Optical fibers in which the refractive index varies with radius are commonly used to transport optical signals. When the diameter of the fiber is many wavelengths, we can use geometric optics. Let the refractive index be

where n₀ and α are constants, and r is radial distance from the fiber’s axis.

(a) Consider a ray that leaves the axis of the fiber along a direction that makes an angle β to the axis. Solve the ray-transport equation (7.48) to show that the radius of the ray is given by

where z measures distance along the fiber.
(b) Next consider the propagation time T for a light pulse propagating along the ray with β ≪ 1, down a long length L of fiber. Show that

and comment on the implications of this result for the use of fiber optics for communication.

Transcribed Image Text:

n=no(1-a²r²) 1/2, (7.50a)