Bessel beam
Encyclopedia
A Bessel beam is a field of electromagnetic, acoustic or even gravitational radiation whose amplitude is described by a Bessel function of the first kind. 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 (or sound), which spreads out after being focussed down to a small spot. 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.
As with a plane wave
a true Bessel beam cannot be created, as it is unbounded and would require an infinite amount of energy
. 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. Approximations to Bessel beams are made in practice by focusing a Gaussian beam
with an axicon
lens to generate a Bessel-Gauss beam.
The properties of Bessel beams make them extremely useful for 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. Similarly, particle manipulation with acoustical tweezers may be feasible with a Bessel beam that scatters and produces a radiation force
resulting from the exchange of acoustic momentum between the wave-field and a particle placed along its path.
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. The fundamental zero-order Bessel beam has an amplitude maximum at the origin, while a high-order Bessel beam (HOBB) has an axial phase singularity along the beam axis; the amplitude is zero there. HOBBs can be of vortex (helicoidal) or non-vortex types.
X-wave
s are special superpositions of Bessel beams which travel at constant velocity
.
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...
and spread out; this is in contrast to the usual behavior of light (or sound), which spreads out after being focussed down to a small spot. 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.
As with a plane wave
Plane wave
In the physics of wave propagation, a plane wave is a constant-frequency wave whose wavefronts are infinite parallel planes of constant peak-to-peak amplitude normal to the phase velocity vector....
a true Bessel beam cannot be created, as it is unbounded and would require an infinite amount of energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
. Reasonably good approximations can be made, however, and these are important in many optical
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...
applications because they exhibit little or no diffraction over a limited distance. Approximations to Bessel beams are made in practice by focusing a Gaussian beam
Gaussian beam
In optics, a Gaussian beam is a beam of electromagnetic radiation whose transverse electric field and intensity distributions are well approximated by Gaussian functions. Many lasers emit beams that approximate a Gaussian profile, in which case the laser is said to be operating on the fundamental...
with an axicon
Axicon
An axicon is a specialized type of lens which has a conical surface. An axicon images a point source into a line along the optic axis, or transforms a laser beam into a ring. It can be used to turn a Gaussian beam into an approximation to a Bessel beam, with greatly reduced diffraction....
lens to generate a Bessel-Gauss beam.
The properties of Bessel beams make them extremely useful for optical tweezing
Optical tweezers
Optical tweezers are scientific instruments that use a highly focused laser beam to provide an attractive or repulsive force , depending on the refractive index mismatch to physically hold and move microscopic dielectric objects...
, 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. Similarly, particle manipulation with acoustical tweezers may be feasible with a Bessel beam that scatters and produces a radiation force
Radiation pressure
Radiation pressure is the pressure exerted upon any surface exposed to electromagnetic radiation. If absorbed, the pressure is the power flux density divided by the speed of light...
resulting from the exchange of acoustic momentum between the wave-field and a particle placed along its path.
The mathematical
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
function which describes a Bessel beam is a solution of Bessel's differential equation, which itself arises from separable solutions to Laplace's equation
Laplace's equation
In mathematics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace who first studied its properties. This is often written as:where ∆ = ∇² is the Laplace operator and \varphi is a scalar function...
and the Helmholtz equation
Helmholtz equation
The Helmholtz equation, named for Hermann von Helmholtz, is the elliptic partial differential equation\nabla^2 A + k^2 A = 0where ∇2 is the Laplacian, k is the wavenumber, and A is the amplitude.-Motivation and uses:...
in cylindrical coordinates. The fundamental zero-order Bessel beam has an amplitude maximum at the origin, while a high-order Bessel beam (HOBB) has an axial phase singularity along the beam axis; the amplitude is zero there. HOBBs can be of vortex (helicoidal) or non-vortex types.
X-wave
X-wave
In physics, X-waves are localized solutions of the wave equation that travel at a constant velocity in a given direction. X-waves can be sound, electromagnetic, or gravitational waves. They are built as a non-monochromatic superposition of Bessel beams. X-waves carry infinite energy....
s are special superpositions of Bessel beams which travel at constant velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
.
External links
- New microscope captures 3D movies of living cells gizmag.com (switched Bessel beams used effectively in real-time microscopy)