Suppression of thermal frequency noise in erbium-doped fiber random lasers

Frequency and intensity noise are characterized for erbium-doped fiber (EDF) random lasers based on Rayleigh distributed feedback mechanism. We propose a theoretical model for the frequency noise of such random lasers using the property of random phase modulations from multiple scattering points in ultralong fibers. We find that the Rayleigh feedback suppresses the noise at higher frequencies by introducing a Lorentzian envelope over the thermal frequency noise of a long fiber cavity. The theoretical model and measured frequency noise agree quantitatively with two fitting parameters. The random laser exhibits a noise level of 6  Hz²/Hz at 2 kHz, which is lower than what is found in conventional narrow-linewidth EDF fiber lasers and nonplanar ring laser oscillators (NPROs) by a factor of 166 and 2, respectively. The frequency noise has a minimum value for an optimum length of the Rayleigh scattering fiber.