Internal and external field fluctuations of a laser oscillator: Part I--Quantum mechanical Langevin treatment

The amplitude and phase noise spectra of the internal and external fields of a laser oscillator are calculated using the quantum mechanical Langevin equations. The outgoing field spectra are demonstrated to be different from the internal field spectra. The outgoing photon flux
\hat{N}
from a laser oscillator operating at far above the threshold has a spectral density equal to the classical shot noise level,
2\langle\hat{N}\rangle
. On the other hand, the internal photon number spectrum is Lorentzian, and the variance is equal to the average photon number,
\langle\hat{N}\rangle
. The difference stems from the quantum mechanical interference between the transmitted internal field and the reflected zero-point fluctuation at the output coupling mirror. The relation between the present analysis and the previous noise theory of a laser is also discussed.