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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

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39

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41

-50

Fig. 3.11. Non-ideal distribution

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42

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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.