The influence of nonlinearity on a singular point in a system of coupled Duffing oscillators

The guided, single-mode propagation of ultrashort optical pulses is commonly described by a well studied and understood generalized nonlinear Schrödinger equation. Here we present and discuss an extended version for multimode optical fibers and waveguides including polarization effects, high-order dispersion, Kerr and Raman nonlinearities, self-steepening effects, as well as wavelength-dependent mode coupling and nonlinear coefficients. We then investigate the symmetry properties of the nonlinear coupling coefficients for the cases of step-index and circularly symmetric conventional fibers and for microstructured fibers with hexagonal symmetry. Finally, we study the computational complexity of the proposed algorithm.

The problem of solitons propagation (electromagnetic waves in the form of solitons) in a medium with a varying nonlinearity coefficient along the propagation trajectory is considered. Сonducted research have shown that the changes occur in the width and amplitude of the soliton while maintaining its energy, with a change in the nonlinearity coefficient of the medium. It is shown that with a sharp change in the nonlinearity coefficient, the soliton is partially destroyed and part of its energy is emitted, i.e. dissipated by the medium. It is shown that an increase in the nonlinearity coefficient leads to a noticeable increase in the amplitude of the soliton with a simultaneous decrease in its width.

High Transmission Capacity P.U.A. Wireless Power Transfer for AUV Using an Optimized Magnetic Coupler

Optical ring or disk resonators can trap traveling optical waves in a closed path, for example, in a waveguide loop or silicon disk cavity. Energy can be added to or extracted from the cavity with the help of waveguide directional couplers. Ring/disk resonators can be fabricated with high quality factor (Q) in diverse material platforms. The high Q of these devices makes them very sensitive to small variations in (i) optical path length (phase), (ii) optical path loss (attenuation), and (iii) coupling coefficient. Any change in the optical path length can cause a shift in the resonance frequency of the ring. Whereas, the change in path loss and coupling coefficient can lead to a change in the Q of the resonator. The micro or nano opto-electro-mechanical systems (MOEMS/NOEMS) provide unique flexibility with a wide change in the tuning parameters. The tuning is obtained by either (i) displacement of the detached parts or (ii) strain in the waveguide/disk. Displacement of a structure detached from the ring/disk closer to the evanescent field can increase the effective refractive index or attenuation. The displacement of a waveguide in the directional coupler altering the gap can change the coupling coefficient. Strain from various sources can lead to refractive index (phase) and absorption changes, in addition to changing the dimensions. Mechanical, electrothermal, piezoelectric, electrostatic, and magnetic actuators have been demonstrated with MOEMS. Mechanical latching has been used to achieve nonvolatile tuning. Multi-beam supported, freestanding, and diaphragm supported structures have shown applications in sensing, optical switching, and energy conversion. MOEMS/NOEMS has recently been shown to provide the desired properties of modern sensors and photonic integrated circuits (PICs) such as low optical power consumption, high resolution, wide tuning range, low complexity, small footprint, low actuator power consumption, and compatibility with standard fabrication technologies. This chapter will start by briefly covering the basics of MOEM tuned ring/disk resonators. Then, the current technology aspects such as tuning mechanism, actuator types, and the fabrication technology will be discussed along with recent innovations. Furthermore, the evolution into NOEMS with specialized applications and materials will be emphasized along with emerging trends.

In this paper, a graphene (GR)/monolayer (ML) blue phosphorous (Blue P)/GR selector was studied based on the first-principles theory. Due to different contact edges, four GR–Blue P lateral heterojunctions were constructed, namely, armchair–armchair (A–A), zigzag–armchair (Z–A), armchair–zigzag (A–Z), and zigzag–zigzag (Z–Z). As demonstrated by the binding energy and Mulliken population, we found that the Z–Z heterojunction was relatively stable. Furthermore, a GR/Blue P/GR selector based on the Z–Z heterojunction interface was proposed with a nonlinear (NL) coefficient is 105. However, the drive current of this device was insufficient. A P atom of the resistive layer was separately substituted with four different atoms (Ni, Cu, N, and Cl) to effectively improve selector performance. The energy band structure was half-metallic when doped with Ni or Cu while the others still maintained semiconductor characteristics, and the bandgap was significantly reduced. The Schottky barrier height and width of the interface (GR–Blue P), with Cl as the substituted impurity, were the smallest, leading to a three order of magnitude increase in the NL coefficient. The calculation shows that GR/Blue P/GR devices can be integrated as selectors in Resistive switching Random Access Memory (RRAM) arrays. This work also has a certain guiding significance for manufacturing new types of two-dimensional lateral selector apparatuses.

For the case of a wideband filter designed on the basis of parallel oscillatory circuits with combined coupling, the influence of the slope of the frequency characteristics of the coupling coefficients in a tuned filter on the values of these coefficients at the resonant frequency is investigated. The slope angle of these curves is controlled by the ratio of the inductive and capacitive components of the coupling coefficients. The actual values of the coupling coefficients are compared with the values obtained from the direct-synthesis formulas.

Transfer efficiency (TE) is an important research topic in the practical application of a wireless power transfer (WPT) system. WPT system is a loosely coupled system; the coupling coefficient changes drastically due to the relative movement of the transmitting and receiving sides. It is difficult to achieve maximum efficiency tracking (MET) only from the research of frequency tracking, impedance matching, and system parameters under a fixed coupling coefficient. This article proposes a novel MET control method of the WPT system with optimized T-type impedance matching network under the real-time identification of a coupling coefficient to realize the MET control. This method synthetically analyzes the nonlinearity of the rectifier circuit, the identification of coupling coefficient, the variation of load resistor, and the controllability of the output voltage, involving the main factors of the MET control. The simulation and experimental results show that the WPT system has a good performance on MET and constant output voltage control; the validity and accuracy of the proposed MET control method are consistently verified.

This chapter discusses the patterns of coupling coefficients between stripline resonators in combline and pseudocombline structures. It was established that there is an electromagnetic coupling between λ/4 (λ/2) resonators in such structures, and they are bandpass filters (BPFs). Between stripline stepped-impedance resonators (SIRs), both positive and negative mixed coupling can be realized. This coupling can vary widely by changing the shape of resonators and the gap between them. Moreover, the tuning of coupling is carried out without the use of a conducting pin, as in the case of microstrip resonators. The patterns of changes in the coupling coefficients between stripline SIRs at higher resonant frequencies were studied. These changes have a wave-like (alternating) character. The effect of transitioning the coupling coefficient through zero can be used to expand the rejection band of BPF by suppressing the nearest spurious bandwidth. It was found that the coupling coefficients between stripline resonators, all of whose side surfaces are metallized, depend only on the geometric parameters and are not dependent on dielectric constant εr. The dielectric constant only moves the coupling frequencies of an insulated stripline structure, while maintaining the ratio between these frequencies. The measurement data for some combline and pseudocombline stripline BPFs are presented.KeywordsCombline and pseudocombline coupling structuresDiscriminating couplingInvariant of coupling coefficientMixed couplingRejection bandTransmission zero

We make some measurement research based on CW SPM method, and obtain the non-linear coefficient for the novel ultra low loss& large effective area single mode fiber. And we also discussed the measure uncertainty and non-linear coefficient influence factor.

We derive novel approximate closed-form expressions for the nonlinear coupling coefficients appearing in the Manakov equations for multimode fibers for space-division multiplexing in the two regimes of strong and weak coupling. The expressions depend only on few fiber design parameters. In particular, the Manakov coefficients are shown to be simple rational numbers which depend solely on the number of guided modes. The overall nonlinearity coefficients are found to decrease with increasing core radius and to stay nearly constant with increasing refractive index difference between core and cladding. Validation is performed through a numerical approach. The consequences of the findings onto fiber design are discussed in terms of achievable data rates. The analysis is mainly focused on the trenchless parabolic graded-index profile, but considerations on the use of realistic trenches and non-parabolic indices, and on the step-index profile are given.

The frequency splitting phenomenon and transmission characteristics have been research hotspots in the field of magnetically coupled resonance wireless power transfer (MCR-WPT). In this paper, non-linear dynamics theory was innovatively introduced into the research, and non-linear coupled transmission dynamics modelling of the MCR-WPT system was established considering the non-linearities of the compensation capacitor. The mechanism of the frequency splitting phenomenon of the MCR-WPT system was revealed through systematic mathematical analyses based on the modelling. The analysis results showed that the system usually has dual natural frequencies which are low resonance frequency and high resonance frequency. Based on non-linear dynamics theory, the transmission characteristics of the system with different non-linear parameters were discussed comprehensively in relation to the modelling. The results of the numerical simulations and theoretical analyses showed that non-linear parameters can cause the jumping phenomena with the output responses, and the output responses in the vicinities of the lower resonance frequencies were extremely sensitive to changes in the coupling coefficient. According to analyses of the linear and non-linear systems, the energy transmissions performed in the vicinity of the high resonance frequency had a wider working frequency band and a better transmission stability under non-linear conditions.

In this study, the change in input impedance according to the coupling coefficient and self-inductance of the coil of a wireless power transfer system is analyzed. The input impedance is the impedance of the power inverter that plays a decisive role in determining the harmonic current of the coil. When the air gap between the transmitting and receiving coils decreased and the coupling coefficient of the wireless power transfer system increased, the slope of the input impedance decreased, and ultimately, the input impedance in the harmonic component decreased; moreover, the larger the inductance of the transmitting coil, the larger the input impedance of the system. The change in the analyzed input impedance was verified through simulations and experiments. Ultimately, measurements proved that the input impedance changes according to the change in the coupling coefficient and coil self-inductance, which affects the harmonic current. As mathematically analyzed, the larger the coupling coefficient and the smaller the self-inductance of the coil, the lower the input impedance of the harmonic component and the higher the harmonic current flowing in the coil, with a difference of less than 3 % between the simulation and experimental results.

Calculation of the surrounding rock pressure on a shallow buried tunnel using linear and nonlinear failure criteria

In recent years, exploring new topological quantum model structures and in depth analyzing the novel physical properties in various multimerized topological lattices have become a hot topic in the field of quantum optics. Among the different model structures, the multimerized non-Hermitian lattice controlled by different parameters in the future research of topological quantum materials, we believe, can exhibit more meaningful novel topological properties. As one of the most classic topological models, the one-dimensional Aubry-André-Harper (AAH) model has received more and more attention in the study of multimerized lattices. In this paper, we focus on the novel topological properties of a trimerized non-Hermitian lattice, and extend the trimer model structure from a one-dimensional chain to a quasi-one-dimensional zigzag structure. The results show that firstly, if the nearest-neighbor forward coupling coefficient in the unit cell is not equal to the backward coupling coefficient, the chiral inversion symmetry of the system is destroyed. It can be observed that the bulk states and the edge states in the trimerization model will be localized on the same edge of the lattice, and the skin effect will appear in the system. With the increase of the nearest-neighbor coupling coefficient, the width of the edge state changes in which the lower edge state of the imaginary part of the spectrum is narrowed until it disappears. The degree of degeneracy of the system changes, and the number of edge states is reduced from four to two. Remarkably, the generalized bulk-boundary correspondence is shown in certain non-Hermitian topological systems. Secondly, when the trimerization model considers the influence of the next-nearest-neighbor coupling, the numerical results show that the upper and lower energy gaps in the energy spectrum and the edge states in the energy spectrum are asymmetrical as the next-nearest-neighbor coupling coefficient is modulated in an appropriate range. The upper energy gaps and the edge states are narrowed, and the edge states of the lower energy gaps are widened. At the same time, the novel topology features of the system can also be used to achieve the quantitative control of the energy spectrum edge states, and other interesting directions are worth exploring.

Subjecting soft piezoelectric ceramics such as lead zirconate titanate (PZT)-5 to uniaxial stress in a direction perpendicular to the principal polarization axis is known to increase its transverse piezoelectric modulus [Krueger, J. Acoust. Soc. Am. 43 (3), 583-559 (1968)], however, practical transducer applications of this effect remain undeveloped. This study explores uniaxial pressure-treatment to develop experimental methods to realize practical pressure treatment, to use dynamic measurements of the electromechanical coupling coefficient k32, piezoelectric modulus, and dielectric constants, and to enhance piezoelectric properties and performance of underwater acoustic cylindrical transducer designs. The results of axial pressure treatment on parameters of the cylinders are shown to increase the coupling coefficient by about 20% and remained stable. The applicability of using pressure treated cylinders in transducer designs is investigated. The performance was analyzed under one-dimensional circumferential static compression and under the hydrostatic compression. When the improved piezoelectric cylinders are used in air-backed transducer designs, the benefit is only useful at shallow depths as it is observed that when subjected to increased hydrostatic pressure, the corresponding induced circumferential stress reduces the piezoelectric properties, namely, the coupling coefficient, to approximately its original pre-treated value. However, when the improved cylinders are used in transducers of the pressure-equalized design, such as liquid filled or free-flooded, the increase in coupling coefficient remains stable with environmental hydrostatic pressure.