arXiv subjects

Jianfeng Wu

Publications and source records attributed to Jianfeng Wu.

At least 19 recordsLinked to original sources

arXiv2026

Little Red Dots as Supermassive Counterparts of SS 433: A Hyper-Eddington Accretion Framework

High-redshift little red dots (LRDs) are compact sources characterized by V-shaped spectral energy distributions (SEDs), broad emission lines, and often prominent Balmer breaks. Their high number density and apparently large black hole masses suggest that they are essential to the early evolution of galaxies and supermassive black holes (SMBHs); however, the nature of their central engines remains uncertain. Here, we propose that LRDs are the supermassive, high-redshift counterparts of the hyper-Eddington accreting Galactic microquasar SS~433, viewed at high inclinations. By scaling the hyper-Eddington accretion physics from stellar-mass black holes to supermassive scales, we show that the observed LRD features, including X-ray weakness, soft optical SEDs, apparent sub-Eddington accretion ratio, and Balmer breaks, emerge naturally from the self-shielding geometry of a puffed-up accretion disk. In this framework, the broad-line regions are ionized by anisotropic radiation escaping from the inner disk, analogous to the unseen UV/X-ray emission revealed by the W50 nebula in SS 433. Their low-inclination or lower-accretion-rate counterparts would appear as little blue dots (LBDs) or normal active galactic nuclei. Our model predicts that the Balmer break strength positively correlates with the broad-line width, that the emission lines are more variable than the optical continuum, that LRDs are intrinsically more luminous than observed, and that LBDs are more variable than LRDs. This unified-scale model redefines LRDs as the essential laboratories for observing the rapid accretion-driven growth that shaped the early assembly of galaxies and their central SMBHs.

astro-ph.HE↗

arXiv2026

The X-ray Variability of the Ultraluminous X-ray Sources in the NGC 4631 galaxy

We perform a systematic study on the long-term X-ray variability for the five ultraluminous X-ray sources (ULXs) in the NGC 4631 galaxy (X1-X5), using Chandra, XMM-Newton, and Swift observations covering a 24-year span. Light curves for the five ULXs are presented, while X-ray spectra were modeled for observations with sufficient counts. The normalized excess variance and structure function are utilized to study the X-ray variability behavior of the ULXs. The normalized excess variance is anti-correlated with average X-ray luminosity for three ULXs, indicating that objects with higher average luminosity tend to exhibit relatively lower amplitude of variability. The structure function values increases with time interval in two sources, showing that flux variations become more significant for longer timescales. These trends are also found in the X-ray variability of active galactic nuclei (AGNs). The similarity between ULXs and AGNs, if confirmed for a larger sample of sources, possibly indicates similar underlying physical mechanisms for their X-ray variability.

astro-ph.HE↗

arXiv2026

Photoionization of the Composite Nebula Surrounding NGC 5408 X-1: Implications for Beamed Emission

NGC 5408 X-1 is one of the best studied ultraluminous X-ray sources (ULXs) and is surrounded by a photoionized nebula. Previous optical spectroscopy established the presence of strong Balmer, [O III], and He II $\lambda4686$ emission from the nebula, but the powering engine remains uncertain. In this work, we present new integral-field observations of NGC 5408 X-1, supplemented by archival long-slit spectroscopy and Hubble Space Telescope (HST) imaging, and confirm the presence of a composite nebula, with a small He III region centered on the ULX and a large, shell-like H II region. We also confirm that the broad He II emission is point-like and most likely associated with the ULX binary system. Photoionization simulations with Cloudy show that the ULX spectral energy distribution (SED), with a total luminosity of $2.4 \times 10^{40}\ {\rm erg\ s^{-1}}$ obtained by fitting the optical/UV/X-ray data, overpredicts both the luminosity and size of the He III region. Instead, adopting the same SED shape with a reduced luminosity of $1.0 \times 10^{39}\ {\rm erg\ s^{-1}}$ together with a blackbody of temperature $30000\ {\rm K}$ and luminosity $1.3 \times 10^{39}\ {\rm erg\ s^{-1}}$ successfully reproduces both the He III and H II regions in terms of their luminosities and sizes. Such a dual-component ionizing spectrum is consistent with HST measurements of the ULX in the optical and UV, while being a factor of 24 lower than the inferred isotropic X-ray luminosity. This implies that the EUV and X-ray emission from the ULX may be mildly beamed toward our line of sight, consistent with the picture of supercritical accretion.

astro-ph.HE↗

arXiv2026

Jet-ISM Interaction and Multi-channel AGN Feedback in the Post-merger Galaxy 4C+29.30

4C+29.30 is a post-merger galaxy hosting a rejuvenated active galactic nucleus (AGN) with a complex multi-scale radio morphology, making it an ideal laboratory to study the interplay between different AGN feedback modes. We present a multi-wavelength analysis combining optical integral field spectroscopy (SDSS/MaNGA and CFHT/SITELLE) with radio continuum imaging (VLASS) to map the ionized gas kinematics and ionization structure across the galaxy. We uncover a galaxy-scale, biconical ionized gas outflow whose axis is misaligned by $\sim$26$^\circ$ from the radio jet. This outflow, characterized by broad line widths and Seyfert-like ionization, is mostly consistent with a radiatively driven wind from the central supermassive black hole, which is accreting at a relatively high Eddington ratio ($L_{\mathrm{bol}}/L_{\mathrm{Edd}} \gtrsim 0.1$). In contrast, the northern radio lobe clearly drives localized gas acceleration and increased velocity dispersion, indicative of jet-driven shocks interacting with the interstellar medium, consistent with previous X-ray findings. The coexistence of a radiatively driven galactic-scale outflow and a distinct, misaligned radio jet demonstrates that multiple AGN feedback channels can operate simultaneously within the same system, providing new evidence for the concurrent action of radiative and mechanical feedback.

astro-ph.GA↗

arXiv2026

A FAST Survey of H I Absorption in Low-power Radio Sources

We conducted a HI 21cm absorption study of a sample of 147 nearby (z < 0.1) low-power radio sources with $10\,\mathrm{mJy} < S_{1.4\,\mathrm{GHz}} < 30\,\mathrm{mJy}$ and $\log(P_{1.4\,\mathrm{GHz}}/\mathrm{W\,Hz^{-1}}) = 20.5-23.7$, using the Five-hundred-meter Aperture Spherical radio Telescope. By investigating the origin and kinematics of HI absorbing gas, we aim to study the interplay between the active galactic nucleus (AGN) and its surrounding interstellar medium. Our observations detect 12 new absorbers, combining results from the pilot survey (three absorbers out of 26 sources), yielding a detection rate of $\sim10.2^{+3.1}_{-2.0}\%$. The detection rate in our sample is lower than in higher-power samples, which is likely due to emission dilution and the dominance of extended sources, indicating a gas-rich and star-forming-dominated population in low-power sources. Among new detections, most line profiles are narrow and show velocities close to systemic ones, consistent with rotating disks, while four show disturbed kinematics indicative of inflows or outflows. The fraction of outflow candidates rises with radio power, while the fraction of inflow ones remains constant, suggesting the effect of radio emission on driving HI outflows. In our sample, compact sources show a higher HI detection rate than extended sources. Contrary to expectations from higher-power samples, MIR-bright sources at low-power radio do not exhibit a higher HI detection rate or more disturbed kinematics. In low-power radio sources, blueshifted absorption occurs only in Seyferts and low-ionization nuclear emitting regions, indicating the connection between atomic outflows and the ionization state of AGN.

astro-ph.GA↗

arXiv2025

PathFound: An Agentic Multimodal Model Activating Evidence-seeking Pathological Diagnosis

Recent pathological foundation models have substantially advanced visual representation learning and multimodal interaction. However, most models still rely on a static inference paradigm in which whole-slide images are processed once to produce predictions, without reassessment or targeted evidence acquisition under ambiguous diagnoses. This contrasts with clinical diagnostic workflows that refine hypotheses through repeated slide observations and further examination requests. We propose PathFound, an agentic multimodal model designed to support evidence-seeking inference in pathological diagnosis. PathFound integrates the power of pathological visual foundation models, vision-language models, and reasoning models trained with reinforcement learning to perform proactive information acquisition and diagnosis refinement by progressing through the initial diagnosis, evidence-seeking, and final decision stages. Across several large multimodal models, adopting this strategy consistently improves diagnostic accuracy, indicating the effectiveness of evidence-seeking workflows in computational pathology. Among these models, PathFound achieves state-of-the-art diagnostic performance across diverse clinical scenarios and demonstrates strong potential to discover subtle details, such as nuclear features and local invasions.

cs.CV↗

arXiv2025

Questing a Coherent Definition of Weak-line Quasars and its Physical Implications

Weak-line quasars (WLQs) are a subset of type 1 quasars with remarkably weak high-ionization broad emission lines but normal optical/UV continua. Using 371,091 quasars from SDSS DR16, we define WLQs by analyzing outliers in three relations: the L1350-CIV blueshift, the Baldwin effect, and the logL2500-alpha_ox. We find two CIV EW thresholds: $8.9\pm0.2$Å and $19.3\pm0.3$Å. WLQs (EW(CIV)<$8.9\pm0.2$Å) have enhanced CIV blueshifts, deviate from the Baldwin effect, and include many X-ray weak objects (nearly half). Normal quasars (EW(CIV)>$19.3\pm0.3$Å) show typical properties, while bridge quasars (intermediate EW) are transitional. WLQs show a positive correlation between line attenuation and ionization energy: high-ionization lines (e.g., HeII, CIV) are suppressed by ~3-4σ compared to low-ionization lines (e.g., MgII, OI). This supports the shielding gas model, where a thick inner accretion disk obscures high-energy photons, suppressing high-ionization lines, while low-ionization lines are less affected. We suggest that WLQs and normal quasars correspond to slim and thin disk regimes, respectively, with bridge quasars as a transitional phase. This work provides a unified criterion for WLQs and highlights the role of accretion-driven shielding gas in their spectral features.

astro-ph.GA↗

arXiv2025

Central Massive Black Holes Are Not Ubiquitous in Local Low-Mass Galaxies

The black-hole occupation fraction ($f_\mathrm{occ}$) defines the fraction of galaxies that harbor central massive black holes (MBHs), irrespective of their accretion activity level. While it is widely accepted that $f_\mathrm{occ}$ is nearly 100% in local massive galaxies with stellar masses $M_\star \gtrsim 10^{10}~M_\odot$, it is not yet clear whether MBHs are ubiquitous in less-massive galaxies. In this work, we present new constraints on $f_\mathrm{occ}$ based on over 20 years of Chandra imaging data for 1606 galaxies within 50 Mpc. We employ a Bayesian model to simultaneously constrain $f_\mathrm{occ}$ and the specific accretion-rate distribution function, $p(λ)$, where the specific accretion rate is defined as $λ=L_\mathrm{X}/M_\star$, and $L_\mathrm{X}$ is the MBH accretion luminosity in the 2-10 keV range. Notably, we find that $p(λ)$ peaks around $10^{28}~\mathrm{erg~s^{-1}}~M_\odot^{-1}$; above this value, $p(λ)$ decreases with increasing $λ$, following a power-law that smoothly connects with the probability distribution of bona-fide active galactic nuclei. We also find that the occupation fraction decreases dramatically with decreasing $M_\star$: in high mass galaxies ($M_\star \approx 10^{11-12}M_\odot$), the occupation fraction is $>93\%$ (a $2σ$ lower limit), and then declines to $66_{-7}^{+8}\%$ ($1σ$ errors) between $M_\star\approx10^{9-10}M_\odot$, and to $33_{-9}^{+13}\%$ in the dwarf galaxy regime between $M_\star\approx10^{8-9}~M_\odot$. Our results have significant implications for the normalization of the MBH mass function over the mass range most relevant for tidal disruption events, extreme mass ratio inspirals, and MBH merger rates that upcoming facilities are poised to explore.

astro-ph.GA↗

arXiv2025

Probing the Strong Gravity Region of Black Holes with eXTP

We present the novel capabilities of the enhanced X-ray Timing and Polarimetry (eXTP) mission to study the strong gravity region around stellar-mass black holes in X-ray binary systems and supermassive black holes in active galactic nuclei. eXTP can combine X-ray spectral, timing, and polarimetric techniques to study the accretion process near black holes, measure black hole masses and spins, and test Einstein's theory of General Relativity in the strong field regime. We show how eXTP can improve the current measurements of black holes of existing X-ray missions and we discuss the scientific questions that can be addressed.

astro-ph.HE↗

arXiv2025

AGNs in the extremely overdense galaxy region BOSS 1441: A Chandra observation

We present a Chandra/ACIS-I study of X-ray sources in BOSS 1441, a protocluster at $z=2.32\pm0.02$ that exhibits a prominent overdensity of Ly$α$ emitters (LAEs). Using a 45 ks observation, we identify seven X-ray sources spatially coincident with LAE density peaks. The average X-ray photon index for the seven sources, derived from an absorbed power-law model with Galactic absorption fixed, is 1.49 (ranging from -0.68 to 2.51), corresponding to an average luminosity of $\rm 6.85\times 10^{44}~erg~s^{-1}$ in the rest-frame 2-33 keV band, with individual luminosities spanning $(3.57 - 13.96)\rm\times 10^{44}~erg~s^{-1}$. Three sources exhibit relatively flat spectral slopes. Two are associated with the MAMMOTH-1 nebula, while the third, located at the edge of BOSS 1441 with a $> 5'$ offset from the LAE density peak, resides in a region with a high submillimeter-band density. We estimate the fraction of X-ray detected AGNs among the LAEs to be $11.5^{+3.8}_{-4.6}\%$, approximately double that of previously studied LAEs. This elevated fraction suggests BOSS 1441 is in a mature evolutionary stage, with even higher AGN fractions expected in massive LAEs such as PKS 1138-262. In contrast, the submillimeter galaxy population shows a lower AGN fraction ($6.9^{+6.9}_{-4.5}\%$), consistent with their typically obscured nature. These results indicate that the protocluster's massive galaxies are evolving into the bright red sequence galaxies observed in local clusters, where AGNs likely play a critical role in quenching their star formation.

astro-ph.GA↗

arXiv2025

Radio continuum and \HI 21-cm line observations of a nearby luminous infrared galaxy IRAS 17526+3253

We present results from our EVN and GMRT observations of the radio continuum and spectral line emission in IRAS 17526+3253, along with an analysis of its arcsecond-scale radio properties using archival VLA data. The EVN observations detected radio continuum emission from both the northwest (NW) and southeast (SE) nuclei. The NW nucleus shows two components with high brightness temperatures and radio luminosities, likely indicating the presence of an AGN core and jet. Meanwhile, our EVN observation failed to detect the OH line emission, possibly due to radio frequency interference and/or the emission being partly resolved out and below our detection limit. The multi-band radio spectral energy distribution (SED) deviates from a single power-law at low frequencies, suggesting low-frequency absorption. The GMRT spectral line data reveal both \HI absorption and emission. The \HI emission is diffuse and shows a velocity gradient from about 7500 \kms in the NW to 7800 \kms in the SE nucleus. On larger scales, the \HI emission extends about 4' along the NW-SE direction, with the southeastern extension matching the optical tidal tail. In addition, the weak \HI absorption features show broad line profiles, possibly due to overlapping \HI gas from the two nuclei. The aforementioned results are consistent with properties of intermediate-stage mergers reported in the literature.

astro-ph.GA↗

arXiv2025

Einstein Probe Discovery of EP J182730.0-095633: A New Black Hole X-ray Binary Candidate in Faint Outburst?

Black hole X-ray binaries (candidates) currently identified in our galaxy are mainly transient sources, with the majority discovered through the detection of their X-ray outbursts. Among these, only four were found during faint outbursts exhibiting peak X-ray luminosities $L_{\rm X}\lesssim10^{36}~{\rm erg~s^{-1}}$, likely due to the previous lack of sensitive, wide-field monitoring instruments in the X-ray band. In this Letter, we present the discovery of an intriguing X-ray transient, EP J182730.0-095633, via the Einstein Probe (EP) and subsequent multi-wavelength follow-up studies. This transient, located on the Galactic plane, experienced a faint and brief X-ray outburst lasting about 20 days. Its X-ray spectrum is non-thermal and consistent with a power-law model with a nearly constant photon index of $Γ\sim2$ throughout the outburst. A long-lasting millihertz quasi-periodic oscillation (QPO) signal was detected in its X-ray light curve, centered around a frequency of $\sim0.04$ Hz. A transient near-infrared source was identified as its counterpart, although no optical emission was detectable, likely due to significant extinction. A radio counterpart was also observed, displaying an inverted radio spectrum with $α\sim0.45$. The X-ray spectral and temporal characteristics, along with the multi-wavelength properties, indicate that the source is a faint low-mass X-ray binary, with the compact object likely being a black hole. This work demonstrates the potential of the EP in discovering new X-ray binaries by capturing faint-level X-ray outbursts.

astro-ph.HE↗

arXiv2025

SAAT: Synergistic Alternating Aggregation Transformer for Image Super-Resolution

Single image super-resolution is a well-known downstream task which aims to restore low-resolution images into high-resolution images. At present, models based on Transformers have shone brightly in the field of super-resolution due to their ability to capture long-term dependencies in information. However, current methods typically compute self-attention in nonoverlapping windows to save computational costs, and the standard self-attention computation only focuses on its results, thereby neglecting the useful information across channels and the rich spatial structural information generated in the intermediate process. Channel attention and spatial attention have, respectively, brought significant improvements to various downstream visual tasks in terms of extracting feature dependency and spatial structure relationships, but the synergistic relationship between channel and spatial attention has not been fully explored yet.To address these issues, we propose a novel model. Synergistic Alternating Aggregation Transformer (SAAT), which can better utilize the potential information of features. In SAAT, we introduce the Efficient Channel & Window Synergistic Attention Group (CWSAG) and the Spatial & Window Synergistic Attention Group (SWSAG). On the one hand, CWSAG combines efficient channel attention with shifted window attention, enhancing non-local feature fusion, and producing more visually appealing results. On the other hand, SWSAG leverages spatial attention to capture rich structured feature information, thereby enabling SAAT to more effectively extract structural features.Extensive experimental results and ablation studies demonstrate the effectiveness of SAAT in the field of super-resolution. SAAT achieves performance comparable to that of the state-of-the-art (SOTA) under the same quantity of parameters.

cs.CV↗

arXiv2025

A Be star-black hole binary with a wide orbit from LAMOST time-domain survey

Binary systems consisting of an early type star and a black hole (BH) are crucial for understanding various astrophysical phenomena, particularly the origins of detected gravitational wave sources. Be binary systems are expected to represent a key evolutionary stage in hosting BHs. However, while hundreds of Be X-ray binaries are known, the only confirmed BH candidate in a Be binary remains highly controversial. We report the discovery of ALS 8814, a Be star-BH binary with a moderately eccentric ($e = 0.23$) and wide orbit ($P = 176.6$ days), revealed by the radial velocity (RV) measurement of the visible Be star. Our analysis, combining flux-calibrated spectra in the Balmer discontinuity region and spectral template matching, yields a mass of $11.2^{+1.4}_{-1.2}$ $M_\odot$ for the Be star. The minimum mass of the unseen companion, assuming an edge-on inclination ($i = 90^{\circ}$), is $9.8\pm 0.7\,M_\odot$. We rule out the presence of non-degenerate companions in ALS 8814, indicating that it can only be a BH. This discovery represents a robust case of a Be-BH binary, identified purely through precise RV measurements from a single set of lines. The extremely low peculiar velocity of ALS 8814 suggests that the BH is formed via a direct core-collapse with a negligible natal kick, implying an almost perfect alignment between the Be star's spin and the orbital plane. In this context, the binary's inclination angle is estimated to be 22$^{\circ}$-49$^{\circ}$ by analyzing the shallow double-peaked profile of the H$α$ emission line. This inclination range corresponds to a BH mass estimate between $15\,M_\odot$ and $58\,M_\odot$. As the only unambiguous Be-BH binary system known to date, ALS 8814 provides valuable constraints on the BH formation in a binary system with a high-mass companion.

astro-ph.SR↗

arXiv2025

PathBench: A comprehensive comparison benchmark for pathology foundation models towards precision oncology

The emergence of pathology foundation models has revolutionized computational histopathology, enabling highly accurate, generalized whole-slide image analysis for improved cancer diagnosis, and prognosis assessment. While these models show remarkable potential across cancer diagnostics and prognostics, their clinical translation faces critical challenges including variability in optimal model across cancer types, potential data leakage in evaluation, and lack of standardized benchmarks. Without rigorous, unbiased evaluation, even the most advanced PFMs risk remaining confined to research settings, delaying their life-saving applications. Existing benchmarking efforts remain limited by narrow cancer-type focus, potential pretraining data overlaps, or incomplete task coverage. We present PathBench, the first comprehensive benchmark addressing these gaps through: multi-center in-hourse datasets spanning common cancers with rigorous leakage prevention, evaluation across the full clinical spectrum from diagnosis to prognosis, and an automated leaderboard system for continuous model assessment. Our framework incorporates large-scale data, enabling objective comparison of PFMs while reflecting real-world clinical complexity. All evaluation data comes from private medical providers, with strict exclusion of any pretraining usage to avoid data leakage risks. We have collected 15,888 WSIs from 8,549 patients across 10 hospitals, encompassing over 64 diagnosis and prognosis tasks. Currently, our evaluation of 19 PFMs shows that Virchow2 and H-Optimus-1 are the most effective models overall. This work provides researchers with a robust platform for model development and offers clinicians actionable insights into PFM performance across diverse clinical scenarios, ultimately accelerating the translation of these transformative technologies into routine pathology practice.

cs.CV↗

arXiv2025

PathOrchestra: A Comprehensive Foundation Model for Computational Pathology with Over 100 Diverse Clinical-Grade Tasks

The complexity and variability inherent in high-resolution pathological images present significant challenges in computational pathology. While pathology foundation models leveraging AI have catalyzed transformative advancements, their development demands large-scale datasets, considerable storage capacity, and substantial computational resources. Furthermore, ensuring their clinical applicability and generalizability requires rigorous validation across a broad spectrum of clinical tasks. Here, we present PathOrchestra, a versatile pathology foundation model trained via self-supervised learning on a dataset comprising 300K pathological slides from 20 tissue and organ types across multiple centers. The model was rigorously evaluated on 112 clinical tasks using a combination of 61 private and 51 public datasets. These tasks encompass digital slide preprocessing, pan-cancer classification, lesion identification, multi-cancer subtype classification, biomarker assessment, gene expression prediction, and the generation of structured reports. PathOrchestra demonstrated exceptional performance across 27,755 WSIs and 9,415,729 ROIs, achieving over 0.950 accuracy in 47 tasks, including pan-cancer classification across various organs, lymphoma subtype diagnosis, and bladder cancer screening. Notably, it is the first model to generate structured reports for high-incidence colorectal cancer and diagnostically complex lymphoma-areas that are infrequently addressed by foundational models but hold immense clinical potential. Overall, PathOrchestra exemplifies the feasibility and efficacy of a large-scale, self-supervised pathology foundation model, validated across a broad range of clinical-grade tasks. Its high accuracy and reduced reliance on extensive data annotation underline its potential for clinical integration, offering a pathway toward more efficient and high-quality medical services.

cs.CV↗

arXiv2025

Symmetry and classification of positive solutions of some weighted elliptic equations

We study the weighted elliptic equation \begin{equation} -div(|x|^{-2a}\nabla u)=|x|^{-bp}|u|^{p-2}u~~~\mbox{in}~\mathbb{R}^N ~~~~~~~~~~~~~~~~~~~~(0.1)\end{equation} with $N\geq 2$, which arises from the Caffarelli-Kohn-Nirenberg inequalities. Under the assumptions of finite energy and $a_1+a_2=N-2$, for nonnegative solutions we prove the equivalence between equation (0.1) with $a=a_1$ and equation (0.1) with $a=a_2$. Without finite energy assumptions, for $2\leq p<2^*$ we give the optimal parameter range in which nonnegative solutions of (0.1) in $\mathbf{L}^\infty_{Loc}(\mathbb{R}^N)$ must be radially symmetric, and give a complete classification for these solutions in this range.

math.AP↗

arXiv2025

Ultralow-loss photonic integrated chips on 8-inch anomalous-dispersion Si$_3$N$_4$-SiO$_2$-Si Wafer

We report the fabrication of 8-inch crack-free, dispersion-engineered Si$_3$N$_4$-SiO$_2$-Si wafers fully compatible with industrial foundry silicon photonics fabrication lines. By combining these wafers with a developed amorphous silicon (a-Si) hardmask etching technique, we achieve ultra-low-loss Si$_3$N$_4$ photonic integrated circuits (PICs) with intrinsic quality factors exceeding $25 \times 10^6$ using electron beam lithography and $24 \times 10^6$ using standard ultraviolet stepper photolithography. Frequency-comb generation is demonstrated on these high-quality Si$_3$N$_4$ PICs, corroborating the designed anomalous dispersion. These results establish the feasibility of mass-manufacturing high-performance, dispersion-engineered Si$_3$N$_4$ PICs using standard foundry-grade processes, opening new pathways for applications in optical communications, nonlinear optics, and quantum optics.

physics.optics↗