8.1 Basic Optical Fiber Links
315
where B e is the 3-dB electrical bandwidth of the receiver and u(t) is the unit step
function which is 1 for t ≥ 0 and 0 for t < 0. The rise time t rx of the receiver is usually
defined as the time interval between g(t) = 0.1 and g(t) = 0.9, that is, t rx = t 10% − t 90% .
This is known as the 10-to-90 percent rise time. Thus, if B e is given in megahertz,
then by solving Eq. (8.4) the receiver front-end rise time t rx in nanoseconds is (see
Problem 8.5)
t r x =
350
B e
(8.5)
In practice, an optical fiber link seldom consists of a uniform, continuous, jointless
fiber. Instead, a transmission link nominally is formed from several concatenated
(joined in tandem) fibers that may have different dispersion characteristics. This is
especially true for dispersion-compensated links operating at 10 Gb/s and higher
(see Chap. 13). In addition, multimode fibers experience modal distributions at fiberto-fiber joints owing to misaligned joints, different core index profiles in each fiber,
and/or different degrees of mode mixing in individual fibers. Determining the fiber
rise times resulting from GVD and modal dispersion then becomes more complex
than for the case of a single uniform fiber.
By using Eq. (3.49) the fiber rise time t GVD resulting from GVD over a length L
can be approximated as
t GV D = |D|Lσ λ
(8.6)
where σ λ is the half-power spectral width of the source. The dispersion D is given by
Eq. (3.52) for a non-dispersion-shifted fiber and by Eq. (3.54) for a dispersion-shifted
fiber. Because the dispersion value generally changes from fiber section to section
in a long link, an average value should be used for D in Eq. (8.6).
The difficulty in predicting the bandwidth (and hence the modal rise time) of
a series of concatenated multimode fibers arises from the observation that the total
route bandwidth can be a function of the order in which fibers are joined. For example,
instead of randomly joining together arbitrary (but very similar) fibers, an improved
total link bandwidth can be obtained by selecting adjoining fibers with alternating
overcompensated and undercompensated refractive-index profiles to provide some
modal delay equalization. Although the ultimate concatenated fiber bandwidth can be
obtained by judiciously selecting adjoining fibers for optimum modal delay equalization, in practice this is unwieldy and time-consuming, particularly because the
initial fiber in the link appears to control the final link characteristics.
A variety of empirical expressions for modal dispersion have thus been developed
[11–13]. From practical field experience, it has been found that for modal dispersion
the bandwidth B M in a link of length L can be expressed to a reasonable approximation
by the empirical relation
B M (L) =
B 0
L q
(8.7)
315
where B e is the 3-dB electrical bandwidth of the receiver and u(t) is the unit step
function which is 1 for t ≥ 0 and 0 for t < 0. The rise time t rx of the receiver is usually
defined as the time interval between g(t) = 0.1 and g(t) = 0.9, that is, t rx = t 10% − t 90% .
This is known as the 10-to-90 percent rise time. Thus, if B e is given in megahertz,
then by solving Eq. (8.4) the receiver front-end rise time t rx in nanoseconds is (see
Problem 8.5)
t r x =
350
B e
(8.5)
In practice, an optical fiber link seldom consists of a uniform, continuous, jointless
fiber. Instead, a transmission link nominally is formed from several concatenated
(joined in tandem) fibers that may have different dispersion characteristics. This is
especially true for dispersion-compensated links operating at 10 Gb/s and higher
(see Chap. 13). In addition, multimode fibers experience modal distributions at fiberto-fiber joints owing to misaligned joints, different core index profiles in each fiber,
and/or different degrees of mode mixing in individual fibers. Determining the fiber
rise times resulting from GVD and modal dispersion then becomes more complex
than for the case of a single uniform fiber.
By using Eq. (3.49) the fiber rise time t GVD resulting from GVD over a length L
can be approximated as
t GV D = |D|Lσ λ
(8.6)
where σ λ is the half-power spectral width of the source. The dispersion D is given by
Eq. (3.52) for a non-dispersion-shifted fiber and by Eq. (3.54) for a dispersion-shifted
fiber. Because the dispersion value generally changes from fiber section to section
in a long link, an average value should be used for D in Eq. (8.6).
The difficulty in predicting the bandwidth (and hence the modal rise time) of
a series of concatenated multimode fibers arises from the observation that the total
route bandwidth can be a function of the order in which fibers are joined. For example,
instead of randomly joining together arbitrary (but very similar) fibers, an improved
total link bandwidth can be obtained by selecting adjoining fibers with alternating
overcompensated and undercompensated refractive-index profiles to provide some
modal delay equalization. Although the ultimate concatenated fiber bandwidth can be
obtained by judiciously selecting adjoining fibers for optimum modal delay equalization, in practice this is unwieldy and time-consuming, particularly because the
initial fiber in the link appears to control the final link characteristics.
A variety of empirical expressions for modal dispersion have thus been developed
[11–13]. From practical field experience, it has been found that for modal dispersion
the bandwidth B M in a link of length L can be expressed to a reasonable approximation
by the empirical relation
B M (L) =
B 0
L q
(8.7)