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    Vol. 12 , Issue 7 , 2023

      News & Views

    • Xuanhang Wang,Bin Xu,Wenjing Tian
      Vol. 12, Issue 7, Pages: 1176-1177(2023) DOI: 10.1038/s41377-023-01188-1
      Abstract:Photochromic spiropyran molecule shows a brand new function for serving as an efficient photoinitiator to activate two-photon photopolymerization, thus paving the way for developing a fast 3D printing technology.  
        
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    • Sangsik Kim
      Vol. 12, Issue 7, Pages: 1178-1179(2023) DOI: 10.1038/s41377-023-01189-0
      Abstract:Concentrically distributed silicon photonic grating arrays generate long-range Besse–Gaussian beams, enabling rotational and range measurements over obstacles. This compact and mass-producible chip unlocks new potentials for long-range sensing and applications.  
        
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    • Xiaoqi Cui,Yi Zhang,Andreas C. Liapis,Zhipei Sun
      Vol. 12, Issue 7, Pages: 1180-1181(2023) DOI: 10.1038/s41377-023-01190-7
      Abstract:The development of a low-cost compact reconstructive spectrometer paves the way towards portable pm-resolution spectroscopy.  
        
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    • Alina Karabchevsky
      Vol. 12, Issue 7, Pages: 1182-1183(2023) DOI: 10.1038/s41377-023-01197-0
      Abstract:Possessing intriguing optoelectronic properties, metal halide perovskites can serve as a large-scale platform for miniaturized photonic circuits with on-chip active devices such as lasers and detectors.  
        
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    • Chonghang Zhao,Hanfei Yan
      Vol. 12, Issue 7, Pages: 1184-1186(2023) DOI: 10.1038/s41377-023-01198-z
      Abstract:Deep neural network can greatly improve tomography reconstruction with limited data. A recent effort of combining ptycho-tomography model with the 3D U-net demonstrated a significant reduction in both the number of projections and computation time, and showed its potential for integrated circuit imaging that requires high-resolution and fast measurement speed.  
        
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      Reviews

    • Minjae Lee,Gwansik Kim,Yeongju Jung,Kyung Rok Pyun,Jinwoo Lee,Byung-Wook Kim,Seung Hwan Ko
      Vol. 12, Issue 7, Pages: 1187-1215(2023) DOI: 10.1038/s41377-023-01119-0
      Abstract:Radiative cooling is a passive cooling technology without any energy consumption, compared to conventional cooling technologies that require power sources and dump waste heat into the surroundings. For decades, many radiative cooling studies have been introduced but its applications are mostly restricted to nighttime use only. Recently, the emergence of photonic technologies to achieves daytime radiative cooling overcome the performance limitations. For example, broadband and selective emissions in mid-IR and high reflectance in the solar spectral range have already been demonstrated. This review article discusses the fundamentals of thermodynamic heat transfer that motivates radiative cooling. Several photonic structures such as multilayer, periodical, random; derived from nature, and associated design procedures were thoroughly discussed. Photonic integration with new functionality significantly enhances the efficiency of radiative cooling technologies such as colored, transparent, and switchable radiative cooling applications has been developed. The commercial applications such as reducing cooling loads in vehicles, increasing the power generation of solar cells, generating electricity, saving water, and personal thermal regulation are also summarized. Lastly, perspectives on radiative cooling and emerging issues with potential solution strategies are discussed.  
        
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    • Jacob Pettine,Prashant Padmanabhan,Nicholas Sirica,Rohit P. Prasankumar,Antoinette J. Taylor,Hou-Tong Chen
      Vol. 12, Issue 7, Pages: 1216-1245(2023) DOI: 10.1038/s41377-023-01163-w
      Abstract:Nonlinear optical spectroscopies are powerful tools for investigating both static material properties and light-induced dynamics. Terahertz (THz) emission spectroscopy has emerged in the past several decades as a versatile method for directly tracking the ultrafast evolution of physical properties, quasiparticle distributions, and order parameters within bulk materials and nanoscale interfaces. Ultrafast optically-induced THz radiation is often analyzed mechanistically in terms of relative contributions from nonlinear polarization, magnetization, and various transient free charge currents. While this offers material-specific insights, more fundamental symmetry considerations enable the generalization of measured nonlinear tensors to much broader classes of systems. We thus frame the present discussion in terms of underlying broken symmetries, which enable THz emission by defining a system directionality in space and/or time, as well as more detailed point group symmetries that determine the nonlinear response tensors. Within this framework, we survey a selection of recent studies that utilize THz emission spectroscopy to uncover basic properties and complex behaviors of emerging materials, including strongly correlated, magnetic, multiferroic, and topological systems. We then turn to low-dimensional systems to explore the role of designer nanoscale structuring and corresponding symmetries that enable or enhance THz emission. This serves as a promising route for probing nanoscale physics and ultrafast light-matter interactions, as well as facilitating advances in integrated THz systems. Furthermore, the interplay between intrinsic and extrinsic material symmetries, in addition to hybrid structuring, may stimulate the discovery of exotic properties and phenomena beyond existing material paradigms.  
        
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    • Mingwei Tang,Yubing Han,Danchen Jia,Qing Yang,Ji-Xin Cheng
      Vol. 12, Issue 7, Pages: 1246-1267(2023) DOI: 10.1038/s41377-023-01182-7
      Abstract:Far-field chemical microscopy providing molecular electronic or vibrational fingerprint information opens a new window for the study of three-dimensional biological, material, and chemical systems. Chemical microscopy provides a nondestructive way of chemical identification without exterior labels. However, the diffraction limit of optics hindered it from discovering more details under the resolution limit. Recent development of super-resolution techniques gives enlightenment to open this door behind far-field chemical microscopy. Here, we review recent advances that have pushed the boundary of far-field chemical microscopy in terms of spatial resolution. We further highlight applications in biomedical research, material characterization, environmental study, cultural heritage conservation, and integrated chip inspection.  
        
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    • Younggeun Lee,Mun Ji Low,Dongwook Yang,Han Ku Nam,Truong-Son Dinh Le,Seung Eon Lee,Hyogeun Han,Seunghwan Kim,Quang Huy Vu,Hongki Yoo,Hyosang Yoon,Joohyung Lee,Suchand Sandeep,Keunwoo Lee,Seung-Woo Kim,Young-Jin Kim
      Vol. 12, Issue 7, Pages: 1268-1300(2023) DOI: 10.1038/s41377-023-01143-0
      Abstract:The realization of hybrid optics could be one of the best ways to fulfill the technological requirements of compact, light-weight, and multi-functional optical systems for modern industries. Planar diffractive lens (PDL) such as diffractive lenses, photonsieves, and metasurfaces can be patterned on ultra-thin flexible and stretchable substrates and be conformally attached on top of arbitrarily shaped surfaces. In this review, we introduce recent research works addressed to the design and manufacturing of ultra-thin graphene optics, which will open new markets in compact and light-weight optics for next-generation endoscopic brain imaging, space internet, real-time surface profilometry, and multi-functional mobile phones. To provide higher design flexibility, lower process complexity, and chemical-free process with reasonable investment cost, direct laser writing (DLW) of laser-induced-graphene (LIG) is actively being applied to the patterning of PDL. For realizing the best optical performances in DLW, photon-material interactions have been studied in detail with respect to different laser parameters; the resulting optical characteristics have been evaluated in terms of amplitude and phase. A series of exemplary laser-written 1D and 2D PDL structures have been actively demonstrated with different base materials, and then, the cases are being expanded to plasmonic and holographic structures. The combination of these ultra-thin and light-weight PDL with conventional bulk refractive or reflective optical elements could bring together the advantages of each optical element. By integrating these suggestions, we suggest a way to realize the hybrid PDL to be used in the future micro-electronics surface inspection, biomedical, outer space, and extended reality (XR) industries.  
        
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      Original Articles

    • Umut T. Sanli,Griffin Rodgers,Marie-Christine Zdora,Peng Qi,Jan Garrevoet,Ken Vidar Falch,Bert Müller,Christian David,Joan Vila-Comamala
      Vol. 12, Issue 7, Pages: 1301-1308(2023) DOI: 10.1038/s41377-023-01157-8
      Abstract:Achromatic doublets are combinations of two individual lenses designed to focus different wavelengths of light in the same position. Apochromatic optics are improved versions of the achromatic schemes which extend the wavelength range significantly. Both achromatic and apochromatic optics are well-established for visible light. However, X-ray achromatic lenses did not exist until very recently, and X-ray apochromatic lenses have never been experimentally demonstrated. Here, we create an X-ray apochromatic lens system using an appropriate combination of a Fresnel zone plate and a diverging compound refractive lens with a tuned separation distance. The energy-dependent performance of this apochromat was characterized at photon energies between 6.5 and 13.0 keV by ptychographic reconstruction of the focal spot and scanning transmission X-ray microscopy of a resolution test sample. The apochromat delivered a reconstructed focal spot size of 940 × 740 nm2. The apochromatic combination shows a four-fold improvement in the chromatic aberration correction range compared to an achromatic doublet configuration. Thus, apochromatic X-ray optics have the potential to increase the focal spot intensity for a wide variety of X-ray applications.  
        
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    • Gordon H. Y. Li,Christian R. Leefmans,James Williams,Alireza Marandi
      Vol. 12, Issue 7, Pages: 1309-1317(2023) DOI: 10.1038/s41377-023-01180-9
      Abstract:Cellular automata are a class of computational models based on simple rules and algorithms that can simulate a wide range of complex phenomena. However, when using conventional computers, these 'simple' rules are only encapsulated at the level of software. This can be taken one step further by simplifying the underlying physical hardware. Here, we propose and implement a simple photonic hardware platform for simulating complex phenomena based on cellular automata. Using this special-purpose computer, we experimentally demonstrate complex phenomena, including fractals, chaos, and solitons, which are typically associated with much more complex physical systems. The flexibility and programmability of our photonic computer present new opportunities to simulate and harness complexity for efficient, robust, and decentralized information processing using light.  
        
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    • Zhihao Liu,Guangwei Hu,Huapeng Ye,Miaoyang Wei,Zhenghao Guo,Kexu Chen,Chen Liu,Biao Tang,Guofu Zhou
      Vol. 12, Issue 7, Pages: 1318-1326(2023) DOI: 10.1038/s41377-023-01174-7
      Abstract:Microlens arrays (MLAs) based on the selective wetting have opened new avenues for developing compact and miniaturized imaging and display techniques with ultrahigh resolution beyond the traditional bulky and volumetric optics. However, the selective wetting lenses explored so far have been constrained by the lack of precisely defined pattern for highly controllable wettability contrast, thus limiting the available droplet curvature and numerical aperture, which is a major challenge towards the practical high-performance MLAs. Here we report a mold-free and self-assembly approach of mass-production of scalable MLAs, which can also have ultrasmooth surface, ultrahigh resolution, and the large tuning range of the curvatures. The selective surface modification based on tunable oxygen plasma can facilitate the precise pattern with adjusted chemical contrast, thus creating large-scale microdroplets array with controlled curvature. The numerical aperture of the MLAs can be up to 0.26 and precisely tuned by adjusting the modification intensity or the droplet dose. The fabricated MLAs have high-quality surface with subnanometer roughness and allow for record-high resolution imaging up to equivalently 10, 328 ppi, as we demonstrated. This study shows a cost-effective roadmap for mass-production of high-performance MLAs, which may find applications in the rapid proliferating integral imaging industry and high-resolution display.  
        
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    • Jianan Fang,Kun Huang,E Wu,Ming Yan,Heping Zeng
      Vol. 12, Issue 7, Pages: 1327-1336(2023) DOI: 10.1038/s41377-023-01179-2
      Abstract:Active mid-infrared (MIR) imagers capable of retrieving three-dimensional (3D) structure and reflectivity information are highly attractive in a wide range of biomedical and industrial applications. However, infrared 3D imaging at low-light levels is still challenging due to the deficiency of sensitive and fast MIR sensors. Here we propose and implement a MIR time-of-flight imaging system that operates at single-photon sensitivity and femtosecond timing resolution. Specifically, back-scattered infrared photons from a scene are optically gated by delay-controlled ultrashort pump pulses through nonlinear frequency upconversion. The upconverted images with time stamps are then recorded by a silicon camera to facilitate the 3D reconstruction with high lateral and depth resolutions. Moreover, an effective numerical denoiser based on spatiotemporal correlation allows us to reveal the object profile and reflectivity under photon-starving conditions with a detected flux below 0.05 photons/pixel/second. The presented MIR 3D imager features high detection sensitivity, precise timing resolution, and wide-field operation, which may open new possibilities in life and material sciences.  
        
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    • Song Han,Jieyuan Cui,Yunda Chua,Yongquan Zeng,Liangxing Hu,Mingjin Dai,Fakun Wang,Fangyuan Sun,Song Zhu,Lianhe Li,Alexander Giles Davies,Edmund Harold Linfield,Chuan Seng Tan,Yuri Kivshar,Qi Jie Wang
      Vol. 12, Issue 7, Pages: 1337-1345(2023) DOI: 10.1038/s41377-023-01200-8
      Abstract:One of the most exciting breakthroughs in physics is the concept of topology that was recently introduced to photonics, achieving robust functionalities, as manifested in the recently demonstrated topological lasers. However, so far almost all attention was focused on lasing from topological edge states. Bulk bands that reflect the topological bulk-edge correspondence have been largely missed. Here, we demonstrate an electrically pumped topological bulk quantum cascade laser (QCL) operating in the terahertz (THz) frequency range. In addition to the band-inversion induced in-plane reflection due to topological nontrivial cavity surrounded by a trivial domain, we further illustrate the band edges of such topological bulk lasers are recognized as the bound states in the continuum (BICs) due to their nonradiative characteristics and robust topological polarization charges in the momentum space. Therefore, the lasing modes show both in-plane and out-of-plane tight confinements in a compact laser cavity (lateral size ~3λlaser). Experimentally, we realize a miniaturized THz QCL that shows single-mode lasing with a side-mode suppression ratio (SMSR) around 20 dB. We also observe a cylindrical vector beam for the far-field emission, which is evidence for topological bulk BIC lasers. Our demonstration on miniaturization of single-mode beam-engineered THz lasers is promising for many applications including imaging, sensing, and communications.  
        
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    • Enes Şeker,Babak Olyaeefar,Khalil Dadashi,Serdar Şengül,Mohammad Hosain Teimourpour,Ramy El-Ganainy,Abdullah Demir
      Vol. 12, Issue 7, Pages: 1346-1353(2023) DOI: 10.1038/s41377-023-01175-6
      Abstract:Large-area lasers are practical for generating high output powers. However, this often comes at the expense of lower beam quality due to the introduction of higher-order modes. Here, we experimentally demonstrate a new type of electrically pumped, large-area edge-emitting lasers that exhibit a high power emission (~0.4 W) and a high-quality beam (M2~1.25). These favorable operational characteristics are enabled by establishing a quasi PT-symmetry between the second-order mode of a large area two-mode laser cavity and that of a single-mode auxiliary partner cavity, i.e., by implementing a partial isospectrality between the two coupled cavities. This in turn enlarges the effective volume of the higher-order modes. As a result, a selective pump applied via current injection into the main laser cavity can provide a stronger modal gain to the fundamental mode, and thus lead to lasing in the single mode regime after filtering out higher order transverse modes. The reported experimental results confirm this intuitive picture and are in good agreement with both theoretical and numerical analysis. Above all, the employed material platform and fabrication process are compatible with the industrial standards of semiconductor lasers. This work provides the first clear demonstration, beyond previous proof-of-concept studies, of the utility of PT-symmetry in building laser geometries with enhanced performance and, at the same time, useful output power levels and emission characteristics.  
        
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    • Jian Zhao,Lulu Jiang,Alex Matlock,Yihong Xu,Jiabei Zhu,Hongbo Zhu,Lei Tian,Benjamin Wolozin,Ji-Xin Cheng
      Vol. 12, Issue 7, Pages: 1354-1369(2023) DOI: 10.1038/s41377-023-01191-6
      Abstract:Amyloid proteins are associated with a broad spectrum of neurodegenerative diseases. However, it remains a grand challenge to extract molecular structure information from intracellular amyloid proteins in their native cellular environment. To address this challenge, we developed a computational chemical microscope integrating 3D mid-infrared photothermal imaging with fluorescence imaging, termed Fluorescence-guided Bond-Selective Intensity Diffraction Tomography (FBS-IDT). Based on a low-cost and simple optical design, FBS-IDT enables chemical-specific volumetric imaging and 3D site-specific mid-IR fingerprint spectroscopic analysis of tau fibrils, an important type of amyloid protein aggregates, in their intracellular environment. Label-free volumetric chemical imaging of human cells with/without seeded tau fibrils is demonstrated to show the potential correlation between lipid accumulation and tau aggregate formation. Depth-resolved mid-infrared fingerprint spectroscopy is performed to reveal the protein secondary structure of the intracellular tau fibrils. 3D visualization of the β-sheet for tau fibril structure is achieved.  
        
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    • Xihang Shi,Yaniv Kurman,Michael Shentcis,Liang Jie Wong,F. Javier García de Abajo,Ido Kaminer
      Vol. 12, Issue 7, Pages: 1370-1380(2023) DOI: 10.1038/s41377-023-01141-2
      Abstract:The science and technology of X-ray optics have come far, enabling the focusing of X-rays for applications in high-resolution X-ray spectroscopy, imaging, and irradiation. In spite of this, many forms of tailoring waves that had substantial impact on applications in the optical regime have remained out of reach in the X-ray regime. This disparity fundamentally arises from the tendency of refractive indices of all materials to approach unity at high frequencies, making X-ray-optical components such as lenses and mirrors much harder to create and often less efficient. Here, we propose a new concept for X-ray focusing based on inducing a curved wavefront into the X-ray generation process, resulting in the intrinsic focusing of X-ray waves. This concept can be seen as effectively integrating the optics to be part of the emission mechanism, thus bypassing the efficiency limits imposed by X-ray optical components, enabling the creation of nanobeams with nanoscale focal spot sizes and micrometer-scale focal lengths. Specifically, we implement this concept by designing aperiodic vdW heterostructures that shape X-rays when driven by free electrons. The parameters of the focused hotspot, such as lateral size and focal depth, are tunable as a function of an interlayer spacing chirp and electron energy. Looking forward, ongoing advances in the creation of many-layer vdW heterostructures open unprecedented horizons of focusing and arbitrary shaping of X-ray nanobeams.  
        
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    • Andres Remis,Laura Monge-Bartolome,Michele Paparella,Audrey Gilbert,Guilhem Boissier,Marco Grande,Alan Blake,Liam O'Faolain,Laurent Cerutti,Jean-Baptiste Rodriguez,Eric Tournié
      Vol. 12, Issue 7, Pages: 1381-1390(2023) DOI: 10.1038/s41377-023-01185-4
      Abstract:Silicon (Si) photonics has recently emerged as a key enabling technology in many application fields thanks to the mature Si process technology, the large silicon wafer size, and promising Si optical properties. The monolithic integration by direct epitaxy of Ⅲ–Ⅴ lasers and Si photonic devices on the same Si substrate has been considered for decades as the main obstacle to the realization of dense photonics chips. Despite considerable progress in the last decade, only discrete Ⅲ–Ⅴ lasers grown on bare Si wafers have been reported, whatever the wavelength and laser technology. Here we demonstrate the first semiconductor laser grown on a patterned Si photonics platform with light coupled into a waveguide. A mid-IR GaSb-based diode laser was directly grown on a pre-patterned Si photonics wafer equipped with SiN waveguides clad by SiO2. Growth and device fabrication challenges, arising from the template architecture, were overcome to demonstrate more than 10 mW outpower of emitted light in continuous wave operation at room temperature. In addition, around 10% of the light was coupled into the SiN waveguides, in good agreement with theoretical calculations for this butt-coupling configuration. This work lift an important building block and it paves the way for future low-cost, large-scale, fully integrated photonic chips.  
        
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    • Zhaoxiang Zhu,Yuanhui Wen,Jiaqi Li,Yujie Chen,Zenghui Peng,Jianxiong Li,Lei Zhu,Yunfei Wu,Lidan Zhou,Lin Liu,Liangjia Zong,Siyuan Yu
      Vol. 12, Issue 7, Pages: 1391-1400(2023) DOI: 10.1038/s41377-023-01202-6
      Abstract:With the distinct advantages of high resolution, small pixel size, and multi-level pure phase modulation, liquid crystal on silicon (LCoS) devices afford precise and reconfigurable spatial light modulation that enables versatile applications ranging from micro-displays to optical communications. However, LCoS devices suffer from a long-standing problem of polarization-dependent response in that they only perform phase modulation on one linear polarization of light, and polarization-independent phase modulation—essential for most applications—have had to use complicated polarization-diversity optics. We propose and demonstrate, for the first time, an LCoS device that directly achieves high-performance polarization-independent phase modulation at telecommunication wavelengths with 4K resolution and beyond by embedding a polarization-rotating metasurface between the LCoS backplane and the liquid crystal phase-modulating layer. We verify the device with a number of typical polarization-independent application functions including beam steering, holographical display, and in a key optical switching element - wavelength selective switch (WSS), demonstrating the significant benefits in terms of both configuration simplification and performance improvement.  
        
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    • Cheng Xu,Zhihao Ren,Hong Zhou,Jingkai Zhou,Chong Pei Ho,Nan Wang,Chengkuo Lee
      Vol. 12, Issue 7, Pages: 1401-1414(2023) DOI: 10.1038/s41377-023-01186-3
      Abstract:Circular dichroism (CD) spectroscopy has been widely demonstrated for detecting chiral molecules. However, the determination of chiral mixtures with various concentrations and enantiomeric ratios can be a challenging task. To solve this problem, we report an enhanced vibrational circular dichroism (VCD) sensing platform based on plasmonic chiral metamaterials, which presents a 6-magnitude signal enhancement with a selectivity of chiral molecules. Guided by coupled-mode theory, we leverage both in-plane and out-of-plane symmetry-breaking structures for chiral metamaterial design enabled by a two-step lithography process, which increases the near-field coupling strengths and varies the ratio between absorption and radiation loss, resulting in improved chiral light-matter interaction and enhanced molecular VCD signals. Besides, we demonstrate the thin-film sensing process of BSA and β-lactoglobulin proteins, which contain secondary structures α-helix and β-sheet and achieve a limit of detection down to zeptomole level. Furthermore, we also, for the first time, explore the potential of enhanced VCD spectroscopy by demonstrating a selective sensing process of chiral mixtures, where the mixing ratio can be successfully differentiated with our proposed chiral metamaterials. Our findings improve the sensing signal of molecules and expand the extractable information, paving the way toward label-free, compact, small-volume chiral molecule detection for stereochemical and clinical diagnosis applications.  
        
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    • Chunhui Yao,Minjias Chen,Ting Yan,Liang Ming,Qixiang Cheng,Richard Penty
      Vol. 12, Issue 7, Pages: 1415-1424(2023) DOI: 10.1038/s41377-023-01195-2
      Abstract:Miniaturization of optical spectrometers is important to enable spectroscopic analysis to play a role in in situ, or even in vitro and in vivo characterization systems. However, scaled-down spectrometers generally exhibit a strong trade-off between spectral resolution and operating bandwidth, and are often engineered to identify signature spectral peaks only for specific applications. In this paper, we propose and demonstrate a novel global sampling strategy with distributed filters for generating ultra-broadband pseudo-random spectral responses. The geometry of all-pass ring filters is tailored to ensure small self- and cross-correlation for effective information acquisition across the whole spectrum, which dramatically reduces the requirement on sampling channels. We employ the power of reconfigurable photonics in spectrum shaping by embedding the engineered distributed filters. Using a moderate mesh of MZIs, we create 256 diverse spectral responses on a single chip and demonstrate a resolution of 20 pm for single spectral lines and 30 pm for dual spectral lines over a broad bandwidth of 115 nm, to the best of our knowledge achieving a new record of bandwidth-to-resolution ratio. Rigorous simulations reveal that this design will readily be able to achieve single-picometer-scale resolution. We further show that the reconfigurable photonics provides an extra degree of programmability, enabling user-defined features on resolution, computation complexity, and relative error. The use of SiN integration platform enables the spectrometer to exhibit excellent thermal stability of ±2.0 ℃, effectively tackling the challenge of temperature variations at picometer-scale resolutions.  
        
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    • Dali Cheng,Eran Lustig,Kai Wang,Shanhui Fan
      Vol. 12, Issue 7, Pages: 1425-1433(2023) DOI: 10.1038/s41377-023-01196-1
      Abstract:The concept of synthetic dimensions in photonics provides a versatile platform in exploring multi-dimensional physics. Many of these physics are characterized by band structures in more than one dimensions. Existing efforts on band structure measurements in the photonic synthetic frequency dimension however are limited to either one-dimensional Brillouin zones or one-dimensional subsets of multi-dimensional Brillouin zones. Here we theoretically propose and experimentally demonstrate a method to fully measure multi-dimensional band structures in the synthetic frequency dimension. We use a single photonic resonator under dynamical modulation to create a multi-dimensional synthetic frequency lattice. We show that the band structure of such a lattice over the entire multi-dimensional Brillouin zone can be measured by introducing a gauge potential into the lattice Hamiltonian. Using this method, we perform experimental measurements of two-dimensional band structures of a Hermitian and a non-Hermitian Hamiltonian. The measurements reveal some of the general properties of point-gap topology of the non-Hermitian Hamiltonian in more than one dimensions. Our results demonstrate experimental capabilities to fully characterize high-dimensional physical phenomena in the photonic synthetic frequency dimension.  
        
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