TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 10, Octobe
r 20
14, pp. 7209
~ 721
3
DOI: 10.115
9
1
/telkomni
ka.
v
12i8.637
6
7209
Re
cei
v
ed Ap
ril 27, 2014; Revi
sed
Jun
e
7, 2014; Acce
pted Jul
y
2, 2
014
Design and Analysis G
i
res-Tournois-Interferometer
Mirrors
Amer B.
Dhey
ab*, Gaillan H. Abdulla
h,
Haider Y. Hammod, Ali
Hassan
Ministr
y
of scie
n
ce an
d techn
o
lo
g
y
/
Director
a
te
of material R
e
searc
h
/Cent
e
r
of Laser Res
earch,
Univers
i
t
y
of
T
e
chn
o
lo
g
y
,
Iraq
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: amer.alj
obur
i
@
yah
oo.com
A
b
st
r
a
ct
W
e
report the
imp
l
e
m
e
n
tatio
n
and o
per
ati
on of GT
I
w
i
th hig
h
-reflectiv
i
ty negativ
e-di
spersi
o
n
diel
ectric mirro
rs for use in tunab
le ultrafast
laser syste
m
s. The mirr
or structure is divid
e
d
into tw
o distinct
regi
ons:
a
n
u
nder
lyin
g hig
h
-reflectivity die
l
ectric
quarter-
w
a
velen
g
th st
ack a
nd
an
o
v
erlyin
g
ne
gati
v
e-
disp
ersio
n
se
ction co
nsisti
n
g
of o
n
ly
a
few
layers
and f
o
rmin
g
simple
multi
p
l
e
Gires–T
o
ur
nois
interfero
m
eters
.
T
he ex
a
m
pl
e
that
w
e
pr
es
ent w
a
s d
e
si
g
ned
tw
o structures w
i
th
diffe
rent sp
acers f
o
r
oper
ation
fro
m
670-
86
0 n
m
a
nd6
80-8
4
0
n
m
has a
ne
a
r-co
n
stant gr
oup-
d
e
lay
disp
ersi
on
of ±3
000fs
2
an
d a
peak
reflectiv
i
ty great
er tha
n
98%. W
e
ca
n
usin
ga
nd
ap
p
licatio
n
of thes
e
mirrors
in
a
mo
de-l
o
cke
d T
i
:
Sapp
hire l
a
ser.
Ke
y
w
ords
:
Gires-T
ourn
o
is
,
F
e
mtos
eco
n
d
,
di
spersi
on co
mp
ensati
o
n
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Gire
s-Tou
r
noi
s inte
rferom
eters a
r
e
g
enerally
u
s
e
d
to
com
p
e
n
sate
hig
h
ly chi
r
pe
d
pico
se
co
nd
s or femtoseco
nd pul
se
s the way they
exist, espe
ciall
y
in narro
w
gain ba
nd-wi
dth
lase
rs li
ke Nd
:YAG. Large amount
s of intracavity
neg
ative GDD a
r
e essential in
ultra-sh
ort pul
se
lase
rs,
in
ord
e
r to
compe
n
s
ate fo
r th
e g
a
in b
and
widt
h an
d
self-ph
a
se
mo
dulati
on
(SPM)
du
e to
nonlin
ear ele
m
ents [2]. In
comp
ari
s
o
n
t
o
a
pri
s
m
pai
r se
que
nce, th
e GTI
is ea
sil
y
three
o
r
de
rs of
magnitud
e
more di
spe
r
siv
e
but also li
near ov
e
r
a much
smalle
r band
width.
The amount
of
available g
r
o
up delay dispersion
can
be furthe
r incre
a
sed by r
eactin
g
the intracavity pulse
several times of the surfa
c
e of the GTI, becau
se
the i
n
trodu
ce
d dispersion i
s
pro
portion
al to the
numbe
r of bo
unces from the su
rfa
c
e. Several
schem
es of GTI ha
ve been p
r
op
ose
d
intro
d
u
c
ing
these l
a
rg
e a
m
ounts
of group d
e
la
y dispersion
(G
DD) [3]. Thi
s
i
s
do
ne by
ch
angin
g
the p
u
lse
angle
of in
ci
den
ce u
pon
the GTI, whi
c
h th
ere
b
y correctly
com
pen
sate
s a
n
a
rrow ban
dwidth
ofintracavity disp
ersion
[4]
.
2
.
Theor
y
A Gires–Tou
r
nois inte
rfero
m
eter is an o
p
tical sta
ndin
g
-wave re
son
a
tor simila
r to
Fabry–
Pérot interferometer, whi
c
h howeve
r
is ope
rated i
n
reflectio
n
and de
sign
e
d
for gene
ra
ting
chromati
c di
spersion. T
he
front mirror i
s
partially
reflective, whe
r
ea
s the b
a
ck mi
rro
r ha
s a
hig
h
reflectivity. If
no lo
sses
occur in the
re
sonator, th
e p
o
we
r reflectiv
i
ty is unity at all wavel
engt
hs,
but the pha
se
of the reflect
ed light is fre
quen
cy-d
epe
ndent du
e to the re
son
ance effect, cau
s
ing
chromati
c di
spersion. T
he
pha
se
cha
n
g
e
of refl
e
c
ted
light an
d the
disp
ersio
n
(i
nclu
ding
gro
u
p
delay di
spe
r
sion
and
hig
her-orde
r
di
spersion
)
cha
nge p
e
ri
odi
cally with o
p
tical frequ
en
cy, if
material di
sp
ersi
on i
s
negl
igible. The
r
e
is no
se
cond
-order dispersion
ex
a
c
tly on-re
son
a
n
c
e
or
anti-resona
nce, and po
sitive or neg
at
ive disp
ersion b
e
t
ween the
s
e
points [7].
A Gires-To
urnois inte
rfero
m
eter con
s
ist
s
of
two paral
lel surfa
c
e
s
, the se
co
nd of whi
c
h is
100 % refle
c
tive as sh
ow i
n
Figure 1. Therefo
r
e,
the
two qua
ntities whi
c
h
cha
r
acteri
ze th
eG
TI
are the refle
c
tion coeffici
ent
r
of the first su
rfa
c
e a
nd the di
stan
ce bet
wee
n
them [6]. Gire
s-
Tournoi
sInterferomete
r (G
TI) is e
s
senti
a
lly a Fab
r
y-Perot res
o
nator with a
100% reflec
tor.
As
with an ide
a
l high-refle
c
tivity mirror, the whol
e re
fle
c
tivity of the device stays 1
0
0
%. In contra
st,
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 10, Octobe
r 2014: 720
9
– 7213
7210
the pha
se del
ay is, as with a Fabry-P
e
rot
,
frequen
cy-d
epen
dent. Th
us the GTI ca
n be used in a
lase
r re
so
nat
or for di
spe
r
si
on com
pen
sa
tion.
Figure 1. Sch
e
matic Setup
of a Gire
s–To
urnoi
sinte
r
ferometer [6]
Therefore, th
e two
qu
antities
whi
c
h
cha
r
acte
ri
ze th
e
GTI are the
reflection
coef
ficient
r
of the first su
rface
and the
distan
ce d b
e
twee
n
them.
The ro
und trip time insid
e
the GTI for an
angle of in
cid
ence
Ɵ
is
then given by [4].
t
1
θ
(
1
)
Whe
r
e:
c
is t
he
spe
ed
of l
i
ght an
d n
th
e ref
r
a
c
tive in
dex of the
m
edium
betwe
en the
mirro
r
s.
If
the pul
se
du
ration i
s
l
ong
er tha
n
t
0
, th
e field
s
of
su
ccessive
rea
c
tion
s of th
e
sam
e
p
u
lse
do
temporally overlap
and the
pulse
envel
ope may be
reshap
ed. Th
is puts
an up
per limit to the
distan
ce
bet
wee
n
the
re
acting
surfa
c
es. But, a
s
t
he di
stan
ce
d be
com
e
s shorte
r, the
G
DD
become
s
sm
aller too, as
can be
seen from the equati
on belo
w
[4].
GDD
2
π
ω
2
π
∅
ω
2
π
t
ω
ω
(
2
)
Whe
r
e,
T
= gro
up del
ay,
=a
ngul
ar frequ
en
cy,
ϕ
= pha
se
,
r
=
reflec
tivity.
In orde
r to obtain co
nsta
n
t
negat
ive GDD ove
r
finite band
width,
∆
>
0, the pha
se has
to be adjuste
d su
ch that the GDD is a
minimum. This
pha
se is a fu
nction of
r,
as se
en in abo
ve
equatio
n. In orde
r to obta
i
n high value
s
of negat
ive
dispe
r
sion a
nd large ba
n
d
width
(
for
sh
ort
pulse duratio
n), one ha
s to increa
se the reflectivi
ty of the intermediate mirror in a controll
ed
manne
r. Th
e
com
m
only u
s
ed
ro
und
tri
p
time
(1) sh
ows n
o
de
pe
nden
cy
with the inte
rmedi
ate
surfa
c
e
refle
c
tivity. We kno
w
, that the hi
gher the
refle
c
tivity, the longer th
e del
ay time within t
he
GTI. Therefo
r
e, as the refl
ectivity increa
se
s, t
he pulse, coming o
u
t of the GTI, g
e
ts stret
c
he
d in
time. Tak
i
ng into acc
o
unt t
he reflec
tivity we deri
ve
an
expre
ssi
on fo
r the d
e
cay time of a p
u
lse
in
a passive re
sonator,
[4, 5]
.
.
1
(
3
)
W
h
er
e
t
0
is gi
ven by
(1). B
y
analyzi
ng
n
u
meri
cally va
riou
s
GTI's we foun
d that
this exp
r
e
ssi
on
gives
a very
good
e
s
timate in th
e
ca
se
of Fo
ur
ie
r transfo
rm limit
ed p
u
lse
widt
h. Amore
u
s
eful
approximatio
n is obtained
by calcul
atin
g the bandwi
d
th
,
∆
GTI
, over which the group del
ay is
linear.
We th
erefo
r
e expa
nd the group
delay as
a f
unctio
n
of freque
ncy ab
o
u
t the points of
maximum GDD. At these p
o
ints the second de
rivati
ve of the grou
p delay is zero and we obt
ain:
T(
ω
)=T
(
ω
)+
ω
ω
∆
ω
ω
ω
∆
ω
(
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
De
sign a
nd Analysi
s
Gire
s-Tournoi
s-Inte
rferom
eter Mi
rro
rs
(Am
e
r B.Dhe
y
ab
)
7211
Linea
rity of th
e group
del
ay is
gua
rante
e
d
a
s
lo
ng
as the third te
rm
in ab
ove e
q
u
a
tion i
s
small
e
r
than the se
co
nd term:
∆
(
5
)
Whe
r
e
we
h
a
ve dropp
ed
in the
den
o
m
inator of
th
e third
term.
Using th
e a
bove
criteri
a
for
linearity we o
b
tain:
∆
∆
.
(
6
)
3. Design an
d Discus
s
io
n
To d
e
sig
n
G
T
I we
take th
ese
pa
ram
e
ters the
refe
rence
wavele
ngth i
s
7
50n
m an
d the
spe
c
tral
rang
e 30
0–10
00n
m. Figure 2
a
nd Fig
u
re
3
shows th
e reflectan
c
e
and
reflectan
c
e
G
DD,
whe
r
e
H a
nd
L are qu
arte
r
wave laye
rs
with indi
ce
s h
i
gh an
d lo
w which
co
rrespo
nd to
HfO
2
an
d
BaF
2
, resp
ect
i
vely, and the refra
c
tive index of subs
trate are Fu
sedS
ilica. The ba
n
d
width of hig
h
reflecta
nce (>98%)a
nd the
reflecta
nce G
DD val
ue i
s
(±300
0). T
abl
e 1
sho
w
s th
e layer struct
ure
for the first de
sign.
Table 1. Laye
r
Structu
r
e of the First Desi
gn
* Materials
Thick
nesses
Index
1 HfO2
98.736
1.8990
2 BaF2
128.205
1.4625
3 HfO2
98.736
1.8990
4 BaF2
128.205
1.4625
5 HfO2
98.736
1.8990
6 BaF2
128.205
1.4625
7 HfO2
98.736
1.8990
8 BaF2
128.205
1.4625
9 HfO2
98.736
1.8990
10 BaF2
128.205
1.4625
11 HfO2
98.736
1.8990
12 BaF2
128.205
1.4625
13 HfO2
98.736
1.8990
14 BaF2
128.205
1.4625
Figure 2. Refl
ection vs. Wa
velength for the
First Desi
gn
Figure 3.
Gro
up Del
a
y Dispersion vs.
Wavele
ngth for the First Desig
n
Then if we ad
d a spa
c
e
r
2
H
and a lo
w reflectan
c
e
stack (HL) to th
e stack form
a
l
as sho
w
n
belo
w
:
Air
/HLHL
H
L
H
LHLHLHL
/
Glas
s…
….
st
ac
k f
o
rmal f
o
r
1
st
design
Air
/HLHL
H
L
H
LHLHLHL
H
LH/
Glas
s…
….
st
ac
k f
o
rm
al f
o
r 2
nd
desi
g
n
670~8
60 n
m
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 10, Octobe
r 2014: 720
9
– 7213
7212
The refle
c
tan
c
e an
d refle
c
tance G
D
D o
f
the stack a
r
e sho
w
in
g in Figure 4, Fi
gure 5.
Table 2 sho
w
s Layer
stru
ct
ure of the second de
sig
n
.
Table 2. Laye
r
Structu
r
e of the Secon
d
Desig
n
* Materials
Thick
nesses
Index
1 HfO2
98.736
1.8990
2 BaF2
128.205
1.4625
3 HfO2
98.736
1.8990
4 BaF2
128.205
1.4625
5 HfO2
98.736
1.8990
6 BaF2
128.205
1.4625
7 HfO2
98.736
1.8990
8 BaF2
128.205
1.4625
9 HfO2
98.736
1.8990
10 BaF2
128.205
1.4625
11 HfO2
98.736
1.8990
12 BaF2
128.205
1.4625
13 HfO2
98.736
1.8990
14 BaF2
128.205
1.4625
15 HfO2
98.736
1.8990
16 BaF2
128.205
1.4625
17 HfO2
98.736
1.8990
The
refle
c
tan
c
e i
s
b
oardin
g
from
225
0n
m to 32
50nm
(650
~900
nm
), but the
refl
ectan
c
e
GDD h
a
s a
h
i
gh n
on-li
nea
r value
in
the
ban
dwi
d
th of
630
~6
45nm.
Finally, if th
e spa
c
er 2
H
in
Figure 4 ch
an
ged to 16
H.
Figure 4. Refl
ection vs. Wa
velength for T
he
S
e
con
d
De
si
gn
Figure 5.
Gro
up Del
a
y Dispersion vs.
Wavele
ngth for the Secon
d
De
sign
4. Conclusio
n
G
T
I mirr
or
s ar
e
us
ed
ma
inly fo
r
pu
ls
e
co
mp
re
ss
ion
in
Yb
:YAG
, Yb
:KG
W
fe
mtos
ec
o
n
d
lase
rs Th
e m
a
in d
r
a
w
ba
cks of th
e
GTI
are
the fu
nda
mentally limit
ed b
and
width
(p
rop
o
rtion
a
l
to
the sq
ua
re root of the giv
en ma
gnitud
e
of G
D
D)
a
nd the limite
d
amo
unt of
control of hi
g
her-
orde
r di
sp
ersion.
Dispe
r
sive mirro
r
s with
si
gnifi
cantly b
r
oa
d
e
r o
p
tical
b
and
width
ca
n be
desi
gne
d as
chirped mi
rro
r
s. Ideally, the GTI is
ope
rated nea
r a maximum or
minimum of the
GDD, and the usabl
e ban
dwidth is
so
me fractio
n
(e.g. one-tent
h) of the free spe
c
tral ra
nge,
whi
c
h i
s
inve
rsely
propo
rtional to
the
re
son
a
tor l
engt
h. In the time
domai
n, this mean
s th
at th
e
pulse du
ratio
n
nee
ds to
b
e
well
above
the rou
n
d
-
trip
time of the
GTI. The ma
ximum magni
tude
of GDD scale
s
with th
e sq
uare
of the re
son
a
tor
le
ngt
h.
From
the a
bove
re
sult, we can see
t
hat
the layer stru
cture
can
be
easily a
dapte
d
for
any
oth
e
r
wavele
ngt
h re
gime.
We
believe th
at this
comp
en
sato
r of thin
-film
has mo
re
po
tential to b
e
depl
oyed i
n
ultrafa
s
t o
p
tics an
d o
p
tica
l
comm
uni
cati
on.
680-
84
0n
m
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
De
sign a
nd Analysi
s
Gire
s-Tournoi
s-Inte
rferom
eter Mi
rro
rs
(Am
e
r B.Dhe
y
ab
)
7213
Referen
ces
[1]
F Gires, P
T
o
u
r
nois. Interfero
m
etreutilis
ab
le
pour
l
a
compr
e
ssio
n
d'imp
u
l
s
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