Parabolicindex

Parabolicindex refers to a refractive-index distribution in gradient-index optics that varies parabolically with the radial distance from the optical axis. A medium with a parabolic index focuses or collimates light without curved external surfaces, relying on internal refractive gradient to bend rays.

Mathematical form: n(r) = n0 - (1/2) g r^2, where r is radial distance, n0 is the on-axis index, and g is the gradient coefficient. In the paraxial approximation, light rays behave like harmonic oscillators, yielding a characteristic focusing length L related to the gradient and on-axis index. The precise behavior depends on the sign and magnitude of g, which determine whether the medium acts as a focusing or defocusing element.

Manufacture and properties: Parabolicindex media are a common type of gradient-index (GRIN) material used in lenses and waveguides. They can reduce optical aberrations compared with conventional surface-shaped lenses and enable compact form factors with smooth axial variation. Fabrication methods include diffusion processes in glass or polymerization techniques in polymers, often requiring careful control of temperature, diffusion rates, and material composition to achieve the desired index profile.

Applications: GRIN lenses and related components built with parabolic index profiles are used in imaging systems, endoscopes, optical communications, and laser beam shaping. Their ability to manipulate light within a compact volume makes them valuable in integrated optics and miniaturized optical assemblies. See also gradient-index optics and parabolic reflector systems for related concepts.