Theory of a negative frequency feedback semiconductor laser

A quantum theory of a semiconductor laser with negative frequency feedback stabilization is presented. The frequency noise and spectral linewidth can be decreased substantially below the modified Schawlow-Townes limit. The operator Langevin equations for a semiconductor laser supplemented by the countermodulation term for a cavity resonant frequency, quantum mechanical description of a power divider for output coupling, and the quantum theory of optical heterodyne/direct frequency discrimination detection are combined to describe the whole system. The ultimate limit for linewidth reduction is delineated. Typical numerical examples show that the linewidth can be decreased below 1 kHz. The principle of operation is discussed, with analogy made to an injection-locked oscillator.