Optical fibers are circular dielectric wave-guides that can
transport optical energy and information. They have a central
core surrounded by a concentric cladding with slightly lower (by
≈ 1%) refractive index. Fibers are typically made of silica with
index-modifying dopants such as GeO2. A protective coating of
one or two layers of cushioning material (such as acrylate) is
used to reduce cross talk between adjacent fibers and the loss-
increasing microbending that occurs when fibers are pressed
against rough surfaces. For greater environmental protection,
fibers are commonly incorporated into cables. Typical cables
have a polyethylene sheath that encases the fiber within a
strength member such as steel or Kevlar strands. The Fiber as a
Dielectric Wave-Guide: Fiber Modes Since the core has a higher
index of refraction than the cladding, light will be confined to
the core if the angular condition for total internal reflectance
is met. The fiber geometry and composition determine the
discrete set of electromagne