Gradient-index (GRIN) optics is the branch of optics covering optical effects produced by a gradient of the refractive index of a material. Such gradual variation can be used to produce lenses with flat surfaces, or lenses that do not have the aberrations typical of traditional spherical lenses. Gradient-index lenses may have a refraction gradient that is spherical, axial, or radial.
In nature The lens of the eye is the most obvious example of gradient-index optics in nature. In the human eye, the refractive index of the lens varies from approximately 1.406 in the central layers down to 1.386 in less dense layers of the lens. This allows the eye to image with good resolution and low aberration at both short and long distances. Another example of gradient index optics in nature is the common mirage of a pool of water appearing on a road on a hot day. The pool is actually an image of the sky, apparently located on the road since light rays are being refracted (bent) from their normal straight path. This is due to the variation of refractive index between the hot, less dense air at the surface of the road, and the denser cool air above it. The variation in temperature (and thus density) of the air causes a gradient in its refractive index, causing it to increase with height. This index gradient causes refraction of light rays (at a shallow angle to the road) from the sky, bending them into the eye of the viewer, with their apparent location being the road's surface. The Earth's atmosphere acts as a GRIN lens, allowing observers to see the sun for a few minutes after it is actually below the horizon, and observers can also view stars that are below the horizon. This effect also allows for observation of electromagnetic signals from satellites after they have descended below the horizon, as in radio occultation measurements.
Applications The ability of GRIN lenses to have flat surfaces simplifies the mounting of the lens, which makes them useful where many very small lenses need to be mounted together, such as in photocopiers and scanners. The flat surface also allows a GRIN lens to be easily optically aligned to a fiber, to produce collimated output, making it applicable for endoscopy as well as for in vivo calcium imaging and optogenetic stimulation in brain. In imaging applications, GRIN lenses are mainly used to reduce aberrations. The design of such lenses involves detailed calculations of aberrations as well as efficient manufacture of the lenses. A number of different materials have been used for GRIN lenses including optical glasses, plastics, germanium, zinc selenide, and sodium chloride. Certain optical fibres (graded-index fibres) are made with a radially-varying refractive index profile; this design strongly reduces the modal dispersion of a multi-mode optical fiber. The radial variation in refractive index allows for a sinusoidal height distribution of rays within the fibre, preventing the rays from leaving the core. This differs from traditional optical fibres, which rely on total internal reflection, in that all modes of the GRIN fibres propagate at the same speed, allowing for a higher temporal bandwidth for the fibre. Antireflection coatings are typically effective for narrow ranges of frequency or angle of incidence. Graded-index materials are less constrained. An axial gradient lens has been used to concentrate sunlight onto solar cells, capturing as much as 90% of incident light when the sun is not at an optimal angle.
Manufacture GRIN lenses are made by several techniques:
Neutron irradiation – Boron-rich glass is bombarded with neutrons to cause a change in the boron concentration, and thus the refractive index of the lens. Chemical vapour deposition – Involving the deposition of different glass with varying refractive indexes, onto a surface to produce a cumulative refractive change. Partial polymerisation – An organic monomer is partially polymerized using ultraviolet light at varying intensities to give a refractive gradient. Ion exchange – Glass is immersed into a liquid melt with lithium ions. As a result of diffusion, sodium ions in the glass are partially exchanged with lithium ones, with a larger amount of exchange occurring at the edge. Thus the sample obtains a gradient material structure and a corresponding gradient of the refractive index. Ion stuffing – Phase separation of a specific glass causes pores to form, which can later be filled using a variety of salts or concentration of salts to give a varying gradient. Direct laser writing – While point-by-point exposing the pre-designed structure an exposure dose is varied (scanning speed, laser power, etc.). This corresponds to spatially tunable monomer-to-polymer degree-of-conversion resulting to a different refractive index. The method is applicable to free-form micro-optical elements and multi-component optics.
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