input of the spectrum analyzer.

Figure 4

Left: Modal behavior in case of two active modes, and total intensity output (top trace). The laser pump is about 50% over the threshold and the temperature is 22.4 °C. The second modal intensity trace is displaced vertically with an offset of $6\mathrm{mV}$ and the total intensity trace is displaced with an offset of $8\mathrm{mV}$. Right: Power spectrum of the total intensity (lower trace) and of one of the two active modes (we have removed the $20\mathrm{dB}$ amplifier present in the case of Fig. 3).

Figure 5

Numerical results for four modes, and total intensity output. $I_1$ corresponds to the reddest mode. To help comparison with the experimental data, a cavity round trip time ${\tau }_p=10\mathrm{ps}$ has been assumed to fix the physical time scale.

Figure 6

Numerical results for the intensities of modes no. 11 (top), no. 12 (middle), and no. 13 (bottom) for a current injection $N_{eq}=2.8$.

Figure 7

Period of the oscillation as a function of the injection current.