MICROOPTICAL COLLIMATED SYSTEM FOR WDM RECEIVER
WITH A BRAGG VOLUME GRATING
Vítězslav Jeřábek
a
, Armas Julio
b
, Karel Bušek
a
, David Mareš
a
, Václav Prajzler
a
,
a
Department of Microelectronics, Faculty of Electrical Engineering Czech Technical
University, Technická 2, 166 27 Prague 6, Czech Republic
b
Facultad de Ingeniería en Ciencias Aplicadas, Universidad Técnica del Norte, Avenida
17 de Julio 521 Barrio El Olivo y General José María Cordova, Ecuador
email: jerabek@fel.cvut.cz,
ABSTRACT:
We report about design and measurement of wavelength division
multiplexing (WDM) microoptical collimation system for WDM receiver
module (WDMReceiver). The collimation system is represented by ray
matrix model and the focal distances obtained in the matrix are verified
experimentally. The optic focal system: “collimation lens PIN photodiode
(PD)” is characterized to found the dependence between the diameter of the
beam collimated and the active area covered in the PIN PD. The optical
micromodule uses a microoptics hybrid integration technology with
collimation lenses and a volume holographic Bragg grating triplex filter
(VHGT) for wavelength multiplexing/ demultiplexing.
Keywords:
Microoptical hybrid integration, WDM transceiver, volume
holographic grating triplexer, collimation lenses.
1
INTRODUCTION
Optical system with collimation/decollimation lenses is an alternative for high efficiency
optical processing
of the beam.
The radiation propagates from MMF across the
collimation lens, VGHT and
decollimation lenses allow the development of simple and
optimized structures in hybrid planar technology in comparison with other usual
approaches. The present optical micromodule indeed leads to a significant simplification
of the receiver
in new circle topology.
The main parameters of the system were the focal distance of the lenses and the
diameter of the beam spot, which has a significant influence on the VHGT optical
characteristics (diffraction efficiency, optical crosstalk, etc.).
The figure 1 shows the location of the three micromodules in the same substrate, the
collimation lens, triplexer and decollimation lens will match by a piezomanipulator to
acquire sufficient position accuracy in the alignment process until maximum diffraction
for both wavelength occurs.
Fig. 1:
Schematic form of the WDM OE receiver
The optoelectronic receivers will be placed depending on the direction of the diffracted
light
. Each diffracted beam is normal to the lens surface and focused to the active area of
the photodiode.
2
DESIGN AND
MEASURE RESULTS
OF THE OPTICAL
MICROMODULE
2.1
The collimation lens
The optical analysis by raytransfer matrix is one of the methods to describe optical
systems in the paraxial approximation. It is widely used –order layout and for analyzing
optical systems. The reason why the raytransfer
matrix is used in the present work is in
order to find simple and explicit expressions for determination of the beam optimal
structural parameters of the focusing system [1]. In the following, modal – field profiles
in the MMF and collimation lens are assumed, to be circularsymmetric and Gaussian and
consider the propagation of a ray in a homogeneous medium [2].
The schema of the collimating system composed of the MMF  collimation lens is
shown in Fig. 2
Fig. 2
The collimation system: MMF – cylindrical lens.
1
1
1
R
n
P
=
2
2
1
R
n
P
=
n
L
t
=
=
1
0
1
2
n
L
T
=
1
1
0
1
1
2
1
R
n
M
=
1
1
0
1
2
2
2
R
n
M
=
1
1
0
1
1
0
1
1
1
0
1
2
2
2
1
2
1
R
n
n
L
R
n
S
×
+
×
×
+
+
×
+
=
n
L
R
n
n
L
R
n
R
n
R
n
R
n
n
L
n
L
R
n
S
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
M
T
M
S
=
The matrix beam model of the optical system composes of coupling between the
multimode fiber (MMF) and the collimation lens was calculated as the multiplication of
the translation matrix T (formula 1) and the refraction matrices M1 and M2 (formula 2
and 3) [1].
(1)
L is the thickness of the lens
n2 is the reflection index of the medium
The refraction at the firs surface is expressed by the matrix
M
1
given in (2):
(2)
R1 is the radius of curvature of the lens surface closest to the light source,
The refraction at the second surface is expressed by the matrix
M
2
given in (3)
(3)
R2 is the radius of curvature of the lens surface farthest to the light source,
The transfer matrix of the collimation lens (S1) is given by (4)
(4)
(5)
If
n
2
,=
n,
the transfer matrix is,
(6)
This might suggest the following abbreviations:
(7)
(8)
(9)
=
D
C
B
A
S
1
(
)
in
y
C
b
A
×
+
=
0
0
=
×
+
C
b
A
=
0
1
0
1
0
in
out
y
D
C
B
A
b
C
A
b
=
×
+
×
+
+
×
+
=
t
P
t
P
P
P
P
t
t
P
S
2
2
1
2
1
1
1
1
1
t
P
P
P
P
t
P
b
FFD
×
+
+
×
+
=
=
2
1
2
1
1
1
Where
L
1 =
length of the collimation lens
R
1
=
radius of curvature of first surface
R
2
=
radius of curvature of second surface
n
= refractive index
S
1
can be defined as
(10)
The system transfer matrix can be represented as (11):
(11)
Its focal plane can be found by letting a ray parallel to the optical axis pass through the
lens and determine the distance
b
from the exit reference plane to the plane where it
intersects the optical axis. Expressing this in matrix notation, is
(12)
This implies that
(13)
This equation should hold for all values of
y
in.
Therefore, it follows that
(14)
The position of the focal plane of the lens described by the matrix
S
1
is therefore
determined by
(15)
and we can identify
b
as the front focal distance
FFD
of the lens.
(16)
Where
L
1 =
3.0 mm is the length of the collimation lens
R
1
=
2.3 mm is the radius of curvature convex () of first surface
R
2
=
is the concave radius of curvature of second surface
n
= refractive index.
Obtains values are shown in the Table 1.
(
)
2
1
=
in
T
P
P
2
2
1
2
1
÷
÷
+
=
n
n
n
n
Table 1.
Main values of the collimation lens for three wavelength 1310 nm, 1490 nm, 1550 nm.
[nm]
n
P
1
[mm
1
]
P
2
[mm
1
]
P
1
t
t
[mm]
FFD [mm]
1550
1.4865
216
0
0.5345
2.153
2.709
1490
1.4870
216.4
0
0.5342
2.151
2.705
1310
1.4885
216.8
0
0.466
2.150
2.692
The compromise distance of the
FFD
for three wavelengths is the average distance FFD
= 2.702 mm.
Other parameter to be analyzed in the collimation lens is the
optical attenuation.
The formula (18) can be used to calculate the transmitter power in the collimation lens,
with this value we calculate the insertion loses or attenuation in the collimation lens due
to Fresnell reflection at the interfaces.
(18)
where
P
T
is the transmitted power
P
in
is the incident power
is the coefficient of reflection
where
(19)
Table 2 shows the attenuation, efficiency and coefficient of reflection of the collimation
lens.
Table 2.
Main parameters of the collimation lens
[nm]
n
P
T
[uW]
P
in
[uW]
Att. [d
B
]
meas
1550
1.4865
367
380
0.151
0.017
1490
1.4870
869
890
0.104
0.011
1310
1.4885
835
860
0.128
0.147
2.2
Optical Measurements for VHGT
The VHGT was set up by micromanipulator to get the maximal diffracted beams
optical power in its diffraction angle for both wavelengths 1490 nm and 1550 nm at the
same time. Three shifts were used for accurate set of Beam Propagation head. The
software of head enable takes the pictures of the optical space field distribution in 2D or
3D.
The space distribution of VHGT optical three optical beams for measurement of
diffracted angle of the beams are shown in the Fig. 3
÷
÷
×
×
=
n
B
B
D
n
cos
sin
1
2
Fig. 3
The three beam space distribution for measurement angle of the diffracted optical beam
A)
in 2D for the wavelength
1=1310 nm,
2=1490 nm and
3=1550 nm
B)
in 3D for the wavelength
1=1310 nm,
2=1490 nm and
3=1550 nm
For measurement of diffraction efficiency was used formula (20). The diffraction
efficiency was find to be
= 75.00 % for wavelength 1490 nm and
=73.21 % for
1550 nm Fig. 4 and Tab. 3 [3]
(20)
Table 3.
The diffraction efficiency
of the VHGT with incident power P0 and diffracted power PD
[μ]
P
0
[μW]
P
D
[μW]
meas
[%]
calc LT
[%]
Δ
[%]
Att. Diff.
[dB]
1550
367
268.7
73.21
71
2.21
1.35
1490
879
659
75
74.9
0.1
1.24
Fig. 4.
2D measurement of diffraction efficiency
The minimal optical crosstalk of the optical beam for both wavelength was very
important requirement to the reach good BER. The optical crosstalk was given by (21)
[
]
dB
P
P
A
2
1
log
10
=
(21)
where P
is optical diffracted power , P
2
is optical power diffracted to direction
opposite wavelength. For BER = 10
9
it was needed
A
> 11 dB. The results of the
measuring is shown in Fig. 5 and in Tab. 4 [4].
Fig. 5.
The optical crosstalk in 3D for the wavelength λ1 =1490 and λ2 =1550 nm with the power
normalized to 360 uW
Table 4.
The optical crosstalk of the VHGT beams measurement
where
P
1
is optical diffracted power,
P
2
is optical power diffracted at the same
direction than
P
1
. For
BER
= 10
9
it was needed
A
> 11 dB.
The crosstalk measured shows us that using the VHGT is possible diffract two beam at
the same time without
undesired effect from each other.
Wavelength
[nm]
Total Power
[
μW]
Diffracted power
P
1
[
μW]
Crosstalk
P
2
[
μW]
A
[dB]
1550
360
263.5
15
1490
12.44
1490
360
270
4
1550
18.29
÷
=
z
x
arctg
diff
The space distribution of VHGT optical beams was shown in the Fig. 4 and to
calculate the diffracted angles for each wavelength we have measured the distance
VHGTBeam Profiler Head [5].
Fig 6 shown us the schema used to measure the respective angles and Tab. 5 the angle
values from datasheet and measured.
Fig. 6
Basic set up to measure the diffracted angles for
=1550 nm and
=1490 nm
(22)
For
= 1550 nm
05
.
20
3
.
6
3
.
2
1550
=
÷
=
mm
mm
arctg
nm
43
.
18
3
.
6
1
.
2
1490
=
÷
=
mm
mm
arctg
nm
Table 5
Diffraction angles from datasheet and measured.
Wavelength
[nm]
datasheet
measured
Δ
[
0
]
1550
19.1
20.05
0.95
1490
18.4
18.43
0.03
2.2
The decollimation lens
2
)
0
(
2
)
0
(
D
z
FFD
D
q
z
m
y
+
×
×
=
+
×
=
Main function of the decollimation lens in the opt
oelectronic micromodule is to provide
optimal radiation focus of the diffracted beam on the active space of PIN PD.
The radio of the active area covered "
y
" in the PIN PD is described in function of the
distance "
z"
and given by
Main function of the decollimation lens in the optoelectronic
micromodule is to provide optimal radiation focus of the diffracted beam on the active
space of PIN PD.
The diameter of the beam exposition to the active area of PIN PD depends on the distance
between the decollimation lens and PIN PD (
z
) and the diameter of the beam
D
(0) as
shown in Fig. 7.
With the formula (23) we obtain the radio of the active area covered.
Thus
(23)
where
y
is the radio of the active area
m
is the slope of a line
q
is the diameter f the beam at z = 0 mm
FFD
is the focal front length of the decollimation lens.
D
(0)/2
is the half diameter of the beam at
z
= 0 mm.
To cover all the active area of the PIN PD, the distance between the decollimation lens
and PIN PD was in
z
= 2.34 mm as shown the Fig. 7 and 8.
Fig. 7.
The schema of the focus system: decollimation lens – PIN PD.
Fig 8
Half beam diameter D(0)/2 in function of distance z
To cover all the active area of the PIN PD, the distance between the decollimation lens
and PIN PD was shown in the table 6.
Table 6
Main parameters between decollimation lens and PIN PD
[nm]
FFD [mm]
y
[
µ
m]
D(0)/2
[µm]
z
[
mm]
1550
2.709
20
200
2.434
1490
2.705
20
200
2.435
1310
2.692
20
200
2.422
The active area of the PIN PD is placed at 2.43 mm in front of the decollimation lens.
3
CONCLUSIONS
For investigated optical micromodule the optical beam demultiplex element as VHGT
was first used. The optical imaging and diffracting system with MMF – collimation lens 
VHGT was designed and measured its properties such as: diffraction efficiency, optical
loss and optical crosstalk parameters. The steps for design and measurement of these
properties were:
1) The optical imaging and diffracting system components was characterized by the ray
transfer matrix system. It was assumed to be modal – field profiles in the MMF and
collimation lens are circular, symmetric and Gaussian. It was considered the propagation
of a light ray in a homogeneous medium. The total ray matrix was derived, solved the
focal points and place of the collimation lens. The optical collimating distance between
MMF and collimation lens was calculated to Z= 2.7 mm in the optical micromodule. The
optical loss by Fresnel reflection in collimation lens 0.23dB was calculated.
In the experimentally part of the investigation and optimization of optical micromodule
properties the optimal set of optical ray diffracting system was found. It was investigated
optimal position MMF and the collimation lens Z = 2.43 mm, for the 190
m half width
of the beam spot diameter. This value was very close to measured value. The divergence
of optical beam for optimal position of collimation lens had minimum value 3.75µm/mm,
The volume holographic grating triplexer (VHGT) diffract angle 18 degrees for 1490 nm
and 19 degrees for 1550 nm were verified. The diffraction efficiency was
=74.9% for
wavelength 1490 nm and
=73.21% for 1550 nm. This value had good agreement with
calculated values. The attenuation crosstalk was 12.44 dB for 1550 nm and 18.29 dB for
1490 nm, which insure in digital transmission BER > 109 after. The total attenuation
between the MMF and PIN PD is 0.481 dB, 0.244 dB and 0.258 dB for 1550 nm, 1490
nm and 1310 nm respectively. The total optical loses of optical and optoelectronic
micromodule optical path including diffraction are 1.831 dB for 1550 nm and 1.484 dB
for 1490 nm.
4
ACKNOWLEDGMENTS
This research has been supported by GA ČR grant Nos. 102/06/0424 and the research
program MSM6840770014 of the Czech Technical University in Prague.
5
REFERENCES
[1]
KLOOS G., "Matrix methods for optical layout", SPIE, (2007), P.13.
[2]
SHIRAISHI K, "A New LensedFiber Configuration Employing Cascade GI
Fiber Chips" Journal of Lightwave technology, vol 18, no 6, June 2000.
[3]
___,
Summary of Holographic Glass Properties,
Ondax Ltd.
Doc. No. 101
80000001
[4]
JOHN GOWAR, Optical Communication Systems,
Prentice Hall, International
series in Optoelectronics,
P. Dean, editor, pag. 411.
[5]
JEŘÁBEK V., ARCININIEGA J, "Hybrid Optoelectronic Receiver with
Gigahertz Bandwidth",
Electronic Horizont
, 2009, vol. 65, no 3, p. 2225
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