Cross-correlation Technique Research Articles

An Absolute Mass, Precise Age, and Hints of Planetary Winds for WASP-121A and b from a JWST NIRSpec Phase Curve

We have conducted a planetary radial velocity measurement of the ultrahot Jupiter WASP-121b using JWST NIRSpec phase curve data. Our analysis reveals the Doppler shift of the planetary spectral lines across the full orbit, which shifts considerably across the detector (∼10 pixels). Using cross-correlation techniques, we have determined an overall planetary velocity amplitude of K p = 215.7 ± 1.1 km s−1, which is in good agreement with the expected value. We have also calculated the dynamical mass for both components of the system by treating it as an eclipsing double-line spectroscopic binary, with WASP-121A having a mass of M ⋆ = 1.330 ± 0.019 M ⊙, while WASP-121b has a mass of M p = 1.170 ± 0.043 M Jup. These dynamical measurements are ∼3× more precise than previous estimates and do not rely on any stellar modeling assumptions that have a ∼5% systematic floor mass uncertainty. Additionally, we used stellar evolution modeling constrained with a stellar density and parallax measurement to determine a precise age for the system, found to be 1.11 ± 0.14 Gyr. Finally, we observed potential velocity differences between the two NIRSpec detectors, with NRS1 lower by 5.5 ± 2.2 km s−1. We suggest that differences can arise from day/night asymmetries in the thermal emission, which can lead to a sensitivity bias favoring the illuminated side of the planet, with planetary rotation and winds both acting to lower a measured K P. The planet’s rotation can account for 1 km s−1 of the observed velocity difference, with 4.5 ± 2.2 km s−1 potentially attributable to vertical differences in wind speeds.

On the Formation Height of Low-corona and Chromospheric Channels of the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO)

The multiwavelength data from the Solar Dynamics Observatory is extensively used in studying the physics of the Sun and its atmosphere. In this study, we estimate the formation heights of low-corona and chromospheric channels of the Atmospheric Imaging Assembly (AIA) over the atmospheres of sunspot umbrae during the quiet condition period within 20 different active regions. The upward propagating slow magnetoacoustic waves of a 3 minute period, which are perpetually present in sunspots, are utilized for this purpose. Employing a cross-correlation technique, the most frequent time lag between different channel pairs is measured. By combining this information with the local sound speed obtained from the characteristic formation temperatures of individual channels, we estimate the respective formation heights. The median values of formation heights obtained across all active regions in our sample are 356, 368, 858, 1180, and 1470 km, respectively, for the AIA 1600, 1700, 304, 131, and 171 Å channels. The corresponding ranges in the formation heights are 247–453, 260–468, 575–1155, 709–1937, and 909–2585 km, respectively. These values are measured with respect to the Helioseismic Magnetic Imager continuum. We find the formation height of UV channels is quite stable (between 250 and 500 km) and displays only a marginal difference between the AIA 1600 and 1700 Å channels during quiet conditions. On the other hand, the formation height of coronal channels is quite variable.

Cross-correlating Dark Sirens and Galaxies: Constraints on H 0 from GWTC-3 of LIGO–Virgo–KAGRA

We apply the cross-correlation technique to infer the Hubble constant (H 0) of the Universe using gravitational-wave (GW) sources without electromagnetic counterparts (dark sirens) from the third GW Transient Catalog (GWTC-3) and the photometric galaxy surveys 2MPZ and WISE-SuperCOSMOS, and combine these with the bright siren measurement of H 0 from GW170817. The posterior on H 0 with only dark sirens is uninformative due to the small number of well-localized GW sources. Using the eight well-localized dark sirens and the binary neutron star GW170817 with electromagnetic counterpart, we obtain a value of the Hubble constant H0=75.4−6+11 km s−1 Mpc−1 (median and 68.3% equal-tailed interval) after marginalizing over the matter density and the GW bias parameters. This measurement is mostly driven by the bright siren measurement, and any constraint from dark sirens is not statistically significant. In the future, with more well-localized GW events, the constraints on expansion history will improve.

High-resolution transmission spectroscopy of the hot-Saturn HD 149026b

Advances in modern technology have enabled the characterization of exoplanetary atmospheres, which can be achieved by exploitation of the transmission spectroscopy technique. We performed visible (VIS) and near-infrared (NIR) high-resolution spectroscopic observations of one transit of HD 149026b, a close-in orbit sub-Saturn exoplanet by using the GIARPS configuration at the Telescopio Nazionale Galileo (TNG). We first analyzed the radial-velocity data, refining the value of the projected spin-orbit obliquity (lambda ). We then performed transmission spectroscopy, looking for absorption signals from the planetary atmosphere. We find no evidence for Halpha \, D2$-$D1 or in the VIS and metastable helium triplet in the NIR using a line-by-line approach. The non-detection of HeI is also supported by theoretical simulations. With the use of the cross-correlation technique (CCF), we do not detect or VO in the visible, or indeed CH$_4$, CO$_2$, H$_2$O, HCN, NH$_3$, or VO in the NIR. Our non-detection of in the planetary atmosphere is in contrast with a previous detection. We performed injection-retrieval tests, finding that our dataset is sensitive to our \, model. The non-detection supports the \, cold-trap theory, which is valid for planets with eq <$ 2200 K, such as HD 149026b. Although we do not attribute it directly to the planet, we find a possibly significant \, signal that is highly redshifted (simeq +20 with respect to the planetary rest frame. Redshifted signals are also found in the \, and \, maps. While we can exclude an eccentric orbit as the cause of this redshifted \, signal, we investigated the possibility of material accretion falling onto the star --- which is possibly supported by the presence of strong \, in the stellar spectrum --- but obtained inconclusive results. The analysis of multiple transits datasets could shed more light on this target.

Enhanced SAR Compression through Multi-Look Doppler Compensation and Auto-Focusing Technique.

This paper presents a simple and streamlined compensation technique for improving the quality of synthetic aperture radar (SAR) images based on the Range Doppler Algorithm (RDA). Incorrect Doppler estimation in the space orbit, caused by unexpected radar motion errors, orbit mismatches, and other factors, can significantly degrade SAR image quality. These inaccuracies result in mismatches between the azimuth-matched filter and the received Doppler chirp signal. To address this issue, we propose a Doppler estimation method that leverages the Fractional Fourier Transform (FrFT) and cross-correlation techniques. The received signals are compared with the azimuth-matched filter based on the rotation angle in the FrFT domain, and the Doppler centroid is adjusted to achieve the optimal alignment. This process ensures high correlation values and enhanced resolution in the final SAR image. The efficacy of the proposed technique is validated through experiments using real spaceborne SAR data from the practical satellite. The results demonstrate significant improvements in image quality and resolution compared to conventional algorithms, highlighting the advantages of our approach for various remote sensing applications.

Precise Relocation and Source Characterization of Two Earthquake Sequences in Yellow Sea Using Regional Lg-Wave Observations

ABSTRACT Two significant earthquakes of magnitude ML 4.6 and 4.5 occurred on 18 January and 3 December 2021 in the central region of the Yellow Sea, respectively. The earthquakes occurred beneath the Gunsan sedimentary basin at about 10 km depth with a strike-slip faulting mechanism on nodal planes striking northwest–southeast (NW–SE) and north-northeast–south-southwest (NNE–SSW). Despite a lack of close-by seismographic stations, we successfully utilized regional Lg-wave observations on both coasts of the sea—the Korean peninsula on the east and eastern China on the west. For nine earthquakes in two event sequences, the Lg-wave differential travel times of the nearby event pairs at the common station are carefully measured using the waveform cross-correlation technique. The double-difference earthquake relocation method is employed to obtain precise relative epicentral locations using the Lg correlation measurements. Relocated epicenters align along the NW–SE direction, indicating that the nodal plane striking the same direction is the likely fault plane on which both sequences occurred. This is the first case reported in the literature in which the causative fault plane has been identified for earthquakes in the central Yellow Sea region. It has an important implication for current regional tectonics; it favors neither old tectonic features trending NE–SW (Qianliyan uplift) nor the north–south alignment of significant earthquakes in the region along the Amur plate boundary. The Lg waves from the earthquake sequences are dominant seismic signals on all three-component records at stations in 160–550 km and allowed us to analyze source properties of the two largest earthquakes using the empirical Green’s function approach. Azimuthal variations of the source corner frequencies suggest that earthquake rupture likely propagated toward southeast (125°) along the fault plane, supporting the aftershock relocation results.

Close Range and High-Resolution Detection of Vibration by Ultrasonic Wave Using Silicon-on-Nothing PMUTs.

This article presents a novel method for close-range, high-resolution ultrasonic time-of-flight (ToF) ranging using piezoelectric micromachined ultrasonic transducers (PMUTs) operating below the device resonance in air. The proposed method involves cross correlation techniques to accurately detect the reflected echo signals despite the presence of ringdown signal interference. For the experiments, a high fill-factor array of silicon-on-nothing (SON) PMUTs was used to enhance the signal-to-noise ratio (SNR). A thorough investigation was conducted to determine the optimal driving frequency for below-resonance ToF ranging, to improve resolution and minimize detection errors. The results of the experiments showed that the system was able to accurately measure sub- μ m vibrations of a metal plate placed 13 mm away from the PMUT array. The system exhibited the ability to detect target object vibrations with a peak-to-peak displacement under 6 μ m and sub- μ m floor noise. Moreover, the maximum detectable vibration frequency reached up to 1 kHz. This study highlights the potential of the proposed ToF ranging method in noncontact vibration monitoring applications across various fields, such as robotics and predictive maintenance.

High-resolution Dayside Spectroscopy of WASP-189 b: Detection of Iron during the GHOST/Gemini South System Verification Run

With high equilibrium temperatures and tidally locked rotation, ultra-hot Jupiters (UHJs) are unique laboratories within which to probe extreme atmospheric physics and chemistry. In this paper, we present high-resolution dayside spectroscopy of the UHJ WASP-189 b obtained with the new Gemini High-resolution Optical SpecTrograph (GHOST) at the Gemini South Observatory. The observations, which cover 3 hr of post-eclipse orbital phases, were obtained during the instrument’s System Verification run. We detect the planet’s atmosphere via the Doppler cross-correlation technique, and recover a detection of neutral iron in the planet’s dayside atmosphere at a significance of 7.5σ in the red arm of the data, verifying the presence of a thermal inversion. We also investigate the presence of other species in the atmosphere and discuss the implications of model injection/recovery tests. These results represent the first atmospheric characterization of an exoplanet with GHOST’s high-resolution mode, and demonstrate the potential of this new instrument in detecting and studying ultra-hot exoplanet atmospheres.

The atmospheric composition of the ultra-hot Jupiter WASP-178 b observed with ESPRESSO

Context. Ultra-hot Jupiters (UHJ) have emerged as ideal testbeds for new techniques for studying exoplanet atmospheres. Only a limited number of them are currently well studied, however. Aims. We search for atmospheric constituents for the UHJ WASP-178 b with two ESPRESSO transits. Additionally, we show parallel photometry that we used to obtain updated and precise stellar, planetary, and orbital parameters. Methods. The two transits we obtained were analysed with narrow-band transmission spectroscopy and with the cross-correlation technique to provide detections at different altitude levels. We focused on searching for Na I, Hα, Hβ, Hγ, Mg I, and Li I lines in narrow-band data, as well as Fe I and Fe II, and attempted to confirm Mg I with the cross-correlation technique. We corrected for the Rossiter-McLaughlin effect and regions with a low signal-to-noise ratio due to Na I absorption in the interstellar medium. We then verified our results via bootstrapping. Results. We report the resolved line detections of Na I (5.5σ and 5.4σ), Hα (13σ), Hβ (7.1σ), and tentatively Mg I (4.6σ). With a cross-correlation, we confirm the Mg I detection (7.8 σ and 5.8 σ), and we additionally report the detections of Fe I (12σ and 10σ) and Fe II (11σ and 8.4σ) on both nights separately. The detection of Mg I remains tentative, however, because the results on the two nights differ. The results also differ compared with the properties derived from the narrow-band data. Conclusions. None of our resolved spectral lines probing the middle to upper atmosphere shows significant shifts relative to the planetary rest frame. Hα and Hβ exhibit a respective line broadening of 39.6 ± 2.1 km s−1 and 27.6 ± 4.6 km s−1, however, indicating the onset of possible escape. WASP-178 b differs from similar UHJ by its lack of strong atmospheric dynamics in the upper atmosphere. The broadening seen for Fe I (15.66 ± 0.58 km s−1) and Fe II (11.32 ± 0.52 km s−1) might indicate the presence of winds in the mid-atmosphere, however. Future studies of the impact of the flux variability caused by the host star activity might shed more light on the subject. Previous work indicated the presence of SiO cloud-precursors in the atmosphere of WASP-178 b and a lack of Mg I and Fe II. However, our results suggest that a scenario in which the planetary atmosphere is dominated by Mg I and Fe II is more likely. In light of our results, we encourage future observations to further elucidate these atmospheric properties.

Relationship of litterfall anomalies with climatic anomalies in a mangrove swamp of the Yucatan Peninsula, Mexico.

Among the set of phenological traits featuring mangrove ecosystems, litterfall production stands out with marked intra-annual and longer-term variation. Furthermore, mangrove forests resilience is one of the most important ecological attribute, reconciling the juxtaposed terrestrial and marine environment such transitional systems occupy. However, world's mangroves are nowadays facing recurrent climatic events, reflected in anomalies depicted by major drivers, including temperature and precipitation. This physical-environmental setting may either constrain or favor overall forest productivity. A combination of time series analysis (spectral density and cross-correlation techniques) and statistical model fitting (General additive model) was implemented to explore trends in total litterfall of a well-developed mangrove forest in southeastern Gulf of Mexico (Celestun Lagoon, SE Mexico) and potential association with the varying behavior of temperature (°C) and precipitation (mm month-1), highlighting their anomalies. The results are consistent with a synchronous response between litterfall production and climatic variables (mean monthly temperature and total monthly precipitation). Concurrent peak litterfall production in Celestun lagoon with high temperatures and precipitation occurred during June and October, featuring a two-month time lag for the response time. More than half of the litterfall anomalies (53.5%) could be reflecting either multiple sources of climatic anomalies (maximum, minimum, and monthly average temperature and monthly total precipitation) or single point events (cyclone landfall). This relationship dynamics showed an interannual persistence (1999-2010). The structure portrayed by the litterfall time-series was not unequivocally related to climatic anomalies. Arguably, climatic anomalies behave with different intensities and even may exhibit complex interactions among them. The study of anomalies provides a baseline for a better grasp of: i) mangrove anomalies responses and ii) their vulnerability to these extremes.

High-resolution Transmission Spectroscopy of Warm Jupiters: An ESPRESSO Sample with Predictions for ANDES

Abstract Warm Jupiters are ideal laboratories for testing the limitations of current tools for atmospheric studies. The cross-correlation technique is a commonly used method to investigate the atmospheres of close-in planets, leveraging their large orbital velocities to separate the spectrum of the planet from that of the star. Warm Jupiter atmospheres predominantly consist of molecular species, notably water, methane, and carbon monoxide, often accompanied by clouds and hazes muting their atmospheric features. In this study, we investigate the atmospheres of six warm Jupiters, K2-139 b, K2-329 b, TOI-3362 b, WASP-130 b, WASP-106 b, and TOI-677 b, to search for water absorption using the ESPRESSO spectrograph, reporting nondetections for all targets. These nondetections are partially attributed to planets having in-transit radial velocity changes that are typically too small (≲15 km s−1) to distinguish between the different components (star, planet, Rossiter-McLaughlin effect, and telluric contamination), as well as the relatively weak planetary absorption lines as compared to the signal-to-noise ratio of the spectra. We simulate observations for the upcoming high-resolution spectrograph ANDES at the Extremely Large Telescope for the two favourable planets on eccentric orbits, TOI-3362 b and TOI-677 b, searching for water, carbon monoxide, and methane. We predict a significant detection of water and CO, if ANDES indeed covers the K-band, in the atmospheres of TOI-677 b and a tentative detection of water in the atmosphere of TOI-3362 b. This suggests that planets on highly eccentric orbits with favourable orbital configurations present a unique opportunity to access cooler atmospheres.

Simultaneous frequency and phase corrections of single-shot MRS data using cross-correlation.

The objective of this study was to propose a novel preprocessing approach to simultaneously correct for the frequency and phase drifts in MRS data using cross-correlation technique. The performance of the proposed method was first investigated at different SNR levels using simulation. Random frequency and phase offsets were added to a previously acquired STEAM human data at 7 T, simulating two different noise levels with and without baseline artifacts. Alongside the proposed spectral cross-correlation (SC) method, three other simultaneous alignment approaches were evaluated. Validation was performed on human brain data at 3 T and mouse brain data at 16.4 T. The results showed that the SC technique effectively corrects for both small and large frequency and phase drifts, even at low SNR levels. Furthermore, the mean square measurement error of the SC algorithm was comparable to the other three methods used, with much faster processing time. The efficacy of the proposed technique was successfully demonstrated in both human brain MRS data and in a noisy MRS dataset acquired from a small volume-of-interest in the mouse brain. The study demonstrated the availability of a fast and robust technique that accurately corrects for both small and large frequency and phase shifts in MRS.

CMBFSCNN: Cosmic Microwave Background Polarization Foreground Subtraction with a Convolutional Neural Network

In our previous study, we introduced a machine learning technique, namely Cosmic Microwave Background Foreground Subtraction with Convolutional Neural Networks (CMBFSCNN), for the removal of foreground contamination in cosmic microwave background (CMB) polarization data. This method was successfully employed on actual observational data from the Planck mission. In this study, we extend our investigation by considering the CMB lensing effect in simulated data and utilizing the CMBFSCNN approach to recover the CMB lensing B-mode power spectrum from multifrequency observational maps. Our method is first applied to simulated data with the performance of the CMB-S4 experiment. We achieve reliable recovery of the noisy CMB Q (or U) maps with a mean absolute difference of 0.016 ± 0.008 μK (or 0.021 ± 0.002 μK) for the CMB-S4 experiment. To address the residual instrumental noise in the foreground-cleaned map, we employ a “half-split maps” approach, where the entire data set is divided into two segments sharing the same sky signal but having uncorrelated noise. Using cross-correlation techniques between two recovered half-split maps, we effectively reduce instrumental noise effects at the power spectrum level. As a result, we achieve precise recovery of the CMB EE and lensing B-mode power spectra. Furthermore, we also extend our pipeline to full-sky simulated data with the performance of the LiteBIRD experiment. As expected, various foregrounds are cleanly removed from the foregrounds contamination observational maps, and recovered EE and lensing B-mode power spectra exhibit excellent agreement with the true results. Finally, we discuss the dependency of our method on the foreground models.

Three-dimensional drift correction of localised non-raster scanning on atomic force microscopy

Abstract Non-raster scanning can increase the scanning frame rate and measurement speed of atomic force microscopes (AFMs). It is also possible to correct the 3D drift during the non-raster scanning. However, the algorithm for the drift correction depends upon the properties of each scan pattern. While localised non-raster scanning using a rosette scan may be faster than the frequently used Lissajous scanning patterns, the drift correction is more challenging because the scan has crossing points only in local neighbouring segments where there are short temporal and spatial separations of the crossing paths. This design note presents a novel solution that successfully overcomes this problem and extends a drift correction method previously developed for Lissajous scans to the 3D drift correction of localised non-raster scanning using a rosette scan trajectory. The drift in the X, Y and Z axes can be determined using the crossing points and locally repeated scans of the same features. The general procedure is presented together with experiments using rosette scans of a two-dimensional lateral calibration standard. Experimental results have demonstrated that the method can effectively correct both the drift in the three axes and sample tilt, leading to significantly improved images. The method requires only localised crossing points in the scan and does not need additional scans to determine the three-dimensional drift based on cross-correlation and least squares techniques, and it can be used with any AFMs capable of rosette scanning.

Exploring the Green Tide Transport Mechanisms and Evaluating Leeway Coefficient Estimation via Moderate-Resolution Geostationary Images

The recurring occurrence of green tides as an ecological disaster has been reported annually in the Yellow Sea. While remote sensing technology effectively tracks the scale, extent, and duration of green tide outbreaks, there is limited research on the underlying driving mechanisms of green tide drift transport and the determination of the leeway coefficient. This study investigates the green tide transport mechanism and evaluates the feasibility of estimating the leeway coefficient by analyzing green tide drift velocities obtained from Geostationary Ocean Color Imager-II (GOCI-II) images using the maximum cross-correlation (MCC) technique and leeway method across various time intervals alongside ocean current and wind speed data. The results reveal the following: (1) Significant spatial variations in green tide movement, with a distinct boundary at 34°40′N. (2) Short-term green tide transport is primarily influenced by tidal forces, while wind and ocean currents, especially the combined Ekman and geostrophic current component, predominantly govern net transport. (3) Compared to 1, 3, and 7 h intervals, estimating the leeway coefficient with a 25 h interval is feasible for moderate-resolution geostationary images, yielding values consistent with previous studies. This study offers new insights into exploring the transport mechanisms of green tides through remote sensing-driven velocity.

Evidence for Nightside Water Emission Found in Transit of Ultra-hot Jupiter WASP-33 b

To date, the dayside thermal structure of ultra-hot Jupiters (UHJs) is generally considered to be inverted, but their nightside thermal structure has been less explored. Here, we explore the impact of nightside thermal emission on high-resolution infrared transmission spectroscopy, which should not be neglected, especially for UHJs. We present a general equation for the high-resolution transmission spectrum that includes planetary nightside thermal emission. This provides a new way to infer the thermal structure of the planetary nightside with high-resolution transmission spectroscopy. Using the cross-correlation technique, we find evidence for the presence of an H2O emission signature on the UHJ WASP-33 b during the transit, indicating an inverted temperature structure on its nightside. Such a result suggests a stronger heat transport through the circulation than currently expected. An alternative explanation is that the rotating visible hemisphere during transit leads to the potential contribution of the limb and dayside atmospheres to the detected emission signature. In the future, the combination of high-resolution, full-phase-curve spectroscopic observations and general circulation models will hopefully solve this puzzle and provide a complete picture of the three-dimensional nature of the chemistry, circulation, and thermal structure of UHJs.

Exploring the ultra-hot Jupiter WASP-178b

Despite recent progress in the spectroscopic characterization of individual exoplanets, the atmospheres of key ultra-hot Jupiters (UHJs) still lack comprehensive investigations. These include WASP-178b, one of the most irradiated UHJs known to date. We observed the dayside emission signal of this planet with CRIRES+ in the spectral K band. By applying the cross-correlation technique and a Bayesian retrieval framework to the high-resolution spectra, we identified the emission signature of 12CO (S/N = 8.9) and H2O (S/N = 4.9), and a strong atmospheric thermal inversion. A joint retrieval with space-based secondary eclipse measurements from TESS and CHEOPS allowed us to refine our results on the thermal profile and thus to constrain the atmospheric chemistry, yielding a solar to super-solar metallicity (1.4 ± 1.6 dex) and a solar C/O ratio (0.6 ± 0.2). We infer a significant excess of spectral line broadening and identify a slight Doppler-shift between the 12CO and H2O signals. These findings provide strong evidence for a super-rotating atmospheric flow pattern and suggest the possible existence of chemical inhomogeneities across the planetary dayside hemisphere. In addition, the inclusion of photometric data in our retrieval allows us to account for stellar light reflected by the planetary atmosphere, resulting in an upper limit on the geometric albedo (0.23). The successful characterization of WASP-178b’s atmosphere through a joint analysis of CRIRES+, TESS, and CHEOPS observations highlights the potential of combined studies with space- and ground-based instruments and represents a promising avenue for advancing our understanding of exoplanet atmospheres.

Investigating the influence of cosmic ray and solar activities on atmospheric weather dynamics within the equatorial electrojet region (Nigeria)

The association between atmospheric weather conditions along the equatorial electrojets and complexity in emergence flux in solar magnetic activity involved in the weather fluctuation processes may be substantial such that it affect the weather conditions particularly in the earth’s equatorial regions. In this study, we have analysed relevant parameters influencing the atmospheric weather conditions across the major cities and zones in Nigeria with solar magnetic activity and cosmic ray intensity covering five solar cycles from 19 to 24. Our investigation was principally based on solar magnetic activity which include solar parameters; flare index, cosmic ray, and atmospheric weather parameters including temperature, relative humidity, and precipitation. We utilized the cross-correlation and wavelet coherence techniques. The study found that the Northern region (Guinea and Sahel Savannah) located along 8.92 to 13.70 degrees latitudes and the Southern regions (Coastal and Derived) located within latitudes 4.5 and 8.9 degree latitudes responded differently to various atmospheric and solar parameters. The temperature and relative humidity in the northern parts is comparatively higher than in the southern region, while the southern region experienced higher precipitation. The flare index and cosmic ray exhibit different patterns as well negatively correlated. The relationships between the precipitations and relative humidity across Nigeria show a distinct behaviour which could be attributed to concentrations of ions influencing cloud properties across the country. There are strong and positive correlations between the two indices, with high coefficients specifically during the examined solar cycles. The difference in responses between Southern and Northern Nigeria could be attributed to mechanism driving the atmospheric weather through the Earth latitudinal couplings.

From breather soliton molecules to chaos in a laser cavity: the scenario of intermittent transitions.

Intermittency is widely observed in various nonlinear dynamical systems as an intriguing transient dynamic far from equilibrium. The internal dynamics formed by a pair of interacting optical solitons are often analogized to typical nonlinear systems. However, whether intermittency exists within the intramolecular motion remains to be investigated. Here, we study the intermittent dynamics of soliton molecules in ultrafast lasers, employing balanced optical cross-correlation techniques with sub-femtosecond temporal resolution. We demonstrate the occurrence of the bursting phase of intense variations of pulse separation within regular breather rhythms. In addition, we discover the intermittent transitions route to chaotic soliton molecules, facilitated by gain control. A series of analysis methods are used to assess the chaotic signals, providing compelling experimental evidence that soliton molecules can be analogized to their matter molecule counterparts. Our experimental findings shed light on the non-equilibrium intramolecular dynamics, providing insight into the transition of the attractors within interacting dissipative solitons in laser and fiber resonators.

Modal group refractive index measurement of few-mode fibers based on time-domain cross-correlation

We propose a measurement method based on the time-domain cross-correlation technique, combined with the cut-back method, enabling the measurement of group refractive indices (n g ) in few-mode fibers (FMF). A Mach–Zehnder interferometric system, equipped with high-precision and extensive range delay devices, is established. The system records off-axis holograms of spatial reference light at various delays interfering with the emitted light from the fiber under test. The interference energy is extracted from these holograms, and a time-domain mode energy curve is developed utilizing the principle of cross correlation. Optimal holograms at each of the curve peaks are used to reconstruct the modal field distribution, effectively separating and accurately identifying each mode within the FMF. By integrating the cut-back method, the n g corresponding to each mode is calculated based on the changes in group delay before and after fiber cutting. The n g of modes in the two-mode fibers was measured and the differential group delay calculated from the measurement agrees with the manufacturer’s specifications. The measured n g of a standard single-mode fiber aligns with the manufacturer’s specifications. Furthermore, the n g of the higher-order modes in four-mode fibers were measured by exciting them at different angles and validating the wave optics theory that the n g of the fiber modes is independent of the excitation angle. This method can simultaneously measure the n g of several modes in a fiber, providing support for the development and application of FMFs.