Plane Wave Model Research Articles

Spatial signature estimation for uniform linear arrays with unknown receiver gains and phases

The problem of spatial signature estimation using a uniform linear array (ULA) with unknown receiver gain and phase responses is studied. Sufficient conditions for identifying the spatial signatures are derived, and a closed-form ESPRIT-like estimator is proposed. The performance of the method is investigated by means of simulations and on experimental data collected with an antenna array in a suburban environment. The results show that the absence of receiver calibration is not critical for uplink signal waveform estimation using a plane wave model.

Two-dimensional photonic bandgap reflectors for free-propagating beams in the mid-infrared

We present a detailed study of a 2D photonic bandgap reflector for free-propagating beams in the mid-infrared. The photonic crystal made from macroporous silicon is a triangular lattice of cylindrical holes in bulk silicon. The reflection spectra are measured from ~2.5 to ~14 µm by using a Fourier transform spectrometer equipped with a microscope. A very high reflectivity is measured for the first-order forbidden bands, reaching 98% between 6 and 8 µm in the TE polarization and -M direction. Smaller performances are obtained at short wavelengths. Different causes of degradation are separately considered. The influence of the beam divergence is first analysed by using a 3D plane wave model. We show that the shapes, widths and positions of the higher-order forbidden bands are modified with a divergent beam, but the reflector performances are not degraded too much at short wavelengths. Diffraction losses at the interface are then estimated using a finite-difference time domain model. The crystal termination and orientation is found to have a critical influence, but diffraction losses only manifest themselves at the shortest investigated wavelengths. Finally, a comparative analysis of differently cleaved samples shows that the small roughness of the interface or the hole radius dispersion are actually the prime cause of degradation as long as diffraction effects remain weak.

DIAMETRAL PLANE-WAVE ANALYSIS FOR SHORT CIRCULAR CHAMBERS WITH END OFFSET INLET/OUTLET AND SIDE EXTENDED INLET/OUTLET

Short elliptical chamber mufflers are used often in the modern day automotive exhaust systems. The acoustic analysis of such short chamber mufflers is facilitated by considering a transverse plane wave propagation model along the major axis up to the low frequency limit. The one dimensional differential equation governing the transverse plane wave propagation in such short chambers is solved using the segmentation approaches which are inherently numerical schemes, wherein the transfer matrix relating the upstream state variables to the downstream variables is obtained. Analytical solution of the transverse plane wave model used to analyze such short chambers has not been reported in the literature so far. This present work is thus an attempt to fill up this lacuna, whereby Frobenius solution of the differential equation governing the transverse plane wave propagation is obtained. By taking a sufficient number of terms of the infinite series, an approximate analytical solution so obtained shows good convergence up to about 1300 Hz and also covers most of the range of muffler dimensions used in practice. The transmission loss (TL) performance of the muffler configurations computed by this analytical approach agrees excellently with that computed by the Matrizant approach used earlier by the authors, thereby offering a faster and more elegant alternate method to analyze short elliptical muffler configurations.

A simultaneously phase-matched tandem optical parametric oscillator

We report the theoretical analysis of a simultaneously phase-matched tandem optical parametric oscillator (STOPO) in which the principal OPO generates a signal which pumps a secondary OPO. Both OPO interactions are assumed to be phase-matched in a single crystal. The cavity has high Q for the signal produced by the principal OPO and has lower Q for the signal of the secondary OPO. The pump and the two idler frequencies are not resonated. The five waves undergoing nonlinear mixing are assumed to be nondegenerate in either frequency or polarization. We show that the useful output, consisting of the two idlers and the signal of the secondary OPO, can be produced with high efficiency over a large dynamic range in the pump intensity. We discuss the tuning with temperature and grating period of a STOPO based on periodically poled LiNbO/sub 3/ pumped at 1.064 /spl mu/m. We present results based on both plane-wave modeling and modeling in three spatial dimensions.

Laser instabilities in a Gaussian cavity mode with Gaussian pump profile

We analytically demonstrate that both single-mode and multimode instabilities may occur in a Gaussian-cavity-mode laser model with Gaussian pump profile. As a necessary condition, the ratio of the beam waist to the pump waist must exceed a given limiting value, which depends on the population decay rate. For an infinitely concentrated pump the plane-wave model instability thresholds are recovered, and there exists an optimum value of the waists ratio for which the second laser threshold is minimum.

Relation of geomagnetically induced currents and local geomagnetic variations

Geomagnetically induced currents (GICs) were recorded in June 1991 to May 1992 in a 400 kV transmission line in southern Finland. Geomagnetic field variations were simultaneously measured at the nearby Nurmijarvi Geophysical Observatory. Two models are presented here to calculate GICs from the time derivative of the magnetic field. A plane wave model with a homogeneous earth is applied by letting the Earth's conductivity be a fitting parameter. Another approach derives experimental impulse responses between GIC and time derivatives. Both methods yield approximately accuracy. When GICs larger than 10 A, 20 A and 30 A are considered the average misfits are ca. 40%, 30%, and 20%, respectively.

Influence of transverse effects on measurement of third-order nonlinear susceptibility by self-induced polarization state changes

Measurements of the third-order nonlinear electric susceptibility component χxyyx3 by means of self-induced changes in the state of polarization of an intense elliptically polarized laser beam are reported. The simultaneous observation of the transverse intensity profile and of the losses allows us to show the influence of field transverse gradients on the polarization state. We show that the plane-wave model cannot explain our experimental results, even at low input intensities. The influence of spatial dispersion on nonlinear susceptibility is demonstrated.

Space-time array processing: The model-based approach

A method of space–time array processing is introduced that is based on the model-based approach. The signal and measurement systems are placed into state-space form, thereby allowing the unknown parameters of the model, such as signal bearings, to be estimated by an extended Kalman filter. A major advantage of the model-based approach is that there is no inherent limitation to the degree of sophistication of the models used, and therefore it can deal with other than plane-wave models, such as cylindrically or spherically spreading propagation models, as well as more sophisticated representations such as the normal mode and the parabolic equation propagation models. Since the processor treats the parameters of interest as unknown parameters to be estimated, there is no explicit beamformer structure, and therefore no accuracy limitations such as fixed beam bin sizes and predetermined number of preformed beams. After a theoretical exposition of the underlying theory, the performance of the processor is evaluated with synthesized data sets. The results indicate that the method is a highly effective approach that is capable of significantly outperforming conventional array processors.

Methods and techniques to characterise Terfenol-D

Characterisation parameters are required in order to provide reliable comparisons of different materials, for quality control in material production and to enable the design of more efficient transducers and control systems. Representation of non-linear, hysteretic behaviour is achieved by modelling either hysteresis loops or resonant response. In each case, by comparing the model predictions with the observed responses, numerical values can be assigned to the parameters that describe the material. Both the hysteresis loops and resonant response methods have a useful role but the latter is inherently more valuable, especially for description of the different contributions to the overall losses under dynamic conditions. A plane wave model of resonant response has the benefit that it can be developed to characterise either materials or devices under working conditions. These characterisation methods and techniques have been applied to different forms of Terfenol-D —random polycrystalline, grain oriented and a laminated sample. The results demonstrate that the resonance modelling can quantify the differences in behaviour between grain-oriented and random polycrystalline samples and that laminations successfully achieve full field penetration at frequencies when a large volume fraction of an unlaminated sample is screened.

Correspondence between discrete and continuous models of excitable media: trigger waves.

We present a theoretical framework for relating continuous partial differential equation (PDE) models of excitable media to discrete cellular automata (CA) models on a randomized lattice. These relations establish a quantitative link between the CA model and the specific physical system under study. We derive expressions for the CA model's plane wave speed, critical curvature, and effective diffusion constant in terms of the model's internal parameters (the interaction radius, excitation threshold, and time step). We then equate these expressions to the corresponding quantities obtained from solution of the PDEs (for a fixed excitability). This yields a set of coupled equations with a unique solution for the required CA parameter values. Here we restrict our analysis to "trigger" wave solutions obtained in the limiting case of a two-dimensional excitable medium with no recovery processes. We tested the correspondence between our CA model and two PDE models (the FitzHugh-Nagumo medium and a medium with a "sawtooth" nonlinear reaction source) and found good agreement with the numerical solutions of the PDEs. Our results suggest that the behavior of trigger waves is actually controlled by a small number of parameters.

Nonlinear optical and bistable properties of a wafer-fused vertical-cavity device based on InGaAsP

We report on a detailed analysis of the nonlinear characteristics at 1.55 μm wavelength of a bistable device realised by wafer fusion of an InGaAsP InP heterostructure on an AlAs GaAs Bragg mirror. A sub-milliwatt threshold power and a switching contrast up to 70 : 1 have been obtained. The bistable behaviour has been observed over more than a 2.5 nm range. The carrier-induced dispersive nonlinearity of the InGaAsP active layer has been investigated, including the saturation behaviour of the nonlinear index change. A saturating value δn s = −3.1 × 10 −2 has been obtained at the wavelength corresponding to a linear absorption of 134 cm −1. The nonlinear refractive index cross-section is found in good agreement with a two-band absorption saturation model. Similarly, the switching thresholds are well described by a simple plane-wave model including nonlinear index saturation.

Spatio-temporal dynamics of multi-stripe semiconductor lasers with delayed optical feedback

We report on the first analysis of the influence of delayed optical feedback on the spatio-temporal dynamics of spatially extended semiconductor laser devices. We start our investigation with the single-stripe laser, where we discuss analogies and differences to common plane-wave models. In the case of the twin-stripe laser, we find that, depending on parameter values, delayed optical feedback may on the one hand cause spatio-temporal instabilities leading to spatio-temporal chaos, and on the other hand induce coherent regimes in an originally chaotic state.

Transverse Effects on Squeezing with Atoms

We evaluate the squeezing of a probe beam with a transverse Gaussian structure interacting with an ensemble of two-level atoms in a cavity. We use the linear input-output formalism where the effect of atoms is described by susceptibility and noise functions, and show that the transverse structure is accounted for by averaging these atomic functions over the intensity profile. The results of the plane-wave and Gaussian-wave theories are compared. We find that, when a large squeezing is predicted, the prediction of the plane-wave model is not reliable outside the Kerr domain. We give an estimate of the squeezing degradation due to the Gaussian transverse structure.

Determination of Acoustical Impedance of Absorbing Surfaces by Two-Microphone Transfer Function Techniques: Theoretical Models

In the first of a series of papers on the measurement of acoustical impedance of absorbing surfaces in-situ, the development of the theoretical methods for the determination of acoustic impedance by the two-microphone transfer function technique is outlined. Each method is based upon a model for propagation of sound above a plane. The impedance calculation models include an expression based on the Weyl-van der Pol equation for propagation over an impedance plane, an exact method based on specular reflection, and an approximate equation based upon specular reflection. The algorithm proposed by Vigran is also derived, and a plane wave model developed for comparison. Conditions under which the results from the different models are equivalent are discussed, along with the practical considerations in programming each model.

Optical parametric amplifiers: a discrete dynamical model of singly resonant operation leading to a novel approach to the design of systems for high-efficiency amplification

A simple plane-wave model of pulsed, singly resonant, optical-parametric-oscillator and optical-parametric-oscillator-amplifier operation leads to a description of such systems in terms of a discrete dynamical system. The theoretical limits on conversion efficiencies derivable from this model were explored. Analysis of the model for an optical parametric oscillator-amplifier (OPOA) indicates that the effect that backconversion has in limiting efficiency can be avoided if one precisely shapes the time profile of the pump pulse and combines it with an OPOA that is Q switched. For a case of type I phase matching with β-barium borate with a specific pump profile and a 65-mJ input pulse, under the assumption of small absorption, the following are demonstrated: (l) the theoretical possibility of amplification to a few joules at quantum efficiencies higher than 90% and (2) the possibility of amplification to approximately 1 J at an energy efficiency near 45% in a configuration satisfying realistic stress constraints. Pulse widths are in the nanosecond range, and spot sizes are in the millimeter range. Issues of implementation are discussed.

Identification of parametric models for ultrasonic double transmission experiments on viscoelastic plates

In this paper, an identification method is proposed for the determination of the acoustic properties of viscoelastic plates based on an immersion pulse-echo technique. A double transmission (DT) configuration is used for the experiments, which facilitates the calibration of the measurement setup. With the DT configuration, parametric models are established for the ultrasonic plane-wave propagation through a viscoelastic plate at both normal and oblique incidence. The effects of beam spreading due to the finite aperture size of the ultrasonic transducer are taken into account by introducing a diffraction correction factor into the plane-wave models. A maximum likelihood estimator, which takes into account the measurement noise on both the input and the output signals, is constructed for the estimation of the parameters of the DT models. From the estimated model parameters, the absorption and dispersion properties and velocities for both shear and longitudinal waves, as well as the density and the thickness of the plate, are obtained simultaneously. Using the estimated parameters, the prediction of the DT measurement can be made at different angles of incidence. The predicted and measured transfer functions are then compared to validate the estimates. Experiments performed on a Plexiglas plate confirm the efficiency and reliability of the method.

Derivation of the mode build-up time of tunable fiber lasers

An analytical expression for the mode build-up time of tunable fiber lasers is derived, based on a plane-wave lumped-circuit laser model and a two-level atomic system. Limiting parameters for the design of a high-speed tunable fiber laser can therefore be identified.

Study of a plane-wave final-state theory of above-threshold ionization and harmonic generation

We compare the predictions of a plane-wave final-state theory of above-threshold ionization with the results of a numerical integration of Schrodinger’s equation. Good qualitative agreement between the model and the numerical integration is observed up to laser intensities of 1014 cm−2 in three-photon ionization of the 1s state of atomic hydrogen. The plane-wave final-state model is also used to calculate the power spectrum of light radiated by the single atom in intense fields, again with good agreement between the model and the numerical integration. The results demonstrate the importance of the above-threshold ionization transitions in accurate calculations of power spectra of radiated light. When the atom is modeled with bound states alone, without the above-threshold ionization inherent in the plane-wave final state, then agreement between the model and the full numerical integration is poor.

Pump interference and optical bistability effects in a Tm, Ho:YAG microlaser

Thermally induced bistability in a Tm, Ho:YAG microlaser has been observed. Theoretical results obtained from a simple plane-wave model are found to describe adequately the experimental transmission and reflection bistability data. The effect of pump interference on the single-mode operation of the laser is discussed.

Azimuth and slowness deviations from the GERESS regional array

Abstract For high signal-to-noise ratio events, body-wave travel times at GERESS stations are well fit by a plane-wave model corresponding to travel time uncertainties of about 1/100 sec. Slownesses obtained in this study are accurate to about 0.5 sec/deg, while azimuth uncertainties are about 2° for regional events and about 5° for teleseismic nuclear events. For illustration, we demonstrate performance for Nevada and Tuamotu nuclear tests and for regional events from Poland. Unbiased measurement requires array topography (about 200 m for GERESS) to be taken into account. If ignored, these elevation variations give rise to a systematic shift of about 0.6 sec/deg to eastern directions, which is almost independent of source location. In principle, arrays extending in vertical direction (“3D array”) can measure the vertical slowness and hence local material velocity c. For GERESS, we find c ≈ 5.2 km/sec. Compared with given accuracies, the regional GERESS array finds statistically significant deviations of slownesses and azimuths. These may be used to investigate lateral heterogeneity at regional scale.