where denotes derivative with respect to the argument i.e.,
.
The characteristic equation contains three unknowns namely . However, there are two more equations
(12b)
(12c)
So using the equations (12a), (12b) & (12c) we can find the modal propagation constant .
(h)
If is real, the mode propagates and if is imaginary the mode is evanescent.
(i)
We have to use numerical techniques to solve the characteristic equation for a given value of . We get multiple
solutions to the problem and each solution gives one mode for a given value of . So depending upon the fiber radius, different number of modes propagates inside an optical fiber.
(12a) 
. 
. However, there are two more equations 
(12b) 
(12c) 
. 
is real, the mode propagates and if 
is imaginary the mode is evanescent. 
. We get multiple 
. So depending upon the fiber radius, different number of modes propagates inside an optical fiber. 
