Q1
(a) Explain clearly how each of the following physical mechanisms causes attenuation
in a silica optical fibre, stating in each case how the attenuation depends on
wavelength:
(i) Intrinsic absorption;
(ii)Extrinsic absorption;
(iii)Rayleigh scattering.
[6 marks]
(b) For a singlemode optical fibre explain concisely what meant by the terms mode
field diameter and normalised spot size. With the aid of a simple sketch graph explain
how the choice of normalised frequency V for a fibre influences the normalised spot
size.
[6 marks]
(c) For a singlemode fibre the mode field radius w is related to the fibre core radius a
by the expression:
- 3/2
-6
w
= 0.65 + 1.619V
+ 2.879V
a
For a given optical fibre at a wavelength of 1500 nm the mode field diameter is found
to be 10.2 µm, when the normalised frequency is 2.15. Show clearly the steps
involved in deciding if singlemode operation is still possible at 1320 nm for this fibre.
Comment briefly on the decision with reference to the two possible definitions of cutoff wavelength in common use.
[9 marks]
(d) With the aid of suitable ray diagrams describe the two types of bending loss that
can occur in a multimode fibre.
Explain why bending loss in a singlemode fibre is wavelength dependent.
[4 marks]
Q2
(a) What is meant by the term “refractive index profile” for an optical fibre? Sketch
each of the four refractive index profiles below and in each case state concisely a
typical application were such a profile would be encountered:
(i)
Step index;
(ii)
Graded index;
(iii)
Depressed cladding;
(iv)
Triangular profile.
[8 marks]
(b) Describe briefly the three generic types of fibre-to-fibre joint in use in fibre
systems. For each type of joint state a significant advantage and disadvantage.
[6 marks]
(c) Two identical multimode step index fibres are aligned together in a fibre joint.
Each fibre has a radius of a µm. Assuming a uniform power distribution in the fibre
core derive an expression for the coupling efficiency expressed if the only joint defect
is a small lateral misalignment of d µm.
[8 marks]
(d) Hence determine the coupling attenuation in dB for a joint between two identical
50/125 µm fibres, assuming that the only source of attenuation is a lateral
misalignment of 3 µm.
[3 marks]
Q1
(a) Loss mechanisms in a Silica Optical Fibre
Intrinsic absorption loss:
Intrinsic absorption is caused by the interaction of the light with one or more of the
components of the glass itself. For silica glass there is a low loss window between 800
and 1600 nm where intrinsic absorption is negligible, by comparison with other loss
mechanisms, such as scattering loss (see below). Intrinsic absorption in this window
falls between 700 nm and 1500 nm, then rises again toward 1700 nm
Extrinsic absorption loss:
Absorption of light caused by impurities in the fibre, such as water and metals ions.
One of the most common impurities is dissolved water in the glass, present as the
hydroxyl or OH ion. In this case the fundamental processes takes place between 2700
nm and 4200 nm, but gives rise to so called absorption overtones at 1380, 950 and
720 nm. Extrinsic absorption depends only on the absorption wavelength of a
particular impurity and on the level of the impurity. Very recently newly developed
fibre manufacturing techniques have virtually eliminated absorption loss peaks giving
rise to silica fibres which show no absorption peaks, This in turn opens up
transmission at wavelengths circa 1400 nm and 1000 nm, which have not been
utilised to date.
Scattering Loss:
Scattering is a process whereby all or some of the optical power in a mode is
transferred into another mode. This frequently causes attenuation, since the transfer is
often to a mode which does not propagate well. (also called a leaky or radiation
mode). One of the most common forms of scattering is Rayleigh, a the dominant loss
mechanism in the low loss silica window between 800 nm and 1600 nm. The
attenuation caused by Rayleigh scattering falls off with wavelength as a function of
the 4th power of wavelength.
[6 marks]
(b) Mode field diameter (MFD) is an important property of SM fibres. The amplitude
distribution of the HE11 mode in the transverse plane in the fibre is not uniform, but is
approximately gaussian in shape. The MFD is defined as the width of this amplitude
distribution at a level 1/e (37%) from the peak or for power 13.5% from the peak
The spot size is the mode field radius w. Its value relative to core radius “a” is given
by the expression:
3
/
2
6
w

=
0
.
6
5
+
1
.
6
1
9
V
+
2
.
8
7
9
V
a
where V is the fibre “V-value”. V thus influences the spot size for given core size, as
shown in the diagram below.
As the V value approaches 2.4 the spot size
approaches the fibre radius. For a V < 2 the
spot size is significantly larger than the core
size, so an optical signal is partially contained
within the cladding and attenuation increases.
Since beyond V = 2.4 singlemode operation is
impossible for this reason V should be between
about 2 and 2.4
w
/
a
3
2
.
5
2
1
.
5
1
1
.
2
1
.
4
1
.
6
1
.
8
2
.
0
2
.
2
2
.
4
V
v
a
l
u
e
N
o
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m
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p
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V
v
a
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u
e
[6 marks]
(c) Problem:
Firstly it is noted that the two unknown parameters are the fibre core radius and the
numerical aperture.
Firstly calculate the actual fibre core radius “a”. Using the formula relating w/a to the
normalised frequency V then since V is 2.15 then w/a is 1.19.
The MFD is 10.2 µm, so the spot size is 5.1 µm. Thus the core radius is 4.28 µm.
Using this value of core radius and the normalised frequency V of 2.15 it is possible
to find the numerical aperture for the fibre, the only missing parameter. Now:
2

V
=
a
.
N
A

For a wavelength of 1500 nm from this expression the NA is found to be 0.120
Using the all of the parameter values available the fibre cutoff wavelength can be
calculated by rearranging the expression above and using the cutoff value of the
normalised frequency V = 2.405.
2

a
N
A
c
=

V
c
Using the above expression the cutoff wavelength is found to be 1341 nm. Below this
wavelength V > 2.405, so singlemode operation is not possible at 1320 nm according
to the strict criteria above.
In practice the theoretical cutoff wavelength above is difficult to measure. An
alternative is EIA (Electronics Industry Association of America) cutoff wavelength,
which states that the cutoff wavelength is:
“The wavelength at which the power in the
HE21 mode is 10% of the power in the HE11
(fundamental mode)”
Since the EIA cutoff wavelength can be 100 nm less than the theoretical cutoff
wavelength it is possible that singlemode operation defined as above could still take
place at 1320 nm. To determine this the power in both the HE11 and the HE21 mode
would need to be calculated.
[9 marks]
(d) Macrobending:
Bending loss caused by tight cable bends. At such a bend illustrated below the
conditions for total internal reflection are not maintained for some rays. This occurs
because for such rays have angles of incidence to the cladding less than the critical
angle in the vicinity of the bend. Thus optical power is lost into the cladding.
Microbending:
Bending loss caused typically by microscopic deformations of the core cladding
interface. At such a deformation illustrated below the conditions for total internal
reflection are not maintained and some rays and thus optical power are lost into the
cladding. It is considered to be more critical than macrobending since it is largely due
to processing flaws rather than mishandling.
The bending loss most often associated with poor cable installation is macrobending
and with poor cable design the loss is most commonly microbending.
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Bending loss and wavelength in a singlemode fibre
The higher the operating wavelength above the cutoff wavelength the lower the fibre
V-value
But a lower V-value means a larger MFR, so for longer wavelengths the MFR and
thus the loss increases. Thus for example the loss due to bending can be expected to
increase at 1550 nm relative to 1330 nm
[4 marks]
Q2
(a) The refractive index profile of a fibre is define as the relationship between
refractive index and distance, in a radial fashion, from the centre of the core
outwards to the cladding and beyond
There are a number of common refractive index profiles
(i) Step index
C
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l
a
d
d
i
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g
Step index is the simplest profile, commonly found in large core multimode fibre,
suited to low bandwidth, short range applications
(ii) Graded index
C
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l
a
d
d
i
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g
In a graded index core the refractive index follows a parabolic like form out from the
centre of the core to the cladding. The result is lower modal dispersion. It is used in
multimode fibre types for modest campus types distances were the limited bandwidth
(typically 200-800 MHz.km) is acceptable
(iii) Depressed cladding
C
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l
a
d
d
i
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g
Depressed cladding profiles are a feature of some singlemode fibres, as opposed to a
conventional matched cladding profile. The advantage of this profile is a reduced
susceptibility to bend loss. Typically such fibre are used over longer distances, but
where bend loss is an issue.
(iv) Triangular profile
C
o
r
e
C
l
a
d
d
i
n
g
A triangular profile is found in some singlemode fibres which are dispersion shifted.
This means that the dispersion minimum no longer occurs in the 1320 nm window,
but instead in the 1550 nm window. Typically used over long distances at high bit
rates.
[8 marks]
(b) Fusion splice
A fusion splice is created using a machine, which fuses the precisely aligned and
cleaved fibre ends together using an electric arc.
The advantages are very low loss and low material cost. A disadvantage is the high
cost of the splice machine.
Optical fibre connector
This form of connection is analogous to an RF electrical connector. A typical
connection involves two connectors and an alignment sleeve. Within each connector
the fibre is epoxied in place in a precisely aligned ferrule. A connection is created by
aligning the two ferrules.
Connectors have the advantage that they are demountable but the disadvantages of
high material cost and a higher average loss per joint.
Mechanical splice
A mechanical splice typically utilises a deformable precision metal tube into which
the two cleaved fibres are placed. Pressure on the tube deforms the tube, holding the
aligned fibre in place.
Advantages include a low tooling cost and low loss and the fact that the splice is
demountable. A disadvantage is the high material cost relative to a fusion splice.
[6 marks]
(c) Model assumes optical power is uniformly distributed over the fibre core, so it is
best suited to step index multimode fibres. Diagram shows two fibre cores out of
alignment by a distance "d", with the overlap of cores is shown by crosshatched area.
Fibre radius is "a"
Coupling efficiency is defined in this simple case as the ratio of overlap to core area
d
+
+
a
In general for a circle with a radius "a" the area of a segment defined by the angle is
given by:
Area = 1/2 a2 ( sin  )
To find the coupling efficiency we need to find the total overlap area. The overlap
area is twice the area of the segment defined by the vertical line x-y in the diagram
below. From the formula above we can now find the area of each segment and thus
x
+
+
a
y
d
the overlap area
To proceed we need to express the area of a segment in terms of the core radius and
the misalignment "d" Consider the right angle triangle shown below as a detail of the
segment. From this we can express  as a function of d/a
a
a
22
d
2
/
a
+
+
 a



+
/
2
d
a
2
d
1

=
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(
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2
d
s
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Thus:
a
2





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a
p
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e
a
=
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=
a
(
s
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n
)
b
u
t
=
1
d

2
a
(
/
)
2
c
o
s
a
1
d
1
d
2


2
a


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(
/
)
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(
(
/
)
)
[
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B
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)
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o
s
(
2
B
)
a
2


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d
2
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

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d
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=
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(
/
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2
.
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(
/
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(
(
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:
2
2
a
d
/
2
a
[
(
)
]
[
()
]
2
d
/
2
a
(
)
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1
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d
2c
2
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

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=
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(
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)
/
o
s
2
d
/
2
a
(
)
1
a
1
d
d
2
2
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
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a
(
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c
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a
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d
/
2
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(
)
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1
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d


2
a


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a
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=
/
(
/
)
/
c
o
s
[8 marks]
(d) Exercise:
For a 50 µm fibre the core radius “a” is 25 µm. For a misalignment “d” of 3 µm the
ratio d/2a is .06.
To find the attenuation at a joint we need to find the coupling efficiency, assuming
that the only source of attenuation is lateral misalignment.
Substituting d/2a into the coupling efficiency formula derived above we get a
coupling efficiency of 92.3%. In dB this represents a loss of 0.34 dB
[3 marks]