Linear Coupling Coefficient Research Articles

Nonlinear directional coupler with variable coupling coefficient and variable nonlinear refractive index coefficient

In this paper, we report on the study of the coupled mode equations for nonlinear directional coupler (NLDC) in which both linear coupling coefficient and nonlinear refractive index coefficient are functions of propagation distance. We show, for the first time, to the best of our knowledge, that the equations for the general case can be transformed to those for the NLDC with constant linear coupling coefficient and that they can also be transformed to equations describing NLDC with constant nonlinear refractive index coefficient but extra loss or gain as long as the original nonlinear coefficients are the same for the two constituent waveguides. Combining the two transformations, we conclude that the equations for a general NLDC can be transformed to a conventional NLDC with extra loss or gain as long as the original nonlinear coefficients are the same for the two constituent waveguides. The potential applications of the proposed transformations are also discussed.

Calculation of uniaxial magnetic anisotropy energy of tetragonal and trigonal Fe, Co, and Ni

The magnetic anisotropy energy (MAE) of Fe, Co, and Ni is presented for tetragonal and trigonal structures along two paths of structural distortion connecting the bcc and the fcc structure. The MAE was calculated from first principles with the full-potential linear muffin-tin orbital method and the force theorem. As is expected from symmetry considerations, the MAE increases by orders of magnitude when the cubic symmetry is broken. For tetragonal structures of Co and Ni a regular behavior of the MAE is observed, i.e., only the symmetry dictated nodes at the cubic structures appear along this path of distortion. In the case of tetragonal Fe, additional reorientations of the easy axis occur that are attributed to a topological change of the Fermi surface upon distortion. For the trigonal structures of all three elements the strain dependence of the MAE is more complicated, with additional reorientations of the easy axis and an unexpectedly large MAE for certain distortions of Ni, and a strongly nonlinear behavior for trigonal structures of Co close to fcc. Furthermore, the linear magnetoelastic coupling coefficients are calculated from the MAE at small distortions from the cubic equilibrium structure of the three elements. Two different Brillouin-zone integration techniques were used to calculate the MAE. Since the Gaussian broadening method smears out details of the Fermi surface, it results in a different MAE as compared to the tetrahedron method in some cases.

Structure functions and breakdown criteria for wave turbulence

We study the structure functions of wave turbulence at small separations. We show that the criteria for breakdown obtained previously by examining the uniform validity of the asymptotic closure govern how close wave turbulence stays to joint Gaussianity. A new result in the case of small separations in that the system behavior is organized by a special point in the ( α, β) plane where α and β are the homogeneity parameters for the linear and nonlinear coupling coefficients. Finally, we explore how modifications of the breakdown criteria are necessary because of the strengths of non-local long-wave–short-wave interactions.

Dynamics of two-mode radiation in optical waveguides with strong mode coupling

Amplitude equations, as well as the effective dispersion and nonlinearity parameters, which define the dynamics of a wave packet formed by two strongly coupled modes, are derived with allowance for the frequency dependence of the linear mode coupling coefficient. These equations are used to study the onset of the modulation instability of the two-mode wave packet, soliton-like pulses, and compression modes. Unlike single-mode systems, the last two effects in optical waveguides may arise for both a negative and positive disper-sion of the waveguide material.

A linear approximation of the coupling coefficient in the WDM coupler

AbstractA linear approximation of the coupling coefficient for the wavelength division multiplexing (WDM) coupler is presented. Our aim is to better understand and to simplify the design of couplers used in optical communications. The theoretical calculation and the derivation of the linear coupling coefficient were obtained based on coupled mode theory and a simplified equation pertaining to rectangular and circular waveguide couplers. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 37: 12–15, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10809

The effect of a linear mode coupling dispersionon the wave packet dynamics in an optical waveguide with Kerr nonlinearity

The influence of a dispersion of the linear mode coupling coefficient of an optical waveguide (OWG) with Kerr nonlinearity on the dispersion parameters and dynamics of an optical pulse propagating in such a system is studied. In OWGs with a strong linear mode coupling, the presence of a dispersion of the mode coupling may lead to a significant decrease in the energy threshold for nonlinear self-compression of pulses as compared to the case of a single-mode OWG.

Nonlinear magnetoelastic effects in ultrathin epitaxial FCC Co(0 0 1) films: : an ab initio study

Those linear and nonlinear magnetoelastic coupling coefficients which determine the magnetostrictive stress and the strain-induced out-of-plane magnetic anisotropy in epitaxially grown FCC Co(0 0 1) films are calculated by the ab initio density functional electron theory. The nonlinear couplings have a strong effect on the change Δ σ 1 m of the in-plane magnetostrictive stress resulting from a change of the magnetization direction from [0 1 0] to [1 0 0], but a negligibly small effect on the out-of-plane anisotropy e MCA. The calculations confirm the experimental result that the measured out-of-plane anisotropy cannot be totally attributed to volume magnetoelastic effects. Estimates are given for the nonlinear magnetoelastic coupling coefficients m 1 γ,2 and m 2 γ,2 .

AlN Acoustic Wave Sensors Using Excimer Laser Micromachining Techniques

ABSTRACTAluminum Nitride (AlN) is a promising piezoelectric material for Acoustic Wave (AW) sensor application due to its high acoustic velocity, linear thermal coefficient and high electromechanical coupling coefficient. Epitaxial AlN thin films were successfully grown on the Sapphire C plane substrate by Plasma Source Molecular Beam Epitaxy (PSMBE). Standard two-port resonator structures were fabricated on the AlN/Sapphire by standard photolithography. Excimer laser micromachining techniques were utilized to fabricate microgroove gratings on the surface of thin film. Beside Surface Acoustic Wave (SAW), Surface Transverse Wave (STW) propagation was also found on the devices with those microgroove and classical metal strip gratings. Laser micromachinined microgroove gratings were found to enhance the propagation of STW. Further, sensors based on STW showed little attenuation in the liquid environment, while sensors based on SAW suffered excess loss when exposed to liquid.

SOLITON DYNAMICS IN TWO WAVEGUIDES WITH DISPERSION PROPERTIES OF THE LINEAR COUPLING COEFFICIENT

The soliton dynamics in two parallel waveguides is investigated numerically with the dispersion of the linear coupling coefficient taken into account. It is shown that the new terms in the system of coupled nonlinear equations which describe the switching process have an important influence on the soliton propagation for short pulses in directional couplers. In this case, depending on the value of the coupling-coefficient dispersion, an effect of distorsion or breakup of the initial pulse can be observed.

Molecular theory of thermomechanical coupling in cholesteric liquid crystals

A cholesteric liquid crystal lacks a center of inversion and it is consequently different from its mirror image. The low symmetry allows linear cross couplings between thermodynamic forces and fluxes that are polar vectors and pseudovectors, respectively. This makes it possible for a temperature gradient, which is a polar vector to induce a director angular velocity, which is a pseudovector. The reverse is also possible; the torque conjugate to the director angular velocity can drive a heat current. This is the basis for the Lehman effect where a temperature gradient parallel to the cholesteric axis causes the local director to rotate. We use linear response theory to derive Green–Kubo relations and nonequilibrium molecular dynamics simulation algorithms for the transport coefficient that couples the temperature gradient and the director angular velocity. The theory is completely general and can consequently be used to find relations for any linear cross coupling coefficient between a polar vector and a pseudovector.

Measurement of the modulus and phase of the linear coupling coefficient by analysis of the transverse beam profile

We study the dynamics of transverse oscillations near the linear coupling resonance excited by a pair of skew quadrupoles at the Laborat\'orio Nacional de Luz S\'{\i}ncrotron UVX electron storage ring through the analysis of the beam profile. Transverse coherent oscillations were excited with a fast kicker and the profile of the oscillating beam was observed by focusing visible synchrotron radiation from a bending magnet onto a fast charge-coupled device camera. Using a single resonance approximation, we calculated the border of the time-averaged transverse beam profile as a function of the complex coupling coefficient $\ensuremath{\kappa}$, which characterizes the distribution of coupling fields along the storage ring. A least-squares fit of the calculated beam profile border to the experimentally obtained isointensity contours provided a new method to determine both the modulus and the phase of $\ensuremath{\kappa}$. The values obtained for the modulus are in good agreement with those from the conventional normal mode tune separation technique, and the values obtained for the phase of $\ensuremath{\kappa}$ agree with calculations based on the model lattice and the known skew quadrupole distribution.

Kerr nonlinear coupler with varying linear coupling coefficient

We investigate a codirectional nonlinear coupler composed of two Kerr nonlinear waveguides. Unlike the conventional device, the linear coupling between the guides is supposed to be a variable function of the propagation distance. We calculate quantum statistical and dynamical properties of the Kerr nonlinear coupler with a coherent input and analyse the influence of coupling variation on oscillations in mean photon number. The possibility to control the switching characteristics and principal squeezing effect by adjusting the form of coupling function is shown.

Doubly resonant sum-frequency generation from molecules with general harmonic potential surfaces

A many-body approach is used to analyse the doubly resonant infrared-visible sum-frequency generation from molecules with general harmonic potential surfaces. This multi-mode model includes arbitrary linear and quadratic electron-phonon coupling coefficients, and is valid at any temperature. Numerical simulations have been performed on a simple two-mode model with equilibrium position displacements, frequency shifts and Duschinsky rotation under electronic excitation. Our study leads us to propose these types of experiments to discriminate between the effects of linear and quadratic electron-phonon coupling terms.

Polarized Optical Absorption Spectroscopy of the Tl 2MnF 5 · H 2O 1D Manganese (III) Single Crystal

The polarized optical absorption spectra of the 1D manganese (III) fluoride Tl 2MnF 5 · H 2O are investigated in the 9.5 -300 K temperature range. Throughout the work, special emphasis is placed on the correlation between the different spectroscopic parameters and the structural and magnetic properties of the title compound. Three prominent, strongly polarized broadhands are observed at 11,700, 17,500, and 20,800 cm -1, which are assigned to the spin-allowed crystal field bands within the d 4 electronic configuration of the Jahn-Teller elongated MnF 3- 6 complex ( D 4h). Both the polarization and the temperature dependence of the oscillator strengths indicate that these bands are electric-dipole-assisted by odd parity vibrations, whereas the spin-forbidden transitions are induced by a pairwise exchange mechanism. A salient feature of the present work is the observation of vibronic progressions to a 1g modes of 525, 505, and 375 cm -1 in the low temperature spectra of the 5 B 1g → 5A 1g and 5 B 2g bands. The nature of these modes and the experimental Huang-Rhys factors are analyzed in terms of the linear electron-phonon coupling coefficients, which are derived by correlating the optical spectra of several fluorides with the local geometry around the Mn(III). The presence of an exciton magnon peak in the low temperature spectra is also noteworthy. The temperature dependence of the intensity of this peak as well as of the spin-forbidden transitions provides evidence of magnetic ordering below T N = 28 K and allows us to estimate an intrachain exchange constant of J = 11 cm -1.

Experiments on the nonlinear stages of excited and natural planar jet shear layer transition

An experimental investigation focusing on the nonlinear stages of planar jet shear layer transition is presented. Experimental results for transition under both “natural” and low level artificial forcing conditions are presented and compared. The local spectral dynamics of the jet shear layer is modeled as a nonlinear system based upon a frequency domain, second-order Volterra functional series representation. The local linear and nonlinear wave coupling coefficients are estimated from time-series streamwise velocity fluctuation data. From the linear coupling coefficient, the mean dispersion characteristics and spatial growth rates may be obtained. With the estimation of the nonlinear power transfer function, the total, linear and quadratic nonlinear spectral energy transfer may be locally estimated. When these measures are used in conjunction with the local quadratic bicoherency and linear-quadratic coupling bicoherency, the local system output power may be completely characterized and the effect of nonlinearity on local mean flow distortion assessed. Particular attention is focused upon quantifying the linear and nonlinear power transfer that characterizes the different stages of the jet shear layer transition for both natural and excited flows. The quadratic power transfer that occurs with deviation from the perfect resonant wavenumber matching condition is clarified as is the dynamic mechanism of subharmonic resonance. The mechanism of spectral broadening is described and contrasted for natural and artificially excited flows.

Nonlinear wave coupling and subharmonic resonance in planar jet shear layer transition

An experimental investigation of the nonlinear spectral development associated with the transition of an initially laminar planar jet shear layer is presented. The local shear layer spectral dynamics are modeled as a nonlinear system containing both linear and quadratically nonlinear system elements. A novel digital signal processing technique is applied which allows the linear and quadratically nonlinear wave coupling coefficients that characterize the local spectral dynamics to be estimated directly from time-series velocity fluctuation data. The method utilized is noniterative and explicitly includes fourth-order spectral moments. From the linear coupling coefficient, the local spatial growth rate and dispersion relation may be obtained. Of particular interest in the work reported is the associated nonlinear wave coupling coefficient which provides a measure of the efficiency of local nonlinear three-wave coupling. These show that the jet shear layer exhibits a strong preference for difference mode interactions. With the estimation of the related nonlinear power transfer function, the total, linear, and quadratic nonlinear spectral energy transfer may be locally estimated. When these measures are used in conjunction with the local quadratic bicoherency and local linear–quadratic coupling bicoherency, the local nonlinear spectral dynamics of the flow may be completely and unambiguously quantified. Particular emphasis is placed upon discerning the mechanism which gives rise to subharmonic resonance with the fundamental. Results show that the amplification of the subharmonic occurs via a parametric resonance with the fundamental rather than by direct quadratic difference interaction. That is, the subharmonic is boosted by a weakly nonlinear mechanism involving a linear growth rate modification due to a resonant phase lock with the fundamental instability.

A criterion of double-mode pulsation from coupling coefficients

A criterion for the occurrence of double-mode pulsations is derived from linear adiabatic coupling coefficients The criterion indicates that double-mode pulsations of classical Cepheids occur at a shorter period range than the observed one, and that the evolutionary mass models are preferable for the double-mode pulsations.

Exact solutions of non-conservative equations for three-wave and second-harmonic resonance

New solutions of the equations of three-wave and second-harmonic resonance are presented, in cases where these equations are non­conservative. With three waves subject to both finite linear damping and complex coupling coefficients, these new solutions depend on a single characteristic variable. In the absence of linear damping, but with complex coupling coefficients, a broad class of solutions depending on three characteristic variables is found. This class is a generalization of the so-called ‘one-lump’ solutions previously known only for conservative equations with real coupling coefficients. For second-harmonic reasonance, analogous new solutions are given for both conservative and non-conservative cases.

The effect of synchronization on the modal selection in classical cepheids

The coupled self-exciting oscillator model is investigated in the non-resonant case and applied to classical cepheids. The modal selection in these models is explained as the result of the synchronization caused by the mutual interaction between different modes. By using linear adiabatic coupling coefficients, it is shown that the fundamental mode suppresses the first overtone mode marginally in short-period classical cepheids. The double periodicity of several cepheids is expected as the result of a small change of physical state in the outer envelopes of these stars.

Pressure Effects of Optical Spectra of Impurity Centers in Solids

Pressure dependences of absorption and emission spectra of impurities in solids are calculated with a one dimensional configuration-coordinate model considering pressure-dependent linear coupling coefficient and force constants which arise through anharmonic terms of the adiabatic potential energies. It is shown that the pressure-dependent force constants play an important role in the understanding of the pressure effects on the peak positions, band-widths and Huang-Rhys parameters.