Wavelet analysis of low frequency fluctuations of a semiconductor laser with optical feedback

Summary form only given. Low frequency fluctuations (LFFs) consist of abrupt intensity drop-outs followed by gradual, stepwise recoveries and occur when the laser operates near threshold with moderate optical feedback. The LFFs in experimental systems are actually a slow envelope modulation of a series of fast picosecond pulses, and simulations based on the single-mode Lang-Kobayashi (LK) equations have shown similar fast pulses. By time averaging the numerical solutions (to simulate the finite bandwidth of the detectors) intensity drop-outs are also found which compare well with experiments, but there is continuing debate on the physical origin of LFFs. Recent measurements of time resolved optical spectra reveal the excitation of several longitudinal modes; during the dropouts they are synchronized and rise and fall together. We show that the discrete wavelet transform gives more compact information about LFFs, and after filtering it gives a better reconstruction of the measured dynamics than does Fourier analysis. The advantage of the wavelet method over traditional filtering is that removing certain frequency bands does not modify the dynamics relying on the remaining bands. We use the wavelet transform to separate the amplitudes of the fast and slow components (in the wave-packet bases) of a signal, and this is used to reconstruct the signal (by wavelet transforming, selecting only some of the wavelet amplitudes, and then inverse transforming and interpolating).