Direction of wave propagation in the cochlea for internally excited basilar membrane

Otoacoustic emissions are an indicator of a normally functioning cochlea and as such are a useful tool for non-invasive diagnosis as well as for understanding cochlear function. While these emitted waves are hypothesized to arise from active processes and exit through the cochlear fluids, neither the precise mechanism by which these emissions are generated nor the transmission pathway is completely known. With regard to the acoustic pathway, two competing hypotheses exist to explain the dominant mode of emission. One hypothesis, the backward-traveling wave hypothesis, posits that the emitted wave propagates as a coupled fluid-structure wave while the alternate hypothesis implicates a fast, compressional wave in the fluid as the main mechanism of energy transfer. In this paper, we study the acoustic pathway for transmission of energy from the inside of the cochlea to the outside through a physiologically-based theoretical model. Using a well-defined, compact source of internal excitation, we predict that the emission is dominated by a backward traveling fluid-structure wave. However, in an active model of the cochlea, a forward traveling wave basal to the location of the force is possible in a limited region around the best place. Finally, the model does predict the dominance of compressional waves under a different excitation, such as an apical excitation.     

The short-wave model and waves in two directions

In the region where a sinusoidal wave in the cochlea reaches its maximum amplitude, the long-wave (or one-dimensional) model of the cochlea is deficient. In this region a short-wave model is more appropriate. However, in its current form, the short-wave model supports only waves in one direction. Therefore, it cannot cope with reflection effects associated with, e.g., inhomogeneities. Theoretical explorations of creation and internal reflection of otoacoustic emissions have almost exclusively been based on the long-wave model. In this article the road is paved for future explorations on a generalized form of the short-wave model, one that supports forward as well as backward waves, and thus can include internal reflections.     

Dual traveling waves in an inner ear model with two degrees of freedom

We calculate traveling waves in the mammalian cochlea, which transduces acoustic vibrations into neural signals. We use a WKB-based mechanical model with both the tectorial membrane (TM) and basilar membrane (BM) coupled to the fluid to calculate motions along the length of the cochlea. This approach generates two wave numbers that manifest as traveling waves with different modes of motion between the BM and TM. The waves add differently on each mass, producing distinct tuning curves and different characteristic frequencies (CFs) for the TM and the BM. We discuss the effect of TM stiffness and coupling on the waves and tuning curves. We also consider how the differential motions between the masses could influence the cochlear amplifier and how mode conversion could take place in the cochlea.     

Backward three-wave optical solitons

Backward symbiotic solitary waves in quadratic media with absorption losses are generated through the nonlinear non-degenerate three-wave interaction. We study these solitary waves in the particular case of a doubly backward quasi-phase matching configuration. The same mechanism responsible for nanosecond solitary wave morphogenesis in the c.w. pumped Brillouin-fiber-ring laser may act for picosecond pulse generation in a quadratic c.w. pumped optical parametric oscillator (OPO). The resonant condition is automatically satisfied in stimulated Brillouin backscattering when the fiber-ring laser contains a large number of longitudinal modes beneath the gain curve. However, in order to achieve quasi-phase matching between the three optical waves in the Χ⁽²⁾ medium, a nonlinear susceptibility inversion grating of sub-μm period is required. Such a quadratic medium supports solitary waves that result from energy exchanges between dispersionless waves of different velocities. We show, by a stability analysis of the non-degenerate backward OPO in the QPM decay interaction between a c.w. pump and backward signal and idler waves that the inhomogeneous stationary solution exhibits a Hopf bifurcation with a single control parameter. Above OPO threshold, the nonlinear dynamics yields self-structuration of a backward symbiotic solitary wave, which is stable for a finite temporal walk-off (i.e. different group velocities) between signal and idler waves. We also study the dynamics of singly backward mirrorless OPO’s (BMOPO’s) pumped by an incoherent field, in line with the recent experimental demonstration of this OPO configuration. We show that this system is characterized, as a general rule, by the generation of a highly coherent backward field, despite the high degree of incoherence of the pump field. This remarkable property finds its origin in two distinct phase-locking mechanisms that originate respectively in the convection and the dispersion properties of the fields. In both cases we show that the incoherence of the pump is transferred to the co-moving field, which thus allows the backward field to evolve towards a highly coherent state. We propose realistic experimental conditions that may be implemented with currently available technology and in which backward coherent wave generation from incoherent excitation may be observed and studied.     

Excitation of low-frequency acoustical signals by a vertical array of interacting emitters in oceanic waveguides

We present the results of experiments on the excitation of joint oscillations in a system of electromagnetic emitters submerged in a fluid having the shape of rigid cylinders with ring elastic membranes in the end faces. A mathematical model of the antenna formed by the given set of sound emitters is constructed. Interaction of emitters is considered through the additive pressures exerted on each of the membranes by sound waves excited by neighboring emitters. Variations in pressures of gases filling the cylinders and their influence on oscillations of membranes are also considered. We put forth a system of the integro-differential equations in partial derivatives with decelerations over time describing the forced joint oscillations of emitters. In the harmonic case, solutions to the system are obtained. Numerical calculations are compared with experimental data to verify the model and improve its parameters.     

High-Frequency Backward Waves in Longitudinally Magnetized Gyrotropic Waveguides

Backward waves in waveguides completely filled with magnetoactive plasma (gaseous or semiconductor plasma) have been investigated numerically. It is shown that two types of backward waves exist in such waveguides: cyclotron backward waves and waveguide HE-modes. While the cyclotron modes are backward waves at arbitrary system parameters (plasma density, magnetic field and waveguide radius), the waveguide backward waves appear only at certain values of there parameters. In addition the cyclotron backward waves can propagate at arbitrary wave-number k_z and at arbitrary phase velocity. The backward waveguide modes exist only at limited values of k_z and of phase velocities.     

Can ion-acoustic waves in plasma be backward waves?

The dispersion relation for ion-acoustic waves in plasma with ion flow has been analyzed. It is shown that these waves may exist (under certain conditions) in the form of backward waves with antiparallel group and phase velocities. The range of ion flow velocities allowing implementation of backward ion-acoustic waves is found.     

The nonlinear interaction of waves generated by the stimulated Raman scattering with plasma in the PALS experiment

This paper is devoted to the study of the nonlinear interaction of the waves generated by stimulated Raman scattering in plasma. The influence of nonlinear interaction of plasma wave with plasma electrons on the sum of action densities of waves generated by the laser wave is solved. The electron acceleration in the forward and backward wave fields is described. The change of the electric field of the quasimode of forward and backward plasma waves of Raman scattering given by trapping of plasma particles is calculated. Numerical results are calculated for typical parameters of the PALS experiment.     

Nonlinear nature of kinetic undamped waves induced by electrostatic turbulence in stimulated Raman backscattering

The influence of low-frequency waves of kinetic nature induced by electron trapping in backward Stimulated Raman Scattering (SRS) is investigated. Semi-lagrangian Vlasov-Maxwell simulations are carried out not only for periodic boundary conditions but also in the case of an open plasma with parabolic shape, in optical mixing. We provide a numerical example of generation of KEEN (kinetic electrostatic electron nonlinear) waves nonlinearly induced from the SRS through a mechanism we first here elucidate. In particular we identify a process of backward scattering of the SRS probe light from the so generated KEEN waves, which may provide a mechanism for the possible experimental observation and measurement of such nonlinear structures.     

Reflection of retrograde waves within the cochlea and at the stapes

A number of authors [de Boer and Viergever, Hear. Res. 13, 101-112 (1984); de Boer et al., in Peripheral Auditory Mechanisms (Springer-Verlag, Berlin, 1986); Hear. Res. 23, 1-7 (1986); Viergever, in Auditory Frequency Selectivity (Plenum, New York, 1986), pp. 31-38; Kaernbach et al., J. Acoust. Soc. Am. 81, 408-411 (1987)] have argued that backward-traveling waves, in striking contrast to waves traveling forward towards the helicotrema, suffer appreciable reflection as they move through the basal turns of the cochlea. Such reflection, if present, would have important consequences for understanding the nature and strength of otoacoustic emissions. The apparent asymmetry in reflection of cochlear waves is shown, however, to be an artifact of the boundary condition those authors impose at the stapes: conventional cochlear models are found not to generate reflections of waves traveling in either direction even when the wavelength changes rapidly and the WKB approximation breaks down. Although backward-traveling waves are not reflected by the secular variation of the geometrical and mechanical characteristics of the cochlea, they are reflected when they reach the stapes. The magnitude of that boundary reflection is computed for the cat and shown to be a large, rapidly varying function of frequency.     

左手系材料界面上的非线性TE电磁波

针对电磁波在非线性左手系材料中的传播性质, 分别研究了左、右手系材料界面以及两左手系材料界面上非线性TE表面波的传播行为讨论了导波的频率特性、色散关系以及群速度随频率的变化规律分析表明,两种界面上的非线性TE表面波均存在频率通带和禁带,且带宽是传播功率的函数揭示了在一定条件下,左、右手系材料界面上既可以支持正向传播的非线性TE表面波,也可以支持反向传播的非线性TE表面波;两左手系材料界面上表面波的传播性质因材料参量的变化差异较大,一定参量条件下,该界面上仅支持反向传播的非线性TE表面波.     

Exotic properties and potential applications of quantum metamaterials

We discuss here potential venues for applications and exotic features of quantum metamaterials. We explore the coupling of conventional electromagnetic metamaterials with quantum emitters and the wave properties of quantum metamaterials obtained by tailoring their effective band structure. We discuss anomalous enhancement effects in the quantum emission properties of individual and collections of small emitters in the presence of metamaterials, as well as matter-wave cloaking and anomalous tunneling phenomena for quantum mechanical waves in artificial materials with exotic band structures.     

Laser amplification with a twist: traveling-wave propagation and gain functions from throughout the cochlea

Except at the handful of sites explored by the inverse method, the characteristics-indeed, the very existence-of traveling-wave amplification in the mammalian cochlea remain largely unknown. Uncertainties are especially pronounced in the apex, where mechanical and electrical measurements lack the independent controls necessary for assessing damage to the preparation. At a functional level, the form and amplification of cochlear traveling waves are described by quantities known as propagation and gain functions. A method for deriving propagation and gain functions from basilar-membrane mechanical transfer functions is presented and validated by response reconstruction. Empirical propagation and gain functions from locations throughout the cochlea are obtained in mechanically undamaged preparations by applying the method to published estimates of near-threshold basilar membrane responses derived from Wiener-kernel (chinchilla) and zwuis analysis (cat) of auditory-nerve responses to broadband stimuli. The properties of these functions, and their variation along the length of the cochlea, are described. In both species, and at all locations examined, the gain functions reveal a region of positive power gain basal to the wave peak. The results establish the existence of traveling-wave amplification throughout the cochlea, including the apex. The derived propagation and gain functions resemble those characteristic of an active optical medium but rotated by 90 degrees in the complex plane. Rotation of the propagation and gain functions enables the mammalian cochlea to operate as a wideband, hydromechanical laser analyzer.     

Phased array with controlled directivity pattern

Amplitude-phase distribution of currents in the emitters that allows independent control of the main lobe and the blind spot on the directivity pattern of the antenna where the gain substantially decreases is analyzed. The problem is solved with the aid of controlled amplitudes and phases of the waves emitted by the antenna array. The main lobe and the blind spot on the directivity pattern are formed using the synthesis of the complex amplitudes of currents in the emitters.     

Behaviors of electrostatic ion cyclotron waves excited in ion beam-plasma systems

Experimental results are presented for a behavior of the electrostatic ion cyclotron waves excited in an ion beam-plasma system. This wave appears as forward and backward waves with respect to the propagating component along the magnetic field.     

Guided wave phase velocity measurement using multi-emitter and multi-receiver arrays in the axial transmission configuration

This paper is devoted to a method of extraction of guided waves phase velocities from experimental signals. Measurements are performed using an axial transmission device consisting of a linear arrangement of emitters and receivers placed on the surface of the inspected specimen. The technique takes benefit of using both multiple emitters and receivers and is validated on a reference wave guide. The guided mode phase velocities are obtained using a projection in the singular vectors basis. The singular vectors are determined by the singular values decomposition (SVD) of the response matrix between the two arrays in the frequency domain. This technique enables to recover accurately guided wave phase velocity dispersion curves. The SVD based approach was designed to overcome limitations of spatio-temporal Fourier transform for receiver array of limited spatial extent as in the case of clinical assessment of cortical bone in axial transmission.     

True surface waves guided by metamaterials

The dispersion properties of surface waves propagating along the interface between a resonant metamaterial and vacuum have been studied. It is shown that such an interface can support both forward and backward waves. The case of degeneracy, where an infinite number of waves with arbitrary retardation correspond to one frequency, has been investigated.     

Particle Simulation of Electrostatic Waves Driven by an Electron Beam

A one-dimensional electrostatic particle-in-cell simulation is performed to study electrostatic wave excitation due to an electron beam in a plasma system. The excited fundamental and harmonic waves are analyzed with the fast Fourier transformation and the wavelet transformation. The second harmonic is suggested to be generated by wave-wave coupling during the nonlinear evolution, which involves forward propagating and backward propagating Langmuir waves. Furthermore, the background electrons may be heated and accelerated by the electrostatic waves.     

Experimental Properties of Optical Phase Conjugation in Cold Atoms in a Magneto-Optical Trap

We employ a sample of cold 87Rb atoms in a magneto-optical trap to study the impulse responses and spatial characters of backward conjugate waves in a four-wave mixing process. We measure the slow and superluminal group velocities of backward conjugate waves, and find the sensitive variation of the spatial mode of backward waves with the probe-pump detuning and the dependence of the reflectance on the magnetic field, while the trapping magnetic field exists.     

Testing coherent reflection in chinchilla: Auditory-nerve responses predict stimulus-frequency emissions

Coherent-reflection theory explains the generation of stimulus-frequency and transient-evoked otoacoustic emissions by showing how they emerge from the coherent "backscattering" of forward-traveling waves by mechanical irregularities in the cochlear partition. Recent published measurements of stimulus-frequency otoacoustic emissions (SFOAEs) and estimates of near-threshold basilar-membrane (BM) responses derived from Wiener-kernel analysis of auditory-nerve responses allow for comprehensive tests of the theory in chinchilla. Model predictions are based on (1) an approximate analytic expression for the SFOAE signal in terms of the BM traveling wave and its complex wave number, (2) an inversion procedure that derives the wave number from BM traveling waves, and (3) estimates of BM traveling waves obtained from the Wiener-kernel data and local scaling assumptions. At frequencies above 4 kHz, predicted median SFOAE phase-gradient delays and the general shapes of SFOAE magnitude-versus-frequency curves are in excellent agreement with the measurements. At frequencies below 4 kHz, both the magnitude and the phase of chinchilla SFOAEs show strong evidence of interference between short- and long-latency components. Approximate unmixing of these components, and association of the long-latency component with the predicted SFOAE, yields close agreement throughout the cochlea. Possible candidates for the short-latency SFOAE component, including wave-fixed distortion, are considered. Both empirical and predicted delay ratios (long-latency SFOAE delay/BM delay) are significantly less than 2 but greater than 1. Although these delay ratios contradict models in which SFOAE generators couple primarily into cochlear compression waves, they are consistent with the notion that forward and reverse energy propagation in the cochlea occurs predominantly by means of traveling pressure-difference waves. The compelling overall agreement between measured and predicted delays suggests that the coherent-reflection model captures the dominant mechanisms responsible for the generation of reflection-source otoacoustic emissions.