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Journal of the Optical Society of America B

Cascaded weak-value amplification for optic-fiber-based Sagnac interferometers

Jing-Hui Huang, Xiangyun Hu, Xue-Ying Duan, Guang-Jun Wang

Published Jul 10, 2023• 2 citations
Publisher

Abstract

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 −9 rad/s≤Ω≤10×10 −9 rad/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.

DOI
10.1364/josab.488186

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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 −9 rad/s≤Ω≤10×10 −9 rad/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.
A modified weak-value-amplification (MWVA) technique to measure a mirror's velocity based on the Vernier effect is proposed. To demonstrate its enhanced sensitivity and higher signal-to-noise ratio (SNR), we use two cascaded Michelson interferometers with similar optical structures. One has a fixed mirror and acts as a fixed part of the Vernier scale, while the other, with a moving mirror, acts as a sliding part of the Vernier scale for velocity sensing. The envelope of the cascaded interferometers shifts much more than a single one with a certain enhancement factor, which is related to the free space range difference between them. In addition, we calculate the SNR based on the Fisher information with both the MWVA and traditional weak-value-amplification (TWVA) techniques. The results show that both the SNR and the sensitivity with our MWVA technique is greater than that of the TWVA technique within the range of our time measurement window. In particular, MWVA can present a viable and effective alternative to the TWVA technique out of the limit of resolution. Furthermore, by using the principles of the Vernier effect, it is applicable and convenient to improve the sensitivity and SNR in measuring other quantities with the TWVA technique.
We study the amplification of a weak magnetic field with the weak-value amplification (WVA) technique based on the Faraday magneto-optic effect. By using a different scheme to perform the Mach–Zehnder interferometer with the probe in momentum space, we have demonstrated a new, to the best of our knowledge, weak measure protocol to detect the small weak magnetic field by amplifying the phase shift of the Faraday magneto-optic effect. Our numerical results show that our scheme with the WVA technique has a higher signal-to-noise ratio than the traditional optical fiber scheme with the open-loop modulation technique. Besides, considering the instrument limitations of our scheme, we have demonstrated the magnetic field resolution at the 10 − 13 T level.
Experiments based on a free-space platform have demonstrated that the weak-value amplification (WVA) technique can provide high sensitivity and precision for optical sensing and metrology. To promote this technique for real-world applications, it is more suitable to implement WVA based on an optical-fiber platform due to the lower cost, smaller scale, and higher stability. In contrast to the free-space platform, the birefringence in optical fiber is strong enough to cause polarization cross talk, and the amplitude-type noise must be taken into account. By theoretical analysis and experimental demonstration, we show that the optic-fiber-based WVA is robust in the presence of amplitude-type noise. In our experiment, even the angular misalignment on optical axes at the interface reaches 0.08 rad, and the sensitivity loss can be maintained at less than 3 dB. Moreover, the main results are valid to a simplified detection scheme that was recently proposed that is more compatible with the future design of optical-fiber-based WVA. Our results indicate the feasibility of implementing WVA based on optical fiber, which provides a possible way for designing optical sensors with higher sensitivity and stability in the future.
We propose precision measurements of ultra-small angular velocities of a mirror within a modified Sagnac interferometer, where the counter-propagating beams are spatially separated, using the recently proposed technique of almost-balanced weak values amplification (ABWV) [Phys. Rev. Lett.116, 100803 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.100803]. The separation between the two beams provides additional amplification with respect to using collinear beams in a Sagnac interferometer. Within the same setup, the weak-value amplification technique is also performed for comparison. Much higher amplification factors can be obtained using the almost-balanced weak values technique, with the best one achieved in our experiments being as high as 1.2×107. In addition, the amplification factor monotonically increases with decreasing of the post-selection phase for the ABWV case in our experiments, which is not the case for weak-value amplification (WVA) at small post-selection phases. Both techniques consist of measuring the angular velocity. The sensitivity of the ABWV technique is ∼38 nrad/s per averaged pulse for a repetition rate of 1 Hz and ∼33 nrad/s per averaged pulse for the WVA technique.
We experimentally realize a great precision enhancement in the small-tilt measurement by using a Sagnac interferometer and balanced homodyne detection (BHD) of high-order optical modes, together with the weak-value amplification (WVA) technique. Smaller minimum measurable tilt and higher signal-to-noise ratio can be obtained by using BHD, compared with the split detection. The precision of 3.8 nrad can be obtained under our present experimental condition. It is shown that combining WVA technique and BHD can strengthen each other's advantages and can behave better for some special application scenarios, such as extremely weak output, wider measurement bandwidth, etc. Moreover, the precision can be further enhanced by experimental parameter optimization.
We propose a scheme for an ultrasensitive weak measurement system with an ultrasmall rotatory dispersion effect to measure angular rotation. Estimation of angular rotation is obtained by the shift of the center wavelength. In our scheme, we obtain a continuously adjustable coupling strength and show that our system provides a 13 times higher sensitivity of 38 840 nm/rad compared with previous work. Here we demonstrate that our scheme may offer an optimal weak value Aw{A}_{w}Aw​ in practice and outperforms conventional measurements in the presence of technical noise. The precision achieved by optimized weak value amplification (WVA) is about three times higher than that of a polarimeter. Our work extends the working regime of WVA. Its simplicity and robustness clear the way for widespread use of WVA involving measurements with commercial cameras and small signals.