Phase Modulation Of Wave Research Articles

Nonlinear Kerr interactions between modulated waves propagating in a single-mode fiber

The interactions induced by the nonlinear refractive index in a single-mode optical fiber (Kerr effect) between a modulated wave and a carrier wave have been investigated for amplitude shift keying (ASK), frequency shift keying (FSK), and phase shift keying (PSK). The theoretical analysis, based on a time-domain solution, exploits the well-known formalism of self-phase modulation to describe the propagation of the input electric field in the fiber. The theoretical results were validated experimentally for amplitude- and phase-modulated waves with heterodyne detection techniques. These experiments mimic a coherent transmission system and allow the measurement of the spectrum of each of the waves that participate in the nonlinear interaction. >

Four-wave mixing in traveling-wave semiconductor laser amplifiers

Nondegenerate four-wave mixing (NDFWM) effects on simultaneous amplification of copropagating and counterpropagating waves with a frequency spacing of a few gigahertz in a 1.5- mu m nonresonant near traveling-wave semiconductor laser amplifier are discussed. Experimental results are in qualitative agreement with a theoretical model assuming the NDFWM process is mainly due to carrier pulsation produced by the beating of copropagating waves in the amplifier. The amplification of a phase-modulated wave is considered. Time-reversal properties of four-wave mixing are demonstrated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Use of reference beam self-feedback phase modulation in the holographic detection of debonding

The use of vibration excitation in the holographic detection of debonding flaws in film-substrate samples is described. The improvements to the technique produced by reference wave phase modulation are discussed and demonstrated.

A method of measuring the nonlinearity parameter B/A of a medium using the angle dependency of β

A new method of measuring B/A using a parametric receiving array is presented. The coefficient of nonlinearity β is treated exactly and is divided into two physically different terms. The effective value of βe (= cos θ + B/2A) is defined as the function of the crossing angle θ of two waves. The angle-dependent pattern of βe is applied to the measurements of B/A. The following two practical methods are presented: (1) using the non interacting angle θn [= cos−1(− B/2A)] and (2) using the front-back ratio of βe. The measurements were carried out using the two above methods for a gaseous medium and using (2) for water. The array lengths of the probing wave used were 90 mm and 40 kHz for gas, and 40 mm and 5 MHz for water, respectively. The phase modulation of the probing wave was observed and the angle dependency of β was detected. It was found that the estimated values of B/A showed good agreement with theoretical values and with the observed results presented by the other researchers.

Measurements of Non-Interacting Angle in the Scattering of Sound by Sound for Gases

Non-interacting angle at which the nonlinear interaction between two crossing waves does not occur is investigated. In the time domain, a new approach to derive the non-interacting angle which depends on the nonlinearity parameter of medium is presented. The exact treatment of the angle-dependent parameter for the nonlinear interaction is carried out. To measure the non-interacting angle, the phase modulation of a probing wave of 40 kHz is observed. The experimental results for gaseous medium of air, freon, or argon show good agreement with the theoretical prediction.

Experiments on the role of amplitude and phase modulations during transition to turbulence

The transition of a laminar two-dimensional wake is studied experimentally to establish the role of amplitude and phase modulations in the spectral-broadening and energy-redistribution process. Multiple instability modes fo and fi are triggered by acoustic excitation. The spectrum of the fluctuating velocity field formed by the growing and interacting instabilities shows the development of a complicated side- band structure reminiscent of amplitude- and phase-modulated waves. Digital com- plex demodulation techniques are used to obtain quantitative measurements of local instantaneous amplitude and phase modulations. Measurements of the modulation time traces, their modulation indices, the lag between phase and amplitude modula- tions, and the power spectra of the modulations are presented. Our results show that both phase and amplitude modulation play a role in the transition process. The dominant modulation frequency of both amplitude and phase is that of the difference mode fv = f1−f0 produced by the interaction of the two excited instabilities. Phase modulation becomes progressively more important as transition proceeds down- stream, and seems to play the dominant role in the spectral-broadening and energy- redistribution process. Measurements of the bicoherency spectrum indicate that sideband structures, and accompanying modulations, are produced by nonlinear interactions between the low-frequency difference mode and higher-frequency in- stability modes. Some limited measurements indicate that finite-amplitude induced nonlinear dispersion effects ω(k, a2) may provide a physical mechanism by which amplitude modulations generated by nonlinear interactions can induce simultaneous phase modulations.

Acoustic wave-front visualization by use of a Kösters prism in the optical Fresnel diffraction region

A simple method for visualizing the wave fronts of a progressive acoustic wave is explained. The Kosters prism works by folding the acoustically phase-modulated optical wave front at its bisecting semitransparent plane. The same temporal frequency components in the folded optical field can interfere with each other in space. Interference fringes spaced by half the acoustic wavelength are obtained over the observation area; the edges of the Kosters prism do not give appreciable diffraction effects. The fringe visibility attains a maximum of 0.54 at the Raman–Nath parameter v = 1.92. Theoretical predictions are fully verified experimentally. The frequency range of acoustic waves to be visualized is discussed; a high-frequency limit is almost nonexistent, but the lowest frequency is limited by the aperture size of the Kosters prism used. This aperture size must be at least four times as large as one acoustic wavelength in the propagation direction of the acoustic wave. Visualization can be made at any planes in the optical Fresnel diffraction region.

Wave modulation in a nonlinear dispersive medium

A model describing the simultaneous amplitude and phase modulation of a carrier wave propagating in a nonlinear dispersive medium is developed in terms of nonlinear wave-wave interactions between the sidebands and a low frequency wave. It is also shown that the asymmetric distribution of sidebands is determined by the wavenumber dependence of the coupling coefficient. Digital complex demodulation techniques are used to study modulated waves in a weakly ionized plasma and the experimental results support the analytical model.

Wide dynamic range phase-comparator using an analogue shift register

A new phase-comparator using bucket brigade device (BBD) is proposed. It is composed of a conventional phase-comparator with a phase shifter using BBD in the feedback path. Its dynamic range is wider than that of the conventional phase-comparator. This phase-comparator will find many applications, such as a demodulator for the widely phase-modulated wave and a component for PLL.

Coherent interaction effects in probe pulse experiments

An investigation is made of resonance absorption of picosecond pulses when time-delayed approximately collinear or exactly counterpropagating pump and probe pulses are superposed in a sample. The coherent and incoherent components of the influence of the probe beam on the absorption are calculated as a function of the delay time. In addition, the influence of phase modulation of the pump wave and emission of waves of different diffraction orders is studied.

Vibration measurement on the human ear drum in vivo

This paper describes the application of electronic speckle pattern interferometry to vibration measurements on the human ear drum in vivo. The technique makes use of a continuous wave laser, reference wave phase modulation, and videorecording of interferograms for subsequent analysis. Preliminary results, like frequency response and amplitude and phase measurements, are presented to illustrate the ability of this technique.

Electronic heterodyne recording and processing of optical holograms using phase modulated reference waves

The use of a phase-modulated reference wave for the electronic heterodyne recording and processing of a hologram is described. Heterodyne recording is used to eliminate the self-interference terms of a hologram and to create a Leith-Upatnieks hologram with coaxial object and reference waves. Phase modulation is also shown to be the foundation of a multiple-view hologram system. When combined with hologram scale transformations, heterodyne recording is the key to general optical processing. Spatial filtering is treated as an example.

Collective modes of a charge-density wave near the lock-in transition

The effects of phase modulation of a charge-density wave on its collective-mode spectrum are computed. The spectrum consists of two branches, a branch of collective modes of the discommensuration lattice and a phason branch which is continuous at the lock-in phase transition.

Elastic scattering of electrons from Ar and Kr in the second-order eikonal approximation

We report the first application of Baker's second-order eikonal approximation (SOEA) to atomic collisions and compare the predictions of SOEA with those of Glauber's first-order eikonal approximation (FOEA). The SOEA takes into account amplitude modulation, in addition to phase modulation of the incoming plane wave. In the case of elastic scattering of electrons from argon and krypton, it is found that the second-order correction term influences to a large extent the angular distribution of scattered electrons. In the intermediate-and high-energy range it is seen that the SOEA gives much better agreement than the FOEA with the staticfield calculation of Fink and Yates.

Vibration phase mapping using electronic speckle pattern interferometry

The contours of constant phases across sinusoidally vibrating objects have been mapped using reference wave phase modulation in time-average electronic speckle pattern interferometry.

Use of modulated reference wave in electronic speckle pattern interferometry

The amplitude range for vibration measurement by time-average recording in electronic speckle pattern interferometry (ESPI) has been extended by sinusoidal phase modulation of the reference wave. The technique is, in part, similar to the reference wave modulation technique known from holography. The low resolution of the ESPI system results in a greater need for an extension of the measuring range. In addition, the technique is more convenient to use combined with ESPI, because of the instantaneous presentation of interferograms by this system. The modulation technique also provides information about the vibration phase. Fringe patterns illustrating applications of this technique are presented.

Surface acoustic wave image scanning using phase modulation

Optical image scanning utilizing the phase modulation of a surface acoustic wave in a separated medium configuration of silicon on lithium niobate has been experimentally demonstrated with two similar techniques. In on e technique the long-lived silicon surface states are charged and the image is scanned by a short counterpropagating acoustic pulse. In the second technique the surface states are charged by a short acoustic pulse but the image is scanned by a short pulse of uniform optical illumination.

Self-action of powerful radio waves in the D-region of the ionosphere

Nonlinear effects in the D-layer of the ionosphere exert a significant influence on the nature of intense radio-wave propagation. In particular, self-action leads to saturation of wave intensity: when the ground transmitter has significant power, the intensity of the wave reflected from the ionosphere depends extremely little on the field of the incident wave. The self-action effect is manifested not only in nonlinear absorption but also in phase modulation of the intense wave. Below, we report results of simultaneous measurements of the amplitude and phase of powerful radio pulses reflected the lower ionosphere.

Holographic Technique for Detecting Small Amplitude Vibrations by Reference Wave Modulation

By the use of a light source of two wavelengths and by the sinusoidal phase modulation of the reference wave in recording a hologram of a vibrating object, small amplitude vibrations which are hardly observable by the normal time average method can be detected as a slight color variation against the colored background of stationary regions on the reconstructed image. Theoretical analysis of the color variation on the image is given and an experiment has been performed by using a He–Ne laser and an Ar-ion laser as light sources. The color variation is easily detectable and the colored background of stationary regions allows the shape of the object to be clearly recognized. The difference in color variation also helps to determine the phase of the object vibration.

Numerical Evaluation of Integrals with Infinite Limits and Oscillating Integrands

The numerical evaluation of slowly convergent integrals with infinite limits and regularly oscillating analytic integrands is discussed. Functions are presented that can be subtracted from the integrands to increase the rate of convergence. One of the integrals used as an example is an often-studied Fourier integral related to the power spectrum of a phase-modulated wave. It is pointed out that, when Fourier integrals whose values are known to be positive, e.g., probability densities, are evaluated by the trapezoidal rule, the values given by the trapezoidal rule are never less than the true values.