This study shows theoretical and experimental results on three main effects determining the frequency stability of a Brillouin 6ber ring laser, namely: the temperature effects and the nonlinear Kern and frequency pulling effects. The oscillation frequency in a Brillouin Fiber Ring Laser is determined mahly by the axial mode of the cold resonator located under the Brillouin gain curve that experiences the highest gain. This oscillation frequency is therefore temperature dependent since both the Free Spectral Range (FSR) and the gain curve center depend on the temperature. The FSR variation gives rise to a continuous lasing frequency variation while the gain curve shift leads to mode hopping. In addition to these temperature effects, the nonlinear Kerr effect and the mode pulling effect will also slightly shift the lasing frequency away from the resonant frequency of the cold resonator. The Kerr effect depends only on the pump power, while the mode pulling effect depends on both the pump power and the relative location between the lasing mode and the gain curve center. The results of this study are useful in many BFRL applications such as Brillouin fiber-optic gyroscopes, microwave generators and frequency shifters.
I. I NTRODUCTION TIMULATED Brillouin Scattering (SBS) is a nonlinear S process that produces a gain in the backward direction in optical fibers. Although it can be detrimental in coherent optical communication systems [l], [2] it found many applications such as selective canier amplification [3], distributed temperature sensing [4], characterization of fiber strain [5], and Brillouin fiber lasers [61, [71.Because of its low laser threshold a Brillouin fiber ring laser (BFRL) using a high-finesse fiber ring resonator is especially attractive and it has been used as a narrow-linewidth fiber laser [8], a microwave frequency generator [9]. and a Brillouin fiber ring gyroscope (BFOG) [lo]-[ 121. The previous studies on BFRL clarified the laser threshold condition [7] and the functional form of the circulating Stokes intensity as a function of the pump intensity [13], [14]. It was also found that at only four-times the threshold the circulating firstorder Stokes wave becomes strong enough to support, in turn, the second-order Stokes wave lasing in the ring resonator. At eight-times the threshold the third-order Stokes wave begins lasing. The presence of higher-order Stokes waves defines operating windows of a BFRL. For example, the first window is defined as the range where only the first Stokes wave is lasing, the second window where upto the second Stokes . IEEE Log Number 9412283.waves are lasing, and so on. The generation of these multiple Stokes waves in a BFRL is treated in [14] including the threshold conditions and the functional forms of circulating intensities for higher-order Stokes waves. The oscillation frequency in a BFRL is mainly determined by the axial mode of the cold resonator located under the Brillouin gain curve that experiences the highest gain. This oscillation frequency depends on the...