In the optical regime, the property of an element (rod or slab of material) that (a) has a refractive index gradient that is a defined function of the radial distance from its optical axis, and (b) by virtue of which gradient, is capable of focusing light in a manner after that of a conventional simple lens. Note 1: For example, a self-focusing slab (i.e., a plane-parallel, usually circular) element that is analogous in function to a convex simple lens, is relatively thin with respect to its diameter. By virtue of the fact that its refractive index is at a maximum along its optical axis (which is perpendicular to the faces of the slab), and decreases radially as a function of distance from the optical axis, it is able to bring a beam of light to a focus. If the thickness of the slab is increased greatly, so that it becomes a rod having a length very many times its diameter, it is able to relay a beam or image in a cyclical fashion in much the same manner as a series of discrete conventional lenses and bring it to a final focus, e.g., at or just outside the endface of the rod. (This phenomenon should not be confused with the relaying of images by means of a spatially coherent bundle of a large number of individual optical fibers, each having a diameter of microscopic proportions, and each of which in effect relays a single pixel, and within which bundle no focusing takes place.) Note 2: Within a self-focusing element, the rays traverse curved paths, unlike the straight internal paths that characterize conventional lenses or lens elements that are made of homogeneous materials having a uniform refractive index. In a conventional single- or multi-element lens, the rays may change direction abruptly at a refractive discontinuity, such as an air-glass boundary, or the boundary between the crown and flint elements of an achromatic lens, but within each such element, the ray paths are straight. Note 3: Self-focusing elements do not produce images of a quality that may be obtained with the best conventional multi-element lenses.