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 5-21 Barrio El Olivo y General José María Cordova, Ecuador

e-mail: jerabek@fel.cvut.cz,

ABSTRACT:

We report about design and measurement of wavelength division

multiplexing (WDM) microoptical collimation system for WDM receiver

module (WDM-Receiver). 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 ray-transfer 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 ray-transfer

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 circular-symmetric 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

VHGT-Beam 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 > 10-9 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.1-3.

[2]

SHIRAISHI K, "A New Lensed-Fiber 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-

80000-001

[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. 22-25

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