Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.3
,
No
.1
, Feb
r
u
a
r
y
2
013
,
pp
.
73
~77
I
S
SN
: 208
8-8
7
0
8
73
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
New Des
i
gn of
Channel Drop Fil
t
er by T
r
ian
g
ular Photon
ic
Crystal
Mohammad Rez
a
Rak
h
sh
ani*, Moh
a
mma
d
Ali
Ma
nsouri-Birjandi**
*
,
**F
acult
y of E
l
ec
tric
al
and
Co
mputer Engin
eer
ing, Univ
ersity
o
f
Si
s
t
an and
B
a
l
u
ches
tan
,
Zahed
a
n,
I
r
an
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Dec 2, 2012
Rev
i
sed
Jan 13, 201
3
Accepte
d
Ja
n 21, 2013
W
e
have design
ed a new t
y
p
e
o
f
optic
a
l
chann
e
l
drop filter (CDF) based on
two dimensional triangular
lattice photonic cr
y
s
tals
. CDF operation is based
on coupling
to
the photon
ic
cr
y
s
tal wavegu
ide. The proposed
structure
is
optim
ized
to wo
rk as
a CDF
.
F
o
r
obtain
i
ng th
e C
D
F
charac
teris
t
i
c
s
and band
structure of th
e filter, th
e finit
e
differen
ce t
i
m
e
dom
ain (FDTD)
m
e
thod and
plane wav
e
ex
pansion (PWE) method are u
s
ed respectively. Dropping
efficiency
at 1556
nm
and quality
factor (
Q
) of
our proposed st
ructure ar
e
100% and 260, r
e
spectively
.
Th
e
quantitie
s of quality
f
actor
and tr
ansmission
effic
i
enc
y
ar
e s
u
itabl
e for op
ti
cal
appli
c
a
tions
. Th
e over
a
ll
s
i
ze of
th
e
proposed add d
r
op filter is 19
1.97
µm
2
, which
is sm
aller tha
n
the fil
t
ers
alread
y
repo
rted
and it is h
i
ghly
d
e
si
rab
l
e
for
photonic integrated circu
its
(PICs).
Keyword:
Ch
ann
e
l d
r
o
p
filter
FDT
D
m
e
t
hod
Pho
t
on
ic cr
yst
a
l
Wavel
e
ngt
h
Copyright ©
201
3 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
:
Mohamm
ad Reza Rakhsha
n
i,
Depa
rtem
ent of Electrical a
nd Co
m
p
u
t
er
Engin
eer
ing
,
Uni
v
ersity of
Sistan and Bal
u
chestan,
Zahe
dan
,
I
r
a
n
.
Em
a
il: m
.
rak
h
s
h
a
n
i
@m
ai
l.u
s
b.ac.ir
1.
INTRODUCTION
Th
e pho
ton
i
c crystals (PhCs) h
a
v
e
attracted
a g
r
eat
d
eal o
f
attentio
n
du
e to
t
h
eir ab
ility to
m
a
ni
pul
at
e l
i
ght
at
wavel
e
n
g
t
h scal
e and so
m
e
feat
ures
such as com
p
actness, elect
r
o
m
a
gnet
i
c
wa
ve em
i
ssi
on
co
n
t
ro
llab
ility, h
i
g
h
rate of p
e
rfo
r
m
a
n
ce sp
eed
,
lon
g
life
p
e
rio
d
,
an
d
p
r
o
p
e
rty fo
r in
tegratin
g
o
n
o
p
tical circu
it
[1]. PhCs are com
posed of pe
riodic
dielectric or m
e
tallo-dielectric nanost
r
uct
u
res that have alternate low a
nd
hi
g
h
di
el
ect
ri
c
const
a
nt
m
a
teri
al
s i
n
o
n
e,
t
w
o
or t
h
ree
di
m
e
nsi
on(s
)
,
whi
c
h af
fect
s t
h
e p
r
o
p
a
g
a
t
i
on o
f
electro
m
a
g
n
e
tic (EM)
wav
e
s
in
sid
e
t
h
e st
ructu
r
e
[2
,3
]. As a resu
lt
o
f
th
i
s
p
e
riod
icity, it p
o
ssesses pho
ton
i
c
ban
d
ga
p (
P
B
G
),
w
h
e
r
e t
h
e
t
r
ansm
i
ssi
on
of l
i
g
ht
i
n
certain
frequ
en
cy
rang
e is ab
solu
tely zero
.
Ph
o
t
o
n
i
c
cry
s
t
a
l
s
(PhC
s
)
are very
sui
t
abl
e
candi
dat
e
s for real
i
zat
i
on o
f
fut
u
re
passi
ve a
nd a
c
t
i
v
e opt
i
cal
devi
ces
because
of t
h
eir ability to
control light-wave prop
agation, high
speed of opera
tion,
better confinem
ent, l
ong
life p
e
riod
an
d su
itab
ility fo
r
in
teg
r
ation
[4
,5
]. By creatin
g th
e d
e
fects
(po
i
n
t
orlin
e) i
n
th
e p
e
riod
ic stru
cture,
i
t
i
s
possi
bl
e t
o
g
u
i
d
e
t
h
e
pr
opa
gat
i
o
n
of l
i
ght
t
h
r
o
u
g
h
t
h
e PB
G re
gi
on
.
Thi
s
pecul
i
a
r
beha
vi
o
r
ca
n l
ead t
o
realize alm
o
st all kinds
of PhC
base
d active and
passi
ve
optical devices
.
Structures ba
sed on
PhCs
e
n
able
researc
h
ers to
design sm
all-s
cale devices [4]. In rece
nt
y
ears, m
a
ny
PhC
based
opt
i
cal
devi
ces a
r
e de
si
gne
d
su
ch
as, po
wer sp
litters [6
],
m
u
l
tip
lex
e
rs [7
], d
e
m
u
ltip
le
x
e
rs [8
], po
larizatio
n
b
eam
s
p
litters [9
], trip
lex
e
rs
[10
]
, switch
e
s
[11
]
, d
i
rectio
nal co
up
lers
[1
2], b
a
nd
st
o
p
filters [1
3
]
,
b
a
n
d
p
a
ss
filters [14
,
1
5
]
, ch
an
n
e
l
drop
filters [1
6
]
.
Filterin
g
d
e
v
i
ce en
ab
ling
u
s
t
o
ex
tract fro
m
o
n
e
wav
e
g
u
i
de o
n
e
wav
e
leng
th
and
send
it to
an
o
t
h
e
r
wav
e
gu
id
e. For
W
a
v
e
leng
th
Div
i
sion
Mu
ltip
lex
i
ng
(WD
M
)
syste
m
s, o
p
tical ch
ann
e
l d
r
op
filter is o
n
e
of th
e
i
m
p
o
r
tan
t
co
mp
on
en
ts to select a sing
le or
m
u
l
tip
le wav
e
l
e
n
g
t
h
ch
ann
e
ls.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
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8
I
J
ECE
Vo
l. 3
,
N
o
. 1
,
Feb
r
u
a
ry
2
013
:
73
–77
74
2.
D
E
SIGN
OF PHC
CD
F
As sho
w
n
in
Fig
.
1
,
o
u
r d
e
sign
is b
a
sed
on
2D tr
ian
g
u
l
ar lattice o
f
silico
n
rod
s
with
refractiv
e in
d
e
x
of
n
Si
=3
.4
6, in an
ai
r
b
ackgro
und
w
ith
n
air
=1
. In
th
is
investig
atio
n
,
th
e ratio
o
f
th
e rod
rad
i
u
s
r
to
t
h
e lattice
constant
a
, i
s
0.
2. I
n
t
h
i
s
st
r
u
ct
u
r
e, ba
n
d
g
a
p o
p
en
s fo
r t
h
e n
o
rm
al
i
zed
fre
que
ncy
0.
3
3
7
a/
λ
t
o
0.
4
42
a/
λ
fo
r
TM
pol
ari
zat
i
o
n (i
n
w
h
i
c
h t
h
e
m
a
gnet
i
c
fi
el
d i
s
i
n
p
r
o
p
a
g
a
t
i
on pl
a
n
e an
d
t
h
e el
ect
ri
c fi
el
d i
s
per
p
e
ndi
c
u
l
a
r)
,
whe
r
e
λ
is the
wavele
ngt
h i
n
free s
p
ace.
The s
p
ectrum
of
t
h
e power t
r
ansm
ission is
obtaine
d
with finite
di
ffe
re
nce t
i
m
e
dom
ai
n (FD
T
D) m
e
t
hod.
F
D
TD i
s
a t
i
m
e
dom
ai
n sim
u
lat
i
on m
e
t
hod f
o
r s
o
l
v
i
n
g M
a
xwel
l
’
s
equat
i
o
ns i
n
ar
bi
t
r
ary
m
a
t
e
ri
al
s and ge
om
et
r
i
cs [17]
.
Bere
nger’s pe
rfectly
m
a
tched layers (PML) are located
aroun
d th
e
who
l
e stru
cture as ab
so
rb
ing
bo
un
d
a
ry co
nd
ition
[18
]
.
Fi
gu
re
1.
Sc
he
m
a
t
i
c
of a
ph
ot
oni
c c
r
y
s
t
a
l
ba
sed C
D
F
Fiv
e
add
ition
a
l ex
tra scatterin
g
rod
s
with b
l
ack
co
lor
are in
tro
d
u
c
ed to
i
m
p
r
ov
e t
h
e sp
ectral
sel
ect
i
v
i
t
y
and obt
ai
n a ve
ry
hi
gh
dr
o
ppe
d
effi
ci
ency
.
T
h
ese scatterers
have e
x
actly the sam
e
refra
ctive
i
nde
xes as al
l
ot
he
r di
el
ect
ri
c
ro
ds i
n
PhC
s
t
ructure and t
h
eir diam
eters is chosen t
o
be
r
S
=0.965
r
fo
r better
p
e
rf
or
m
a
n
ce [
4
].
Fig.
2(a) s
k
etc
h
es t
h
e
band
diagram
of the
struct
ure without
a
n
y defect
s. Whe
n
t
h
e
line defect
is
introduced i
n
the struct
ure, the PBG is broke
n
and the
guided m
ode
s are a
llowed t
o
propagate inside t
h
e PB
G
reg
i
o
n
as sh
own
in
Fig. 2
(
b).
Bo
th
po
in
t and lin
e d
e
f
ects are in
trod
u
c
ed
fo
r
d
e
sign
ing
the filter. Th
e guid
e
d
m
o
d
e
s are regu
lated
b
y
con
t
ro
lling
th
e
d
e
fect size and
sh
ap
e. In
g
e
n
e
ral, a ring
reson
a
tor is
p
o
s
itio
n
e
d
betwee
n two
optical wa
vegui
d
es
provides
a
n
ideal
basi
c
struct
ure
for C
D
F such th
at power
in one wa
veguide
i
s
t
r
ans
f
er
red
i
n
t
o
t
h
e
ot
her
t
h
ro
u
gh t
h
e
reso
nance
o
f
t
h
e
ri
ng
,
whi
c
h i
s
us
ed t
o
ad
d
or
re
m
ove a cha
nne
l
fr
om
th
e m
u
lt
ip
lex
e
d
inp
u
t/ou
t
pu
t sig
n
a
ls.
Fig
.
3
sh
ows th
e sc
he
m
a
tic
layo
u
t
o
f
CDF,
wh
ich
con
s
ists of bu
s and
dr
o
ppi
ng
wa
ve
gui
des.
A
Gaussian
pulse in
pu
t si
g
n
a
l is lau
n
c
h
e
d
i
n
to
t
h
e i
n
pu
t
po
rt and
its
o
u
t
p
u
t
is d
e
tected at th
e
po
rts
‘A
’ an
d ‘B
’
us
i
ng
po
wer m
oni
t
o
r
.
The
no
r
m
al
i
zed t
r
ansm
i
ssi
on spect
r
u
m
i
s
obt
ai
ne
d
by
t
a
ki
ng F
a
st
Fou
r
i
e
r
trans
f
orm
(FFT)
of the
fields
that
are
calcul
a
ted by
2D FDTD m
e
thod.
The
no
rm
al
i
z
ed t
r
a
n
sm
i
ssi
on spect
ra
fo
r t
w
o
out
put
p
o
rt
s
(
A
an
d B
)
i
n
t
h
e C
D
F a
r
e di
s
p
l
a
y
e
d i
n
Fi
g
.
3 as re
d and
blue lines, res
p
ectively. It can be see
n
th
at
th
e sp
ectral selectiv
ity is s
i
g
n
i
fican
tly i
m
p
r
ov
ed,
10
0%
dr
o
ppi
n
g
ef
fi
ci
ency
can be
o
b
t
a
i
n
ed
at
t
h
e reso
na
nt
wavel
e
ngt
h o
f
15
5
6
nm
. Th
e
q
u
a
lity facto
r
(
Q
) o
f
dr
o
ppi
ng
pea
k
i
s
2
6
0
.
S
u
c
h
Q
v
a
lu
es
ar
e
enou
gh
fo
r
op
ti
cal
com
m
uni
cat
i
on a
ppl
i
cat
i
o
ns.
Fig.
4(a
)
and (b)
depicts the
electric filed pa
ttern of res
o
nance and off
resonance at 1556
nm
and
1
530
nm
,
respe
c
t
i
v
el
y
.
At
resona
nt
wa
vel
e
n
g
t
h
o
f
λ
=155
6
nm
, the electric field of the
bus
wa
veguide
is t
o
out
put
p
o
rt
‘B
’, w
h
ereas
at
‘
o
f
f
” reso
na
nce
λ
=1530
nm
, the signal di
rectly reaches
to the tra
n
sm
ission
port
‘A
’.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE I
S
SN
:
208
8-8
7
0
8
New D
e
sign
o
f
Ch
ann
el D
r
op
Filter b
y
Tri
a
ng
u
l
a
r
Pho
t
on
ic Crysta
l (Moham
mad
Reza
Rakh
sh
an
i)
75
(a)
(b
)
Fi
gu
re
2.
B
a
n
d
di
ag
ram
of t
r
i
a
ng
ul
ar
l
a
t
t
i
ce, (a)
be
f
o
re a
n
d
(b
)
Aft
e
r
i
n
t
r
o
duci
n
g
l
i
n
e
def
ect
Fi
gu
re
3.
N
o
r
m
al
i
zed op
tical powe
r tra
n
sm
ission cha
r
actri
stic of C
D
F
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:20
88-
870
8
I
J
ECE
Vo
l. 3
,
N
o
. 1
,
Feb
r
u
a
ry
2
013
:
73
–77
76
(a)
(b
)
Figu
re
4.
(a
) El
ectric field
pattern
o
f
t
h
e
P
h
C
base
d C
D
F at
(
a
)
15
5
6
nm
(
a
t
r
e
son
a
n
ce) and, (b
) 153
0
nm
(o
ff
reso
na
nce)
.
3.
CO
NCL
USI
O
N
A 2D
ph
ot
o
n
i
c
cry
s
t
a
l
C
D
F had bee
n
i
n
t
r
o
d
u
ced an
d i
nve
st
i
g
at
ed t
h
ro
u
gh F
D
TD
m
e
t
hod i
n
trian
g
u
l
ar lattice silico
n
ro
d
s
. 1
0
0
%
d
r
o
p
efficien
cy
an
d
q
u
ality facto
r
o
f
2
6
0
can
b
e
o
b
t
ain
e
d
at 155
6
nm
th
at
th
is is an
im
p
o
r
tan
t
ad
v
a
n
t
age fo
r CDF is
p
r
o
p
o
s
ed
t
h
an
the CDFs already repo
rted
i
n
t
h
e literature.
We
h
a
ve
sh
own
th
at th
ere is flex
ib
ility
in
d
e
sign
o
f
the CDF w
ith
pho
ton
i
c crystal. Su
ch
stru
ct
u
r
e
may o
ffer promisin
g
appl
i
cat
i
o
ns
fo
r
ph
ot
o
n
i
c
i
n
t
e
grat
e
d
ci
rc
ui
t
s
base
d
on
P
h
C
s
and
ot
her
na
n
o
p
h
o
t
o
ni
c st
r
u
ct
ures
.
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4.
BIOGRAP
HI
ES OF
AUTH
ORS
M
o
hammad Re
z
a
Rak
h
s
h
ani
has
rec
e
iv
ed his
B.S
c
.
and
M
.
S
c
.degre
es
in
E
ectr
i
ca
lEngin
eer
ing
from University
of Sistan and
Baluchestan,
Zah
e
da
n, Ir
an in
201
0, 2012, re
spectively
. His resear
ch
inter
e
sts includ
e numerical
el
ectromagnetic,
photonic b
a
ndg
ap stru
ctur
es and applications of
photonic cr
y
s
tals in
integr
ated
cir
c
uit.
M
o
hammad Ali M
a
nsour
i
-Birjandi
receiv
e
d
his
BS
c and M
S
c degre
e
s
in
el
ectr
i
ca
l eng
i
ne
er
ing
from the University
of Sistan an
d Baluchestan, I
r
an and the University
of
Tehran, Iran in 1986 and
1991, respectively
.
He th
en joined the Univ
ersity
of Sistan an
d Baluch
estan,
Iran. In 2008,
h
e
obtain
e
d his
P
h
D degre
e
in
e
l
ec
t
r
ica
l
eng
i
ne
ering
from
Trab
iatM
o
d
ares
Unive
r
s
i
t
y
, Ir
an.
As
an as
s
i
s
t
ant
p
r
ofes
s
o
r at
the
U
n
ivers
i
t
y
of S
i
s
t
a
n
and B
a
lu
ches
t
a
n, h
i
s
res
e
arch
areas
are
photonics, optoelectronics, an
alo
g
integrated
cir
c
u
its,
and metamaterial. Dr.
Mansouri has served
as
a rev
i
ewer
for
a
num
ber of journ
a
ls
and
conf
eren
ces
.
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