A Bessel beam is a beam of electromagnetic radiation whose intensity is described by a Bessel function. A true Bessel beam is non-diffractive. This means that as it propagates, it does not diffract and spread out; this is in contrast to the usual behavior of light, which spreads out after being focussed down to a small spot. A true Bessel beam cannot be created, because it would require an infinite amount of energy.^[1] Reasonably good approximations can be made, however, and these are important in many optical applications because they exhibit little or no diffraction over a limited distance. Bessel beams are also self-healing, meaning that the beam can be partially obstructed at one point, but will re-form at a point further down the beam axis. Electromagnetic radiation can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. ... In physics, intensity is a measure of the time-averaged energy flux. ... In mathematics, Bessel functions, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are canonical solutions y(x) of Bessels differential equation: for an arbitrary real or complex number α. The most common and important special case is where α is an integer n, then α is referred to... See also list of optical topics. ...

These properties together make Bessel beams extremely useful to research in optical tweezing, as a narrow Bessel beam will maintain its required property of tight focus over a relatively long section of beam and even when partially occluded by the dielectric particles being tweezed. An optical tweezer is a scientific instrument that uses a focused laser beam to provide an attractive or repulsive force, depending on the index mismatch (typically on the order of piconewtons) to physically hold and move microscopic dielectric objects. ... A term indicating that the state of something, which is normally open, is now totally closed. ...

The mathematical function which describes a Bessel beam is a solution of Bessel's differential equation, which itself arises from separable solutions to Laplace's equation and the Helmholtz equation in cylindrical coordinates. Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... Friedrich Wilhelm Bessel (July 22, 1784 – March 17, 1846) was a German mathematician, astronomer, and systematizer of the Bessel functions (which, despite their name, were discovered by Daniel Bernoulli). ... In mathematics, Laplaces equation is a partial differential equation named after its discoverer Pierre-Simon Laplace. ... The Helmholtz equation, named for Hermann von Helmholtz, is the following elliptic partial differential equation: The Helmholtz equation often arises in the study of physical problems involving partial differential equations (PDEs) in both space and time. ...

Bessel beams are made in practice by focusing a Gaussian beam with an axicon lens. In optics, a Gaussian beam is a beam of electromagnetic radiation whose transverse electric field and intensity (irradiance) distributions are described by Gaussian functions. ... There are very few or no other articles that link to this one. ...

References

1. ^ Kishan Dholakia; David McGloin, and Vene Garcés-Chávez (2002). Optical micromanipulating using a self-reconstructing light beam. Retrieved on 2007 February 6.
   See also V. Garcés-Chávez; D. McGloin, H. Melville, W. Sibbett and K. Dholakia (2002). "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam". Nature 419. Retrieved on 2007-02-06.