Coupling Of Normal Modes Research Articles

Saturation of normal-mode coupling in aluminum-oxide-aperture semiconductor nanocavities

The photon density required for the saturation of normal-mode coupling in oxide-apertured nanocavities is measured to be 90 photons/μm2 by pump-probe experiments. The photon number is only 300 for a semiconductor nanocavity with a 2 μm diameter aluminum-oxide aperture, drastically reduced from 200 000 for a 50 μm waist on a planar microcavity.

Stick–slip motion in a friction oscillator with normal and tangential mode coupling

The note deals with a two-degree-of freedom frictional oscillator in contact with a surface moving at constant velocity. The mass of the system can oscillate freely on a vertical spring inside the slider. The contact between the slider and the surface is characterized by a constant friction coefficient. The paper describes the construction of solutions including those leading to a limit cycle with stick–slip. The conditions on the parameters that lead to the existence of these limit cycles are derived. This analysis shows that the coupling between normal and tangential vibrations can lead to stick–slip phenomena.

Normal-Mode Linewidths in a Semiconductor Microcavity with Various Cavity Qualities

We measure the normal-mode linewidths in a semiconductor microcavity with various exciton–photon interaction strengths. Variation of the normal mode coupling and thus of the exciton–photon interaction is obtained reducing the cavity quality by stepwise removing of top mirror pairs. Excellent agreement of the measured linewidths with results of a linear dispersion theory is obtained.

Heme symmetry, vibronic structure, and dynamics in heme proteins: ferrous nicotinate horse myoglobin and soybean leghemoglobin.

We report the visible and Soret absorption bands, down to cryogenic temperatures, of the ferrous nicotinate adducts of native and deuteroheme reconstituted horse heart myoglobin in comparison with soybean leghemoglobin-a. The band profile in the visible region is analyzed in terms of vibronic coupling of the heme normal modes to the electronic transition in the framework of the Herzberg-Teller approximation. This theoretical approach makes use of the crude Born-Oppenheimer states and therefore neglects the mixing between electronic and vibrational coordinates; however, it takes into account the vibronic nature of the visible absorption bands and allows an estimate of the vibronic side bands for both Condon and non-Condon vibrational modes. In this framework, an x-y splitting of the Q transition for native and deuteroheme reconstituted horse myoglobin is clearly assessed and attributed to electronic perturbations that, in turn, are caused by a reduction of the typical D(4h) symmetry of the system due to heme distortions of B(1g)-type symmetry and/or to an x-y asymmetric position of the nicotinate ring; in deuteroheme reconstituted horse myoglobin the asymmetric heme peripheral substituents add to the above effect(s). On the contrary, in leghemoglobin-a no spectral splitting upon nicotinate binding is observed, pointing to a planar heme configuration in which only distortions of A(1g)-type symmetry are effective and to which the nicotinate ring is bound in an x - y symmetric position. The local dynamic properties of the heme pocket of the three proteins are investigated through the temperature dependence of spectral line broadening. Leghemoglobin-a behaves as a softer matrix with respect to horse myoglobin, thus validating the hypothesis of a looser heme pocket conformation in the former protein, which allows a nondistorted heme configuration and a symmetric binding of the bulky nicotinate ligand.

Theory of Drift Waves in Rotating Toroidal Plasma Configurations

Drift waves in a rotating toroidal plasma are considered for an axisymmetric, large aspect-ratio tokamak with concentric, circular magnetic surfaces. The analysis performed is based on rigorously derived eigenmode equations, coupled in poloidal mode numbers through the toroidal effects. Plasma rotation is driven by the radial electrostatic field typical for the H confinement mode of plasma in tokamaks. The strong and weak coupling approximation that takes into account the toroidal coupling of normal modes centered on the neighbouring rational surfaces are considered. The derived eigenmode equation of the Weber type has two classes of solutions giving either marginally stable global drift modes or propagating drift waves which experiences shear damping Analytical dispersion relations for both global and propagating drift waves are obtained and their simple solutions are found for some limiting cases.

Outgoing and Global Drift Waves in Rotating Toroidal Plasma Configuration

The drift waves in rotating toroidal plasma are studied for an axisymmetric, large-aspect-ratio tokamak with concentric and circular magnetic surfaces. Plasma rotation is driven by the radial electrostatic field typical for the H confinement mode of plasma in tokamaks. Low-frequency electrostatic oscillations of low-beta plasma are considered in assumptions of adiabatic electrons and plasma quasineutrality. In order to describe drift oscillations in the plasma edge region, where the radial electric field and plasma rotation velocity are high, a weak coupling approximation that takes into account the toroidal coupling of normal modes centred on the neighbouring rational surfaces is considered. The derived eigenmode equation of the Weber type has two classes of solutions giving either marginally stable global drift modes or propagating drift waves which experience shear damping. The analytical dispersion equations, for both global and propagating drift waves are derived and the simple dispersion relations for some limiting cases are determined.

Linewidths in a semiconductor microcavity with variable strength of normal-mode coupling

The variation of the normal-mode coupling in a semiconductor microcavity is demonstrated by reducing the cavity quality through stepwise removing top mirror pairs. The dependence of the measured normal-mode coupling linewidths on the cavity quality is well reproduced by calculations on the basis of a linear dispersion theory with broadened excitons in a microcavity.

A modeling study of acoustic propagation through moving shallow-water solitary wave packets

Propagation of 400-Hz sound through continental-shelf internal solitary wave packets is shown by numerical simulation to be strongly influenced by coupling of normal modes. Coupling in a packet is controlled by the mode coefficients at the point where sound enters the packet, the dimensions of the waves and packet, and the ambient depth structures of temperature and salinity. In the case of a moving packet, changes of phases of the incident modes with respect to each other dominate over the other factors, altering the coupling over time and thus inducing signal fluctuations. The phasing within a moving packet varies with time scales of minutes, causing coupling and signal fluctuations with comparable time scales. The directionality of energy flux between high-order acoustic modes and (less attenuated) low-order modes determines a gain factor for long-range propagation. A significant finding is that energy flux toward low-order modes through the effect of a packet near a source favoring high-order modes will give net amplification at distant ranges. Conversely, a packet far from a source sends energy into otherwise quiet higher modes. The intermittency of the coupling and of high-mode attenuation via bottom interaction means that signal energy fluctuations and modal diversity fluctuations at a distant receiver are complementary, with energy fluctuations suggesting a source-region packet and mode fluctuations suggesting a receiver-region packet. Simulations entailing 33-km propagation are used in the analyses, imitating the SWARM experiment geometry, allowing comparison with observations.

Excited states and emission spectroscopy of organometallic compounds interpreted by time-dependent theory

Luminescence spectra of organometallic molecules in crystals or glasses are discussed and interpreted by using the time-dependent theory of electronic spectroscopy. Emphasis is placed on determining bond length and bond angle changes (excited-state distortions) between the ground and excited electronic states. The physical meaning of the dynamic processes and the molecular properties are described and illustrated with both theoretical calculations and experimental spectra. The discussion begins with spectra involving only one displaced normal mode, and continues with the effects of multiple normal modes. Both common features and unusual effects (the `Beat' and the `MIME') are described and interpreted. Finally, the effects of normal mode coupling and of electronic state coupling are briefly described.

Theory of Nonlinear Exciton Saturation in Semiconductor Microcavities

Excitonic nonlinearities in semiconductor microcavities are studied within a semiclassical theory based on Maxwell's equations and generalized semiconductor Bloch equations. Results are presented analyzing the saturation of excitonic normal-mode coupling due to an incoherent thermalized carrier plasma. The coherent nonlinear response is studied in the time domain assuming microcavity excitation with ultrashort pulses of different intensity.

Numerical simulation of the mutual conversion of ordinary and extraordinary waves in a magnetised plasma by artificial ionospheric turbulence

Abstract Some effects of normal mode coupling in weakly anisotropic inhomogeneous plasma are analysed on the basis of the numerical solution of transfer equations for the Stokes parameters. The numerical analysis of normal mode conversion on a set of isolated irregularities demonstrates the possibility of an effective polarisation transformation on such structures. It is shown that by the appropriate selection of discrete irregularities of the external magnetic field direction or plasma electron concentration resulting in radio-wave refraction, one can control electromagnetic radiation polarisation characteristics. Analytical expressions for mean Stokes parameters have been obtained for the rare isolated irregularities. The opportunity for the simulation of mutual wave conversion processes in the ionospheric heating experiments is discussed.

Nonlinear emission dynamics from semiconductor microcavities in the nonperturbative regime

Time-resolved normal-mode-coupling (NMC) oscillations in the nonlinear regime of a semiconductor microcavity with a large splitting to linewidth ratio are studied experimentally using upconversion. A reduction of the modulation depth of the NMC oscillations and reflection dips without a change in the NMC splitting and oscillation period is observed. Microscopic calculations attribute the observed features to excitonic broadening due to dephasing induced by carrier-carrier and polarization scattering processes.

Ultrashort pulse propagation effects in semiconductor microcavities

A microscopic theory is used to study femtosecond pulse propagation through a semiconductor microcavity containing one or more quantum wells. The ultrafast cavity mode build-up is investigated and the dynamical interplay of the field with the quantum-well electron-hole excitations is analyzed. Normal-mode coupling as well as radiative coupling between the quantum wells is shown to depend strongly on the placement of the quantum wells inside the microcavity.

Self-consistent-field perturbation theory for the Schrödinger equation

A method is developed for using large-order perturbation theory to solve the systems of coupled differential equations that result from the variational solution of the Schr\"odinger equation with wave functions of product form. This is a noniterative, computationally efficient way to solve self-consistent-field (SCF) equations. Possible applications include electronic structure calculations using products of functions of collective coordinates that include electron correlation, vibrational SCF calculations for coupled anharmonic oscillators with selective coupling of normal modes, and ab initio calculations of molecular vibration spectra without the Born-Oppenheimer approximation.

Linear and nonlinear optical properties of excitons in semiconductor quantum wells and microcavities

Linear and nonlinear light propagation in single and multiple quantum wells and in semiconductor microresonators are studied on the basis of Maxwell’s equations. The treatment includes radiative broadening of quantum-confined excitons, radiative coupling between quantum wells as well as coupling of quantum wells to the cavity field of a microresonator for steady state or ultrashort pulse excitation. The dynamical evolution of the coherent quantum-well polarization under the influence of many-body effects is studied within a microscopic model. The theory is used to investigate the influence of exciton saturation and dephasing on pulse propagation and excitonic normal-mode coupling.

Excitonic Nonlinearities of Semiconductor Microcavities in the Nonperturbative Regime.

A microscopic theory for excitonic nonlinearities and light propagation in semiconductor microcavities is applied to study normal-mode coupling (NMC) for varying electron-hole-pair densities. The nonlinear susceptibility of quantum confined excitons is determined from quantum kinetic equations including dephasing due to carrier-carrier and polarization scattering. The predicted disappearing of the normal-mode transmission peaks with negligible change in the NMC splitting agrees well with cw pump-probe measurements on samples showing remarkable splitting-to-linewidth ratios.

Three coupled oscillators: normal mode coupling in a microcavity with two different quantum wells

GaAs/AlAs microcavities containing two different quantum wells have been grown and their normal mode coupling studied. We present experimental results that exhibit three-dip reflectivity spectra characteristic of three coupled oscillators. A theoretical model based on a nonlocal dielectric response and a transfer matrix method is used to model the microcavities and yields good agreement with experiment.

A theoretical and simulation study of acoustic normal mode coupling effects due to the Barents Sea Polar Front, with applications to acoustic tomography and matched-field processing

Normal mode coupling due to a shallow water coastal front is considered, using oceanographic data from the 1992 Barents Sea Polar Front (BSPF) experiment as input to normal mode and parabolic equation (PE) acoustic propagation models. Criteria for the sensitivity of mode coupling to coastal front widths are derived, and applied to the BSPF as a representative example. The effects of coastal fronts on tomographic schemes are considered, particularly in terms of travel time-based tomography. The effects of frontal mode coupling on matched-field processing schemes are also considered, using both the maximum likelihood and variable coefficient likelihood methods, which show differing sensitivities to mismatch. Finally, directions for future research are discussed.

Surface wave scattering from sharp lateral discontinuities

The problem of surface wave scattering is re‐explored, with quasi‐degenerate normal mode coupling as the starting point. For coupling among specified spheroidal and toroidal mode dispersion branches, a set of coupled wave equations is derived in the frequency domain for first‐arriving Rayleigh and Love waves. The solutions to these coupled wave equations using linear perturbation theory are surface integrals over the unit sphere covering the lateral distribution of perturbations in Earth structure. For isotropic structural perturbations and surface topographic perturbations, these solutions agree with the Bom scattering theory previously obtained by Snieder and Romanowicz. By transforming these surface integrals into line integrals along the boundaries of the heterogeneous regions in the case of sharp discontinuities, and by using uniformly valid Green's functions, it is possible to extend the solution to the case of multiple scattering interactions. The proposed method allows the relatively rapid calculation of exact second order scattered wavefield potentials for scattering by sharp discontinuities, and it has many advantages not realized in earlier treatments. It employs a spherical Earth geometry, uses no far field approximation, and implicitly contains backward as well as forward scattering. Comparisons of asymptotic scattering and an exact solution with single scattering and multiple scattering integral formulations show that the phase perturbation predicted by geometrical optics breaks down for scatterers less than about six wavelengths in diameter, and second‐order scattering predicts well both the amplitude and phase pattern of the exact wavefield for sufficiently small scatterers, less than about three wavelengths in diameter for anomalies of a few percent.

Screech tones from free and ducted supersonic jets

It is well known that screech tones from supersonic jets are generated by a feedback loop. The loop consists of three main components. They are the downstream propagating instability wave, the shock cell structure in the jet plume, and the feedback acoustic waves immediately outside the jet. Evidence will be presented to show that the screech frequency is largely controlled by the characteristics of the feedback acoustic waves. The feedback loop is driven by the instability wave of the jet. Thus the tone intensity and its occurrence are dictated by the characteristics of the instability wave. In this paper the dependence of the instability wave spectrum on the azimuthal mode number (axisymmetric or helical/flapping mode, etc.), the jet-to-ambient gas temperature ratio, and the jet Mach number are studied. The results of this study provide an explanation for the observed screech tone mode switch phenomenon (changing from axisymmetric to helical mode as Mach number increases) and the often-cited experimental observation that tone intensity reduces with increase in jet temperature. For ducted supersonic jets screech tones can also be generated by feedback loops formed by the coupling of normal duct modes to instability waves of the jet. The screech frequencies are dictated by the frequencies of the duct modes. Super resonance, resonance involving very large pressure oscillations, can occur when the feedback loop is powered by the most amplified instability wave. It is proposed that the observed large amplitude pressure fluctuations and tone in the test cells of Arnold Engineering Development Center were generated by super resonance. Estimated super-resonance frequency for a Mach 1.3 axisymmetric jet tested in the facility agrees well with measurement.