The resonant fiber optic gyroscope (RFOG) represents a cutting-edge generation of fiber optic inertial devices, leveraging the Sagnac effect within a fiber optic ring resonator. It gauges the angular velocity of external rotation by measuring the resonant frequency difference of light beams traveling clockwise and counterclockwise in the fiber optic ring resonator. In comparison to interferometric fiber optic gyroscopes, the RFOG offers advantages such as reduced length, compact dimensions, minimal thermal nonreciprocal noise, heightened detection accuracy, a wide dynamic range, and superior theoretical accuracy. Nevertheless, the progress of RFOGs is constrained by noise factors such as polarization fluctuations, the optical Kerr effect, and Rayleigh backscattering within the resonator. To address these limitations, the broadband source-driven RFOG emerges by mitigating parasitic noise through its low coherence. However, the current challenge lies in detection noise, particularly relative intensity noise (RIN), serving as the primary impediment to accuracy. Consequently, there is a pressing need to formulate a comprehensive theoretical model for RIN in broadband source-driven RFOGs. Such a model serves as the foundational framework for devising various schemes aimed at suppressing RIN, thereby advancing the precision of these gyroscopes. We fulfill this need by establishing a theoretical model grounded in the spectral width of the broadband source and resonator parameters.

Regarding our need to construct a theoretical model for RIN in a broadband light source-driven RFOG, we choose an amplified spontaneous emission (ASE) with a center wavelength of 1550 nm as light source (Fig. 1 and Fig. 2). The power spectral density of the system is comprehensively analyzed to delineate the spectral alterations induced by the resonant cavity's characteristics in response to RIN (Fig. 5). To ascertain the primary contribution of the existing RIN, we employ the random walk method, which is visually depicted in Fig. 6. The validity of our theoretical model is subsequently corroborated through practical measurements involving the RIN spectrum across varying spectral ratios of the resonant cavity, and the Allan variance is assessed for diverse laser spectral widths (Fig. 8 and Fig. 9). These experimental validations solidify the reliability and applicability of our proposed theoretical framework.

In the broadband source-driven RFOG, an ASE with a center wavelength of 1550 nm serves as the light source. The sensing device is a 500 m fiber ring resonator with a diameter of 12 cm. Experimental measurements of the RIN spectrum for the resonator with different splitting ratios and the Allan variance for varying laser spectral widths are presented in Fig. 8 and Fig. 9. Notably, the observed RIN spectrum aligns closely with the theoretical predictions, validating the accuracy of our proposed model. Crucially, our results demonstrate that increasing the laser spectral width is beneficial for enhancing the angle random walk performance of the gyroscope. This observation underscores the practical significance of our theoretical framework and suggests a promising avenue for optimizing gyroscope performance through spectral width modulation. These findings provide valuable insights into the field, emphasizing the potential for improved gyroscope precision through strategic adjustments to laser spectral characteristics.

We construct a theoretical model of RIN in RFOGs driven by a broadband source. The model here proposed considers the effects of laser spectral width and resonator parameters simultaneously, making it more realistic. Power spectral density analysis of the transmission process of RIN in the gyroscope system is performed, and the influence of different system parameters on the RIN in the RFOG driven by a broadband source is obtained. A large laser spectral width and a high-precision resonator with high-frequency modulation can effectively reduce the influence of RIN. The establishment of this theoretical model provides a basis for suppressing RIN in RFOGs driven by broadband sources.