Combined Effects Of Diffraction Research Articles

Statistics of acoustic waves propagating through turbulent media

Propagation of acoustic waves through atmospheric turbulence is relevant to different problems : outdoor sound propagation, blast waves generated from explosions or gunshots, propagation of sonic booms. While propagating in turbulent air, acoustic waves are distorted by the combined effects of diffraction and scattering induced by atmospheric inhomogeneities. Accurately controlled experiments are needed to validate theoretical models for sound propagation in inhomogeneous media. In this paper, probability distribution functions will be presented for linear and nonlinear acoustic wave propagation through thermal or kinematic turbulence. Experimental data will be compared with numerical simulation using parabolic approaches. [Work supported by the Labex CeLyA of Universite de Lyon, operated by the French National Research Agency (ANR-10-LABX-0060/ ANR-11- IDEX-0007).]Propagation of acoustic waves through atmospheric turbulence is relevant to different problems : outdoor sound propagation, blast waves generated from explosions or gunshots, propagation of sonic booms. While propagating in turbulent air, acoustic waves are distorted by the combined effects of diffraction and scattering induced by atmospheric inhomogeneities. Accurately controlled experiments are needed to validate theoretical models for sound propagation in inhomogeneous media. In this paper, probability distribution functions will be presented for linear and nonlinear acoustic wave propagation through thermal or kinematic turbulence. Experimental data will be compared with numerical simulation using parabolic approaches. [Work supported by the Labex CeLyA of Universite de Lyon, operated by the French National Research Agency (ANR-10-LABX-0060/ ANR-11- IDEX-0007).]

Fluid-enhanced tunable diffraction with an elastomeric grating

We replicate a diffraction grating by soft lithography. Tunable diffraction is accomplished by modifying groove spacing through the application of strain on the elastomeric replica. The range of strain-variable diffraction angles is extended by adding a refracting liquid layer to the grating. Using a water layer, the diffraction angle is tuned from 38 to 33.4 deg with an applied strain of 17.7%. With an equal amount of strain, employing a glycerol layer results in the diffraction angle varying from 38.8 to 34.4 deg. Our experimental results are accurately described by the combined effects of diffraction by a deformable grating and refraction by a fluid with a curved surface.

Low-frequency pulse propagation over irregular terrain

The shape of a low-frequency pulse that propagates to the far side of a hill depends primarily on two physical mechanisms: a diffracted wave and a surface wave. Both of these mechanisms depend on frequency, so that the pulse shape and frequency spectrum of the received pulse differ significantly from those near the source. As is well known, diffraction acts like a low-pass filter. The surface wave has a more complicated frequency dependence that depends on the terrain, the frequency dependence of the ground impedance, and the near-ground sound speed profile. For a given range, these parameters determine a frequency band that contains most of the surface wave energy. The surface wave thus functions as a low-frequency bandpass filter. The combined effects of diffraction and surface wave propagation on pulse propagation over a hill are studied using a parabolic equation model and a piecewise linear mapping to flatten the irregular terrain. Numerical calculations are presented for selected terrain features, ground impedances, and sound speed profiles. [Research supported by the U.S. Army Armament, Research Development and Engineering Center (ARDEC).]

Singular Optics: Optical Vortex Streets

S ingular light beams that contain topological wave-front dislocations are ubiquitous in optics.1 Screw dislocations, or vortices, are a common type of dislocation. They are dark holes nested in light beams that feature a helical phase ramp around a core where the light intensity vanishes. The phase of the field changes by 2 m (m being the topological charge of the vortex) along any closed loop around the vortex core. Vortices abound in nature and thus appear spontaneously in many optical settings, including speckle fields, optical cavities and doughnut laser modes. They can also be readily generated, e.g., with phase masks, and nested in host beams. Light beams with nested vortices have widespread, far-reaching applications in fields as diverse as the biosciences, laser cooling and trapping, micromechanics and quantum information. Since the number and location of the vortices existing in a light beam at different observation planes are dictated by the evolution of the host beam, parametric mixing of waves opens the door to a variety of new phenomena. Because of the parametric interaction, the waves exchange not only energy with each other but also nonlinear phase shifts, thus wave fronts. For this reason, new vortices and vortex trajectories are created in the new fields that are generated. Charge-doubling in second-harmonic generation schemes, and arithmetic charge operations in threewave processes, have been observed with wide beams. However, the combined effects of diffraction and Poynting vector walk-off introduce a new range of possibilities, including the spontaneous nucleation of multiple vortex twins whose subsequent explosion under appropriate conditions yields quasi-aligned patterns of single-charge vortices, or vortex streets.2,3 We recently reported what is believed to be the first experimental observation of such phenomena.4 The experiments were conducted in a 25-mm-long lithium triborate crystal cut for phase-matching for second-harmonic generation pumped at 1064 nm. In this geometry, the fundamental wave propagates as an ordinary beam, the second-harmonic wave at 532 nm propagates as an extraordinary beam, and both beams experience a moderate Poynting vector walk-off with angle = 0.4 degrees. To pump the crystal, we used 8-ns pulses from a Q-switched Nd:YAG laser. Screw-phase dislocations were nested in the pump beam by use of high-diffraction efficiency computer-generated off-axis holograms. Figure 1 illustrates a typical outcome of the observations. Vortex streets appear in a variety of natural phenomena.5 For example, in aerodynamics, periodic pressure and density fluctuations produced by so-called von Karman vortex streets are responsible for the familiar whistling of thin wires in the wind, or the whistling sound made when a thin stick is waved briskly in the air. Similarly, vortex streets generated by ocean drift currents, e.g., the Gulf Stream interacting with Cozumel Island off the Yucatan coast, have been recorded. Such vortex streets are formed by physical effects absent in our setting, where the vortices are generated by the interference of multiple walking beams. Yet our observations add to previous evidence to stress that the analogy existing between singular optics and fluid dynamics is a continuously inspiring source for the discovery of new phenomena involving light.

Vortex streets in walking parametric wave mixing

The combined effects of diffraction and Poynting vector walk-off in second-harmonic generation with pump beams that contain screw phase dislocations is addressed for what is believed to be the first time. We predict the spontaneous nucleation of multiple vortex twins whose subsequent explosion can yield quasi-aligned patterns of single-charge vortices.

Dynamics of self-focused femtosecond laser pulses in the near and far fields

We investigate the propagation of femtosecond pulses in a nonlinear, dispersive medium at powers several times greater than the critical power for self focusing. The combined effects of diffraction, normal dispersion and cubic nonlinearity lead to pulse splitting. We show that detailed theoretical description of the linear propagation of the pulse from the exit face of the nonlinear medium (near field) to the measuring device (far field) is crucial for quantitative interpretation of experimental data.

Investigations of nonlinear femtosecond pulse propagation with the inclusion of Raman, shock, and third-order phase effects

The propagation of intense femtosecond pulses in a nonlinear, dispersive bulk medium is investigated numerically in the regime where the combined effects of diffraction, normal dispersion, and cubic nonlinearity lead to pulse splitting. We present numerical solutions of a modified $(3+1)$-dimensional nonlinear Schr\"odinger equation, accounting for the Raman effect, linear and nonlinear shock terms, third-order dispersion, and initial temporal third-order phase modulation. The calculated results are found to be in good agreement with experimental measurements.

Amplitude and phase measurements of femtosecond pulse splitting in nonlinear dispersive media

Frequency-resolved optical gating is used to characterize the propagation of intense femtosecond pulses in a nonlinear, dispersive medium. The combined effects of diffraction, normal dispersion, and cubic nonlinearity lead to pulse splitting. The role of the phase of the input pulse is studied. The results are compared with the predictions of a three-dimensional nonlinear Schrödinger equation.

Saturation Effects in Optical Limiters Utilizing Thick Nonlinear Media

AbstractOptical Limiters which operate by exploiting nonlinear absorption and nonlinear refraction are most effective towards an incoming laser beam when the active material is somewhat thicker than one Rayleigh length. A variety of thick optical limiter configurations are described and modeled by appropriately integrating the formulas for thin nonlinear media with gaussian-shaped beams. The attenuating effects of linear losses are allowed for, and the approach is exact to the first order in optical power or irradiance. Irradiance-dependent and fluence-dependent absorbers are considered. For a gaussian-shaped input beam, we find that the combined effects of diffraction and nonlinear absorption produce, in the thick-medium limit, a transmitted beam which retains a gaussian-shaped profile at the far field, but which is now uniformly attenuated according to the magnitudes of the nonlinear and linear absorption parameters. This implies that the normalized transmittance is independent of the size of the receiving aperture. As the optical beam power increases the limiting behaviour saturates. We have discovered a simple saturation formula which agrees well with numerically calculated transmittances for thick irradiance-dependent absorbers within the strongly nonlinear regime. Under certain conditions this formula also describes the behaviour of refractive limiters, providing a simple and accurate technique for modeling limiters over a broad parameter range.

Ionization-induced defocusing of intense laser pulses in high-pressure gases

Two-dimensional simulation results are presented for the case of an intense ultrashort laser pulse propagating through an initially neutral high-pressure gas. The combined effects of diffraction and ionization lead to self-defocusing of the pulse, which reduces the peak intensity from its vacuum value and restricts the maximum achievable plasma density. The effects of gas pressure and focusing geometry are investigated, and the impact of defocusing on relevant experiments is discussed.

Linear and nonlinear propagation of a pulsed sound beam in a dissipative fluid

Linear and nonlinear propagation of pulsed sound beams is considered. The combined effects of diffraction, absorption, and nonlineartry are discussed within the linear and the weakly nonlinear (quasilinear) approximation of the Khokhlov‐Zabolotskaya‐Kuznetsov nonlinear parabolic equation. For the special case of a Gaussian on‐source amplitude distribution, short pulses can be followed all the way from the sound source and into the dissipative far field, both within a linear and a weakly nonlinear model. The results obtained are related to the theory of scattering of sound by sound [Berntsen et al., J. Acoust. Soc. Am. 86, 1968–1983 (1989)], and to the self‐demodulation of transient carriers [H. O. Berktay, J. Sound Vib. 2, 435–461 (1965)]. [Work supported by the Norwegian Research Council for Science and Humanities.]

Collapse of optical pulses

Under the combined effect of diffraction, anomalous dispersion, and nonlinear refraction, an optical pulse can collapse simultaneously in time and space. Such a collapse could yield short pulses with extremely large optical fields. Light bullets-pulses that propagate without change in space or time-are also possible. The condition for such a collapse and possible experiments are discussed.

Focal shifts in diffracted converging spherical waves

It is known that when a converging, monochromatic, spherical wave is diffracted at a circular aperture, the point of maximum intensity may not be at the geometric focus of the incident wave, but may be located closer to the aperture. In the present note this effect is calculated using somewhat simpler mathematical procedures than have been used in previous publications. The result is interpreted as the combined effect of diffraction and the inverse square law.

Nonlinear precession of elliptically polarized Gaussian beams

Equations describing the propagation of an elliptically polarized Gaussian beam, focused in a nonlinear medium of finite length, are derived. Allowance is made for the beam inhomogeneity, nonlinearity, diffraction, and polarization state. These equations are required for measurements of the nonlinear polarization of the medium. By using these, it is possible to explain the discrepancy between certain experimental results of measurements of the nonlinear polarizability. In particular, in the case of deep focusing of the radiation in the sample, the parameters of the polarization ellipse at the exit from the medium are identical to those at the entrance. Moreover, the combined effect of diffraction and nonlinearity amounts to nonlinear rotation of the ellipse as a whole through a certain angle which is half the conventionally used axial angle of calculated within the geometric-optics approximation. Examples are given of the use of these results to explain the scatter of the published measurements. Results are also given of original experiments to measure the nonlinear precession of elliptically polarized laser radiation and these confirm the validity of the calculations.

Transient propagation of optical beams in active media

The coherent interaction of short optical pulses with a nonlinear active resonant medium is calculated. The rigorous and self-consistent solution of the coupled nonlinear Maxwell-Bloch equations including transverse and time-dependent phase variations predicts the onset on an on-resonance self-focusing that agrees very well with a previous perturbation treatment and with recent experiments in sodium and neon. The formation of this dynamic self-action effect is elucidated as being due to the combined effects of diffraction and the inertial response of the active media. Accuracy and computational economy are achieved simultaneously by redistributing the computational grid points according to the physical requirements of the problem. Evenly spaced computational grids are related to variable grids in physical space by a range of stretching and rezoning techniques including adaptive rezoning where the coordinate transformation is determined by the actual physical solution.