Injection modulation in coupled laser oscillators

Injection modulation is the effect observed when laser oscillation is perturbed by an injected signal below the threshold of locking. In this regime the oscillation becomes a wave modulated in frequency as well as in amplitude. The modulation envelope has a characteristic waveform which depends on the amplitude and phase of the injected signal. Starting from the Lamb´s equations for a dual-mode oscillator, we develop a theory of the injection modulation and calculate the waveforms in amplitude and frequency. The treatment applies both to the external injection into a laser and to the case of mutual coupling between two modes. Experimental results for a dual mode He-Ne laser are found to be in good agreement with the theory. It is pointed out how the injection modulation effects are appreciable even at very weak levels of injected amplitudes, e.g., down to 10^-5with respect to the oscillation field amplitude.