Optical Low Coherence Interferometry:
waveguide and resonant ring characterization
A. Melloni, R. Costa, G. Cusmai,
F. Morichetti and M. Martinelli
A.Melloni – Erice 2003
1
Optical reflectometry techniques
• OLCR gives the field transfer function of the Device Under Test
• Both the reflection r(t) and the transmission t(t) can be measured
• Micrometrical resolution suitable for integrated optical devices
Operative range
OTDR
OFDR
OLCR
1 mm
A.Melloni – Erice 2003
1 mm
1m
1 km
106m
2
What is OLCR suitable for?
• Waveguide group effective index (ng)
• Waveguide birefringence (B)
• Waveguide loss (a)
• Waveguide second order dispersion (b2)
• Coupling coefficient of directional couplers (k)
•…
• Recover the intensity and phase transfer function
A.Melloni – Erice 2003
3
Basics of OLCR
DUT
Optical
Source
Splitter
PD
Combiner
OPD
Optical Path Delay
Michelson interferometer (reflection)
Mach-Zehnder interferometer (trasmission)
DUT
3dB
DUT
3dB
PD
3dB
PD
A.Melloni – Erice 2003
Micro-mechanical translator
4
Theory of the OLCR
The PD detects the cross-correlation U(t) of the two arms of
the interferometer, that is
U (t )  
S 
 F  S ( )  H ( )      g t   h t    cos  t 

 

-1
0
1
g t

Power spectral density
of the optical source
H 

 
h t
V(x)=|g(x)|
0.5
U(t
0

-0.5
Field transfer function
of the DUT
-1
-100
-50
0
50
100
Optical path difference
A.Melloni – Erice 2003
5
Experimental setup (transmission)
Super-luminescent diode (SLD):
•Central wavelength 1538 nm
•Coherence length 17 mm (62nm)
PM launch fiber :
• TE/TM characterization
Polarization
controller
SLD
Coupler
3dB
PM fiber
c1
DUT
Coupler
3dB
c2
+
_
mirror
Micro-mechanical translator:
• 2x300 mm full range
• positioning accuracy <0.5 mm
(linear encoder)
A.Melloni – Erice 2003
Balanced Photodetector :
• No CW signal
• No common mode fluctuations
• 3dB signal enhancement
6
Experimental setup (reflection)
Super-luminescent diode (SLD):
•Central wavelength 1538 nm
•Coherence length 17 mm (62nm)
PM launch fiber :
• TE/TM characterization
Polarization
controller
SLD
Coupler
3dB
PM fiber
c1
DUT
Coupler
3dB
c2
+
_
mirror
Micro-mechanical translator:
• 2x300 mm full range
• positioning accuracy <0.5 mm
(linear encoder)
A.Melloni – Erice 2003
Balanced Photodetector :
• No CW signal
• No common mode fluctuations
• 3dB signal enhancement
7
Low-coherence optical source (SLD)
Normalised SLD spectrum
SLD Autocorrelation
0
1
S() [dB]
-5
62 nm
-10
Lc=34 mm
0.5
-15
-20
0
-25
-0.5
-30
-35
-40
1400
1450
1500
1550
1600
Wavelength [nm]
A.Melloni – Erice 2003
1650
1700
-1
-40
-20
0
20
40
Optical path difference [mm]
8
Fiber-to-fiber reference pattern (1)
Interference pattern in absence of any DUT (fiber-to-fiber)
Effect of the PM launch
fiber
One interference pattern
for each mode of the PM
fiber
d0=BPMLPM
BPM Birefringence of the
PM fiber
LPM Length of the
PM fiber
A.Melloni – Erice 2003
d0=420mm
1
0.5
0
-0.5
-1
286.8
287
287.2 287.4 287.6
Optical path difference [mm]
287.8
9
Fiber-to-fiber reference pattern (2)
Interference pattern in absence of any DUT (fiber-to-fiber)
Effect of the second order
chromatic dispersion b2
 2
 1   8 c ln 2

Lc


i
b 2 ,i z i 

2

Lc

b2,i Dispersion of the i-th
component of the
experimental setup
A.Melloni – Erice 2003
''
1
Widening of each
interference pattern
L0
L 0  91 m m
L 0  98 m m
'
0.5
2
0
-0.5
-1
286.8
287
287.2 287.4 287.6
Optical path difference [mm]
287.8
10
Straight waveguide: effective group index
''
Dg
1
ng 
1
Dg
D
'
g
0.5
0.5
0
0
-0.5
-0.5
L geom
Lgeom waveguide
geometrical length
-1
286.8
-1
213
213.2
213.4
213.6
213.8
214
Optical path difference [mm]
Experimental results
287
287.2
287.4
287.6
287.8
Optical path difference [mm]
1.56
1.55
1.0
1.4
1.8
2.1
Exp.
ng
1.506
1.512
1.533
1.542
BPM
ng
1.512
1.525
1.532
1.534
1.54
ng
wg width [mm]
1.53
1.52
Exp. Accuracy(*) : ±10-3
(*) limited by the ±50mm uncertainty on Lgeom
1.51
1.5
1
1.4
1.8
2.2
waveguide width [mm]
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11
Straight waveguide: birefringence
B 
1
d1  d 0
1
d1
0.5
0
0
-0.5
-0.5
L geom
Lgeom waveguide
geometrical length
d0
0.5
-1
286.8
-1
213
213.2
213.4
213.6
213.8
214
Optical path difference [mm]
287
287.2
287.4
287.6
287.8
Optical path difference [mm]
x 10
Experimental results
-4
wg width [mm]
1.0
1.4
1.8
2.1
Exp.
-60
-66
-24
6
B
-12.3
-13.6
-4.9
1.2
BPM
B
-8.8
-6.2
-2.8
-0.6
Exp.
accuracy(*)
d1-d0 [mm]
:
±10-5
(*) limited by the ±0.5mm uncertainty on the
translator positioning
A.Melloni – Erice 2003
B
0
-5
-10
1
1.4
1.8
2.2
waveguide width [mm]
12
Straight waveguide: chromatic dispersion
1
1
Lc source
coherence
length
''
1
L
'
L1
0.5
0.5
0
0
-0.5
-0.5
-1
286.8
-1
213
213.2
213.4
213.6
213.8
214
Optical path difference [mm]
Experimental results
b2 
2
8 ln 2 c L g eo m
L
287
287.2
287.4
287.6
287.8
Optical path difference [mm]
300

 L0 


 1

 Lc 

Exp. accuracy(*) : ± 5 ps2/km
250
2
b2 [ps2/km]
2
Lc
2

 L1 


 1 
  Lc 

''
L0
'
0
200
150
100
50
(*) limited by the ±0.5mm uncertainty on the
translator positioning
0
1
1.4
1.8
2.2
waveguide width [mm]
A.Melloni – Erice 2003
13
Ring resonator (RR)
Lr
a
Lr
Geometrical length of the ring
a
Propagation loss
gi
Directional coupler insertion loss
k
jg i t i
 ge
 a Lr
  kLr
H (z) 
A.Melloni – Erice 2003
g i ri
ki
round trip loss
round trip phase shift
r  z
1
1  rz
zz 

r
1
z p  r
14
OLCI of a ring resonator
A2
t 
4
2

A1
r
A1
 zz  z p
2
A3
A2

A4
A3
 ...  r   z p
A7
A5
A6
A4
A2
A3
0
-2
A3 A1
A
2
2

r
2
t
2
-4
200
220
240
260
280
Optical path difference [mm]
A.Melloni – Erice 2003
15
Experimental results on RR
Lr  8 0 1 8 m m
( 25 GHz )
'
'
A2
'
A3
 0.4
'
A1
A2
''
A3
A2
''
 z p  0.66
z z  1.06
 z p  0.75
z z  1.16
'
'
'
 0.42
'
A2
A1
''
''
Maximum
phase
response
Measured value
Accuracy
ng
1.5488
± 10-4
B
4.5·10-5
± 2·10-5
k
a dB/turn
A.Melloni – Erice 2003
k’
0.34
k’’
0.37
0.95
± 0.01
± 0.1
16
Chromatic dispersion in a RR
90
width [mm]
80
’
b
2
b2 [ps2/km]
b2’’
Measured
value
Accuracy
104
±5
117
±5
70
60
50
40
30
0
A.Melloni – Erice 2003
1
2
3
4
5
6
Optical path difference normalised to Lr
7
17
Polarization rotation in a RR
EDUT
A4
Coupler
3dB
c2
A3
EDUT
+
A2
dq A
1
q
Eref
_
Eref
A
'
2
'
1

A
r
''
A2
''
1
A
t  cos(  d  )
2
cos( )
t  sin(  d  )
2

r
A.Melloni – Erice 2003
sin( )
'
A3
'
 r
A2
''
A3
A
''
2
 r
cos(  2 d  )
cos(  d  )
q  0.6 rad
sin(  2 d  )
dq  0.05 rad
sin(  d  )
(±0.01 rad)
18
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19
Mach Zehnder Interferometer (MZI)
L
k1
a
 L MZI geometrical unbalance
k2
a
Directional coupler
ki
gi
g i ri
jg i t i
A.Melloni – Erice 2003
Propagation loss
ri
directional coupler
insertion loss
2
 ti  1
2
20
Interference pattern of a MZI
Bar 1
Cross 1
5
5
'
AL ,b1
''
AS ,b1
AS ,b1
2.5

AS , b 1
r1 r2
e
t1 t 2
0
-2.5
-2.5
268.4
268.6
268.8
269
269.2
5
'
A
A L ,b1
''
L ,b1
AL , x1
AS , x 1

r1 t 2
-5
e
aL
0
238.2
238.4
238.6
A.Melloni – Erice 2003
238.8
239
AS , x1 AL ,b1
268.8
269
269.2
''
AL , x1
AL , x1
0
A L , x 1 AS ,b 1
268.6
'
t1 r2
2.5
-5
238
268.4
5
2.5
-2.5
AS , x1
2.5
0
-5
268.2
''
'
AS , x1
aL

t
2
2
2
2
r
-2.5
-5
238.2
238.4
238.6
238.8
239
21
239.2
Interference pattern of a MZI
Bar 2
AL ,b 2
AS ,b 2

Cross 2
t1 t 2
e
r1 r2
aL
AL , x 2
AS , x 2
AL , x1 AL , x 2
AS , x1 A L , x 2
A.Melloni – Erice 2003


t1 r2
e
aL
r1t 2
AL ,b1 AL ,b 2
A L , x 2 AS , b 2
2

AS , x 2 AL ,b 2
 e
t1
r1
 2a  L
AS ,b1 AL ,b 2
22
2
Experimental results on the MZI
Note: ng, B and b2 can be measured by comparing the interference pattern
of the long path (L) to that of the short path (S) of the MZI
Measured
value
Accuracy
ng
1.5411
± 5·10-5
B
2.3·10-4
± 5·10-5
68
±5
k1
0.412
± 0.01
k2
0.408
± 0.01
a dB/cm
0.92
± 0.05
b2 [ps2/km]
A.Melloni – Erice 2003
23