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## Patent Issued for Method and Apparatus for Producing Stationary Intense Wave Fields of Arbitrary Shape

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"Once a shape is chosen the method according to the present invention allows to evaluate a priori the amplitude, the phase velocity, the relative phases and the transverse and longitudinal wave numbers of each Bessel beam of the superposition, simultaneously recognizing and controlling the effect of each one of the parameters entering into play in order to obtain a total control of the longitudinal shape of the stationary wave field and by superposing high order Bessel beams even a partial control of the transverse shape of the stationary wave field.

"The method requires to fix the volume of space wherein the stationary wave field has to be confined, and the stationary field itself by means of a trigonometric series, and then to define amplitude, and the other parameters (velocity or axicon angle, and phase) of each single Bessel beams entering the mentioned superposition of Bessel beams which provides the mathematical description of the desired stationary wave field. No limitation exists relatively to the kind of the considered waves. So the method associated with this invention can be applied to any kind of waves, like electromagnetic waves, acoustic waves (including sysmic or geophysical waves, and in general mechanical waves), and also gravitational waves, and so on.

"In a particular embodiment of the method according to the present invention the method considers only the superposition of Bessel beams having the same frequency.

"Nevertheless also a superposition of Bessel beams having different frequencies within a certain frequency bandwith or a superposition of Bessel beams which pulsed can lead to a STATIONARY (intense) wave field

"Within a part of the present invention, a method for producing a source, which is suitable for generating such stationary and spatially confined wave fields, is also suggested.

"In its general definition, the mentioned method for producing a source comprises the following steps:

"providing one source for a single Bessel beam;

"generating an array of many (more than one) of the said sources of Bessel beams;

"configuring each source, of the said array of Bessel beam sources, according to amplitude, phase, longitudinal and transverse wavenumbers, and relative phase of each one of the Bessel beams of the superposition for method in order to yield the stationary wave field described above.

"As seen above, the proposed method allows designing, once predefined the desired behaviour of the field, the transducers able to produce such a field with a very high approximation (limited by the number of the said Bessel beam sources, which cannot be more than 2N+1, where N is the maximum number of Bessel beams entering the superposition considered by the present invention. Indeed, the method is applied by suitably superposing Bessel beams and particularly, but not exclusively Bessel beams of the same frequency, and calculating relative phase and amplitude and wavenumbers of each of the N Bessel beams entering the desired superposition.

"The invention provides also several embodiments of different devices and several methods applying the above-mentioned localized stationary wave fields, which are described in greater detail in the following description and in the annexed claims.

"Detailed Method for Generating a Localized Stationary Wave Field According to the Invention

"Let us start from the basic Bessel beam solution (with axial symmetry) of the wave equation:

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