Phase Relation of Harmonics in Nonlinear Focused Ultrasound

The phase relation of harmonics in high-intensity focused ultrasound is investigated numerically and experimen- tally. The nonlinear Westervelt equation is solved to model nonlinear focused sound field by using the finite difference time domain method. Experimental waveforms are measured by a robust needle hydrophone. Then the relative phase quantity is introduced and obtained by using the zero-phase filter. The results show that the nth harmonic relative phase quantity is approximately （n - 1） π/3 at geometric center and increases along the axial direction. Moreover, the relative phase quantity decreases with the increase of source amplitude. This phase relation gives an explanation of some nonlinear phenomena such as the discrepancy of positive and negative pressure.

A monolithic distributed phase shifter based on right-handed nonlinear transmission lines at 30 GHz

The epitaxial material, device structure, and corresponding equivalent large signal circuit model of GaAs planar Schottky varactor diode are successfully developed to design and fabricate a monolithic phase shifter, which is based on right-handed nonlinear transmission lines and consists of a coplanar waveguide transmission line and periodically distributed GaAs planar Schottky varactor diode. The distributed-Schottky transmission-line-type phase shifter at a bias voltage greater than 1.5 V presents a continuous 0°–360° differential phase shift over a frequency range from 0 to 33 GHz. It is demonstrated that the minimum insertion loss is about 0.5 dB and that the return loss is less than-10 dB over the frequency band of 0–33 GHz at a reverse bias voltage less than 4.5 V. These excellent characteristics, such as broad differential phase shift, low insertion loss, and return loss, indicate that the proposed phase shifter can entirely be integrated into a phased array radar circuit.

Phased Array Beam Fields of Nonlinear Rayleigh Surface Waves

This study concerns calculation of phased array beam fields of the nonlinear Rayleigh surface waves based on the integral solutions for a nonparaxial wave equation. Since the parabolic approximation model for describing the nonlinear Rayleigh waves has certain limitations in modeling the sound beam fields of phased arrays, a more general model equation and integral forms of quasilinear solutions are introduced. Some features of steered and focused beam fields radiated from a linear phased array of the second harmonic Rayleigh wave are presented.

Nonlinear phase error analysis of equivalent thickness in a white-light spectral interferometer

A white light spectral interferometry based on a Linnik type system was established to accurately measure the thin film thickness through transparent medium.In practical work,the equivalent thickness of a beam splitter and the mismatch of the objective lens introduce nonlinear phase errors.Adding a transparent medium also increases the equivalent thickness.The simulation results showthat the equivalent thickness has a significant effect on thin film thickness measurements.Therefore,it is necessary to perform wavelength correction to provide a constant equivalent thickness for beamsplitters.In the experiments,some pieces of cover glasses as the transparent medium were added to the measured beam and then a standard thin film thickness of 1052.2±0.9 nm was tested through the transparent medium.The results demonstrate that our system has a nanometer-level accuracy for thin film thickness measurement through transparent medium with optical path compensation.

Nonlinear phase dynamics of ideal kink mode in the presence of shear flow

We investigate nonlinear phase dynamics of an ideal kink mode,induced by E×B flow.Here the phase is the cross phase(θ_(c))between perturbed stream function of velocity(f)and magnetic field(y),i.e.θ_(c)=θf−θψ.A dimensionless parameter,analogous to the R_(i)chardson number,R_(i)=16gkink w^(2)E^(2)(γkink:the normalized growth rate of the pure kink mode;wE:normalized E×B shearing rate)is defined to measure the competition between phase pinning by the current density and phase detuning by the flow shear.When R_(i)>1,θ_(c) is locked to a fixed value,corresponding to the conventional eigenmode solution.When R_(i).1,θ_(c) enters a phase slipping or oscillating state,corresponding to a nonmodal solution.The nonlinear phase dynamics method provides a more intuitive explanation of the complex dynamical behavior of the kink mode in the presence of E×B shear flow.

Use of piecewise polynomial phase modeling to compensate ionospheric phase contamination in skywave radar systems

Recognition and correction of ionospheric phase path contamination is a vital part of the global radar signal processing sequence. A number of model-based correction algorithms have been developed to deal with the radar performance degradation due to the ionospheric distortion and contamination. This paper addresses a novel parametric estimation and compensation method based on High-order Ambiguity Function (HAF) to solve the problem of phase path contamination of HF skywave radar signals. When signal-to-noise ratio and data sequence available satisfy the predefined conditions, the ionospheric phase path contamination may be modeled by a polynomial phase signal (PPS). As a new parametric tool for analyzing the PPS, HAF is introduced to estimate parameters of the polynomial-phase model and reconstruct the correction signal. Using the reconstructed correction signal, compensation can be performed before coherent integration so that the original echo spectrum can be restored. A piecewise scheme is proposed to track rapid variation of the phase contamination based on HAF method, and it can remove the Doppler spread effect caused by the ionosphere nonstationarity. Simulation and experimental results are given to demonstrate the efficiency of the proposed algorithm.

A low noise, high fidelity cross phase modulation in multi-level atomic medium

We develop a hybrid scheme of cross phase modulation based on electromagnetically induced transparency(EIT)and active Raman gain(ARG)in a multi-level atomic medium.The cross phase modulation,with low loss and without noise,is demonstrated in a room-temperature ^(85)Rb vapor.We show that a p radian nonlinear Kerr phase shift of the signal light relative to a reference light is observed when the signal light is modulated by the phase control field with the low light intensity.We also show that the linear and the third-order absorption can be eliminated via the Raman gain,and the phase noise of the signal light can be ignored when the phase control light is applied in this hybrid scheme.

Integrated Fabry–Perot interferometer based on Er/Yb co-doped fiber for all-optical phase modulation

Fast and stable phase control is essential for many applications in optics. Here, we propose an all-fiber all-optical phase modulation scheme based on a Fabry–Perot interferometer(FPI) and an Er/Yb co-doped fiber(EYDF). By using the EYDF as an F-P cavity via rational design, a phase shift with a modulation sensitivity of 0.0312π/mW is introduced to the modulator.The phase shifts in the EYDF consist of a thermal phase shift and a nonlinear phase shift with a ratio of 19:1, and the corresponding temporal responses of the modulation are 204 ms and 2.5 ms, respectively. In addition, the compact FPI is encapsulated to provide excellent stability for the modulator.

EQ^(rot)_1 Nonconforming Finite Element Method for Nonlinear Dual Phase Lagging Heat Conduction Equations

EQrot nonconforming finite element approximation to a class of nonlinear dual phase lagging heat conduction equations is discussed for semi-discrete and fully-discrete schemes. By use of a special property, that is, the consistency error of this element is of order O（h2） one order higher than its interpolation error O（h）, the superclose results of order O（h2） in broken Hi-norm are obtained. At the same time, the global superconvergence in broken Hi-norm is deduced by interpolation postprocessing technique. Moreover, the extrapolation result with order O（h4） is derived by constructing a new interpolation postprocessing operator and extrapolation scheme based on the known asymptotic expansion formulas of EQrot element. Finally, optimal error estimate is gained for a proposed fully-discrete scheme by different approaches from the previous literature.

Modeling of the nonlinear acoustic field generated from a phased array using Gaussian superposition technique

The nonlinearity has significant effect on the ultrasonic therapy using phased ar- rays. A numerical approach is developed to calculate the nonlinear sound field generated from a phased array based on the Gaussian superposition technique. The parameters of the phased array elements are first estimated from the focal parameters using the inverse matrix algorithm; Then the elements are expressed as a set of Gaussian functions; Finally, the nonlinear sound field can be calculated using the Gaussian superposition technique. In the numerical simulation, a 64~ 1 phased array is used as the transmitter. In the linear case, the difference between the results of the Gaussian superposition technique and the Fresnel integral is less than 0.5%, which verifies the feasibility of the approach. In the nonlinear case, the nonlinear fields of single-focus modes and double-focus modes are calculated. The results reveal that the nonlinear effects can improve the focusing performance, and the nonlinear effects are related with the source pressures and the excitation frequencies.

Triethylammonium picrate： An above-room-temperature phase transition material to switch quadratic nonlinear optical properties

To switch quadratic nonlinear optical（NLO） effects has become an exciting branch of the NLO material science. However, solid-state molecular crystals showing tunable and switchable NLO behaviors remain scarce. Here, we report an organic picrate-based binary molecular crystal, triethylammonium picrate（TEAP）, which undergoes an above-room-temperature phase transition at T_c=319 K, being solidly confirmed by the thermal and dielectric measurements. A large thermal hysteresis of ~7 K discloses the first-order feature for its phase transition. More strikingly, the quadratic NLO effects of TEAP can be switched in the vicinity of Tc. That is, TEAP exhibits NLO-active response of ~1.5 times as large as that of KDP below T_c（i.e., NLO-on state）, while its NLO effects totally disappear above T_c（NLO-off state）. Structure analyses disclose that the order-disorder transformations of triethylammonium cations and picrate anions collectively contribute to its phase transition, as well as switchable NLO behaviors. This work opens up a new pathway to the designing and assembling of stimuli-responsive materials.

EXISTENCE UNIQUENESS AND ASYMPTOTIC STABILITY OF PERIODIC SOLUTIONS OF A NONLINEAR EQUATION IN PHASE LOCKED TECHNOLOGY

In [1] and [2], the authors made a deep qualitative analysis of the equationwith the character of tangent detected phase and they mathematically provided atheoretical basis of why the phase looked loop has no look--losing point. However,according to many practical experts, it is rather difficult to put such a phaselooked loop into practice, though it has fine properties. W. C. Lindsey [3] made a