TELKOM
NIKA
, Vol.13, No
.3, Septembe
r 2015, pp. 8
20~827
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v13i3.1733
820
Re
cei
v
ed Ma
rch 1
1
, 2015;
Re
vised J
une
3, 2015; Accepted June 1
5
, 2015
Simple, Easy-use and Low-cost Software for Design of
Single and Cascaded Microring Resonators Using
Semi-numerical Method
Budi Muly
an
ti
1*
, Lilik Has
a
nah
2
, Tommi Hariy
a
di
1
, Arjuni B Pantja
w
a
ti
1
,
Heru Yu
w
o
n
o
3
, P.
Susthita Menon
4
, Sahbudin Sha
a
ri
4
1
Departme
n
t of Electrical En
gi
neer
ing E
ducat
ion
2
Departme
n
t of Ph
y
s
ics E
duc
ation, Un
iv
ersit
a
s Pend
idik
an
Indon
esi
a
(UPI),
Jala
n Dr. Setia
bud
hi 2
07, Ban
dun
g 40
154, In
don
esia, T
e
lp/fax: 0
22 2
013
1
63/02
2 20
11
57
6
3
Arsari Group, Jala
n Jen
d
. Sudirman, Ka
v 1
0
-
11, Jakarta Se
latan, Ind
ones
i
a
4
Institute of Microen
gin
eeri
ng
and
N
a
n
oel
ectronics (IMEN), Univers
i
ti Keb
a
ngsa
an Mal
a
ys
ia (UKM),
436
00 UKM Ba
ngi, Sel
a
n
gor, Mala
ysi
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: b_mul
ya
nti@
ya
ho
o.com
A
b
st
r
a
ct
Devel
o
p
m
ent o
f
a simpl
e
, eas
y and
low
-
cost softw
are for desig
nin
g
of w
a
vegu
ide-c
o
u
p
le
d sin
g
l
e
and casc
ad
ed
micror
ing r
e
s
onator (MR
Rs) using se
mi
-n
umerica
l
calc
u
l
atio
n bas
ed o
n
transfer matrix
m
e
th
od (TMM), is presented i
n
this pap
er. The softw
are uses a devic
e mode
l w
h
ich is e
m
b
e
d
ded
on t
h
e
hig
h
i
n
d
e
x c
o
ntrast (HIC) st
ructure
of sil
i
c
on-o
n
-ins
ulat
or
(SOI) w
i
th mono
moda
l c
a
vi
ty for T
E
-mod
e
pol
ari
z
a
t
i
ons, o
perati
ng
arou
n
d
15
50
n
m
o
p
tical w
a
ve
le
ngt
h. T
he
ma
in
ai
m
of the softw
are is to
esti
mate
the microri
ng r
e
son
a
tor p
e
rfo
r
ma
nce
para
m
eters, such as
free spectra
l
ra
nge (F
SR) a
n
d
qua
lity factor (
Q
-
factor). T
he so
ftw
are is very
simple
a
nd
ea
sy to use.
W
i
t
h
a sta
n
d
a
rd
l
aptop
co
mp
ute
r
, it only
takes
few
secon
d
s to o
b
tain tra
n
s
m
is
sion r
e
spo
n
se
, F
S
R and Q
-
factor of sin
g
l
e MRR
for v
a
rie
d
w
a
veg
u
i
des
separ
ation d
i
stance a
nd rin
g
radi
us. T
he results w
e
re
then verifie
d
usin
g simulati
on
meth
od bas
ed on fi
ni
t
e
integr
ation tec
hni
que
usin
g 3
D
electro
m
ag
n
e
tic si
mu
l
a
tor,
w
h
ich ne
ed a
hig
h
me
mory
and
process
o
r
of
computer
and
take days to
e
x
ecute the s
i
mulati
on.
W
e
fo
und
only s
m
all
discrep
ancy,
w
h
ich in
avera
ges
are ab
out 4.25
% and 1
0
.80
%
for F
S
R and Q-factor, respec
tively. In gene
ral, the results obtai
ne
d from thi
s
softw
are are closer to 3D el
ec
troma
g
n
e
tic si
mu
lati
on resu
lts.
Ke
y
w
ords
: mi
croring, se
mi-n
umerica
l
meth
od, matrix
tran
sfer, free spectral ran
ge, qu
ali
t
y factor
Copy
right
©
2015 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
Microrin
g resonators
(M
RRs) i
s
a ve
ry
important
device th
at i
s
bei
ng d
e
velope
d
nowaday
s be
cau
s
e
of thei
r ability to suppo
rt the
cr
eation of hi
g
h
den
sity integrate
d
circu
i
ts.
Variou
s ap
pli
c
ation
s
of M
R
Rs have
be
en develo
ped
, such
as
wa
velength filter [1], multiplexing
[2], sen
s
ors [
3
], modulatio
n wave, [4]
a
nd bio
m
edi
ca
l [5] appli
c
ati
ons
.
F
o
r se
n
s
ing appli
c
ati
on,
there
are ma
ny types
of sensor
th
at ha
ve bee
n d
e
ve
loped
such a
s
fo
r
Wirel
e
ss Sensor Network
(WS
N) a
ppli
c
ation [6, 7].
MRRs h
a
s
se
veral advanta
ges that of in
terest to ma
n
y
rese
arche
r
s in
this field, that are (1) its
smaller a
nd co
mpact
size, (2) can be int
egrate
d
with
other
comp
o
nents
(light so
urce,
detecto
r, cou
p
ler, and m
a
n
y
others), and
(3) very ea
sy
to mass p
r
od
uce
d
[8].
For de
signi
n
g
single a
n
d
casca
ded
MRRs a
s
well as othe
r MRRs config
uration
s
,
several num
e
r
ical m
e
thod
s have been
develop
ed, such a
s
tra
n
sf
er matrix met
hod (T
MM) [
9
],
finite-differenc
e time-domain (FDT
D) [1
0], confo
r
mal
tran
sform
a
tion metho
d
[1
1] or mo
delin
g in
terms of se
mi-an
a
lytic couple
d
-m
ode
theor
y (CMT) [12-15], with each
method ha
s its
advantag
es
a
nd di
sadva
n
tage
s. The
CMT in
spa
c
e
and time
dom
ains i
s
im
ple
m
ented
usual
ly in
two
spa
c
e
di
mensi
o
n
s
(2
D)
and
ra
rel
y
in 3D [16]. The
FDT
D
method i
s
th
e mo
st po
pu
lar
simulatio
n
to
ol for that p
u
rpo
s
e, b
u
t due to
its i
n
here
n
t we
aknesse
s (stai
r
ca
sing
error and
nume
r
ical di
spersion
), oth
e
r
solutio
n
s
are l
o
o
k
ed
fo
r. The
3
D
F
D
TD an
alysi
s
of an
add
-d
rop
filter co
nfigu
r
ation, de
scrib
ed in
the
stu
d
y of
Fujii
et al. [17], illu
strates high
requireme
nts
in
terms of com
puter resources.
On
the
othe
r hand, TMM h
a
s sh
own
results
t
hat are quite
reliabl
e for
mo
delin
g optical
micro-re
son
a
tors an
d ju
st take
s mi
nut
es in
t
he
ca
lculatio
n [18]
. TMM is a
semi
-num
eri
c
al
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Sim
p
le, Easy-use and L
o
w-co
st Softwa
r
e for De
sign
of Single and
Ca
scade
d… (Budi Mulyanti
)
821
method that
has
bee
n wid
e
ly kno
w
n fo
r solving
pro
b
l
e
ms of M
a
th
ematics an
d
Physics, nam
ely
dividing the total system i
n
to
N su
b-
sy
st
em
s,
in wh
ich a s
ub-
sy
st
em only
int
e
ra
ct
s wit
h
it
s
neigh
bors. In the early 1970
s, analytical me
tho
d
wa
s develop
ed by Yariv
kno
w
n a
s
CMT
(co
uple
d
mo
de theo
ry) u
s
e
s
a mat
r
ix analytic e
n
e
r
gy-cou
pling
[19]. Based
on this
wo
rk,
it is
possibl
e now to formulate nume
r
ical sol
u
tions in
ord
e
r to simulat
e
MRRs prop
erties
with much
less comp
uting co
st
co
mpared
to FDT
D
si
mul
a
tions de
scri
bed a
bove
with
comp
arabl
e
ac
cur
a
cy
.
In this study, we propo
se
d a simple, ea
sy-
use a
nd lo
w co
st softwa
r
e develo
ped
usin
g a
semi
-num
eri
c
al method, n
a
mely the tra
n
sfer m
a
trix method (TM
M
) to estimat
e
the values of
MRRs’ prope
rties, namely FSR
a
nd
th
e Q-fa
ctor.
T
h
e
re
sults a
r
e th
en verifie
d
by
a F
D
T
D
’s m
o
st
popul
ar co
m
m
ercial software
CST
Microwave
Studio
,
usin
g 3
D
el
ectro
m
ag
neti
c
simulato
r
b
a
se
d
on finite integration te
chn
i
que, whi
c
h
need
s a
high
memory an
d pro
c
e
s
sor
of compute
r
and
take
s days to
execute the
simulatio
n
.
2. Rese
arch
Metho
d
2.1.
Dev
i
ce Model
MRRs d
e
vice
model u
s
e
d
in this
study, wa
s ba
sed
o
n
SOI stru
ctu
r
e with
high
refractive
index contra
st and op
erati
ng at
15
50 n
m
of wavele
ngth a
s
sch
e
m
atically sho
w
n in Fi
gu
re
1
whi
c
h co
mpri
se
s of a ring waveg
u
ide cl
osely co
uple
d
to double straight bus
wa
veguide
s (Fig
ure
1(a
)) an
d th
e cross secti
on of the waveguid
e
structure is
sh
own in Fig
u
re 1(b
)
. The
bus
waveg
u
ide
s
serve a
s
evan
escent li
ght i
nput a
nd
out
put coupl
ers,
while
the
ring
wave
guide
a
c
ts
as th
e wavel
ength
sele
cti
v
e eleme
n
t.
R
d
epict
s the
ring
ra
diu
s
,
gap
i
s
the
se
paratio
n di
sta
n
ce
betwe
en
strai
ght and
rin
g
waveg
u
ide,
W
i
s
the
wav
eguid
e
wi
dth
and
H
i
s
the
total waveg
u
i
de
height. Th
e f
u
lly etch
ed
waveguid
e
structure i
s
con
s
ide
r
ed
throu
ghout thi
s
st
udy. The
cro
s
s-
se
ction of the
MRRs d
e
vice is 0.30
μ
m x
0.55
μ
m, on
top of 1
μ
m-t
h
ick bu
ried
o
x
ide (BOX) l
a
yer
.
The
cro
s
s-se
ction of
su
ch
waveg
u
ide
s
wa
s
cho
s
en
to ensure si
ngle-mod
e
propag
ation n
e
a
r
1550
nm telecommuni
catio
n
s wavelen
g
ths [20].
Figure 1.
(a)
Lay out and (b) cro
ss
se
ction of singl
e
MRR
with do
uble straight
waveg
u
ide
s
2.2.
Calcu
t
ion of
MRR c
h
ara
c
teristics usin
g CMT and T
MM
Effec
t
ive refrac
trive index,
, can be d
e
ri
ved usin
g [19
]
:
(
1
)
Whe
r
e
β
is p
r
opa
gation
co
nstant. By kn
owin
g
β
and
the operatin
g wavele
ngth
,
λ
, the value of
can be o
b
tai
ned. The
cou
p
ling coeffien
t can be calculated u
s
ing
Figure 2.
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 : 820 – 827
822
Figure 2. Cou
p
ling effect b
e
twee
n the st
raight waveg
u
ide an
d the ring with ra
diu
s
R
In Figure 2, it can be
see
n
that the cou
p
ling len
g
th,
, betwee
n
the
straight a
nd
ring
waveg
u
ide
s
, i
n
which the
in
put si
gnal
of
straig
ht
wavel
ength i
s
co
up
led
with the
ri
ng
wavele
ngt
h.
The amo
unt
of coupli
ng is
determi
ned b
y
the magnitu
de of the co
u
p
ling coefficie
n
t,
k
. Therefo
r
e,
the cou
p
ling l
ength,
, can b
e
cal
c
ulate
d
usin
g [21]:
(2)
Whe
r
e
λ
i
s
operatin
g wav
e
length,
and
are effective refra
c
tive ind
e
x for even and odd
wavele
ngth, resp
ectively. And by using:
(3)
The value of cou
p
ling
coef
ficient,
, can be cal
c
ul
ated
.
Figure 3. MRRs
config
urati
on and re
p
r
e
s
ente
d
co
upli
ng matrix P and Q
MRRs
config
uration
ca
n b
e
forme
d
by
one o
r
two
st
raight
waveg
u
ide
s
and
on
e or m
o
re
than one ri
ng
waveguid
e
s.
The input si
gnal ente
r
s o
ne end of a straig
ht wave
guide an
d go
es
forth at the
ot
her
end.
Du
ri
ng its travel i
n
a
st
rai
ght waveguid
e
,
mo
st
si
gnal
will be cou
p
led a
nd
towards the
ring
wavegui
d
e
. If there i
s
more than
o
ne ri
ng, the
sign
al will
be
co
upled
ag
a
i
n
towards the n
e
xt ring, or it coul
d be cou
p
led to
ward
s
anothe
r strai
ght waveg
u
id
e. In Figure 3
,
P
is a
s
sumed t
o
be a
cou
p
l
i
ng matrix be
tween th
e straight and
rin
g
waveg
u
ide
s
or
a coupli
n
g
matrix bet
we
en the
two
ri
ng
waveg
u
id
es,
while
Q i
s
a
cou
p
ling
matrix of
sig
nal p
r
op
agati
o
n
along
th
e wa
veguide ring, then
the
tran
sfer equ
at
ion
for MRR
ca
n
be exp
r
e
s
sed
in the follo
wi
ng
equatio
n [19]:
′
∗
∗
′
,
|
|
|
|
1
(
4
)
Whe
r
e
κ
is a
norm
a
lized couplin
g co
efficient an
d t is si
gnal tra
n
smitted in the ring
waveg
u
i
de.
Furthe
rmo
r
e,
the cou
p
ling
matrix can b
e
obtained u
s
i
ng [19]:
′
′
,
1
1
∗
(
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Sim
p
le, Easy-use and L
o
w-co
st Softwa
r
e for De
sign
of Single and
Ca
scade
d… (Budi Mulyanti
)
823
And pro
pag
ation matrix Q is [19,20]:
′
′
,
0
0
(
6
)
Whe
r
e R i
s
ri
ng radi
us, an
d
β
is pro
pag
ation co
nsta
n
t
mentioned i
n
Equation (3
).
Since FSR i
s
defined a
s
a
distan
ce of two
adja
c
ent pe
ak inten
s
ity [19], therefore:
2
⁄
(
7
)
Whe
r
e L i
s
a
circumfe
ren
c
e of micro
r
in
g circle a
nd
c
is spe
ed of li
ght in a medi
um that can
be
expre
s
sed a
s
:
(
8
)
Whe
r
e
is sp
eed of light in
the vacuum.
Based o
n
Fig
u
re 4 an
d by usin
g bou
nda
ry conditio
n
o
f
[19]:
∝
(
9
)
Whe
r
e
α
i
s
a
b
so
rption
co
efficient pe
r
unit length,
a
c
cordi
ngly th
e tran
smitan
ce in
the
straight
waveg
u
ide is
[19]:
|
|
|
|
|
|
|
|
(
1
0
)
Figure 4. Ligh
t wave tran
smitted in the straig
ht wave
guide
And the total power in the
microrin
g is [19]:
|
|
α
|
|
|
|
|
|
(
1
1
)
If
⁄
, then fro
m
equatio
n (10), full widt
h at half ma
ximum (FWHM)
can
be
obtaine
d from
:
∆
≅
|
|
;
|
|
1
(
1
2
)
And the Q-fa
ctor
can be e
x
presse
d as:
∆
|
|
|
|
(
1
3
)
3. Results a
nd Discu
ssi
on
The software develop
ed in this study ca
n be
used to study device perfo
rman
ce
su
ch a
s
freque
ncy
re
spo
n
se, FSR, the Q-fa
cto
r
, finesse, an
d FWHM fo
r singl
e a
s
well as
ca
sca
ded
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 : 820 – 827
824
MRR
devices, was
re
sulte
d
in this
stud
y. The GUI
p
age of the
sof
t
ware
ca
n be
see
n
in Fig
u
re 5.
All of the de
sign pa
ram
e
te
rs,
su
ch
as
ri
ng radiu
s
, ga
p, width
of waveguid
e
, ref
r
active i
ndex
es
can
be e
a
sil
y
incorpo
r
ate
d
into the G
U
I pre
c
e
ded
by cho
o
si
ng
the MRR co
nfiguratio
n. The
results
of the
simul
a
tion, n
a
mely fre
que
ncy re
spon
se
, FSR, the Q
-
facto
r
, fine
sse, and
FWHM
will be soon
shown in the GUI pag
e.
Figure 5. The
GUI page of
softwa
r
e resu
lted in this stu
d
y.
3.1. Single MRR
The sim
u
latio
n
s were d
one
by varying ring
radi
us a
n
d
wavegui
de s
eparation di
stance of
4-12 µm an
d 100-150 nm,
respe
c
tively at incident
wav
e
length of 1.5
5
µm. The other pa
ram
e
te
rs
are
ke
pt co
n
s
tant, incl
udi
ng SiO
2
an
d
Si refra
c
tive
index of 1.5
277 a
nd 3.4
7
77, re
sp
ectiv
e
ly,
SiO
2
and Si
height of 1.0 and 0.55 µm,
resp
ective
ly and the wave
guide wi
dth o
f
0.30 µm. T
he
results were
then
verifie
d
by
re
sults
of sim
u
lation
usi
n
g
sim
u
l
a
tion m
e
thod
ba
sed
o
n
fi
nite
integratio
n te
chni
que
usi
n
g 3D ele
c
tro
m
agneti
c
sim
u
lator,
whi
c
h
need
s
a hig
h
memo
ry a
nd
pro
c
e
s
sor
of comp
uter
an
d take
s d
a
ys to execute
the si
mulation
.
The fre
que
ncy pe
rforma
nce
for singl
e micro
r
in
g for dif
f
erent value
s
of ring radi
u
s
and 1
00 n
m
of waveg
u
ide sepa
rati
on
distan
ce, is
shown in Figu
re 6.
Figure 6. Single MRR tran
smissio
n
re
sp
one of the drop port for dif
f
erent value
s
of ring ra
diu
s
, R
= 6 and 1
0
µm at wavegui
de se
paration
distan
ce, wa
veguide
width
,
and waveg
u
ide heig
h
t are
100nm, 0.30
µm and 0.55
µm, resp
ectiv
e
ly
Figure 6
sho
w
s pe
aks
of tran
smi
ssi
on i
ndicat
ed po
wer
in
resona
n
c
e co
ndition. It
can be
see
n
clea
rly the p
o
si
sitio
n
of two a
d
j
a
ce
nt pe
aks that can
be
tra
c
ed
at di
fferent valu
e
of
wavele
ngth
d
epen
ds on
ri
ng
radiu
s
. Su
ppo
se fo
r
6 µ
m
of
ring
ra
di
us
and
10
0
n
m
of
sep
a
ration
Evaluation Warning : The document was created with Spire.PDF for Python.
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Sim
p
le, Easy-use and L
o
w-co
st Softwa
r
e for De
si
gn
of Single and
Ca
scade
d
… (Budi Mulyanti
)
825
distan
ce, resonant pe
aks
occur
at
1.55
20 and
1.566
3 of wavele
n
g
th, therefo
r
e
the FSR valu
e of
those p
a
ra
me
ters i
s
14.29n
m.
To comp
are
our
TMM
si
mulation
re
sults, we
cal
c
ulate the
fre
quen
cy resp
onse u
s
in
g
Finite Integration Te
chni
que (FIT) u
s
ing 3D
ele
c
troma
gneti
c
simulator
with
the sam
e
ring
para
m
eters and config
urations. We use
co
mme
rc
ial softwa
r
e
from Com
p
uter
Simul
a
tion
Tech
nolo
g
y AG named
CST Studio Suite to perform
3D FIT sim
u
lation. From
simulatio
n
using
CST Studio
Suite, we o
b
t
ained FS
R
value at 1
5
.4
0nm for rin
g
radi
us
6 µm
and
100
nm
of
sep
a
ratio
n
di
stan
ce. We can se
e that the sm
aller
th
e radi
us of th
e ring, the g
r
eater the di
st
ance
betwe
en two
adja
c
ent re
so
nant pea
ks.
From
our T
MM sim
u
lati
on an
d CST
simul
a
tion,
the high
est
FSR obtai
n
e
d
at the
smalle
st rin
g
radiu
s
, therefore the valu
e
of FSR
is in
versely p
r
op
o
r
tional to the
effective leng
th
microrin
g, L
(= 2
π
R). On
the ave
r
ag
e, the differen
c
e
between
se
mi-num
eri
c
al
simulatio
n
s with
and
CST
si
mulation
s i
s
4.25%, a
s
shown in
Fi
g
u
re
7. We
may
con
c
lud
e
that only small
discre
pan
cy betwe
en both
simulation
s.
Figure 7. FRS values of Single MRR for different valus of ring radiu
s
3.2. Double
and Triple Serially
Casca
ded MRR
The analy
s
is
wa
s also don
e with dou
ble
and triple se
rially ca
scad
ed microri
ng
for the
same
value
s
of sep
a
ration
distan
ce
an
d rin
g
r
adiu
s
,
i.e: 0.1 µm
and 6
µm, re
spe
c
tively. The
device
perfo
rmance of the
doubl
e an
d triple
ca
scade
d microri
n
g
s
are
simul
a
ted
and
comp
ared
to a si
ngle
m
i
cro
r
in
g an
d t
he results
are interprete
d
in Figu
re
8.
Two
re
son
a
n
t
pea
ks
occu
r at
1.5520
and
1
.
5663 givin
g
FSR eq
ual to
14.5 nm
reg
a
rd
le
ss the n
u
mbe
r
of mi
crori
n
g
s
orde
r. To
verify the results
,
we c
onfirmed the sim
u
lations results with CST si
mulation.
Figure 8. The
FSR values f
o
r differe
nt for the si
ngl
e, double a
nd trip
le ca
scade
d microrin
gs at
ring radiu
s
an
d sep
a
ratio
n
distan
ce of 6
µm and 100 n
m
respe
c
tively.
Furthe
rmo
r
e,
to study the perfo
rman
ce
of mi
cro
r
in
g device, the Q
-
facto
r
wa
s e
s
timate
d
usin
g
semi
-n
umeri
c
al
sim
u
lation. Fig
u
re 9
sh
ows th
e plot
s of
Q-f
a
ctor to
se
pa
ration
dista
n
ce i
n
the rang
e of 0.1
μ
m and 0.15
μ
m at con
s
tant ring
radi
us of 6
μ
m.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
9
30
TELKOM
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Vol. 13, No. 3, September 20
15 : 820 – 827
826
Figure 9. The
plots of Q-fa
ctor to s
epa
ra
tion distan
ce i
n
the rang
e o
f
0.1
μ
m and 0.15
μ
m at
con
s
tant rin
g
radiu
s
of 6
μ
m of semi-nu
m
eri
c
al an
d CST sim
u
lations.
It is shown that greate
r
Q
-
facto
r
occu
rs at
la
r
g
er
sep
a
r
a
tion
d
i
s
t
an
c
e
. T
h
e
ob
se
r
v
a
b
le
Q-fa
ctor diffe
ren
c
e
in th
e
se
pa
ration
distan
ce
of
0.1
μ
m and
0.15
μ
m i
s
375
a
n
d
6
10,
respe
c
tively. Clea
rly, the gap si
ze h
a
s a
signi
fi
cant effect o
n
the Q-fa
ct
or, yet the FSR
unaffecte
d
. Despite th
e lo
w lo
ss
pro
d
u
c
ed
at the na
rro
w g
ap, it is difficult to f
abri
c
ate a
n
d
fine
etchin
g i
s
re
quire
d. Fu
rth
e
rmo
r
e,
we
found
a mi
smatch
in th
e Q
-
facto
r
v
a
lue
s
for bo
th
simulatio
n
s.
The la
rge
s
t di
fference was
found for th
e gap
size
of 1
2
0 nm
with 2
0
.5% differen
c
e.
This ag
ain
du
e to
different
in effective
re
fracti
ve i
ndex
value
s
wh
ere the
r
e i
s
no
straig
htforward
way of
cal
c
ulating the
effective ref
r
active in
d
e
x, espe
cially i
n
be
nd
wav
eguid
e. The
r
eby,
approximatio
ns a
r
e
con
s
i
dere
d
in the
MRR
model
i
n
g. Ho
weve
r, both re
sult
s experie
nced
the
same
tren
d,
whi
c
h the
Q-f
a
ctor rai
s
e
d
as the
sepa
ration
ga
ps wi
den
s.
The ob
serva
b
le Q-fa
ctor
differen
c
e a
c
ross the sepa
ration gap of
0.12
μ
m is 1
0
, which cont
ribute to 2.6
%
in percent
age,
while the ave
r
age of deviat
i
on is 10.8
0
%, which
can b
e
con
s
id
ere
d
relatively low.
4. Conclusio
n
The sim
p
le,
easy-use an
d low-cost so
ftware for
de
sign of
single
and serial
cascad
ed
microrin
g re
sonators
(M
RRs) usin
g
th
e
semi-num
e
r
ical
meth
od
ha
s b
een
d
e
velope
d in
this
study. Th
e
so
ftware
can
be
used to
e
s
ti
mate th
e
M
R
Rs pe
rforman
c
e
pa
ramete
rs, such
as F
S
R
and Q
-
fa
ctor in only fe
w se
con
d
s u
s
ing a
stan
da
rd la
ptop
co
mputer. T
h
e
re
sults
of the
simulatio
n
were th
en ve
ri
fied u
s
ing
si
mulation
met
hod
ba
sed
o
n
finite inte
g
r
ation te
ch
ni
que
usin
g 3D el
e
c
trom
agn
etic simulato
r. In gene
ral,
we found only
small di
scre
pan
cy, which
in
averag
es a
r
e
about 4.25%
and 10.8
0
% for
FSR a
nd
Q-fa
ctor, re
sp
ectively.
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TELKOM
NIKA
ISSN:
1693-6
930
Sim
p
le, Easy-use and L
o
w-co
st Softwa
r
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sign
of Single and
Ca
scade
d… (Budi Mulyanti
)
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