Specialty Optical Fibers Handbook

modes that propagate along the z axis, form a standing wave along the x axis in

region 1, and decay exponentially in region 2. The same result can be obtained by

solving the wave equation over the regions and matching boundary conditions at

the interfaces. The guided mode is said to be cutoff when u

1

 u

c

, where k

2

is real

and b  n

2

k

0

. An unguided wave below cutoff that nevertheless meets the

transverse resonance conditions is sometimes known as a ‘‘leaky wave.’’

2.3.3 Optical Fiber: A Cylindrical Waveguide

The ray optics analysis for a cylindrical waveguide such as an optical fiber is

complicated by the existence of skew rays in three dimensions, which propagate

helically and do not cross the fiber axis. Here, we outline the solution of the field