Coherent laser detection by frequency-shifted optical feedback

Abstract

The dynamical response of a laser to frequency-shifted optical feedback is investigated both theoretically and experimentally. The ultrahigh sensitivity of a class-B laser (i.e., a laser with a cavity damping rate ${\ensuremath{\gamma}}_{c}$ higher than the population damping rate ${\ensuremath{\gamma}}_{1})$ to external light injection is demonstrated by the optical detection of weak optical feedback. Compared to a conventional optical beating, the intensity modulation induced by the coherent interaction between the laser electric field and the frequency-shifted reinjected electric field can be several orders of magnitude higher. This method permits high sensitive interferometry and hence imaging. We call this laser detection technique laser optical feedback imaging (LOFI). When the optical frequency shift is resonant with the laser relaxation frequency, the intracavity amplification of the beating is maximum and the enhancement is given by the laser damping rate ratio ${\ensuremath{\gamma}}_{c}/{\ensuremath{\gamma}}_{1}.$ This amplification is of the order of ${10}^{6}$ for a microchip laser. We also show that without optical feedback the strong fluctuations of the laser output power are well described by the Langevin noise process. In a broad range around the laser relaxation frequency the laser quantum noise is also resonantly amplified and is then several orders of magnitude higher than the detector noise. In these conditions, the LOFI is a shot noise limited detection technique. Reflectivity as low as ${10}^{\ensuremath{-}13}$ is then easily detectable with a laser output power of a few milliwatts with a detection bandwidth of 1 kHz. Experimentally, for weak optical feedback the laser fluctuations are principally composed of the LOFI modulation signal at the shifted frequency and of the laser quantum noise amplified at the relaxation frequency. For strong optical feedback, nonlinear effects appear in the laser dynamics. In these conditions, harmonics and parametrics peaks appear in the power spectrum. The LOFI detection system is then saturated.