5.2 Coupling Improvement with Lensing Schemes
223
= 0.25(0.22)
2
= 0.012 = 1.2%
Thus the coupling efficiency is reduced to 25 percent compared to the case in
which the source and fiber radii are equal, that is, when η max = (NA)
2 .
5.3 Losses Between Fiber Joints
A significant factor in any fiber optic system installation is the requirement to interconnect fibers in a low-loss manner. These interconnections occur at the optical
source, at the photodetector, at intermediate points within a cable where two fibers
are joined, and at intermediate points in a link where two cables are connected. The
particular technique selected for joining the fibers depends on whether a permanent
bond or an easily demountable connection is desired. A permanent bond is generally
referred to as a splice, whereas a demountable joint is known as a connector.
Every joining technique is subject to certain conditions that can cause various
amounts of optical power loss at the joint. The loss at a particular junction or through
a component is called the insertion loss. These losses depend on parameters such as
the input power distribution to the joint, the length of the fiber between the optical
source and the joint, the geometrical and waveguide characteristics of the two fiber
ends at the joint, and the fiber end-face qualities.
The number of modes that can propagate in each fiber limits the coupling of
optical power from one fiber to another. For example, if a fiber in which 500 modes
can propagate is connected to a fiber in which only 400 modes can propagate, then,
at most, 80 percent of the optical power from the first fiber can be coupled into the
second fiber (if we assume that all modes are equally excited). For a graded-index
fiber with a core radius a and a cladding index n 2 , and with k = 2π/λ, the total
number of modes can be found from the expression [6]
M = k
2
a
0
n
2
(r ) − n
2
2
r dr
(5.18)
where n(r) defines the variation in the refractive-index profile of the core. This can
be related to a general local numerical aperture NA(r) through Eq. (2.40) to yield
M = k
2
a
0
N A(r )
2 r dr = k
2 N A(0)
2
a
0
1 −
r
a
α
r dr
(5.19)
In general, any two fibers that are to be joined will have varying degrees of
differences in their radii a, axial numerical apertures NA(0), and index profiles α.
Thus the fraction of energy coupled from one fiber to another is proportional to the
223
= 0.25(0.22)
2
= 0.012 = 1.2%
Thus the coupling efficiency is reduced to 25 percent compared to the case in
which the source and fiber radii are equal, that is, when η max = (NA)
2 .
5.3 Losses Between Fiber Joints
A significant factor in any fiber optic system installation is the requirement to interconnect fibers in a low-loss manner. These interconnections occur at the optical
source, at the photodetector, at intermediate points within a cable where two fibers
are joined, and at intermediate points in a link where two cables are connected. The
particular technique selected for joining the fibers depends on whether a permanent
bond or an easily demountable connection is desired. A permanent bond is generally
referred to as a splice, whereas a demountable joint is known as a connector.
Every joining technique is subject to certain conditions that can cause various
amounts of optical power loss at the joint. The loss at a particular junction or through
a component is called the insertion loss. These losses depend on parameters such as
the input power distribution to the joint, the length of the fiber between the optical
source and the joint, the geometrical and waveguide characteristics of the two fiber
ends at the joint, and the fiber end-face qualities.
The number of modes that can propagate in each fiber limits the coupling of
optical power from one fiber to another. For example, if a fiber in which 500 modes
can propagate is connected to a fiber in which only 400 modes can propagate, then,
at most, 80 percent of the optical power from the first fiber can be coupled into the
second fiber (if we assume that all modes are equally excited). For a graded-index
fiber with a core radius a and a cladding index n 2 , and with k = 2π/λ, the total
number of modes can be found from the expression [6]
M = k
2
a
0
n
2
(r ) − n
2
2
r dr
(5.18)
where n(r) defines the variation in the refractive-index profile of the core. This can
be related to a general local numerical aperture NA(r) through Eq. (2.40) to yield
M = k
2
a
0
N A(r )
2 r dr = k
2 N A(0)
2
a
0
1 −
r
a
α
r dr
(5.19)
In general, any two fibers that are to be joined will have varying degrees of
differences in their radii a, axial numerical apertures NA(0), and index profiles α.
Thus the fraction of energy coupled from one fiber to another is proportional to the