TABLE OF CONTENTS The time averaged Poynting vector component along the z-axis per unit area is expressed, by Eq. (1.45), as
where u z is a unit vector in the z-direction. The power carried by the optical fiber is then given by
The analytical expressions for the transmission power in each mode are described in the following.
The transmission power in the core and cladding are calculated from Eqs. (3.21) (3.23) and (3.48) as follows:
where we used the integral formula of the Bessel functions
For the calculation of Eq. (3.49), we first rewrite it in the following form:
Then we substitute the dispersion equation for the TE mode (3.19) into the recurrence relation of Bessel function J 2( u) [ n = 1 in Eq. (3.42b)]:
and we also use the recurrence relation for the modified Bessel function of the second kind to obtain the expression for J 2( u):
Putting Eq. (3.55) into (3.53) and using the dispersion Eq. (3.19) again, Eq. (3.53) is reduced to
Then the optical power carried in the core and cladding regions is
The total power carried by the TE mode is given by
The unknown constant A can be determined from Eq. (3.59) when we specify the total power flow P in optical fiber. Ratios of the power confinement ratios to the total power in each core and cladding region are expressed as
