Int
ern
at
i
onal
Journ
al of Ele
ctrical
an
d
Co
mput
er
En
gin
eeri
ng
(IJ
E
C
E)
Vo
l.
10
,
No.
4
,
A
ugus
t
2020
,
pp.
4162
~
41
67
IS
S
N:
20
88
-
8708
,
DOI: 10
.11
591/
ijece
.
v
10
i
4
.
pp
4162
-
41
67
4162
Journ
al h
om
e
page
:
http:
//
ij
ece.i
aesc
or
e.c
om/i
nd
ex
.ph
p/IJ
ECE
Offset ef
fect on t
he S
-
Ben
d struct
ure losse
s a
nd
opti
mizati
on
of
its size f
or inte
grated opti
cs
F. Brik
1
,
S.
H
ariz
e
2
,
A.
F
ar
es
3
,
K.
Saouc
hi
4
1,2
,3,4
Depa
rtment
of
Elec
tron
ic
s,
E
ngine
er
ing
Sci
en
ce
s F
ac
u
lty
,
Uni
ver
sit
y
B
adj
i
Mokhtar
-
Annaba
,
A
lge
ri
a
1
,3,4
La
bora
tor
y
o
f
LE
RICA,
Instr
um
ent
at
ion
and
C
om
m
unic
at
ion of Anna
ba
,
Univ
ersity
B
adj
i
Mokhtar
-
Annaba
,
Al
ger
ia
2
La
bora
tor
y
of
Autom
at
ic
and
S
igna
l
of
Annab
a (LASA
),
Univer
sit
y
Badji
Mokht
ar
-
Annaba
,
Alg
e
ria
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Ma
y
28, 201
9
Re
vised Feb
28, 2
020
Accepte
d
Ma
r
8,
2020
The
S
-
Bend
str
uct
ure
s
ar
e
heavil
y
expl
o
it
ed
t
o
jo
in
optical
c
om
ponent
s.
Reduc
ing
th
e
p
ower
loss
ca
us
ed
b
y
t
he
cur
v
e
is
the
m
ai
n
obje
c
ti
ve
in
the
d
esign
st
ep
of
th
ese
components.
How
ev
e
r
integra
t
ed
op
t
ic
a
l
c
irc
u
it
s
req
uire
S
-
Bend
wave
guide
to
b
e
low
loss
and
co
m
pac
t
siz
ed.
In
t
his
pape
r
,
we
pre
sent
a
cont
rib
uti
on
to
l
ink
th
e
cur
ved
stru
ct
ur
e
to
th
e
stra
ight
wave
guid
e
b
y
using
the
sim
ulated
bend
func
t
io
n
ava
i
la
bl
e
in
th
e
Bea
m
prop
agation
too
l
of
the
Rsoft
comm
erc
i
al
software
p
ac
kag
e.
Sim
ula
tion
result
s
conf
i
r
m
tha
t
thi
s
appr
oac
h
al
lows
a
r
educ
t
ion
of
th
e
si
ze
of
the
cur
v
ed
stru
ct
ure
wi
th
offset
with
rel
a
ti
ve
l
y
m
ini
m
um
of
losses for photonic fi
e
ld.
Ke
yw
or
d
s
:
In
te
gr
at
ed
opti
cs
Offset
Ra
diu
s
of c
urv
at
ur
e
Si
m
ulate
d
te
ch
nique
Copyright
©
202
0
Instit
ut
e
o
f Ad
vanc
ed
Engi
n
ee
r
ing
and
S
cienc
e
.
Al
l
rights re
serv
ed
.
Corres
pond
in
g
Aut
h
or
:
Fatim
a Brik,
Dep
a
rtm
ent o
f El
ect
ro
nics
,
LERICA
Labo
rator
y
of
Anna
ba,
Un
i
ver
sit
y B
ad
j
i M
ok
htar
-
A
nnaba
,
Anna
ba,
23000,
Alge
ria.
Em
a
il
: fb
rik
2002@yah
oo.fr
1.
INTROD
U
CTION
The
ra
pid
dev
e
lop
m
ent
of
opti
cal
fibe
r
te
ch
nolog
y
i
n
te
le
c
omm
un
ic
at
ion
s
ha
s
re
quire
d
a
gro
wing
nee
d
for
act
ive a
nd
passive
integ
ra
te
d
opti
cal
com
po
nen
ts.
Wa
veguide
s r
e
pre
sent
the
base
of m
os
t of
t
he
in
te
gr
at
ed
ci
rcu
it
s
to
im
pro
ve
their
pe
rfor
m
ance
w
hile
reducin
g
th
e
com
po
ne
nts
d
im
ension
s
,
b
ut
the
cu
rv
at
ur
e
of
the
wav
e
guide
s
le
ads
to
a
power
loss
an
d
a
co
ns
trai
nt
on
a
tran
sm
issi
on
abili
ty
.
The
S
-
Be
nd
st
ru
ct
ures
are
widely
use
d
to
com
bin
e
diff
e
ren
t
el
em
ents
of
a
ci
rc
uit
in
order
to
buil
d
a
va
r
i
e
t
y
o
f
o
p
t
i
c
a
l
c
om
p
o
n
e
nt
l
i
k
e
s
p
l
i
t
t
e
r
[
1
]
,
l
a
s
e
r
s
[
2
,
3
]
,
c
o
u
p
l
e
r
s
[
4
,
5
]
,
s
w
i
t
c
h
e
s
[
6
,
7
]
a
n
d
m
o
d
u
l
a
t
o
r
s
[
8
-
1
0
]
.
Ma
ny
so
luti
ons
ha
ve
be
e
n
su
g
geste
d
to
de
crease
the
los
ses,
but
to
le
ss
en
b
e
ndin
g
los
s,
the
be
ndin
g
rad
i
us
has
t
o
be
increase
d.
T
his
will
m
ake th
e t
otal si
ze of the
phot
on
ic
i
nteg
rated
circuits l
ar
ge
r, t
hing that is
not s
uitable
to
t
he
inte
gr
at
e
d o
ptic.
The first
pro
posit
ion
of lat
eral wa
vegui
de
s
hift for l
os
s
r
e
du
ct
ion
has bee
n
pre
se
nted
by
Ma
rcu
se
a
nd
Kitof
[
11
,
12
]
,
th
ough
only
t
he
t
ran
sit
io
n
be
nd
i
ng
l
os
s
w
as
c
on
si
der
e
d.
A
nothe
r
al
te
r
native
stu
dy
on
a
ri
b
wav
e
guide
is
pr
ese
nted
i
n
[
13
-
15
]
.
I
n
[
16
-
19]
it
was
the
or
et
ic
al
ly
pro
pos
e
d
a
n
opti
m
iz
at
ion
m
et
ho
d
usi
ng
a
sp
li
ne
bend,
wh
ic
h
re
duce
s
the
be
ndin
g
loss
but
re
quir
es
a
la
rg
e
f
oo
t
pr
i
n
t.
Re
centl
y,
the
a
pp
li
cat
ion
of
the
be
nd
com
po
se
d
of
cl
oith
oi
d
cu
rv
e
has
be
en
dem
on
st
ra
te
d
[
20,
21]
.
It
is
no
te
d
that
i
n
the
a
bove
w
orks,
diff
e
re
nt appro
aches,
m
et
ho
ds an
d
m
at
erial
s ar
e
us
ed
d
e
pe
ndin
g
on the
des
ired
a
ppli
cat
ion
.
In
t
his
pa
per,
t
he
ef
fect
of
the
diff
e
re
nt
offset
in
the
c
urve
d
s
tructu
re
is
in
ve
sti
gated
an
d
a
perform
ance
evaluati
on
of
t
he
S
-
Be
nd
is
c
arr
ie
d
on
with
the
Be
am
prob
s
i
m
ulator
inte
grat
ed
in
t
he
Rs
oft
s
of
t
war
e.
T
he
pa
pe
r
po
i
nts
u
p
ra
dia
ti
on
a
nd
tra
ns
it
ion
l
os
ses
as
t
he
m
ai
n
so
urces
of
the
pr
op
a
ga
ti
on
l
os
ses.
T
he
first
a
re
relat
ed
to
li
gh
t
goin
g
out
of
t
he
wa
ve
guides
duri
ng
t
he
pro
pag
at
io
n
at
the
S
-
be
nd
p
at
h,
w
hile
the
se
cond
is
ass
ocia
te
d
to
the loss
pr
oduc
ed wh
e
n
t
he
S
-
Be
nd are
a
tt
ac
hed to t
he
str
ai
gh
t
outp
ut w
a
ve
gu
i
de.
Using
Sim
ulate
d
Tec
hniq
ue
Be
nd,
wh
ic
h
i
s
the
a
ppr
opri
at
e
m
et
ho
d
f
or
the
m
od
el
in
g
of
a
si
ng
le
structu
re
or
a
s
eries
of
cu
r
ves,
we
est
ablis
hed
the
prese
nce
of
th
e
e
xistence
of
tw
o
ty
pe
s
of
losses:
pu
re
be
nd
i
ng
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N:
20
88
-
8708
Offse
t ef
fe
ct
o
n t
he S
-
Be
nd str
ucture
losses
and opti
miz
atio
n
(
F.
Brik
)
4163
losse
s
(
ra
diati
on
)
a
nd
tran
sit
ion
l
os
ses
[22]
.
Ther
ea
fter
,
an
appr
oach
le
a
di
ng
to
t
ran
sit
io
n
losses
re
du
ct
ion
is
pro
po
se
d.
It
co
ns
ist
s
on
the
in
tro
du
ct
io
n
of
a
sh
ift
w
hich
al
lows
ce
nteri
ng
the
seco
nd
guide
on
the
m
axim
u
m
of
t
he
m
od
e
guide
of
t
he
fi
r
st.
The
pa
pe
r
i
s
struct
ur
e
d
in
to
two
sect
ions:
In
sect
io
n
2,
the
sim
ulate
d
bend
te
chn
iq
ue a
nd
2.
ANALY
SIS
METHO
D
In this
pap
e
r,
the
sim
ulate
d
Be
nd and t
he of
f
set
m
e
tho
d are
pro
po
se
d
t
o
s
t
udy
the
S
-
Be
nd
Stru
ct
ur
e
.
2.
1.
Be
nd
t
ec
hniq
ue
The
necessa
ry
com
pu
ta
ti
on
ti
m
e
of
a
c
urve
d
waveg
uid
e
dir
ect
si
m
ulati
on
is
ver
y
high.
T
his
is
due
t
o
the
fact
that
th
e
si
m
ulati
on
ne
cessi
ta
te
s
a
finer
gr
i
d
a
nd
siz
e
dom
ai
n.
But,
a
dif
fere
nt
a
nd
ap
pro
pr
ia
te
way
f
or
the
sim
ulatio
n
of
a
c
urve
d
str
uctu
re
is
ava
il
able
in
the
Be
a
m
Pr
ob
sim
ulato
r
.
The
c
om
pu
ta
ti
on
al
c
or
e
of
t
his
pro
gr
am
is
bas
ed
on
a
Be
am
Pr
opa
gation
Me
thod
(BPM
),
w
hi
ch
is
the
m
os
t
widely
us
e
d
te
c
hn
i
qu
e
for
m
odel
in
g
fiber
op
ti
c
a
nd
integ
rated
op
t
ic
s
de
vices
[
23
]
.
The
pr
i
ncipl
e
of
t
his
m
et
hod
is
ba
se
d
on
t
he
dec
om
po
sit
ion
of
the
pro
pag
at
i
on
of
an
el
ect
r
om
agn
et
ic
wav
e
in
a
ho
m
og
e
ne
ou
s
m
edium
ov
er
a
distance
δz
.
This
te
ch
niqu
e
us
es
finite
diff
e
re
nc
e
m
et
ho
ds
to
so
lve
the
wave
eq
uatio
n.
In
ad
diti
on,
the
pro
gr
am
neces
saril
y
us
es
bo
unda
ry
conditi
ons
[
24]
.
T
he pr
oble
m
o
f
the
physi
cal
propa
gation o
f
t
he wave
r
e
quir
es tw
o key
el
em
ents:
-
The dist
rib
utio
n of t
he
refract
ive in
dex,
(
,
,
)
.
-
The
el
ect
ric a
nd m
agn
et
ic
f
ie
ld at the
en
t
ry,
(
,
,
)
.
The
al
gorithm
r
eq
uires
ad
diti
on
al
i
nput
par
a
m
et
ers
su
c
h
as:
-
A
fi
nite d
om
ain
of com
pu
ta
ti
on
:
(
,
)
,
(
,
)
-
The
siz
e
of the
tran
s
ve
rse gri
d,
.
-
The
siz
e i
n
t
he l
ongitud
i
nal
directi
on, Δz.
U
s
i
n
g
t
h
e
s
i
m
u
l
a
t
e
d
b
e
n
d
t
e
c
h
n
i
q
u
e
,
t
h
e
c
a
l
c
u
l
a
t
e
d
m
o
d
e
i
n
t
h
e
c
u
r
v
e
d
a
r
e
a
i
s
e
a
s
i
l
y
o
b
t
a
i
n
e
d
.
T
h
e
b
e
n
d
i
n
g
m
e
t
h
o
d
c
o
n
s
i
s
t
s
o
f
t
r
a
n
s
f
o
r
m
i
n
g
t
h
e
s
i
m
u
l
a
t
e
d
g
e
o
m
e
t
r
y
o
f
a
c
u
r
v
e
d
w
a
v
e
g
u
i
d
e
i
n
t
o
a
s
t
r
a
i
g
h
t
w
a
v
e
g
u
i
d
e
b
y
m
o
d
i
f
y
i
n
g
t
h
e
r
e
f
r
a
c
t
i
v
e
i
n
d
e
x
o
b
t
a
i
n
e
d
b
y
u
s
i
n
g
a
m
u
l
t
i
p
l
i
c
a
t
i
o
n
b
y
a
c
o
e
f
f
i
c
i
e
n
t
(
1
+
x
/
R
)
.
I
t
h
a
s
b
e
e
n
p
r
o
v
e
d
t
h
a
t
t
h
i
s
a
p
p
r
o
a
c
h
i
s
v
e
r
y
p
r
e
c
i
s
e
f
o
r
a
w
a
v
e
g
u
i
d
e
w
i
d
t
h
w
e
l
l
b
e
l
o
w
t
h
e
c
u
r
v
a
t
u
r
e
r
a
d
i
u
s
(
W
<
<
R
)
.
2.
2
.
T
he off
se
t
tec
hnique
Gen
e
rall
y,
m
o
des
c
urve
d
wa
ve
gu
i
de
are
di
sp
la
ced
ou
tsi
de
of
t
he
tu
r
n,
so
a
m
od
e
ca
n
be
s
hifte
d
la
te
rall
y
in
a
gu
ide
with
resp
e
c
t
to
each
oth
er
i
n
or
der
to
im
prov
e
t
he
al
ig
nme
nt
of
the
c
urve
d
wa
ve
gu
i
de
m
od
e
s.
At
the
ju
nctio
n
bet
ween
eac
h
segm
ent
of
the
S
-
Be
nd
str
uct
ur
e
,
the
inte
gral
overla
p
between
the
in
put
m
od
e
and
t
he
ou
t
pu
t
m
od
e
will
be
cal
culat
ed
an
d
op
ti
m
iz
ed.
A
m
on
it
or
is
i
m
ple
m
ented
to
ca
lc
ulate
the
ove
rlap
of
the pr
op
a
gatio
n
in
the
fiel
d st
ru
ct
ur
e a
nd
its
m
od
e
as w
el
l
.
First,
the
m
odes
of
eac
h
se
gm
ent
of
the
c
urve
d
str
uctu
re
will
be
cal
culat
ed
us
in
g
b
en
d
te
chn
iq
ue
.
T
he
n
,
a
n
opti
m
iz
at
ion
of
ea
ch
s
hift
at
the
jun
ct
io
ns
of
the
wa
veguide
s
w
il
l
be
i
m
ple
m
e
nted
so
t
hat
it
return
s
the
value
of
th
e
ov
e
rlap
betw
een
the
m
od
es
.
T
o
fi
nd
t
he
optim
iz
ed
m
at
c
hing
m
od
e
off
set
at
eac
h
se
gm
ent
j
unct
io
n
,
the
i
nteg
ral
ov
e
rla
p
bet
ween
the
in
put
a
nd
outpu
t
m
od
es
wil
l
be
cal
culat
e
d
an
d
the
n
m
axi
m
iz
ed.
By
de
finiti
on,
the
fiel
d
at
t
he
be
ginnin
g
of
t
he
st
ru
ct
ur
e
wi
ll
be
t
he
la
un
c
h
fiel
d.
T
her
e
f
or
e
,
th
e
m
on
it
or
will
return
t
he
re
quire
d
value
at
this
point
an
d
t
he
BPM
si
m
ula
ti
on
s
houl
d
be
set
so
th
at
it
does
not
act
ually
pro
pag
at
e
at
al
l,
bu
t
only
cal
c
ul
at
es
the
first
da
ta
point.
By
s
et
ti
ng
t
he
la
un
c
h
posit
ion
al
on
g
X,
the
la
unc
h
fiel
d
can
be
offset
in
relat
ion
to
the
structu
re,
a
nd
the
opti
m
a
l
va
lue
can
be
f
ound
by
sca
nn
i
ng
ov
e
r
the
la
unc
h
offset.
3.
DESIG
N A
N
D
SI
M
ULATI
ON RES
ULTS
3.1
.
The cur
ved
s
t
ructure
Figure
1
sho
w
s
the
S
-
Be
nd
s
tructu
re
m
od
el
ed
unde
r
the
R
SO
FT
s
of
t
ware.
It
c
onsist
s
of
a
strai
ght
input
wa
ve
gu
i
de
of
le
ngth
Li
n
(i
n
Re
d
c
olor),
tw
o
arc
wa
veguide
s
with
opposit
e
cu
rv
a
ture
(yel
low
a
nd
bl
ue
colo
rs),
a
nd
st
r
ai
gh
t
outp
ut
w
aveguide
of
le
ngth
L
ou
t
(i
n
Re
d
c
olor)
respec
ti
vely
.
The
wa
veguide
s
a
re
m
ade
of
Sil
ic
a
and
they
co
ns
ide
re
d
ste
pp
i
ng
in
de
x.
T
he
t
otal
le
ngth
of
t
he
str
uctu
r
e
is
giv
e
n
as
[
22
]
:
(
)
=
2
ɤ
+
L
in
+
Lo
ut
At
first
,
the
w
avelen
gth
c
orr
esp
onding
to
t
he
str
uctur
e
f
unct
ion
is
c
ho
s
en
to
be
1.5
5µm
and
it
s
dim
ension
s
a
r
e:
D
if
fer
e
nce
ind
e
x
(
∆
n=0.0
15)
,
Ra
diu
s
(R
=150
0µm
),
L
e
ng
t
h
of
i
nput
and
ou
t
pu
t
str
ai
gh
t
w
ave
guide
(Li
n=L
ou
t=
300µ
m
)
,
ang
le
of
cu
rv
at
ur
e
(
ɤ
=
1
7
°
)
and
widt
h o
f
the
wav
e
guide
(
W=5
µm
).
The
Be
a
m
P
rob
m
on
it
or
di
sp
la
ys
the
tran
sm
it
te
d
po
we
r
in
the
total
le
ngth
of
the
str
uctu
re
.
Fig
ure
2
pr
e
sents
the
sim
ulati
on
resu
lt
s
ob
ta
ine
d
by
t
he
m
on
it
or
of
the
Be
am
pro
p
sim
ulator,
w
hich
al
lo
ws
to
post
the
i
ntensity
of
t
he
el
ect
ric
fiel
d
(
a
)
an
d
t
he
losses
in
po
wer
in
t
he
dif
f
eren
t
segm
ents
wa
vegui
des
f
or
m
ing
the
c
urved
str
uctu
re
(
b),
a
nd
this f
or (
Ra
dius=
1500µm
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
10
, No
.
4
,
A
ugus
t
2020
:
4162
-
4167
4164
Figure
1. The
S
-
Be
nd st
ru
ct
ure
under s
of
tw
are
pack
a
ge
(a)
(b)
Figure
2. Lo
ss
es of
powe
r
in
the total
len
gth o
f
S
-
Be
nd
without
offset,
(a)
m
on
it
or
inte
nsi
ty
,
(
b)
powe
r
los
s
in the t
otal l
en
gth
of the
str
uc
ture
-
The p
ow
e
r
tra
nsm
issi
on
is esti
m
at
ed
to 70%
re
su
lt
ing i
n
a
lo
ss of
30% fo
r
a
ra
diu
s
of
1500
μm
Fr
om
Fig
ur
e
2,
it
can
be
ob
se
r
ved
that
the
t
ra
ns
it
ion
losse
s
be
tween
the
tw
o
arcs
of
Ra
dius
cu
rv
at
ur
e
are
m
or
e
i
m
portant
tha
n
the
ot
her
j
unct
io
n
lo
sses.
T
o
s
how
t
he
in
flue
nce
of
these
losse
s
on
the
tra
ns
m
issi
on
of
the
powe
r
in
t
he
str
uctu
re
in
S
-
Be
nd,
we
present
the
sim
ulati
on
ob
ta
in
e
d
by
c
on
si
der
i
ng
a
s
hift
between
the v
a
rio
us
seg
m
ents o
f
ju
nctions.
3.2
.
T
he
cur
ved
s
t
ructure
wi
th
offse
t
Actuall
y
,
the
presente
d
str
uct
ur
e
has
the
sam
e
cha
racteri
sti
cs
as
the
S
-
Be
nd
one
without
offset,
with
t
h
e
p
a
r
t
i
c
u
l
a
r
i
t
y
o
f
n
o
t
a
l
i
g
n
e
d
g
u
i
d
e
s
a
s
d
e
m
o
n
s
t
r
a
t
e
d
i
n
F
i
g
u
r
e
3
.
T
h
e
o
f
f
s
e
t
s
n
o
t
e
d
(
o
f
f
s
e
t
1
,
o
f
f
s
e
t
2
a
n
d
o
f
f
s
e
t
3
)
represe
nt
the
s
hift
bet
ween
t
he
in
pu
t
gu
i
de
-
first
c
urve
d
guide,
c
urve
d
guide
-
cu
rv
e
d
guide
-
ou
t
pu
t
gu
i
de
an
d
curve
d
g
uid
e
r
especti
vely
,
m
easur
e
d
perpe
nd
ic
ularly
to
t
he
pr
op
a
gatio
n
directi
on
z
as
show
n
in
F
ig
ur
e
4.
The
infl
uen
c
e
of
the
off
set
on
t
he
l
os
ses
ge
ner
at
e
d
i
n
a
c
urvatu
re
struct
ur
e
ha
s
bee
n
e
xam
ined
to
est
ablish
the
best
offset
wh
ic
h
e
na
bles
the
pro
pag
at
io
n
of
th
e
op
ti
cal
po
wer
with
out
dete
rior
at
io
n.
Since
t
her
e
are
thr
e
e
segm
ent
j
unct
ion
s
,
the
cal
culat
ion
will
ha
ve
to
be
pe
rfor
m
ed
thr
ee
tim
es.
Using
the
offset
m
et
hod,
we
c
o
n
s
i
d
e
r
e
d
f
i
r
s
t
o
n
l
y
t
h
e
o
f
f
s
e
t
b
e
t
w
e
e
n
t
h
e
t
w
o
a
r
c
s
(
F
i
r
s
t
c
u
r
v
e
d
g
u
i
d
e
-
s
e
c
o
n
d
c
u
r
v
e
d
g
u
i
d
e
)
n
o
t
e
d
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N:
20
88
-
8708
Offse
t ef
fe
ct
o
n t
he S
-
Be
nd str
ucture
losses
and opti
miz
atio
n
(
F.
Brik
)
4165
(
o
f
f
s
e
t
2
=
-
0
.
9
μ
m
)
and
(
off
s
et
1=off
set
3=0).
In
Fig
ur
e
5,
the
tran
sm
issi
o
n
a
nd
l
os
ses
of
the
s
hifted
str
uctu
re
are
sho
wn.
It
c
an
be
see
n
that
the
tra
ns
it
io
n
losses
bet
ween
the
tw
o
arc
s
a
re
widely
re
duced
by
the
valu
e
of
the opti
m
al
o
ffset
.
Figure
3.
S
ketch of
the
c
urve
d st
ru
ct
ur
e
w
it
h
sh
ift
unde
r
s
of
t
war
e
p
ac
kag
e
Figure
4.
P
os
it
ion o
f
t
he
diff
e
r
ent off
set
s
(a)
(b)
Figure
5
.
N
orm
al
iz
ed
transm
issi
on
of the
shi
fted
c
urved str
uctu
re (
offset
2=
-
0.9
µm
),
(
a)
m
on
it
or
inten
sit
y
,
(
b)
powe
r
los
s
in the t
otal l
en
gth
of the
str
uc
ture
-
The p
ow
e
r
tra
nsm
issi
on
is
91% r
es
ulti
ng in a
loss o
f 9%
for
a
rad
ii
R=
1500μm
.
In
Fig
ur
e
6,
th
e
norm
al
iz
ed
transm
issi
on
(c
on
t
our
Ma
p)
a
nd
the
powe
r
l
os
s
i
n
the
S
-
B
end
str
uctu
re
for
the
offse
ts
op
ti
m
iz
ed
offs
et
1,
offset2
an
d offset
3 are
di
sp
la
ye
d.
-
The p
ow
e
r
tra
nsm
issi
on
is
98.
68% r
e
su
lt
in
g
i
n
a
sig
nificantl
y decrease
d
l
oss o
f 1.
32
%
fo
r R
= 15
00μm
.
Table
1
su
m
m
a
rizes
the
diff
e
r
ent
op
ti
m
iz
ed
pa
ram
et
ers.
For
the
s
hifted
str
uc
ture,
the
m
axim
u
m
po
wer
can
be
ac
hieve
d
f
or
the
op
ti
m
al
values
of
offset
at
the
diff
e
ren
t
ju
nctio
n,
in
c
on
tra
st
t
o
t
he
str
uctur
e
with
out
offset.
I
n
c
onse
qu
e
nce,
the
di
m
ension
of
the
curve
d
st
ru
ct
ure
is
decr
ea
sed
t
o
1380µm
wh
i
ch
is
c
om
patibl
e
with
integrate
d op
ti
cs tren
ds
[
25
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
10
, No
.
4
,
A
ugus
t
2020
:
4162
-
4167
4166
(a)
(b)
Figure
6
.
N
orm
al
iz
ed
transm
issi
on
of the
shi
fted
c
urved str
uctu
re, (a)
Mo
nitor i
ntensity
,
(
b) lo
sses
of po
wer i
n
t
he
total
leng
t
h of t
he
s
tructu
re
Table
1
.
List
of sig
nifica
nt
pa
ram
et
ers
of
th
e
sh
ifte
d
c
urve
d
struct
ur
e
Pa
ra
m
eters
Valu
es (µ
m
)
Rad
iu
s (R)
15
00
Leng
th
of
the waveg
u
id
e (
Lin=Lo
u
t)
300
Of
f
set 1
0
.5
Of
f
set 2
-
0.
9
Of
f
set 3
0
.5
Total len
g
th
(S)
1380
4.
CONCL
US
I
O
N
In
this
pa
per,
a
te
ch
nique
a
vai
la
ble
in
the
Rs
of
t
softwa
re
pa
ckag
e
cal
le
d
ʺ
Si
m
ulate
d
Be
nd
ʺ
has
bee
n
sh
ow
n
a
nd
t
he
resu
lt
s
e
xpose
d.
It
has
bee
n
pu
t
into
e
vid
e
nc
e
that
t
her
e
ar
e
tw
o
m
ai
n
los
s
s
ources.
T
he
first
is
du
e
to
t
he
cu
r
vatu
re
ra
dius,
wh
il
e
the
seco
nd
occ
urs
w
he
n
the
cu
rv
e
d
guide
a
nd
the
ri
gh
t
guide
m
odes
ha
ve
a
sp
at
ia
l
distri
bu
ti
on
a
nd
a
dissim
il
ar
eff
e
ct
ive
inde
x
w
hen
switc
hing
from
on
e
t
o
a
no
t
her
in
t
he
cu
rv
e
d
structu
re.
Aim
i
ng
at
re
duci
ng
the
lo
sses
a
nd
i
m
pr
ovin
g
t
he
struct
ur
e
ef
fici
ency,
the
offs
et
m
et
ho
d
has
been
introd
uced.
By
com
pen
sat
in
g
the
diff
e
re
nce
betwee
n
t
he
gu
ide
m
od
es
le
ad
ing
to
an
optim
iz
at
ion
of
the
c
u
r
ve
d
structu
re d
im
e
ns
io
ns
.
A
n
e
va
luati
on
of
the
c
urve
d
str
uctu
re
with off
set
a
nd w
it
hout o
f
fse
t
has
bee
n
pr
es
ented.
It
has
bee
n
c
oncl
uded
that
putt
ing
offset
at
the
j
unct
io
n
r
edu
ce
s
the
los
ses
f
or
the
sa
m
e
le
vel
of
th
e
siz
e.
In
pe
rs
pecti
ve,
it
is
inten
ded
to
com
plete
th
is
w
ork
with
e
xp
e
rim
ental
data
and
to
in
ves
ti
gate
this
str
uc
ture
base
d on ph
otonic cry
sta
ls t
o r
edu
ce
it
s g
e
ome
tric
al
p
aram
eter
s as
w
el
l as t
he vari
ou
s
loss
es.
ACKN
OWLE
DGE
MENTS
We
a
re
gr
at
e
f
ul
to
Mr.
Mo
ham
ed
Bou
c
hem
at
,
prof
es
sor
in
M
ent
our
i
U
niv
e
rsity
,
Alge
ria
an
d
Mr.
A
bd
e
sslam
.
Ho
ci
ni,
pro
fessor
in
un
i
ve
rsity
of
M
’sila
,
for
there
frui
tful
disc
us
sio
n
an
d
help
th
rough
ou
t
this w
ork.
REFERE
NCE
S
[1]
Ret
no
W
iga
j
at
ri
Purnam
ani
ngsi
h,
N
y
i
R
ade
n
P
oespa
wati,
El
h
a
dj
Doghe
che,
"III
-
Nitri
de
Sem
iconductors
b
ase
d
Optic
a
l
Pow
er
S
pli
tter
Devi
ce
De
sign
for
under
wa
te
r
Applicat
ion
,
"
Int
ernati
onal
Jo
urnal
of
E
lectrical
and
Comput
er
Engi
ne
ering
(
IJ
ECE
)
,
vol
.
8
,
n
o
.
5
,
pp.
3866
-
387
4,
Oct
ob
er
2018
.
[2]
Mitha
q
M.
Meh
d
y
Al
-
Sult
ani, "
Stud
y
the
eff
ect
of thin
fi
lm
thick
ness
on
th
e op
ti
c
al
f
eature
s
of
(IR
5
la
ser
d
y
e
/CdSe
nanopa
rt
ic
l
es)
s
ample,
"
TEL
KOMNIKA
Tel
ec
o
mm
unic
ati
on,
C
omputing,
Elec
t
ronics
and
Cont
rol
,
v
o
l.
17,
n
o
.
6,
pp.
2877
-
2884
,
Dec
.
2019.
[3]
Mahm
oud
Ta
wfi
eq,
Jorg
Frick
e,
André
Mull
er,
Pi
et
ro
Della
C
asa
,
Pete
r
Ressel,
Ar
nim
Ginola
s,
Ha
ns
W
enz
el,
Bern
d
Sum
pf
and
Gunt
her
Tra
nkl
e,
"Ch
ara
c
te
ris
at
ion
an
d
compari
son
be
twee
n
diff
ere
nt
S
-
bend
shappe
d
GaAs
Y
-
Branch
distri
bute
d
Br
ag
g
ref
lector
l
ase
rs
emit
ti
ng
a
t
976
nm
,
Sem
ic
onduc
tor
,
"
in
Semi
con
duct
or
S
ci
en
ce
a
nd
Techno
logy
,
vol.
33
,
n
o
.
11
,
Sep
.
2018
.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N:
20
88
-
8708
Offse
t ef
fe
ct
o
n t
he S
-
Be
nd str
ucture
losses
and opti
miz
atio
n
(
F.
Brik
)
4167
[4]
F
l
o
r
i
a
n
D
ü
r
r
a
n
d
H
a
g
e
n
R
e
n
n
e
r
,
"
A
n
a
l
y
t
i
c
a
l
d
e
s
i
g
n
f
o
r
X
c
o
u
p
l
e
r
s
,
"
J
o
u
r
n
a
l
o
f
L
i
g
h
t
w
a
v
e
T
e
c
h
n
o
l
o
g
y
,
v
o
l
.
2
3
,
n
o
.
2
,
pp.
876
-
885
,
Ma
r
.
2005
.
[5]
Partha
Pra
ti
m
Sahu,
P.
P.
Sahu
,
"D
ouble
S
-
ben
d
struct
ur
e
for
a
compac
t
two
m
ode
in
te
rfe
ren
c
e
coupler,
"
Appl
i
ed
Optic
s,
vo
l. 50,
no.
3
,
pp
.
242
-
2
45,
Jan
.
2011
.
[6]
Nurdiani
Za
uh
ar
i,
Abang
Enmar
Ehc
an
,
Mohd
S
yuhai
m
i
Abd
Rah
m
an,
"S
-
Bend
Si
li
con
-
On
-
Insula
t
or
(SO
I)
La
rg
e
cro
ss
sec
t
ion
Ri
b
wave
gu
ide
for
dire
c
ti
ona
l
coupler,
"
Inte
rnat
iona
l
journal
o
f
Elec
t
rical
and
Compu
te
r E
ngineering
(
IJE
CE)
,
vol.
7,
NO
.
6,
PP
.
3299
-
3305,
De
c
.
201
7.
[7]
F.
Brik,
N.
Para
i
re,
T.
Bouch
emat
and
M.
Bou
chem
at
,
"M
ini
m
izat
ion
of
the
the
rm
al
eff
e
ct
in
a
wa
vegui
de
struct
u
r
e
opti
c
al
sw
itch
,
"
Appl
ie
d
physi
cs
B
,
vo
l.
97,
n
o.
4,
841
-
847,
Dec
.
2
009.
[8]
Fati
m
a
Bri
k,
Abderra
ouf
Fare
s,
Fahima
Fare
s,
"
Dete
rm
ina
t
ion
o
f
diff
ere
nt
p
ara
m
et
ers
of
an
optic
al
sw
it
ch
struct
u
r
e
with
a
m
et
a
ll
i
c
m
irror
,
"
6th
Internat
ion
al
Conf
er
enc
e
on
Com
put
at
ion
al
and
Experim
ent
al
Sci
enc
e
and
Engi
n
ee
r
in
g
(IC
CESEN
-
2019)
Antaly
a
,
TUR
KEY 23
-
27
Oct
.
2019.
[9]
Po
Dong,
Long
Chen
and
Youn
g
-
Kai
Chen
,
"H
i
gh
-
spee
d
low
vo
lt
ag
e
single
driv
e
push
pull
si
li
c
on
Mac
h
Z
ehnd
er
m
odula
tors,
"
Op
ti
c
Ex
press
,
vol
.
20,
no
.
6
,
pp
.
61
63
-
6169,
Mar
.
2
012.
[10]
A.
Mus
a
b
,
et
al
.
,
"Enh
anc
ing
th
e
p
erf
orm
ance
o
f
strip
and
180d
eg
slo
t
wave
gu
i
de
b
ends
fo
r
integra
t
ed
optical
wave
guide m
odula
tor
,
" Optical
engi
ne
eri
ng,
vol
.
58
,
no.
2
,
2019.
[11]
N. M
.
Ridz
u
an,
M. F
.
L
.
Abdull
a
h,
M. B
.
Othm
an
,
M. B
.
Jaa
f
ar,
"A
Carr
ie
r
le
ss
Am
pli
tude
Phase
(
CAP
) M
odula
ti
o
n
form
at
:
Persp
ec
t
i
ve
and
Pros
pec
t
i
n
Opti
ca
l
Tra
ns
m
ission
S
y
stem
,
"
Int
ernati
onal
J
ournal
of
El
e
ct
ri
cal
and
Compute
r
Engi
nnering
(
IJ
ECE
)
,
vol
.
8
,
n
o
.
1
,
pp.
585
-
595,
Feb
.
2018
.
[12]
D.
Mar
cuse
,
"L
e
ngth
op
ti
m
iz
a
ti
o
n
of
an
S
-
Shap
e
d
tr
ansit
ion
b
et
w
ee
n
offset
op
ti
c
a
l
wav
egui
d
e
tra
n
siti
on
,
"
App
li
ed
opti
cs
,
vol
.
17,
n
o.
5
,
pp
.
763
-
76
8
,
Mar
.
1978
.
[13]
T.
Kitoh
,
N
.
Takat
o,
M.
Yasu,
M.
Kawa
chi
,
"B
endi
ng
loss
in
S
il
ica
base
d
wav
e
guide
b
y
using
l
at
er
al
offset
s,"
i
n
Journal
of
Light
wave
Te
chnol
og
y
,
vo
l. 13, no. 4,
pp.
555
-
562
,
Ap
r
.
1995
.
[14]
A.
M.
Shaj
akha
n
,
Shee
l
Adit
y
a
,
"S
lope
‐m
at
che
d
S‐bends for
in
cl
in
ed
integra
te
d‐opt
ic
wav
egui
des
,
"
Mic
rowave
an
d
opt
ic
al
Techno
l
o
gy
Let
t
ers
,
vo
l. 2
4
,
no
.
4
,
pp
.
267
-
271
,
Feb
.
2000
.
[15]
Jare
d
F.
Bauters,
Mich
ael
L.
D
av
enpor
t,
Mar
ti
jn
J
.
R.
Hec
k
,
J.
K.
Do
y
le
nd
,
Arnold
Chen
,
Alex
ander
W
.
Fang,
and
John E
.
Bow
ers,
"S
il
ic
on
on
ult
r
a
-
low
-
loss wave
g
uide phot
oni
c
integra
t
ion
platfor
m
,
"
Optic
s
e
xpre
ss
,
vol
.
21,
n
o
.
1,
pp.
544
-
555
,
Jan
.
2013
.
[16]
N
u
r
d
i
a
n
i
Z
a
u
h
a
r
i
,
A
b
a
n
g
E
n
m
a
r
E
h
c
a
n
,
"
L
a
r
g
e
c
r
o
s
s
s
e
c
t
i
o
n
R
i
b
S
i
l
i
c
o
n
-
on
-
i
n
s
u
l
a
t
o
r
(
S
O
I
)
S
-
B
e
n
d
w
a
v
e
g
u
i
d
e
,
"
i
n
O
p
t
i
k
,
vol.
130
,
pp
.
141
4
-
1420,
Feb
.
20
17
.
[17]
Zha
ng
B
ing
-
na
,
Zhu
Da
-
q
ing,
Lei
W
ei,
Ze
ng
Si
-
h
ua,
"Configura
t
i
on
opti
m
izati
on
of
S
-
shape
d
b
en
d
wave
gu
ide
usi
ng
B
-
spline
,
"
Ch
ines
e
journa
l
o
f laser
,
vol
.
31
,
no
.
1
1,
2004
.
[18]
Rupesh
Kum
ar
Nava
la
kh
e,
Nan
dit
a
Das
Gupta
,
Buo
y
Krihn
a
Das,
"F
abr
ic
a
ti
o
n
and
cha
r
acte
ri
za
t
ion
of
strai
g
ht
and
compa
ct
S
-
Bend
opt
ic
a
l
w
ave
guid
es
on
a
Sili
con
-
on
-
insul
at
or
p
la
tfo
rm
,
"
Appl
ie
d
Opti
cs
,
vol.
48,
no.
3
1,
pp.
G125
-
G130, N
ov
.
2009.
[19]
Zhe
n
Hu
,
Ya
Y
an
Lu
,
"Com
puti
ng
op
ti
m
al
wa
vegui
des
b
ends
with
const
ant
width
,
"
in
Journa
l
of
Lightwa
ve
Technol
ogy
,
vo
l. 25, no. 10, pp. 3
161
-
3167,
Oc
t. 2
007.
[20]
G.
Li
,
J.
Yao
,
e
t
al
.
,
"U
lt
ra
low
-
lo
ss
,
high
-
d
ensity
SO
I
opti
c
al
wav
egui
de
ro
u
ti
ng
fo
r
m
ac
ro
chi
p
in
te
r
conne
c
ts
,
"
Opt
ics
Ex
press
,
vol
.
20
,
no.
11,
pp.
1203
5
-
12039,
2012
.
[21]
Fujisawa
Ta
k
eshi
,
e
t
al
.
,
"
Low
loss,
compac
t
,
and
f
abr
icati
on
-
tol
er
a
nt
Si
-
wire
90°
w
ave
guid
e
bend
u
sing
cl
othoi
d
a
n
d
n
o
r
m
a
l
c
u
r
v
e
s
f
o
r
l
a
r
g
e
s
c
a
l
e
p
h
o
t
o
n
i
c
i
n
t
e
g
r
a
t
e
d
c
i
r
c
u
i
t
s
,
"
O
p
t
.
E
x
p
r
e
s
s
,
v
o
l
.
2
5
,
n
o
.
8
,
p
p
.
9
1
5
0
-
9
1
5
9
,
A
p
r
.
2
0
1
7
.
[22]
Fati
m
a Br
ik,
Sal
iha
Hari
ze
,
Abde
rra
ouf F
ar
es,
"R
educ
t
ion of
an
S
-
Bend s
tru
ct
ur
e s
iz
e
for
opt
ic
t
el
e
comm
unic
at
ion
,
"
2019
IEEE
In
te
r
nati
o
nal
Confe
r
enc
e
on
Design
&
Te
st
of
In
te
gr
ate
d
M
ic
ro
&
N
ano
-
Syste
ms
(
D
TS)
,
Gammart
h
-
Tuni
s, Tunisia,
p
p.
1
-
5
,
2019
.
[23]
Y.
Chung,
N.
Dogli,
"A
n
assess
m
ent
of
f
ini
t
e
d
i
ffe
ren
c
e
b
ea
m
p
ropa
gation
m
et
h
od,
"
in
IE
EE
Jo
urnal
of
Quan
tu
m
El
e
ct
ronics
,
vol
.
26,
no.
8,
pp.
13
35
-
1339,
Aug
.
19
90.
[24]
La
llam
Far
ah,
Bada
oui
Hadj
ir
a,
Abri
Meha
dj
i,
"D
esign
of
a
Sel
ec
t
ive
Filt
er
base
d
on
2D
Photonic
Cr
y
st
a
ls
Mate
ri
al
s
,
"
Inte
r
nati
onal
Journal
of
E
lectric
a
l
an
d
Computer
Eng
ine
ering
(
IJE
CE
)
,
vol.
7,
no
.
4
,
pp.
1833
-
183
8
,
Aug
.
2017.
[25]
Mehdi
Za
m
ani,
Mansoureh
Am
anol
la
hi
,
Abdess
el
am
Hocini
,
"P
hotoni
c
ban
d
gap
spec
tr
a
in
Octonacc
i
all
superc
onducting
ape
r
iodi
c
photo
nic
cr
y
s
ta
ls
,
"
Ph
ysic
a
B:
Cond
ese
d
Mat
te
r
,
vol
.
5
56,
pp
.
151
-
157
,
Mar
.
2019
.
Evaluation Warning : The document was created with Spire.PDF for Python.