TELKOM
NIKA
, Vol.13, No
.3, Septembe
r 2015, pp. 8
36~843
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v13i3.2094
836
Re
cei
v
ed Ma
y 3, 2015; Re
vised July 8,
2015; Accept
ed Jul
y
20, 2
015
Simplified Linear Configuration Model of 3x3 Single
Mode Fiber Coupler using Matrix Transfer
Saktioto*
1
, Dedi Ira
w
an
2
, Defrianto
3
1
Dept.of Ph
y
s
ic
s, F
a
cult
y
of Math and N
a
tura
l Scienc
es, Uni
v
ersit
y
of Ri
au,
Indones
ia
2
Advance
d
Ph
otonics Sci
enc
e Institute, Un
i
v
ersiti T
e
knolo
g
i Mal
a
ysia, M
a
la
ysi
a
3
Dept.of Industi
al Eng
i
ne
eri
ng,
F
a
cult
y
of
Sci
ence a
nd T
e
chnol
og
y, Ria
u, Indo
nesi
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: Saktioto@
y
a
hoo.com
A
b
st
r
a
ct
Experi
m
ental d
e
sig
n
and o
p
e
r
ation of a dir
e
ction
a
l fiber c
oup
ler hav
ing i
dentic
al-o
utput
ratio is
successful
ly fa
bricate
d
. T
h
e
coup
lin
g r
egi
o
n
is
i
m
p
o
se
d b
y
fusio
n
te
mpe
r
ature
80
0-13
5
0
0
C inj
e
ctin
g
t
h
e
Hydro
gen
g
a
s
at 1At
m
. Co
nc
urrently
the
co
upl
ed-
mo
de
th
eory
is us
ed
to
mod
e
l
pow
er
transfer b
e
tw
een
the w
a
vegu
ide
s
by using tra
n
s
fer matrix
met
hod. By 1
m
W
source i
n
p
u
t po
w
e
r to one of three i
n
p
u
t ports, it
show
s that po
w
e
r propa
gati
on a
m
on
g thr
ee co
upl
ed fi
b
e
rs is n
o
r
m
al
i
z
e
d
;
the
optic
al fib
e
r are
ne
arly
ide
n
tical
and
a
simi
lar se
para
t
ion betw
e
e
n
the
m
. T
he matr
ix config
urati
o
n
of 3x3 is
also
used to ca
lcul
a
t
e
the p
o
lar
i
z
a
tio
n
effect of d
i
re
ctiona
l fib
e
r co
upl
er. It is
foun
d that th
e i
n
cid
ent p
o
w
e
r po
la
ri
z
e
d w
i
th v
a
rio
u
s
ang
le ca
uses
pow
er outp
u
t at both
three
output p
o
rts decreas
e exp
o
n
ent
ia
lly. This 3
x
3 directi
o
n
a
l fibe
r
coup
ler des
ig
n is a sign
ificant
passiv
e
co
mpo
nent
for vario
u
s
functions p
o
w
er splitter and
routers.
Ke
y
w
ords
: dir
e
ction
a
l fib
e
r coup
ler, cou
p
le
d mo
de the
o
ry,
pow
er transfer, polari
z
at
ion
Copy
right
©
2015 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
Over two de
cad
e
s, the u
s
e of optical
net
work in comm
uni
cati
on system h
a
s greatly
develop
ed a
nd expa
nde
d
from a
sin
g
l
e device to
an
o
p
tical circuit
that consi
s
ts of
m
any
comp
one
nts. One of
the compon
ents,
t
he
o
p
tical
direction
a
l fibe
r co
uple
r
i
s
a
pa
ssive
devi
c
e
that is im
port
ant key as a
combi
n
e
r
, divider,
spli
tter,
routers a
nd o
p
tical
swit
chi
ng [1]. Usu
a
l
l
y a
simple
dire
cti
onal fibe
r co
upler
co
nsi
s
t
s
of two fibe
rs
cou
p
led
h
a
ving two o
u
t
put ports
with
typical coupli
ng ratio [2]. Since m
any
optical
sig
nal
need
to be
o
perate
d
a
nd f
unctio
ned, a
n
d
a
deman
d to transfe
r inform
ation, more th
an two fiber
couple
r
s a
r
e required.
The fiber
cou
p
ler with th
re
e fibers h
a
s b
een wea
k
ly joined by heati
ng its co
uple
d
regio
n
[3]. The prob
lems em
erg
e
when the fa
brication of couplin
g ratio
can
not be co
ntrolled d
ue to
different sep
a
ration b
e
tween three fib
e
rs m
a
ke
different
cou
p
lin
g coeffici
ents among
st them.
Thus, a full-wave surfa
c
e i
n
tegral e
quati
on me
thod
was u
s
ed to m
odel rig
o
ro
us powe
r
co
upli
n
g
of 3x3 fibe
r
couple
r
[4, 5].
This i
s
to
e
s
tablish a
po
wer m
odel
with
a p
o
lari
ze
d i
nput
whi
c
h b
e
ing
con
s
id
ere
d
for tria
ngul
ar
fiber coupl
er by as
sumin
g
that po
wer cou
p
ling
be
havior fo
r th
ese
norm
a
l mode
s is do
minantl
y
decide
d
by the ve
ctor fiel
ds at the ce
nter of fibers.
Becau
s
e th
e
triangul
ar
configuration
of co
u
p
ling
region i
s
co
mplicate
d
to
maintain
durin
g fusio
n
,
a simple lin
ear a
r
range
ment of
thre
e fibers co
up
led be
come
s important to
be
cha
r
a
c
teri
ze
d
.
Therefo
r
in
this pa
per, a
ppro
a
ch
of si
mple line
a
r
configur
ation o
f
3x3 dire
ctio
nal
fiber
cou
p
le
r
is fab
r
icated
by fusio
n
a
n
d
elo
ngatio
n
method. A
n
o
rmali
z
e
d
co
upling
po
we
r at
cou
p
led regi
on is formul
a
t
ed usin
g co
upling mo
de
theory by a tran
sfer mat
r
i
x
method. This
matrix is also use
d
to examine the perfo
rmance of
fiber c
o
upler in term of polariz
ation effec
t.
2
.
M
e
t
h
od
An experim
e
n
tal set up
sho
w
n in Fi
gure
1 is b
a
se
d on fu
sion and
elo
ngation
techni
que
s. It is ca
rri
ed o
u
t
by placing t
h
ree
sin
g
le m
ode fibe
rs
(S
MF) on th
e st
age
s. A corni
n
g
fiber (SMF-2
8e®), with
di
ameter
of co
re
an
d cl
ad
di
ng
1
25 and
8.2
mi
cro
m
et
er re
spe
c
tivel
y
,
is
con
n
e
c
ted to the diode la
ser an
d displa
yed to the
ph
oto detecto
r. The two fibe
rs are twiste
d and
held by a vacuum sy
stem
with both en
d
s
. All par
am
e
t
ers a
r
e recorded by data
acq
u
isitio
n ca
rd
installe
d to the comp
uter
system.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Sim
p
lified Linear Configu
r
a
t
ion Model of 3X3
Single M
ode Fibe
r Co
upler u
s
in
g…
(Saktioto
)
837
The initial
ste
p
is to p
r
e-set
para
m
eters
of
cou
p
ling
ra
tio, pulling le
ngth, x-y-z
po
sition of
torch fla
m
e, a
nd flowi
ng of
H
2
ga
s. 1 m
W
lase
r lau
n
ch
ed to the o
n
e
of input po
rts is
dete
c
ted
by
a photo d
e
tector and
ke
pt for calibration.
While t
he fu
sion a
nd p
u
lli
ng process i
s
started.
Duri
ng
heating
the cou
p
ling regi
on,
the
fibers are elon
ga
ted by pullin
g stage
s
with suitabl
e pu
lling
spe
ed of
≈
10
0µm/s. Heati
ng and pulli
n
g
pro
c
e
ss
will
be automatically stopped
whe
n
the pre
-
set
cou
p
ling ratio
is
re
ached. For safety
re
aso
n
,
the co
upling
regi
on
is saved an
d pa
ckaged.
The
mech
ani
cal o
peratio
n is m
o
tori
zed in mi
cro
m
eters
scale.
Figure 1. Experime
n
tal set
up to fabricate SMF cou
p
ler
The n
e
xt set
up of fu
se
d
3x3 SMF
couple
r
i
s
to
desi
gn a
nd i
n
vestigate
po
larization
cha
r
a
c
teri
stics a
s
given i
n
Figu
re
2.
Contin
uou
s Wave (CW) lase
r
a
s
an optical
source
i
s
laun
che
d
to o
u
ter fibe
r (fib
er 3
)
with
wa
velengt
h op
eration is 1
550
nm. A lase
r b
eam is
pola
r
i
z
ed
by different angle of polari
z
er b
e
fore m
o
ving at
one
of outer fiber (Waveguid
e
3). An optical
Spectrum An
alyzer
(OSA)
and Opti
cal Powe
r
Meter
(OPM) are set
to detect the output.
Figure 2. Measu
r
em
ent of Polari
zation
a
t
the output ports 3x3 SMF
coupl
er
3.
Theore
t
ical
Consid
era
t
ion of Optic
a
l Wav
e
guide Con
f
igura
t
ion
Optical
po
we
r si
gnal
prop
agation
in th
e couple
d
waveguid
e
me
dium
wa
s d
e
termine
d
clea
rly from t
he Maxwell e
quation u
s
in
g
cou
p
ling
-
mo
de theo
ry (CMT) meth
od [
6
]. The mod
e
ling
and
experi
m
ent of p
o
wer paramete
r
s
of SMF
cou
p
l
er h
a
ve b
e
e
n
stu
d
ied
[7]. It sho
w
e
d
t
h
e
c
o
up
lin
g r
a
tio
as
fu
nc
tion
o
f
c
o
up
ling
co
e
ffic
i
en
t
b
e
t
w
e
e
n
the fib
e
r
s
.
Ass
u
me
th
e mo
de
l is
simplified
wh
ere
the
refractive indices of
co
uple
d
fibe
rs a
r
e
con
s
tan
t, and g
eom
e
t
rical
fibers
are
also
ide
n
tical
as
sho
w
n
in
Figu
re
3. T
h
e am
plitude
of po
we
r ex
chang
es bet
ween t
w
o
fibers a
s
given by (1).
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 3, September 20
15 : 836 – 843
838
Figure 3. Ilustration of geo
metrical fuse
d fiber co
uple
r
(1)
Whe
r
e
,
and
are p
o
wer amplitud
es in
Waveg
u
i
de
(WG) 1,
WG 2
an
d
WG 3
respe
c
tively. The
co
upling
co
efficient i
s
d
enot
e
d
by
, an
d L
is couplin
g le
ngt
h. Since th
e
intera
ction
b
e
twee
n the
three
wave
g
u
ide
s
o
c
curs from th
e
waveguid
e
1
to the n
eare
s
t
waveg
u
ide,
waveg
u
ide
2
,
thus the
couplin
g
c
oeff
i
cient
of
wa
veguide
1 t
o
wavegui
de
3,
can b
e
negl
e
c
ted. The eig
envecto
rs of
matrix 3x3,
can be con
s
tru
c
ted a
s
:
(2)
And by defining
, Equation
(1) can be trans
fo
rme
d
to matrix differe
ntial equatio
n
:
(
3
)
Substituting
Equation (1
)
to
will yield a ma
trix transf
e
r for 3x3 op
tical dire
ction
a
l
c
o
up
le
r
as
fo
llo
w
s
.
(4)
Whe
r
e,
(5)
a
P
b
P
c
P
13
31
an
d
V
11
2
1
22
0
2
11
2
V
1
UV
P
11
22
33
20
0
()
()
()
0
2
0
(
)
()
0
(
)
k
Uz
Uz
d
Uz
j
k
Uz
dz
Uz
k
U
z
P
VU
11
22
33
()
(
0
)
()
(
0
)
()
(
0
)
Pz
P
Pz
T
P
Pz
P
22
2
2
2
2
2
2
11
2
2
1
1
1
1
2
1
2
22
2
2
22
12
12
1
2
22
22
11
1
2
1
1
22
11
22
22
12
1
2
22
22
2
2
2
2
1
2
12
2
1
1
2
12
1
22
2
2
22
12
12
1
2
co
s
c
o
s
cos
1
cos
c
os
co
s
co
s
1
co
s
c
o
s
iz
Te
Lj
L
L
jL
jL
L
Lj
L
L
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Sim
p
lified Linear Configu
r
a
t
ion Model of 3X3
Single M
ode Fibe
r Co
upler u
s
in
g…
(Saktioto
)
839
And
is an em
pirical co
uplin
g coeffici
ent that can be
calcul
ated
from the expe
rimental
work of normali
ze
d freque
ncy [8], and:
4.
Resul
t
s and
Discus
s
ion
of Norm
alize
d
Po
w
e
r Pro
p
aga
t
ion
The propa
gat
ion of optical
power in sili
ca-f
ibe
r
wave
g
u
ide couple
r
descri
bed by
cou
p
led
mode th
eory
sho
w
s the
strength of th
e
cou
p
ling
co
efficient to tran
sfer
po
wer from a
waveg
u
i
de
to othe
r
wave
guide. It
sig
n
ificantly de
pe
nds on
s
epa
ration b
e
twe
e
n
fibe
rs axis
at co
uple
d
re
gion.
Since fibe
r couple
r
succe
ssfully fab
r
ica
t
ed with
waveguid
e
s a
r
e
wea
k
ly co
upl
ed, the fiber
cro
ss
section and
separation are ne
arly identical, and
power dete
ct
ed at output
ports
will be
norm
a
lized. Ho
wever, the
transfe
r po
wer b
e
twe
e
n
the wavegui
des i
s
variou
s not only e
a
ch
config
uratio
n
or
arrang
eme
n
t of that th
ree fibe
rs
joi
n
ed, but
also t
he o
p
tional
i
nput p
o
rt fe
d
by
power. In thi
s
di
scussion,
linear
arran
gement
s
of three
wave
gu
ides
at cou
p
l
i
ng re
gion
are
purp
o
sed.
Powe
r i
s
la
u
n
ch
ed to
out
er
waveg
u
ide
(WG
1 o
r
WG 3
)
, the
po
wer tra
n
sfe
r
betwe
en
th
r
e
e wa
ve
gu
id
es
c
a
n be
d
e
t
er
mine
d fr
o
m
ma
tr
ix tr
a
n
s
f
o
r
m
wh
ic
h is g
i
ve
n b
y
(4
) in
tw
o
con
d
ition
s
. The first co
ndit
i
on, power is
laun
che
d
in to waveg
u
ide
1 or wave
gui
de 3 as a lin
ear
order. By substituting
in (4)
as
shown in
Figure 4 will yield,
1
√
2
(6a)
√
√
2
(6b)
1
√
2
(6c)
Figure 4. Power tran
sfer b
e
twee
n the three wa
vegui
d
e
s with vari
ab
le cou
p
ling
co
efficient
Power P
1
pro
pagate
s
g
r
a
d
ually from i
n
itial wave
guid
e
(WG 1
)
to th
e center waveguid
e
(W
G 2
)
. Pow
e
r P
2
affected by the
coupling
coeffici
ent
,
will optimi
z
e it at
waveguide 3
(fiber
3). The seco
nd co
ndition,
input po
wer i
s
fed in the
center of the three
waveg
u
i
des. Similarly
,
b
y
substituting
in (4), will yield,
(
7
a
)
2
()
2
eA
B
d
C
d
a
2
2
2
5.
278
9
(
3.
66
3
V
)
(
0
.
38
41
V
)
0
.
77
69
(
1
.2
252
V
)
(0.
0
1
5
2
V
)
0.0
1
7
5
(
0
.0
06
4
V
)
(
0
.
00
09
V
)
A
B
C
22
2
12
1
nn
n
d
d
a
12
3
(
0
)
1
,
a
nd
(
0
)
(
0)
0
AA
A
23
21
3
(0
)
1
,
a
n
d
(0
)
(
0
)
0
AA
A
13
1
si
n
2
2
jz
Az
A
z
j
z
e
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 3, September 20
15 : 836 – 843
840
(7b)
Figure 5. Power tran
sfer b
e
twee
n the three wa
vegui
d
e
s with vari
ab
le cou
p
ling
co
efficient
Figure 5
shows that power in
put will
be di
stributed symmet
r
ically to the two outer
waveg
u
ide (WG 1 an
d WG 3) an
d power P
2
is minim
u
m.
5.
Resul
t
and Discussion o
f
Polarization
Effec
t
s
Polari
zation i
s
a factor that affects the se
nsitivity and
stability of
the opti
c
al
network
system,
espe
cially for the
passive
device of fibe
r
optics sy
stem
s, p
o
lari
zation
m
a
y ca
use lo
sses
in that device
.
It is possibl
e to a fiber couple
r
to have signifi
cant l
o
sse
s
ca
use
d
by polari
z
at
ion
effects d
e
termined from the coupl
ed-mode the
o
ry.
By rewriting
the differenti
a
l matrix for
MXN
fiber cou
p
ler as (8), wh
ere
,
and
are
th
e
elect
r
ic fiel
d
for the
output
powers a
n
d
input po
wers
are respe
c
tively:
(
8
)
Every amplitu
des
ha
s two
comp
one
nt vector
pol
ari
z
a
t
ion, they are
x and y
com
pone
nt.
Definin
g
is m
a
trix of coupli
ng for si
ngle
fiber, a
nd
is th
e matrix
of
cou
p
ling
bet
wee
n
two
a
d
jacent fibe
rs. Where
,
a
n
d
a
re the
two
polari
z
atio
n
mode
s, an
d t
w
o
-
pola
r
i
z
ation mo
de
s, a
nd
pol
ari
z
e
d
mode
s of t
w
o
adja
c
e
n
t fibe
rs of
cou
p
ling coef
ficients respe
c
tively.
Con
s
id
er all
fibers
are
identically isolat
ed an
d
wea
k
ly co
up
led, having
different
polari
z
atio
n, and the
cou
p
ling coeffici
ent of
this
mode
is a
s
sumed
zero. The coupli
n
g
coeffici
ents b
e
twee
n two i
dentical mo
d
e
s
of pol
ari
z
ation a
r
e
a
s
sumed
and
=
=
.
Equation (1) ca
n be wr
it
ten by Equation (9
).
2
co
s
2
j
z
Az
z
e
()
i
A
z
(0)
i
A
th
i
1
11
2
21
1
3
31
1
1
(0)
(
)
0
...
0
(0
)
()
0
.
.
.
(0
)
()
0
0
.
.
.
.
.
.
.
...
.
.
.
.
.
.
...
.
.
.
.
.
.
...
0
(0
)
(
)
0
...
0
N
M
A
Az
B
C
A
Az
C
B
C
A
Az
C
B
C
d
j
dz
A
AZ
C
B
x
xy
xy
y
B
1
ix
jx
ix
j
y
ix
jy
iy
j
y
C
ixjx
iyjy
ix
jy
x
y
an
d
x
y
ix
jy
ix
j
x
x
x
iy
j
y
yy
xx
yy
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Sim
p
lified Linear Configu
r
a
t
ion Model of 3X3
Single M
ode Fibe
r Co
upler u
s
in
g…
(Saktioto
)
841
(9)
Or, it
can
be
sim
p
lified i
n
term
of tran
spo
s
e
ma
trix
de
scribin
g
t
he m
a
trix tra
n
smi
ssi
on
of
the
MXN fiber
co
upler in
clu
d
in
g the two pol
arized mo
de
s.
(
1
0
)
The pol
ari
z
at
ion ch
ara
c
te
ristics of sin
g
le mode fibe
r coupl
er
can
be investiga
t
ed by
applying mat
r
ix (1), then in
sertin
g the bo
unda
ry co
ndi
tion to the cal
c
ulatio
n. In this re
se
arch, the
polari
z
atio
n chara
c
te
risti
c
s of 3x3 are p
u
rpo
s
e
d
to b
e
investigate
d
.To examin
e the pola
r
izatio
n
behavio
r of fiber coupl
er, three fibe
rs are simplified in
linear a
rra
ng
ement.
Con
s
id
er
the cou
p
ling coef
ficient
given by
(5)
i
s
h
e
ld
to be con
s
tan
t
along the fib
e
r, an
d
the coupli
n
g
re
gion
is
very short,
it can
be
assume
d
,
, a
n
d
. By using
matrix equati
on of pola
r
i
z
ation of mult
iport fibe
r
cou
p
ler give
n
by (9), Equat
ion (5
) be
com
e
s:
(11)
The Eq
uation
(1
1)
dep
end
s u
pon
the
op
tional in
put p
o
we
r
whi
c
h
is laun
ch
ed. F
o
r exam
ple,
if the inp
u
t po
wer to th
e
ce
nter
(fiber 2
)
,
the out
p
u
t po
wer at fibe
r
1
and
fiber 3
a
r
e give
n by th
e
following Equation.
11
2
2
3
3
11
2
2
3
3
...
.
.
.
t
xy
x
y
x
y
M
x
M
y
t
x
y
x
y
x
y
Mx
My
EE
E
E
E
E
E
E
z
TE
E
E
E
E
E
E
E
1
2
x
y
22
2
2
24
xx
y
y
x
y
12
3
2
242
32
1
xy
iL
MM
M
Te
M
M
M
M
MM
22
2
1
1
22
1
*
2
22
11
2
2
22
2
1
1
22
2
1
co
s
1
c
o
s
s
i
n
s
i
n
c
o
s
1
22
2
2
1
s
i
n
c
o
s
1
c
os
1
c
os
s
i
n
22
2
2
2
2
si
n
s
in
co
s
s
in
si
n
22
2
2
xy
xy
xy
i
LL
L
Li
L
M
i
LL
L
LL
i
LL
L
Li
L
M
*
22
2
11
22
22
2
1
1
22
3
2
22
11
2
2
2
2
si
n
s
in
si
n
s
in
c
o
s
22
2
2
1
cos
1
co
s
s
in
s
i
n
c
o
s
1
22
2
2
1
si
n
c
os
1
c
o
s
1
c
os
si
n
22
2
2
xy
xy
xy
LL
L
LL
i
i
LL
L
Li
L
M
i
LL
L
LL
i
*
22
2
1
1
22
4
*
22
2
11
22
2
2
si
n
s
in
co
s
s
in
si
n
22
2
2
2
2
si
n
s
in
si
n
s
in
c
o
s
22
2
2
xy
xy
LL
L
Li
L
M
LL
L
LL
i
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 3, September 20
15 : 836 – 843
842
2
22
22
11
2
22
2
21
2
2
22
22
31
2
2
4
1
sin
s
in
c
o
s
22
2
2
sin
s
in
2
2
sin
s
in
c
o
s
22
xy
xy
xy
LL
SL
L
SL
LL
SL
(12
Figure 6 sh
ows goo
d a
g
ree
m
ent a
m
ong outp
u
t
powe
r
in b
o
th three o
u
t
put ports
decrea
s
e
s
expone
ntially by increa
sin
g
th
e an
gle of
pol
arization i
n
(1
2). However,
initial po
we
r
at
P
1
is slightly highe
r than t
hat of powe
r
at P
2
and P
3
. This is a wea
k
n
e
ss of 3x3 as a po
we
r
splitter
sin
c
e
the coupl
ed
region
is linea
r a
rra
nge
men
t. P
2
and P
3
are held
ide
n
t
ical
a
nd simil
a
r
power.
Figure 6. De
crea
sing of out
put powers ve
rsus diffe
ren
t
angle of pol
arization
6.
Conclu
sion
De
sign
an
d o
peratio
n
of nu
meri
cal
experiment
of
po
wer
pro
pag
atio
n in
3x3 fib
e
r
cou
p
ler
usin
g cou
p
le
d mode theo
ry sho
w
s tha
t
output pow
er in both three port
s
are
norm
a
lized. It is
cla
ssifie
d
tha
t
the ch
aract
e
risti
c
s of o
u
t
put po
wer d
epen
d on
wh
ich
waveg
u
id
e laun
ch
ed
by
lase
r
beam.
The
de
sign
of
3x3
dire
ction
a
l fibe
r
cou
p
l
e
r
ca
n b
e
u
s
e
d
a
s
a
route
r
s wh
en
the l
a
ser
beam fed to the waveg
u
id
e 1, and it is promi
s
in
g
good power divi
der if input po
wer fee
d
s to the
waveg
u
ide 2
or ce
nter waveguid
e
s of lin
ear 3x3 fi
ber
cou
p
ler. However, polari
z
a
t
ion corre
c
tio
n
need
s to be
con
s
ide
r
ed
for the de
cre
a
sin
g
of
output power
caused by increa
sing a
ngl
e of
polari
z
atio
n.
Ackn
o
w
l
e
dg
ements
We
woul
d like to than
k to Physics Dep
a
rtm
ent, Fa
culty of Math and
Natural
Scien
c
e
s
,
University of Riau, Pe
kan
b
a
ru, I
ndo
ne
si
a, Dire
cto
r
ate
Gene
ral of
High
er Ed
ucation, Minist
ry of
Educatio
n, Indone
sia, the
I
n
stitute of Ad
vance
d
Photo
n
ic Sci
e
n
c
e,
Faculty of Sci
ence, Unive
r
siti
Tekn
ologi M
a
laysia, Mal
a
ysia, Faculty of Sc
ience
and Te
ch
nol
ogy, Universi
tas Islam
Ne
geri
SUSKA Pekanbaru, Indonesia
for generous
suppor
t i
n
this research.
Referen
ces
[1]
Alan W
.
Optical W
a
vegu
ide T
heor
y. Lo
nd
on:
Sn
yder an
d Jh
on D. Love. 1
9
83.
[2]
Chin-
L
i
n
Ch
en
. F
oundati
ons
F
o
r Guide
d
-W
ave Opti
cs. W
e
st Lafa
y
ette,
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na: Per
d
u
e
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200
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[3]
Saktioto, Jali
l
Ali, Moham
ed
F
adha
li. Simpl
i
f
ied cou
p
li
ng
p
o
w
e
r mo
del for
fiber fusio
n
.
Journa
l of Opto-
electro
n
ic Rev
i
ew
. 2009; 17(3
)
: 193-19
9.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Sim
p
lified Linear Configu
r
a
t
ion Model of 3X3
Single M
ode Fibe
r Co
upler u
s
in
g…
(Saktioto
)
843
[4]
Saktioto, Jal
il
Ali, Moham
ed
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adha
li, T
heoretical a
nd
empi
rical com
paris
o
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p
li
ng c
oefficie
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urna
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e
chno
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z
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e
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li
ng
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yzi
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a
riz
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ti
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epe
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uil
a
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r
iang
ul
a
r
3
x
3
w
e
akl
y
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u
sed F
i
ber
Cou
p
ler.
Optic
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i
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u
r
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chno
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n
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en,
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illiam
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rizati
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