ANALYSIS OF COUPLED-MODE FLUTTER OF PIPES CONVEYING FLUID ON THE ELASTIC FOUNDATION

The governing equation of solid-liquid couple vibration of pipe conveying fluid on the elastic foundation was derived. The critical velocity and complex frequency of pipe conveying fluid on Winkler elastic foundation and two-parameter foundation were calculated by po,ver series method. Compared,with pipe without considering elastic foundation, the numerical results show that elastic foundation can increase the critical flow velocity of static instability and dynamic instability of pipe. And the increase of foundation parameters may increase the critical flow velocity of static instability and dynamic instability of pipe, thereby delays the occurrence of divergence and flutter instability of pipe. For higher mass ratio beta, in the combination of certain foundation parameters, pipe behaves the phenomenon of restabilization and redivergence after the occurrence of static instability, and then coupled-mode flutter takes place.

Analysis and engineering of coupled cavity waveguides based on coupled-mode theory

The analytical expression for the transmission spectra of coupled cavity waveguides （CCWs） in photonic crystals （PCs） is derived based on the coupled-mode theory （CMT）. Parameters in the analytical expression can be extracted by simple numerical simulations. We reveal that it is the phase shift between the two adjacent PC defects that uniquely determines the flatness of the impurity bands of CCWs. In addition, it is found that the phase shift also greatly affects the bandwidth of CCWs. Thus, the engineering of the impurity bands of CCWs can be realized through the adjustment of the phase shift. Based on the theoretical results, an interesting phenomenon in which a CCW acts as a single PC defect and its impurity band possesses a Lorentz lineshape is predicted. Very good agreement between the analytical results and the numerical simulations based on transfer matrix method has been achieved.

A three-dimensional coupled-mode model for the acoustic field in a two-dimensional waveguide with perfectly reflecting boundaries

This paper presents a three-dimensional （3D） coupled-mode model using the direct-global-matrix technique as well as Fourier synthesis. This model is a full wave, two-way three-dimensional model, and is therefore capable of providing ac- curate acoustic field solutions. Because the problem of sound propagation excited by a point source in an ideal wedge with perfectly reflecting boundaries is one of a few three-dimensional problems with analytical solutions, the ideal wedge prob- lem is chosen in this work to validate the presented three-dimensional model. Numerical results show that the field results by analytical solutions and those by the presented model are in excellent agreement, indicating that the presented model can serve as a benchmark model for three-dimensional sound propagation problems involving a planar two-dimensional geometry as well as a point source.

Three-dimensional coupled-mode model and characteristics of low-frequency sound propagation in ocean waveguide with seamount topography

Large-scale topography, such as a seamount, substantially impacts low-frequency sound propagation in an ocean waveguide, limiting the application of low-frequency acoustic detecting techniques. A three-dimensional(3D) coupledmode model is developed to calculate the acoustic field in an ocean waveguide with seamount topography and analyze the3D effect. In this model, a correction is introduced in the bottom boundary, theoretically making the acoustic field satisfy the energy conservation. Furthermore, a large azimuth angle calculation range is obtained by using the operator theory and higher-order Pade approximation. Additionally, the model has advantages related to the coupling mode and parabolic equation theory. The couplings corresponding to the effects of range-dependent environment are fully considered, and the numerical implementation is kept feasible. After verifying the accuracy and reliability of the model, low-frequency sound propagation characteristics in the seamount environment are analyzed. The results indicate lateral variability in bathymetry can lead to out-of-plane effects such as the horizontal refraction phenomenon, while the coupling effect tends to restore the abnormal sound field and produces acoustic field diffraction behind the seamount. This model effectively considers the effects of the horizontal refraction and coupling, which are proportional to the scale of the seamount.

Complete leaky mode coupling in dual-core photonic crystal fibre based on the coupled-mode theory

This paper theoretically investigates the dependence of leaky mode coupling between inner core fundamental mode and outer core defect mode on phase and loss matching in pure silica dual-core photonic crystal fibres with the multi-pole method. The complete mode coupling can take place when both the phase and loss matching conditions are satisfied at the avoided anti-crossing wavelength. It shows the influences of cladding structure parameters including the diameters of cladding air holes d1, diameters of outer core holes d2 and hole to hole pitch A on the characteristics of leaky modes coupling. The coupled-mode theory is used to analyse the mode transition characteristics and the complete coupling can be clearly indicated by comparing the real and imaginary parts of propagation constant of the leaky modes.

A numerically stable coupled-mode formulation for acoustic propagation in range-dependent waveguides

In this paper,a stepwise coupled-mode model with the use of the direct global matrix approach is proposed.This method is capable of handling two-dimensional problems with either a point source in cylindrical geometry or a line source in plane geometry.With the use of the direct global matrix approach,this method is numerically stable.In addition,by introducing appropriately normalized range solutions,this model is free from the numerical overflow problem.Furthermore,we put forward source conditions appropriate for the line-source problem in plane geometry.As a result,this method is capable of addressing the scenario with a line source on top of a sloping bottom.Closed-form expressions for coupling matrices are derived and applied in this paper for handling problems with pressure-release boundaries and a homogeneous water column.The numerical simulations indicate that the proposed model is accurate,efficient,and numerically stable.Consequently,this model can serve as a benchmark model in range-dependent propagation modeling.Although this method is verified by an ideal wedge problem in this paper,the formulation applies to realistic problems as well.

Analysis and comparison between two coupled-mode methods for acoustic propagation in range-dependent waveguides

Two coupled-mode methods, namely DGMCM （Direct-Global-Matrix Coupled- Mode Method） and CCMM （Consistent Coupled-Mode Method）, are analyzed and compared. First, both of these two methods provide two-way solutions, and hence they are accurate models. Second, the series of local vertical modes in DGMCM converges as fast as that in CCMM, whereas DGMCM has a more tolerable requirement of the number of segments than CCMM. Third, these two models obtain the field solution by solving the coupled-mode system with different coefficient matrices, in which the computational effort for the required parameters is almost the same. Finally, DGMCM can handle some problems which are difficult for CCMM, such as in a waveguide with a rough bottom, a line source located right on top of a sloping bot- tom, or in the presence of multiple sources. In DGMCM, closed-form expressions for coupling matrices in a two-layer waveguide are given. In addition, the formulation for the line-source problem in plane geometry is derived to update CCMM.

General coupled-mode analysis of a geometrically symmetric waveguide array with nonuniform gain and loss

The exceptional point(EP)is one of the typical properties of parity–time-symmetric systems,arising from modes coupling with identical resonant frequencies or propagation constants in optics.Here we show that in addition to two different modes coupling,a nonuniform distribution of gain and loss leads to an offset from the original propagation constants,including both real and imaginary parts,resulting in the absence of EP.These behaviors are examined by the general coupled-mode theory from the first principle of the Maxwell equations,which yields results that are more accurate than those from the classical coupled-mode theory.Numerical verification via the finite element method is provided.In the end,we present an approach to achieve lossless propagation in a geometrically symmetric waveguide array.

Generalized Coupled-Mode Theory for Nonorthogonal Modes

A generalized theory of power-nonorthogonal coupled-modes in a lossless multi-waveguide structure is presented. A set of orthogonal eigenmodes in a multi-wave-guide structure with constant parameters is formed by combining the nonorthogonal modes. In the waveguide structure with slowly varying parameters, however, the local modes formed by the same combination are still coupled. Finally, an example of two-waveguide coupler is given.

Circular Bragg lasers with radial PT symmetry:Design and analysis with a coupled-mode approach

Parity–time(PT) symmetry has been demonstrated in the frame of classic optics. Its applications in laser science have resulted in unconventional control and manipulation of resonant modes. PT-symmetric periodic circular Bragg lasers were previously proposed. Analyses with a transfer-matrix method have shown their superior properties of reduced threshold and enhanced modal discrimination between the radial modes. However, the properties of the azimuthal modes were not analyzed, which restricts further development of circular Bragg lasers. Here, we adopt the coupled-mode theory to design and analyze chirped circular Bragg lasers with radial PT symmetry. The new structures possess more versatile modal control with further enhanced modal discrimination between the azimuthal modes. We also analyze azimuthally modulated circular Bragg lasers with radial PT symmetry, which are shown to achieve even higher modal discrimination.

A coupled-mode sound propagation model with complex effective depth

A coupled-mode sound propagation model with complex effective depth is presented,in order to involve the effect of branch line integral for acoustic field in a range-dependent waveguide.The equations of motion and continuity are used to obtain the coupled equations,which satisfy boundary conditions in the waveguide with varying topography and contain one coupling matrix.Meanwhile,the couplings between discrete and continuous spectrum are dealt with based on complex effective depth theory.Numerical simulations show that the accuracy of transmission loss is improved by the coupled mode model when eigenvalues of trapped modes are located near the branch point.The acoustic field in a non-horizontally stratified waveguide can be calculated efficiently and accurately by this model,and the energy corresponding to trapped modes,leaky modes and branch line integral can be considered adequately.

Dynamic Behaviors of Axially Moving Viscoelastic Plate with Varying Thickness

Structural components of varying thickness draw increasing attention these days due to economy and light-weight considerations. In view of the absence of research in vibration analysis of viscoelastic plate with varying thickness, this study devotes to investigate the dynamic behaviors of axially moving viscoelastic plate with varying thickness. Based on the thin plate theory and the two-dimensional viscoelastic differential constitutive relation, the differential equation of motion of the axially moving viscoelastic rectangular plate is derived, the plate constituted by Kelvin-Voigt model has linearly varying thickness in the y-direction. The dimensionless complex frequencies of axially moving viscoelastic plate with four edges simply supported are calculated by the differential quadrature method, curves of real parts and imaginary parts of the first three-order dimensionless complex frequencies versus dimensionless moving speed are obtained, the effects of the aspect ratio, thickness ratio, the dimensionless moving speed and delay time on the dynamic behaviors of the axially moving viscoelastic rectangular plate with varying thickness are analyzed. When other parameters keep constant, with the decrease of thickness ratio, the real parts of the first three-order natural frequencies decrease, and the critical divergence speeds of various modes decrease too, moreover, whether the delay time is large or small, the frequencies are all complex numbers.

STABILITY ANALYSIS OF MAXWELL VISCOELASTIC PIPES CONVEYING FLUID WITH BOTH ENDS SIMPLY SUPPORTED

On the basis of some studies of elastic pipe conveying fluid, the dynamic behavior and stability of Maxwell viscoelastic pipes conveying fluid with both ends simply supported, which are gyroscopic conservative system, were investigated by using the finite difference method and the corresponding recurrence formula. The effect of relaxation time of vis coelastic materials on the variation curve between dimensionless flow velocity and the real part and imaginary part of dimensionless complex frequencies in the first-three-order modes were analyzed concretely. It is found that critical flow velocities of divergence instability of Maxwell viscoelastic pipes conveying fluid with both ends simply supported decrease with the decrease of the relaxation time, while after the onset of divergence instability ( buckling) critical flow velocities of coupled-mode flutter increase with the decrease of the relaxation time. Particularly, in the case of greater mass ratio. with the decrease of relaxation time, the onset of coupled-mode flutter delays, and even does not take place. When the relaxation time is greater than 10(3), stability behavior of viscoelastic pipes conveying fluid is almost similar to the elastic pipes conveying fluid.

Benchmark solutions for sound propagation in an ideal wedge

Sound propagation in a wedge-shaped waveguide with perfectly reflecting boundaries is one of the few range- dependent problems with an analytical solution, and hence provides an ideal benchmark for a full two-way solution to the wave equation. An analytical solution for the sound propagation in an ideal wedge with a pressure-release bottom was presented by Buckingham and Tolstoy [Buckingham and Tolstoy 1990 J. Acoust. Soc. Am. 87 1511]. The ideal wedge problem with a rigid bottom is also of great importance in underwater acoustics. We present an analytical solution to the ideal wedge problem with a perfectly reflecting bottom, either rigid or pressure-release, which may be used to provide a means for investigating the sound field in depth-varying channels, and to establish the accuracy of numerical propagation models. Closed-form expressions for coupling matrices are also provided for the ideal waveguides characterized by a ho- mogeneous water column bounded by perfectly reflecting boundaries. A comparison between the analytical solution and the numerical solution recently proposed by Luo et al. [Luo W Y, Yang C M and Zhang R H 2012 Chin. Phys. Lett. 29 014302] is also presented, through which the accuracy of this numerical model is illustrated.

Chalcogenide As₂S₃Sidewall Bragg Gratings Integrated on LiNbO₃Substrate

This paper introduces the design and applications of integrated As2S3 sidewall Bragg gratings on LiNbO3 substrate. The grating reflectance and bandwidth are analyzed with coupled-mode theory. Coupling coefficients are computed by taking overlap integration. Numerical results for uniform gratings, phase-shifted gratings and grating cavities as well as electro-optic tunable gratings are presented. These integrated As2S3 sidewall gratings on LiNbO3 substrate provide an approach to the design of a wide range of integrated optical devices including switches, laser cavities, modulators, sensors and tunable filters.

Effects of propagation phase on the coupling of plasmonic optical modes

The temporal coupled-mode theory(TCMT)has made significant progress in recent years,and is widely applied in explaining a variety of optical phenomena.In this paper,the optical characteristics of the metasurface composed of nano-bars and nano-rings are simulated.The simulation results are well explained by TCMT under the coupled basis vector.However,when the structural asymmetry is large,the fitting of results shows that the total radiation loss is not conservative,in contradiction to the requirement of traditional TCMT.We solved this inconsistency by introducing the propagation phase into the near-field coupling term of TCMT.The studies show that,unlike the local mode near the exceptional point which corresponds to the radiation loss of the bright mode,the global mode near the diabolic point is closely related to the propagation phase.Furthermore,the structure near the diabolic point shows characteristic cross-coupling with the change of period.This study proposes a new theoretical framework for comprehending the interaction of light and matter and offers some guiding implications for the application of TCMT to a variety of related domains.

Dual-Coupled Robust Wireless Power Transfer Based on Parity-Time-symmetric Model

The characteristics of the wireless power transfer(WPT)system vary under different transfer distances.As distance increases,efficiency drops off sharply,limiting the wider use of WPT technology.In order to mitigate this problem,this paper proposes a novel dual-coupled WPT system,where both electric-coupled mechanism and magnetic-coupled mechanism are utilized to enhance the transfer efficiency.Furthermore,a Parity-Time(PT)-symmetric circuit is utilized to realize robustness of the system.The coupled-mode model of the system is established and the expressions of operating frequency,transfer efficiency and output power are deduced.Analysis results indicate that in the unbroken PT-symmetric state,compared with single-coupled systems,the proposed system can keep constant performance within a longer distance;in broken PT-symmetric state,the proposed system has higher transfer efficiency.Simulated results and comparative results are in accordance with the theoretical analysis.Within 1.4m,this scheme can transfer power with constant efficiency of 77%and constant output power of 70W.

High-order nonreciprocal add-drop filter

Topological photonics have led to robust optical behavior of optical devices, which has alleviated the influence of manufacturing defects and perturbations on the device performance. Meanwhile, temporal coupled-mode theory(t-CMT) has been developed and applied widely. However, the t-CMT of cascaded coupled cavities(CCC) system and its corresponding high-order filter has yet to be established. Here, the t-CMT of CCC system is established based on the existing t-CMT. By combining the CCC with topological waveguides, a versatile design scheme of high-order nonreciprocal add-drop filter(HONAF) is proposed. The relationship between the coupling effect of cavities and transmission and the filtering performance of HONAF is analyzed quantitatively. Then, a method to improve the transmission efficiency and quality factor of the filter is given. The proposed HONAF is based on the combination of gyromagnetic photonic crystals and decagonal Penrose-type photonic quasicrystals. The transmission and filtering performance of the HONAF are numerically analyzed, which verifies the consistency between theoretical prediction and numerical simulation. The established t-CMT of CCC system can be widely used in coupled resonator optical waveguides and their related systems. The proposed HONAF with excellent performance can also be applied to wavelength division multiplexing/demultiplexing systems.

Compound solitons in fiber Bragg grating

Single soliton and compound solitons are described by coupled-mode equation. It is noted that three parameters, which are dimensionless group velocity, normalized frequency, and grating strength, influence formed solitons by emulation. The novel designs of parallel and serial multi-grating are advanced, and the compound solitons formed from parallel multi-grating are linear superposition; the compound solitons formed from serial multi-grating are nonlinear superposition, and finally two general formulae are obtained. Furthermore, it is theoretically shown that the compound grating solitons are prominent and flexible signals in optical communication.

Robust modal phase matching in subwavelength x-cut and z-cut lithium niobate thin-film waveguides

We use the nonlinear coupled-mode theory to theoretically investigate second-harmonic generation(SHG) in subwavelength x-cut and z-cut lithium niobate(LN) thin-film waveguides and derive the analytical formula to calculate SHG efficiency in x-cut and z-cut LN thin-film waveguides explicitly.Under the scheme of optimal modal phase matching(MPM), two types of LN thin films can achieve highly efficient frequency doubling of a 1064 nm laser with a comparable conversion efficiency due to very consistent modal field distribution of the fundamental wave and second-harmonic wave with efficient overlap between them.Such a robust MPM for high-efficiency SHG in both the subwavelength x-cut and z-cut LN thin-film waveguides is further confirmed in a broad wavelength range, which might facilitate design and application of micro–nano nonlinear optical devices based on the subwavelength LN thin film.