In super-regenerative detection, a weak external signal is amplified in an oscillator that is periodically switched on and then quenched. It is shown that very weak optical signals, slightly above the noise level, can be detected effectively by a laser used as a super-regenerative receiver. The detector output for different signal levels and its operating characteristics are determined by numerical integration of stochastic differential equations that represent the growth of laser radiation from a background consisting of signal and noise.
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
106 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.
Selective detection of signal over noise is essential to measurement and signal processing. Time-frequency filtering has been the standard approach for the optimal detection of non-stationary signals. However, there is a fundamental tradeoff between the signal detection efficiency and the amount of undesirable noise detected simultaneously, which restricts its uses under weak signal yet strong noise conditions. Here, we demonstrate quantum parametric mode sorting based on nonlinear optics at the edge of phase matching to improve the tradeoff. By tailoring the nonlinear process in a commercial lithium-niobate waveguide through optical arbitrary waveform generation, we demonstrate highly selective detection of picosecond signals overlapping temporally and spectrally but in orthogonal time-frequency modes as well as against broadband noise, with performance well exceeding the theoretical limit of the optimized time-frequency filtering. We also verify that our device does not introduce any significant quantum noise to the detected signal and demonstrate faithful detection of pico-second single photons. Together, these results point to unexplored opportunities in measurement and signal processing under challenging conditions, such as photon-starving quantum applications.