Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
5, N
o
. 1
,
Febr
u
a
r
y
201
5,
pp
. 23
~30
I
S
SN
: 208
8-8
7
0
8
23
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Dynamic Response of Two-Elec
trode Dist
ri
buted Feedback
Laser
f
o
r St
able Signal Mode Operation
H. B
o
usse
ta
*,
A. Z
a
t
n
i
*
,
A
.
Amg
h
ar
*
*
,
A.
M
o
ume
n
*
,
A.
E
l
yam
ani
*
* M.S.I.T
Labor
ator
y
,
Depar
t
ment of Co
mputer
Engineering, hig
h
school of
t
ech
nolog
y
,
Ibn
Zohr
University
, Agadir
M
o
rocco
** Departmen
t
o
f
ph
y
s
ics, facu
lty
of scienc
es, Ib
n Zohr Univ
ersity
, Agadir
Morocco
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Sep 8, 2014
Rev
i
sed
No
v
13
, 20
14
Accepted Dec 10, 2014
The long
itudin
a
l spatial hole bur
ning (LSHB) eff
ect h
a
s been kno
wn to limit
the performance of distributed
fee
dback (DFB) semiconductor lasers to
achi
e
ve a be
tt
er
d
y
nam
i
c s
i
gn
al
m
ode
operatio
n (DSMO). So, in order to
ensure a stab
le (
D
SMO), we pro
pose
a novel d
e
vice d
e
sign of two electrode
DFB lasers with
longitudin
a
l v
a
ri
ation
in t
h
e
coup
ling co
effi
cie
n
t (
d
istribute
d
coupling
coefficient (DCC)), th
e structur
e also contains a phas
e
shifted
in
m
i
ddle of
the
ca
vit
y
.
B
y
m
eans
of the
finite d
i
ff
erence time domain (FDTD)
numerical metho
d
, we analy
ze d
ynamic re
sponse of our structure
and we als
o
compare the res
u
lts with the conven
tion
a
l two electrode DFB laser (TE-
DFB). The numeric
al sim
u
lation
shows
that, a better d
y
n
a
mic signal mode
has been achiev
ed b
y
TE-DCC-DFB lase
rs in com
p
arison with TE-
DFB laser
due to its better
and high side mode
suppression ratio (SMSR). Therefore, th
e
TE-DCC-DFB lasers will be us
eful to ex
tend t
h
e transm
ission distance
in
optical f
i
ber
co
mmunication s
y
s
t
ems.
Keyword:
Distrib
u
ted fee
dbac
k
lase
rs
Dynam
i
c response
Finite differe
n
ce tim
e
dom
ain
Nu
m
e
rical si
mu
latio
n
Copyright ©
201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Ham
za Bousse
ta,
M
.
S.I
.
T La
b
o
r
a
t
o
ry
,
De
part
m
e
nt
o
f
C
o
m
put
er E
ngi
neeri
n
g
,
hi
gh
sc
ho
ol
o
f
t
ech
n
o
l
o
gy
, I
b
n
Z
o
h
r
Uni
v
e
r
si
t
y
,
Aga
d
ir
M
o
rocc
o.
Em
a
il: Ha
m
za.
b
o
u
sseta@g
m
a
il.co
m
1.
INTRODUCTION
Ad
va
nced se
m
i
cond
uct
o
r l
a
ser are key
devi
ces i
n
hi
gh s
p
ee
d m
o
der
n
o
p
t
i
cal
com
m
uni
cat
i
o
n
sy
st
em
s [1-7]
.
Am
ong m
a
ny
di
ffe
re
nt
l
a
ser st
ruct
ures
, t
h
e di
st
ri
b
u
t
e
d
f
eedbac
k
(DFB
) st
ruct
ure
has
been
wi
del
y
use
d
i
n
sem
i
cond
uct
o
r l
a
sers t
o
ac
hi
eve a st
ab
le DSMO due to t
h
eir sm
all size
, high optical out
put
po
we
r, fa
st
res
p
o
n
se a
n
d l
o
w
t
h
res
hol
d cu
rre
nt
[
8
-
12]
. T
h
e
r
efo
r
e,
Int
r
o
duc
i
nga
/4
p
h
a
se sh
i
f
t in
th
e gratin
g
st
ruct
u
r
e i
s
ef
f
ect
i
v
e fo
r achi
e
vi
n
g
st
abl
e
si
gnal
m
ode o
p
e
r
at
i
on
beca
use
of
hi
g
h
si
de m
ode s
u
pp
ressi
o
n
rat
i
o
[1
3-
1
4
]
.
H
o
we
ver
,
t
h
e
prese
n
ce of t
h
e
phase
shi
f
t
whe
n
t
h
e co
up
ling
co
efficien
t is larg
e or
at higher
i
n
jection
currents
, ge
nerally causes spa
tial non
uni
form
ities of photon and ca
rrier
de
nsities or e
ffe
ctive inde
x along t
h
e
cavi
t
y
[1
5]
, t
h
i
s
phe
n
o
m
e
non
cal
l
e
d spat
i
a
l
h
o
l
e
b
u
r
n
i
n
g (
S
HB
) e
ffect
[
1
6]
, Thi
s
S
H
B
i
s
fo
u
nd t
o
en
ha
n
ce t
h
e
si
de m
ode.
Usual
l
y
a vari
et
y
of
m
e
t
hods
can be use
d
t
o
sol
v
e t
h
i
s
i
ssu
e, t
h
e fi
rst
one
consi
s
t
e
d i
n
e
n
l
a
r
g
i
n
g t
h
e
t
h
res
hol
d gai
n
m
a
rgi
n
by
i
n
t
r
od
uci
n
g
ga
i
n
co
upl
i
ng
m
echani
s
m
or con
s
t
r
uct
i
ng
di
st
ri
b
u
t
e
d c
o
u
p
l
i
n
g
coefficient gra
tin (DCC-DFB
)
[17
-
20
], th
e secon
d
is to
weaken the no uniform
di
stribu
tion of car
riers
,
fo
r
ex
am
p
l
e th
ey
can
b
e
o
b
t
ain
e
d
b
y
u
tilizin
g
m
u
l
tip
le d
i
screte p
h
a
se sh
ift (MPS-DFB
)
[21
]
o
r
b
y
in
trodu
cing
l
o
n
g
i
t
udi
nal
c
h
i
r
pe
d grat
i
n
g f
o
r
b
r
ag
g pe
ri
o
d
[5]
,
[
22]
a
n
d
[
23]
.
In o
u
r p
r
evi
o
u
s
w
o
r
k
, we pr
op
ose
a
t
w
o
el
ect
ro
de
DFB laser
with
stro
ng
er cen
t
re coup
lin
g and
a
/4
p
h
a
se sh
ift in
th
e cen
ter of t
h
e cav
ity (TE-DCC-DF
B
)
,
t
h
i
s
st
ruct
u
r
e i
s
anot
her
way
t
o
i
m
prove
t
h
e
out
put
param
e
t
e
rs suc
h
as
S
M
SR
and
p
o
w
er
o
u
t
p
ut
. S
o
, i
n
t
h
i
s
pap
e
r,
we h
a
ve
si
m
u
l
a
t
e
d t
h
e
d
y
n
am
i
c
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
5, No
. 1, Feb
r
uar
y
20
1
5
:
2
3
– 30
24
p
a
ram
e
ters o
f
TE-DCC-DFB
laser and
com
p
ared
it with
con
v
e
n
tion
a
l
TE-DFB laser in
ord
e
r t
o
sho
w
th
e
sup
e
rio
r
ity
of
ou
r st
ruct
ure.
The rem
a
i
nder
of t
h
i
s
pa
per i
s
or
ga
ni
zed as
f
o
l
l
o
w:
t
i
m
e dom
ai
n
m
odel
i
n
cl
udi
n
g
t
h
e c
o
upl
e
d
m
odel
equat
i
o
ns
an
d
n
u
m
e
ri
cal
sim
u
l
a
t
i
ons m
e
tho
d
a
r
e
b
r
i
e
fl
y
descri
be
d i
n
sect
i
o
n
2.
Sim
u
l
a
t
i
ons
re
sul
t
s
o
f
pr
o
pose
d
st
r
u
c
t
ure,
nam
e
ly
thos
e co
ncer
ni
ng
dy
nam
i
c charact
eri
s
t
i
c
s i
n
sect
i
on
3. F
i
nal
l
y
, we cl
osed t
h
e
pape
r
by
a
bri
e
f c
oncl
u
si
o
n
i
n
sect
i
o
n
4
.
2.
THEOR
Y
AN
D DESC
RIPT
ION OF MO
DEL
The laser struc
t
ure analyzed i
n
our m
odel is depi
cted sc
he
matically on Figure 1. T
h
e s
t
ructure is
related
to two electrod
e
s, the first
electrod
e
ex
tend
from
0
z
to
/2
zL
. Co
nt
rariwise
the
s
econ
d
electrode
, from
/2
zL
to
zL
, the
bias
curre
nt
I
A
an
d I
B
are i
n
j
ected ind
e
p
e
nd
en
tly in
to th
e cav
it
y. Th
e
stru
cture is d
i
vid
e
d
i
n
to fo
ur sectio
n
s
, th
e le
ng
th
of th
e cen
t
er an
d sid
e
sectio
n
s
is L
c
an
d
L
s
(L
c(s)
is th
e len
g
t
h
o
f
th
e section with
coupling coe
fficient
()
cs
k
), respectively.
The norm
a
lize
d
co
upl
i
ng c
o
effi
ci
ent
o
f
si
de
sections a
n
d
of center sections are
s
s
kL
and
cc
kL
, res
p
ectively.
Fi
gu
re
1.
Sc
he
m
a
t
i
c
di
agram
of
TE-
DC
C
-
D
F
B
l
a
ser
Tak
i
ng
i
n
to
acco
un
t the longitu
d
i
n
a
l ch
an
ge of th
e coup
lin
g co
efficien
t
in
th
e stru
ctu
r
e i.e
k
is
z
d
e
p
e
nd
en
t. Thu
s
,
fo
r
TE-DC
C-DFB laser, th
e co
up
ling
coefficien
t
ratio
as:
0.
75
0.
33
cc
ss
kL
r
kL
(1
)
with
Tot
a
l
kL
de
fi
ne
d as
2(
)
Total
s
s
c
c
kL
k
L
k
L
(2
)
The s
p
atiotemporal dynam
i
c of the
DFB is
characterize
d
by the carrier
num
ber de
nsit
y
N
and t
h
e
electric field
of
00
(,
)
(
,
)
(,
)
o
iz
iz
i
t
total
E
z
t
F
z
te
B
z
te
e
(3
)
Whe
r
e
F
and
B
re
prese
n
t
t
h
e
sl
o
w
l
y
va
ry
i
n
g
en
vel
o
pes
of
t
h
e
fo
rwa
r
d a
n
d
ba
ckwa
r
d
w
a
ves
,
w
h
i
c
h
are coupled through t
h
e laser structure a
n
d
0
is the re
fere
nce
fre
que
ncy
.
0
is th
e prop
ag
atio
n
con
s
tan
t
at
bra
g
g f
r
e
que
nc
y
,
gi
ve
n
by
0
/
, with
is th
e p
e
riod
o
f
th
e
g
r
ati
n
g
T
h
e
rat
e
e
quat
i
o
ns
o
f
t
h
e
carri
e
r
de
nsi
t
y
a
nd t
i
m
e depen
d
e
n
t
co
u
p
l
e
d
wave e
q
uat
i
ons
o
f
t
h
e sl
o
w
l
y
vary
i
n
g
e
n
vel
o
p
a
r
e gi
ve
n by
[1
7]
:
,
23
(,
)
(
,
)
(,
)
(
,
)
ab
I
dN
z
t
N
z
t
B
N
zt
C
N
zt
dt
qV
(,
)
(
,
)
1(
,
)
go
o
CA
N
z
t
N
P
z
t
Pz
t
(4
)
r
a
Z
k
s
k
c
k
c
L
c
L
c
L
s
0
L/2
L
r
b
I
A
I
B
k
s
Θ
=
π
/2
L
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
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8-8
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8
Dyn
a
m
i
c
Res
p
ons
e
of
Tw
o
-
El
ect
rode
Di
st
ri
b
u
t
e
d
Feed
b
a
ck
Laser
f
o
r
St
abl
e Si
g
n
a
l
M
ode
…
(
H. Bousset
a
)
25
()
1
(,
)
(
,
)
(,
)
(
,
)
iz
s
g
F
zt
g
z
t
i
zt
e
F
z
t
Ct
z
()
()
(
,
)
(
,
)
iz
ik
z
e
B
z
t
G
z
t
(5
)
()
1
(,
)
(
,
)
(,
)
(
,
)
iz
s
g
Bz
t
g
z
t
i
z
t
e
Bz
t
Ct
z
()
()
(
,
)
(
,
)
iz
ik
z
e
F
z
t
G
z
t
(6
)
Wi
t
h
g
C
is th
e g
r
oup
v
e
locity,
s
is th
e o
p
tical lo
ss co
efficien
t,
q
is the elec
tron cha
r
ge
, the
param
e
ter
stands for the elec
trons lifetim
e,
V
is th
e cav
ity v
o
l
u
m
e,
is a n
o
n
-lin
ear co
efficien
t to
tak
e
in
to
accoun
t satu
ration
effects,
()
kz
is the coupling c
o
efficient. Als
o
,
,
A
B
I
is the uniform
current bias of
el
ect
rode
de
n
o
t
e
d
by
t
h
e
s
ubs
cri
p
t
,
B
is the bim
o
lecular recom
b
ination c
o
efficient,
C
is th
e
Au
ger
reco
m
b
in
atio
n
coefficient,
z
is the phase shift at
z
po
sitio
n
,
,
Nz
t
is th
e carrier d
e
n
s
ity,
0
N
is th
e
carrier
de
nsity at transpa
r
e
n
cy and
22
(,
)
(
,
)
(,
)
P
zt
F
z
t
B
zt
(7
) i
s
t
h
e ph
ot
o
n
den
s
i
t
y
[17]
.
,
g
zt
is th
e
m
a
t
e
ri
al
gai
n
, gi
ve
n by
[
1
7]
:
(,
)
(,
)
21
(
,
)
oo
A
Nz
t
N
gz
t
Pz
t
(8
)
Whe
r
e
is
the optical confine
m
ent factor,
0
A
is the diffe
renti
a
l gain. The
(,
)
zt
represent the
fre
que
ncy
detu
nin
g
defi
ned
as
[
17]
:
2
(,
)
(
,
)
ef
f
o
zt
n
z
t
(9
)
Wi
t
h
0
is an approxim
ate e
m
iss
i
on
wa
velength. T
h
e effec
tive
ref
r
active in
de
x ca
n
be e
x
p
r
e
ssed as
[
1
7]
:
(,
)
(
,
)
4
o
Ho
o
ef
f
e
f
f
o
A
nz
t
n
N
z
t
N
(1
0)
Whe
r
e
o
eff
n
is the
e
ffective i
n
dex
at transpare
n
cy
and
H
rep
r
ese
n
t the
pha
se am
plitude c
o
upli
n
g
f
actor.
The s
p
o
n
tane
o
u
s em
ission fields co
uple
d
in
to the
forward and backwa
rd
wave
s are
G
, thus th
e
autocorrelation function
defi
nes as
[17]:
2
*
(,
)
(
'
)
(
'
)
(
,
)
(
',
')
g
K
BN
z
t
t
t
z
z
Gz
t
G
z
t
CL
(1
1)
Whe
r
e
is the
spontaneou
s c
o
uplin
g
facto
r
,
K
is the
Peterm
ann c
o
efficient.
For a c
o
m
puterized calc
u
lation, the c
o
uple
d
e
quatio
ns
(5) and (6) are solved
num
e
rical
ly using the
finite di
ffe
renc
e tim
e
dom
ain (F
DT
D)
[2
4]
,t
hen
this m
e
th
o
d
is
base
d
on
s
o
lvin
g t
h
e c
o
u
p
led
wa
ve e
q
u
a
tions
in the tim
e do
m
a
in by
a
firs
t or
der
di
ffe
re
nce a
p
p
r
oxim
a
tion to
the
pa
r
tial differe
nce
[
24
-
25]
.
So
,
w
e
can
showe
d
t
h
at :
(,
)
(
,
)
(
(
(
,
)
(
,
)
s
F
tt
z
z
F
t
z
z
g
z
t
i
z
t
()
(,
)
(
)
(
,
)
(
,
)
]
iz
F
t
z
i
k
z
B
tz
e
G
tz
(1
2)
(,
)
(
,
)
(
(
(
,
)
(
,
)
s
B
t
tz
z
B
tz
z
g
z
t
i
z
t
-(
)
(,
)
(
)
(
,
)
(,
)
]
iz
Bt
z
i
k
z
F
t
z
e
G
t
z
(1
3)
The FDT
D
m
e
thod can
be ut
ilized
to si
m
u
late the dynam
i
c response
s of the DFB laser by solvi
n
g
th
e co
up
led equ
a
tio
ns
(
1
2
)
an
d (13
)
.
Th
er
ef
or
e, in
th
is w
o
r
k
we
ha
ve d
e
velo
ped
a FD
TD
al
go
rithm
,
w
h
ich
has bee
n
ap
pli
e
d to th
ose eq
uation
s
. The
num
erical
proc
edu
r
e o
f
this
m
e
thod in
v
o
lv
es dividi
ng t
h
e
cavity
length
into
se
v
e
ral u
n
if
orm
gr
ating s
u
b-secti
ons
200
S
of equal length
/.
g
zL
S
C
t
.
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I
S
SN:
2
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-87
08
IJEC
E V
o
l. 5, No
. 1, Feb
r
uar
y
20
1
5
:
2
3
– 30
26
3.
NU
MER
I
C
A
L
RES
U
LTS AN
D DIS
C
US
SION
S
The m
a
in goal
of
this
pape
r i
s
the sim
u
ltaneous
assessm
ent of
dy
nam
i
c characteristics o
f
TE-
DC
C
-
DFB laser
structure a
n
d the
com
p
arison wi
th the c
o
nv
entional TE-DFB
laser stru
ctur
e,
Tab
l
e
1
shows th
e
param
e
ters use
d
in
these
sim
u
lations
.
In
th
e f
o
llowi
ng
dis
c
ussio
n
t
h
e
per
f
o
r
m
a
nce com
p
aris
on
bet
w
ee
n th
e
two
st
ruct
ures under variou
s syste
m
param
e
t
e
rs
will be
previewed in detai
l
.
First, we present
the dynam
i
c
re
presentation of the laser
output
p
o
w
er
, F
i
gu
re
2.a a
n
d
b s
h
o
w
s
th
e
evol
ution
of th
e ph
oto
n
de
nsi
t
y
as a functio
n o
f
tim
e
at
zL
and also illustrat
e
s the
optical output spectrum
for the conventional TE-DFB laser. B
o
th
sections are
bi
ased sufficient
l
y as
86
A
I
mA
for section A (left
section
s
L
+ left section
c
L
) an
d
75
B
I
mA
for section B (right section
c
L
+ right section
s
L
)
To
facilitate com
p
arison, the tr
ansient response and the
optical
out
put
spectrum
of the TE-DCC-
DFB laser are
also show i
n
Figure
3.a a
nd b. t
h
e
op
tical spectr
u
m
is obtained
by
per
f
o
r
m
i
ng fast F
o
u
r
ie
r
trans
f
o
r
m
(FF
T
) fo
r optical o
u
tp
ut
field
wit
h
in [
3
,
4
]
n
s.
Table
1.
pa
ra
m
e
ter values
u
s
ed i
n
sim
u
lations
par
a
m
e
ter
s
sym
bol
value
Linear reco
m
b
inai
son
4.
1
0
-9
s
-1
Bi
m
o
li
cular reco
mbinaison
B
10
16
m
-3
s
-1
Auger
r
eco
m
b
inais
on
C
3 .
1
0
-4
1
m
-6
s
-1
Differential gain
0
A
2,
7.
10
-2
0
m
2
In
tern
al lo
ss
s
3
000
m
-1
Ef
f
ective index transparency
0
ef
f
n
3.
2
transparency C
a
rri
er density
0
N
1.
1
0
24
m
-3
L
i
newidth enhancem
ent factor
c
H
5,
4
Gr
oup velocity
g
C
3.
1
0
8
/3
,7
m
s
-1
Peter
m
ann factor
K
1
Peak wavelength a
t
transparency
0
1,
5
6
48.
10
-6
m
Optical conf
ine
m
e
n
t f
actor
0
.
35
Gr
ating per
i
od
22
7.
03
9.
1
0
-9
m
Non linear
gai
n
coef
f
i
cient
1,
5.
10
-2
3
L
s
aser
cavity
length
L
50
0.
10
-6
m
Volu
m
e
for active
region
V
90.
1
0
-6
m
Spontaneou
s
coupl
ing factor
5.
1
0
-5
gr
oup index
g
n
3.
7
(a)
(b
)
Figu
re
2.
(a
) T
r
ansie
n
t res
p
on
se (
86
A
I
mA
and
75
B
I
mA
) a
n
d
(
b
)
O
u
tp
ut
optic
al spectr
u
m
for
conventional
TE-DFB lasers
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I
J
ECE
I
S
SN:
208
8-8
7
0
8
Dyn
a
m
ic Res
p
ons
e
of Tw
o
-
El
ectrode
Distrib
u
te
d Feed
b
a
ck Laser
for St
abl
e
Sig
n
a
l
M
ode
…
(
H. Bousset
a
)
27
Ho
we
ver
,
a car
eful st
udy
of
F
i
gu
res
2.a a
n
d
3.a s
h
ow t
h
at, t
h
e lasin
g
out
p
u
t o
f
the c
o
nv
e
n
tional T
E
-
DFB laser starts after
passi
ng
needed time to satisfy
the threshold
condition a
nd it starts with strong
am
plitude as th
e cons
eq
ue
nce
of
beatin
g bet
w
een t
w
o m
o
d
e
s.Fo
r TE
-DC
C
-DFB
laser
,
the lasin
g
o
u
tp
u
t
starts
to oscillate in
sm
a
ll a
m
pl
itude and
after approxim
ate
l
y t=1
s
, stable
osc
illations are observed
. Then,
it can be
obs
er
ved in th
e Figu
re 2.
b an
d 3.
b, f
o
r the con
v
e
n
tional
TE-DFB laser, the existence
of
diffe
rent f
r
eq
u
e
ncies
.
This is bec
a
use
the effect of the m
odes beatin
g in
o
p
tical po
wer
[1
7]
.
Also
there a
r
e side
m
odes in ad
dition
t
o
the m
a
in one
and t
h
eir am
plitudes are c
o
m
p
ara
b
le to th
e
m
a
in
m
ode an
d they
can
n
o
t be ig
no
re
d, als
o
th
e
SM
SR
is estim
a
ted to be
8
d
B
. Fu
rthe
rm
ore, f
o
r the
ot
he
r structure the
SMSR is
m
o
re
than
43
dB
du
e to the
single m
ode o
u
tp
ut po
we
r, the m
ode beating cam
e from
th
e onset of si
de m
ode in the cavity as the result of
LSHB [1
7
]
.
Ind
eed
Th
e conven
tio
n
a
l TE-
D
FB laser
cav
ity is r
a
p
i
d
l
y su
b
j
ected
to
LSHB,
bu
t th
e TE-
DCC
-
DFB laser cavity see
m
s to be
widely prevent
e
d against it.
(a)
(b
)
Figu
re 3.
Lo
n
g
itudinal (a)
Tra
n
sient res
p
o
n
se
(
86
A
I
mA
and
75
B
I
mA
) a
n
d (b) Out
put
optical spectrum
fo
r TE
-
D
C
C
-
D
F
B
lasers.
I
n
or
der
to
un
der
s
tand
th
e ef
fects of
LSHB
o
n
the
power a
l
ong t
h
e ca
vity, the
Figure
4.a shows t
h
e
m
a
gnitude
of
fo
rwa
r
d, bac
k
war
d
an
d tota
l internal p
o
w
e
r alon
g the
cavity
for TE
-DFB
laser a
nd
f
o
r
com
p
arisons,
we also show t
h
e case
of c
o
nventional T
E
-DCC-DFB
lase
r structure in F
i
gure
4.b
It is obvi
ou
s fr
om
both fig
u
re
s that th
e internal optical p
o
w
er inc
r
ease
d
at
the
m
i
ddle o
f
the struct
ure.
Hence
,
for the TE
-DC
C
-DFB the
optical output power is incr
eased in right of
cavity
to 11m
W i
.
e hig
h
e
r
po
we
r
out
put com
p
ared to the
o
ther
structure,
the
reason is that
m
o
re
photons ac
cum
u
lated at the right facet of cavity
[2
5]
.
(a)
(b
)
Figu
re
4.
Wa
v
e
length
F
o
r
w
ar
d,
bac
k
wa
r
d
a
n
d total in
te
rnal
po
we
r alo
n
g
th
e cavity
. (a
) T
E
-D
FB
lasers
a
n
d
(b) conventional TE-
DCC-
DFB laser
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN:
2
088
-87
08
IJEC
E V
o
l. 5, No
. 1, Feb
r
uar
y
20
1
5
:
2
3
– 30
28
The Lo
n
g
itudi
nal pr
ofiles o
f
carrier de
nsity
and
powe
r can also indicat
e the occurre
nce of m
u
lti
m
ode ope
ratio
n in
lasers
stru
ctures.
He
nce,
the Fig
u
r
e
5
display
s
the
Lo
n
g
itudi
nal p
r
ofil
es o
f
ca
rrier
de
nsity
in di
ffe
rent
m
o
m
e
nts fo
r the
two
s
truct
u
re
s,
the
first
o
n
e i
s
take
n at t=
1
ns i.e
be
f
o
re
the m
odes
beat
ing a
n
d
th
e seco
nd
at t=2
n
s
i.
e du
r
i
ng
th
e b
eatin
g.
(a)
(b
)
Figu
re
5.
Lo
n
g
itudinal ca
rrier
de
nsity
pr
o
f
iles in t
w
o
different instants of t
h
e
tra
n
sient res
p
o
n
se
o
f
(a)
co
nv
en
tio
n
a
l DFB laser
s
and
(b
) TE-DCC-DFB laser
s
.
We see that, for
bot
h struct
ures, the
r
e is a discontin
uity
of the carrie
r
de
ns
ity at the
mi
ddle of the
cavity (the interface bet
w
ee
n the left and ri
ght electrode
).
This disc
ontinuity is reasona
ble as long as there is
sufficient resistance between these two sections A
and B [25]. For the conventional
TE-DFB laser, it is
observed that t
h
e carrier
profile is
m
odified
betwee
n the
two i
n
stants, this
is because of the
occ
u
rrenc
e
of
a
second m
ode in the cavity. In contrast for t
h
e TE-DCC-
DFB laser struct
ure, the carrier density longitudi
nal
pr
ofile rem
a
ins
clam
ped.
Figu
re
6.
N
o
r
m
alized carrier
de
nsity
ver
s
us
ti
m
e
for c
o
n
v
e
n
tional
TE-
DF
B
an
d TE
-DC
C
-DFB
.
Wit
h
inj
ection currents
86
A
I
mA
an
d
75
B
I
mA
No
w, I
n
the Fi
gu
re 6 we
pres
ent this No
rm
alized
carrier de
nsity
as a func
tion of tim
e.It
is obvi
ou
s
from
this figure, that the dumping
of
tr
an
s
i
en
t o
f
th
e
T
E
-
D
CC-DFB laser
is better than
for the conventi
onal
TE-DFB laser
structure and a
l
so, the fi
rst struct
ure stabilized at t=0,8ns,
howeve
r the second stabilized at
t=1.7
5
n
s.
Also
we obs
er
ved
that
the val
u
e of
N
in TE-DCC-DFB
laser aft
e
r stab
ilization is m
u
ch less t
h
an
the ot
her st
ruct
ure
,
the
reas
on
fo
r this
p
h
e
n
o
m
enon
can
be
explaine
d i
n
[
2
6]
. Finally
, to
sho
w
t
h
e ef
fec
t
s o
f
the cha
nge str
u
ctu
r
e’s
param
e
ters on si
de m
ode sup
p
r
e
ssio
n
r
a
tio
(
S
MSR)
,
Figu
r
e
7
disp
lays a co
m
p
ar
ison
betwee
n the t
w
o st
ruct
ures.
We see clearly
that, when t
h
e biasing curre
nt is less than
30
B
I
mA
, the both
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN:
208
8-8
7
0
8
Dyn
a
m
ic Res
p
ons
e
of Tw
o
-
El
ectrode
Distrib
u
te
d Feed
b
a
ck Laser
for St
abl
e
Sig
n
a
l
M
ode
…
(
H. Bousset
a
)
29
str
u
ctur
e m
a
n
i
f
e
st a go
od
SM
SR.
Howev
e
r
,
wh
en
th
e
b
i
asin
g is abov
e
3
0
m
A
,
th
e SMSR f
o
r
th
e conven
tio
n
a
l
TE-
DFB
laser
deg
r
a
d
ed
rapi
d
l
y
to a
m
i
nim
u
m
value equa
l to
1
0dB
. In
c
o
ntrast
to TE-DCC-DFB laser, the
go
o
d
sig
n
al
m
ode
op
eratio
n
can be m
a
intained si
gni
fican
t
l
y
within bra
d
cur
r
ent ra
ge, t
h
e
m
a
xim
u
m
values of
SMSR reach i
s
45dB. T
h
e results of t
h
is figure
shows t
h
at, the TE
-DCC-DFB laser has gi
ven a
better
transient
SMSR, this indicates
that the
LSHB also
play
s a
role i
n
SMSR
[27-28].
Figu
re
7.
De
pe
nde
nce
o
f
SM
SR
o
n
biasin
g
cur
r
ent
f
o
r t
h
e
con
v
e
n
tional
T
E
-D
FB
lasers
a
n
d
TE
-DC
C
-
D
F
B
lasers.
4.
CO
NCL
USI
O
N
In t
h
is
pape
r
and
with
the
help
o
f
a c
o
m
pute
r
alg
o
rit
h
m
based o
n
t
h
e F
D
T
D
m
odel,
we
hav
e
presented a traveling wave
la
rge si
gnal sim
u
lations
of dy
nam
i
c ch
aracteristics of
TE-D
CC-
DFB laser
.
Th
e
spontaneous emission, spatial hole bu
rni
n
g, longitudinal variation of car
rier and photon densities have been
taken int
o
consideration in t
h
e m
odeling.
The conven
ti
onal TE-DFB laser which is
characte
r
ized
by its
uni
fo
rm
coupli
ng c
o
e
fficient
alon
g the ca
vity
, and t
h
e TE
-
D
C
C
-
D
F
B
laser with a
/4
phase shift in center
cavity
and st
ro
nge
r ce
nter c
o
uplin
g c
o
ef
ficient ha
ve b
een
investigate
d
and
com
p
are
d
.O
n
t
h
e
o
t
h
e
r
si
de
,
t
h
e
results of sim
u
lations showed that, the f
i
rst str
u
cture is
not in single m
ode
operation,
but the
second one acts as a
single frequency
source with
an output
power
equal
to 11
m
W
and SM
SR
will
be
m
o
re
th
an 45dB
. In addition
the charac
ter
i
s
t
ics of TE-DCC-DFB la
ser structure have im
proved the signa
l
mode st
a
b
il
it
y. Therefore the
results
shows that the best dynam
i
cs signal
m
ode
can be achieved by
the TE-DC
C
-
DFB
lasers.
REFERE
NC
ES
[1]
Abedelkar
i
m Zatni,
et.al. Stud
y
of the short pu
lse gene
r
a
t
i
on of
the thr
ee qu
arte
r
wave shift DF
B laser (3QW
S-
DFB).
Annals of Telecommunica
tions
. 2005
; 60:
698-718.
[2]
A. Zatn
i, J.
Le
bihan. Analy
s
is
of FM and AM responses of a tuna
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BIOGRAP
HI
ES OF
AUTH
ORS
Ham
za. BOUS
S
ETA rece
ived
the M
S
c degr
ee in
ele
c
tron
ic
s
,
and com
m
unica
tion s
y
s
t
em
engineering fro
m faculty
of sciences University
Mohamed 1 in 2009; he is curr
en
tly
working th
e
PhD at the
centr
e of doctor
a
l stu
d
ies (Ibnou Zoh
r
CED). His res
earch
interests include d
e
sign,
characterization
,
modelling and optimization of
optoelectron
i
c components and
communications
s
y
ste
m
s.
Abdelkarim
. ZA
TNI was
educat
ed at th
e T
e
le
co
m
Bretagne Uni
v
ers
i
t
y
F
r
anc
e
;
He obtain
e
d a
PhD at the Nat
i
onal School of
Engine
ers of Brest France
in
1994. He has
been t
each
ing
experi
enc
e
for
22
years
.
He i
s
currentl
y
a P
r
ofes
s
o
r and th
e Head of
co
m
puter s
c
ien
c
e
department in I
bnou Zohr University
at High
er School of technolog
y
Agad
ir, Morocco; He
conducts h
i
s res
earch
and
t
each
e
s
in com
pute
r
sci
e
nce
.
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