azu_td_1349475_sip1_... - Arizona Campus Repository

Setting w (x) equal to zero and solving first for the case of a lens with no
20
aberrations, the integral in Equation 2.6 may be converted into polar
coordinates,
|
«muz 2
I exp[-{\+o 2 ) r 2 ] 2itrdr
Jo 2.8
Rmax is the maximum radius of the exit pupil as determined by h, the aperture
stop radius,
r = -hmax
®S. 2.9
To maximize coupling between the source and receiving fibers, the mode profile
of the source must match the mode profile of the receiver. Setting a equal to
one to satisfy this condition, and solving Equation 2.8 gives the coupling
efficiency between the two fibers,
T = [l-exp{-2r% iax)] 2 m 2.10
Equation 2.10 may be rewritten in terms of the NA of the source fiber and lens
NA. With the aperture stop at the lens, the lens NA is defined by
NA lens = -
h 7
R 2.11
where R' is the distance from the exit pupil plane to the image plane. For a
Gaussian mode, the NA of the source fiber defined on the receiver side of the