Mode Dispersion Research Articles

Nonlinear fiber effects in ultra-high power 10 × 10 Gbit/s WDM-IM free-space systems for satellite links.

We investigate an unexplored type of nonlinear impairments that will take place in a very short fiber after the booster amplifier in a Free Space Optical (FSO) system for space communications. In Earth-satellite links, optical power levels up to 100 W could be required at the transmitter side to achieve the foreseen 100 Gbit/s capacity, because of the extremely high losses. These systems thus need an optical booster amplifier having very high optical power and it should be connected to the transmitting telescope by means of a short fiber (few meters). Here, we discuss and investigate the impact of the nonlinear fiber effects by means of numerical simulations, and estimate the impairments in a Wavelength Division Multiplexing (WDM) 10 × 10 Gbit/s system with intensity modulation. The obtained results clearly indicate that, in this system, the most relevant effect is Four Wave Mixing. We proved that this can be observed as soon as the total power exceeds 20 W. Due to the short fiber length, the system impairments are not affected by chromatic dispersion or channel spacing. We demonstrate that an effective means to reduce the impact is by adopting Polarization Interleaving, i.e., odd and even channels with orthogonal state of polarization. This solution could not work in long terrestrial links because of polarization mode dispersion, yet it can be effectively exploited in short fiber patch cords. These results can be used as a guideline to control this type of impairment in high-power FSO systems for satellite links.

Validity of matched-field source localization in under-ice shallow water

Underwater source localization, such as matched-field processing (MFP), triangulation, and waveguide invariant, have been extensively investigated in temperate oceans. Seasonal or yearlong ice floes or ice cover exist in high-latitude sea regions and the polar ocean. In under-ice shallow water, sound interacts frequently with ice and sea bottom, which results in dramatic reflection, attenuation, and modal dispersion. The boundary effects generate more uncertainties in model-based source localization methods, for example, the MFP method. In this work, we develop the preliminary scheme of the under-ice MFP. The performances of the incoherent Bartlett and minimum variance algorithms are verified by real data collected by a 12-element Vertical line array with a space of 1 m for a source (650–750 Hz) at 2.7-km range and 5-m depth in the northern Yellow Sea in winter. The experimental findings demonstrate that the range error is within 2% and the depth error is within 10%. The error primarily originates from the uncertainty of sea bottom parameters.

A frequency-Hankel transform method to extract multimodal Rayleigh wave dispersion spectra from active and passive source surface wave data

Rayleigh wave dispersion energy spectra have been widely used to extract dispersion curves and invert underground S-wave velocity structures for engineering geophysics and seismology. We develop a frequency-Hankel (F-H) transform method to extract high-quality multimodal Rayleigh wave dispersion energy spectra from active and passive source Rayleigh wave data. The F-H transform method is inspired by the frequency-Bessel (F-J) transform method and considers the physical meaning of Green’s functions for Rayleigh wave dispersion analysis. The F-H transform method can naturally avoid crossed artifacts caused by converging waves on F-J spectrograms and obtain more multimodal dispersion spectra of the same quality with fewer Rayleigh wave data than the F-J transform method. Synthetic and field Rayleigh wave data from active and passive sources for near-surface exploration and ambient noise tomography are used to demonstrate the validity, accuracy, and applicability of the F-H transform method. The F-H transform method unifies the formulas of the F-J transform method and its modifications for active and passive sources of Rayleigh wave data. The F-H transform method is a robust and efficient multimodal Rayleigh wave dispersion analysis method for active and passive source Rayleigh wave data.

Radial profiling of shear slowness from borehole acoustic measurements acquired in thinly laminated formations

AbstractBecause of their relatively shallow volume of investigation, borehole acoustic measurements can be affected by abnormal near‐wellbore conditions such as irregular calliper, drilling‐induced formation damage and mud‐filtrate invasion, among others. Additionally, borehole‐slowness measurements inherently deliver rock elastic properties spatially averaged across the length of the multi‐receiver array included in the waveform acquisition system. The consequence is that the interpretation of borehole acoustic measurements needs to account for both radial variations of elastic properties and axial spatial averaging effects across thinly laminated formations before conducting seismic‐well log ties and rock physics interpretations. We introduce an inversion‐based interpretation method to estimate radial shear‐slowness variations from frequency‐dependent slownesses in vertical wells penetrating horizontally layered formations. The inversion procedure is efficiently implemented with an optimized two‐dimensional fast‐forward‐modelling method that simulates borehole acoustic modes in the presence of invaded and thinly laminated formations. Furthermore, the inversion method consists of two sequential steps: Firstly, layer‐by‐layer dispersion slownesses are processed to mitigate axial spatial averaging effects on borehole acoustic measurements; secondly, radial variations of elastic properties are estimated from inversion results obtained from the first step. The new inversion‐based interpretation workflow estimates a layer‐by‐layer single‐radial‐step shear slowness model, including altered and virgin radial zones. By considering both radial and axial averaging effects, the implementation of the two‐step inversion‐based interpretation method in thinly laminated and radially invaded formations consistently improves the definition of shear slowness between invaded and virgin radial zones compared to traditional radial‐profiling methods. The accuracy of the estimated shear slowness heavily relies on the sensitivity of dispersion modes to radial variations in formation shear slowness.

Photonic MMW Generation Using PM-DPMZM for Full Duplex 32×10 Gbps RoF-WDM System

Abstract This paper presents a study of a 32×10 Gbps Radio over Fiber and Wavelength Division Multiplexing (RoF-WDM) full-duplex system that uses Phase Modulators and a Dual-Port Mach-Zehnder Modulator (PMs-DPMZM) for bidirectional data transfer. The system employs Millimeter-Wave (MMW) signaling over optical fiber and focuses on selecting a technology that provides high transmission capacity per wavelength, improved spectral efficiency, and resistance against optical transmission impairments. The proposed method was validated using simulation results to confirm the efficiency of the proposed system in generating a 40 GHz signal and efficiently detecting and modulating the RF signals. The results demonstrate that the system exhibits strong resistance against dispersion, non-linear effects, and noise, delivering satisfactory performance for distances of up to 220 km. By analyzing the input power, the paper establishes a relationship between input power and signal quality, revealing that an optimal power of 0 dBm leads to an improved Quality Factor (QF) and reduced transmission errors. Furthermore, the evaluation of received optical power indicates the power level required to maintain an acceptable error rate, approximately -20.9690 dBm for downstream data transfer and -20.7245 dBm for upstream data transfer at the BER limit. The simulation performance also demonstrates the transmission efficiency achieved through a high Polarization Mode Dispersion (PMD) coefficient of up to 0.8. The analytical calculations conducted in this work provide valuable insights for optimizing and enhancing the performance of RoF-WDM networks.

Polarization dependent gain in Raman fiber amplifiers with multiple pumps.

In this paper, the polarization dependent gain (PDG) in Raman fiber amplifiers (RFAs) with multiple pumps is studied thoroughly. A comprehensive model, which takes the random polarization mode dispersion, the nonlinear coupling between the pumps, and the degree of polarization (DOP) of the pumps into account, is proposed. The complex nonlinear and random coupling inside the optical fiber is described by a set of nonlinear stochastic differential equations (SDEs), which enable co-simulation of the polarized part and the depolarized part of the multiple pumps. It is revealed that the average PDG and the PDG standard deviation are linearly proportional to the DOP of the pumps, which agrees with the single mode case. More importantly, when the pump wavelength is far away from the signal amplification range (pump-signal wavelength difference larger than 100 nm), its DOP still affects the PDG of the signal. Such a phenomenon is caused by the fact that the pumps interact with each other and the pump DOP could transfer among the pumps, which could enhance the PDG of the RFA. The findings in the work will have important implications for the design of the optical transmission systems with the multi-pump RFAs.

Phonon spectra split in vertically aligned bilayer crystal of binary complex plasma

Structural and dynamical properties of a bilayer binary strongly coupled dusty plasma system in a sheath of an rf discharge are experimentally investigated. Microparticles of two different sizes are aligned into vertical pairs due to ion focusing (plasma wakes) downstream from the upper particles in the ion flow toward the bottom electrode. The pairs are ordered into a 2D hexagonal crystalline structure. The collective mode dispersion relations are measured and analyzed. Splitting of the modes in the bilayer lattice is observed and theoretically described. The relative intensities of the mode branches reflect non-reciprocal features of the wake-mediated interaction between the microparticles. The conditions of stability of vertically aligned bilayer structure are discussed, and relevant plasma parameters are estimated.

Solving crystallization/precipitation population balance models in CADET, part I: Nucleation growth and growth rate dispersion in batch and continuous modes on nonuniform grids

We have developed, implemented and validated 1D and 2D population balance models (PBMs) in the open-source process simulator CADET. 1D PBMs incorporate the particle size as an internal coordinate and are associated with dynamic mass balances to describe particle-based processes in batch and continuous stirred tank reactors. 2D PBMs include the spatial position as an additional external coordinate to describe particulate systems in dispersive plug flow reactors. Along with particle nucleation and growth, growth rate dispersion is considered. Using the finite volume method, cell face fluxes are reconstructed by upwind, Koren and two weighted essentially non-oscillatory (WENO) schemes. Analytical Jacobians are derived to reduce runtime. The implementations utilize arbitrary grids in the internal coordinate. The implementations are validated and benchmarked using seven test cases. The L1 error norm, L1 error convergence rate, and moments up to sixth order are analyzed. Runtime and approximation errors are reported and discussed in detail.

Improved beamforming schemes for estimation of multimode surface wave dispersion curves from seismic noise with reducing effect of the irregular array geometry and/or anisotropic source distribution

SUMMARY Dense array observation and seismic interferometry have revolutionized the imaging schemes of the earth structure. It is becoming possible to directly obtain the lateral variation of the earth's structure by applying array-based methods such as the cross-correlation beamforming (CBF) of the ambient noise to the subsets of the dense array, without tomography. CBF has been proven to extract the azimuth-averaged multimode surface wave dispersion curves. However, the resolution of the dispersion image generated by conventional CBF is low at high frequencies in the frequency–velocity (f-v) domain. Moreover, the irregular array geometry and uneven source distribution would bias the result of CBF, especially for the estimation of azimuth-dependent velocity. In this paper, two beamforming (BF) es are suggested to improve the resolution of multimode dispersion images in the f-v domain. First, the geometrical spreading of the wavefield is corrected to enhance the amplitude at high frequency (or large distance) and thereby improve the resolution of the dispersion image at high frequency. We call this scheme weighted correlation beamforming (WCBF). The azimuth-averaged velocity can be estimated with sufficient resolution using WCBF by stacking the BF output at each azimuth. We show that WCBF is the 2-D Fourier transform of the spatial wavefield from the viewpoint of the wavefield transform. Secondly, a modified beamforming scheme (MCBF) is suggested to reduce the effect of uneven source and/or irregular array geometry. The delay and summation in MCBF are performed only for plane waves incident from the stationary phase region. The azimuth-dependent velocity can therefore be estimated by MCBF with less dependence on the array geometry, as well as on the uneven source distribution. In terms of the estimation of azimuth-averaged phase velocity, we show the F-J method, another array-based method for extracting multimode surface waves from ambient noise using the Fourier–Bessel transform, is the azimuth-averaged version of WCBF. The reliability of WCBF and MCBF is verified based on the synthetic and field data using the array with different geometry. The dispersion image of multimode Rayleigh wave phase velocity at local and regional scales can be generated by WCBF or MCBF with high resolution. In particular, multimode dispersion curves at the local scale can be measured by MCBF with sufficient accuracy using quite short recordings from hours to days. This offers the possibility of a rapid assessment of the media properties.

Blind Polarization Demultiplexing of Shaped QAM Signals Assisted by Temporal Correlations.

While probabilistic constellation shaping (PCS) enables rate and reach adaption with finer granularity [1], it imposes signal processing challenges at the receiver. Since the distribution of PCS-quadrature amplitude modulation (QAM) signals tends to be Gaussian, conventional blind polarization demultiplexing algorithms are not suitable for them [2]. It is known that independently and identically distributed (iid) Gaussian signals, when mixed, cannot be recovered/separated from their mixture. For PCS-QAM signals, there are algorithms such as [3], [4] which are designed by extending conventional blind algorithms used for uniform QAM signals. In these algorithms, an initialization point is obtained by processing only a part of the mixed signal, which have non-Gaussian statistics. In this paper, we propose an alternative method wherein we add temporal correlations at the transmitter, which are subsequently exploited at the receiver in order to separate the polarizations. We will refer to the proposed method as frequency domain (FD) joint diagonalization (JD) probability aware-multi modulus algorithm (pr-MMA), and it is suited to channels with moderate polarization mode dispersion (PMD) effects. Furthermore, we extend our previously proposed JD-MMA [5] by replacing the standard MMA with a pr-MMA, improving its performance. Both FDJD-pr-MMA and JD-pr-MMA are evaluated for a diverse range of PCS (entropy ) over a first-order PMD channel that is simulated in a proof-of-concept setup. A MMA initialized with a memoryless constant modulus algorithm (CMA) is used as a benchmark. We show that at a differential group delay (DGD) of 10% of symbol period and 18 dB SNR/pol., JD-pr-MMA successfully demultiplexes the PCS signals, while CMA-MMA fails drastically. Furthermore, we demonstrate that the newly proposed FDJD-pr-MMA is robust against moderate PMD effects by evaluating it over a DGD of up to 40% of . Our results show that the proposed FDJD-pr-MMA successfully equalizes PMD channels with a DGD up to 20% of .

Optimal Recovery of Rayleigh‐Wave Overtones by Multi‐Directional Acquisition

AbstractRayleigh waves are ubiquitously used for subsurface characterization through dispersion curve inversion, whose quality depends on the number of useable overtones. Traditional analysis is based on vertical receivers and, for active surveys, sources. However, for layered media, eigenfunction theory shows that optimal recovery of any given dispersion mode and frequency can be achieved by either vertical source‐vertical receiver or radial source‐radial receiver configurations, with source directivity being more dominant. Multi‐directional near‐surface wave‐equation modeling and field examples, including distributed acoustic sensing data, validate these predictions. Statistical analysis of compaction‐type near‐surface models shows that overtones are better recovered for radial‐radial surveys in large portions of the useable spectrum, extending beyond 60% for the second and above modes. We conclude that incorporating radial‐radial data acquisition is beneficial and should become standard procedure in active surveying, as well as analyzing the radial component in ambient noise and earthquake‐induced Rayleigh waves.

Feature detection in guided wave ultrasound measurements using simulated spectrograms and generative machine learning

Guided wave ultrasound field measurements capture reflections from aluminothermic welds in the rail track at unknown distances from a transducer. The measured guided wave signals are complex and challenging to interpret due to multiple dispersive modes propagating in the rail, changing environmental conditions, and noise. Data-driven machine learning techniques have been applied to complex signal-processing problems and have shown significant potential in learning and resolving complex problems. This study aims to understand the implications of using various simulated data sets for application within an appropriate learning framework to capture the underlying features of the field measurements and maximise the performance of these techniques. The use of simulated spectrograms, including variations of signal attributes (attenuation, positions of welds, noise, and mode reflection coefficients) generally observed in experimental measurements, allows the reflections of individual modes to be isolated or combined for training. This allows us to present the training data in three distinct forms. The first dataset has the highest mode reflection information density per sample and consists of simulated spectrogram data with multiple reflections of modes from multiple welds, like experimentally obtained spectrograms. The second training dataset consists of spectrograms with multiple mode reflections; however, only for a single weld reflection per spectrogram. The third training set contains a reflection of a single mode from a single weld in each spectrogram. The data-driven models applied are principal component autoregression and variational auto-encoders. The reconstruction error and latent space interpretability were considered as metrics for the algorithms’ ability to learn using test sets, i.e., unseen data. The results show that datasets with sufficient feature variation and higher mode reflection information density better construct the test set of simulated and experimental spectrograms. However, training using the third dataset shows more interpretable latent variables for an artificial growing defect attached to the rail. Furthermore, data-driven machine learning methods trained using simulated spectrogram data are useful for reconstructing and learning features from experimental measurements, provided that the training data have representative mode feature variation and noise.

Exploiting Zone-Folding Induced Quasi-Bound Modes to Achieve Highly Coherent Thermal Emissions.

Thermal emissions with high coherence, although not as high as those of lasers, still play a crucial role in many practical applications. In this work, by exploiting the geometric perturbation-induced optical lattice tripling and the associated Brillion zone folding effect, we propose and investigate thermal emissions in the mid-infrared with simultaneous high temporal and spatial coherence. In contrast with the case of period-doubling perturbation in our previous work, the steeper part of the guided mode dispersion band will be folded to the high-symmetry Γ point in the ternary grating. In this case, a specific emission wavelength corresponds to only a very small range of wavevectors. Consequently, apart from the high temporal coherence characterized by an experimental bandwidth around 30 nm, the achieved thermal emissions also feature ultrahigh spatial coherence. Calculations show that at the thermal emission wavelengths in the mid-infrared, the spatial coherence length can easily reach up to mm scale.

Low frequency inversion method based on multi-layer holizontal variation shallow seafloor model

Sound propagation in shallow water is significantly influenced by geoacoustic properties. Estimating these geoacoustic parameters is essential for sound field analysis and sonar performance assessment. As a common practice, the seafloor is often treated as a single-layer or two-layer range-independent geoacoustic model to reduce the number of involved parameters. However, acoustic parameters inverted through these two geoacoustic models are typically limited in their applicability to a specific frequency range, thus posing challenges when applied across a broader frequency range. A range-dependent multi-layer geoacoustic model based on experimental measurements obtained with a sub-bottom profiler is proposed in this study. The inversion scheme combines three inversion methods to estimate geoacoustic parameters, considering the different sensitivities of geoacoustic parameters to different physical parameters within the acoustic field. Firstly, modal dispersion is used to invert the geoacoustic parameters of each layer, with the dispersion curve obtained through warping transform and the Wigner-Ville distribution. After that, both the localization using matched field processing and the dispersion curve fitting demonstrate the effectiveness of the inversion results for each layer, although the peak of the probability distribution of sound speed in the first layer is broader than in others. Secondly, matched field processing is employed to invert the geoacoustic parameters of the first layer. This method is based on the theory that as frequency increases, the depth of sound rays penetrating the seabed decreases, revealing changes in the first layer's sound speed with the seabed depth. Lastly, bottom attenuation coefficients at different frequencies are inverted by the transmission loss (TL), and a fitting relationship between the attenuation coefficient and the frequency is derived. The inversion results obtained by using the range-dependent multi-layer geoacoustic model are compared with results estimated by the single-layer geoacoustic model. The findings indicate that the transmission loss (TL) error from the range-dependent multi-layer geoacoustic model in this study is smaller than that from the single-layer geoacoustic model, especially in the lower frequency band. The range-dependent multi-layer geoacoustic model proves to be suitable for a broader frequency range, providing better precision in explaining various acoustic phenomena.

Numerical analysis of the geophysical parameter sensitivity on the multimode Love wave dispersion curves

The characteristics of multimode Love wave dispersion curves are dependent on various geophysical parameters, namely shear wave velocity (SWV), layer thickness and density. This paper presents a novel numerical analysis of these parameters to determine which ones have a significant effect on the dispersion curves of multimode Love waves. Identifying parameter sensitivity is a crucial step in the inversion procedure of geophysical modeling. Our numerical analysis focuses on perturbing three geophysical parameters that influence the dispersion curves. The results confirm that SWV parameter is the most sensitive. By employing the same perturbation procedure, our numerical analysis reveals that the SWV parameter has a highly significant impact on the multimode Love wave dispersion curves. The average relative error (RE) values are found to be 27.33% for alpha = −0.2 and 25.51% for alpha = +0.2. Conversely, perturbing the layer thickness parameter demonstrates no significant influence on the dispersion curves, resulting in average RE values of 5.69% for alpha = −0.2 and 7.96% for alpha = +0.2. Furthermore, the perturbation of the density parameter exhibits an extremely negligible impact on the multimode Love wave dispersion curves, with average RE values on the order of 10−14%.

Africa's Crustal Architecture Inferred From Probabilistic and Perturbational Inversion of Ambient Noise: ADAMA

AbstractAfrica's continental crust hosts a variety of geologic terrains and is crucial for understanding the evolution of its longest‐lived cratons. However, few of its seismological models are yet to incorporate the largest continent‐wide noise dispersion data sets. Here, we report on new insights into Africa's crustal architecture obtained using a new data set and model assessment product, ADAMA, which comprises a large ensemble of short‐period surface wave dispersion measurements: 5–40 s. We construct a continent‐wide model of Africa's Crust Evaluated with ADAMA's Rayleigh Phase maps (ACE‐ADAMA‐RP). Dispersion maps, and uncertainties, are obtained with a probabilistic approach. This model update, and a crustal taxonomy derived from unsupervised machine learning, reveals that the architecture of Africa's crust can be classified into two main types: primitive (C1: faster velocities with little gradients) and modified (C2–C4: slower velocities in the shallow crust with more pronounced gradients). The Archean shields are “primitive,” showing little variation or secular evolution. The basins, orogens, and continental margins are “modified” and retain imprints of surface deformation. The crustal taxonomy is obtained without a‐priori geological information and differs from previous classification schemes. While most of our reported features are robust, probabilistic modeling suggests caution in the quantitative interpretations where illumination is compromised by low‐quality measurements, sparse coverage or both. Future extension of our approach to other complementary seismological and geophysical data sets—for example, multimode earthquake dispersion, receiver functions, gravity, and mineral physics, will enable continent‐wide lithospheric modeling that extends resolution to the upper mantle.

Acoustic metasurfaces with Frieze symmetriesa).

Frieze patterns follow a set of tiling instructions including reflection, rotation, and translation, and tile the infinite strip. Many metamaterials function due to the underlying symmetry, and its strategic breaking, of their constituent sub-structures that allow tailoring of the dispersion of modes supported by the structure. We design, simulate, and experimentally characterize seven one-dimensional acoustic metasurfaces whose unit cells each belong to one of the distinct Frieze groups.

Tracing the origins of mode coupling for beam quality optimization in high-power fiber laser delivery systems

Abstract Suppressing mode degradation is the key issue for high-power laser delivery; however, diagnosing mode degradation in its entirety, ranging from the contents and origins to locations, has always been a major obstacle. Here, a versatile approach for tracing the origins of mode coupling is demonstrated through addressing the differential intermodal dispersions of fiber modes. Full recognition for modal contents and the origins of mode degradation are experimentally completed in a two-mode fiber laser delivery system, which assists a significant improvement of beam quality M2 from 1.35 to 1.15 at the highest power of over 300 W. This method yields a quantitative characterization for manipulating the individual mode of dual-mode coupling origins or their combinations. This work points toward a promising strategy for the online tracing of mode coupling in cascade fiber links, thus enabling further pursuit of seeking extreme beam quality in high-power fiber laser systems.

Strong anapole-plasmon coupling in dielectric-metallic hybrid nanostructures.

The nanoscale ampification of light-matter interactions exhibits profound potential in multiple scientific fields, such as physics, chemistry, surface science, materials science, and nanophotonics. Nonetheless, achieving robust optical mode coupling within cavities faces significant hurdles due to modal dispersion and weak optical field confinement. In this theoretical investigation, we demonstrate the viability of strong coupling between the anapole mode of a slotted silicon nanodisk and the plasmonic modes of an Ag nanodisk dimer at visible light frequencies. By introducing anapole modes, we successfully confine light to subwavelength volumes, suppressing radiative losses and achieving a remarkable Rabi splitting of 468 meV. This substantial coupling is facilitated by the large spatial overlap of intense optical fields. Capitalizing on this strong mode coupling, we generate novel hybrid energy states with significant electromagnetic field enhancement. Our study serves as a valuable blueprint for designing platforms based on strong anapole mode coupling at visible frequencies and paves the way for deeper explorations into nanoscale light-matter interactions.

Enhancing Long-Haul 15-Mode Fiber Performance: Mode Permutation for Reduced Modal Dispersion

Enhancing Long-Haul 15-Mode Fiber Performance: Mode Permutation for Reduced Modal Dispersion