Quantum noise of an injection-locked laser oscillator

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Abstract
The quantum noise of an injection-locked laser oscillator is analyzed by the operator Langevin equation. The problem is also treated by the Fokker-Planck equation and the same results are obtained in the same regimes of applicability. The steady-state solution of the Fokker-Planck equation gives the probability distribution of amplitude and phase, the Langevin equation arrives more directly at the spectrum of amplitude and phase. The phase of the injection-locked oscillator is related to the phase of the injection signal and thus constitutes a measurement of phase. In the limit of complete inversion and zero internal loss of the laser resonator, the associated uncertainty is twice that dictated by the uncertainty principle. This result is interpreted by comparing it with the uncertainty introduced by a linear amplifier which can perform a simultaneous measurement of amplitude and phase.