Progress on ellipsometry utilizing quantum 
entangled light sources

doi:10.3969/j.issn.1007-5461.2025.04.002

Abstract

Abstract: Ellipsometers are essential tools used to measure the optical properties of samples, such as thin film thickness, optical constants of samples and structural profiles, by measuring the change in polarization state of polarized light before and after passing through the samples, which have wide applications in various fields, including physics, chemistry, materials science, and so on. Currently, the integration of new light sources with ellipsometry to enhance the performance of ellipsometers and expand their application scope is one of the hotspots in related research fields. Due to their unique nonclassical properties and high signal-to-noise ratio, quantum entangled light sources have attracted extensive attention in the field of quantum precision measurement. In recent years, research on the principles and applications of quantum ellipsometer, which combines quantum light sources and ellipsometry, has been increasing. The fundamentals and types of classical ellipsometers are reviewed firstly in this paper. Then, based on this, the basic principles and research progress of quantum ellipsometers are mainly introduced, followed with the prospects of their future development direction.

Key words: quantum information, quantum entangled light sources, classical polarimeter, quantum polarimeter, quantum precision measurement

CLC Number:

O431.2

NIU Sujian , , XIE Mengyu , , ZHOU Zhiyuan , SHI Baosen , . Progress on ellipsometry utilizing quantum entangled light sources[J]. Chinese Journal of Quantum Electronics, 2025, 42(4): 450-463.

References

[1]. Drude P. Ueber die Gesetze der Reflexion und Brechung des Lichtes an der Grenze absorbirender Krystalle [J]. Annalen der Physik, 1887, 268(12): 584-625. [2]. Hauge P S, Dill F H. Design and operation of ETA, an automated ellipsometer [J]. IBM Journal of Research and Development, 1973, 17(6): 472-489. [3]. Fujiwara H. Spectroscopic ellipsometry: principles and applications [M]. John Wiley & Sons, 2007. [4]. Gil J J, Ossikovski R. Polarized light and the Mueller matrix approach [M]. CRC press, 2022. [5]. Giovannetti V, Lloyd S, Maccone L. Quantum-enhanced measurements: beating the standard quantum limit [J]. Science, 2004, 306(5700): 1330-1336. [6]. Nagata T, Okamoto R, O'brien J L, et al. Beating the standard quantum limit with four-entangled photons [J]. Science, 2007, 316(5825): 726-729. [7]. Pezzé L, Smerzi A. Entanglement, nonlinear dynamics, and the Heisenberg limit [J]. Physical review letters, 2009, 102(10): 100401. [8]. Kuzmich A, Mandel L. Sub-shot-noise interferometric measurements with two-photon states [J]. Quantum and Semiclassical Optics: Journal of the European Optical Society Part B, 1998, 10(3): 493. [9]. Sun F W, Liu B H, Gong Y X, et al. Experimental demonstration of phase measurement precision beating standard quantum limit by projection measurement [J]. Europhysics Letters, 2008, 82(2): 24001. [10]. Mitchell M W, Lundeen J S, Steinberg A M. Super-resolving phase measurements with a multiphoton entangled state [J]. Nature, 2004, 429(6988): 161-164. [11]. Xiang G Y, Higgins B L, Berry D W, et al. Entanglement-enhanced measurement of a completely unknown optical phase [J]. Nature Photonics, 2011, 5(1): 43-47. [12]. Zhou X Q, Cable H, Whittaker R, et al. Quantum-enhanced tomography of unitary processes [J]. Optica, 2015, 2(6): 510-516. [13]. Pedram A, Besaga V R, Gassab L, et al. Quantum estimation of the Stokes vector rotation for a general polarimetric transformation [J]. New Journal of Physics, 2024, 26(9): 093033. [14]. Rudnicki ?, Sánchez-Soto L L, Leuchs G, et al. Fundamental quantum limits in ellipsometry [J]. Optics Letters, 2020, 45(16): 4607-4610. [15]. Feng S, Pfister O. Sub-shot-noise heterodyne polarimetry [J]. Optics letters, 2004, 29(23): 2800-2802. [16]. Huang Z, Macchiavello C, Maccone L. Usefulness of entanglement-assisted quantum metrology [J]. Physical Review A, 2016, 94(1): 012101. [17]. Demkowicz-Dobrzański R, Maccone L. Using entanglement against noise in quantum metrology [J]. Physical review letters, 2014, 113(25): 250801. [18]. Jones R C. A new calculus for the treatment of optical systems. VII. Properties of the N-matrices [J]. Journal of the Optical Society of America, 1948, 38(8): 671-685. [19]. Stokes G G. On the composition and resolution of streams of polarized light from different sources [J]. Transactions of the Cambridge Philosophical Society, 1851, 9: 399. [20]. Wolf E. Optics in terms of observable quantities [J]. Il Nuovo Cimento (1943-1954), 1954, 12: 884-888. [21]. Jones R C. New calculus for the treatment of optical systems. VIII. Electromagnetic theory [J]. Journal of the Optical Society of America, 1956, 46(2): 126-131. [22]. Goldberg A Z. Quantum theory of polarimetry: From quantum operations to Mueller matrices [J]. Physical Review Research, 2020, 2(2): 023038. [23]. Yang Kun, Wang Xiang Zhao, Bu Yang. Research progress of ellipsometer [J]. Laser & Optoelectronics Progress, 2007, 44(3): 43-49. 杨坤, 王向朝, 步扬. 椭偏仪的研究进展 [J]. 激光与光电子学进展, 2007, 44(3): 43-49. [24]. Zhu Xu Dan, Zhang Rong Jun, Zheng Yu Xiang, et al. Spectroscopic ellipsometry and its applications in the study of thin film materials [J]. Chinese Optics, 2019, 12(6): 1195-1234. 朱绪丹, 张荣君, 郑玉祥, 等. 椭圆偏振光谱测量技术及其在薄膜材料研究中的应用 [J]. 中国光学, 2019, 12(6): 1195-1234. [25]. Dong J, Zhou H. Polarimeters from bulky optics to integrated optics: A review [J]. Optics Communications, 2020, 465: 125598. [26]. Berry H G, Gabrielse G, Livingston A E. Measurement of the Stokes parameters of light [J]. Applied optics, 1977, 16(12): 3200-3205. [27]. Meng X, Li J, Song H, et al. Full-Stokes Fourier-transform imaging spectropolarimeter using a time-division polarization modulator [J]. Applied Optics, 2014, 53(24): 5275-5282. [28]. De Martino A, Kim Y K, Garcia-Caurel E, et al. Optimized Mueller polarimeter with liquid crystals [J]. Optics letters, 2003, 28(8): 616-618. [29]. Alali S, Yang T, Vitkin I A. Rapid time-gated polarimetric Stokes imaging using photoelastic modulators [J]. Optics letters, 2013, 38(16): 2997-3000. [30]. Azzam R M A. Arrangement of four photodetectors for measuring the state of polarization of light [J]. Optics letters, 1985, 10(7): 309-311. [31]. Compain E, Drevillon B. Broadband division-of-amplitude polarimeter based on uncoated prisms [J]. Applied optics, 1998, 37(25): 5938-5944. [32]. Gruev V, Ortu A, Lazarus N, et al. Fabrication of a dual-tier thin film micropolarization array [J]. Optics express, 2007, 15(8): 4994-5007. [33]. Morel O, Seulin R, Fofi D. Handy method to calibrate division-of-amplitude polarimeters for the first three Stokes parameters [J]. Optics express, 2016, 24(12): 13634-13646. [34] Pors A, Nielsen M G, Bozhevolnyi S I. Plasmonic metagratings for simultaneous determination of Stokes parameters [J]. Optica, 2015, 2(8): 716-723. [35] Balthasar Mueller J P, Leosson K, Capasso F. Ultracompact metasurface in-line polarimeter [J]. Optica, 2016, 3(1): 42-47. [36] Zhang X, Yang S, Yue W, et al. Direct polarization measurement using a multiplexed Pancharatnam–Berry metahologram [J]. Optica, 2019, 6(9): 1190-1198. [37]. Rothen A. The ellipsometer, an apparatus to measure thicknesses of thin surface films [J]. Review of Scientific Instruments, 1945, 16(2): 26-30． [38]. Jasperson S N, Schnatterly S E. An improved method for high reflectivity ellipsometry based on a new polarization modulation technique [J]. Review of Scientific Instruments, 1969, 40(6): 761-767. [39]. Adachi S. Optical constants of crystalline and amorphous semiconductors: numerical data and graphical information [M]. Springer Science & Business Media, 2013. [40]. Abouraddy A F, Toussaint K C, Sergienko A V, et al. Ellipsometric measurements by use of photon pairs generated by spontaneous parametric downconversion [J]. Optics Letters, 2001, 26(21): 1717-1719. [41]. Abouraddy A F, Toussaint K C, Sergienko A V, et al. Entangled-photon ellipsometry [J]. Journal of the Optical Society of America B, 2002, 19(4): 656-662. [42]. Aiello A, Puentes G, Woerdman J P. Linear optics and quantum maps [J]. Physical Review A, 2007, 76(3): 032323. [43] Anderson D G M, Barakat R. Necessary and sufficient conditions for a Mueller matrix to be derivable from a Jones matrix [J]. JOSA A, 1994, 11(8): 2305-2319. [44]. Banaszek K, D’ariano G M, Paris M G A, et al. Maximum-likelihood estimation of the density matrix [J]. Physical Review A, 1999, 61(1): 010304. [45]. Abouraddy A F, Sergienko A V, Saleh B E A, et al. Quantum entanglement and the two-photon Stokes parameters [J]. Optics Communications, 2002, 201(1-3): 93-98. [46]. He C, He H, Chang J, et al. Polarisation optics for biomedical and clinical applications: a review [J]. Light: Science & Applications, 2021, 10(1): 194. [47] Besaga V R, Lopushenko I V, Sieryi O, et al. Bridging classical and quantum approaches in optical polarimetry: Predicting polarization-entangled photon behavior in scattering environments [J]. arxiv preprint arxiv:2411.06134, 2024. [48]. Magnitskiy S, Agapov D, Chirkin A. Quantum ghost polarimetry with entangled photons [J]. Optics Letters, 2022, 47(4): 754-757. [49]. Pedram A, Besaga V R, Gassab L, et al. Quantum estimation of the Stokes vector rotation for a general polarimetric transformation [J]. New Journal of Physics, 2024, 26(9): 093033. [50]. Toussaint Jr K C, Di Giuseppe G, Bycenski K J, et al. Quantum ellipsometry using correlated-photon beams [J]. Physical Review A, 2004, 70(2): 023801. [51]. Graham D J L, Parkins A S, Watkins L R. Ellipsometry with polarisation-entangled photons [J]. Optics Express, 2006, 14(16): 7037-7045. [52]. Zou Xue Feng, Li Feng Jiao, Cui Liang, et al. Fiber based Scheme for Quantum Ellipsometry [J]. Acta Sinica Quantum Optica, 2019 (1): 15-21. 邹雪峰, 李凤娇, 崔亮, 等. 基于光纤的量子椭圆偏振光测量装置 [J]. 量子光学学报, 2019 (1): 15-21. [53]. Pedram A, Besaga V R, Setzpfandt F, et al. Nonlocality enhanced precision in quantum polarimetry via entangled photons [J]. Advanced Quantum Technologies, 2024: 2400059. [54]. You C J, Rodriguez-Fajardo V, Francis L, et al. Nonlocal Mueller polarimetry[C]//Polarized Light and Optical Angular Momentum for Biomedical Diagnostics 2024. SPIE, 2024, 12845: 42-48. [55]. Lung S, Wang K, Pedersen N R H, et al. Robust Classical and Quantum Polarimetry with a Single Nanostructured Metagrating [J]. ACS photonics, 2024, 11(3): 1060-1067. [56]. Tischler N, Krenn M, Fickler R, et al. Quantum optical rotatory dispersion [J]. Science advances, 2016, 2(10): e1601306. [57]. Yoon S J, Lee J S, Rockstuhl C, et al. Experimental quantum polarimetry using heralded single photons [J]. Metrologia, 2020, 57(4): 045008. [58]. Restuccia S, Gibson G M, Cronin L, et al. Measuring optical activity with unpolarized light: Ghost polarimetry [J]. Physical Review A, 2022, 106(6): 062601. [59] Xie M Y, Niu S J, Li Y H, et al. Quantum entanglement enabled ellipsometer for phase retardance measurement [J]. arxiv preprint arxiv:2402.17401, 2024. [60]. Saxena A, Kaur M, Devrari V, et al. Quantum ghost imaging of a transparent polarisation sensitive phase pattern [J]. Scientific Reports, 2022, 12(1): 21105. [61]. Zhang Y, He Z, Tong X, et al. Quantum imaging of biological organisms through spatial and polarization entanglement [J]. Science Advances, 2024, 10(10): eadk1495. [62]. Li Wei Qi. Research on development and application of a high-precision broadband Mueller matrix ellipsometer [D]. Wuhan: Huazhong University of Science and Technology, 2016. 李伟奇. 高精度宽光谱穆勒矩阵椭偏仪研制与应用研究[D]. 武汉：华中科技大学, 2016. [63]. Zhang Song. Research on development and application of the Photoelastic-modulated high-speed Mueller matrix ellipsometer [D]. Wuhan: Huazhong University of Science and Technology, 2021. 张松. 光弹调制高速穆勒矩阵椭偏仪研制与应用研究 [D]. 武汉：华中科技大学,2021. [64]. Chang Jin Tao. A study on design of polarimetric measurement system for biomedical applications [D]. Beijing: Tsinghua University, 2016. 常金涛. 生物体系偏振测量系统的设计 [D]. 北京：清华大学, 2016. [65]. Janassek P, Blumenstein S, Els??er W. Recovering a hidden polarization by ghost polarimetry [J]. Optics Letters, 2018, 43(4): 883-886. [66]. Hannonen A, Hoenders B J, Els?sser W, et al. Ghost polarimetry using Stokes correlations [J]. Journal of the Optical Society of America A, 2020, 37(5): 714-719. [67]. Magnitskiy S, Agapov D, Chirkin A. Ghost polarimetry with unpolarized pseudo-thermal light [J]. Optics letters, 2020, 45(13): 3641-3644.

Progress on ellipsometry utilizing quantum entangled light sources

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	LU Xiaotong , , CHANG Hong , . Quantum precision measurement based on optical lattice atomic clocks [J]. Chinese Journal of Quantum Electronics, 2025, 42(4): 437-449.
[2]	YANG Yu, , ZHANG Pei , , LI Fuli , . Quantum multiparameter estimation enhanced by feedback control [J]. Chinese Journal of Quantum Electronics, 2025, 42(4): 464-475.
[3]	LU Maolin , , BAI Miaoqing, QIN Chengbing , . Noise‐resistant frequency‐domain imaging based on single‐photon detector arrays [J]. Chinese Journal of Quantum Electronics, 2025, 42(4): 537-545.
[4]	YUAN Hao , , LUO Bing , CHEN Jianjun , , CHEN Zhen, , YANG Wenguang , , ZHANG Hao , ZHANG Linjie , , ZHANG Haofeng. Corona discharge signal measurement based on Rydberg atoms [J]. Chinese Journal of Quantum Electronics, 2025, 42(4): 556-564.
[5]	DU Yijie , LYU Ziyao , HU Weidong , HE Jun , LIU Zhihui , DONG Tao, JIN Shichao. Atomic‑antenna‑based quantum precision measurement of low‑frequency electric fields and applications [J]. Chinese Journal of Quantum Electronics, 2024, 41(5): 701-712.
[6]	SHI Xiping, LIU Weiyue. Research on Doppler compensation in linear optical sampling algorithm [J]. Chinese Journal of Quantum Electronics, 2024, 41(5): 729-737.
[7]	LIU Xueming , CHEN Yongcong , AO Ping. Quantum control optimization in thermal noise environment [J]. Chinese Journal of Quantum Electronics, 2024, 41(1): 103-112.
[8]	YANG Han , FENG Yan , XIE Sijiang , . Quantum auction protocol based on semi⁃quantum secure direct communication [J]. Chinese Journal of Quantum Electronics, 2024, 41(1): 125-134.
[9]	YANG Donghan , LI Zhiqiang , WU Xi , PAN Wenjie , YANG Hui. Optimization of Oracle circuits based on minimum weight and template matching [J]. Chinese Journal of Quantum Electronics, 2024, 41(1): 151-160.
[10]	NIU Yiren , GUAN Zhijin , LI Haifeng , LU Junyu. A conversion method for improving fidelity of quantum circuits [J]. Chinese Journal of Quantum Electronics, 2024, 41(1): 161-169.
[11]	WANG Shengbin , DOU Menghan , WU Yuchun , GUO Guoping , GUO Guangcan . Research progress of distributed quantum computing [J]. Chinese Journal of Quantum Electronics, 2024, 41(1): 1-25.
[12]	WANG Shuo , PAN Jiazheng , WEI Xingyu , JIANG Junliang , ZHANG Kaixuan , LI Zishuo , GUO Tingting , XU Wenqu , ZUO Quan , ZHOU Tianshi , SHENG Yifan , SUN Guozhu , WU Peiheng , . FPGA⁃based linear detection and characterization of microwave coherent source [J]. Chinese Journal of Quantum Electronics, 2023, 40(6): 850-857.
[13]	HU Qianqian , FENG Bao , YAN Longchuan , ZHAO Xiaohong , CHEN Zhiyu , LI Wenting , LI Wei . HU Qianqian 1,2, FENG Bao 1,2, YAN Longchuan 3, ZHAO Xiaohong 4, CHEN Zhiyu 3, LI Wenting 5, LI Wei 5* [J]. Chinese Journal of Quantum Electronics, 2023, 40(5): 712-718.
[14]	ZHANG Bo , QU Diqing , LUO Jun , DU Xiangjian , FANG Yuqiang , JIANG Lianjun , GAO Song , YU Lin , SUN Fang , TANG Shibiao . A defense scheme of pulse illumination attack for quantum key distribution systems [J]. Chinese Journal of Quantum Electronics, 2023, 40(5): 719-725.
[15]	HUANG Guan , LOU Xiaoping. Semi⁃quantum private comparison protocol based on four⁃particle GHZ state [J]. Chinese Journal of Quantum Electronics, 2023, 40(5): 726-737.