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5 Optical Power Coupling
number of modes common to both fibers M comm (if a uniform distribution of energy
over the modes is assumed). The fiber-to-fiber coupling efficiency η F is given by
η F =
M comm
M E
(5.20)
where M E is the number of modes in the emitting fiber (the fiber that launches power
into the next fiber).
The fiber-to-fiber coupling loss L F is given in terms of η F as
L F = −10 log η F
(5.21)
Drill Problem 5.6 When the number of modes M R in a receiving fiber is less
than the number of modes M E in an emitting fiber, Eq. (5.20) can be written as
η F = M R /M E . From Eq. (2.30) the number of modes in a step-index multimode
fiber is
M =
2πan 1
λ
2
(a) If two joined fibers are identical except for their radii, where a R = 0.90a E ,
show that the fiber-to-fiber coupling efficiency is η F = 0.81. (b) Show that the
coupling loss is L F = 0.92 dB.
An analytical estimate of the optical power loss at a joint between multimode
fibers is difficult to make because the loss depends on the power distribution among
the modes in the fiber. For example, consider first the case where all modes in a
fiber are equally excited, as shown in Fig. 5.7a. The emerging optical beam thus
fills the entire exit numerical aperture of this emitting fiber. Suppose now that a
second identical fiber, called the receiving fiber, is to be joined to the emitting fiber.
For the receiving fiber to accept all the optical power emitted by the first fiber, there
must be perfect mechanical alignment between the two optical waveguides, and their
geometric and waveguide characteristics must match precisely.
On the other hand, if steady-state modal equilibrium has been established in the
emitting fiber, most of the energy is concentrated in the lower-order fiber modes.
This means that the optical power is concentrated near the center of the fiber core,
as shown in Fig. 5.7b. The optical power emerging from the fiber then fills only
the equilibrium numerical aperture (see Fig. 5.4). In this case, because the input
NA of the receiving fiber is larger than the equilibrium NA of the emitting fiber,
slight mechanical misalignments of the two joined fibers and small variations in
their geometric characteristics do not contribute significantly to joint loss.
5 Optical Power Coupling
number of modes common to both fibers M comm (if a uniform distribution of energy
over the modes is assumed). The fiber-to-fiber coupling efficiency η F is given by
η F =
M comm
M E
(5.20)
where M E is the number of modes in the emitting fiber (the fiber that launches power
into the next fiber).
The fiber-to-fiber coupling loss L F is given in terms of η F as
L F = −10 log η F
(5.21)
Drill Problem 5.6 When the number of modes M R in a receiving fiber is less
than the number of modes M E in an emitting fiber, Eq. (5.20) can be written as
η F = M R /M E . From Eq. (2.30) the number of modes in a step-index multimode
fiber is
M =
2πan 1
λ
2
(a) If two joined fibers are identical except for their radii, where a R = 0.90a E ,
show that the fiber-to-fiber coupling efficiency is η F = 0.81. (b) Show that the
coupling loss is L F = 0.92 dB.
An analytical estimate of the optical power loss at a joint between multimode
fibers is difficult to make because the loss depends on the power distribution among
the modes in the fiber. For example, consider first the case where all modes in a
fiber are equally excited, as shown in Fig. 5.7a. The emerging optical beam thus
fills the entire exit numerical aperture of this emitting fiber. Suppose now that a
second identical fiber, called the receiving fiber, is to be joined to the emitting fiber.
For the receiving fiber to accept all the optical power emitted by the first fiber, there
must be perfect mechanical alignment between the two optical waveguides, and their
geometric and waveguide characteristics must match precisely.
On the other hand, if steady-state modal equilibrium has been established in the
emitting fiber, most of the energy is concentrated in the lower-order fiber modes.
This means that the optical power is concentrated near the center of the fiber core,
as shown in Fig. 5.7b. The optical power emerging from the fiber then fills only
the equilibrium numerical aperture (see Fig. 5.4). In this case, because the input
NA of the receiving fiber is larger than the equilibrium NA of the emitting fiber,
slight mechanical misalignments of the two joined fibers and small variations in
their geometric characteristics do not contribute significantly to joint loss.