Higher-order harmonics of limited diffraction Bessel beams
28 Feb 2000-Journal of the Acoustical Society of America (Acoustical Society of America)-Vol. 107, Iss: 3, pp 1212-1214
TL;DR: The result shows that the nth-order harmonic of the Bessel beam, like its fundamental component, is radially limited diffracting, and that the main beamwidth of the n fourth- order harmonic is exactly 1/n times that of the fundamental.
Abstract: We investigate theoretically the nonlinear propagation of the limited diffraction Bessel beam in nonlinear media, under the successive approximation of the KZK equation. The result shows that the nth-order harmonic of the Bessel beam, like its fundamental component, is radially limited diffracting, and that the main beamwidth of the nth-order harmonic is exactly 1/n times that of the fundamental.
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TL;DR: The extended theory of high-frame rate imaging theory is extended to include explicitly various transmission schemes such as multiple limited-diffraction array beams and steered plane waves, and shows that image resolution and contrast are increased over a large field of view.
Abstract: Fast three-dimensional (3-D) ultrasound imaging is a technical challenge. Previously, a high-frame rate (HFR) imaging theory was developed in which a pulsed plane wave was used in transmission, and limited-diffraction array beam weightings were applied to received echo signals to produce a spatial Fourier transform of object function for 3-D image reconstruction. In this paper, the theory is extended to include explicitly various transmission schemes such as multiple limited-diffraction array beams and steered plane waves. A relationship between the limited-diffraction array beam weighting of received echo signals and a 2-D Fourier transform of the same signals over a transducer aperture is established. To verify the extended theory, computer simulations, in vitro experiments on phantoms, and in vivo experiments on the human kidney and heart were performed. Results show that image resolution and contrast are increased over a large field of view as more and more limited-diffraction array beams with different parameters or plane waves steered at different angles are used in transmissions. Thus, the method provides a continuous compromise between image quality and image frame rate that is inversely proportional to the number of transmissions used to obtain a single frame of image. From both simulations and experiments, the extended theory holds a great promise for future HFR 3-D imaging
181 citations
TL;DR: Filamentation of Bessel-Gauss pulses propagating in borosilicate glass is found to produce damage lines extending over hundreds of micrometers and consisting of discrete, equidistant damage spots that are potentially applicable in laser microfabrication of transparent materials.
Abstract: Filamentation of Bessel-Gauss pulses propagating in borosilicate glass is found to produce damage lines extending over hundreds of micrometers and consisting of discrete, equidistant damage spots. These discrete damage traces are explained by self-regeneration of Gauss-Bessel beams during propagation and are potentially applicable in laser microfabrication of transparent materials.
73 citations
TL;DR: This work experimentally, numerically and theoretically report acoustic truncated Bessel beams of flat-intensity along their axis in the ultrasound regime using phase-only holograms, which may have potential applications in ultrasonic imaging, biomedical ultrasound and particle manipulation applications using passive lenses.
Abstract: We report zero-th and high-order acoustic Bessel beams with broad depth-of-field generated using acoustic holograms. While the transverse field distribution of Bessel beams generated using traditional passive methods is correctly described by a Bessel function, these methods present a common drawback: the axial distribution of the field is not constant, as required for ideal Bessel beams. In this work, we experimentally, numerically and theoretically report acoustic truncated Bessel beams of flat-intensity along their axis in the ultrasound regime using phase-only holograms. In particular, the beams present a uniform field distribution showing an elongated focal length of about 40 wavelengths, while the transverse width of the beam remains smaller than 0.7 wavelengths. The proposed acoustic holograms were compared with 3D-printed fraxicons, a blazed version of axicons. The performance of both phase-only holograms and fraxicons is studied and we found that both lenses produce Bessel beams in a wide range of frequencies. In addition, high-order Bessel beam were generated. We report first order Bessel beams that show a clear phase dislocation along their axis and a vortex with single topological charge. The proposed method may have potential applications in ultrasonic imaging, biomedical ultrasound and particle manipulation applications using passive lenses.
61 citations
TL;DR: The validity of the generalized Westervelt equation as a model equation for a Piola-Kirchoff acoustic pressure and as an equation for the acoustic pressure is discussed and it turns out that the model follows from two geometric approximations which are valid when the radius of curvature of the phase fronts is much larger than the particle displacements.
Abstract: A model equation is derived for nonlinear medical ultrasound. Unlike the existing models, which use spatial coordinates, material coordinates are used and hence a model for a heterogeneous medium is able to be derived. The equation is a generalization of the Westervelt equation, and includes the nonlinearity, relaxation, and heterogeneity of soft tissue. The validity of the generalized Westervelt equation as a model equation for a Piola–Kirchoff acoustic pressure and as an equation for the acoustic pressure is discussed. In the second case it turns out that the model follows from two geometric approximations which are valid when the radius of curvature of the phase fronts is much larger than the particle displacements. The model is exact for plane waves and includes arbitrary nonlinearity in the stress–strain relation.
38 citations
TL;DR: In this paper, the second-harmonic generation in a Bessel beam is investigated analytically, with emphasis on the effect of absorption, and it is shown that absorption has a strong influence on the far-field beam profile.
Abstract: Second-harmonic generation in a Bessel beam is investigated analytically, with emphasis on the effect of absorption. It is shown that absorption has a strong influence on the far-field beam profile. Numerical results are presented for higher harmonics and for waveform distortion in a Bessel beam that forms a shock.
15 citations
References
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Book•
01 Jan 1970
17,608 citations
TL;DR: The first experimental investigation of nondiffracting beams, with beam spots as small as a few wavelengths, can exist and propagate in free space, is reported.
Abstract: It was recently predicted that nondiffracting beams, with beam spots as small as a few wavelengths, can exist and propagate in free space. We report the first experimental investigation of these beams.
2,919 citations
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01 Jan 1964
TL;DR: A handbook of mathematical functions that is designed to provide scientific investigations with a comprehensive and self-contained summary of the mathematical functions arising in physical and engineering problems is presented in this article.
Abstract: A handbook of mathematical functions that is designed to provide scientific investigations with a comprehensive and self-contained summary of the mathematical functions that arise in physical and engineering problems.
2,918 citations
Journal Article•
2,441 citations
TL;DR: In this paper, exact nonsingular solutions of the scalar-wave equation for beams that are non-diffracting were presented, which means that the intensity pattern in a transverse plane is unaltered by propagating in free space.
Abstract: We present exact, nonsingular solutions of the scalar-wave equation for beams that are nondiffracting. This means that the intensity pattern in a transverse plane is unaltered by propagating in free space. These beams can have extremely narrow intensity profiles with effective widths as small as several wavelengths and yet possess an infinite depth of field. We further show (by using numerical simulations based on scalar diffraction theory) that physically realizable finite-aperture approximations to the exact solutions can also possess an extremely large depth of field.
2,283 citations