arXiv subjects

H. T. Liu

Publications and source records attributed to H. T. Liu.

At least 19 recordsLinked to original sources

arXiv2026

The Most Luminous H$β$ Reverberation Mapping of E1821+643 Indicates the Lower Boundary of the Radius-Luminosity Relation

The radius-luminosity ($R_{\rm BLR}$-$L_{5100}$) relation is fundamental to active galactic nucleus (AGN) studies, enabling supermassive black hole (SMBH) mass estimates and AGN-based cosmology applications. However, its high-luminosity end remains poorly calibrated due to insufficient reliable reverberation mapping (RM) data. We present a four-year RM campaign of the luminous quasar E1821+643 using the Lijiang 2.4-m telescope, supplemented by archival multi-wavelength data. E1821+643 is the most luminous AGN with an \hb\ RM measurement to date. The measured time lag of $83.2_{-18.7}^{+17.5}$ days is a factor of 5.6 shorter than predicted by the canonical $R_{\rm BLR}$-$L_{5100}$ relation. By compiling the full \hb\ RM sample, we find that such deviation defines a lower envelope ($0.2R_{\rm BLR}$) of measured lags across the entire luminosity range, while the upper envelope lies near $2R_{\rm BLR}$, implying that the scatter for individual AGNs can reach 1 dex. Spectral decomposition reveals two distinct \hb\ components: a core component with a lag of $267.0_{-17.6}^{+16.6}$ days closer to the $R_{\rm BLR}$-$L_{5100}$ relation, and a redshifted tail with a much shorter lag of $-49.0_{-34.5}^{+50.5}$ days. The short-lag component not only accounts for the significantly shortened overall lag, but also leads to an opposite interpretation of the intrinsic BLR kinematics. These effects can introduce systematic uncertainties in black hole mass estimates by factors of up to tens. Our findings demonstrate that shortened lags in high-accretion-rate AGNs arise from multi-component BLR structures, posing substantial challenges to single-epoch mass estimates and impacting SMBH demographics and cosmological applications.

astro-ph.GA↗

arXiv2025

Discovery of a Luminosity-dependent Continuum Lag in NGC 4151 from Photometric and Spectroscopic Continuum Reverberation Mapping

Accretion onto supermassive black holes (SMBHs) powers active galactic nuclei (AGNs) and drives feedback that shapes galaxy evolution. Constraining AGN accretion disk structure is therefore essential for understanding black hole growth and feedback processes. However, direct constraints on disk size remain rare -- particularly from long-term, multi-season spectroscopic reverberation mapping (RM), which is critical for isolating the intrinsic disk response from the broad-line region (BLR). We present results from an intensive multi-wavelength RM campaign of NGC 4151 during its brightest state in nearly two decades. This represents the third high-cadence monitoring over the past decade, capturing accretion states spanning the transitional regime between thin and thick disks, making NGC 4151 the only AGN with continuum RM observations across such a wide range in accretion states. Combining spectroscopy from the Lijiang 2.4 m telescope with coordinated Swift UV/X-ray monitoring, we measure inter-band continuum lags from UV to optical. The wavelength-dependent lags follow a tight $τ\propto λ^{4/3}$ relation, consistent with reprocessing in a thin disk, but exceed theoretical predictions by a factor of 6.6. Our lag spectrum reveals clear excesses near the Balmer and possibly Paschen jumps, confirming diffuse continuum (DC) contamination from the BLR. By comparing the three campaigns, we discover a non-monotonic lag-luminosity trend ($>3σ$), which cannot be explained by DC emission alone. We propose the lags reflect combined disk and BLR contributions, and present the first evidence that the DC component follows an intrinsic Baldwin effect. These results offer new insights into SMBH mass measurements and theoretical models of AGN inner structure.

astro-ph.GA↗

arXiv2025

First-principles design of excitonic insulators: A review

The excitonic insulator (EI) is a more than 60-year-old theoretical proposal that yet remains elusive. It is a purely quantum phenomenon involving the spontaneous generation of excitons in quantum mechanics and the spontaneous condensation of excitons in quantum statistics. At this point, the excitons represent the ground state rather than the conventional excited state. Thus, the scarcity of candidate materials is a key factor contributing to the lack of recognized EI to date. In this review, we begin with the birth of EI, presenting the current state of the field and the main challenges it faces. We then focus on recent advances in the discovery and design of EIs based on the first-principles Bethe-Salpeter scheme, in particular the dark-exciton rule guided screening of materials. It not only opens up new avenues for realizing excitonic instability in direct-gap and wide-gap semiconductors, but also leads to the discovery of novel quantum states of matter such as half-EIs and spin-triplet EIs. Finally, we will look ahead to possible research pathways leading to the first recognized EI, both computationally and theoretically.

cond-mat.mtrl-sci↗

arXiv2025

Morpho-Photometric Classification of KiDS DR5 Sources Based on Neural Networks: A Comprehensive Star-Quasar-Galaxy Catalog

We present a novel multimodal neural network (MNN) for classifying astronomical sources in multiband ground-based observations, from optical to near infrared, to separate sources in stars, galaxies and quasars. Our approach combines a convolutional neural network branch for learning morphological features from $r$-band images with an artificial neural network branch for extracting spectral energy distribution (SED) information. Specifically, we have used 9-band optical ($ugri$) and NIR ($ZYHJK_s$) data from the Kilo-Degree Survey (KiDS) Data Release 5. The two branches of the network are concatenated and feed into fully-connected layers for final classification. We train the network on a spectroscopically confirmed sample from the Sloan Digital Sky Survey cross-matched with KiDS. The trained model achieves 98.76\% overall accuracy on an independent testing dataset, with F1 scores exceeding 95\% for each class. Raising the output probability threshold, we obtain higher purity at the cost of a lower completeness. We have also validated the network using external catalogs cross-matched with KiDS, correctly classifying 99.74\% of a pure star sample selected from Gaia parallaxes and proper motions, and 99.74\% of an external galaxy sample from the Galaxy and Mass Assembly survey, adjusted for low-redshift contamination. We apply the trained network to 27,335,836 KiDS DR5 sources with $r \leqslant 23$ mag to generate a new classification catalog. This MNN successfully leverages both morphological and SED information to enable efficient and robust classification of stars, quasars, and galaxies in large photometric surveys.

astro-ph.GA↗

arXiv2025

Unprecedented Continuum Time Delay Variation Phenomenon in an Active Supermassive Black Hole

Resolving the accretion disks and broad line regions (BLRs) of active galactic nuclei (AGNs) can probe the physics behind supermassive black holes (SMBHs) fueling and weigh SMBHs. With time-domain observations, the reverberation mapping (RM) technique measures time delays between different light curves, probing the AGN inner structures that are otherwise often too compact to resolve spatially with current facilities. Theoretically, the SMBH accretion disk structure does not evolve over decades. Here we report the significant variations in the continuum time delays of NGC 4151. In the high-flux state, our high-cadence ($\sim 2$ days) spectroscopy reveals that continuum time delays are $3.8^{+1.8}_{-1.0}$ times larger than those in the low-flux state and $14.9\pm 2.0$ times longer than the classical standard thin disk prediction. Notably, the continuum time delays can be comparable with the time delay between H$β$ and the $5100\ \mathrmÅ$ continuum, and the latter is commonly used to calculate the BLR sizes. Hence, the BLR sizes are underestimated if the continuum time delays are not considered, which introduces $\sim 0.3$ dex systematic uncertainties on RM SMBH masses. Our findings underscore that simultaneous continuum and BLR RMs are vital for better deciphering the SMBH accretion and mass function.

astro-ph.HE↗

arXiv2024

Reverberation Mapping of Two Variable Active Galactic Nuclei: Probing the Distinct Characteristics of the Inner and Outer Broad-line Regions

Current reverberation mapping (RM) studies primarily focus on single emission lines, particularly the \hb\ line, which may not fully reveal the geometry and kinematic properties of the broad-line region (BLR). To overcome this limitation, we conducted multiline RM observations on two highly variable active galactic nuclei (AGNs), KUG 1141+371 and UGC 3374, using the Lijiang 2.4 m telescope. Our goal was to investigate the detailed structure of different regions within the BLR. We measured the time lags of multiple broad emission lines (\ha, \hb, \hg, \hei, and \heii) and found clear evidence of radial ionization stratification in the BLRs of both AGNs. Velocity-resolved RM analysis revealed distinct geometry and kinematics between the inner and outer regions of the BLRs. Assuming that velocity-resolved lags reflect the kinematics of BLR, our observations indicate that: (1) in KUG 1141+371, the inner BLR exhibits outflow signatures, while the outer region is consistent with virialized motion; (2) in UGC 3374, the inner region displays virial motion, while the outer region shows inflow. Furthermore, we detected ``breathing" behavior in the outer BLR regions of both AGN, while the inner BLR regions show ``anti-breathing", which may be linked to intrinsic BLR properties. We discuss these findings in the context of various BLR formation models, highlighting importance of long-term, multiline RM campaigns in understanding of BLR structure and evolution. Additionally, our results suggest that the observed stratification in BLR geometry and kinematics may contribute to the scatter in black hole mass estimates and the rapid changes in velocity-resolved RM signatures reported in recent studies.

astro-ph.GA↗

arXiv2024

Velocity-resolved Reverberation Mapping of Changing-look Active Galactic Nucleus NGC 4151 during Outburst Stage. II. Four Season Observation Results

We present the results of a four-year velocity-resolved reverberation mapping (RM) campaign of the changing-look active galactic nucleus (CL-AGN) NGC 4151 during its outburst phase. By measuring the time lags of the \ha, \hb, \hg, \hei, and \heii\ emission lines, we confirm a stratified broad-line region (BLR) structure that aligns with predictions from photoionization models. Intriguingly, we observed an ``anti-breathing" phenomenon, where the lags of broad emission lines decreased with increasing luminosity, contrary to the typical expectation. This anomaly may be attributed to the influence of the ultraviolet-optical lag or non-virialized motions in the BLR gas. Velocity-resolved RM and ionization mapping analyses revealed rapid and significant changes in the BLR geometry and kinematics on timescales within one year, which cannot be interpreted by any single mechanism, such as an inhomogeneous BLR, variations in radiation pressure, or changes in the illuminated ionizing field. Additionally, the \hb\ lags of NGC 4151 and other CL-AGNs agree with the radius-luminosity relationship established for AGNs with low accretion rates, implying that the CL phenomenon is more likely driven by intrinsic changes in the accretion rate rather than obscuration. These findings provide new insights into the complex internal processes of CL-AGNs and highlight the importance of long-term, multi-line RM for understanding BLR structures, geometry, and kinematics.

astro-ph.GA↗

arXiv2024

Velocity-Resolved Ionization Mapping of Broad Line Region. I. Insights into Diverse Geometry and Kinematics

Broad emission lines of active galactic nuclei (AGNs) originate from the broad-line region (BLR), consisting of dense gas clouds in orbit around an accreting supermassive black hole. Understanding the geometry and kinematics of the region is crucial for gaining insights into the physics and evolution of AGNs. Conventional velocity-resolved reverberation mapping may face challenges in disentangling the degeneracy between intricate motion and geometry of this region. To address this challenge, new key constraints are required. Here, we report the discovery of an asymmetric BLR using a novel technique: velocity-resolved ionization mapping, which can map the distance of emitting gas clouds by measuring Hydrogen line ratios at different velocities. By analyzing spectroscopic monitoring data, we find that the Balmer decrement is anticorrelated with the continuum and correlated with the lags across broad emission line velocities. Some line ratio profiles deviate from the expectations for a symmetrically virialized BLR, suggesting that the red-shifted and blue-shifted gas clouds may not be equidistant from the supermassive black hole (SMBH). This asymmetric geometry might represent a formation imprint, provide new perspectives on the evolution of AGNs, and influence SMBH mass measurements.

astro-ph.GA↗

arXiv2024

Measuring the Virial Factor in SDSS DR7 AGNs with Redshifted H$β$ and H$α$ Broad Emission Lines

Under the hypothesis of gravitational redshift induced by the central supermassive black hole, and based on line widths and shifts of redward shifted H$β$ and H$α$ broad emission lines for more than 8000 SDSS DR7 AGNs, we measure the virial factor in determining supermassive black hole masses. The virial factor had been believed to be independent of accretion radiation pressure on gas clouds in broad-line region (BLR), and only dependent on inclination effects of BLR. The virial factor measured spans a very large range. For the vast majority of AGNs ($>$96%) in our samples, the virial factor is larger than $f=1$ usually used in literatures. The $f$ correction makes the percent of high-accreting AGNs decrease by about 100 times. There are positive correlations of $f$ with the dimensionless accretion rate and Eddington ratio. The redward shifts of H$β$ and H$α$ are mainly the gravitational origin, confirmed by a negative correlation between the redward shift and the dimensionless radius of BLR. Our results show that radiation pressure force is a significant contributor to the measured virial factor, containing the inclination effects of BLR. The usually used values of $f$ should be corrected for high-accreting AGNs, especially high redshift quasars. The $f$ correction increases their masses by one--two orders of magnitude, which will make it more challenging to explain the formation and growth of supermassive black holes at high redshifts.

astro-ph.GA↗

arXiv2022

Velocity-resolved Reverberation Mapping of Changing-look Active Galactic Nucleus NGC~4151 During Outburst Stage: Evidence for Kinematics Evolution of Broad-line Region

Changing-look active galactic nucleus NGC~4151, which has attracted a lot of attention, is undergoing the second dramatic outburst stage in its evolutionary history. To investigate the geometry and kinematics of the broad-line region (BLR), and measure the mass of supermassive black hole in NGC~4151, we perform a seven-month photometric and spectroscopic monitoring program in 2020--2021, using the 2.4 m telescope at Lijiang Observatory. We successfully measure the time lags of the responses from broad \ha, \hb, \hg, \hei, and \heii\ emission lines to continuum variation, which are $7.63_{-2.62}^{+1.85}$, $6.21_{-1.13}^{+1.41}$, $5.67_{-1.94}^{+1.65}$, $1.59_{-1.11}^{+0.86}$, and $0.46_{-1.06}^{+1.22}$ days, respectively, following radial stratification. The ratios of time lags among these lines are $1.23 : 1.00 : 0.91 : 0.26 : 0.07$. We find that the continuum lag between the ultraviolet and optical bands can significantly affect the lag measurements of \hei\ and \heii. Virial and infalling gas motions coexist in this campaign, which is different from previous results, implying the evolutionary kinematics of BLR. Based on our measurements and previous ones in the literature, we confirm that the BLR of NGC~4151 is basically virialized. Finally, we compute the black hole mass through multiple lines, and the measurement from \hb\ to be $ 3.94_{-0.72}^{+0.90} \times 10^7 M_{\odot}$, which is consistent with previous results. The corresponding accretion rate is $0.02_{-0.01}^{+0.01} L_{\rm Edd} c^{-2}$, implying a sub-Eddington accretor.

astro-ph.GA↗

arXiv2022

Measuring the Virial Factor in SDSS DR5 Quasars with Redshifted H$β$ and Fe ii Broad Emission Lines

Under the hypothesis of gravitational redshift induced by the central supermassive black hole, and based on line widths and shifts of redward shifted H$β$ and Fe ii broad emission lines for a sample of 1973 $z<0.8$ SDSS DR5 quasars, we measured the virial factor in determining supermassive black hole masses, usually estimated by the reverberation mapping (RM) method or the relevant secondary methods. The virial factor had been believed to be from the geometric effect of broad-line region. The measured virial factor of Fe ii is larger than that of H$β$ for 98% of these quasars. The virial factor is very different from object to object and for different emission lines. For most of these quasars, the virial factor of H$β$ is larger than these averages that were usually used in determining the masses of black holes. There are three positive correlations among the measured virial factor of H$β$, dimensionless accretion rate and Fe ii/H$β$ line ratio. A positive three-dimensional correlation is found among these three quantities, and this correlation indicates that the virial factor is likely dominated by the dimensionless accretion rate and metallicity. A negative correlation is found between the redward shift of H$β$ and the scaled size of broad-line region radius in units of the gravitational radius of black hole. This negative correlation will be expected naturally if the redward shift of H$β$ is mainly from the gravity of black hole. Radiation pressure from accretion disk may be a significant contributor to the virial factor.

astro-ph.GA↗

arXiv2021

Magnetically tunable Shubnikov-de Hass oscillations in MnBi2Te4

Shubnikov-de Hass oscillations are directly observed in undoped antiferromagnetic topological insulator MnBi2Te4. With increasing magnetic fields, the oscillation period decreases gradually in the magnetic transition from canted antiferromagnetism to ferromagnetism and then saturates in high magnetic fields, indicating the field-induced evolution of the band structure. From the analysis of the high-field oscillations, a nontrivial Berry phase and a small effective mass are extracted, in agreement with the predicted Weyl semimetal phase in ferromagnetic MnBi2Te4. Furthermore, rotating the magnetization of MnBi2Te4 can lead to a splitting of the high-field oscillations, which suggests the enhanced asymmetry of the Weyl cones in tilted fields. Therefore, the observation of these magnetically tunable quantum oscillations clearly demonstrates the indispensable role of field in tuning the band structure or physical properties of MnBi2Te4.

cond-mat.mtrl-sci↗

arXiv2021

Velocity-resolved Reverberation Mapping of Changing-look AGN NGC 2617

NGC 2617 has attracted a lot of attention after the detection of the changes in spectral type, and its geometry and kinematics of broad-line region (BLR) are still ambiguous. In this paper, we present the high cadence ($\sim$ 2 days) reverberation mapping campaign of NGC 2617 from 2019 October to 2020 May undertaken at Lijiang 2.4 m telescope. For the first time, the velocity-resolved reverberation signature of the object was successfully detected. Both H$α$ and H$β$ show an asymmetrical profile with a peak in the velocity-resolved time lags. For each of both lines, the lag of the line core is longer than those of the relevant wings, and the peak of the velocity-resolved lags is slightly blueshifted. These characteristics are not consistent with the theoretical prediction of the inflow, outflow or Keplerian disk model. Our observations give the time lags ofH$α$, H$β$, H$γ$, and He I, with a ratio of $τ_{\rm{H}α}$:$τ_{\rm{H}β}$:$τ_{\rm{H}γ}$:$τ_{\rm{He~I}}$ = 1.27:1.00:0.89:0.20, which indicates a stratified structure in the BLR of the object. It is the first time that the lags of H$α$ and He I are obtained. Assuming a virial factor of $f$ = 5.5 for dispersion width of line, the masses of black hole derived from H$α$ and H$β$ are $\rm{23.8^{+5.4}_{-2.7}}$ and $\rm{21.1^{+3.8}_{-4.4}} \times 10^{6}M_{\odot}$, respectively. Our observed results indicate the complexity of the BLR of NGC 2617.

astro-ph.GA↗

arXiv2020

Reverberation Mapping of Changing-look Active Galactic Nucleus NGC 3516

The changes of broad emission lines should be a crucial issue to understanding the physical properties of changing-look active galactic nucleus (CL-AGN). Here, we present the results of an intensive and homogeneous 6-month long reverberation mapping (RM) monitoring campaign during a low-activity state of the CL-AGN Seyfert galaxy NGC 3516. Photometric and spectroscopic monitoring was carried out during 2018--2019 with the Lijiang 2.4 m telescope. The sampling is 2 days in most nights, and the average sampling is $\sim$3 days. The rest frame time lags of H$α$ and H$β$ are $τ_{\rm{H}α}=7.56^{+4.42}_{-2.10}$ days and $τ_{\rm{H}β}=7.50^{+2.05}_{-0.77}$ days, respectively. From a RMS H$β$ line dispersion of $σ_{\rm{line}} = 1713.3 \pm 46.7$ $\rm{km}$ $\rm{s^{-1}}$ and a virial factor of $f_σ$ = 5.5, the central black hole mass of NGC 3516 is estimated to be $M_{\rm{BH}}= 2.4^{+0.7}_{-0.3} \times 10^{7} M_{\odot}$, which is in agreement with previous estimates. The velocity-resolved delays show that the time lags increase towards negative velocity for both H$α$ and H$β$. The velocity-resolved RM of H$α$ is done for the first time. These RM results are consistent with other observations before the spectral type change, indicating a basically constant BLR structure during the changing-look process. The CL model of changes of accretion rate seems to be favored by long-term H$β$ variability and RM observations of NGC 3516.

astro-ph.GA↗

arXiv2020

Spectroscopic Monitoring of Blazar S5 0716+714: Brightness-Dependent Spectral Behavior

In this paper, we report the new results of spectroscopic observations of $γ$-ray blazar S5 0716+714 from 2019 September to 2020 March with the 2.4 m optical telescope at Lijiang Observatory of Yunnan Observatories. The median cadence of observations is $\sim$ 1 day. During the second observation period (Epoch2), the observational data reveal an extremely bright state and a bluer-when-brighter (BWB) chromatism. The BWB trend of Epoch2 differs significantly from that of the first observation period (Epoch1). A significantly brightness-dependent BWB chromatism emerges in the total data of Epoch1 and Epoch2. The BWB trend becomes weaker towards the brighter states, and likely becomes saturated at the highest state. Based on a log-parabolic function, a power-law of synchrotron peak flux and frequency $ν_{\rm{p}}$, and a power-law of the curvature of synchrotron spectrum and its $ν_{\rm{p}}$, simulation well reproduces the brightness-dependent BWB trend of S5 0716+714. The BWB trend is seemingly controlled by the shift of $ν_{\rm{p}}$ with respect to the observational window, and effectively may be dominated by the variations of electron average energy and magnetic field in emitting region.

astro-ph.HE↗

arXiv2019

Quasi-simultaneous Spectroscopic and Multi-band Photometric Observations of Blazar S5 0716+714 during 2018-2019

In order to study short timescale optical variability of $γ$-ray blazar S5 0716+714, quasi-simultaneous spectroscopic and multi-band photometric observations were performed from 2018 November to 2019 March with the 2.4 m optical telescope located at Lijiang Observatory of Yunnan Observatories. The observed spectra are well fitted with a power-law $F_λ=Aλ^{-α}$ (spectral index $α>0$). Correlations found between $\dotα$, $\dot{A}$, $\dot{A}/A$, $\dot{F_{\rmλ}}$, and $\dot{F_{\rmλ}}/F_{\rmλ}$ are consistent with the trend of bluer-when-brighter (BWB). \textbf{The same case is for colors, magnitudes, color variation rates, and magnitude variation rates of photometric observations.} The variations of $α$ lead those of $F_{\rmλ}$. Also, the color variations lead the magnitude variations. The observational data are mostly distributed in the I(+,+) and III(-,-) quadrants of coordinate system. Both of spectroscopic and photometric observations show BWB behaviors in S5 0716+714. The observed BWB may be explained by the shock-jet model, and its appearance may depend on the relative position of the observational frequency ranges with respect to the synchrotron peak frequencies, e.g., at the left of the peak frequencies. \textbf{Fractional variability amplitudes are $F_{\rm{var}}\sim 40\%$ for both of spectroscopic and photometric observations. Variations of $α$ indicate variations of relativistic electron distribution producing the optical spectra. }

astro-ph.GA↗

arXiv2019

Search for Intra-day Optical Variability in $γ$-ray--loud Blazars S5 0716+714 and 3C 273

We present the photometric observations of blazars S5 0716+714 and 3C 273 with high temporal resolution (30--60s) in the $I$ or $R$ bands. The observations were performed with a 1.02 m optical telescope from 2007 March 07 to 2012 May 16. The $F$-test, one-way analysis of variance (ANOVA) test, and $z$-transformed discrete correlation function (ZDCF) cross-correlation zero lag test are used to search for intra-day variability (IDV). Four and five reliable IDVs survive three tests for S5 0716+714 and 3C 273, respectively. IDVs are found for S5 0716+714 and 3C 273. A flare on 2008 May 08 has $ΔI \approx$ 0.06$\pm$0.01 mag in a duration of 0.54 hr for S5 0716+714. A flare on 2011 May 10 shows $ΔR \approx$ 0.05$\pm$0.01 mag in a duration of 0.40 hr for 3C 273. Sharp dips appear on 2011 May 9 for 3C 273, and show $ΔR \approx$ 0.05$\pm$0.01 mag. Under the assumptions that the IDV is tightly connected to black hole mass, $M_{\bullet}$, and that the flare durations are representative of the minimum characteristic timescales, we can estimate upper bounds to $M_{\bullet}$. In the case of the Kerr black holes, $M_{\bullet} \la 10^{8.91} M_{\odot}$ and $M_{\bullet} \la 10^{9.02} M_{\odot}$ are given for S5 0716+714 and 3C 273, respectively. These mass measurements are consistent with those measurements reported in the literatures. Also, we discuss the origins of optical variations found in this work.

astro-ph.GA↗

arXiv2018

Quasinormal mode solvers for resonators with dispersive materials

Optical resonators are widely used in modern photonics. Their spectral response and temporal dynamics are fundamentally driven by their natural resonances, the so-called quasinormal modes (QNMs), with complex frequencies. For optical resonators made of dispersive materials, the QNM computation requires solving a nonlinear eigenvalue problem. This rises a difficulty that is only scarcely documented in the literature. We review our recent efforts for implementing efficient and accurate QNM-solvers for computing and normalizing the QNMs of micro- and nano-resonators made of highly-dispersive materials. We benchmark several methods for three geometries, a two-dimensional plasmonic crystal, a two-dimensional metal grating, and a three-dimensional nanopatch antenna on a metal substrate, in the perspective to elaborate standards for the computation of resonance modes.

physics.comp-ph↗