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Retrospective Theses and Dissertations
Fall 1979
Optical Fiber Dispersion Characterization Optical Fiber Dispersion Characterization
Alan Edward Geeslin University of Central Florida
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OPTICAL FIBER DISPERSION CHARACTERIZATIO~
By
ALAN EDitVARD GEESLIN B.S.E., Florida Technological University, 1978
THESIS
Submitted in partial fulfilbrent of the requirerrents for the degree of .rvt..a.ster of Science in F.ngineeri_ng
1n the Graduate Studies Program of the College of Engineering at the University of Central Florida; Orlando, Florida
Fall Quarter 1979
OPTICAL FIBER DISPERSION CHARACTERIZATION
ALAN EDWARD GEESLIN
ABSTRACT
This thesis discusses the dispersion of optical pulses
in fiber \"aveguides. Procedures for determining the transfer
function of an optical fiber using either time domain measure-
ments or frequency domain measurements are given. A test set
is described which uses time domain measurements for dispersion
characterization. Complex transfer function data are presented
for various fiber lengths as well as optical connectors. Pre
diction of bandwidths of long fibers from bandwidth/measurements
taken on shorter length fibers is discussed. A relation between
the bandwidth of cascaded connectors in terms of the bandwidth
of a single connector is obtained.
Approved by: Director of Thesis
ACKNONLEDGMENTS
The author \vishes to express appreciation to the many
people who contributed to the preparation of this thesis. Drs. Sedki
and Achia Riad deserve special thanks for their valuable advice and
guidance. Mr. Mike Padgett fran the Electro-Optics I.ab at the Kennedy
Space Center, where much of the work for this thesis was perfonned,
gave valuable teclmical advice and assistance. Also, appreciation is
extended to Glen Birket and Steve Salvage for their assistance in
constructing and testing sane of the circuits used in the experiment.
iii
TABLE OF CONTENTS
. . . . . . . . . . . . . . . . . . . . . . . Chapter
I • rnTROOOcriCN . . . . . . . . . . . . . . . . . . . . II.
III.
IV.
v.
VI.
PULSE DISPERSIQ~ • . . . . . . . . . . . . . . . . . . . Pulse Dispersion Phenomenon Types of Optical Fibers • • Pulse Dispersion Evaluation
. . . . .
. . . . . . . . . . . . . . . . . .
. . . EXPERIMENTAL SET UP . . . . . . . . . . . . . . . . . . ~vires . . . . • • • . • • • • . . . . . . . . . Signal Processing Software • • Experimental Procedure • • • • • • • . . .
FIBER BANI»v"TDI'H VS. IENGI'H :MEASUREMENTS . . . . . . . . Experirrent and Results • • Discussion of the Results . . . . . . . .
a:t-INEcroR TESTING AND EVAIIJATICN . . . . . . . . . . . . Experirrent and Results . Sumnary and Conclusions.
CONCLUSIONS. • • • • • • •
. . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . APPTh"UIX . . . . . . . . . ~ . . . . . . . . . . . . . . . . . REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . .
iv
iii
1
3
3 4 6
19
20 22 26
45
45 49
73
73 76
88
90
99
OIAPTER I
INTRODUCI'ICN
This thesis is concerned with the pulse dispersiorr evaluation
of an optical fiber. Optical fiber waveguides have several advantages
over other rreans of ccmnunication, such as greater information handling
capacity, light weight, srrall size and reduced losses. They are nCM
becaning more important in the carmunications industJ:y, because of
requirerrents for systems with greater information handling capacity,
as well as increasLT}g costs of many altemate systems.
To properly evaluate optical waveguides, it is necessaxy
to be able to determine several important paramaters about them,
such as attenuatiort, nurrerical aperture, pulse dispersion, bandwidth
and rrechanical strength. Pulse dispersion testing is used to determine
a fiber' s bandwidth and is the tcpic of this thesis.
It is also necessary to evaluate connectors which may be
placed in the ccmnunication link, in order to predict the dispersion
pr<JI.=P-rties of a fiber link built with these components.
The effects of pulse dispersion are seen in the broadening
and rounding of an input pulse, and has the overall effect of reducing
bandwidth. The insertion of connectors in an optical fiber link will
cause a further reduction of bandwidth. Although extensive studies
have been given to attenuation due to connectors, none have been
found addressing their dynamic performance.
This thesis will study the effects of connectors on the
fil::er bandwidth, detennine the bandwidths of several lengths of
fiber, and atterrpt to detennine a relation between the measurerrents
of shorter lengths and longer ones, thus allONing prediction of long
fiber bandwidths fran shorter fiber measurerrents.
2
Chapter II covers pulse dispersion aspects in greater detail.
A discussion of tine danain :rreasurerrents vs. frequency danain rreasure
nents for measuring fiber bandwidths and detennining the transfer
ftmction is conducted.
Chapter III describes the experimental set up used in pulse
dispersion testing.
Olapter IV describes the experi.nent perfonned to detennine
the relati01Ship between a fiber's bandwidth and its length, and
discusses the results.
Chapter V describes the experiment perfonred to detennine
the effects of co..ru"1ectors on the fiber's bandwidth and discusses
the results.
Chapter VI presents a surrroary of the work done and suggests
additional research.
CHAPI'ER II
PULSE DISPERSION
Intrcxluction
This chapter will begin by presenting pulse dispersion as
a physical phencnenon in cptical fibers. Then, a ccmparison between
different types of fibers regarding their dispersion characteristics
will be presented. Finally, rrethcrls of fiber dispersion evaluation
will be discussed and analyzed.
Pulse Dispersion PhenCil'enon
Pulse dispersicn may be thought of as the spreading or
ratmding of an input pulse during its passage (transmission)_ through
a system, fig. 2.1. In optical fibers, there are two types of pulse
dispersion; material dispersion and rncx:1al dis:persion.
Materal dispersion occurs because of the dependence of
the material' s index of refracticn an the optical wavelength of the
transmitted light (Havell 1978) . Fig. 2. 2 sh<»~s a typical dependence.
This dependence results in a variation in the velocity of propagation
of various wavelength carponents which make up the optical pulse.
Ccrnponents with le11ger wavelength travel with greater velocity than
shorter ones. Thus the amount of material dispersion in a given
material is a function of both the optical spectnnn and material
properties. Material dispersion can be reduced by proper selection
4
of glass dopants, and by using sources with narrav spectnims (Gallawa
1979) •
Moclal dispersion is caused by the different path lengths taken
by different light rays in a multi -mode fiber, fig. 2. 3. Modes of
higher order travel a greater distance, per tmit length of fiber, than
lCMYer ones. '!his results in a variation in the velocity of propaga-
tion of various mcrlal carponents making up the optical pulse. Higher
order m::xles travel slONer than laver order rncx:les. Thus, the a:rrount
of rro:lal dispersion in a given fiber is a fnnction of both the number
and order of rrodes launched onto the fiber, and the difference in path
lengths taken by the mcrles. Modal dispersion may be minimized by
prcper design of the index profile; typically one whose refractive
index decreases as the square of the guide radius (Kawakami 1968) , as
will be seen in the follONing section.
Types of (£tical Fibers
There are three main types of fibers in cannon usuage; single
rrroe fiberS 1 Step-index rnultimode fiberS 1 and graded-index multimode
fibers.
Single Mode Fibers
Single mode fibers are fabricated to allCM propagation of
only a single mcrle. A step-index fiber is used, which consists of
a rcxl of dielectric with index of refraction n1 , called the core,
surrom1ded by a medium with index of refraction n2 , called the cladding,
(n1
>n2), fig. 2.4. It has been shown that if
2 -n 2
< 2 .. 405 (2.1)
5
only a single mode, designated the HE11 merle, will propagate (Barnoski
1976) .
. By all<:Ming only a single mode to propagate, modal dispersion
is avoided, leaving only material dispersion. Thus, both lCM dispersion
and high bandwidth are achieved. To achieve propagation in one mode,
h~~ver, the diarreter of the core is around 2 to 4l-lm (H~ell 1978) •
Since present cptical sources have ernmitting surfaces which are much
larger than this, (in the order of 631Jm), it is not practical to couple
large arrounts of :p::Mer onto these fibers.
Step-Index Multirrode Fibers
Step-index multirrode fibers are fabricated to allCM propagation
of rrore than one mode. A step-index fiber with
\a j ni - n~ > 2.405 (2.2)
is classified as a rnultinode fiber (Banloski 1976). This increase is
usually done by increasing the diameter of the core. The larger core
area allONS more energy to be coupled into the fiber fran the source. ,,
.Mcx1al dispersion occurs, h011ever, because of the different path lengths
between high and lON order nodes.
Graded Index Multinode Fibers
A graded-index multirrode fiber is one in which the core
index decreases paralx:>lically from the center outward, as desdribed by
n(r) = n1 J l- 2(n1-n2;n1) (r/a) 2 (2.3)
where n1
is the refractive index at r = 0, n2 is the cladding index,
r the fiber radius (125llm) and a the core radius (501-lffi), fig. 2.5
6
(Gallawa 1979).
In these fibers, the light rays are bent in a sinusoid-like
curve about the fiber axis, fig. 2. 6. The increased velocity of the
rays away fran the axis (in the laver index region) canpensates for
the increased path length resulting in laver dispersion. Core
diameters of around 63~ allow efficient coupling with available
sources, all<Ming rrore energy to be placed on the fiber.
This thesis will deal only with graded-index rro.Iltimcx::1e fibers,
because of their ability to accept energy fran sources and because
of their reduced dispersion. For these reasons, graded-index
multimcrle fibers have becare the rrost carm:Jn type of fiber used
for wide-band carmunication systems.
In the section to follCM, rrethcx:1s of pulse dispersion evaluation
in fibers will be discussed and analyzed.
Pulse Dispersion Evaluation
In the discussion that follcws, pulse dispersion refers to
the total dispersion, which is the canbination of both material and
nodal dispersion. There are two main rnethcrls of pulse dispersion
evaluation; direct estimate using pulse spreading and detennination
of the impulse response and/or ccxrplex transfer function.
Pulse Spreading Estimate
If an input pulse v. (t) is applied to a system, the output 1.
v (t) will be altered due to the transmission medium, fig. 2.1. 0
Pulses of this type are usually described by their full 'Width measured
7
at half of their maximum value, or full duration-half maximum, {FDHM).
The arrotmt of pulse spreading may be detennined by detennining the
difference between input and output pulse widths.
The pulse spreading due to nodal dispersion is given by
6t = L l l J (vg)l ,m - vg(O,O)
max max
(2.4)
where (v ) 1 is the group velocity for a nod.e of order (l,m) and g ,m
L is the length of the fiber, or
6t = nL [-n2 __ _
c 2nk2
(1 + m + 1)21 max max J (2.5)
where n is the indax of refraction at the center of the waveguide,
c is the speed of light in free space, n2 is the rate of change of n
with radius, and k is 2~, N = 1,2,3· • ••
In the effects of material dispersion are also included,
the relation beccnes
lit= 2L [nn2 c ck3
2 dn ]' (1 = m = 1) - ~ llw (2. 6)
where dn/dw is the change inn with the change in the frequency of
the optical source, and /J.w is the width of the frequency spread of
the source (Yariv 1976) .
Once the pulse spreading is detennined, the maximum frequency
which the system \vill pass is detennined fran the relation
f = 1 max !J.t
This nethod, while it does give an idea of the system bandwidth,
provides very little information about the transfer function.
(2. 7)
8
Advantages of this method are that little time is required for
the rreasureroent, and there is no need for signal acquisition or
processing. A disadvantage of this rrethod is that the result is often
inaccurate since the result is highly dependent on the shape of the
input pulse.
Irrpulse Response/Ccrcplex Transfer Function
As will be seen in this section, the determination of the
Inpulse Response/Carplex Transfer Ftmction yields canplete infonnation
about a fiber's response to various types of inputs, independent of
the input wavefonn.
A fiber may be characterized by either its inpulse response
waveform, h(t), or its carplex transfer function, H(ejw). The
inpulse response is the output of a system when excited by an ideal
Dirac delta inpulse. It is presented in the time danain, and the
output y (t) for a knONn input x (t) is found using the relation
y(t) = x(t) * h(t) (2.8)
where * denotes the convolution operation. Obtaining h (t) fran this
relation requires deconvolution in the time danain.
The canplex transfer function, H (ej w) is presented in the
frequency danain, and is the canplex ratio between the harmonic
output, Y(ejw) and the hanronic input X(ejw). Since H(ejw) is pre-
sented in the frequency dcmain, it provides a clear picture of fre
quency and phase distortion, as well as the usuable bandwidth of
the system. The output of a system Y(ejw) is found using the
relation, fig. 2.7,
9
(2. 9)
Obtaining H (ejw) fran this relation involves division in the fre-
quency dcmain, or
H(ejw) = Y(ejw)
X(ejw) {2 .10)
Signals in the tine and frequency dOIPain are related by the
Fourier transform pair
V(ejw) =}"" v(t) e -j 2llft dt (2.11) -oo
v(t) = j oo V(ejw) e+j2ITft df -oo
(2.12}
where V(ejw) is a canplex frmction.
'When using frequency dcmain rreasurerrents, the output signal
Y (ej ~ is treasured and recorded while the input signal X (ej w) is
held at a fixed frequency. The value of the transfer function for
that frequency InClY then be calculated as described above. To obtain
the transfer function, the process must be repeated for all frec;{Uencies
of interest.
This rrethcxl of testing is very tine consuming, since it requires
rreasurenent of both the input and output signals over all frequencies
of i.T"lterest.
Using time danain rtEasurerrents, a single rreasurement of the
input x(t) and the output y(t) are sufficient. Although a true
Dirac delta irrpulse cannot be generated, a duration limited inpulse
may be used for x ( t) • The Fourier transfonn may be used to convert
the input x(t) to X(ejcu) in the frequency danain, and y(t) to Y(.ejw).
Then, the transfer function H(ejtu) is found using eq. (2.10). If
10
desired, the impulse response may be otained by applying the inverse
Fourier transfonn to H(ejw) to obtain h(t). This is the deconvolution
process, fig. 2.8.
Surrmary
In order to determine the transfer functicn of optical
fibers, whose bandwidth may extend beyond 1 GHz, it is necessacy to
employ tirre danain rreasurerrents. This is because, at present, there
are no optical sources capable of being driven at the high frequencies
required, and still emit enough energy to be able to evaluate fibers
of practical length for camumication systems (Hc:Mell 1978). Also,
tine dara.in testing allCMS rapid convenient measurements which reduce
errors caused by changes in rceasurerrent equiprrent with time. Such
testing has becane even more attractive in recent years due to the
developrrent of lON cost carputers and A/D converters.
Step-index fibers are no longer of practical i.rrportance
in rrost high-bandwidth systems, due to improved perfonnance of graded
index fibers. Graded-index rnult.im:xle fibers, because of their unique
canbination of adequate source coupling and acceptable pulse dispersion,
have beccne the rrost ccmnon type of fiber to use in wide-bandwidth
system.
The experirrent, presented in the next chapter, will study the
pulse dispersion of graded-index multimode fibers using tirre danain
analysis.
--?
Sys
tem
>
Inp
ut
Ou
tpu
t
Fig
. 2
. 1.
Pu
lse s
pre
adin
g d
ue
to t
ran
smis
sio
n t
hro
ug
h a
sy
stem
J-1
J-1
12
n
1.472
1.470
1.468
1.466
1.464
1.462
1.460
1.458
1.456
1.456 ~----------------~----~----~------~urn .5 .6 .7 .8 .9 1.0 1.1
Fig. 2.2 Dependence of index of refraction (n) on wavelength (llm)
hig
h o
rder
m<X
le
lCM
ord
er
mcx
:le
Fig
. 2
. 3.
Mod
al d
isp
ers
ion
in
dic
ati
ng
dif
fere
nt
path
len
gth
s
14
I I I I I I I I I I I I
E-cladding (n2
)
Fig. 2. 4. Step-index fiber index profile
15
n
1.490
1.485
1.48
100 60 40 20 0 20 40 60 80 100
Fig. 2. 5. Graded-index fiber index profile
16
• \0
• N
X (
ejw
) .....
... I
Y(e
jw)
H (e
jw)
;""
Fig
. 2
. 7.
Rela
tio
n b
etw
een
in
pu
t an
d o
utp
ut
ccrn
pone
nts
in t
he f
req
uen
cy d
anai
n
....,
....J
X (
t)
-r
y ( t
) .
F
X (e
jw) ~
. Y
(ejw
) H
(elW
)=
X (e
iw)
~
y (e
j~)
H (e
jw}
_ r
-t
- -
F =
FOU
RIE
R T
RAN
SFO
RM
r-
1 =
INV
ER
SE
FO
UR
IER
T
RA
NS
FO
RM
Fig
. 2
. 8.
The
dec
on
vo
luti
on
pro
cess
h ( t
)
O!APTER III
EXPERIMENTAL SET UP
Intrcrluction
This chapter will describe the experimental set up and
procedure used in pulse dispersion testing. The devices used will
be described and reasons for their choice given. Finally, observations
made during the experiment regarding alignrrent sensitivity and larmch
conditions will be discussed.
Experimental Set Up
The experimental test set up used for pulse dispersion
testing is shavn in fig. 3.1. The cptical link consisted of an in
jection laser dicxle (ILD) for an optical source, and an avalanche
photcxlicx:1e (APD) for the optical detector. For accurate test results,
the response tine of the ILD/APD canbination must be at least as
fast as that of the fiber being tested.
The optical output fran the liD was focused through a lens
and lannched onto the fiber. The fiber was held at both ends by
vact.mm chucks equipped with three-axis positioners, to allaN precise
alignrrent of all components for maximum ~er transfer. When the
pulses left the fiber, they were focused onto the surface of the
optical detector. The output of the photodetector was then sampled,
and signal analysis performed on the aa;ruired signal as mentioned
in Chapter II.
A sanpling oscilloscope was used, because of the requirerrent
for picosecond time resolution. A variable trigger de~ unit was
also required, in order to ccnpensate for signal delay caused by
the test equitm=nt and the fiber being tested. Finally, a mini
ccroputer was required for signal acx;ruisi tian and processing.
The pulse dispersion test was an insertion type rreasurerrent.
First, a reference or "input" wavefonn, x(t), was obtained using a
short (1 to 2m} fiber placed between the IID and the APD. This was
done to allaH ease of rreasw:enent and accol.IDt for input and output
latmch concli tions similar to those experienced during the actual
testing of the fiber.
20
The response wavefann, y (t), was then obtained by replacing
the short reference fiber by the fiber being tested. Because align
nent is extrerrely critical, three-axis positioners were used in
all rreasurenents to maximize the anplitude of the detected waveform.
D=vices
This section describes the devices used in the test, and
reasons for their selection.
c:ptical Source
The optical source chosen was an RCA SG2002 semiconductor
injection laser dicxle, (IID). It is capable of generating O.lns
cptical pulses, and can generate up to 2 watts of optical poNer.
To drive this ILD, an inpulse generator was rEqUired which
could generate 4 to lOA pulses of lOOps to lns duration. The
irrpulse generator used in this exper.i.rrent is sh~ in fig. 3.2.
An avalanche transistor is used to generate the current pulses.
21
The variable capacitor is used to adjust the amplitude of the pulse,
and assure that no secondary pulses occur.
A circuit for providing thennal cooling of the avalanche
transistor was built and is sham in fig. 3.2. This served to
remove excess heat fran the transistor, and allCJNed repetition rates
of up to 15kHz. It also maintained the circuit at a constant
temperature (20°C} vvhich helped reduce errors due to thennal drift
during the wavefonn aCXjllisi tion process.
Trigger Circuit
A trigger circuit is required to trigger the :i.npulse generator
and the sanpling oscilloscope. This circuit must have lav jitter,
since any jitter it produces will appear in the neasured waveform
and introduce errors.. The circuit used for this purpose is shCMn
in fig. 3. 4. This circuit also includes an adjustable delay to can
pensate for signal delays.
A trigger delay is required because of the delay between the
triggering of the ILD irrpulse generator and the arrival of the
output signal at the input of the sarrpling oscilloscope. This delay
ti.rre is de:pendQ~t on the length of the fiber being tested.
The delay circuit contained within the sampling oscilloscope
provides delays of up to lOOns, which allONS testing of fibers up
to about 500m in length without additional delay.
For longer lengths of fiber, an extelllal delay circuit was
required.. A Berkeley Nucleonics Corporation delay generator,
rncx:1el 7030,was used. This device provides delays of between
75ns and 99 .. 999us, with a maximum of lOOps of jitter.
Optical Detector
The optical detector used was a Mitsubishi avalanche
photcxliode, m:xlel PD1002, which is specified by the manufacturer
to have a gain-bandwidth product of 800GHz. For this experirrent,
it was operated at a gain of 1000, indicating a cutoff frequency
of 800MHz. The bias and coupling circuit used with this dicrle is
shown in fig. 3.5.
Sarrpling Oscilloscope and Minicarputer
A Tektronic Digital Processing Oscilloscope (DPO) was used
for aCX}Uiring and digitizing data. The plug-in used with the DPO
was an S-2/7512 sampling unit of the sarre manufacture, providing a
transition duration of 75ps, which is equivalent to a bandwidth
( 3dB dCMn) of 4. 6GHz.
22
The DPO was interfaced to a Hewlett-Packard 9825 minicarputer,
whic~ was used for data acquisition and processing.
The test set as described displayed about 20ps of jitter
noise, which was reduced by signal averaging.
Signal Processing Software
Signal processing software is used to obtain the desired
information, H(e]{tl) fran the infonnation available, x(t} and y(t).
The concept is to transfonn both the input x(t) and the output y(t)
to the frequency danain using the fast Fourier transform {FFT) and
perform conplex division to obtain
23
H{ejw) = Y{ejw)/X(ejw) (3.1)
The actual process is sarewhat more involved.
One of the limitations of the test system is the limited
number of sanple points which the oscilloscope can provide. The
oscilloscope can provide a rnaxirm.lm of 512 ti.rre danain samples.
The fr~cy danain resoluticn of the FFr is related to
both the number of data points and the tine interval between them
by the relation
( !1 T) ( !1 f) = 1/N (3.2)
where T is the tim= between samples in the tine danain, f is the
frequency difference between two consecutive sarrples in the frequency
danain, and N is the number of sanple points.
If it can be assumed that the signal has a value of zero
outside the tirre windav as seen by the oscilloscope, additional
zeros may be added up to the capability of the processing equiprrent.
With the HP9825 system, up to 1024 points nay be processed. Therefore,
the choice of the time windav of the oscilloscope will determine the
tirre and frequency resolution.
The desired time windCM may be detennined by considering
the frequency danain relation
BW = 0.35 It (3.3)
where BW is the bandwidth, (3dB), and t is the fastest transition
duration to be rreasured. The time windON must be chosen such that the
24
desired signal does not occur between sarrple pulses in either the t.ime
or frequency danain. Also, it is desirable to have equal resolution
in both the tine and frequency danains so that conversion between
the two will not intrcxluce large errors.
The transition duration in an acquired waveform may be
expressed as
(3.4}
where Nt is the number of points in the tiire danain sanple contained
within the transition duration, and the cx:>rrespanding bandwidth in
the frequency danain may be expressed as
(3.5)
where Nf is the number of points in the frequency danain transform
contained within the required bandwidth, fig. 3. 6.
With the above considerations, it is easily shown that the
required acquisi lion t:irre window is
T = (t) (25) (3.6)
where T is the length of the tine windcw (Riad 1979) .
For a typical pulse used in the test set, with t = 0. 733ns,
the desired tirre windo..v is 18. 3ns. This corresponds to a sweep
rate of 18.3ns/10cliv, or about 2ns/div, which is the range used.
Therefore,
~ T = 20ns I 512 = 39ps
and
~ f = (1/1024) I (39ps) = 25MHz
(3. 7)
(3. 8)
For :pJint to point correstxJndence, both reference and response
pulses must be taken with the sarre T.
25
After the wavefonns have been converted to the frequency
danain, carplex division is required to obtain the transfer function.
At high frequencies, \mere signal levels are quite lew, errors may
result when the reference function X (ejw) approaches zero. These
errors are removed by filtering the transfer function. A seventh
order Chebychev filter was used in the experirrent.
The f~cy danain resolution may. be increased by applying
the inverse Fourier transfonn (.IFFT) to M sanple points out of the
original N sanple points, fig. 3. 7. The value chosen forM must be
less than N, and ITD..l.St be a pc:Mer of two. Also, to inclu:1e the band-
width of the transfer function in the band processed by the IFFT, it
is required that M/2 > Nf. As before, the tine and frequency danains
are related by Fq. (.3.2) with N replaced by M, or
11 Tm = (1/M) (1/~ f) (3.9)
where the subscript "m" refers to the :rrodified frmction. If addition-
al "zeros" are added until the number of points again equal N (or .
512) the FFT will provide a frequency danain transfer fnnction with
N sanple points with a frequency spacing
/j f = (1/N) (L1 T) = (6 f) {M/N) m
(3.10)
Since M is less than N, the frequency danain resolution has been
increased by a factor of N/M.
In this experiment, M was chosen to be 128. This yielded
~ f = 128/512 (11 f) = (0.25) (25MHz) = 6.25MHz (.3 .. 11) m
The transfer function is presented as 1 I H (eJcu), or atten-
uation and phase functions of frequency:
AaTEN = -10 log10
H(ejw) (3.12)
26
and
]t..u PHASE = -arg (H (e ) ) (3.13)
where arg ( ) is the ccntinuous argurrent function.
The continuous argurrent function must be reconstructed fran
the carputed argurrent functioo which varies fran -ln to +lrr, fig. 3.8.
The carputed argurrent function can be made continuous by adding or
subtracting multiples of ln° as shCMn in fig. 3.9. This continuous
argurent will contain a linear phase carponent which results fran
differences between the delay generator delay and the signal delay.
Its renoval allavs the phase cha:cacteristics due to dispersion to be
viewed, but does not affect its information, fig. 3 .. 10.
Software to perfonn the alx>ve functions is sh(J{ID in a block
diagram in the Appendix.
Experirrental Procedure
This section describes a mode scrambler, the reasons for its
use, and the prc:x:edure used to acquire data.
M:xle Scrambler
For accurate results, unifonn launch conditions are rEqUired
for all reasurerrents. A mode scrambler provides a unifo:rm modal
distribution for the launch into the test fiber, approximating a
steady state conditio.11. For an optical source with a non-ideal
intensity distribution as in fig. 3.11, the mode scrambler provides
a more unifonn optical distribution for launch onto the test fiber,
fig. 3.12.
If a fiber were being tested by latmching directly fran a
source with an intensity distribution similar to that shown in
27
fig. 3.11, the rreasurerrent would be very sensitive to misalignment ..
The m:xlal distribution can be changed significantly by very small
aligrnrent changes. Since the optical intensity distribution falling
on the core is not unifonn, the m:xlal distribution cannot be controlled. ..
launch conditions will vary between rreasurarents, resulting in
rreasurarent errors. The use of the rrocle scrambler significantly
increases the accuracy of bandwidth rreasurenent against changes in
launch conditions.
A node scrambler is shavn in fig. 3.13. This device consists
of three 1m lengths of fiber, a step-graded fiber 1 follONed by a
graded-index fiber 1 followed by another step-graded fiber. This
configuration has been shONn to have a srooothing and circularization
of the optical source near-field pattern by the step index fiber, and
an angular mixing of the source far-field pattern by the graded
index fiber (Love 1979) .
In bandwidth rreasurarents lx>th with and without the node
scra1nbler 1 the source was rroved up to ± 1 core radius fran the
center position in the radial direction. Bandwidth measured at these
points indicate a rreasurerrent difference of ±1.28% using a rrode
scra-nbler and a difference of ±18.l% without one (Love 1979).
The node scrambler used in this experirrent contained a
second 1m length of graded-index fiber to allaN use of connectors
for ease of fiber neasurerrent 1 fig. 3. 14. This avoided the uncertan
tity of a step-index/graded-index inferface and a connector/connector
interface occurring at the same point. Such an occurrence could
cause excessive attenuation or an unkna-m nodal launch condition.
The mode scrambler used had an attenuation of about 2dB .•
Fiber Alignnent and Connectors
28
Proper fiber alignnent and end preparation is vital to re
peatable tests and rreaningful results. Losses in excess of 3dB can
occur for radial displacements of O.Olrrm (Shmnacher 1977}. Axial
misalignrrent is less critical, but can still cause a 2dB loss for
a separation equal to the diarreter of the fiber. Because fiber align
m:mt is critical, it is desirable to have an easy, repeatable means
of accurate fiber alignnent.
To allaN ease of fiber rreasurenent, a connector was used
between the merle scrambler and the fiber being tested. This connector
was in the optical link during all measurements, and was included in
all reference rreasurenents. Therefore, it is assumed that its effect
was accounted for during signal processing and rerroved.
The connectors used VJere manufactured by Deutsch and allav
rapid connection and disconnection of the optical fibers, fig. 3.15.
A co!mector set consists of two optical fiber connector plugs and a
feedthru connector receptacle. Each fiber to be cormected is first
tenninated in an optical fiber connector plug. This device protects
the end of the fiber v.,nen it is not connected to another fiber or
other device. A protective shield is extended when the connector
plug is not :in use, protecting the fiber frau damage.
Connector plugs are joined using a feedthru connector receptacle,
29
which depresses the protective shield on l:x::>th connectors, and brings
the fiber connectors into alignrrent. Index matching fluid is used
to reduce the refractive index differences across the connection and
reduce losses.
A connector tennination tool was provided by the connector
manufacturer to install the connector and break the fiber.
The ends of the fiber on the input end (Iill) and the output
end (APD) of the fiber link ~re held in pace by vacuum chucks, fig.
3.16. These devices held the fiber securely during testing, but alla.v
ed ease of rerroval. The fibers were placed in the vacuum chucks such
that the end of the fiber was even with the end of the vacuum chuck
nearest the source or detector.
Fibers placed in the vacuum chucks were first stripped of
their plastic coating, cut with a fiber cutting tool to assure a
SITJ:.X)th end, and their end touched to adhesive tape to remove direct
or other contamination fran the end of the fil:er.
Fine adjustrrents were then rna.de using the three-axis position
ers. The adjustrrents were made to maximize the output arrplitude as
viev.:ed on the oscilloscope. It was :possibl:e to move both the fiber
holders and the optical source and detector. Radial displacements
were more critical than axial ones. The lenses were fixed, and were
not adjusted.
Waveform Acquisition
After alignrrent was canpleted, the detected wavefonn was
acx;IUired. For a wavefonn viewed on an oscilloscope to be meaningful,
30
it is necessary to knCM the horizontal and vertical scales, and the
:pJint on the screen which is the zero volt or "ground" reference. To
obtain this reference, the optical path was interrupted by placing
a piece of qpaque material between the IID and the launch end of the
fiber. This was done so that any background radiation, radio fre
qu~'lcy emission or other noise will be included in the ground reference
and thus would be absent in the acquired waveform.
To reduce errors caused by noise and jitter, the ground re
ference was sampled several times, and the ground reference used was
the average of the samples. In this experiment, all waveforms were
sarrpled 50 tines. Signal averaging was perfonned by the carputer;
the averaged reference was then stored in memory.
Next, the roaterial blocking the optical path was removed, and
the waveform o~tained using averaging techniques as described above.
At the cc:mpletion of this process, the waveform was subtracted fran
the ground reference, point-by-:pJint, horizontal and vertical scale
factors read from the oscilloscope under computer control, and the
values of attenuators, if used, entered from the keyboard. Wideband
atte~uators were used, and were observed not to have a noticeable
effect an the mea~;ured waveform.
With this i:.11formation, the waveform, as seen by the oscilloscope
was n~ fully de£ ined, a1d was saved in canputer memory.. The
"reference" fiber was then rerroved frcm the test set and replaced by
the fiber under test, and the process repeated. VJhen the two wavefonns
have been acquired, the testing proceeds to the signal analysis 1 which
is as described earlier.
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37
38
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39
40
PHASE
CONTiNUOUS PHASE FUNCTION
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/
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ELINHNATED
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Fig. 3. 10. Elimination of linear phase
41
-50
Fig. 3.11. Non-ideal distribution
Fig. 3. 12. Uniform distribution
42
Splice
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OfAPTER IV
FIBER BANI:M:IJrH VS. LENGTH MEASUREMENTS
Intrcxluction
This chapter will describe the experinent perfomed to
detennine the relationship between a fiber's length and its band
width. The experirrental results are ccrrpared with theoretical values.
Fiber bandwidth measurerTEnts are usually specified as a
frequency-length product. This allavs the bandwidth rreasurernent
to be easily applied to longer or shorter lengths of the sane
fiber. Tests of this type have been reported by Gallawa (1979),
Dannwolf et al {1976) 1 and Gans et al {1977) , with bandwidths of
up to 1. 34GHz-km being reported (Riad 1979) .
When canbining several fibers of knavn bandwidth to form
a longer length fiber 1 it is desirable to be able to predict the
resulting bandwidth of the canbined system.
Experirrent and Results
To detennine the relation between a fiber's length and
its bandwidth, ten separate fibers, each of 600m length, were used.
The fibers were available in cabled fo:rm, with both ends of each
fiber accessible.
First, the bandwidth of each fiber was neasured, using the
procedure outlined in Chapter III. A merle scrambler was used for
46
all rreasurements 1 and a connector was used between the merle scrambler
and the fiber being tested. This connector was also used 'When taking
the reference pulse 1 by using the reference fiber between the rncxle
scrambler and the APD vacuum chuck, fig. 4 .1.
The pulse dispersion test involved relative differences
between the reference and the response pulse 1 therefore, this con
nector 1 since it was present in both wavefonns 1 is not expected to
have been detrirrental to the test accuracy.
After placing the fibers in the test set, the ouput of the
detected waveform was maximized by fine adjust:ment of the three-axis
positioners. Because the merle scrambler was used during all rreasure
rrents, the alignrrB"1t of the larmch end was not disturbed, and did not
require adjust:ment during the course of the test. The launch end
alignment was checked periodically during the test and was seen not
to vary by a rreasurable arrotmt.
A possible reason that realignrrent would be reg:uired is a ·
drift in the operating point of the ILD. This would rrost likely cane
about because of ten-perature variation of the transistor and diode
in the ILD circuit. The CCXJling circuit was able to maintain the
tenperature of the ILD inpulse generator to within ±o.l°C. The ILD
and avalanche transistor \vere in close thermal contact with the cooler,
so little terrperature difference was expected beh\-reen the two. After
an initial wann-up ar1d therrral stabilization pericx:l of about 30 minutes,
the anplitude and shape of the pulse were observed to remain constant
throughout a nonnal working day.
47
A single reference pulse was used for several tests. Test
ing was not begun until the test set, and the IID inpulse generator
in particular, was allaved to stabilize.
The variable delay tmit was not required to obtain the re
ference pulse. 'When testing the 600m fibers 1 hc:Mever, a delay of
2900ns was used, to canpensate for the signal delay through the fiber.
A typical reference pulse is shown in fig. 4. 2, and a typical response
pulse for a 600m fiber is shown in fig. 4. 3.
After signal processing as described in Chapter III 1 the
above waveforms yielded the transfer function shown in fig. 4.4.
The bandwidth was defined as the point having 3dB greater attenuation
than that of the lavest frequency point in the frequency danain data.
The bandwidths of the ten fibers are shONrl in table 4.1. Another
fiber (#1) was not used in the exper.i.nent.
Next, alternate 600rn lengths were spliced together to obtain
five 1. 2km lengths of fiber. A fusion splicer was used for
all splicing. The splice was located 600m fran the detector 1 thus
any high order rra:les caused by the splice are assurred to have been
attenuated to negligible levels prior to the pulses arrival at the
detector.
'The fibe.rs were cOlUlected such that the direction of propa
gation \vas always in the sarre direction, since fiber lengths tested
in the opposite direction could have different dispersion characteris
tics. This could care about due to differences in index profiles,
and non-symnetrical prcperties of the fused splices.
Each 1. 2km loop was then evaluated. The response pulse for
48
loop 2-3 is shown in fig. 4.5 and the response pulse for loop 4-5
is shONn in fig. 4. 6. After signal processing, these wavefonns
yielded the transfer functions of figs. 4. 7 and 4.8 respectfully.
Another reference pulse was obtained prior to starting the rreasure-
nents of the 1.2km lengths. The delay unit was set to 5840ns. The
3dB bandwidths were determined as before, and are shONI1 in table 4.2.
loops 2-3 and 4-5 were then spliced tcx:;ether to obtain a
2. 4km loop. Loops 6-7 and 8-9 were also canbined to obtain another
2.4km loop. The response pulse for loop 2-5 is shc:M1 in fig. 4.9
and the response pulse for lCXJp 6-9 is shCMn in fig. 4.10. After
signal processing, these waveforms yielded the transfer functions
of figs. 4.11 and 4.12 respectfully. Bandwidths of 450MHz were found
respectfully. During the testing of the 2.4km loops, the delay
generator was set to ll720ns.
Finally, the two 2. 4km loops were canbined to fonn a single
4. 8km loop. Another reference was obtained prior to testing the
4.8km loop. The delay generator was set to 23560ns.
It was noted tbat the output pulse had spread considerably,
relative to the input, fig. 4.13. It was necessary to go to the
Sns/div scale on the oscilloscope to obse:rve the entire waveform
wit.lrin the tL.Te windCM. A rreasurement was then taken on the 5ns/div
scale.
It was thought that perhaps the splice which was joining the
two 2. 4km loops was defective, and was causing the large amount of . dispersion. This splice was broken and repeated, and a second measure
rrent taken. It was still necessary to use the Sns/div scale to view
49
the entire pulse within the tine windON. The transfer function for
the 4.8km loop is shONn in fig. 4.14. The bandwidth of the 4.8km
locp was found to be 160.MHz.
Discussion of the Results
It was observed that several of the transfer functions con
tained a noticeable dip in the value of attenuation at a frequency
of arotmd 1300MHz to 1400MHz. This occurred because of the relation
between a pulse in the ti.rre danain and its frequency transfonnation.
If the input wavefonn is approximated by a triangular pulse, its
frequency transfonnation is seem to be of the fo:rm sin xjx, as shown
in fig. 4.15 (Stremler 1977}. The "zeros" of the frequency trans
formation are detennined by the width of the pulse.
The width of a typical reference pulse (measured at the
base) is about 1.5ns, fig. 4.2 The value ofT corresponds to half
of this quantity, or 0. 75ns. This indicates a first "zero" in the
frequency danain of 1333MHz.
At points where the magnitude of the frequency transfonns
approach zero, errors occurred in the division prcx::Ess used to
obtain the transfer function. When detennining the bandwidth of
transfer functions \vhose 3dB point fell within the disturbance,
a srocx:Jth curve was graphically placed through the data, neglecting
the disturbance. Other nndulations which occur on the plots are
also due to di visim errors and were averaged in the sarre manner.
The data were CXJITpared against two possible bandwidth
relationships. First, an inverse quadratic relationship was invest-
50
igated. In such a :relation, one can write
__ 2 2 2 2 1/Bw == (l/B1 + l/B2 + ••. + 1~ > (.4 .1)
where BW is the bandwidth of the overall system, and B1
, B2
, ... ~ are the individual bandwidths of the subsystems which make up the
cx:rrplete systan spare (Millman & Halkias 1972) •
The other bandwidth relation was an inverse linear one for
which
(4.2)
Predicted bandwidths using the inverse quadratic relationship
were calculated for all 1.2krn loops, using data obtained fran the
600m rreasurements. Predicted bandwidths for the 2. 4km fibers were
calculated fran bet-ill the 600m rreasurerrents and the 1. 2km rreasured
values. Predicted bandwidths for the 4. 8km loop -were ma.de fran the
600m rreasured values and the 2. 4krn rreasured values. This data 1 along
with rreasured values and percent error 1 is presented in table 4 .. 3 ..
Data calculated in a similar marmer using the inverse linear relation-
ship is given in table 4.4.
For fiber lengths 1. 2km and less, the inverse quadratic
relationship was found to be more accurate. For lengths greater
than 2. 4km, a linear approximation was seen to be more accurate.
This suggested that the actual bandwidth relationship might be of the
fonn
(4. 3)
where l<m<2.. calculations based on the 600m measurements are shovvn
in table 4.5 for m=l.S and in table 4.6 for ITF1.75.
It is seen that bandwidths calculated using values of m of 1.5
or 1. 75 are not in as good agreement as the inverse quadratic
relation (m=2) for fibers 1. 2km or less in length. For fibers in
the range of 2. 4km, using m=l. 5 appears to yield the rrost accurate
value while for longer lengths, the inverse linear approximation
51
(ITFl) appears to be a better approximation. This suggests a depen
dence on m on fiber length, since the bandwidth of short fibers
{ 1. 2km) is most accurately predicted using m=2 1 while bandwidths of
long fibers (4.8krn) are prerlicted with best accuracy using m=l.
St.nl'I"C\ary and Conclusions
Using rreasured bandwidths of short fiber lengths 1 it was
possible to predict to sane degree the bandwidths of longer fibers.
For fiber lengths up to aromd 1. 2km, usable predictions were possible
using an inverse quadratic relation. For fiber lengths greater than
4km, an inverse linear relation was found to be rrost accurate. For
fibers whose length is between these extreires, a mcxlified relation
was a bet·ter approximation.
A possible cause for the discrepancy is that sane of the short
lengths of fiber, due to slightly different index profiles, may have
responded differently to the light they received fran the preceeding
fiber than to the light they received fran the rrode scrambler. When
all fibers were initially tested using the merle scrambler, the latmch
conditions were assumed to be uniform. Hcwever, during testing of
cascaded sections it is possible that fibers which received their
light output fran preceeding fibers may not have received the sarre
modal distribution as they did during initial testing. Depending on
52
the marmer in which the modal distribution was changed by preceed.ing
fibers, this resulted in both higher and laver bandwidths for the
cascaded system.
TABIE 4.1
BANIW[Ol'H OF 600rn FIBERS
FIBER NUMBER 2 3 4 5 6 7 8 9
10 11
TABLE 4.2
BANIW[DrH (GHz) 1.4 1.24 1.4 1.6 1.1 1.84 1.15 1.46 1.56 1.48
B.1\NIMri1rH OF 1.2Km FIBERS
IroP 2-3 4-5 6-7 8-9
10-11
BANIW[IJrH (GHz) 0.88 1.64 0.93 0.92 1.39
53
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CHAPrER v
~R TESTING .AND EVAWATICN
Introduction
This chapter will describe the experiment perfonned to deter
mine the affect that cormectors have on bandwidth. Much work has
been done to detennine the lCM f~ency attenuation of connectors,
but none has been formd addressing their dynamic perfonnance. Such
knCMledge is r€Cjllired if connectors are to be used in wide bandwidth
cx:mnuni.cation systems. Connectors are likely to be used tmder a
variety of conditions, ranging fran closely spaced applications such
as optical patch panels, to spacing at great distances, such as
terminations of long cables. Their performance must be known at both
these extremes.
Experirrent and Results
The connectors used in this study were manufactured by Deutsch.
They are of the "Yv""et type, which use an index matching fluid to reduce
the refractive index difference across the connection and reduce loss
es. A connector set co.'1sists of two optical fiber connector plugs
and a feedtluu connector receptacle, fig. 3. 16.
Each fiber to be connected is first terminated in an optical
fiber oonnector plug. This device protects the end of the fiber when
it is not connected. to another fiber or another device. A protective
shield ·is extended when the connector plug is not ill use, protecting
the fiber fran damage. Connector plugs are joined using a feedthru
connector receptacle, which depresses the protective shield on both
connectors, and brings the fiber connectors into alignment. These
connectors are specified by the manufacturer to have an attenuation
of ldB or less.
74
To determine the bandwidth affect of connectors, a 6m length
of fiber was spliced in the center of two 600m fibers, fig. 5.1. Fused
~lices were used on the output end to avoid disturbing the APD fiber
adjustment. The affect of this connector was expected to be removed
during signal processing, since it was present during the aa.IU:iring of
the reference pulse. The 600m length after the connector test area
allONed steady state conditions to be reached after the connector
under test, and removed any cladding light which was created by it.
The bandwidth of the entire link was rreasured four times to
detennine an average value for the reference bandwidth and to detennine
the repeatability of the test set. Bandwidths of 810, 830, 770 and
832r~z were d:>tained, giving an average value of 810.5MHz, with a max
irnL-r.n error of 60MHz. A typical resp::>nse pulse and transfer function
are sha-m in figs. 5. 2 and 5. 3 respectfully.
Next, a single connector was installed, al:x>ut 0.6m fran the
end of the 6m fiber, on the end closest launch end of the test loop.
'fue test was repeated with the connector in the loop. The response
pulse is shON!l in fig. 5. 4 •
Additional connectors were added to the previous loop and
additional bandwidth measurements taken. Measurements were taken
75
with 3, 6 and 9 connectors. All connectors were contained within the
6m length, and were spaced at approximately 0.6m intervals, starting
fran the end closest the launch end. The response pulse obtained
with 3 connectors is sham in fig. 5. 5. The response pulses for 6 and
9 connectors are shOtm in figs. 5.6 and 5. 7 respectfully.
To determine the bandwidth of the connectors, it was necessary
to rerrove the bandwidth effects of the remainder of the connector loop.
This was done by using, as a reference pulse, the pulse obtained when
rreasuring the bandwidth of the connector lcx:p, fig. 5. 2. To detennine
the: bandwidths of connectors, response pulses obtained with the required
number of connectors in the lc::>q> were used.
The signal processing was the sarre as that used to detennine
fiber bandwidth except that no filter was used, and resolution enhance-
rrent was not performed. The filter was not used because the 3dB band-
width was within -L~e frequency range v..trich was usually filtered.
Because it was not possible to filter the data, it was not possible
to erllance the resolution of the frequency danain data. Thus, the
frequency resolution for the connector transfer functions is 25MHz.
The transfer fimctions obtained for the case of 1, 3, 6 and
9 connectors are shONn in figs. 5. 8 , 5. 9 , 5. 10 and 5. 11 respectfully.
The resulting 3dB bandwidths are shCMn in table 5.1.
TABLE 5.1
mNNECIDR BANIJiiTDI'H DATA
Number of Connectors 1 3 6 9
Bandwidth (GHz) 2.40 2.72 3.16 3.52
76
An initial inspection showed that in all cases, the bandwidth was
in excess of 2GHz, which was well above the bandwidth limitation of the
fiber. The data do not appear to follav any particular trend, and
the variation between the rreasurernents are likely the result of
"noisy" division.
Because the filter could not be used, erroneous results which
occurred at high frequencies, where the response function becarre
extrerrely small, were not removed fran the data. As seen fran the
transfer frmctions, the 3dB bandwidths are in the high frequency
"noisy" area. As a result, the ban&vidth could not be detennined
with the sane degree of accuracy as when the filter is used.
It was noted that cascading several connectors did not signi
ficantly reduce the bandwidth.
Surrmary and Conclusions
Cormectors were evaluated for bandwidth lirni tation rmder
conditions simulating both widely spaced (1) and closely spaced
(multiple) connectors. In both cases, it was found that the bandwidth
of the connectors did not fall below 2. 4GHz, even with a cascade
system of 9 oonnectors. This figure is well above the bandwidth
of the fibers to which they are attached. This indicates that
with present firers, the cormectors do not adversely affect the band
width.
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CHAPTER VI
CONCIDSICNS
Intrcx:luction
This chapter discusses the results of the experinent and
additional researdl suggested by the results.
Fiber Bandwidth Measurements
It was found that the bandwidths of cascaded fibers folla.v
an inverse quadratic relation for fiber lengths less than 1. 2km, and
an inverse linear relation for short fiber rreasurem=nts applied to
longer fiber { 4. Bkm) . Between these limits, the actual bandwidth
was seen to fall retween the predictions made by these two relations.
It is felt that additional information is needed about the
index profile and the resulting mcx:1al distribution of each fiber in
order to make a nnre accurate bandwidth prediction. The mode scrambler
provided a normal distribution to each fiber during its initial testing,
but this same mcx:lal distribution may not have been seen by all fibers
during the cascaded system rreasurernents.
Depending on the index profile of the first fiber, a larger
or smaller number of higher order modes may have been received by the
second fiber. This difference in modal distribution may have resulted
in different amounts of pulse dispersion and therefore different
bandwidths ..
89
One way which this might be demonstrated would be to include
a merle scrarrbler between eaCh 600m length of fiber. This would cause
the roodal distribution entering each fiber to be the same as that
encountered during single fiber testing. This procedure would, havever,
introduCE additional attenuation, which could be a prcblem 'When measur
ing long lengths of fiber. If necessary, additional gain could be
provided by an extemal wideband arcplifier.
Connector Bandwidth ~asurerrents
It was found that the bandwidth of optical connectors is
much greater than present optical fibers. A series of up to 9 cascaded
connectors exhibits essentially the sane bandwidth as a single connector.
To accurately evaluate the bandwidth of connectors, a test systems with
a wider bandwidth than the present one may be required.
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REFERENCES
Andrews, J. R. "Autanatic Network Measurerrents in the Tine Danain." Proceedings of IEEE 66 (April 1978): 414.
Barnoski, Michael, ed., Frmdarrentals of Optical Fiber Crnmunications. New York: Academic Press, 1976.
Conradi, J. ; Kapran F. ; and ~t, J. "Fiber-optical Transmission Between 0. 8 and 1.4)..llll." IEEE Transactions on Electron Devices 26 (February 2, 1979): 180.
Dannwolf, J.; Gottfried, s.; Sargent, G.; and Strum, R. "OpticalFiber Impulse-Res:ponse Measurerrent System." IEEE Transactions on Instrurrentation and :Measurenent 25 (December 1976): 401-406.
Gallawa, R. "Recent r:Evelcpnents in Optical Waveguide Carmunications." Electr~tical Systans o=sign 11 (July 1979): 42.
Gan, W.; Andrews, J; and Riad, S. "Application of an Autcmated Pulse M=asurenent System to Telecamnmication Measurements. " Paper presented at the URSI Measurement and Telecarmunications Conference, Larmion, France, October 3-7, 1977.
Gec.'<eler, S. "Dispersion in Optical Fibers: New Aspects." Applied 9Ptics 17 (April 1, 1979): 1023.
Ha.-Jell, D. "Optical Carmunication Systems." Electronic Products Magazine 21 (September 1978): 42.
Kawa'kami, S. and Nishizawa, J. "An Optical Waveguide with Optimum Distribution of the Refractive Index with Reference to Wavefonn Distortion." IEEE Transactions on Microwvave Theo:ry and Techniques 16 (October 1968): 814-818.
Krurrner, R. "Observation of a Cascade Effect for cptical Fiber Splices." Paper presented at the Topical Meeting on Optical Fiber Carrm.mication, Washington, OC., March 6-8, 1979.
love, D. "Navel ~e Scrambler." Paper presented at the Topical .Meeting on Optical Fiber Ccmnunication, Washington, OC., March 6-8, 1979.
Millman, Jacob and Halkias, Cristos. Integrated Electronics: Analog and Digital Circuits and Systems. New York: MCGraw-Hill, 1972.
100
Nemoto, S. and Yip, G. "Propagation of Rectangular and Gaussian Pulses in a Self-Focusing Optical Fiber." Applied Optics 17 (January 1, 1978): 57.
Olshansky, R. and Keck, D. "Pulse Broadening in Graded-Index Optical Fibers." Applied Optics 15 (February 1976) : 487.
Riad, S. 110ptical Fiber Dispersion Characterization Study ... Final Re:port, NASl0-9455, NASA. Presented at Kermedy Space Center, Florida, December 11, 1979.
Schumacher, W. "Fiber Optic Connector Design to Eliminate Tolerance Affects." Paper presented at the lOth Annual Connector Sy!rq;:x)sium, Chen:y Hill, New Jersey, 1977.
Stremler, Ferrel. Introduction to Carmunication Systems. Reading, Massachusetts: Addison-Wesley, 1977.
Thyagarajan, K. and Ghatak, A. "Pulse Broadenir..g in Optical Fibers." Applied Optics 16 (October 1977): 2583.
Yariv, A. Introouction to (£tical Electronics. New York: Holt, Rinehart & Winston, 1976.