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In this paper, we propose a scheme for angular rotation Ω measurement in an optic-fiber-based Sagnac interferometer based on cascaded weak-value amplification (CWVA). CWVA is a modified standard weak-value amplification (SWVA) technique for further enhancing temporal shifts based on the principle of the Vernier effect. By choosing the appropriate CWVA parameters and the repetition time intervals of the Vernier scale, the temporal shifts in SWVA can be further amplified by measuring the envelope shifts in CWVA. Our comprehensive simulations demonstrate that CWVA enables the detection of minuscule rotations in the range of 1.0×10−9rad/s≤Ω≤10×10−9rad/s, with significantly improved sensitivity and superior signal-to-noise ratios compared to SWVA. The enhancement with a larger detection band may have great influence on physics and related sciences, such as rotational seismology and gravitational sensing.

In this paper, we propose our advantageous research leading to a new scheme for angular rotation $\Omega$ measurement in an optic-fiber-based Sagnac interferometer based on cascade weak-value amplification (CWVA). CWVA is a modified standard weak-value amplification (SWVA) technique for further enhancing the temporal shifts based on the principle of the Vernier effect. By choosing the appropriate CWVA parameters and the repetition time intervals of the Vernier scale, the temporal shifts in SWVA can be further amplified by measuring the envelope shifts in CWVA. Our simulation results indicated that CWVA can demonstrate the detection of tiny rotations at the range of 1.0 $\times$ $10^{-9}$ rad/s $\leq$ $\Omega$ $\leq$ 10 $\times$ $10^{-9}$ rad/s with higher sensitivity and larger signal-to-noise ratios than SWVA. The enhancement with a larger detection band may have a high influence on physics and related sciences, like rotational seismology and gravitational sensing.