Overlap Factor Research Articles

Second Harmonic Generation with 48% Conversion Efficiency from Cavity Polygon Modes in a Monocrystalline Lithium Niobate Microdisk Resonator

AbstractThin‐film lithium niobate (TFLN) based optical microresonators offer large nonlinear coefficient d33 and high light‐field confinement, allowing highly efficient second‐order optical nonlinear frequency conversion. Here, ultra‐efficiency SHG from high‐Q polygon modes is achieved by maximizing the utilization of the highest nonlinear coefficient d33 in a monocrystalline X‐cut TFLN microdisk resonator for the first time. The polygon modes are designed and formed with two parallel sides perpendicular to the optical axis of the lithium niobate crystal by introducing weak perturbations into the microdisk through a tapered fiber, which maximizes the utilization of d33. The polygon modes exhibit ultrahigh intrinsic Q factors up to 3.86 × 107, due to the fact that polygon modes are located far from the relatively rough sidewall of the microdisk. Moreover, the pump and second harmonic polygon modes share high modal overlap factor of ≈80%. Consequently, SHG from cavity polygon modes with absolute conversion efficiency as high as 48.08% is realized at an on‐chip pump level of only 4.60 mW without fine domain structures, surpassing the best results (23% and 30%) reported in other two domain‐inversion‐free phase matching schemes and even approaching the record (52%) in periodically poled TFLN microresonators.

Stochastic analysis of frequency-domain adaptive filters

This study investigates the convergence behaviors of a family of frequency-domain adaptive filters (FDAFs) under both exact- and under-modeling situations. The stochastic analysis is conducted by transforming the frequency-domain equations into their time-domain counterparts. We discuss the transient and steady-state convergence behaviors of four FDAF versions, i.e., the constrained FDAFs with and without step-normalization, the unconstrained FDAFs with and without step-normalization, and we also present the upper bounds of step size for mean stability and mean-square stability. Starting from the expression for the steady-state mean weight vector, this study investigates whether the FDAFs can converge to unknown system impulse responses and optimum Wiener solutions. Moreover, we provide the closed-form minimum mean-square error (MMSE) that each FDAF can achieve. The difference between the current work and our previous one is threefold. First, the presented time-domain analysis is much easier to handle and has a more explicit physical meaning than that in the frequency domain. Second, we here consider an arbitrary overlap factor between consecutive blocks, while our previous analysis only focuses on 50% overlap. Third, the presented MMSE expressions and excess mean-square error (EMSE) approximations have not been given before. Simulations reveal high consistency between the experimental and theoretical results.

Environmental and Spatial Effects on Co‐Occurrence Network Size and Taxonomic Similarity in Stream Diatoms, Insects and Fish

ABSTRACTAimThe influences of environmental and spatial processes on species composition have been at the center of metacommunity ecology. Conversely, the relative importance of these processes for species co‐occurrences and taxonomic similarity has remained poorly understood. We hypothesised that at a subcontinental scale, shared environmental preference would be the major driver of co‐occurrences across species groups. In contrast, co‐occurrences due to shared dispersal history were more likely in dispersal‐limited taxa. Finally, we tested whether taxa co‐occurring due to similar responses to environmental and spatial processes were more taxonomically similar than expected by chance.LocationThe conterminous United States.Time Period1993–2019.Major Taxa StudiedStream diatoms, insects and fish.MethodsWe generated co‐occurrence networks and developed methodology to determine the proportions of nodes and edges explained by pure environment alone (after accounting for space), pure space alone (after accounting for the environment), pure environment and pure space together, and spatially structured environment. Taxonomic similarity of taxa co‐occurring because of environmental and/or spatial controls or because of unmeasured processes was compared to that of a null model.ResultsPure environment alone, spatially structured environment, and pure environment and pure space together explained the greatest proportion of nodes and edges in the co‐occurrence networks of diatom species and genera, and insect genera. Conversely, pure environment and pure space together best explained the nodes and edges in the co‐occurrence network of fish species and genera. Co‐occurring taxa were more closely related than the random expectation in all comparisons.Main ConclusionsThe environment controlled co‐occurrences in all groups, while the influence of space was the strongest in fish, the most dispersal‐limited group in our study. All co‐occurring taxa were more taxonomically related than expected by chance due to environmental or spatial overlap or unaccounted factors.

Watt-scale near-diffraction-limited mid-infrared laser delivery by a chalcogenide anti-resonant fiber.

We have developed an effective one-step extrusion method to prepare a nodeless chalcogenide hollow-core anti-resonance fiber, characterized by excellent symmetry and less requirements for drawing pressure in achieving the desired wall thickness. The resulting fiber exhibits excellent uniformity, with an ultra-large effective mode area of 21970 µm2 and a low overlap factor of η = 0.03%. It can withstand an input power exceeding 10 W at 4.5 µm and maintain a stable output power of 1.2 W at an input power of 5.25 W, all while preserving a high beam quality with an M2 value of 1.09. The output single-mode laser remains highly stable when the translation offset of the laser coupling into the fiber is less than 100 µm. The chalcogenide hollow-core fibers with watt-level mid-infrared laser delivery power and near-diffraction-limited beam quality can be used for practical applications in industry, medicine, and defense.

Design and Characteristics of Photonic Crystal Resonators for Surface-Emitting Quantum Cascade Lasers

We present our recent development of the surface-emitting quantum cascade laser with a PC (photonic crystal) resonator and a strain-compensated MQW (multiple quantum well) active layer operating at around 4.3 μm. We describe the laser performance mainly from the viewpoint of the design and analysis of the PC resonators, which include both numerical calculations by FEM (finite element method) and analytical calculations using the k·p perturbation theory and group theory. We analyze the resonance quality factor, overlap factor, extraction efficiency, and far-field pattern, and show how the output power and beam quality have been improved by the appropriate design of the PC resonator.

Suppression of the Effect of Parametric Instability in the LIGO Voyager Gravitational Wave Detector

The number of unstable combinations of elastic and Stokes optical modes of the LIGO Voyager gravitational wave detector, frequencies and spatial distributions of displacement vectors of elastic modes of mirrors were calculated. The values of overlap factors for unstable modes up to ninth-order optical modes are calculated, taking into account the azimuthal condition of parametric instability. An analysis of the influence of the temperature dependence of the Young’s modulus of the mirror material on the number of unstable modes in the Fabry-Perot resonator was performed.

Analysis of the perceived intensity of vibratory stimuli driven by the Modal Overlap Factor

The vibro-tactile perception experiment reported in this paper aims to investigate correlations between the perceived vibratory intensity and the Modal Overlap Factor (MOF) of vibratory stimuli. The MOF is often used to physically characterise the vibratory behavior of a structure and can be estimated from the product of frequency, modal density and modal loss factor. In this experiment, stimuli are applied to the participant's hands by means of a steering wheel set in vibration by a shaker. The vibratory stimuli are synthesized from filtered white noise convolved with an impulse response defined as a sum of damped sine waves. The MOF can be controlled by selecting the number of sine waves, their frequency and damping ratio. A set of 100 stimuli, with MOF values ranging from 2 to 200%, in the 5-305Hz range, and equalized in acceleration, is used. Each of the 80 participants is asked to rate twice the perceived intensity of 10 stimuli, pseudo-randomly chosen among the 100 stimuli. Data are analyzed to establish trends between perceived vibratory intensity and the physical parameters of the stimuli.

Modal gain characteristics of few-mode erbium-doped fiber amplifiers with pump mode beating

Using the linear polarization (LP) mode decomposition method, we theoretically analyze the beat effect between the same polarization components of the vector pump modes and propose a pump beat model of few-mode erbium-doped fiber amplifiers (FM-EDFAs). The relationship of the overlap factor with the signal gain in the beat model is verified by the amplification of LP01 and LP11 modes for the first time, that is, the differential modal gain (DMG) is dependent on the integral of the overlap factor difference over the EDF length. We also simulate the effect of pump mode beating on signal amplification: the modal gain varies periodically with the pump mode phase, and the beat length can affect the fluctuation period and amplitude of the DMG. The DMG can further be reduced by controlling the initial phases of the vector modes and properly designing the beat length of the FM-EDF. The similar process can expand to more signal modes, such as the simultaneous amplification of LP01x, LP11ex, LP11oy, LP21ex and LP21oy modes. The LP mode decomposition method is also applied to the beat effect between signal modes or the amplification of orbital angular momentum (OAM) modes. One can expect to implement an experiment on the FM-EDFA amplification with pump mode beating by optimally designing the FM-EDF structure, using a properly narrow linewidth pump laser and precisely controlling the pump mode coherence.

Analysis on acoustic modes and Brillouin gain spectra of backward stimulated Brillouin scattering in W-type acoustic waveguide optical fibers.

The acoustic Helmholtz equations of W-type acoustic waveguide fibers, including WI- and WII-type acoustic velocity of vl,2 < vl,3 < vl,1 and vl,2 < vl,1 < vl,3, separately are solved by using the method of separation of variables, and their characteristic equations are derived according to the boundary condition and the acoustic Helmholtz equations. The distribution and cut-off of acoustic modes are analyzed by introducing acoustic normalized frequencies. The dependence of the acoustic inner core radius, the acoustic velocities in the acoustic inner and acoustic outer core on acoustic modes, and Brillouin gain spectra (BGS) is investigated. The results indicate that two significant peaks of the BGS are induced by acousto-optic coupling of L01 and L02 acoustic modes with LP01 optical mode. The acousto-optic overlap factor of the L01 acoustic mode decreases first and then increases, and that of the L02 acoustic mode increases first and then decreases with the rise of acoustic inner core radius. Due to the difference of the acoustic mode field distribution, the gain peak induced by L01 mode is sensitive to the acoustic velocity of the acoustic inner core, and that of the L02 mode is sensitive to the acoustic velocity of the acoustic outer core. These conclusions agree well with the reported experimental results, and provide theoretical references for research and application of backward stimulated Brillouin scattering of acoustic waveguide optical fibers.

High Performance Electrically‐Injected InGaN Microdisk Lasers through Simultaneous Enhancement of Optical Confinement and Overlap Factor (Laser Photonics Rev. 18(8)/2024)

High Performance Electrically‐Injected InGaN Microdisk Lasers through Simultaneous Enhancement of Optical Confinement and Overlap Factor (Laser Photonics Rev. 18(8)/2024)

Spatiotemporal Mechanisms of the Coexistence of Reintroduced Scimitar-Horned Oryx and Native Dorcas Gazelle in Sidi Toui National Park, Tunisia.

Examining the distribution patterns and spatiotemporal niche overlap of sympatric species is crucial for understanding core concepts in community ecology and for the effective management of multi-species habitats within shared landscapes. Using data from 26 camera-traps, recorded over two years (December 2020-November 2022), in Sidi Toui National Park (STNP), Tunisia, we investigate habitat use and activity patterns of the scimitar-horned oryx (n = 1865 captures) and dorcas gazelle (n = 1208 captures). Using information theory and multi-model inference methods, along with the Pianka index, we evaluated the habitat characteristics influencing species distribution and their spatial niche overlap. To delineate daily activity patterns, we applied kernel density estimation. Our findings indicate minimal spatial overlap and distinct environmental factors determining suitable habitats for each species. Furthermore, we found significant temporal niche overlaps, indicative of synchrony in daily activity patterns, with both species showing peak activity at dawn and dusk. Our results indicated that oryx and gazelle differ in at least one dimension of their ecological niche at the current density levels, which contributes to their long-term and stable coexistence in STNP.

High Performance Electrically‐Injected InGaN Microdisk Lasers through Simultaneous Enhancement of Optical Confinement and Overlap Factor

AbstractDespite the considerable research interest in InGaN‐based microdisk lasers, owing to their unique circular geometry distinct from vertical cavity surface‐emitting lasers (VCSEL) or edge‐emitting lasers, commercial products remain scant due to deficient performance under electrical injection. This study proposes an innovative method integrating a thin‐film configuration with a metallic undercut, significantly augmenting optical confinement, overlap factor, and thus lasing performance. This approach results in a diminished lasing threshold from 1500 to 670 Wcm−2 and a record high quality (Q) factor of 10100 under electrical injection. Strain relaxation in the metallic undercut, identified via scanning near‐field optical microscopy (SNOM), beneficially mitigates the Quantum Confined Stark Effect (QCSE), boosting the internal quantum efficiency of the laser. Furthermore, a beneficial blue‐shift in the emission spectrum aligns with the lasing peak, strengthening the Q factor. A tactfully implemented recessed top contact enables electrical injection lasing without optical performance compromise. The study provides invaluable insights for future microdisk laser technology advancements, potentially leading to specialized functionalities, including quantum optics, thereby opening new avenues for research and applications in this field.

An Efficient and Adaptive Granular-Ball Generation Method in Classification Problem.

Granular-ball computing (GBC) is an efficient, robust, and scalable learning method for granular computing. The granular ball (GB) generation method is based on GB computing. This article proposes a method for accelerating GB generation using division to replace k -means. It can significantly improve the efficiency of GB generation while ensuring an accuracy similar to that of the existing methods. In addition, a new adaptive method for GB generation is proposed by considering the elimination of the GB overlap and other factors. This makes the GB generation process parameter-free and completely adaptive in the true sense. In addition, this study first provides mathematical models for the GB covering. The experimental results on some real datasets demonstrate that the two proposed GB generation methods have accuracies similar to those of the existing method in most cases, while adaptiveness or acceleration is realized. All the codes were released in the open-source GBC library at https://www.cquptshuyinxia.com/GBC.html or https://github.com/syxiaa/gbc.

Machine learning for the early prediction of acute respiratory distress syndrome (ARDS) in patients with sepsis in the ICU based on clinical data

BackgroundAcute respiratory distress syndrome (ARDS) is a fatal outcome of severe sepsis. Machine learning models are helpful for accurately predicting ARDS in patients with sepsis at an early stage. ObjectiveWe aim to develop a machine-learning model for predicting ARDS in patients with sepsis in the intensive care unit (ICU). MethodsThe initial clinical data of patients with sepsis admitted to the hospital (including population characteristics, clinical diagnosis, complications, and laboratory tests) were used to predict ARDS, and screen out the crucial variables. After comparing eight different algorithms, namely, XG boost, logistic regression, light GBM, random forest, GaussianNB, complement NB, support vector machine (SVM), and K nearest neighbors (KNN), rebuilding a prediction model with the best one. When remodeling with the best algorithm, 10% was randomly selected to test, and the remaining was trained for cross-validation. Using the area under the curve (AUC), sensitivity, accuracy, specificity, positive and negative predictive value, F1 score, kappa value, and clinical decision curve to evaluate the model's performance. Eventually, the application in the model illustrated by the SHAP package. ResultsTen critical features were screened utilizing the lasso method, namely, PaO2/PAO2, A-aDO2, PO2(T), CRP, gender, PO2, RDW, MCH, SG, and chlorine. The prior ranking of variables demonstrated that PaO2/PAO2 was the most significant variable. Among the eight algorithms, the performance of the Gaussian NB algorithm was significantly better than that of the others. After remodeling with the best algorithm, the AUC in the training and validation sets were 0.777 and 0.770, respectively, and the algorithm performed well in the test set (AUC = 0.781, accuracy = 78.6%, sensitivity = 82.4%, F1 score = 0.824). A comparison of the overlap factors with those of previous models revealed that the model we developed performs better. ConclusionSepsis-associated ARDS can be accurately predicted early via a machine learning model based on existing clinical data. These findings are helpful for accurate identification and improvement of the prognosis in patients with sepsis-associated ARDS.

Simultaneous sensing profiles of beam attenuation coefficient and volume scattering function at 180° using a single-photon underwater elastic-Raman lidar.

Lidar has emerged as a promising technique for vertically profiling optical parameters in water. The application of single-photon technology has enabled the development of compact oceanic lidar systems, facilitating their deployment underwater. This is crucial for conducting ocean observations that are free from interference at the air-sea interface. However, simultaneous inversion of the volume scattering function at 180° at 532 nm (βm) and the lidar attenuation coefficient at 532 nm (K l i d a r m) from the elastic backscattered signals remains challenging, especially in the case of near-field signals affected by the geometric overlap factor (GOF). To address this challenge, this work proposes adding a Raman channel, obtaining Raman backscattered profiles using single-photon detection. By normalizing the elastic backscattered signals with the Raman signals, the sensitivity of the normalized signal to variations in the lidar attenuation coefficient is significantly reduced. This allows for the application of a perturbation method to invert βm and subsequently obtain the K l i d a r m. Moreover, the influence of GOF and fluctuations in laser power on the inversion can be reduced. To further improve the accuracy of the inversion algorithm for stratified water bodies, an iterative algorithm is proposed. Additionally, since the optical telescope of the lidar adopts a small aperture and narrow field of view design, K l i d a r m tends to the beam attenuation coefficient at 532 nm (cm). Using Monte Carlo simulation, a relationship between cm and K l i d a r m is established, allowing cm derivation from K l i d a r m. Finally, the feasibility of the algorithm is verified through inversion error analysis. The robustness of the lidar system and the effectiveness of the algorithm are validated through a preliminary experiment conducted in a water tank. These results demonstrate that the lidar can accurately profile optical parameters of water, contributing to the study of particulate organic carbon (POC) in the ocean.

MOLECULAR DYNAMICS STUDY OF THE THERMAL TRANSPORT PROPERTIES IN THE GRAPHENE/C3N MULTILAYER IN-PLANE HETEROSTRUCTURES

We investigated the interfacial thermal conductance of the graphene/C&lt;sub&gt;3&lt;/sub&gt;N multilayer in-plane heterostructures by nonequilibrium molecular dynamics simulation. The results showed that the interfacial thermal conductance is 12.97 GW/(m&lt;sup&gt;2&lt;/sup&gt;&amp;#183;K) and the thermal rectification ratio is 23.80&amp;#37; in the bilayer of the multilayer parallel stacked heterostructure. The interfacial thermal conductance and the thermal rectification ratio of the multilayer staggered stacked heterostructure decreased with number of the layers increasing and both convergent as the layers. The phonon participation ratio and interaction energy of two stacking types exhibits a similar trend with interfacial thermal conductance as the number of layers changes. The interfacial thermal conductance of both structures is raised substantially with temperature. The interfacial thermal conductance of multilayer heterostructures could be adjusted by altering the defect type, concentration, and distribution proportion and the changes in phonon activities were investigated through phonon density of states and overlap factor S. This work proves the reference for thermal management applications in microelectronic devices.

Interfacial thermal conductance of gallium nitride/graphene/diamond heterostructure based on molecular dynamics simulation

&lt;sec&gt;Gallium nitride chips are widely used in high-frequency and high-power devices. However, thermal management is a serious challenge for gallium nitride devices. To improve thermal dissipation of gallium nitride devices, the nonequilibrium molecular dynamics method is employed to investigate the effects of operating temperature, interface size, defect density and defect types on the interfacial thermal conductance of gallium nitride/graphene/diamond heterostructure. Furthermore, the phonon state densities and phonon participation ratios under various conditions are calculated to analyze the interface thermal conduction mechanism.&lt;/sec&gt;&lt;sec&gt;The results indicate that interfacial thermal conductance increases with temperatures rising, highlighting the inherent self-regulating heat dissipation capabilities of heterogeneous. The interfacial thermal conductance of monolayer graphene structures is increased by 2.1 times as the temperature increases from 100 to 500 K. This is attributed to the overlap factor increasing with temperature rising, which enhances the phonon coupling between interfaces, leading the interfacial thermal conductance to increase.&lt;/sec&gt;&lt;sec&gt;Additionally, in the study it is found that increasing the number of layers of both gallium nitride and graphene leads the interfacial thermal conductance to decrease. When the number of gallium nitride layers increases from 10 to 26, the interfacial thermal conductance decreases by 75%. The overlap factor diminishing with the layer number increasing is ascribed to the decreased match of phonon vibrations between interfaces, resulting in lower thermal transfer efficiency. Similarly, when the number of graphene layers increases from 1 to 5, the interfacial thermal conductance decreases by 74%. The increase in graphene layers leads the low-frequency phonons to decrease, consequently lowering the interfacial thermal conductance. Moreover, multilayer graphene enhances phonon localization, exacerbates the reduction in interfacial thermal conductance.&lt;/sec&gt;&lt;sec&gt;It is found that introducing four types of vacancy defects can affect the interfacial thermal conductance. Diamond carbon atom defects lead its interfacial thermal conductance to increase, whereas defects in gallium, nitrogen, and graphene carbon atoms cause their interfacial thermal conductance to decrease. As the defect concentration increases from 0 to 10%, diamond carbon atom defects increase the interfacial thermal conductance by 40% due to defect scattering, which increases the number of low-frequency phonon modes and expands the channels for interfacial heat transfer, thus improving the interfacial thermal conductance. Defects in graphene intensify the degree of graphene phonon localization, consequently leading the interfacial thermal conductance to decrease. Gallium and nitrogen defects both intensify the phonon localization of gallium nitride, impeding phonon transport channels. Moreover, gallium defects induce more severe phonon localization than nitrogen defects, consequently leading to lower interfacial thermal conductance.&lt;/sec&gt;&lt;sec&gt;This research provides the references for manufacturing highly reliable gallium nitride devices and the widespread use of gallium nitride heterostructures.&lt;/sec&gt;

Phonon Thermal Transport at Interfaces of a Graphene/Vertically Aligned Carbon Nanotubes/Hexagonal Boron Nitride Sandwiched Heterostructure

Molecular dynamics simulation is used to calculate the interfacial thermal resistance of a graphene/carbon nanotubes/hexagonal boron nitride (Gr/CNTs/hBN) sandwiched heterostructure, in which vertically aligned carbon nanotube (VACNT) arrays are covalently bonded to graphene and hexagonal boron nitride layers. We find that the interfacial thermal resistance (ITR) of the Gr/VACNT/hBN sandwiched heterostructure is one to two orders of magnitude smaller than the ITR of a Gr/hBN van der Waals heterostructure with the same plane size. It is observed that covalent bonding effectively enhances the phonon coupling between Gr and hBN layers, resulting in an increase in the overlap factor of phonon density of states between Gr and hBN, thus reducing the ITR of Gr and hBN. In addition, the chirality, size (diameter and length), and packing density of sandwich-layer VACNTs have an important influence on the ITR of the heterostructure. Under the same CNT diameter and length, the ITR of the sandwiched heterostructure with armchair-shaped VACNTs is higher than that of the sandwiched heterostructure with zigzag-shaped VACNTs due to the different chemical bonding of chiral CNTs with Gr and hBN. When the armchair-shaped CNT diameter increases or the length decreases, the ITR of the sandwiched heterostructure tends to decrease. Moreover, the increase in the VACNT packing density also leads to a continuous decrease in the ITR of the sandwiched heterostructure, attributed to the extremely high intrinsic thermal conductivity of CNTs and the increase of out-of-plane heat transfer channels. This work may be helpful for understanding the mechanism for ITR in multilayer vertical heterostructures, and provides theoretical guidance for a new strategy to regulate the interlayer thermal resistance of heterostructures by optimizing the design of sandwich layer thermal interface materials.

Building ultra-thin Inconel 718 sheet joints using low-frequency PLBW scheme: Weld bead quality, keyhole dynamics, and solidification characteristics

Low-frequency pulsed laser beam welding (PLBW) was employed in building 0.32 mm-thick Inconel 718 superalloy butt joints which are frequently applied in manufacturing high-temperature functional units in the aviation industry. Several process parameter combinations concerning peak laser power, welding speed, and pulse frequency were implemented to explore the macro morphology, microstructure, and mechanical properties of the welded joints. Examinations exhibit that the resulting weld beads possess high continuity at the surface with an overlap factor ranging from 0.58 to 0.73. The cross-sectional profile changes from a V-shape to an H-shape with increasing heat input. Finer grain structures composed of γ matrix and γ/Laves eutectic penetration are observed within the FZ center, as compared to that near the fusion line. Excellent performance is achieved in microhardness and tensile tests. Numerical simulation based on an integrated mathematic model reveals periodic keyhole and weld pool dynamics depending on the pulsing laser power. During a typical pulse interval, keyhole geometry collapses within a fraction of a millisecond, leading to a sharp cooling stage at ∼4 × 106 K/s, and then, the melt cools due to the thermal convection with a normal cooling rate of 105 K/s. The full growth of the adjacent weld spot results in the secondary melting zone (SMZ), wherein the columnar dendrites can be refined mainly due to the heterogeneous nucleation as compared to the primary melting zone (PMZ).

MSSA-based adaptive low-frequency noise reduction using spectrum overlap measure

A multistage singular spectrum analysis based method is presented to extract the useful component from the residue stage by stage. In every stage of the decomposition, the sum of the signal-dominated SSA components is treated as the denoised signal. The signal-to-noise ratios of the denoised signals first increase and then decrease. A measurement called spectrum overlap factor (SOF) is proposed to estimate the optimal stage which achieves the highest SNR. First, the factor is calculated to measure the spectrum overlap degree between the residue and the denoised signal in every stage. Then, the curve of the SOF with respect to the number of stages is analyzed. Further, the minimum of the SOFs, which indicates the less spectrum overlap, allows for the estimation of the optimal stage. The proposed strategy avoids inappropriate parameter selection effectively since the estimation of the optimal stage is automatic. Besides, simulation results show that the proposed method has satisfactory denoising performance in different test scenarios.