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Nanophotonics

Jones‐matrix imaging based on two‐photon interference

Tsz Kit Yung, Hong Liang, Jiawei Xi, Wing Yim Tam, Jensen Li

Published Oct 22, 2022• 12 citations
Publisher

Abstract

Two-photon interference is an important effect that is tightly related to the quantum nature of light. Recently, it has been shown that the photon bunching from the Hong-Ou-Mandel (HOM) effect can be used for quantum imaging in which sample properties (reflection/transmission amplitude, phase delay, or polarization) can be characterized at the pixel-by-pixel level. In this work, we perform Jones matrix imaging for an unknown object based on two-photon interference. By using a reference metasurface with panels of known polarization responses in pairwise coincidence measurements, the object's polarization responses at each pixel can be retrieved from the dependence of the coincidence visibility as a function of the reference polarization. The post-selection of coincidence images with specific reference polarization in our approach eliminates the need in switching the incident polarization and thus parallelized optical measurements for Jones matrix characterization. The parallelization in preparing input states, prevalent in any quantum algorithms, is an advantage of adopting two-photon interference in Jones matrix imaging. We believe our work points to the usage of metasurfaces in biological and medical imaging in the quantum optical regime.

DOI
10.1515/nanoph-2022-0499

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Two-photon interference is an important effect that is tightly related to the quantum nature of light. Recently, it has been shown that the photon bunching from the Hong-Ou-Mandel (HOM) effect can be used for quantum imaging in which sample properties (reflection/transmission amplitude, phase delay, or polarization) can be characterized at the pixel-by-pixel level. In this work, we perform Jones matrix imaging for an unknown object based on two-photon interference. By using a reference metasurface with panels of known polarization responses in pairwise coincidence measurements, the object's polarization responses at each pixel can be retrieved from the dependence of the coincidence visibility as a function of the reference polarization. The post-selection of coincidence images with specific reference polarization in our approach eliminates the need in switching the incident polarization and thus parallelized optical measurements for Jones matrix characterization. The parallelization in preparing input states, prevalent in any quantum algorithms, is an advantage of adopting two-photon interference in Jones matrix imaging. We believe our work points to the usage of metasurfaces in biological and medical imaging in the quantum optical regime.
Metasurfaces provide a promising route for structuring light and generating holograms with designed amplitude, phase, and polarization profiles, leading to a versatile platform for integrating and constructing optical components beyond the conventional ones. At the same time, incorporating coincidence in imaging allows a high signal-to-noise ratio for imaging in very low light levels. As beneficial from the recent development in both metasurfaces and single-photon avalanche diode (SPAD) cameras, we combine the polarization-sensitive capability of metasurfaces with Hong-Ou-Mandel (HOM)-type interference in generating images with tailor-made two-photon interference and polarization coincidence signatures. By using orthogonal linear-polarized photons as incidence, correlated, anticorrelated, and uncorrelated polarization coincidence features can be observed within the same image from the pairwise second-order coherence statistics across different pixels of the image. Our work adds polarization to the demonstrated amplitude and phase sensitivity in the domain of "HOM microscopy" and can be useful for biological and security applications.
Two-photon interference in a Hong-Ou-Mandel (HOM) interferometer can be used as a quantum sensing mechanism due to the sensitivity of the interference dip to perturbations of the photon indistinguishability. In particular, recent works have generalized this concept to microscopy setups, but the sensitivity to optical path differences constrains its application to samples with thickness variation typically below a few micrometers if tracking changes in the coincidences at a fixed delay. Extending the concept to polarization microscopy and circumventing this limitation, this manuscript explores the use of a narrowband photon pair source with coherence length >1 mm to broaden the HOM dip. Thus, realistic sample-thickness variations introduce negligible temporal distinguishability, and changes in coincidence rate at the dip centre are then dominated by sample-induced polarization effects. To compute the polarization rotation, we develop a statistical model for the interferometer, derive the Fisher information, and establish a maximum-likelihood estimator for the local fast-axis angle. Recording dip and baseline frames at each sample position via raster scanning, the experimental results validate the framework, agreeing with classical polarized-intensity images while demonstrating operation at a maximum-precision regime and insensitiveness to layer thickness. Overall, the approach enclosed provides a quantum-based quantitative imaging of birefringent structures, which can motivate further advantageous applications, including enhanced signal-to-noise ratio and lower damage imaging of photosensitive samples.
We propose a theoretical polarization tomography scheme within the quantum imaging with undetected photons (QIUP) framework that extracts the Jones matrix elements, describing the sample's polarization response from interference visibilities and phase shifts. By exploiting inherent constraints among the Jones matrix elements based on the assumptions of fully polarized pure states and linear, non-depolarizing components, the method reduces the number of unknowns required for reliable reconstruction. The same interference-based protocol is also demonstrated for a fully generalized Jones matrix, extending the approach to a broader class of polarization responses. This scheme is well suited for polarization-resolved QIUP implementations with minimal measurement requirements and enables non-invasive characterization of complex samples at different probing and detection wavelengths.
Abstract Coincidence measurement has become an emerging technique for optical imaging. Based on measuring the second-order coherence g2, sample features such as reflection/transmission amplitude and phase delay can be extracted with developed algorithms pixel-by-pixel. However, an accurate measurement of g2 requires a substantial number of collected photons which becomes difficult under low-light conditions. Here, we propose a deep-learning approach for Jones matrix imaging using photon arrival data directly. A variational autoencoder (β-VAE) is trained using numerical data in an unsupervised manner to obtain a minimal data representation, which can be transformed into an image with little effort. We demonstrate as few as 88 photons collected per pixel on average to extract a Jones matrix image, with accuracy surpassing previous semi-analytic algorithms derived from g2. Our approach not only automates formulating imaging algorithms but can also assess the sufficiency of information from a designed experimental procedure, which can be useful in equipment or algorithm designs for a wide range of imaging applications.
Hong-Ou-Mandel (HOM) interference [1] is a bunching phenomenon based on the bosonic nature of photons. When two photons that are perfectly indistinguishable from each other are mixed using a half beam splitter (HBS), they always bunch and exhibit the absence of coincidence resulting in a specific interferogram called HOM dip. The important property of the HOM interference is that the decrease in coincidence reflects the degree of indistinguishability of the input photons, i.e., it provides information regarding the probability of overlap of the input photons. Thus, this property should enable the estimation of a target photon in an unknown quantum state using a probe photon in a known state. In this work, we realize the above concept as the quantum state tomography (QST) applicable to d-dimensional photonic qudits, which we call HOM-QST [2]. Interestingly, we observe that HOM-QST is robust against various imperfections and that the probe photon can be replaced by classical light. Furthermore, we confirm this by demonstrating a proof-of-principle experiment using two-dimensional polarization qubits.