Fiber Bundle With Graded-Index Fibers
Unlike step-index fibers, graded-index fibers can focus light in certain cases. This does not make graded-index fibers useful for image transmission or other fiber-bundle applications, but short segments of graded-index fibers can function as focusing components in some optical systems.
compare the path of a light ray in step-index fiber and graded-index fiber
When you looked at how a cone of light was transmitted through a long fiber, you saw output as a cone of the same angle. Now look instead at the path of an individual ray through a short segment of graded-index fiber, shown in figure and compare that with the path of a light ray in step-index fiber.
There is an important but subtle difference. Total internal reflection from a step-index boundary keeps light rays at the same angle to the fiber axis all along the fiber. However, graded-index fibers refract light rays, so the angle of the ray to the axis is constantly changing as the ray follows a sinusoidal path. If you cut the fiber after the light ray has gone through 180° or 360° of the sinusoid, the light emerges at the same angle to the axis that it entered. However, if the distance the light ray travels is not an integral multiple of 180° of the sinusoid, it emerges at a different angle. This property allows segments of graded index fiber to focus light.
Graded-index fiber lenses
In the design of graded-index fiber lenses (usually sold under the trade name Selfoc), the key parameter is the fraction of a full sinusoidal cycle that light goes through before emerging. That fraction is called the pitch. A 0.23-pitch lens, for instance, has gone through 0.23 parameter of of a cycle, or 0.23 X 360° = 82.8°. The value of the pitch depends on various factors including refractive-index gradient, index of the fiber, core diameter, and wavelength of light.
Although the lenses are segments of fiber, they are short by fiber-optic standards, just a few millimeters long. Thus, they can be considered as rod lenses as well as fiber lenses.
These tiny fiber lenses are used in a variety of applications. Some are used in fiber-optic transmitters to focus light from an LED or diode laser so that it can be coupled efficiently into a fiber. Others are used in optical systems such as fax machines and scanners. A linear array of fiber-optic microlenses can focus light reflected from a small area of a page onto a linear array of sensors that detect the light. Ideally each sensor collects light focused by one microlens.