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Applied Optics

Optical refractive inverse weak value tiltmeter

Garrett K. Josemans, Benjamin A. Baldwin, John Edward Gray, Patrick H. Graves, Kevin L. Bertschinger

Published Dec 5, 2024• 0 citations
Publisher

Abstract

We present an expanded mathematical model of the optical weak value amplification device introduced by Duck, Stevenson, and Sudarshan in 1989 [ Phys. Rev. D 40 , 2112 ( 1989 ) PRVDAQ 0556-2821 10.1103/PhysRevD.40.2112 ]. We model the pointer behavior in and around the weak value and inverse weak value amplification regions with respect to the incidence angle of the birefringent crystal. We present laboratory measurements that support the validity of this model. We measure a tilt sensitivity of ∼.58m/rad, which represents an amplification of 390 times over nonamplified refraction. This corresponds to an increase in SNR of ∼110 times with respect to shot noise. This paper demonstrates the novel utility of a birefringence-based WVA device as a sensitive tiltmeter, to our knowledge.

DOI
10.1364/ao.538556

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We present an expanded mathematical model of the optical weak value amplification device introduced by Duck, Stevenson, and Sudarshan in 1989 [ Phys. Rev. D 40 , 2112 ( 1989 ) PRVDAQ 0556-2821 10.1103/PhysRevD.40.2112 ]. We model the pointer behavior in and around the weak value and inverse weak value amplification regions with respect to the incidence angle of the birefringent crystal. We present laboratory measurements that support the validity of this model. We measure a tilt sensitivity of ∼.58m/rad, which represents an amplification of 390 times over nonamplified refraction. This corresponds to an increase in SNR of ∼110 times with respect to shot noise. This paper demonstrates the novel utility of a birefringence-based WVA device as a sensitive tiltmeter, to our knowledge.
We present an investigation into the tilt sensitivity of the canonical, optical, weak-value amplification device (COWVAD), introduced by Duck, Stevenson, and Sudarshan in 1989, for potential application in a Coriolis vibratory gyroscope (CVG). We model the breakdown of the weak-value amplification effect in this device with respect to angle of incidence between the laser beam and the surface of the birefringent crystal. Additionally, we model the effect of beam divergence due to misalignment of the crystals optic axis. We found that the presence of beam divergence allows the architecture to be placed in an inverse weak-value amplification configuration. We found that weak-value amplification occurs at angles other than those reported in Duck 1989. We also present laboratory measurements that support the validity of the mathematical model. The maximum tilt sensitivity measured was ~.58 m/rad, which, while 390 times greater than it would be without weak-value amplification, does not represent the maximum possible sensitivity of the device through weak-value amplification.
We study the weak-value amplification (WVA) in a phase measurement with an optical interferometer in which shot noise limits the sensitivity. We compute the signal and the shot noise including the full-order interaction terms of the WVA, and show that the shot-noise contribution to a phase shift in a pointer variable is always larger than the final variance of the pointer variable. This yields the difference in estimating the noise level up to a factor of 1.5. To clarify an advantage for practical uses of the WVA, we discuss the signal-to-noise ratio and its optimization in the presence of the shot noise.
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 present a follow-on experiment to the recent study from The University of Rochester [ Opt. Lett. 42 , 2479 ( 2017 ) OPLEDP 0146-9592 10.1364/OL.42.002479 ], which reported a new architecture for an inverse weak-value tiltmeter. We recreate the Rochester tiltmeter and specifically investigate mirror oscillations in the low-kilohertz frequency regime, which is relevant to certain potential applications, such as Coriolis vibratory gyroscopes. We find that the inverse weak-value amplification effect persists in this regime, although our measured noise floors are higher than those obtained in the Rochester experiment—approximately 2 p r a d / H z for mirror oscillation frequencies between 1 and 25 kHz.
The first experimental realization of a measurement of the weak value of a variable, a concept recently introduced by Aharonov, Albert and Vaidman, is presented. Weak measurements (measurements of a weak value) address the situation in which the separation of the eigenvalues caused by a weakly interacting measurement device is small compared to the width of the distribution of the individual eigenvalues. By appropriate choice of the pre- and post-selected state it is possible that the overlapping eigenvalues will interfere producing a value outside the range of eigenvalues. We demonstrate that the weak value is a practical method of amplifying and resolving the separation between overlapping eigenvalues in an optical experiment proposed by Duck, Stevenson and Sudarshan. In this experiment a birefringent crystal spatially separates two linear polarization components of a Gaussian laser beam by a distance much smaller than the beam waist.
We investigate the weak measurement experiment demonstrated by Ritchie et al. [N. W. M. Ritchie, J. G. Story, and R. G. Hulet, Phys. Rev. Lett. 66, 1107 (1991)] from the viewpoint of the statistical hypothesis testing for the weak-value amplification proposed by Susa and Tanaka [Y. Susa and S. Tanaka, Phys. Rev. A 92, 012112 (2015)]. We conclude that the weak-value amplification is a better method to determine whether the crystal used in the experiment is birefringent than the measurement without postselection, when the angles of two polarizers are almost orthogonal. This result gives a physical description and intuition of the hypothesis testing and supports the experimental usefulness of the weak-value amplification.