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Optics Express

Estimation of Kerr angle based on weak measurement with two pointers

Lan E Luo, Tong Li, Yinghang Jiang, Liang Fang, Bo Liu, Zhiyou Zhang

Published Apr 3, 2023• 13 citations
Publisher

Abstract

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.

DOI
10.1364/oe.487363

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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.
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.
In this paper, a weak measurement scheme with double pointers (mean value shift and intensity shift of the post-selected light) is presented to simultaneously measure the tiny polarization change (phase and amplitude) of light in a single experimental apparatus. Furthermore, rather than using charge-coupled-device (CCD) to measure the pointer shift, we use the two-channel photoreceiver combined with lock-in amplifier (LIA) to measure the intensities of a split-Gaussian mode in this work. In this way, we introduce two intensity contrast ratios (ICRs) as special pointers to characterize the mean value and intensity shifts. As a result, the measurement precision of the polarization rotation is on the order of magnitude of 10−7rad\,10^{-7}rad10−7radin the experiment. These findings provide a distinctive insight into the weak measurement and have important implications for the accurate measurement of complex optical parameters.
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.
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.
Measuring the polarization state of light has become a challenging study owing to its requirement to simultaneously extract the phase and amplitude parameters with high precision. Here, we present a weak measurement (WM) scheme with two pointers to determine a general polarization state. For the output spectrum from the WM regime, one pointer with the light frequency is used to measure the phase parameter while the other with the post-selected probability is to measure the amplitude. The optimized regime permits the simultaneous measurements of two parameters since the shift results of both two pointers are read in the same working regions. The simulated results show high sensitivity for both two parameters, and high precision that can be comparable with that by other existing schemes. Our scheme can be applied to measure other complex physical effects, providing a method for future ultra-sensitive sensing and metrology.
In the application of weak measurements, such as the estimation of magnetic parameters, the purely real weak coupling of standard weak measurement (SWM) does not correspond to the true physical parameters. To accommodate more complex application scenarios, we further explore three different weak measurement models in which both complex weak coupling and complex weak values coexist. This paper theoretically analyzes pointer variations and applicable ranges in SWM, double pointer weak measurement (DPWM), and almost-balanced weak measurement (ABWM) under specific conditions. Notably, only ABWM can successfully distinguish the real and imaginary components of weak values under complex weak-coupling conditions. While SWM and DPWM can also solve for weak values, they fail to obtain a unique and correct test value. The ABWM technique provides a higher sensitivity than SWM when measuring extremely small parameters. Furthermore, we apply ABWM to the magneto-optical Kerr effect measurement of a Ni-Fe film. This research deepens the understanding of weak measurement techniques and introduces new methods for multiparameter measurements.