Phase Modulation Of Wave Research Articles

Tides as phase-modulated waves inducing periodic groundwater flow in coastal aquifers overlaying a sloping impervious base

This paper presents procedures for analysing the interactions between tidal waves and coastal aquifers overlaying a sloping impervious bed, using Boussinesq equation and wave equation. Fourier series solutions of a linearised Boussinesq equation are presented subject to a periodic boundary condition (BC). The periodic BC is a phase-modulated periodic solution of the wave equation which has been shown to satisfactorily simulate uneven twin peaks of semi-diurnal tides as observed in a study area on the east coast of Queensland, Australia. Numerical analyses show that the Fourier series solutions of Boussinesq equation subject to periodic BCs reveal two important features of the tidal waves. First, the tidal waves damp towards landward, and second, the half amplitude of the tide above the mean sea level is greater than that below it. While the first feature is clearly expected, the second feature is physically more meaningful and important, and is confirmed by the field data.

Phase modulation of a neutron wave and diffraction of ultracold neutrons on a moving grating

We report the result of the experiment of UCN diffraction on a moving grating. The resulting spectrum is found to be discrete in good agreement with theory. This purely quantum effect may be interpret as a result of phase modulation of the neutron wave or as diffraction in time. Also, this experiment demonstrates the validity of the Galilean transformation of the neutron wave function in a new and very clear way.

Adaptive photodetectors for vibration monitoring

We present characteristics of laser vibrometer using semiconductor GaAs and molecular SnS2 adaptive photodetectors (AP) based on the effect of the non-steady-state photoelectromotive force. AP enable efficient direct conversion of high-frequency phase modulation of speckle-like optical wave reflected from the vibrating object into an output electrical signal with concomitant setting of optimal operation point of the interferometer and suppression of amplitude laser noise. The sensitivity of the setup is analyzed and further improvements in operation of AP are discussed.

Retrieving the Amplitude and Phase Parameters of an Ultrashort Wave Packet by Autocorrelation Methods

Based on an analysis of the signal of an interferometric intensity autocorrelator, we demonstrate theoretically and experimentally a simple technique for retrieving the temporal distributions of the amplitude and phase of an ultrashort light pulse. Assuming that a phase-modulated wave packet has a Gaussian envelope, we derive an analytical expression for the autocorrelator signal in the cases of linear- and quadratic-chirp optical pulses. The experimental and theoretical results are in excellent agreement. In particular, we show that a linear chirp (quadratic phase modulation) can be measured with a good experimental accuracy of no worse than 10%. This yields the possibility of measuring the parameter k2, which describes the dispersion characteristics of a medium in the second order of the dispersion theory, with the same accuracy. Measuring a quadratic chirp by the proposed method is possible only if such a chirp is sufficiently large.

Diffraction effects in the parametric interaction of acoustic waves: application to measurements of the nonlinearity parameter B/A in liquids.

This paper deals with diffraction effects related to the determination of nonlinearity parameters B/A in liquids using the parametric interaction. A diffraction model, based on plane wave expansions, is applied to weak nonlinear interactions between two ultrasonic waves propagating in an absorbing medium. A validation of the model has been carried out with an experiment performed using an optical interferometer. A method is proposed to measure nonlinearity parameters with the parametric interaction of two waves with a high frequency ratio. With respect to diffraction effects, the parametric interaction can then be identified with a phase modulation of the high frequency wave. A prototype, using the interaction of a 30-MHz frequency continuous wave with an acoustic pulse of central frequency 2.5 MHz, has been designed. The proposed method is validated by nonlinearity parameters measurements in well-known liquids (water and ethanol). The uncertainty on absolute measurements is discussed, and a relative method is proposed to increase the accuracy. This method enables measurements without any transducer calibration.

Resolution enhanced proximity printing by phase andamplitude modulating masks

Photolithography based on proximity printing offers a highthroughput and cost effective patterning technology for production of, forinstance, large area liquid crystal displays. The resolution of thistechnique is limited due to wave-optical effects in the proximity gapbetween the binary amplitude mask and the substrate. We can improve theresolution drastically by replacing the conventional photomask with a maskcausing both amplitude and phase modulation of the illumination wave. Wedescribe a wave-optical design procedure for such masks. The feasibilityof the method is demonstrated by results from computer simulations andpractical experiments. We show that, for a 50 µm gap, a 3 µmline/space pattern is resolved clearly for visible light illumination,whereas under conventional conditions the image is completely degraded.The proximity mask used in our experiments was fabricated by e-beamlithography with four height levels and two amplitude transmissionvalues.

Focusing of nonlinear wave groups in deep water

The freak wave phenomenon in the ocean is explained by the nonlinear dynamics of phase-modulated wave trains. It is shown that the preliminary quadratic phase modulation of wave packets leads to a significant amplification of the usual modulation (Benjamin-Feir) instability. Physically, the phase modulation of water waves may be due to a variable wind in storm areas. The well-known breather solutions of the cubic Schrodinger equation appear on the final stage of the nonlinear dynamics of wave packets when the phase modulation becomes more uniform.

Limitation of the frequency stability by local oscillator phase noise: new investigations and natural improvements

In frequency standards in which the atoms have a continuous interaction with the probe signal, local oscillator phase noise may limit medium term frequency stability. This spurious effect cannot be suppressed whenever there Is any truncation in the spectrum of the resonator response. Nevertheless, a simultaneous processing of the probe signal, similar to that of the NIST, and of the resonator response (by means of an appropriate demodulation) makes it possible to reduce this limiting effect. Previously achieved with a square wave frequency modulation, this result is now extended to various frequency modulations. An uncontrolled distortion in the demodulation waveform may significantly degrade the performance. For the case of a square wave phase modulation, the limiting effect also exists, but it is smaller than for a frequency modulation. When the phase noise of the local oscillator is naturally "not flat", it is possible to easily reduce the spurious effect: using the quasi-static approximation, one can calculate various optimized demodulation waveforms and the corresponding improvements. For the simplest optimized demodulation (f (M), 3f(M)), theoretical predictions are experimentally confirmed for flicker phase noise and flicker frequency noise.

Magnetic resonance investigations of phase transitions and modulation wave motions in incommensurate solids

We measured87Rb nuclear magnetic resonance (NMR) and35Cl nuclear quadrupole resonance (NQR) Hahn spin-echo magnetization decays in the incommensurate (I) phase of Rb2ZnCl4 and, in each case, obtained a Hahn echo decay that was shorter than the Carr-Purcell-Meiboom-Gill decay and one which decayed with a time constant proportional to the cube of the echo time. From these measurements we obtained from both the87Rb NMR and35Cl NQR measurements values for the diffusion coefficients that are comparable in magnitude, a fact that strongly supports the existence of slow modulation wave diffusionlike motions in the I phase, since such motions should affect both Rb and Cl ions similarly. In addition, we used87Rb two-dimensional exchange-difference NMR to study atomic motions in the incommensurate (I) and paraelectric (P) phases to elucidate the nature of the I-P transition. We measured as a function of the mixing time the frequency shifts of the cross peaks from the main diagonal and observed a gradual increase towards an asymptotic value in the I phase but a sudden jump to the final value in the P phase. We interpreted the motions observed in the P phase as normal modes arising from simultaneous reorientations of ZnCl4 tetrahedra and corresponding Rb ions displacements between two sites. These normal modes freeze out in the I phase and change to the diffusionlike motion of the modulation wave. We also performed35Cl NQR lineshape andT 1 measurements in K2ZnCl4 and obtained conclusive evidence for the presence of a narrow 1q (singly modulated) I phase between 146 and 149 K.

Radio-frequency Stark effect modulation of single-molecule lines

Stark effect modulation experiments were performed on single-molecule lines of terrylene in crystalline matrices of n-hexadecane and naphthalene at low temperatures. Modulation frequencies in the MHz range were used. The resulting fluorescence excitation spectra are distinctly different, depending on the relationship between the modulation frequency ω m and the molecular line width Γ. For ω m⪡ Γ, the single-molecule line exhibits a smooth broadening and apparent splitting into two components, whereas for ω m⪢ Γ it develops equidistant sidebands as in the case of phase modulation of an electromagnetic wave. It is further demonstrated that Stark effect modulation in the radio-frequency regime can be used to record absorption signals of single molecules with good signal-to-noise ratio.

Phase Modulation of the Light Wave Propagating in an Optical Fiber by Acoustic Waves

The optical fiber acoustooptic phase modulator offers the advantages of small size, light weight and low diffraction and optical coupling loss. In this paper, we present the fabrication process and results of our proposed device. A ZnO thin-film bulk acoustic wave transducer was fabricated on a glass substrate which was then bonded on the optical fiber. We experimentally obtained an amplitude-modulated lightwave signal with an input of 9 V at 94 MHz with our measurement system.

Nonlinear phase shift and all-optical switching in quasi-phase-matched quadratic media

Recently it was shown that in quasi-phase-matched quadratic media the average intensities are subject to an induced Kerr effect. We analytically study the influence of this induced cubic nonlinearity on the amplitude and phase modulation of the fundamental wave and predict efficient all-optical switching.

Numerical study of microwave reflectometry in plasmas with two-dimensional turbulent fluctuations

This article describes a numerical study of the role played by two-dimensional turbulent fluctuations in microwave reflectometry—a radar technique for density measurements using the reflection of electromagnetic waves from a plasma cutoff. The results indicate that, if the amplitude of fluctuations is below a threshold which is set by the spectrum of poloidal wave numbers, the measured backward field appears to originate from a virtual location behind the reflecting layer, and to arise from the phase modulation of the probing wave, with an amplitude given by one-dimensional geometric optics. These results suggest a possible scheme for turbulence measurements in tokamaks, where the backward field is collected with a wide aperture antenna, and the virtual reflecting layer is imaged onto the plane of an array of detectors. Such a scheme should be capable of providing additional information on the nature of the short-scale turbulence observed in tokamaks, which still remains one of the unresolved issues in fusion research.

Transient Fields of a Sound Source Driven by Various Wave Shape Pulses

In recent years, linear FM wave pulses and phase modulated wave pulses have been used to improve resolution and signal to noise ratios. In this paper, we report on transient sound fields generated by a sound source which is driven by linear FM wave pulses and phase modulated wave pulses. Time varying sound pressure at a distance R from the center of a sound source is calculated, varying the angle θ from the center axis of the sound source. A new display method to represent the calculated transient sound fields is proposed. In the method, the angle θ is taken as the abscissa, the time t is taken as the ordinate, and amplitude of sound pressure is represented in color. The effectiveness of this display method is demonstrated by examining calculated results of sound fields produced by sine wave pulses and the representation of these results using the proposed method. The method allows us to observe simultaneously a time varying waveform of sound pressure at each observation point and directivity at each instant of time. Transient sound fields produced by linear FM wave pulses and phase modulated wave pulses are calculated and represented by the display method. Characteristics of these fields are discussed using the calculated and represented results.

Phase boom for an electromagnetic wave in a ferromagnet

We study the propagation of an electromagnetic wave with a high intensity in a ferromagnetic medium, in a way analogous to the mathematical theory of nonlinear geometric optics. We find that the evolution of the modulation of a quasi-monochromatic plane wave is described by a nonlinear transport equation. In the simplest case, we retrieve a result described by other models: the main nonlinear effect is a phase modulation proportional to both the time and the square of the amplitude of the wave. But the most interesting feature is that the rapidly oscillating wave generates slowly varying waves that belong to soliton propagation modes, and that the latter react on the former by a phase factor. Two regimes occur, depending whether the slowly varying waves travel slower or faster than the modulation of the rapidly oscillating wave. An analogue to the boom of a supersonic airplane can thus be observed in the phase modulation of the incident wave.

Efficient broadband sum frequency based on controlled phase-modulated input fields: theory for 351-nm ultrabroadband or ultrashort-pulse generation

A new method of efficient sum-frequency generation for broadband input fields is proposed and analyzed. It involves the mixing of controlled phase-modulated waves for phase matching over a broad bandwidth. Regardless of the form of the modulation, phase matching can be maintained over the whole pulse duration, provided that the ratio of the chirp parameters of the incident waves is correctly chosen, thereby driving highly efficient sum-frequency generation. The case of 1.05-μm frequency tripling with KDP crystals is analyzed in detail and is shown to be applicable to the efficient generation of either broadband nanosecond pulses or ultrashort and intense pulses at 351 nm.

Monitoring bending motions of piezoceramic plates with homodyne interferometer based on adaptive photodetectors

We report on simple high-sensitivity interferometric technique of detecting vibrations of piezoceramic plates using adaptive photodetectors. It enables efficient direct conversion of high-frequency phase modulation of speckle-like optical wave reflected from vibrating plate into an output electrical signal with concomitant setting of optimal operation point of the interferometer and suppression of amplitude laser noise.

Photorefractive two-wave mixing in the presence of high-speed optical phase modulation

Equations that describe the steady-state dependence of the coherent-coupling properties of photorefractively induced refractive-index gratings on high-speed periodic biphase, sinusoidal, and triangular phase modulation impressed on one of the input optical beams are found and solved for both depleted and undepleted pump conditions. The period of the phase modulation wave form was kept short compared with the grating-formation time but did not cause significant spectral broadening. The results obtained were verified with data obtained from measurements of two-wave mixing in the photorefractive material, InP:Fe.

On-line reconstruction of electron holograms

Electron-off-axis holography has proven to be a most promising tool for the collection of the complete information about amplitude and phase modulation of the complex electron image wave in one single micrograph. Then amplitude and phase can be reconstructed numerically, offering almost any wave-optical possibility for the evaluation of the electron object wave at the exit surface, including the elimination of the influence of coherent aberrations of the objective lens in the image wave. Bottle-neck of the whole two step - registration and reconstruction - procedure has long been the need for highly accurate conversion of the holograms to numerical data as well as the available computational power, since the necessary Fast Fourier Transforms are time consuming numerical operations. Modern CCD slow-scan detectors and the permanently increasing computing power speed up this process and. combined with state of the art FEG microscopy, supply the reconstructed amplitude and phase of the image wave to the microscopist on-line.

Compensation of the phase fluctuation in a transmission line by optical phase conjugation

The required conditions for a compensation of the fluctuating phase distortion in a transmission line by optical phase conjugation are analyzed, and the resulting possible transmission length is estimated. The effective compensation of the phase fluctuation is demonstrated by using a phase-modulated phase-conjugate wave generated by four-wave mixing in a semiconductor laser amplifier, and a modulation index suppression of -4 dB is achieved.