Method and apparatus for producing stationary intense wave fields of arbitrary shape

A device comprising one or more of electromagnetic, optical, or acoustic tweezers comprising:

• a source configured to generate a stationary wave field at one or more predetermined spots in space, the source comprising:
• an array of Bessel or other beam sources having a high transverse confinement, each of the sources of the array being devoted to generation of a Bessel beam or other beam having different parameters of amplitude, phase, and longitudinal and transversal wavenumber;
• and
• a system driving each of the sources of the array to generate the Bessel beam having frequency identical or different to the one of the Bessel beams generated by the other sources of the array,
• wherein the stationary wave field is generated according to a method comprising the following steps:
• a) defining at least a volume limited in the direction of an axis z of propagation of a beam, the volume being a longitudinal interval having 0≦z≦L, where z is a longitudinal position and L is a length of a longitudinal interval;
• b) defining a priori within the longitudinal interval an intensity pattern μF(z)μ2, where μ is a cylindrical coordinate and F(z) is a function, describing a desired localized and stationary wave field, the function F(z) being represented by a discrete Fourier Series or by another expansion based on atrigonometric orthogonal functions;
• c) providing a discrete, generic superposition of Bessel beams or other transversally confined beams;
• d) calculating a maximum allowed number of Bessel beams to be superposed;
• e) calculating amplitudes, phase velocities, and transverse and longitudinal wavenumbers of each Bessel beam or other transversally confined beam of the superposition, needed to obtain a predefined STATIONARY intensity pattern within the longitudinal interval;
• and
• f) recognizing and controlling an effect of each of the amplitudes, phase velocities, and transverse and longitudinal wavenumbers in step e) for controlling a longitudinal shape of the stationary localized wave field.