Where are arbitrary constants which are to be evaluated from the boundary conditions.
(d)
Once we get the longitudinal components of the electric and magnetic fields, we can find the transverse field
components inside the core and the cladding way the relations given above.
Applying the boundary conditions i.e., the tangential components of electric field and the tangential components of magnetic field are continuous along the core cladding boundary, we get what is called the characteristic equation of the mode.
(e)
The tangential components at the core cladding boundary are the and the components.
The boundary conditions are then given as:
At ,
1.
2.
3.
4.
The boundary conditions give four equations in terms of arbitrary constants, and the modal phase constant, .
(f)
We find the equation for the propagation constant, of the wave, by eliminating the arbitrary constants. Elimination of
the arbitrary constants gives the characteristic equation of mode inside an optical fiber as
are arbitrary constants which are to be evaluated from the boundary conditions. 
and the 
components. 
, 
and the modal phase constant, 
. 
of the wave, by eliminating the arbitrary constants. Elimination of 
