As shown in Figure 1, the core of the optical fiber is a cylinder of radius , and of refractive index . The refractive index
of cladding is and the cladding is of infinite radius.
2.
The appropriate coordinate system to analyze this problem is the cylindrical coordinate system, . The wave
propagates in the direction and the fields have definite distributions in the cross sectional plane, defined by . Any radial direction from the center of the fiber is denoted by and the azimuthal angle measured from a reference axis (x-axis) in the cross-sectional plane is denoted by .
3.
To investigate an electromagnetic problem we start with the Maxwell's equations. Here we investigate the propagation of
light in the fiber without worrying about the origin of the light inside the fiber. In other words we assume that the Maxwell's equations which govern the electromagnetic radiations inside the fiber are source free .
4.
Maxwell's equations for a source-free medium (i.e., the charge density and the conduction current densities in the
medium are zero):
(a)
(1)
(b)
(2)
(c)
(3)
(d)
(4)
where is the electric displacement vector, B is the magnetic flux density, E is the electric field, and H is the magnetic field intensity.
We have two more equations, called the constitutive relations, as
where is the permeability of the medium and is the permittivity of the medium.
, and of refractive index 
. The refractive index 
and the cladding is of infinite radius. 
. The wave
direction and the fields have definite distributions in the cross sectional plane, defined by 
. Any radial direction from the center of the fiber is denoted by 
and the azimuthal angle measured from a reference axis (x-axis) in the cross-sectional plane is denoted by 
. 
(1) 
(2) 
(3) 
(4) 
is the electric displacement vector, B is the magnetic flux density, E is the electric field, and H is the magnetic field intensity. 
is the permeability of the medium and 
is the permittivity of the medium. 
