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Simultaneous Measurement of Magneto-Optical Rotation and Ellipticity using Two-Pointer Weak Measurement

Tong Li, Yifan Wang, Lan Luo, S. J. Zhang, Shushu Shi

Published Jan 23, 2026• 0 citations
Publisher

Abstract

Magneto-optical (MO) effects, manifested as a complex rotation of light polarization under an external magnetic field, are widely utilized in optical isolators, sensors, data storage, and magnetic imaging. Accurate measurement of both the rotation angle (the real part) and the ellipticity (the imaginary part) is essential for fundamental research and device applications. However, existing measurement schemes generally cannot determine these two quantities simultaneously within a single experimental process. In this work, we propose a scheme based on weak measurement using two pointers, enabling the simultaneous measurement of the rotation angle and ellipticity within a single meter state. This method was experimentally implemented to measure the magneto-optical Kerr effect under various configurations—longitudinal, polar, and transverse. Moreover, the proposed approach is also applicable to the measurement of the Faraday effect and magnetic linear birefringence, demonstrating its broad applicability. This work contributes to the advancement of high-precision measurement techniques for MO effects and supports their wider application across multiple fields.

DOI
10.1364/opticaopen.31131277.v1

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Magneto-optical (MO) effects, manifested as a complex rotation of light polarization under an external magnetic field, are widely utilized in optical isolators, sensors, data storage, and magnetic imaging. Accurate measurement of both the rotation angle (the real part) and the ellipticity (the imaginary part) is essential for fundamental research and device applications. However, existing measurement schemes generally cannot determine these two quantities simultaneously within a single experimental process. In this work, we propose a scheme based on weak measurement using two pointers, enabling the simultaneous measurement of the rotation angle and ellipticity within a single meter state. This method was experimentally implemented to measure the magneto-optical Kerr effect under various configurations—longitudinal, polar, and transverse. Moreover, the proposed approach is also applicable to the measurement of the Faraday effect and magnetic linear birefringence, demonstrating its broad applicability. This work contributes to the advancement of high-precision measurement techniques for MO effects and supports their wider application across multiple fields.
Magneto-optical (MO) effects, manifested as a complex rotation of light polarization under an external magnetic field, have found renewed and advanced applications in integrated photonics, intelligent sensing, ultrafast magnetic recording, and high-resolution magnetic imaging. Accurate measurement of both the rotation angle (the real part) and the ellipticity (the imaginary part) is essential for fundamental research and device applications. However, existing measurement schemes generally require separate measurements or distinct detection configurations and therefore cannot simultaneously retrieve both quantities in a single measurement. In this work, we propose a scheme based on weak measurement using dual-pointers, enabling the simultaneous measurement of the rotation angle and ellipticity within a single meter state. This method was theoretically and experimentally implemented to measure the magneto-optical Kerr effect (MOKE), the Faraday effect, and the Cotton-Mouton effect, demonstrating its broad applicability. This work contributes a characterization technique for the complex angle of MO effects, supporting potential applications across spintronics, quantum materials, and advanced optical sensing.
The present paper introduces a quantum weak measurement (WM) scheme for the measurement of the complex magneto-optical Kerr effect (MOKE). We achieve the simultaneous measurement of the Kerr rotation angle and the ellipticity in a single WM process by utilizing two auxiliary pointers derived from the same meter state. The experimental measurement precision for both the Kerr rotation angle and the ellipticity is capable of reaching 10−4 deg. This technique is also employed for the determination of the complex magneto-optical constant Q. The proposed method overcomes the limitation of acquiring the complex magneto-optical Kerr parameters through a multi-step measurement process, which was previously encountered. This breakthrough holds immense significance for efficiently measuring and applying the complex MOKE with high precision and cost-effectiveness.
In this paper, we propose a weak measurement method using two pointers to estimate the magneto-optical Kerr angle, which is robust to ellipticity. The double pointers are the amplified displacement shift and intensity of the post-selected light beam, which are the conventional information carried by the light beam and can be directly output by a detector (such as a charge-coupled device). We demonstrate that the product of the double pointers is only related to the phase variation between two basic vectors and independent of the amplitude errors. In the measurement process, when there is an amplitude change or additional amplitude noise between two eigenstates, the product of two pointers is very useful in extracting phase information and shielding amplitude noise. In addition, the product of two pointers has a good linear relationship with the phase variation and a larger dynamic measurement range. This method is applied to measure the magneto-optical Kerr angle of NiFe film. The Kerr angle can be directly obtained using the product of the light intensity and the amplified displacement shift. This scheme is of great significance for the measurement of the Kerr angle of magnetic films.
The extraordinary concept of weak value amplification and a number of other seemingly counter-intuitive wave phenomena are manifestations of fine interference effects. In this report, we show that weak value amplification naturally arises in the cases of nearly destructive interference between the two orthogonal states of the observable which mimics the corresponding near destructive interference between the eigenstates of the measuring observable as a consequence of nearly mutually orthogonal pre and post selections of the system states. In order to elucidate this, we first experimentally demonstrate a weak measurement concept that uses near destructive interference of two paths of an interferometer having slightly rotated linear polarization states of light. By generating nearly destructive interference between the two paths with small amplitude and phase offsets of the waves, we observe both real and imaginary (respectively) weak value amplification of the small polarization rotation leading to large rotation of the polarization vector orientation and dramatic changes in the circular polarization descriptor fourth Stokes vector element of light, respectively. We go on to demonstrate that the giant enhancement of magneto-optical Kerr rotation, by which we can claim that we have found a non-modulation based and cost-effective magneto-optical Kerr effect (MOKE) measurement. At the end, we show successful weak value amplification of spin Hall shift in magneto-optical sample in both longitudinal and polar MOKE. Our ongoing work is to find out the relation between magneto-optical Kerr rotation and spin Hall shift of light in magnetic material.
A precise, accurate, and relatively straightforward in situ method to measure and control the ellipticity of light resonantly interacting with an atomic vapor is described. The technique can be used to minimize vector light shifts. The method involves measurement of ellipticity-induced resonances in the magnetic-field dependence of nonlinear magneto-optical rotation of frequency-modulated light. The light propagation direction is orthogonal to the applied magnetic field B\mathbf{B}B and the major axis of the light polarization ellipse is along B\mathbf{B}B. When the light modulation frequency matches the Larmor frequency, elliptically polarized light produces a precessing atomic spin orientation transverse to B\mathbf{B}B via synchronous optical pumping. The precessing spin orientation causes optical rotation oscillating at the Larmor frequency by modulating the atomic vapor's circular birefringence. Based on this technique's precision, in situ nature (which avoids systematic errors arising from optical interfaces) and independent control of the most important systematic errors, it is shown that the accuracy of light ellipticity measurements achievable with this technique can exceed that of existing methods by orders of magnitude.
Ultra-sensitive measurement of the magneto-optical rotation, due to interaction of linearly-polarized light passing through room-temperature Rb85 atoms, in response to change in longitudinal magnetic field (δBz) is demonstrated using the weak measurement method. The polarization rotation angle measurement sensitivity (δϕ) of 16 μrad and hence of the magnetometer of 1 nT, achieved using the weak measurement method is better than the balanced optical polarimetry results by a factor of three. The improvement in the measurement sensitivity is realized via optical amplification of the polarization rotation angle via spin-orbit coupled light beam-field. The method is devoid of external rf(/ac) modulation, allows for optimal tunability of sensitivity depending on the dynamic range of the applied magnetic field and the sensitivity can be further enhanced by operating in the spin exchange relaxation free regime of alkali spin polarization.