REDUCnON
OF
PULSE DI!jTORTION IN
TRAVELLING
WAVE
SEMICONDUCTOR
OPTICAL
AMPLIFIERS
M.
J.Sonei a. J.F.Gonzalez, S.Ruiz-Mo eno
&
J.Gui a
Dp o.
Teo ia
de
la
Se lal y Comunicaciones. ETSIT-BARCELONA,
UPC
c/Jo ge Gi ona
Salgado
s/n.
08034
BARCELONA. SPAIN.
ABSTRACT-
The
nonlinea
phenomenon inhe-
en
in
a elling
wa e
semiconduc o
op-
ical
ampli ie s
can
p oduce
se e al ha m-
ul
e ec s
in
ansmission sys ems
such
as
pulse
dis o ion
in
mul i-Gbi /s
in en-
si y-modula ion sys ems.
In
his
communi-
ca ion,
is
pasan ed
a
heo e ical
in es-
iga ion
o
he
possibili y
o
educing
he
gain
sa u a ion
du ing
he
pulse
am-
pli ica ion
p ocess
by means o he com-
pensa ion
o
he
ca ie
densi y
a ia-
ions.
This
should
be
e y use ul in many
op ical
sys ems
and,
specially,
in
high
speed
communica ion
sys ems.
1.
INTRODUCTION
T a elling wa e semiconduc o op ical am-
pli ie s (TWOA)
a e
eme ging
as
p ac ical
componen s
o
use in op ical communica-
ions sys ems. using bo h di ec and
cohe en de ec ion. Se e al wo ks
[11,[21
ha e shown
ha
hey
posses
many ad an-
ages,
being i s high gain o e
a
e y
wide bandwid h one o he mos ou s anding
cha ac e is ic. Because o
i s
la ge band-
wid h
TWOA
a e
specially sui able
o
am-
pli y na ow op ical pulse
[31.
The de ice
gain can be signi ican ly educed du ing
he pulse p opaga ion and, in consequence,
he ailing pulse
edge
can ecei e less
gain han he leading edge causing he
pulse dis o ion. This
is
due o he gain
sa u a ion om dec ease o ca ie
densi y.
On he o he hand, in
a
high bi
a e
ansmission sys em is hinkable ha he
ime in e al be ween wo consecu i e sig-
nals is compa able o
o
e en smalle han
he ca ie li e ime o he de ice.
As
a
consequence, he ca ie densi y will no
be enough ime
o
eco e . Clea ly, he
gain expe ienced by each indi idual pulse
will be di e en om each o he and de-
penden on he o egoing signals. In his
communica ion we s udy he possibili y
o
educing he a ia ions
o
he
ca ie
densi y and
so
he sa u a ion gain unde
dynamic condi ions. The me hod p oposed
o
educe he sa u a ion gain akes in o
ac-
coun he p opaga ion coo dina e because
he
ca ie
densi y diminu ion
is
la ge
a
he end
o
he ampli ie .
In
Sec ion
2
we s ablish bo h he basic equa ions which
go e n he dynamics
o
he
ampli ica ion
p ocess and he heo e ical
base
o he
compensa ion scheme o he
ca ie
den-
si y. Some esul s
a e
p esen ed in Sec-
ion
3.
whe e we discuss he e ec s o
compensa ion on he ampli ied pulse and on
he
ca ie
densi y. The main conclusions
a e
d awn in Sec ion
4.
2.
NONLINEAR MODEL
OF
A
TWOA
2.1
Basic Equa ions
In he s udy
o
pulse p opaga ion in TWOA,
he ampli ie is modeled
as
a
se
o wo
le el sys ems wi h ansi ion ene gies
ex ending o e he whole
ange
o he con-
duc ion and alence bands. The basic
equa ions which go e n pulse p opaga ion
in semiconduc o op ical ampli ie
a e
(3)
whe e
(1)
and
(2)
come om he wa e
e-
qua ion and hey gi e he longi udinal a-
ia ion o powe , P, and phase,
#,
o he
pulse.
Gp
and Lp
a e
he powe gain and
he losses in he medium espec i ely, F
is he phase gain and
N
is he
ca ie
densi y. The equa ion
(3)
is
he ca ie
densi y
a e
equa ion which go e n he
ca-
ie
densi y wi hin he ac i e egion. Ne
CH2964-5/91/0000-0186$01.00
01991
IEEE
186
is
he ca ie densi y due o bias cu- he i s e m is cons an and ep esen s
en ,
TS
is
he
ca ie
li e ime,
h
is he pumping
ca ie
densi y necessa y o
he Plank cons an ,
U
is he op ical e- ob ain he small
signal
gain, ha
is,
(9)
quency and wad is he ac i e egion
c oss
and he second e m
is
he compensa ion
as
a ea.
The gain unc ions can be exp essed
Go
=
GplN=N~~,
p=O
Gp(N,P)= TG(N)[l-Kp(P)I
(4)
e m de ined by
whe e
is he con inemen ac o .
G(N)
wi h
his,
he
solu ion
o
equa ion
(3)
can
con ains he dependence wi h he ca ie be app oxima e
as
Nc Neo
when pulse wid h
is much sho e han he ca ie li e ime.
densi y, which is ep esen ed by
a
polynoi
Bu equa ion
(10)
p esuppose
o
know he
mica1 app oxima ion gi en by
G(N)
=
ZAIN
supp esion unc ions which
a e
de ined
I41
o
he
ampli ie
which
is
un hinkable.
wi h i4-04.
KP(p)
and
a e
he gain gain and he op ical
powe
a
each poin
P/P
s
(6)
Howe e , i we assume ha
exi s
an ideal
compensa ion he gain can app oxima e
as
Kp(P)=
Gp(N)
Go
(11)
(Go-Lpl~
(12)
ha is,
(11)
and
(12)
a e
easonable ap-
p oxima ions
as
o en
as
N(z. )=NBo.
Then,
subs i u ing in equa ion
(10)
we ob ain
and
so,
P(z, )
I
PIN( 1.e
(7)
being
13
and phenomenological
and
ps
a
no malized
powe
which depends
on
he semiconduc o medium. The pa ame e s
TS
Go
(GO-LP)Z.~~~(~)
alues used in he simula ions a e
hu
w*dWe
NBC(Z,~)
=
-
summa ized in Table
I.
wd
L
A
Ao
Ai
A2
A3
A4
LP
a
13
Ps
NBO
7s
0.3
pm2
300
pm
1.55
pn
0.3
-1.92.1
o5
2.42-
10'
-8.47
*
1
O5
1.55.
lo;
-1.06-
lo1
4000
m-
0.3
ns
5.0
4.5
420
mW
2.5
-
10
"65
Table
I
2.2
Theo e ical compe n
s
a ion
o
In he same way han
[SI,
in o de o com-
pensa e he diminu ion o he ca ie den-
si y we ha e sepa a ed
Ne
in o wo e ms
(8)
non1 inea i y
i
n
TWOA
Ne(z. )
=
NBO
+
Nec(z, )
(13)
he e o e, he compensa ion unc ion de-
pends on he inpu op ical signal and he
z-coo dina e by
a
exponen ial unc ion. I
is possible o app oxima e his unc ion
by sec ions di iding he ampli ie in o
a
numbe m o equal sec ions. In each
o
hese he pumping ca ie densi y akes
he mean alue o
Nec(z, ),
hen we can
ob ain
whe e i=l,..,m is he sec ion numbe and
L
is he ampli ie leng h. I
m=l
(only one
sec ion) he esul is he same ha
[51
doing
Lp
x
GO.
So
hen he scheme p oposed
o compensa e he ca ie densi y
is
d awn
in igu e
1.
3.
RESULTS
AND DISCUSSION
The
se
o equa ions
(11,
(2)
and
(3)
can
187
_
%--x
I’nu
(0
II
1
7II-1
_-
PI11
--
(I)
I
--I
lWOA
]----
Figu e
I:
Compensa ion scheme.
no be sol ed analy ically and, in conse-
quence, is necessa y i s nume ical solu-
ion. In he simula ions we ha e consi-
de ed
a
Gaussian pulse o which
whe e
Ein
is he inpu pulse ene gy and
o
is ela ed o he ull wid h
a
hal maxi-
mum (FWHM) by p=1.665 o. In igu e
2
is
ep esen ed he ca ie densi y
as
a
unc-
ion o he p opaga ion coo dina e
z
o
he pulse peak when he e is no compen-
sa ion, cu e
(c),
and when he e is he-
o e ical compensa ion (131, cu es (b) and
(3.
The di e ence be ween hese las
cu es is ha (b) does no ake in o ac-
coun he sup ession gain e ms in con-
as
o
(a)
whe e hey a e aken in o ac-
coun . O cou se, when he e is no compen-
sa ion he ca ie densi y dec ease along
ampli ie leng h when pulse is passing.
Ne e heless, when compensa ion is ope a-
ing he ca ie densi y is ap oxima ely
cons an i he gain sup ession e ms
a e
no aking in o acoun (K~(P)=KF(P)=O). On
he con a y, when hey
a e
aking in o
accoun exi s
a
ligh inc emen
a
he end
o he ampli ie . The alue o ca ie
densi y gi en by
(13)
is la ge han he
alue gi en by (10) because he i s does
no look
a
he gain disminu ion due o
op ical powe in he medium (sup ession
phenomenon).
In igu e
3
is shown he e olu ion o
ca-
ie
densi y along ampli ie leng h when
he e is compensa ion conside ing he he-
o e ical case (cu e (a)), only one
sec-
ion (cu e (b)) and ou sec ions (cu e
(cl).
We
can obse e ha he a e age
o
he ca ie densi y in each sec ion is
app oxima ely cons an and equal o he
ca ie densi y ob ained in he heo e-
ical
compensa ion case. This is he main
eason om wha he shape and phase o
he ampli ied pulse
a e
independen o he
N
(m-’)
2.55E Q24
3
Z.SOE+O24
2.48 024
2.4OE 024
2.35E 024
2.3JOE 024
Figu e
2:
Theo e ical compensa ion.
2.45€+024
2.4OE+024
1
2.3=+024
Figu e
3:
E olu ion
o
ca ie densi y o
sec ions numbe used
as
we will
see
in i-
gu es
4
and
5.
Howe e , he sec ion numbe
has in luence on he inal le el achie ed
o
he ca ie densi y and, he e o e, on
he ecupe a ion ime o ini ial
s a e
(be o e he pulse ampli ica ion)
o
he
ampli ie . I his ime dec eases, he
se-
pa a ion be ween wo consecu i e pulses
can dec ease, being he gain o each in-
di idual pulse he same.
The inpu pulse phase ep esen ed by equa-
ion (15) is equal o ze o, ne e heless
will be modi ied du ing he ampli ica ion
p ocess. The di e ence be ween he
ins an aneous equency and he op ical
equency can be ob ained
as
di e en
sec
ions.
1 ddJ
2n
d
A ec
=
-
- -
(16)
188
(Pd
Figu e 4: Ampli ied pulse powe .
A
ec .
0.03
-0.12
3
20
40
80
1
Figu e
5:
Ou pu equency displacemen .
In igu es 4 and
5
a e
shown he shape and
equency displacemen , A ec, o de am-
pli ied pulse, espec i ely. The cu es
(e)
ep esen he si ua ion whe e he e is
no compensa ion and he o he s
a e
o he
compensa ion si ua ion. The cu es
(a)
and
(b) ep esen he heo e ical compensa ion
wi hou and wi h sup ession gain, and
(c)
and (d) ep esen he compensa ion
case
wi h sup ession gain o one and ou
sec ions espec i ely. The igu e
4
shows
as
he ampli ied pulse wi hou compen-
sa ion is ligh ly assyme ic ( he pulse
maximum shi s o he leading pulse edge)
as
a
consequence ha he ailing pulse
edge ecei e lowe gain han he ailing
edge. In
a
Compensa ion si ua ion (cu es
(b),(c) and (d)) he shape o ampli ied
pulse is independen o he numbe o
ampli ie sec ions. This is due o each
sec ion has he same a e age gain along
he ampli ie leng h. In igu e
5
can be
obse ed ha whi hou compensa ion he
equency displacemen inc eases almos
linea ly o e he cen al pa o he
pulse. Such
a
linea cha ac e is ic im-
plies ha he pulse
can
be comp essed in
a
dispe si e medium. Like he shape, he
equency displacemen is independen o
he numbe o sec ions. On he o he hand,
he displacemen maximum is lowe in
a
compensa ion si ua ion. No ed ha in
a
compensa ion si ua ion wi hou sup ession
(cu e
(a))
A ec
is
almos equal o he
inpu one. This esul con i ms ha he
compensa ion o he ca ie densi y dimi-
nu ion is mo e e ec i e
a
leas impo -
an is he sup ession phenomenon.
4.
CONCLUSIONS
In his communica ion we ha e p esen ed
heo e ical esul s ela e o dynamic
compensa ion o he sa u a ion gain in
semiconduc o op ical ampli ie s. The me-
hod o educe he sa u a ion gain con-
sis s o
a
inhomogeneous pump o he
ampli ie . This inhomogenei y can be achi-
e ed using
a
mul isegmen ampli ie . The
ob ained esul s show ha when he numbe
o sec ions inc ease, he ime in e al
be ween wo consecu i es pulses can de-
c ease being dynamic gain equal o each
indi idual pulse.
On he o he hand, his compensa ion
me hod is alid o low a ia ions
o
he
ca ie densi y in ela ion
o
he
injec ed ca ie densi y
(NBo).
Unde his
condi ions, he dynamic gain is close o
small signal gain o he ampli ie .
5.
REFERENCES
189
1--
IT
I
II
J.C.Simon,
"Semiconduc o Lase Ampli-
ie o Single Mode Op ical",
J.
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1983.
T. Sai oh
&
T.
Mukai,
"1,s
pm
GaInAsP
T a el
1
ing-Wa e Semiconduc o Lase s
Amp1
i
ie s",
IEEE
J.
Q.Elec on.,
V.
23,
no.6,
1987.
I. E. Ma shall,
e
al."Picosecond Pulse
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G.
P.
Ag awa1,"Spec al
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Gain Sa u a ion In Semiconduc o La-
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S ong-Signal Theo y",
J.
Applied
Physics, .
63,
no.4,
1988.
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e
al.,
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o
non1 inea i y in Sc.op ica1 ampli ie s"
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