Optical vortex

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Diagram of different modes, four of which are optical vortices. Columns show the helical structures, phase-front and intensity of the beams Helix oam.png
Diagram of different modes, four of which are optical vortices. Columns show the helical structures, phase-front and intensity of the beams

An optical vortex (also known as a photonic quantum vortex, screw dislocation or phase singularity) is a zero of an optical field; a point of zero intensity. The term is also used to describe a beam of light that has such a zero in it. The study of these phenomena is known as singular optics.

Contents

The concept of "optical vortices" was first described by Coullet et al. in 1989, based on solutions of the Maxwell-Bloch equations. [1] According to one review, studies in 1989-1999 mainly focused on fundamentals; studies in 1999-2009 developed many applications; and studies in 2009-2019 made a number of technological breakthroughs. [1]

Explanation

In an optical vortex, light is twisted like a corkscrew around its axis of travel. Because of the twisting, the light waves at the axis itself cancel each other out. When projected onto a flat surface, an optical vortex looks like a ring of light, with a dark hole in the center. The vortex is given a number, called the topological charge, according to how many twists the light does in one wavelength. The number is always an integer, and can be positive or negative, depending on the direction of the twist. The higher the number of the twist, the faster the light is spinning around the axis.

This spinning carries orbital angular momentum with the wave train, and will induce torque on an electric dipole. Orbital angular momentum is distinct from the more commonly encountered spin angular momentum, which produces circular polarization. [2] Orbital angular momentum of light can be observed in the orbiting motion of trapped particles. Interfering an optical vortex with a plane wave of light reveals the spiral phase as concentric spirals. The number of arms in the spiral equals the topological charge.

Optical vortices are studied by creating them in the lab in various ways. They can be generated directly in a laser, [3] [4] or a laser beam can be twisted into a vortex using any of several methods, such as computer-generated holograms, spiral-phase delay structures, or birefringent vortices in materials.

Properties

A Laguerre-Gaussian beam is an optical vortex with a line singularity along the beam axis

An optical singularity is a zero of an optical field. The phase in the field circulates around these points of zero intensity (giving rise to the name vortex). Vortices are points in 2D fields and lines in 3D fields (as they have codimension two). Integrating the phase of the field around a path enclosing a vortex yields an integer multiple of 2π. This integer is known as the topological charge, or strength, of the vortex.

A hypergeometric-Gaussian mode (HyGG) has an optical vortex in its center. The beam, which has the form

is a solution to the paraxial wave equation (see paraxial approximation, and the Fourier optics article for the actual equation) consisting of the Bessel function. Photons in a hypergeometric-Gaussian beam have an orbital angular momentum of . The integer m also gives the strength of the vortex at the beam's centre. Spin angular momentum of circularly polarized light can be converted into orbital angular momentum. [5]

Creation

Methods of creating optical vortices work by taking a plane wave or Gaussian beam and increasing the phrase of the wave at each by point , where is the orbital angular momentum of the beam and is the angle along the place transverse to the direction of light propagation. [6] Generation methods include spiral phase plates, holograms, spiral fresnel lenses, cylindrical lenses, spatial light modulators, and q-plates, as well as others. [6]

Vortices created by CGH OpticalVortices.jpg
Vortices created by CGH

Detection

An optical vortex, being fundamentally a phase structure, cannot be detected from its intensity profile alone. Furthermore, as vortex beams of the same order have roughly identical intensity profiles, they cannot be solely characterized from their intensity distributions. As a result, a wide range of interferometric techniques are employed.

An interference pattern of a vortex beam with an inclined plane wave, results in a fork-like interferogram

Applications

There are a broad variety of applications of optical vortices in diverse areas of communications and imaging.

See also

References

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