Explore the vast range of titles available.

Terahertz (THz) technology holds great promise in biomedical imaging, non‐destructive testing, biosensing, and telecommunications, but its adoption is limited by weak light–matter interactions and strong dissipative losses in conventional metamaterials. To overcome these limitations, a dual strategy is introduced that combines interdigitated electric split‐ring resonators (ID‐eSRRs) with the complex‐frequency wave (CFW) technique. Electrical gating from 0–200 V tunes the graphene Fermi level from 0.3756 to 0.6505 eV, providing a wide and continuous resonance shift for fingerprint‐aligned sensing. The CFW method reconstructs loss‐compensated spectra from real‐frequency data, generating virtual gain and markedly sharpening resonances. Simulations show that the optimized ID‐eSRR achieves a refractive index sensitivity of 196 GHz/RIU for 100 nm analytes, while CFW amplification increases the quality factor from 8.54 to 427.96, a 50.1‐fold enhancement. This improvement enables reliable discrimination of DNA variants with refractive index differences as small as Δn=0.005 $\\Delta n = 0.005$at n≈1.6 $n \\approx 1.6$ . The demonstrated approach provides a generalizable route to simultaneously enhance sensitivity and Q $Q$ ‐factor, thereby overcoming the long‐standing sensitivity–Q $Q$trade‐off and advancing the development of high‐performance THz sensors for ultrasensitive biomedical diagnostics. A dual strategy combining interdigitated graphene resonators and complex‐frequency waves yields a 54‐fold Q $Q$ ‐factor enhancement and superior sensitivity, establishing a high‐FOM platform for ultrasensitive terahertz biosensing.

Singularity annihilation, generation, and evolving (SAGE) lead to the topological phase transition (TPT) in electronic, photonic and acoustic systems. Traditionally the singularity study of Hermitian systems is only focused on the real frequency domain. In this work, we systematically investigate the complicated SAGE in complex frequency domain (CFD) for one-dimensional (1D) Hermitian and non-Hermitian systems and a more general picture is revealed. First, we study the abnormal phenomenon that one singularity evolves from the first band to the zero frequency and then into the pure imaginary frequency for Hermitian 1D photonic crystals (PhCs). New results, e.g. the general condition for the singularity at zero frequency, the stricter definition of the Zak phase of first band and the phenomenon that more singularities are pushed from first band into the imaginary frequency, are found. Second, a general evolving picture of SAGE in CFD for Hermitian systems is constructed. Complicated processes of singularities in CFD are observed, such as the SAGE not only on the real frequency axis but also on the imaginary frequency axis, the closed evolving loops for singularities which connected imaginary-frequency axis and real-frequency axis. Even more, when the PhCs is degenerated since the permittivity on one kind layer becomes same as the neighbor layer, the singularities on the integral reduced frequency will move to infinite far away and come back with half-integral shift. Third, when gain or absorption is introduced in, the SAGE on a tilted axis is also observed. The phenomenon of one singularity moving back to real frequency axis for non-Hermitian systems means that the stable states with resonance could be realized. Such complicated and general singularity evolving picture in CFD opens a new window for the studies of TPT and the rich new topological phenomena could be expected. Besides the theoretical importance, the evolution of singularity can also be used to engineer the band properties of PhCs. Some novel applications, such as the super-broadband sub-wavelength high-transmission layered structure and the broadband deep-sub-wavelength absorber, are proposed.

The homogeneity of the static magnetic field is crucial for nuclear magnetic resonance (NMR) experiments. The NMR instrumentation is often used to map this field. A spectrum containing information about the static magnetic field is obtained from the signal of a suitable experiment. The digital signal is usually available as a set of real numbers, which can be processed by Fourier transformation either directly or after being transformed into complex numbers. In the first case, the resulting spectrum consists of complex numbers representing an even frequency function. In the second case, the resulting numbers are also complex, but the spectrum is odd. The calculation with an even frequency function was performed and published at this institution. The calculation with an odd function was also solved and published at this institution, but it was not the main focus of the research and publication. Therefore, some questions arose, which this research sought to answer. In both cases, the research method was computer simulation.

The increasing penetration of renewable energy leads to a continuous reduction in system inertia, for which conventional synchronization criteria based solely on frequency consistency can no longer accurately capture the coupled dynamics of frequency and voltage during transients. To address this issue, this paper employs the concept of complex frequency and develops an analysis framework that integrates theory, indices, and simulation for assessing synchronization stability in low-inertia power systems. Firstly, the basic concepts and mathematical formulation of complex frequency and complex frequency synchronization are introduced. Then, dynamic criteria for local and global complex synchronization are established, upon which a complex inertia index is proposed. This index unifies the supporting role of traditional frequency inertia and the voltage support capability associated with voltage inertia, enabling the quantitative evaluation of the strength of coordinated frequency–voltage support and disturbance rejection within a region. Finally, transient simulations on a modified WSCC nine-bus system are carried out to validate the proposed method. The results show that the method can clearly reveal the synchronization relationships between subnetworks and the overall system, providing a useful theoretical reference for stability analysis and control strategy design in low-inertia power systems.

A simplified model of the absorption coefficient of traditional Helmholtz resonators (THR) was established, and the influence of different geometric parameters on the absorption coefficient of THR was analyzed. To realize the low-frequency broadband acoustic structure design, an accurate theoretical model for the sound absorption coefficient of the curled acoustic metasurface (CAM) unit was established. Based on the complex frequency plane method (CFPM), the CAM units with perfect sound absorption at four discrete frequencies were designed. The low-frequency broadband acoustic metasurfaces in parallel under decoupled and coupled conditions were studied, and the thickness is only 12 mm. The high efficiency of sound absorption above 0.8 was achieved in the frequency range of 758 Hz–940 Hz. The experiment verifies the efficient sound absorption effect of the CAM unit and the broadband sound absorption effect under coupled conditions. The research in this paper has a certain potential applications for low-frequency broadband noise control technology.

The Fourier transform is widely accepted as the time-to-frequency conversion procedure, although it has some limitations. Currently, measurements in the time domain are usually transient (non-periodic waveforms) within a finite window time and discrete (non-continuous) sampled signals. The accuracy of the Fourier transform decreases as the window time and sampling frequency decrease. This is where the wavelet transform proves to be a valuable tool in this analysis. This paper presents a novel method for estimating the complex electrical impedance of power transformers by analyzing transient electrical signals with the continuous wavelet transform. The great importance of knowing the complex electrical impedance of the transformer is that it allows knowing the state and condition of the internal parts, such as the core and the windings, whose behavior depends on the frequency with which the transformer is fed. The wavelet transform is employed in the proposed method to improve the analysis of the frequency response (FRA), following the same procedure commonly used with the Fourier transform. The proposed method is validated by performing an experimental test on a 28 MVA power transformer. The results show that the new method using the continuous wavelet transform is a power tool that enhances the extraction of the total electrical impedance curve (magnitude–phase) compared to the Fourier transform. This enables real-time frequency response analysis in transformers, facilitating accurate diagnosis.

Identification of modal parameters of ultra-precision machine tools is an important method to study the dynamic characteristics of structures. Compared with theoretical modeling method, modal testing is a more concise and efficient way. Traditional experimental methods such as an impact hammer testing are unsuitable for use under operational conditions. This paper demonstrates the principle of a complex frequency-domain method for modal identification of ultra-precision fly-cutting machine tools. Modal testing is performed while cutting a circular copper workpiece, which means that all structural modes are excited by cutting force, rather than external vibration sources. Before extracting modal parameters, the raw data is preprocessed with a Kalman filter to reduce the impact of spindle frequency and its harmonics. The time-domain data is then transformed into power spectral density data, and the least-squares method is used to fit modal parameters in the frequency domain. Then, both the single-reference and poly-reference modal experiments are implemented. The steady-state criterion is established to evaluate the quality of calculating results. Finally, contrastive experiments between the proposed and experimental methods validate the effectiveness of the least-squares complex frequency-domain method, and the dominant natural frequencies are thoroughly investigated.

Bubble-based metamaterials have been extensively studied both theoretically and experimentally thanks to their simple geometry and their ability to manipulate acoustic waves. The latter is partly dependent on the structural characteristics of the metamaterial and partly dependent on the incident acoustic wave. Initially, the selection of specific structural characteristics is explained by presenting the Fourier transformations of the reflected waves for different arrangements of a bubbly meta-screen subject to Gaussian excitation. Next, the numerical study focuses on the changes induced to the response of a bubbly meta-screen, subject to different excitation pulses. For complex frequency excitation the bubbles delay to return to their equilibrium position for a couple of moments, hence the energy is stored in the system during those moments. This research provides a new strategy to actively control the response of a bubbly meta-screen and seeks to inspire future studies towards further optimization of the incident pulse based on the functionalities in need.

This paper attempts to provide a clear explanation of how the concept of double frequency complex plane is applied to the calculation of complex electrical power. This is a step to remove the confusion associated with the calculation of complex electrical power that has persisted in the scientific community to this day. It starts with a discussion on the conventional method of calculation of complex power and its relation with the Steinmetz’s original method of power calculation in steady state AC circuit. An excerpt from the writing of Steinmetz is then included in which he enumerated mathematical equations that were used to make adjustments while calculating two times the supply frequency complex electrical power from the supply frequency complex voltage and current. Since the equations appear to contradict the laws of conventional complex algebra, considerable confusion arose soon after the Steinmetz’s publication. This confusion persists even today. Usual text books do not touch upon this issue and merely describe the mathematical equation required for calculation of complex power. This paper tries to provide a justification behind the adjustment equations involving double frequency complex plane used for complex power calculation through a simple R-L circuit and provide analytical explanation of the equations enumerated by Steinmetz.

We present a method for complex frequency estimation in several variables, extending the classical one-dimensional ESPRIT algorithm, and consider how to work with data sampled on nonstandard domains, i.e., going beyond multirectangles.