Agbo, S.O., Cherin, A.H, Tariyal, B.K. “Lightwave”
The Electrical Engineering Handbook
Ed. Richard C. Dorf
Boca Raton: CRC Press LLC, 2000
42
Lightwave
42.1Lightwave Waveguides
Ray Theory?Wave Equation for Dielectric Materials?Modes in Slab
Waveguides?Fields in Cylindrical Fibers?Modes in Step-Index
Fibers?Modes in Graded-Index Fibers?Attenuation?Dispersion
and Pulse Spreading
42.2Optical Fibers and Cables
Introduction?Classification of OpticalFibers and Attractive
Features?Fiber Transmission Characteristics?Optical Fiber Cable
Manufacturing
42.1 Lightwave Waveguides
Samuel O. Agbo
Lightwave waveguides fall into two broad categories: dielectric slab waveguides and optical fibers. As illustrated
in Fig. 42.1, slab waveguides generally consist of a middle layer (the film) of refractive index n
1
and lower and
upper layers of refractive indices n
2
and n
3
, respectively.
Optical fibers are slender glass or plastic cylinders with annular cross sections. The core has a refractive
index, n
1
, which is greater than the refractive index, n
2
, of the annular region (the cladding). Light propagation
is confined to the core by total internal reflection, even when the fiber is bent into curves and loops. Optical
fibers fall into two main categories: step-index and graded-index (GRIN) fibers. For step-index fibers, the
refractive index is constant within the core. For GRIN fibers, the refractive index is a function of radius r given by
(42.1)
In Eq. (42.1), D is the relative refractive index difference, a is the core radius, and a defines the type of
graded-index profile. For triangular, parabolic, and step-index profiles, a is, respectively, 1, 2, and ￥. Figure 42.2
shows the raypaths in step-index and graded-index fibers and the cylindrical coordinate system used in the
analysis of lightwave propagation through fibers. Because rays propagating within the core in a GRIN fiber
undergo progressive refraction, the raypaths are curved (sinusoidal in the case of parabolic profile).
Ray Theory
Consider Fig 42.3, which shows possible raypaths for light coupled from air (refractive index n
0
) into the film
of a slab waveguide or the core of a step-index fiber. At each interface, the transmitted raypath is governed by
Snell’s law. As q
0
(the acceptance angle from air into the waveguide) decreases, the angle of incidence q
i
increases
nr
n
r
a
ra
nnar
()
;
();
=
-
?
è
?
?
?
÷
é
?
ê
ê
ù
?
ú
ú
<
-=<
ì
í
?
?
?
?
?
1
12
1
12
2
12
12
D
D
a
/
/
Samuel O. Agbo
California Polytechnic State
University
Allen H. Cherin
Lucent Technologies
Basant K. Tariyal
Lucent Technologies
? 2000 by CRC Press LLC
until it equals the critical angle, q
c
, making q
0
equal to the maximum acceptance angle, q
a
. According to ray
theory, all rays with acceptance angles less than q
a
propagate in the waveguide by total internal reflections.
Hence, the numerical aperture (NA) for the waveguide, a measure of its light-gathering ability, is given by
(42.2)
By Snell’s law, sin
q
c
= n
2
/n
1
. Hence,
(42.3)
For step-index fibers, the preceding analysis applies to meridional rays. Skew (nonmeridional) rays have
larger maximum acceptance angles, q
as
, given by
(42.4)
FIGURE 42.1 Dielectric slab waveguide: (a) the Cartesian coordinates used in analysis of slab waveguides; (b) the slab
waveguide; (c) light guiding in a slab waveguide.
FIGURE 42.2 The optical fiber: (a) the cylindrical coordinate system used in analysis of optical fibers; (b) some graded-
index profiles; (c) raypaths in step-index fiber; (d) raypaths in graded-index fiber.
NA n a n
c
==-
?
è
?
?
?
÷
01
2
sin sinq
p
q
NA n n=-
[]1
2
2
2
12/
sin
cos
q
g
as
NA
=
? 2000 by CRC Press LLC
where NA is the numerical aperture for meridional rays and g is the angle between the core radius and the
projection of the ray onto a plane normal to the fiber axis.
Wave Equation for Dielectric Materials
Only certain discrete angles, instead of all acceptance angles less than the maximum acceptance angle, lead to
guided propagation in lightwave waveguides. Hence, ray theory is inadequate, and wave theory is necessary,
for analysis of light propagation in optical waveguides.
For lightwave propagation in an unbounded dielectric medium, the assumption of a linear, homogeneous,
charge-free, and nonconducting medium is appropriate. Assuming also sinusoidal time dependence of the
fields, the applicable Maxwell’s equations are
? 2 E = –jwmH (42.5a)
? 2 H = jweE (42.5b)
? 2 E = 0 (42.5c)
? 2 H = 0 (42.5d)
The resulting wave equations are
?
2
E – g
2
E = 0 (42.6a)
?
2
H – g
2
H = 0 (42.6b)
where
g
2
= w
2
me = (jk)
2
(42.7)
and
(42.8)
In Eq. (42.8) k is the phase propagation constant and n is the refractive index for the medium, while k
0
is
the phase propagation constant for free space. The velocity of propagation in the medium is n = 1 / .
FIGURE 42.3 Possible raypaths for light coupled from air into a slab waveguide or a step-index fiber.
kkwm
w
n
== =n
0
e
me
? 2000 by CRC Press LLC
Modes in Slab Waveguides
Consider a plane wave polarized in the y direction and propagating in z direction in an unbounded dielectric
medium in the Cartesian coordinates. The vector wave equations (42.6) lead to the scalar equations:
(42.9a)
(42.9b)
The solutions are
E
y
= Ae
j (w t – kz)
(42.10a)
(42.10b)
where A is a constant and h = is the intrinsic impedance of the medium.
Because the film is bounded by the upper and lower layers, the rays follow the zigzag paths as shown in
Fig. 42.3. The upward and downward traveling waves interfere to create a standing wave pattern. Within the film,
the fields transverse to the z axis, which have even and odd symmetry about the x axis, are given, respectively, by
E
y
= A cos(hy) e
j(w t – b z)
(42.11a)
E
y
= A sin(hy) e
j(w t – b z)
(42.11b)
where b
and h are the components of k parallel to and normal to the z axis, respectively. The fields in the upper
and lower layers are evanescent fields decaying rapidly with attenuation factors a
3
and a
2
, respectively, and are
given by
(42.12a)
(42.12b)
Only waves with raypaths for which the total phase change for a complete (up and down) zigzag path is an
integral multiple of 2p undergo constructive interference, resulting in guided modes. Waves with raypaths not
satisfying this mode condition interfere destructively and die out rapidly. In terms of a raypath with an angle
of incidence q
i
= q in Fig. 42.3, the mode conditions [Haus, 1984] for fields transverse to the z axis and with
even and odd symmetry about the x axis are given, respectively, by
(42.13a)
(42.13b)
?
?
?
2
2
0
E
z
E
y
y
-=
?
?
?
2
2
0
H
z
H
x
x
-=
H
E
A
e
x
y jt z
=
-
=
-
hh
wk()
me
EAe e
y
jt z
y
d
=
-
-
?
è
?
?
?
÷
-
3
3
2
a
wb()
EAe e
y
jt z
y
d
=
- +
?
è
?
?
?
÷
-
2
2
2
a
wb()
tan
cos
sin
hd
n
nn
2
1
1
1
22
2
2
12
?
è
?
?
?
÷
=-
[]
q
q
/
tan
cos
sin
hd
n
nn
22
1
1
1
22
2
2
12
-
?
è
?
?
?
÷
=-
[]
p
q
q
/
? 2000 by CRC Press LLC
where h = k cos q = (2pn
1
/l) cos q and l is the free space wavelength.
Equations (42.13a) and (42.13b) are transcendental, have multiple solutions, and are better solved graphically.
Let (d/l)
0
denote the smallest value of d/l, the film thickness normalized with respect to the wavelength,
satisfying Eqs. (42.13a) and (42.13b). Other solutions for both even and odd modes are given by
(42.14)
where m is a nonnegative integer denoting the order of the mode.
Figure 42.4 [Palais, 1992] shows a mode chart for a symmetrical slab waveguide obtained by solving
Eqs. (42.13a) and (42.13b). For the TE
m
modes, the E field is transverse to the direction (z) of propagation,
while the H field lies in a plane parallel to the z axis. For the TM
m
modes, the reverse is the case. The highest-
order mode that can propagate has a value m given by the integer part of
(42.15)
To obtain a single-mode waveguide, d/l should be
smaller than the value required for m = 1, so that only the
m = 0 mode is supported. To obtain a multimode
waveguide, d/l should be large enough to support many
modes.
Shown in Fig. 42.5 are transverse mode patterns for the
electric field in a symmetrical slab waveguide. These are
graphical illustrations of the fields given by Eqs. (42.11)
and (42.12). Note that, for TE
m
, the field has m zeros in
the film, and the evanescent field penetrates more deeply
into the upper and lower layers for high-order modes.
For asymmetric slab waveguides, the equations and their
solutions are more complex than those for symmetric slab waveguides. Shown in Fig. 42.6 [Palais, 1992] is the
mode chart for the asymmetric slab waveguide. Note that the TE
m
and TM
m
modes in this case have different
FIGURE 42.4Mode chart for the symmetric slab waveguide with n
1
= 3.6, n
2
= 3.55.
ddm
n
m
ll q
?
è
?
?
?
÷
=
?
è
?
?
?
÷
+
0
1
2 cos
m
d
nn=-
[]
2
1
2
2
2
12
l
/
FIGURE 42.5Transverse mode field patterns in the
symmetric slab waveguide.
? 2000 by CRC Press LLC
propagation constants and do not overlap. By contrast, for the symmetric case, TE
m
and TM
m
modes are
degenerate, having the same propagation constant and forming effectively one mode for each value of m.
Figure 42.7 shows typical mode patterns in the asymmetric
slab waveguide. Note that the asymmetry causes the evanes-
cent fields to have unequal amplitudes at the two boundaries
and to decay at different rates in the two outer layers.
The preceding analysis of slab waveguides is in many ways
similar to, and constitutes a good introduction to, the more
complex analysis of cylindrical (optical) fibers. Unlike slab
waveguides, cylindrical waveguides are bounded in two
dimensions rather than one. Consequently, skew rays exist in
optical fibers, in addition to the meridional rays found in
slab waveguides. In addition to transverse modes similar to
those found in slab waveguides, the skew rays give rise to
hybrid modes in optical fibers.
Fields in Cylindrical Fibers
Let y represent E
z
or H
z
and b be the component of k in z direction. In the cylindrical coordinates of Fig. 42.2,
with wave propagation along the z axis, the wave equations (42.6) correspond to the scalar equation
(42.16)
The general solution to the preceding equation is
y(r) = C
1
J
l
(hr) + C
2
Y
l
(hr);k
2
> b
2
(42.17a)
y(r) = C
1
I
l
(qr) + C
2
K
l
(qr);k
2
< b
2
(42.17b)
In Eqs. (42.17) and (42.17b), J
l
and Y
l
are Bessel functions of the first kind and second kind, respectively,
of order l; I
l
and K
l
are modified Bessel functions of the first kind and second kind, respectively, of order l;
C
1
and C
2
are constants; h
2
= k
2
– b
2
and q
2
= b
2
– k
2
.
E
z
and H
z
in a fiber core are given by Eq. (42.17a) or (42.17b), depending on the sign of k
2
– b
2
. For guided
propagation in the core, this sign is negative to ensure that the field is evanescent in the cladding. One of the
FIGURE 42.6Mode chart for the asymmetric slab waveguide with n
1
= 2.29, n
2
= 1.5, and n
3
= 1.0.
FIGURE 42.7Transverse mode field patterns in the
asymmetric slab waveguide.
?y
?
?y
?
?y
?
kby
2
22
2
2
22
11
0
r
rr
r
+++-=
F
()
? 2000 by CRC Press LLC
coefficients vanishes because of asymptotic behavior of the respective Bessel functions in the core or cladding.
Thus, with A
1
and A
2
as arbitrary constants, the fields in the core and cladding are given, respectively, by
y(r) = A
1
J
l
(hr) (42.18a)
y(r) = A
2
k
l
(hr) (42.18b)
Because of the cylindrical symmetry,
y(r,t) = y(r,f)e
j(w t – b z)
(42.19)
Thus, the usual approach is to solve for E
z
and H
z
and then express E
r
, E
f
,
H
r
, and H
f
in terms of E
z
and H
z
.
Modes in Step-Index Fibers
Derivation of the exact modal field relations for optical fibers is complex. Fortunately, fibers used in optical
communication satisfy the weekly guiding approximation in which the relative index difference, ?, is much
less than unity. In this approximation, application of the requirement for continuity of transverse and tangential
electric field components at the core-cladding interface (at r = a) to Eqs. (42.18a) and (42.18b) results in the
following eigenvalue equation [Snyder, 1969]:
(42.20)
Let the normalized frequency V be defined as
(42.21)
Solving Eq. (42.20) allows b
to be calculated as a function of V. Guided modes propagating within the core
correspond to n
2
k
0
￡ b
￡ n
1
k. The normalized frequency V corresponding to b
= n
1
k is the cut-off frequency
for the mode.
As with planar waveguides, TE (E
z
= 0) and TM (H
z
= 0) modes corresponding to meridional rays exist in
the fiber. They are denoted by EH or HE modes, depending on which component, E or H, is stronger in the
plane transverse to the direction or propagation. Because the cylindrical fiber is bounded in two dimensions
rather than one, two integers, l and m, are needed to specify the modes, unlike one integer, m, required for
planar waveguides. The exact modes, TE
lm
, TM
lm
, EH
lm
, and HE
lm
, may be given by two linearly polarized
modes, LP
lm
. The subscript l is now such that LP
lm
corresponds to HE
l + 1,m
, EH
l – 1,m
, TE
l – 1,m
, and TM
l – 1,m
.
In general, there are 2l field maxima around the fiber core circumference and m field maxima along a radius
vector. Figure 42.8 illustrates the correspondence between the exact modes and the LP modes and their field
configurations for the three lowest LP modes.
Figure 42.9 gives the mode chart for step-index fiber on a plot of the refractive index, b/k
0
, against the
normalized frequency. Note that for a single-mode (LP
01
or HE
11
) fiber, V < 2.405. The number of modes
supported as a function of V is given by
(42.22)
haJ
ha
Jha
qa qa
qa
l
l
l
l
±
±
=±
1
1
()
()
()
()
k
k
Vaqh ann aNA=+= -
( )
=() ()
2212
01
2
2
2
12
2
/
/
k
p
l
N
V
=
2
2
? 2000 by CRC Press LLC
Modes in Graded-Index Fibers
A rigorous modal analysis for optical fibers based on the solution of Maxwell’s equations is possible only for
step-index fiber. For graded-index fibers, approximate methods are used. The most widely used approximation
is the WKB (Wenzel, Kramers, and Brillouin) method [Marcuse, 1982]. This method gives good modal solutions
FIGURE 42.8 Transverse electric field patterns and field intensity distributions for the three lowest LP modes in a step-
index fiber: (a) mode designations; (b) electric field patterns; (c) intensity distribution. (Source: J. M. Senior, Optical Fiber
Communications: Principles and Practice, Englewood Cliffs, N.J.: Prentice-Hall, 1985, p. 36. With permission.)
FIGURE 42.9 Mode chart for step-index fibers: b = (b /k
0
– n
2
)/(n
1
– n
2
) is the normalized propagation constant. (Source:
D. B. Keck, Fundamentals of Optical Fiber Communications, M. K. Barnoski, Ed., New York: Academic Press, 1981, p. 13.
With permission.)
? 2000 by CRC Press LLC
MINIATURE RADAR
n inexpensive miniaturized radar system developed at Lawrence Livermore National Labs
(LLNL) may become the most successful technology ever privatized by a federal lab, with a
potential market for the product estimated at between $100 million and $150 million.
The micropower impulse radar was developed by engineer Tom McEwan as part of a device designed
to measure the one billion pulses of light emitted from LLNL’s Nova laser in a single second. The system
he developed is the size of a cigarette box and consists of about $10 worth of parts. The same measurement
had been made previously using $40,000 worth of equipment.
Titan Technologies of Edmonton, AL, Canada, was the first to bring to market a product using the
technology when they introduced storage-tank fluid sensors incorporating the system. The new radar
allowed Titan to reduce its devices from the size of an apple crate to the size of a softball, and to sell
them for one-third the cost of a comparable device. The Federal Highway Administration is preparing
to use the radar for highway inspections and the Army Corps of Engineers has contracted with LLNL to
use the system for search and rescue radar. Other applications include a monitoring device to check the
A
? 2000 by CRC Press LLC
for graded-index fiber with arbitrary profiles, when the refractive index does not change appreciably over
distances comparable to the guided wavelength [Yariv, 1991]. In this method, the transverse components of
the fields are expressed as
E
t
= y(r)e
j lf
e
j(w t – b z)
(42.23)
(42.24)
In Eq. (42.23), l is an integer. Equation (42.16), the scalar wave equation in cylindrical coordinates can now
be written with k = n(r) k
0
as
(42.25)
where
HE
tt
=
b
wm
d
dr
d
dr
pr r
2
2
2
1
2
0++
é
?
ê
ê
ù
?
ú
ú
=() ()y
heartbeats of infants to guard against Sudden Infant Death Syndrome (SIDS), robot guide sensors,
automatic on/off switches for bathroom hand dryers, hand-held tools, automobile back-up warning
systems, and home security.
AERES, a San Jose-based company, has developed a new approach to ground-penetrating radar using
impulse radar. The first application of the technology was an airborne system for detecting underground
bunkers. The design can be altered to provide high depth capability for large targets, or high resolution
for smaller targets near the surface. This supports requirements in land mine searches and explosive
ordinance disposal for the military. AERAS has developed both aircraft and ground-based systems
designed for civilian applications as well as military. Underground utility mapping, such as locating pipes
and cables; highway and bridge under-surface inspection; and geological and archeological surveying are
examples of the possible civilian applications. (Reprinted with permission from NASA Tech Briefs, 20(10),
24, 1996.)
(42.26)
Let r
1
and r
2
be roots of p
2
(r) = 0 such that r
1
< r
2
. A ray propagating in the core does not necessarily reach
the core-cladding interface or the fiber axis. In general, it is confined to an annular cylinder bounded by the
two caustic surfaces defined by r
1
and r
2
. As illustrated in Fig. 42.10, the field is oscillatory within this annular
cylinder and evanescent outside it. The fields obtained as solutions to Eq. (42.25) are
(42.27a)
(42.27b)
(42.27c)
(42.27d)
Equations (42.27b) and (42.27c) represent fields in the same region. Equating them leads to the mode
condition:
(42.28)
In Eq. (42.28) l and m are the integers denoting the modes. A closed analytical solution of this equation for
b is possible only for a few simple graded-index profiles. For other cases, numerical or approximate methods
FIGURE 42.10End view of a skew ray in a graded-index fiber, its graphical solution in the WKB method, and the resulting
field that is oscillatory between r
1
and r
2
and evanescent outside that region.
pr nr
r
22
0
2
2
2
2
() ()=--kb
l
y()
[()]
exp () ;r
A
rpr
prdrr r
r
r
=-
é
?
ê
ù
?
ú
<
ò
12
1
1
/
**
y
p
()
[()]
sin () ;r
B
rpr
prdr r r
r
r
=+
é
?
ê
ê
ù
?
ú
ú
<
ò
12
1
41
/
y
p
()
[()]
sin () ;r
C
rpr
prdr r r
r
r
=+
é
?
ê
ê
ù
?
ú
ú
<
ò
12
2
4
2
/
y()
[()]
exp () ;r
D
rpr
prdrr r
r
r
=-
é
?
ê
ù
?
ú
<
ò
12
2
2
/
**
nr
r
dr m
r
r
2
0
2
2
2
2
12
21
2
1
2
() ( )kb
p
--
é
?
ê
ù
?
ú
=+
ò
l
/
? 2000 by CRC Press LLC
are used. It can be shown [Marcuse, 1982] that for fiber of graded index profile a, the number of modes
supported N
g
, and the normalized frequency V, (and hence the core radius) for single mode operations are
given, respectively, by
(42.29)
(42.30)
For parabolic (a = 2) index profile Eq. (40.29) give N
g
= , which is half the corresponding number of modes
for step index fiber, and Eq. (40.30) gives V ￡ 2.405 . Thus, compared with step index fiber, graded index
fiber will have larger core radios for single mode operation, and for the same core radius, will support a fewer
number of modes.
Attenuation
The assumption of a nonconducting medium for dielectric waveguides led to solutions to the wave equation
with no attenuation component. In practice, various mechanisms give rise to losses in lightwave waveguides.
These mechanisms contribute a loss factor of e
–az
to Eq. (42.10) and comparable field expressions, where a is
the attenuation coefficient. The attenuation due to these mechanisms and the resulting total attenuation as a
function of wavelength is shown in Fig. 42.11 [Osanai et al., 1976]. Note that the range of wavelengths (0.8 to
1.6 mm) in which communication fibers are usually operated corresponds to a region of low overall attenuation.
Brief discussions follow of the mechanisms responsible for the various types of attenuation shown in Fig. 42.11.
Intrinsic Absorption
Intrinsic absorption is a natural property of glass. In the ultraviolet region, it is due to strong electronic and
molecular transition bands. In the infrared region, it is caused by thermal vibration of chemical bonds.
Extrinsic Absorption
Extrinsic absorption is caused by metal (Cu, Fe, Ni, Mn, Co, V, Cr) ion impurities and hydroxyl (OH) ion
impurity. Metal ion absorption involves electron transition from lower to higher energy states. OH absorption
FIGURE 42.11Attenuation of a germanium-doped low-loss silica glass fiber. (Source: H. Osanai et al., “Effects of dopants
on transmission loss of low-OH content optical fibers,” Electronic Letters, vol. 12, no. 21, p. 550, 1976. With permission.)
N
V
g
=
+
?
è
?
?
?
÷
?
è
?
?
?
÷
a
a22
2
V=
+?
è
?
?
?
÷
2405
2
1
2
.
a
a
V
2
4
-----
2
? 2000 by CRC Press LLC
is caused by thermal vibration of the hydroxyl ion. Extrinsic absorption is strong in the range of normal fiber
operation. Thus, it is important that impurity level be limited.
Rayleigh Scattering
Rayleigh scattering is caused by localized variations in refractive index in the dielectric medium, which are
small relative to the optic wavelength. It is strong in the ultraviolet region. It increases with decreasing wave-
length, being proportional to l
–4
. It contributes a loss factor of exp(–a
R
z). The Rayleigh scattering coefficient,
a
R
, is given by
(42.31)
where dn
2
is the mean-square fluctuation in refractive index and V is the volume associated with this index
difference.
Mie Scattering
Mie scattering is caused by inhomogeneities in the medium, with dimensions comparable to the guided
wavelength. It is independent of wavelength.
Dispersion and Pulse Spreading
Dispersion refers to the variation of velocity with frequency or wavelength. Dispersion causes pulse spreading,
but other nonwavelength-dependent mechanisms also contribute to pulse spreading in optical waveguides. The
mechanisms responsible for pulse spreading in optical waveguides include material dispersion, waveguide
dispersion, and multimode pulse spreading.
Material Dispersion
In material dispersion, the velocity variation is caused by some property of the medium. In glass, it is caused
by the wavelength dependence of refractive index. For a given pulse, the resulting pulse spread per unit length
is the difference between the travel times of the slowest and fastest wavelengths in the pulse. It is given by
(42.32)
In Eq. 42.32, n2 is the second derivative of the refractive index with respect to l, M = ( l/c)n2 is the material
dispersion, and Dl is the linewidth of the pulse. Figure 42.12 shows the wavelength dependence of material
dispersion [Wemple, 1979]. Note that for silica, zero dispersion occurs around 1.3 mm, and material dispersion
is small in the wavelength range of small fiber attenuation.
Waveguide Dispersion
The effective refractive index for any mode varies with wavelength for a fixed film thickness, for a slab waveguide,
or a fixed core radius, for an optical fiber. This variation causes pulse spreading, which is termed waveguide
dispersion. The resulting pulse spread is given by
(42.33)
where M
G
= ( l/c)n2
eff
is the waveguide dispersion.
a
p
l
dd
R
nV=
?
è
?
?
?
÷
8
3
3
4
22
()
DDDt
l
ll=
-
=-￠￠
c
nM
DDDt
l
ll=
-
=-￠￠
c
nM
Geff
? 2000 by CRC Press LLC
Polarization Mode Dispersion
The HE
11
propagating in a single mode fiber actually consists of two orthogonally polarized modes, but the
two modes have the same effective refractive index and propagation velocity except in birefringent fibers.
Birefringent fibers have asymmetric cores or asymmetric refractive index distribution in the core, which result
in different refractive indices and group velocities for the orthogonally polarized modes. The different group
velocities result in a group delay of one mode relative to the other, known as polarization mode dispersion.
Birefringent fibers are polarization preserving and are required for several applications, including coherent
optical detection and fiber optic gyroscopes. In high birefringence fibers, polarization dispersion can exceed
1 ns/km. However, in low birefringence fibers, polarization mode dispersion is negligible relative to other pulse
spreading mechanisms [Payne et al., 1982].
Multimode Pulse Spreading
In a multimode waveguide, different modes travel different path lengths. This results in different travel times
and, hence, in pulse spreading. Because this pulse spreading is not wavelength dependent, it is not usually
referred to as dispersion. Multimode pulse spreads are given, respectively, for a slab waveguide, a step-index
fiber, and a parabolic graded-index fiber by the following equations:
(slab waveguide) (42.34)
(step-index fiber) (42.35)
(GRIN fiber) (42.36)
FIGURE 42.12 Material dispersion as a function of wavelength for silica and several solids. (Source: S.H. Wemple, “Material
dispersion in optical fibers,” Applied Optics, vol. 18, no. 1, p. 33, 1979. With permission.)
Dt
mod
()
=
-nn n
cn
11 2
2
D
D
t
mod
=
n
c
1
D
D
t
mod
=
n
c
1
2
8
? 2000 by CRC Press LLC
Total Pulse Spread
Total pulse spread is the overall effect of material dispersion, waveguide dispersion, and multimode pulse spread.
It is given by
(42.37)
where
Dt
dis
=
total dispersion = –(M + M
G
)Dl
In a multimode waveguide, multimode pulse spread dominates, and dispersion can often be ignored. In a
single-mode waveguide, only material and waveguide dispersion exist; material dispersion dominates, and
waveguide dispersion can often be ignored.
Total pulse spread imposes an upper limit on the bandwidth of an optical fiber. This upper limit is equal to
1/(2Dt
T
)Hz.
Defining Terms
Linewidth: The range of wavelengths emitted by a source or present in a pulse.
Meridional ray: A ray that is contained in a plane passing through the fiber axis.
Mode chart: A graphical illustration of the variation of effective refractive index (or, equivalently, propagation
angle q) with normalized thickness d/l for a slab waveguide or normalized frequency V for an optical fiber.
Refractive index: The ratio of the velocity of light in free space to the velocity of light in a given medium.
Relative refractive index difference: The ratio (n
1
2
– n
2
2
)/2n
1
2
? (n
1
– n
2
)/n
1
, where n
1
> n
2
and n
1
and n
2
are
refractive indices.
Related Topics
31.1 Lasers ? 37.2 Waveguides
References
H.A. Haus, Waves and Fields in Optoelectronics, Englewood Cliffs, N.J.: Prentice-Hall, 1984.
D.B. Keck, “Optical fiber waveguides,” in Fundamentals of Optical Fiber Communications, 2nd ed., M. K. Bar-
noski, Ed., New York: Academic Press, 1981.
D. Marcuse, Light Transmission Optics, 2nd ed., New York: Van Nostrand Reinhold, 1982.
H. Osanai et al., “Effects of dopants on transmission loss of low-OH-content optical fibers,” Electronic Letters,
vol. 12, no. 21, 1976.
J.C. Palais, Fiber Optic Communications, Englewood Cliffs, N.J.: Prentice-Hall, 1992.
D.N. Payne, A.J. Barlow, and J.J.R. Hansen, “Development of low-and-high birefringence optical fibers,” IEEE
J. Quantum Electron., QE-18 no. 4, pp. 477–487, 1982.
J.M. Senior, Optical Fiber Communications: Principles and Practice, Englewood Cliffs, N.J.: Prentice-Hall, 1985.
J.M. Snyder, “Asymptotic expressions for eigenfunctions and eigenvalues of a dielectric or optical waveguide,”
Trans. IEEE Microwave Theory Tech., vol. MTT-17, pp. 1130–1138, 1969.
S.H. Wemple, “Material dispersion in optical fibers,” Applied Optics, vol. 18, no. 1, p. 33, 1979.
A. Yariv, Optical Electronics, 4th ed., Philadelphia: Saunders College Publishing, 1991.
Further Information
IEEE Journal of Lightwave Technology, a bimonthly publication of the IEEE, New York.
IEEE Lightwave Telecommunications Systems, a quarterly magazine of the IEEE, New York.
Applied Optics, a biweekly publication of the Optical Society of America, 2010 Massachusetts Avenue NW,
Washington, DC 20036.
D. Macruse, Theory of Optical Waveguides, 2nd ed., Boston: Academica Press, 1991.
DD Dtt t
T
22 2
=+
mod dis
? 2000 by CRC Press LLC
42.2 Optical Fibers and Cables
1
Allen H. Cherin and Basant K. Tariyal
Communications using light as a signal carrier and optical fibers as transmission media are termed optical fiber
communications. The applications of optical fiber communications have increased at a rapid rate, since the
first commercial installation of a fiber-optic system in 1977. Today every major telecommunication company
is spending millions of dollars on optical fiber communication systems. In an optical fiber communication
system voice, video, or data are converted to a coded pulse stream of light using a suitable light source. This
pulse stream is carried by optical fibers to a regenerating or receiving station. At the final receiving station the
light pulses are converted to electric signals, decoded, and converted into the form of the original information.
Optical fiber communications arc currently used for telecommunications, data communications, military
applications, industrial controls, medical applications, and CATV.
Introduction
Since ancient times humans have used light as a vehicle to carry information. Lanterns on ships and smoke
signals or flashing mirrors on land are early examples of uses of how humans used light to communicate. It
was just over a hundred years ago that Alexander Graham Bell (1880) transmitted a telephone signal a distance
greater than 200 m using light as the signal carrier. Bell called his invention a “photophone” and obtained a
patent for it. Bell, however, wisely gave up the photophone in favor of the electric telephone. Photophone at
the time of its invention could not be exploited commercially because of two basic drawbacks: (1) the lack of
a reliable light source and (2) the lack of a dependable transmission medium.
The invention of the laser in 1960 gave a new impetus to the idea of lightwave communications (as scientists
realized the potential of the dazzling information-carrying capacity of these lasers). Much research was under-
taken by different laboratories around the world during the early 1960s on optical devices and transmission
media. The transmission media, however, remained the main problem, until K.C. Kao and G.A. Hockham in
1966 proposed that glass fibers with a sufficiently high-purity core surrounded by a lower refractive index
cladding could be used for transmitting light over long distances. At the time, available glasses had losses of
several thousand decibels per kilometer. In 1970, Robert Maurer of Corning Glass Works was able to produce
a fiber with a loss of 20 dB/km. Tremendous progress in the production of low-loss optical fibers has been
made since then in the various laboratories in the United States, Japan, and Europe, and today optical fiber
communication is one of the fastest growing industries. Optical fiber communication is being used to transmit
voice, video, and data over long distance as well as within a local network.
Fiber optics appears to be the future method of choice for many communications applications. The biggest
advantage of a lightwave system is its tremendous information-carrying capacity. There are already systems
that can carry several thousand simultaneous conversations over a pair of optical fibers thinner than human
hair. In addition to this extremely high capacity, the lightguide cables are light weight, they are immune to
electromagnetic interference, and they are potentially very inexpensive.
A lightwave communication system (Fig. 42.13) consists of a transmitter, a transmission medium, and a
receiver. The transmitter takes the coded electronic signal (voice, video, or data) and converts it to the light
signal, which is then carried by the transmission medium (an optical fiber cable) to either a repeater or the
receiver. At the receiving end the signal is detected, converted to electrical pulses, and decoded to the proper
output. This article provides a brief overview of the different components used in an optical fiber system, along
with examples of various applications of optical fiber systems.
Classification of Optical Fibers and Attractive Features
Fibers that are used for optical communication are waveguides made of transparent dielectrics whose function
is to guide light over long distances. An optical fiber consists of an inner cylinder of glass called the core,
1
This section, including all illustrations, is modified from A. H. Cherin and B. K. Tariyal, “Optical fiber communication,”
in Encyclopedia of Telecommunications, R. A. Meyers, Ed., San Diego: Academic Press, 1988. With permission.
? 2000 by CRC Press LLC
surrounded by a cylindrical shell of glass of lower refractive index, called the cladding. Optical fibers (light-
guides) may be classified in terms of the refractive index profile of the core and whether one mode (single-
mode fiber) or many modes (multimode fiber) are propagating in the guide (Fig. 42.14). If the core, which is
typically made of a high-silica-content glass or a multicomponent glass, has a uniform refractive index n
1
, it
is called a step-index fiber. If the core has a nonuniform refractive index that gradually decreases from the center
toward the core-cladding interface, the fiber is called a graded-index fiber. The cladding surrounding the core
has a uniform refractive index n
2
that is slightly lower than the refractive index of the core region. The cladding
of the fiber is made of a high-silica-content glass or a multicomponent glass. Figure 42.14 shows the dimensions
and refractive indexes for commonly used telecommunication fibers. Figure 42.15 enumerates some of the
advantages, constraints, and applications of the different types of fibers. In general, when the transmission
medium must have a very high bandwidth—for example, in an undersea or long-distance terrestrial system—a
single-mode fiber is used. For intermediate system bandwidth requirements between 200 MHz-km and
2 GHz-km, such as found in local-area networks, either a single-mode or graded-index multimode fiber would
be the choice. For applications such as short data links where lower bandwidth requirements are placed on the
transmission medium, either a graded-index or a step-index multimode fiber may be used.
FIGURE 42.13Schematic diagram of a lightwave communications system.
FIGURE 42.14Geometry of single-mode and multimode fibers.
? 2000 by CRC Press LLC
Because or their low loss and wide bandwidth capabilities, optical fibers have the potential for being used
wherever twisted wire pairs or coaxial cables are used as the transmission medium in a communication system.
If an engineer were interested in choosing a transmission medium for a given transmission objective, he or she
would tabulate the required and desired features of alternate technologies that may be available for use in the
applications. With that process in mind, a summary of the attractive features and the advantages of optical
fiber transmission will be given. Some of these advantages include (a) low loss and high bandwidth; (b) small
size and bending radius; (c) nonconductive, nonradiative, and noninductive; (d) light weight; and (e) providing
natural growth capability.
To appreciate the low loss and wide bandwidth capabilities of optical fibers, consider the curves of signal
attenuation versus frequency for three different transmission media shown in Fig. 42.16. Optical fibers have a
“flat’’ transfer function well beyond 100 MHz. When compared with wire pairs of coaxial cables, optical fibers
have far less loss for signal frequencies above a few megahertz. This is an important characteristic that strongly
influences system economics, since it allows the system designer to increase the distance between regenerators
(amplifiers) in a communication system.
The small size, small bending radius (a few centimeters), and light weight of optical fibers and cables are
very important where space is at a premium, such as in aircraft, on ships, and in crowded ducts under city streets.
Because optical fibers are dielectric waveguides, they avoid many problems such as radiative interference,
ground loops, and, when installed in a cable without metal, lightning-induced damage that exists in other
transmission media.
FIGURE 42.15Applications and characteristics of fiber types.
FIGURE 42.16Attenuation versus frequency for three different transmission media. Asterisk indicates fiber loss at a carrier
wavelength of 1.3 mm.
? 2000 by CRC Press LLC
Finally, the engineer using optical fibers has a great deal of flexibility. He or she can install an optical fiber
cable and use it initially in a low-capacity (low-bit-rate) system. As the system needs grow, the engineer can
take advantage of the broadband capabilities of optical fibers and convert to a high-capacity (high-bit-rate)
system by simply changing the terminal electronics.
Fiber Transmission Characteristics
The proper design and operation of an optical communication system using
optical fibers as the transmission medium requires a knowledge of the trans-
mission characteristics of the optical sources, fibers, and interconnection
devices (connectors, couplers, and splices) used to join lengths of fibers
together. The transmission criteria that affect the choice of the fiber type
used in a system are signal attenuation, information transmission capacity
(bandwidth), and source coupling and interconnection efficiency. Signal
attenuation is due to a number of loss mechanisms within the fiber, as shown in Table 42.1, and due to the
losses occurring in splices and connectors. The information transmission capacity of a fiber is limited by
dispersion, a phenomenon that causes light that is originally concentrated into a short pulse to spread out into
a broader pulse as it travels along an optical fiber. Source and interconnection efficiency depends on the fiber’s
core diameter and its numerical aperture, a measure of the angle over which light is accepted in the fiber.
Absorption and scattering of light traveling through a fiber leads to signal attenuation, the rate of which is
measured in decibels per kilometer (dB/km). As can be seen in Fig. 42.17, for both multimode and single-mode
fibers, attenuation depends strongly on wavelength. The decrease in scattering losses with increasing wavelength
is offset by an increase in material absorption such that attenuation is lowest near 1.55 mm (1550 nm).
The measured values given in Table 42.2 are probably close to the lower bounds for the attenuation of optical
fibers. In addition to intrinsic fiber losses, extrinsic loss mechanisms, such as absorption due to impurity ions,
and microbending loss due to jacketing and cabling can add loss to a fiber.
The bandwidth or information-carrying capacity of a fiber is inversely related to its total dispersion. The
total dispersion in a fiber is a combination of three components: intermodal dispersion (modal delay distortion),
material dispersion, and waveguide dispersion.
Intermodal dispersion occurs in multimode fibers because rays associated with different modes travel different
effective distances through the optical fiber. This causes light in the different modes to spread out temporally as
it travels along the fiber. Modal delay distortion can severely limit the bandwidth of a step-index multimode fiber
to the order of 20 MHz-km. To reduce modal delay distortion in multimode fibers, the core is carefully doped to
create a graded (approximately parabolic shaped) refractive index profile. By carefully designing this index profile,
the group velocities of the propagating modes are nearly equalized. Bandwidths of 1.0 GHz-km are readily
attainable in commercially available graded-index multimode fibers. The most effective way of eliminating
intermodal dispersion is to use a single-mode fiber. Since only one mode propagates in a single-mode fiber,
modal delay distortion between modes does not exist and very high bandwidths are possible. The bandwidth
of a single-mode fiber, as mentioned previously, is limited by the combination of material and waveguide
dispersion. As shown in Fig. 42.18, both material and waveguide dispersion are dependent on wavelength.
FIGURE 42.17Spectral attenuation rate. (a) Graded-index multimode fibers. (b) Single-mode fibers.
TABLE 42.1Loss Mechanisms
Intrinsic material absorption loss
Ultraviolet absorption tail
Infrared absorption tail
Absorption loss due to impurity ions
Rayleigh scattering loss
Waveguide scattering loss
Microbending loss
? 2000 by CRC Press LLC
Material dispersion is caused by the variation of the refractive
index of the glass with wavelength and the spectral width of the
system source. Waveguide dispersion occurs because light travels
in both the core and cladding of a single-mode fiber at an effective
velocity between that of the core and cladding materials. The
waveguide dispersion arises because the effective velocity, the
waveguide dispersion, changes with wavelength. The amount of
waveguide dispersion depends on the design of the waveguide
structure as well as on the fiber material. Both material and
waveguide dispersion are measured in picoseconds (of pulse
spreading) per nanometer (of source spectral width) per kilome-
ter (of fiber length), reflecting both the increases in magnitude in
source linewidth and the increase in dispersion with fiber length.
Material and waveguide dispersion can have different signs and effectively cancel each other’s dispersive effect
on the total dispersion in a single-mode fiber. In conventional germanium-doped silica fibers, the “zero-
dispersion’’ wavelength at which the waveguide and material dispersion effects cancel each other out occurs
near 1.30 mm. The zero-dispersion wavelength can be shifted to 1.55 mm, or the low-dispersion characteristics
of a fiber can be broadened by modifying the refractive index profile shape of a single-mode fiber. This profile
shape modification alters the waveguide dispersion characteristics of the fiber and changes the wavelength
region in which waveguide and material dispersion effects cancel each other. Figure 42.19 illustrates the profile
shapes of “conventional,’’ “dispersion-shifted,” and “dispersion-flattened’’ single-mode fibers. Single-mode fibers
operating in their zero-dispersion region with system sources of finite spectral width do not have infinite
bandwidth but have bandwidths that are high enough to satisfy all current high-capacity system requirements.
Optical Fiber Cable Manufacturing
Optical fiber cables should have low loss and high bandwidth and should maintain these characteristics while
in service in extreme environments. In addition, they should be strong enough to survive the stresses encoun-
tered during manufacture, installation, and service in a hostile environment. The manufacturing process used
TABLE 42.2Best Attenuation Results (dB/km)
in Ge-P-SiO
2
Core Fibers
Wavelength (nm)
D ? 0.2%
(Single-mode
Fibers)
D ? 1.0%
(Graded-index
Multimode Fibers)
850 2.1 2.20
1300 0.27 0.44
1500 0.16 0.23
FIGURE 42.19Single-mode refractive index profiles.
FIGURE 42.18 Single-mode step-index dis-
persion curve.
? 2000 by CRC Press LLC
to fabricate the optical fiber cables can be divided into four steps: (1) preform fabrication, (2) fiber drawing
and coating, (3) fiber measurement, and (4) fiber packaging.
Preform Fabrication
The first step in the fabrication of optical fiber is the creation of a glass preform. A preform is a large blank of
glass several millimeters in diameter and several centimeters in length. The preform has all the desired properties
(e.g., geometrical ratios and chemical composition) necessary to yield a high-quality fiber. The preform is
subsequently drawn into a multi-kilometer-long hair-thin fiber. Four different preform manufacturing processes
are currently in commercial use.
The most widely used process is the modified chemical vapor deposition (MCVD) process invented at the
AT&T Bell Laboratories. Outside vapor deposition process (OVD) is used by Corning Glass Works and some
of its joint ventures in Europe. Vapor axial deposition (VAD) process is the process used most widely in Japan.
Philips, in Eindhoven, Netherlands, uses a low-temperature plasma chemical vapor deposition (PCVD) process.
In addition to the above four major processes, other processes are under development in different labora-
tories. Plasma MCVD is under development at Bell Laboratories, hybrid OVD-VAD processes are being devel-
oped in Japan, and Sol-Gel processes are being developed in several laboratories. The first four processes are
the established commercial processes and are producing fiber economically. The new processes are aimed at
greatly increasing the manufacturing productivity of preforms, and thereby reducing their cost.
All the above processes produce high-silica fibers using different dopants, such as germanium, phosphorus,
and fluorine. These dopants modify the refractive index of silica, enabling the production of the proper core
refractive index profile. Purity of the reactants and the control of the refractive index profile are crucial to the
low loss and high bandwidth of the fiber.
MCVD Process. In the MCVD process (Fig. 42.20), a fused-silica tube of extremely high purity and dimen-
sional uniformity is cleaned in an acid solution and degreased. The clean tube is mounted on a glass working
lathe. A mixture of reactants is passed from one end of the tube and exhaust gases are taken out at the other
end while the tube is being rotated. A torch travels along the length of the tube in the direction of the reactant
flow. The reactants include ultra-high-purity oxygen and a combination of one or more of the halides and
oxyhalides (SiCl
4
, GeCl
4
, POCl
3
, BCl
3
, BBr
3
, SiF
4
, CCl
4
, CCl
2
F
2
, Cl
2
, SF
6
, and SOCl
2
).
The halides react with the oxygen in the temperature range of 1300–1600°C to form oxide particles, which
are driven to the wall of the tube and subsequently consolidated into a glassy layer as the hottest part of the
flame passes over. After the completion of one pass, the torch travels back and the next pass is begun. Depending
on the type of fiber (i.e., multimode or single-mode), a barrier layer or a cladding consisting of many thin
layers is first deposited on the inside surface of the tube. The compositions may include B
2
O
3
-P
2
O
5
-SiO
2
or
F-P
2
O
5
-SiO
2
for barrier layers and SiO
2
, F-SiO
2
, F-P
2
O
5
-SiO
2
, or F-GeO
2
-SiO
2
-P
2
O
5
for cladding layers. After the
required number of barrier or cladding layers has been deposited the core is deposited. The core compositions
FIGURE 42.20Schematic diagram of the MCVD process.
? 2000 by CRC Press LLC
depend on whether the fiber is single-mode, multimode, step-index, or multimode graded-index. In the case
of graded-index multimode fibers, the dopant level changes with every layer, to provide a refractive index profile
that yields the maximum bandwidth.
After the deposition is complete, the reactant flow is stopped except for a small flow of oxygen, and the
temperature is raised by reducing the torch speed and increasing the flows of oxygen and hydrogen through
the torch. Usually the exhaust end of the tube is closed first and a small positive pressure is maintained inside
the deposited tube while the torch travels backward. The higher temperatures cause the glass viscosity to
decrease, and the surface tension causes the tube to contract inward. The complete collapse of the tube into a
solid preform is achieved in several passes. The speed of the collapse, the rotation of the tube, the temperature
of collapse, and the positive pressure of oxygen inside the tube are all accurately controlled to predetermined
values in order to produce a straight and bubble-free preform with minimum ovality. The complete preform
is then taken off the lathe. After an inspection to assure that the preform is free of defects, the preform is ready
to be drawn into a thin fiber.
The control of the refractive index profile along the cross section of the deposited portion of the preform is
achieved through a vapor delivery system. In this system, liquids are vaporized by passing a carrier gas (pure
O
2
) through the bubblers, made of fused silica. Accurate flows are achieved with precision flow controllers that
maintain accurate carrier gas flows and extremely accurate temperatures within the bubblers. Microprocessors
are used to automate the complete deposition process, including the torch travel and composition changes
throughout the process. Impurities are reduced to very low levels by starting with pure chemicals, and there is
further reducing of the impurities with in-house purification of these chemicals. Ultra-pure oxygen and a
completely sealed vapor-delivery system are used to avoid chemical contamination. Transition-metal ion impu-
rities of well below 1 ppb and OH
–
ion impurities of less than 1 ppm are typically maintained to produce high-
quality fiber.
The PCVD Process. The PCVD process (Fig. 42.21) also uses a starting tube, and the deposition takes place
inside the tube. Here, however, the tube is either stationary or oscillating and the pressure is kept at 10–15 torr.
Reactants are fed inside the tube, and the reaction is accomplished by a traveling microwave plasma inside the
tube. The entire tube is maintained at approximately 1200°C. The plasma causes the heterogeneous depositions
of glass on the tube wall, and the deposition efficiency is very high. After the required depositions of the cladding
and core are complete, the tube is taken out and collapsed on a separate equipment. Extreme care is required
to prevent impurities from getting into the tube during the transport and collapse procedure. The PCVD process
has the advantages of high efficiency, no tube distortion because of the lower temperature, and very accurate
profile control because of the large number of layers deposited in a short time. However, going to higher rates
of flow presents some difficulties, because of a need to maintain the low pressure.
The PMCVD Process. The PMCVD is an enhancement of the MCVD process. Very high rates of deposition
(up to 10 g/min, compared to 2 g/min for MCVD) are achieved by using larger diameter tubes and an RF
plasma for reaction (Fig. 42.22). Because of the very high temperature of the plasma, water cooling is essential.
An oxyhydrogen torch follows the plasma and sinters the deposition. The high rates of deposition are achieved
because of very high thermal gradients from the center of the tube to the wall and the resulting high thermo-
phoretic driving force. The PMCVD process is still in the development stage and has not been commercialized.
FIGURE 42.21Schematic diagram of the PCVD process.
? 2000 by CRC Press LLC
The OVD Process.The OVD process does not use a starting tube; instead, a stream of soot particles of desired
composition is deposited on a bait rod (Fig. 42.23). The soot particles are produced by the reaction of reactants
in a fuel gas-oxygen flame. A cylindrical porous soot preform is built layer by layer. After the deposition of the
core and cladding is complete, the bait rod is removed. The porous preform is then sintered and dried in a
furnace at 1400–1600°C to form a clear bubble-free preform under a controlled environment. The central hold
left by the blank may or may not be closed, depending on the type of preform. The preform is now ready for
inspection and drawing.
The VAD Process.The process is very similar to the OVD
process. However, the soot deposition is done axially instead
of radially. The soot is deposited at the end of a starting silica-
glass rod (Fig. 42.24). A special torch using several annular
holes is used to direct a stream of soot at the deposition
surface. The reactant vapors, hydrogen gas, argon gas, and
oxygen gas flow through different annular openings. Nor-
mally the core is deposited and the rotating speed is gradually
withdrawn as the deposition proceeds at the end. The index
profile is controlled by the composition of the gases flowing
through the torch and the temperature distribution at the
deposition surface. The porous preform is consolidated and
dehydrated as it passes through a carbon-ring furnace in a
FIGURE 42.22Schematic diagram of the PMCVD process.
FIGURE 42.23Schematic diagram of the outside vapor deposition. (a) Soot deposition. (b) Consolidation.
FIGURE 42.24Schematic diagram of the vapor
axial deposition.
? 2000 by CRC Press LLC
controlled environment. SOCl
2
and Cl are used to dehydrate the preform. Because of the axial deposition, this
process is semicontinuous and is capable of producing very large preforms.
Fiber Drawing
After a preform has been inspected for various defects such as bubbles, ovality, and straightness, it is taken to
a fiber drawing station. A large-scale fiber drawing process must repeatedly maintain the optical quality of the
preform and produce a dimensionally uniform fiber with high strength.
Draw Process.During fiber drawing, the inspected preform is lowered into a hot zone at a certain feed rate
V
p
, and the fiber is pulled from the softened neck-down region (Fig. 42.25) at a rate V
f
. At steady state,
pD
p
2
V
p
/4 = pD
f
2
V
f
/4 (42.38)
where D
p
and D
f
are the preform and fiber diameters, respectively. Therefore,
V
f
=(D
p
2
/D
f
2
)V
p
(42.39)
A draw machine, therefore, consists of a preform feed mechanism, a heat source, a pulling device, a coating
device, and a control system to accurately maintain the fiber diameter and the furnace temperature.
Heat Source.The heat source should provide sufficient energy to soften the glass for pulling the fiber without
causing excessive tension and without creating turbulence in the neck-down region. A proper heat source will
yield a fiber with uniform diameter and high strength. Oxyhydrogen torches, CO
2
lasers, resistance furnaces,
and induction furnaces have been used to draw fibers. An oxyhydrogen torch, although a clean source of heat,
suffers from turbulence due to flame. A CO
2
laser is too expensive a heat source to be considered for the large-
scale manufacture of fibers. Graphite resistance furnaces and zirconia induction furnaces are the most widely
used heat sources for fiber drawing. In the graphite resistance furnace, a graphite resistive element produces
the required heat. Because graphite reacts with oxygen at high temperatures, an inert environment (e.g., carbon)
is maintained inside the furnace. The zirconia induction furnace does not require inert environment. It is
extremely important that the furnace environment be clean in order to produce high-strength fibers. A zirconia
induction furnace, when properly designed and used, has produced very-high-strength long-length fibers (over
2.0 GPa) in lengths of several kilometers.
Mechanical Systems.An accurate preform feed mechanism and drive capstan form the basis of fiber speed
control. The mechanism allows the preform to be fed at a constant speed into the hot zone, while maintaining
the preform at the center of the furnace opening at the top. A centering device is used to position preforms
that are not perfectly straight. The preform is usually held with a collet-type chuck mounted in a vertically
movable carriage, which is driven by a lead screw. A precision stainless-steel drive capstan is mounted on the
FIGURE 42.25The fiber drawing process.
? 2000 by CRC Press LLC
shaft of a high-performance dc servomotor. The fiber is taken up on a proper-diameter spool. The fiber is
wound on the spool at close to zero tension with the help of a catenary control. In some cases fiber is proof-
tested in-line before it is wound on a spool. The proof stress can be set at different levels depending on the
application for which the fiber is being manufactured.
Fiber Coating System. The glass fiber coming out of the furnace has a highly polished pristine surface and
the theoretical strength of such a fiber is in the range of 15–20 GPa. Strengths in the range of 4.5–5.5 GPa are
routinely measured on short fiber lengths. To preserve this high strength, polymeric coatings are applied
immediately after the drawing. The coating must be applied without damaging the fiber, it must solidify before
reaching the capstan, and it should not cause microbending loss. To satisfy all these requirements, usually two
layers of coatings are applied: a soft inner coating adjacent to the fiber to avoid microbending loss and a hard
outer coating to resist abrasion. The coatings are a combination of ultraviolet- (UV) curable acrylates, UV-
curable silicones, hot melts, heat-curable silicones, and nylons. When dual coatings are applied, the coated fiber
diameter is typically 235–250 mm. The nylon-jacketed fiber typically used in Japan has an outside diameter of
900 mm. All coating materials are usually filtered to remove particles that may damage the fiber. Coatings are
usually applied by passing the fiber through a coating cup and then curing the coating before the fiber is taken
up by the capstan. The method of application, the coating material, the temperature, and the draw speed affect
the proper application or a well-centered, bubble-free coating.
Fiber drawing facilities are usually located in a clean room where the air is maintained at class 10,000. The
region of the preform and fiber from the coating cup to the top of the preform is maintained at class 100 or
better. A class 100 environment means that there are no more than 100 particles of size greater than 0.5 mm in
1 ft
3
of air. A clean environment, proper centering of the preform in the furnace and fiber in the coating cup,
and proper alignment of the whole draw tower ensure a scratch-free fiber of a very high tensile strength. A
control unit regulates the draw speed, preform feed speed, preform centering, fiber diameter, furnace temper-
ature, and draw tension.
The coated fiber wound on a spool is next taken to the fiber measurement area to assure proper quality
control.
Proof Testing of Fibers. Mechanical failure is one of the major concerns in the reliability of optical fibers.
Fiber drawn in kilometer lengths must be strong enough to survive all of the short- and long-term stresses that
it will encounter during the manufacture, installation, and long service life. Glass is an ideal elastic isotropic
solid and does not contain dislocations. Hence, the strength is determined mainly by inclusions and surface
flaws. Although extreme care is taken to avoid inhomogeneities and surface flaws during fiber manufacture,
they cannot be completely eliminated. Since surface flaws can result from various causes, they are statistical in
nature and it is very difficult to predict the long-length strength of glass fibers. To guarantee a minimum fiber
strength, proof testing has been adopted as a manufacturing step. Proof testing can be done in-line immediately
after the drawing and coating or off-line before the fiber is stored.
In proof testing, the entire length of the fiber is subjected to a properly controlled proof stress. The proof
stress is based on the stresses likely to be encountered by the fiber during manufacture, storage, installation,
and service. The fibers that survive the proof test are stored for further packaging into cables.
Proof testing not only guarantees that the fiber will survive short-term stresses but also guarantees that the
fiber will survive a lower residual stress that it may be subjected to during its long service life. It is well known
that glass, when used in a humid environment, can fail under a long-term stress well below its instantaneous
strength. This phenomenon is called static fatigue. Several models have been proposed to quantitatively describe
the relationship between residual stress and the life of optical fibers. Use is made of the most conservative of
these models, and the proof stress is determined by a consideration of the maximum possible residual stress
in service and the required service life.
Fiber Packaging
In order to efficiently use one or more fibers, they need to be packaged so that they can be handled, transported,
and installed without damage. Optical fibers can be used in a variety of applications, and hence the way they
are packaged or cabled will also vary. There are numerous cable designs that are used by different cable
manufacturers. All these designs, however, must meet certain criteria. A primary consideration in a cable design
? 2000 by CRC Press LLC
is to assure that the fibers in the cables maintain their optical properties (attenuation and dispersion) during
their service life under different environmental conditions. The design, therefore, must minimize microbending
effects. This usually means letting the fiber take a minimum energy position at all times in the cable structure.
Proper selection of cabling materials so as to minimize differential thermal expansion or contraction during
temperature extremes is important in minimizing microbending loss. The cable structure must be such that
the fibers carry a load well below the proof-test level at all times, and especially while using conventional
installation equipment. The cables must provide adequate protection to the fibers under all adverse environ-
mental conditions during their entire service life, which may be as long as 40 years. Finally, the cable designs
should be cost effective and easily connectorized or spliced.
Five different types (Fig. 42.26) of basic cable designs are currently in use: (a) loose tube, (b) fluted, (c) ribbon,
(d) stranded, and (e) Lightpack Cable. The loose tube design was pioneered by Siemens in Germany. Up to
10 fibers are enclosed in a loose tube, which is filled with a soft filling compound. Since the fibers are relatively
free to take the minimum energy configuration, the microbending losses are avoided. Several of these buffered
loose tube units are stranded around a central glass-resin support member. Aramid yarns are stranded on the
cable core to provide strength members (for pulling through ducts), with a final polyethylene sheath on the
outside. The stranding lay length and pitch radius are calculated to permit tensile strain on the cable up to the
rated force and to permit cooling down to the rated low temperature without affecting the fiber attenuation.
FIGURE 42.26Fiber cable designs. (a) Loose tube design. (b) Slotted design. (c) Ribbon design. (d) Stranded unit.
(e) Lightpack
TM
Cable design.
? 2000 by CRC Press LLC
In the fluted designs, fibers are laid in the grooves of plastic central members and are relatively free to move.
The shape and size of the grooves vary with the design. The grooved core may also contain a central strength
member. A sheath is formed over the grooved core, and this essentially forms a unit. Several units may then
be stranded around a central strength member to form a cable core of desired size, over which different types
of sheaths are formed. Fluted designs have been pioneered in France and Canada.
The ribbon design was invented at AT&T Bell Laboratories and consists of a linear array of 12 fibers
sandwiched between two polyester tapes with pressure-sensitive adhesive on the fiber side. The spacing and the
back tension on the fibers is accurately maintained. The ribbons are typically 2.5 mm in width. Up to 12 ribbons
can be stacked to give a cable core consisting of 144 fibers. The core is twisted to some lay length and enclosed
in a polyethylene tube. Several combinations of protective plastic and metallic layers along with metallic or
nonmetallic strength members are then applied around the core to give the final cable its required mechanical
and environmental characteristics needed for use in specified conditions. The ribbon design offers the most
efficient and economic packaging of fibers for high-fiber-count cables. It also lends the cable to preconnector-
ization and makes it extremely convenient for installation and splicing.
The tight-bound stranded designs were pioneered by Japanese and are used in the United States for several
applications. In this design, several coated fibers are stranded around a central support member. The central
support member may also serve as a strength member, and it may be metallic or nonmetallic. The stranded
unit can have up to 18 fibers. The unit is contained within a plastic tube filled with a water-blocking compound.
The final cable consists of several of these units stranded around a central member and protected on the outside
with various sheath combinations.
The Lightpack Cable design, pioneered by AT&T, is one of the simplest designs. Several fibers are held
together with a binder to form a unit. One or more units are laid inside a large tube, which is filled with a
water-blocking compound. This design has the advantage of the loose tube design in that the fibers are free of
strain, but is more compact. The tube-containing units can then be projected with various sheath options and
strength members to provide the final cable.
The final step in cabling is the sheathing operation. After the fibers have been made into identifiable units,
one or more of the units (as discussed earlier) form a core which is then covered with a combination of sheathing
layers. The number and combination of the sheathing layers depend on the intended use. Typically, a polyeth-
ylene sheath is extruded over the filled cable core. In a typical cross-ply design, metallic or nonmetallic strength
members are applied over the first sheath layer, followed by another polyethylene sheath, over which another
layer of strength members is applied. The direction of lay of the two layers of the strength members is opposite
to each other. A final sheath is applied and the cable is ready for the final inspection, preconnectorization, and
shipment. Metallic vapor barriers and lightning- and rodent-protection sheath options are also available.
Further armoring is applied to cables made for submarine application.
In addition to the above cable designs, there are numerous other cable designs used for specific applications,
such as fire-resistant cables, military tactical cables, cables for missile guidance systems, cables for field com-
munications established by air-drop operations, air deployment cables, and cables for industrial controls. All
these applications have unique requirements, such as ruggedness, low loss, and repeaterless spans, and the cable
designs are accordingly selected. However, all these cable designs still rely on the basic unit designs discussed
above.
Defining Terms
Attenuation: Decrease of average optical power as light travels along the length or an optical fiber.
Bandwidth: Measure of the information-carrying capacity of the fiber. The greater the bandwidth, the greater
the information-carrying capacity.
Barrier layer: Layer of deposited glass adjacent to the inner tube surface to create a barrier against OH
diffusion.
Chemical vapor deposition: Process in which products of a heterogeneous gas-liquid or gas-solid reaction
are deposited on the surface of a substrate.
Cladding: Low refractive index material that surrounds the fiber core.
Core: Central portion of a fiber through which light is transmitted.
? 2000 by CRC Press LLC
Cut-off wavelength: Wavelength greater than which a particular mode ceases to be a bound mode.
Dispersion: Cause of distortion of the signal due to different propagation characteristics of different modes,
leading to bandwidth limitations.
Graded-index profile: Any refractive index profile that varies with radius in the core.
Microbending: Sharp curvatures involving local fiber axis displacements of a few micrometers and spatial
wavelengths of a few millimeters. Microbending causes significant losses.
Mode: Permitted electromagnetic field pattern within an optical fiber.
Numerical aperture: Acceptance angle of the fiber.
Optical repeater: Optoelectric device that receives a signal and amplifies it and retransmits it. In digital
systems the signal is regenerated.
Related Topics
31.3 Circuits ? 71.1 Lightwave Technology for Video Transmission
References
M.K. Barnoski, Ed., Fundamentals of Optical Fiber Communications, New York: Academic Press, 1976.
B. Bendow and S. M. Shashanka. Eds., Fiber Optics: Advances in Research and Development, New York: Plenum
Press, 1979.
A.H. Cherin, Introduction to Optical Fibers, New York: McGraw-Hill, 1983.
T. Li, Ed., Optical Fiber Communications, New York: Academic Press, 1985.
J.E. Midwinter, Optical Fibers for Transmission, New York: Wiley, 1979.
S.E. Miller and A.G. Chynoweth, Eds., Optical Fiber Telecommunications, New York: Academic Press, 1979.
Y. Suematsu and I. Ken-ichi, Introduction to Optical Fiber Communication, New York: Wiley, 1982.
? 2000 by CRC Press LLC
