Intern
ati
o
n
a
l
Jo
urn
a
l
o
f
Ad
va
nces
in Applied Sciences (IJ
A
AS)
V
o
l.
2, N
o
. 3
,
Sep
t
em
b
e
r
2013
, pp
. 13
3
~
13
6
I
S
SN
: 225
2-8
8
1
4
1
33
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
/
IJAAS
Photoni
c
Crys
tal Slab Add-Drop Filter
Mohammad
Rez
a
Rak
h
sh
ani, Moh
a
mmad Ali
Manso
u
ri-Birja
ndi
F
acult
y
of
Ele
c
tr
ica
l
and
Com
put
er Eng
i
ne
ering,
Univers
i
t
y
os
S
i
s
t
an and
Ba
luch
es
tan,
Z
a
hedan
,
Iran
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Dec 21, 2012
Rev
i
sed
Ap
r
14
, 20
13
Accepte
d
May 4, 2013
A new t
y
pe of o
p
tical add drop f
ilter
(ADF) based on slab photonic cr
y
s
tals
resonant
cavities
is proposed. ADF ope
ration is based
on coupling
between
the
photonic
c
r
y
s
tal wa
ve
guides.
Usi
ng the
finite
diffe
re
nce
time
doma
i
n
(FDTD)
method and plane wave e
xpansion
(PWE)
method, the ADF
chara
c
t
e
ris
t
i
c
s
a
nd band s
t
ructur
e of the fi
lt
er, r
e
s
p
ectiv
el
y ar
e o
b
tain
ed. Th
e
proposed structure is optimized to work
as an ADF. Dropping e
fficiency
at
1560
nm
and qu
ality
f
actor (
Q
) of our proposed structure are 90
% and 195,
res
p
ect
ivel
y.
Th
e quantit
ies
of qualit
y fa
ctor and
trans
m
is
s
i
on effici
enc
y
ar
e
suitable
for opt
ica
l
app
lic
ation
s
. This struc
t
ur
e is high
l
y
a
t
t
r
act
ive fo
r
photonic integrated circuits (PICs).
Keyword:
Add
d
r
op
filter
FDT
D
m
e
t
hod
Pho
t
on
ic cr
yst
a
l
R
e
sona
nt
ca
vi
t
y
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,
Faculty of Elec
trical an
d
C
o
m
put
e
r
E
ngi
neer
i
ng,
Uni
v
ersity of
Sistan
and Bal
u
chestan,
P.
O
.
B
o
x 9816
4-1
6
1
,
Zah
e
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
I
n
19
78
Y
a
b
l
on
ov
itch
[1
]
and
j
ohn
[
2
]
f
i
r
s
t
p
r
op
os
ed the i
d
ea that
pe
riodic dielectric structures a
r
e
abl
e
t
o
p
r
o
v
i
d
e p
hot
oni
c
ba
nd
ga
p
(PB
G
)
fo
r
di
st
i
n
ct
re
gi
o
n
s i
n
t
h
e
f
r
e
que
ncy
s
p
ect
r
u
m
,
just
l
i
k
e
t
h
at
o
f
electro
n
i
c band
g
a
p
(EB
G
) in
so
lid
-stat
e
crystals
behavi
or. Owing to features
like com
p
ac
tness
,
electro
m
a
g
n
e
tic wav
e
em
issi
o
n
con
t
ro
llab
ility, h
i
gh
rate
of
p
e
rform
a
n
ce sp
eed
,
l
o
ng
life p
e
riod
an
d
prop
ert
y
fo
r i
n
t
e
grat
i
n
g
on o
p
t
i
cal
ci
rcui
t
,
t
h
e ph
ot
o
n
i
c
cry
s
t
a
l
s
(PhC
s) ha
s been
used f
o
r de
si
gni
ng
opt
i
cal
devi
ce
s
since 1978. PhC is a struct
ure in
wh
ich
th
e
op
tical refractive in
d
e
x
sh
ows
a p
e
ri
o
d
i
c m
o
du
latio
n
with
a l
a
ttic
e
constant in wa
velength
pe
rform
a
nce.
Defe
cts in
phot
onic c
r
ystals can
be
of
point, linear or s
u
rface type. Ea
c
h
of m
e
nt
i
one
d
defect
s c
o
ncl
u
des
desi
g
n
abl
e
at
t
r
i
but
es
a
n
d features with
a specifi
c
usa
g
e. For insta
n
ce, the
poi
nt de
fect could act as a
ca
v
i
t
y
wi
t
h
a very
l
o
w m
ode v
o
l
u
m
e
[3]
.
The al
l
o
we
d m
odes t
h
at
appea
r
ed i
n
PB
G
m
a
ke p
o
ssi
bl
e
t
h
e p
r
opa
gat
i
o
n
of
wa
vel
e
n
g
t
h
i
n
t
h
e
st
ruct
u
r
e [
4
]
.
So fa
r, m
a
ny
opt
i
cal
devi
ces have
been
desi
gne
d ba
sed
on
ph
ot
o
n
i
c
cry
s
t
a
l
s
such as o
p
t
i
cal
swi
t
c
hes
[5
], [6
], filters [7
], [8
],
p
o
wer sp
litter [9
] an
d
wav
e
len
g
t
h d
e
m
u
lt
ip
lex
e
r [1
0
]
. Th
ese dev
i
ces are b
e
ing
u
s
ed
main
ly in
o
p
tical co
mm
u
n
i
c
a
tio
n
system
s,
lik
e a wav
e
leng
th
Div
i
sion
m
u
l
tip
lex
i
n
g
(WDM
) system. As an
essen
tial elem
e
n
t of su
ch
syst
e
m
s, add
d
r
op
filter (ADF)
is
b
e
ing
u
s
ed
for
selectin
g
a ch
an
n
e
l
with a sp
ecific
wav
e
len
g
t
h
.
Th
e cav
ities wh
ich
are co
up
led to
th
e wav
e
gui
d
e
s can
b
e
u
s
ed
as wav
e
leng
th
selecting
dev
i
ces.
Cav
ities in
a s
p
ecific wav
e
len
g
t
h
,
wh
ich
is
th
e cav
ity
reson
a
n
t
wav
e
len
g
th
, lo
calize electro
m
a
g
n
e
tic en
erg
y
fro
m
an
in
pu
t
wav
e
gu
id
e i
n
to th
e cav
ity and
th
en
t
r
an
sm
it it
to
d
r
op
wav
e
gu
id
e.
In t
h
i
s
pape
r,
an
AD
F st
r
u
ct
ure
has
bee
n
desi
g
n
ed
by
sl
ab P
h
C
ca
vi
t
y
fo
r sel
ect
i
ng
desi
re
d
wavel
e
ngt
h.
A
sl
ab P
h
C
o
f
t
r
i
a
ng
ul
ar l
a
t
t
i
ce of ai
r
h
o
l
e
s
has
a l
a
rge t
r
a
n
s
v
e
r
se el
ect
ri
c (T
E) ba
n
d
gap a
n
d i
t
i
s
expecte
d
to se
rve as a
good
platform
for P
hot
oni
c i
n
t
e
gra
t
ed ci
rcui
t
s
an
d ul
t
r
a
-
com
p
act
opt
i
cal
devi
c
e
s.
I
n
th
is stru
cture, p
o
wer tran
sm
it
effi
ciency is
90% while ful
l
width at
h
a
lf
m
a
x
i
m
u
m (FWHM
)
is ab
ou
t 8
nm
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
252
-88
14
I
J
AA
S
V
o
l. 2, No
.
3
,
Sep
t
emb
e
r :
1
3
3
–
136
13
4
These cha
r
act
eristics are highly appropria
t
e for de
vi
sing a cavity based ADF. T
h
e ove
rall size
of the
pr
o
pose
d
de
vi
ce i
s
ab
o
u
t
8
5
.
3
7
μ
m
2
whic
h is
appropriate for p
hot
onic i
n
tegrated circuits.
2.
D
E
SIGN
AND
SIMU
LA
TION
OF
PHC A
D
F
In t
h
i
s
pa
pe
r,
as sh
ow
n i
n
F
i
g.
1,
ou
r
goal
i
s
desi
g
n
i
n
g
a com
p
act
st
ruct
u
r
e f
o
r
A
D
F
base
d
o
n
photonic cryst
a
ls air holes.
The configurat
ion is com
pos
ed of three lay
e
rs of Sio
2
(to
p
clad
din
g
),
Si (slab)
,
Sio
2
(
l
ow
er
clad
d
i
n
g
)
,
w
ith thick
n
e
ss of
10
0, 200
,
10
00
nm
,
res
p
ectively. The
ai
r holes have
a radi
us
r
=0.3
a
whe
r
e
a
is d
e
no
ted
as th
e latt
ice co
n
s
tan
t
an
d
eq
u
a
l to
a
=4
20
nm
. In t
h
i
s
st
ruct
ure
,
ba
n
d
ga
p o
p
ens f
o
r t
h
e
n
o
r
m
alized
f
r
e
q
u
e
n
c
y
0
.
2
555<
a
/
λ
<0
.32
3
6
fo
r TE po
larizatio
n
(i
n
wh
ich th
e electric fi
eld
is in
p
r
op
ag
atio
n
pl
ane a
n
d t
h
e
m
a
gnet
i
c
fi
el
d
i
s
per
p
e
ndi
c
u
l
a
r),
w
h
ere
λ
is th
e wav
e
leng
t
h
in
free
sp
ace. Sin
ce t
h
is typ
e
of
hol
e
-
ar
ray
Ph
C
s
sl
ab fav
o
r
ph
ot
o
n
i
c
ba
nd
gap (PB
G
)
main
ly fo
r TE po
larizatio
n, we fo
cus on
th
e TE-like
p
o
l
arizatio
n
i
n
th
is work. Th
is cav
ity stru
ctu
r
e
h
a
s a cen
t
ral air ho
le
with
rad
i
u
s
R
0
, a
n
d f
o
ur
pe
ri
o
d
s
of ai
r
hol
es
wi
t
h
dec
r
easi
ng
ra
di
i
t
o
war
d
s t
h
e o
u
t
s
i
d
e
di
rect
i
o
n wi
t
h
ra
di
us
R
1
, R
2
, R
3
, and R
4
re
spectively. T
h
e
radii
of t
h
e air holes
R
0
~ R
4
equal
t
o
0.
3
8
a
, 0.372
a
, 0.
36
0
a
, 0.
35
4
a
and
0.343
a
[8]. T
o
inc
r
eas
e the transm
ission
po
we
r o
f
po
rt
B
we ca
n sha
p
e t
h
e cavi
t
y
as
pse
u
d
o
-ci
r
cul
a
r.
As s
h
o
w
n i
n
Fi
g.
1, t
h
e ai
r
hol
es
wi
t
h
radi
use R
2
o
f
th
e cav
ity are sh
ifted toward
s th
e cen
ter
u
p
to qu
arte
r
of lattice con
s
tan
t
, allowing
t
h
e cav
ity to
b
e
sh
ap
ed
like a circle.
The spect
rum
of t
h
e
po
wer t
r
ansm
i
ssi
on i
s
obt
ai
ne
d wi
t
h
fi
ni
t
e
di
ffe
ren
ce t
i
m
e
dom
ain (F
DT
D
)
m
e
t
hod.
FD
T
D
i
s
a t
i
m
e dom
ai
n sim
u
l
a
t
i
on m
e
t
hod f
o
r s
o
l
v
i
n
g M
a
xwe
l
l
’
s eq
uat
i
ons
i
n
ar
bi
t
r
ary
m
a
teri
al
s
and
ge
om
et
ri
cs [1
1]
. B
e
re
n
g
e
r’s
per
f
ect
l
y
m
a
t
c
hed l
a
y
e
rs
(PML) a
r
e located around the whole struc
t
ure as
ab
so
rb
ing
b
oun
d
a
ry
co
nd
ition
[12
]
.
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
AD
F
Fig. 2(a
)
sketc
h
es
the band diag
ram
of t
h
e st
ruct
u
r
e wi
t
h
out
a
n
y
de
fect
s.
When t
h
e line de
fect 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
odes are reg
u
l
a
t
e
d by
co
nt
r
o
l
l
i
ng t
h
e
defe
ct
si
ze and sha
p
e. I
n
ge
ne
ral
,
a cavi
t
y
i
s
po
si
t
i
oned
bet
w
e
e
n t
w
o
optical waveguides provides a
n
ideal
basic struct
ure for
ADF such t
h
at po
wer in
o
n
e
wav
e
gu
id
e is transferred
in
to
th
e
o
t
h
e
r th
ro
ugh
th
e
reson
a
n
ce
of th
e cav
ity,
wh
i
c
h
is u
s
ed
t
o
ad
d
or rem
o
ve a ch
an
n
e
l
fro
m
th
e
m
u
l
tip
lex
e
d
i
n
p
u
t/ou
t
pu
t si
g
n
als.
A Ga
ussi
an p
u
l
se i
nput
si
g
n
al
i
s
l
a
unched i
n
t
o
t
h
e i
n
p
u
t
po
rt
wi
t
h
l
a
bl
e ‘I
’ and i
t
s
out
p
u
t
i
s
det
ect
ed
at
t
h
e port
s
‘
A
’,
‘B
’ an
d ‘
C
’ usi
n
g p
o
we
r
m
oni
t
o
r
.
The
norm
a
l
i
zed t
r
ansm
i
ssi
on sp
ect
rum
i
s
obt
ai
ned by
t
a
ki
ng
Fast
Fo
uri
e
r t
r
a
n
s
f
o
r
m
(FFT) o
f
t
h
e fi
el
ds
that are calculated
by FDT
D
m
e
thod. T
h
e normalized
t
r
ansm
i
ssi
on s
p
ect
ra
fo
r t
h
ree
out
put
p
o
rt
s
(
A
, B
a
nd C
)
i
n
t
h
e A
D
F a
r
e
d
i
spl
a
y
e
d i
n
Fi
g
.
3 as
bl
ue,
gre
e
n an
d
red lines
, res
p
ectively. It can be see
n
that
the spect
ral selectiv
ity
is si
g
n
i
fican
tly i
m
p
r
ov
ed, 90
% dropp
ing
effi
ci
ency
ca
n be obt
ai
ne
d
at
t
h
e
res
o
nant
w
a
vel
e
n
g
t
h
o
f
1
5
6
0
nm
. Th
e
q
u
ality facto
r
(
Q
) o
f
dr
opp
ing
peak
i
s
19
5.
S
u
ch
Q
a
n
d dropping efficiency val
u
e
s
are e
n
ough for
optical comm
unication applications. It c
a
n
be
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
AA
S I
S
SN
:
225
2-8
8
1
4
Pho
t
on
ic Crysta
l S
l
a
b
Ad
d-Dro
p
Filter (Mo
h
a
mma
d Reza
Ra
khshan
i)
13
5
seen t
h
at
hi
g
h
po
we
r t
r
a
n
sf
er
fr
om
t
h
e i
n
pu
t
t
o
t
h
e
d
r
op
p
o
rt
t
h
r
o
ug
h t
h
e
res
ona
nt
ca
vi
t
y
i
s
p
o
ssi
bl
e
i
n
o
u
r
ADF.
On
th
e oth
e
r
wo
rd
s, th
e po
wer i
n
th
e in
pu
t
wav
e
gu
ide is ex
t
r
acted
by u
s
ing
reso
n
a
n
t
tun
n
e
lling
pro
c
ess
an
d coup
led
i
n
to
po
r
t
B.
Th
e
co
up
led m
o
d
e
in
th
e
reson
a
n
t
cav
ity ro
tates
in
th
e co
un
ter-clo
ckwise d
i
rectio
n
wi
t
h
t
h
e
p
r
opa
gat
i
n
g
wa
ve
gui
de m
ode,
w
h
i
c
h l
ead
s t
o
t
h
e
f
o
r
w
ar
d
d
r
o
p
p
i
n
g
.
(a)
(b
)
Fi
gu
re
2.
B
a
n
d
di
ag
ram
of st
r
u
ct
u
r
e,
(a)
be
fo
re a
n
d
(
b
)
A
f
t
e
r i
n
t
r
o
duci
n
g
l
i
n
e
defect
Fi
gu
re
3.
N
o
r
m
al
i
zed op
tical powe
r tra
n
sm
ission cha
r
acteristic of
ADF
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
252
-88
14
I
J
AA
S
V
o
l. 2, No
.
3
,
Sep
t
emb
e
r :
1
3
3
–
136
13
6
In c
o
m
p
ared
wi
t
h
ot
her
wo
rk
, t
h
e de
si
g
n
of t
h
e
A
D
F
prese
n
t
e
d i
n
t
h
i
s
pa
per see
m
s t
o
be m
o
re
appropriate for actual fabr
icatio
n
an
d app
licatio
n
.
Th
e
prop
o
s
ed
st
ru
ct
u
r
e p
r
ov
id
es a
po
ssib
ility o
f
ADF and
h
a
s t
h
e ab
ility t
o
b
e
h
i
gh
ly su
i
t
ab
le fo
r i
n
tegratio
n
.
3.
CO
NCL
USI
O
N
A sl
ab p
hot
o
n
i
c
cry
s
t
a
l
ADF ha
d bee
n
prese
n
t
e
d an
d i
nvest
i
g
at
e
d
t
h
ro
ug
h F
D
T
D
m
e
t
hod i
n
trian
g
u
l
ar lattice o
f
air
h
o
l
es in
Si
slab
.
We h
a
v
e
sho
w
n
th
at th
ere is fl
ex
ib
ility in
d
e
sig
n
o
f
th
e
ADF wit
h
p
h
o
t
on
ic cryst
a
l. 9
0
% drop
efficien
cy and q
u
a
lity facto
r
o
f
1
9
5
can
be o
b
t
ain
e
d
at
1
560
nm
th
at t
h
is is an
i
m
p
o
r
tan
t
advan
t
ag
e
fo
r
ADF is
propo
sed
th
an
t
h
e
AD
Fs al
read
y
rep
o
rted in
t
h
e literatu
re.
The m
o
s
t
i
m
p
o
r
tan
t
ch
aracteristic o
f
th
i
s
stru
ctu
r
e is it
’s easily
t
o
fa
b
r
i
cat
i
on a
n
d i
n
t
e
grat
i
o
n.
S
u
ch
st
ruct
u
r
e m
a
y
of
fer
pr
om
i
s
i
ng ap
pl
i
cat
i
ons f
o
r
ph
ot
o
n
i
c
i
n
t
e
grat
ed ci
rc
ui
t
s
b
a
s
e
d
on
P
h
C
s
a
n
d
ot
he
r
nan
o
p
h
o
t
o
ni
c st
r
u
ct
u
r
es.
REFERE
NC
ES
[1]
E. Yablonov
itch
.
"Inhibited spontaneous emi
ssion in solid-state p
h
y
sics electronics",
Phys. R
e
v
.
L
e
tt
., V
o
l
.
58. P
p
.
2059-2062, 198
7.
[2]
S. John. "Strong localization of p
honics in ce
rtain
disordered dielectric Super lattices",
Phys. Rev
.
L
e
t.
,
Vol.
58.
Pp.
2486-2489, 198
7.
[3]
J. D. Joannopoulos, et al
.
Pho
t
onic Crystals: Mold
ing the Flow
of
Light
, Princ
e
ton
Universit
y
Press, Princ
e
-ton
, NJ
,
USA, 1995.
[4]
R. D. Mead
e,
et al. "Accurate theoretica
l an
alysis of photonic
band-gap mater
i
als",
Phys
. Re
v
.
B,
Vol. 48. Pp
.
8434-8437, 199
3.
[5]
M. A. Mansouri-
Birjandi,
et
al. "
U
ltrafast low-thr
e
shold al
l-optical switch
implemented b
y
arr
a
y
s
of ring reson
a
tor
s
coupled to a Mach–Zehnd
er interferomete
r arm:
based on 2D pho
tonic cr
y
s
tals",
Applied Opti
cs,
Vol. 47. Pp. 5041-
5050, 2008
.
[6]
J. Zimmermann, et al. "Photonic cr
y
s
ta
l waveg
u
ide direction
a
l couplers as wa
veleng
th selectiv
e optical filters",
Optics Communi
cation
,
Vol. 230
. Pp. 387-392
, 20
04.
[7]
M. Y. Mahm
o
ud, et al
. "Optical channel dr
op
filters based on photonic cr
y
s
t
a
l ring r
e
sonators",
Optics
Communications,
Vol. 285
. Pp. 3
68-372, 2012
.
[8]
Z.
Zhang
and
M. Qiu. "Compact in-p
lane channel drop
filter
design usi
ng
a s
i
ngle cav
ity
with two deg
e
ner
a
te
modes in 2D ph
otonic cr
y
s
tal slabs",
Opt.
Expres
s,
Vol. 13. Pp. 2
596-2604, 2005
.
[9]
I. Park,
et a
l
.
"P
hotonic
cr
y
s
tal
p
o
wer-splitt
er bas
e
d on dir
ect
ional
coupling"
,
Opt.
Ex
pre
ss,
Vol. 12
. Pp. 3599-3604
,
2004.
[10]
M. R. Rakhsha
ni and M. A.
Mansouri-Birjan
di. "Het
erostruct
u
re four ch
anne
l wavel
e
ngth de
m
u
ltiplexe
r usin
g
square photonic
cr
y
s
tals ring
res
onators",
Journa
l of
Electromagnetic
Waves and
Applications
,
Vol. 26
. Pp. 1700
-
1707, 2012
.
[11]
A. Taf
l
ove, and
S. C. H
a
gness.
Computational
Electrodynami
c
s: The
Fini
te-D
ifferen
c
e Time-
D
omain Method
,
Artech House, I
n
c., 2005.
[12]
J. P. Berenger. "
A
perfectly
matched lay
e
r for the absorption of electromagnetic w
a
ves",
J. Computational Ph
ysics
,
vol. 14
. Pp. 185-
200, 1994
.
Evaluation Warning : The document was created with Spire.PDF for Python.