TELKOM
NIKA
, Vol. 11, No. 5, May 2013, pp. 2442 ~
2447
ISSN: 2302-4
046
2442
Re
cei
v
ed
Jan
uary 15, 201
3
;
Revi
sed Ma
rch 9, 2
013;
Acce
pted Ma
rch 1
8
, 2013
Raman Slow Light in Distributed Raman Fiber Sensors
Dape
ng Wan
g
*, Ning Li,
Aimei Yan, Yingxin Xie, F
e
ng
y
u
Wang
Beiji
ng Guo
d
i
a
ntong N
e
t
w
ork
T
e
chnolog
y C
o
., L
T
D., Na
ri Group C
o
rpor
atio
n, Beiji
ng 1
001
20, Chi
na.
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: bupt_
w
a
e
@s
ina.com
*
, li-ni
n
g
@ sge
p
ri.sgc
c.com.cn,
ya
na
imei
@sge
pri.sgcc.com.cn, xi
e
y
in
g
x
in
@
s
gepr
i.sgcc.co
m.cn, w
a
ngfen
g
y
u@s
gepr
i.sg
cc.com.cn
Ab
stra
ct
Distribut
ed Ra
ma
n sens
or offers a number
of advant
ag
e
s
to the impl
e
m
e
n
tatio
n
of smart gri
d
,
w
h
ich is
ai
me
d to
i
m
prov
e
relia
bi
lity a
n
d
ener
gy effici
en
cy as c
o
mpar
ed w
i
th tra
d
iti
ona
l p
o
w
e
r gr
id
.
How
e
ver, the
fantastic
prop
er
ties of sl
ow
li
g
h
t are r
a
re
ly c
onsi
dere
d
i
n
th
e for
m
er stu
d
i
e
s o
n
the
Ra
ma
n
sensor
systems. In this
paper, t
he effects
of Ram
a
n slow
-light
on room
-temper
ature s
i
ngle-
m
ode optic
a
l
fiber se
nsors
are ex
a
m
in
ed
by extracti
ng
the
R
a
man
puls
e
-de
l
ay
te
rms
fro
m
extend
ed no
nli
n
e
a
r
Schrod
ing
e
r e
quati
on (
N
LSE
)
. Nu
meric
a
l s
t
udy sh
ow
s
that puls
e
para
m
eters
such
a
s
puls
e
p
o
siti
o
n
,
freque
ncy c
h
ir
p, an
d
enve
l
o
pe
distortio
n
may
b
e
gr
eatl
y
affected
by
slow
li
ght. T
w
o i
m
p
o
rtant
po
ints o
f
pu
mp
pow
er
a
r
e sh
ow
cle
a
rl
y kee
p
in
g th
e
Ra
man
pu
lse
z
e
ro
w
a
lk-off or c
h
irp
free,
resp
ectively.
W
e
de
mo
nstrate a
met
hod
bas
e
d
on
pu
mp p
o
w
e
r adj
ustme
n
t for co
mp
en
sating th
e sl
o
w
light in
duc
e
d
impair
m
ent.
Ke
y
w
ords
: fib
e
r sensor, slow
light, stimulate
d
Ram
a
n scattering, chirp, sm
art grid
Copy
right
©
2013 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
Distri
buted fi
ber
sen
s
o
r
is of critical im
por
tan
c
e i
n
many appli
c
a
t
ions me
asuri
ng strain,
temperature,
pressu
re a
nd other qu
antities [1
-5].
Smart grid, which i
s
aimed to improve
reliability and
energy effici
ency as
com
pare
d
with
traditional po
wer grid, empl
oys fiber se
n
s
ors
as th
e info
rm
ation inte
rface. In the
pa
st y
ears, dist
ri
buted Ram
a
n
sen
s
ors ha
ve
bee
n
wi
d
e
ly
resea
r
ched a
nd variou
s scheme
s
have
been p
r
op
ose
d
for high-accura
cy, high-spatial-re
soluti
on
measurement
s to meet the r
equi
rem
ents
of smart g
r
id.
Re
cently, the
gro
und
bre
a
k
ing
of a
c
hi
eving
sl
ow a
nd
supe
rlumi
nal light
pro
pagatio
n
velocity have
cau
s
e
d
keen
intere
st of slo
w
an
d fast
lig
ht [6-12]. In fiber
sen
s
o
r
s, both stimul
ated
Rama
n scattering
(S
RS) and stimulate
d
Brillo
uin
scattering
(SBS
)
can
intro
d
u
c
e
strong
gro
u
p
velocity disp
ersi
on
s [4-6] to slo
w
do
wn the lig
ht speed
at roo
m
tempe
r
atu
r
e. The
slo
w
light
based
on SB
S ha
s a
rest
ricted
ban
dwi
d
th ab
out
G
H
z an
d S
R
S
allows
data
rates
up
to n
e
a
rly
terabits pe
r seco
nd d
ue to
the Ram
an
re
son
a
n
c
e
widt
h [6], [8]. It is
quite impo
rta
n
t to su
rvey the
effects of Ra
man slo
w
ligh
t
on sen
s
ors f
o
r the future
appli
c
ation
s
.
In this p
ape
r,
we d
e
mo
nstrate theo
retica
lly t
hat slo
w
li
ght affect
s pu
lse p
a
ramete
rs such
as
pul
se
po
sition, freq
uen
cy chirp, an
d
envelo
pe
di
stortion.
All t
he effe
cts are de
rived
fro
m
Rama
n
re
son
ance of th
e fi
ber. T
he
wal
k
-off enla
r
g
ed
by slo
w
li
ght
expedite
s the
gain
saturati
on.
Whe
n
the
pu
mp p
u
lse
atte
nuated
en
ou
gh the
g
r
ou
p
delay
will al
so be
dull
ed. T
hese
studie
s
are
mainly towards to
the
det
ailed
ch
ara
c
t
e
r
of hig
h
resolution
distri
b
u
ted
Rama
n
fiber
sen
s
o
r
s for
the potential
appli
c
ation
s
in sma
r
t grid.
2. Rese
arch
Metho
d
Rama
n scattering i
s
the pro
c
e
ss by
whi
c
h ene
rg
y transferred
from high freque
ncy
comp
one
nts
of optical fiel
d to the
lower frequ
en
cy com
pon
ents in the
diele
c
tri
c
me
dia.
Thi
s
amplificatio
n
of lowe
r freque
ncy
co
mpone
nts i
s
asso
ciated
with the d
r
e
ssi
ng of me
dium
refra
c
tive ind
e
x unde
r the con
s
trai
nt of cau
s
ality. Th
e cha
r
a
c
ter
o
f
Raman
scattering i
s
de
ci
ded
by the Raman susceptibilit
y. Raman susceptibility
R
is a compl
e
x function of fre
q
uen
cy whi
c
h
has b
een
we
ll studied in
SiO
2
glasse
s. The imagin
a
ry com
pon
e
n
ts
of
R
related to t
h
e
Rama
n g
a
in
profile
can
be me
asured
by the
exp
e
rime
nts, a
n
d
then
the
real
comp
one
nts
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046
TELKOM
NIKA
Vol. 11, No
. 5, May 2013 : 2442 – 244
7
2443
related to the effec
t
ive ref
r
active ind
e
x
()
n
near Raman
resona
nce ca
n be o
b
taine
d
from
lying in the
requi
rem
ent
of the so
-call
ed Kra
m
ers–Kronig
rel
a
tion. A co
mmonly u
s
e
d
assumptio
n
i
s
that th
e fre
quen
cy d
epe
nden
ce
of th
e Raman
su
sceptibility is linea
r. On
e
can
cal
c
ulate the
Rama
n scattering
-in
duced
time delay as [6]
11
()
g
fg
R
gIL
tL
vv
(1)
whe
r
e
g
is the steady-state
Raman g
a
in
,
L
is the len
g
th of medium,
I
is the pum
p
intensity,
g
v
is the g
r
ou
p
spe
ed of
sto
k
e
s
wave,
f
g
v
is
the
backg
rou
nd g
r
oup
spee
d
a
n
d
R
is
the gain line
w
idth. Thus the
group velo
cit
y
of the pulse
with pump is
1
1
()
g
Rf
g
gI
v
v
(2)
To reveal th
e origin
of time delay in theo
retically, we a
s
sume that th
e pump exp
e
riences
a negligibl
e
d
epletion, thu
s
the diffe
rential equatio
n of Raman
re
sp
onse is
*
()
(
)
(
)
e
x
p
(
()
)
s
sR
p
s
p
R
A
if
A
R
t
t
A
t
A
t
i
t
t
d
t
z
(3)
whe
r
e
p
A
and
s
A
are the pu
mp and sto
k
e
s
field re
spe
c
tively. Con
s
id
erin
g the
intera
ction
of
a cw pum
p
wave with
a
pu
lsed
si
gnal
,
fo
r the
follo
win
g
theo
ry, we
assume
that t
he
pump expe
rie
n
ce
s a negli
g
ible depletio
n
as a result
of the interacti
on with the pulse si
gnal. T
h
e
well-kn
own re
lation for the amplitude
s a
nd pha
se
s in
the Rama
n in
teractio
n re
ad
s as
()
(
)
e
x
p
(
()
)
s
sR
p
s
R
A
if
I
R
t
t
A
t
i
t
t
d
t
z
(4)
whe
r
e
2
||
Pp
I
A
is the pump inten
s
it
y.
In frequen
cy domain, the stoke
s
field ca
n be expre
ssed as
(
,
)
|
()
|
e
x
p
(
()
)
(
,
0
)
ss
AL
H
i
A
(5)
whe
r
e
|
(
)
|
exp(
(
)
)
sR
P
R
Hz
f
I
, and
()
(
)
s
RP
R
zf
I
is the
amplitude a
n
d
pha
se tran
sfer function, resp
ecti
vely. The gro
up del
a
y
is then cal
c
ulated by
()
()
R
sR
P
zf
I
(6)
We quote t
he definition
the gain co
efficient
0
2
ss
R
gf
f
and the inverse o
f
group
veloc
i
ty
1
1
gR
s
R
p
vf
I
f
,
n
f
are the n-th Taylor series coe
fficient
s of Raman susceptibility.
The sig
nal is
finally describ
ed as
2
11
2
2
2
2
2
(
)
||
(
|
|
(
1
)
||
)
22
ss
s
s
s
f
gg
R
p
s
s
s
R
p
s
AA
i
A
g
vv
A
A
i
A
f
A
A
zt
t
(7)
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TELKOM
NIKA
ISSN:
2302-4
046
Ram
an Slow
Light in Di
stri
buted Ram
an Fiber Sen
s
o
r
s (Dape
ng Wang)
2444
where
2s
is th
e group
velo
city dispe
r
si
on
(GV
D
) coefficient
of si
gna
l pul
se. Th
e
high
orde
r coeffici
ents (
3
n
) are o
m
itted.
Eq. 7 p
r
ovide
s
the
ap
proximate relation
ship
bet
wee
n
the im
agina
ry (gain
)
and
the
real
(pha
se
)
part
of Ra
man
su
sceptibility. Raman
pul
se
g
r
oup
spee
d
chang
e i
s
d
e
ci
ded
by the
g
a
in
cha
nge a
c
cording to this re
lationship.
We
adopt the c
o
upled NLSE to s
t
udy the char
ac
ters
of
puls
e
walk-off.
The group
delay
of Ra
man
pul
se
rel
a
tes to t
he p
u
mp
po
wer
I
be
sid
e
s th
e fibe
r p
a
ra
m
e
ters
su
ch
as
g
,
L
, which
mean
s the de
pletion of pu
mp pulse will
dedu
ce the d
e
lay time impairme
n
t.
3. Results a
nd Analy
s
is
To illustrate
the dynami
c
properties of
li
ght slow down, we deli
berately
choose the
optical
fiber p
a
ram
e
ters in
a hig
h
ly no
nlinear hol
l
o
w-core photo
n
ic cry
s
tal
fibe
r
fi
lled with carb
on
disulfid
e [12]
to fulfill the magnitud
e
of
wa
l
k
-off co
mpen
sation
required. Th
e
para
m
eters
are
pulse width
0
5
Tp
s
, nonlin
ear
co
efficient
11
0.01
mW
, walk
-off length
20
w
Lm
, fiber
length
2
Lk
m
, Raman fre
quen
cy d
e
tuning
/2
7
.
5
TH
z
, effec
t
ive core
area
2
20
ef
f
A
m
, GVD
c
oeffic
i
ent
2
2
20
/
ps
km
, Rama
n
gai
n
13
10
/
gm
W
. The
effects of
slo
w
light o
n
the
pulse walk-o
ff and chi
r
p
a
r
e then
stu
d
ied num
eri
c
all
y
and compa
r
ed
with the co
ndi
tion without sl
ow light.
3.1. Slo
w
Lig
h
t Effects on
Walk-Off an
d Frequen
c
y
Chirp
Figure
1.
sho
w
s ho
w walk-off decre
ases with
the pump powe
r
incre
a
se by the sl
ow light
effect, thoug
h it is usuall
y
con
s
ide
r
ed
as a
co
n
s
ta
nt depi
cted b
y
the blue cu
rve. In the small
sign
al conditi
on, the pum
p
power i
s
mu
ch
stron
g
e
r
than the
sig
n
a
l, thus
the
depletio
n of the
pump
is ne
gli
g
ible. T
he
pu
lse
wal
k
-off d
e
crea
se
s
dire
ctly with
the
pump
po
we
r
increa
se
a
s
i
s
descri
bed by
the red
curve
.
This relatio
n
is
simple
but
shoul
d be re
vised when t
he pump p
o
wer
is stron
g
e
n
o
ugh be
cau
s
e
of
the slo
w
lig
ht
effec
t. It’s i
n
tere
sting th
a
t
the nu
meri
cal re
sult
s
sho
w
a turning p
o
in
t at the pump power ab
out 1.55W a
s
is d
epicte
d
by the blac
k cu
rve
,
deviating from
the an
alytical
pre
d
ictio
n
.
We
define
thi
s
p
o
int a
s
the minimum
walk-off initial
power. Pul
s
e
wal
k
-
off can be ab
ated com
p
letl
y in the well chosen fiber
system.
Figure 1. Pulse walk-off as a function of the pum
p po
wer. Blue
curve, without sl
ow light. Re
d
curve, an
alytical re
sult
s in the und
eplete
d
con
d
ition. Black cu
rve, numeri
c
al resu
lts.
As is re
sea
r
ched, the total freque
ncy chi
r
p
acro
ss the
sign
al pulse can be full con
t
rolled
by tuning the
pump po
we
r for its de
pe
nden
ce o
n
sl
ow light. The
chirp de
cre
a
se
s when t
he
pump
po
wer i
n
crea
se
with
out the
effect
of sl
ow
light,
as the
blue
curve
in
Figu
re 2
sho
w
s.
The
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ISSN: 23
02-4
046
TELKOM
NIKA
Vol. 11, No
. 5, May 2013 : 2442 – 244
7
2445
red curve d
e
scrib
e
s that th
e pulse chi
r
p
increa
se
s ra
p
i
dly when the
pump po
we
r gro
w
s
stro
ng
er,
as
th
e
a
nalytical re
sults
of small sig
nal condition
predi
cted. We pro
v
ide
mo
re de
tails
of chi
r
p
at
the pu
mp
exh
austio
n
regio
n
. Wh
en th
e
energy of
pu
mp p
u
lse
i
s
transfe
red
to t
he
sign
al e
n
o
ugh
the chi
r
p al
so
has a tu
rnin
g point a
s
is
sho
w
n by
the
black curve.
It is clearly th
at the freque
ncy
chirp with or
without slo
w
l
i
ght
have opp
osite sig
n
at most time, and Rama
n pul
se is ne
arly chirp
free at l
o
w
pump
po
wer regi
on
com
pare
d
to th
e
non
-sl
o
w-lig
ht co
ndition.
The
chi
r
p
h
a
s
a
positive maxi
mum value,
whi
c
h intimat
e
s a
nothe
r
ch
irp fre
e
poi
nt. And the Ra
man gai
n is fi
nally
saturated i
n
t
he hi
gh p
u
m
p
area,
whi
c
h is re
asona
ble
con
s
ide
r
i
ng the
sl
ow light effect
on
the
freque
ncy chi
r
p.
Figure 2. Pulse freq
uen
cy chirp as a fun
c
tion of
the p
u
mp po
we
r. Blue cu
rve, without slo
w
lig
ht.
Red
curve, a
nalytical re
sul
t
s in the unde
pleted c
onditi
on. Black
cu
rve, numeri
c
al
result
s. Gre
e
n
curve, nu
meri
cal re
sult
s of final Rama
n gain.
3.2. Optical Fields Propa
gation in Fiber
w
i
th/
w
i
t
h
o
ut Slo
w
Ligh
t
Nume
ri
cal si
mulation results ba
sed
o
n
co
upled
wave equatio
n
is sh
own in
Figure 3.
This fig
u
re
sh
ows both th
e
intensity an
d
freque
ncy
distribution
with
out co
nsi
deri
ng the
slo
w
li
ght
effect. The si
gn of the gro
up velocity di
spe
r
si
on al
so
affects the field distri
butio
n, and we di
scu
ss
norm
a
l dispersion in thi
s
pa
per only.
(a)
(b)
Figure 3. Pump (blu
e, dashed) a
nd si
gn
al (re
d,
solid
) without sl
ow l
i
ght after pro
pagatio
n.
(a)
Profiles in tim
e
domain. (b) Frequ
en
cy spectrum.
Rama
n pul
se
moves to th
e leadi
ng e
d
ge of the p
u
m
p pul
se in t
he no
rmal
di
spe
r
si
on
regio
n
. The
walk-off betwe
en the p
u
mp
and the
sig
n
a
l
is fixed
with
out slo
w
lig
ht, thus th
e en
ergy
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TELKOM
NIKA
ISSN:
2302-4
046
Ram
an Slow
Light in Di
stri
buted Ram
an Fiber Sen
s
o
r
s (Dape
ng Wang)
2446
is tran
sferred
mainly from the low freq
uen
cy
comp
o
nents of the pump pul
se
as is
sho
w
n
in
Figure 3
(
a).
The p
u
mp
sp
ectru
m
be
co
mes
asymm
e
trical
as th
e p
u
mp atten
uat
ed in the
lea
d
ing
side, a
s
is sh
own in Fig
u
re 3(b
)
. It could be fu
ther f
ound that the
signal p
u
lse
is low di
stort
e
d
comp
ared wit
h
the pump.
The
g
r
e
en cu
rve
is
th
e
Ra
man p
u
lse
ch
irp
(THz).The
ze
ro
freq
uen
cy
chirp point a
r
i
s
e
s
at Rama
n pulse trailin
g edge rathe
r
than the pea
k.
Assu
ming p
u
m
p power eq
uals a
bout 1.
7W, the
gro
u
p
velocity mismat
ch indu
ced wal
k
-
off can b
e
ca
ncel
ed by th
e slo
w
light e
ffect as
i
s
sh
own i
n
Figu
re 4. Gro
u
p
-
velocity match
i
ng
betwe
en the
two p
u
lses
m
a
ke
s
slo
w
lig
ht exactly
co
mpen
sating
the g
r
ou
p-vel
o
city di
spe
r
si
on.
Rama
n p
u
lse
is exa
c
tly sy
nch
r
on
ou
s
wi
th the pum
p
pulse, co
nnot
ing a l
o
w
distortion. In thi
s
con
d
ition the
pulse sh
ape
s both in tim
e
and fr
equ
e
n
cy dom
ain
are all
well
shape
d, as Fi
gure
4(a
)
and Fig
u
r
e 4(b)
sho
w
respe
c
tively.
(a)
(b)
Figure 4. Pump (blu
e, dashed) a
nd si
gn
al (re
d, solid
) with slo
w
ligh
t
after propa
g
a
tion at zero
wal
k
-off po
we
r. (a) Profiles
in time domai
n. (b) Frequ
e
n
cy sp
ect
r
um
.
The green
cu
rve in Figure 4(a
)
sh
ows th
at t
he zero freque
ncy chirp point move
s to the
leadin
g
ed
ge
of Ram
an
p
u
lse,
whi
c
h
mean
s the
p
u
lse
chi
r
p i
s
not equ
al to
zero n
early i
n
the
most time. Th
is deviation from the pul
se
pea
k co
ul
d b
e
interp
reted
as the influ
e
n
c
e of the
cro
ss
pha
se mod
u
l
a
tion.
(a)
(b)
Figure 5. Pump (blu
e, dashed) a
nd si
gn
al (re
d, solid
) with slo
w
ligh
t
after propa
g
a
tion at zero
chirp po
we
r. (a) Profile
s in time domai
n. (b) Freque
ncy
spe
c
trum.
Adjusting
the
pump
po
we
r t
o
0.85
W
ca
n
sync
hro
n
ize t
he effe
cts
rel
a
ted a
nd
ch
a
nge th
e
zero freq
uen
cy chi
r
p poi
n
t
as is sho
w
n in Figu
re
5(a
)
. The di
stortion of pu
mp and
sign
al
freque
ncy
sp
ectra
are al
so de
scrib
ed
by Figure 5
(
b
)
. Ram
an
pul
se
wal
k
s ba
ck to the l
eadi
ng
edge of the p
u
mp wh
en th
e grou
p velocity mismat
ch
emerge
s agai
n. Fort
unately
,
the chang
e of
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ISSN: 23
02-4
046
TELKOM
NIKA
Vol. 11, No
. 5, May 2013 : 2442 – 244
7
2447
envelop
e is slightly com
p
ared
with the zero
wal
k
-off condition.
The pulse pea
k ce
ntere
d
absen
ce
of chirp
ca
n b
e
i
n
terp
reted
a
s
the g
r
ou
p a
nd p
h
a
s
e vel
o
city ne
arly h
a
ving the
sa
me
variation ten
d
ency. Except
the co
ndition
menti
one
d ab
ove, freque
ncy shift always exists a
c
ross
the whole
Ra
man p
u
lse. A
nd the
ind
epe
nden
ce
bet
ween th
e p
r
op
agate
s
spe
e
d
of si
gnal
ph
a
s
e
and si
gnal e
n
v
elope resulting the chirp l
eadin
g
or la
g
g
ing the p
u
lse positio
n wh
ich is m
odifie
d
by the tuning of
walk
-off. The
group and ph
ase veloc
i
ty nearly have the same variation
tenden
cy, thus the pul
se p
eak i
s
chi
r
p free.
The effect of
the pulse walk-off gives
rise to th
e p
u
lse d
e
lay or advanceme
n
t in cw
pump
sen
s
o
r
. It should b
e
notice
d
th
at the pulse
chirp ultimat
e
ly affect on
the optical f
i
eld
intensity. Slo
w
light
prim
a
r
ily influen
ce
s the
sig
nal
pulse po
sitio
n
in the
sm
a
ll sign
al a
nd
cw
pump conditi
on. The dela
y
of signal pu
lse enh
an
ce
s the energy a
m
plification a
nd sh
orten
s
the
fiber effective
length when
the pump
d
epletion i
s
n
o
t negligibl
e
. As to the p
u
lse
d
pum
p, the
depletion is related to the walk off. Gain sa
turation
degrades the perform
ance of the sensor
whe
n
the pu
mp power i
s
stron
g
eno
ug
h.
4. Conclusio
n
In co
ncl
u
sio
n
, we
have
demo
n
st
rat
ed the
effects
of Rama
n
sl
ow-light on
room
-
temperature
singl
e-m
ode
optical
fibe
r sensors by
extractin
g
th
e Raman
pul
se
-d
elay terms from
extended
no
nlinea
r Schro
d
inge
r e
quati
on. The
gai
n
satu
ration
cuts d
o
wn the
flexibility of the
sen
s
o
r
. The comp
en
satio
n
can be a
c
hieved in
a well ch
osen
system by a
d
justin
g the pump
power.
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ces
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pn
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e
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r
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chno
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