17 TH IEEE/LEOS Conference Puerto Rico, 7-11 th November, 2004

©UCL 2004

17TH IEEE/LEOS Conference

Puerto Rico, 7-11th November, 2004

Multimode Laterally Tapered Bent Waveguide

Ioannis Papakonstantinou, David R. Selviah and F. Anibal Fernandez

Department of Electronic and Electrical EngineeringUniversity College London

Outline

• Research Motivation

• Modelling Approach

• Results - Discussion

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Research Motivation• To minimise cost of connectors

between the laser-detector arrays and the backplane waveguides

• Passive alignment of the optical connectors

• A large amount of misalignment must be tolerated

• Tapered waveguide entrances seem ideal

• In a dense configuration of boards and connectors the waveguides are curved to avoid the neighbouring connector

• A bent taper conserves space

Optical Backplane

Optical waveguides

Laser – Detector array

Connector area

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The Bent Taper

• In a “bent taper” the lateral dimension, a, tapers linearly with respect to angle, θ to the final width, b

x

c

z

y

c

a

b

θ r

Bend Taper

a

c

b

y

zx

Linear Taper• In a “linear taper” the lateral dimension, a, tapers linearly with respect to the – z axis to the final width, b

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R

r

x

y

u

v

)(uneff

y ≡

Co-ordinate Transform• The transform u = r – R, v =

Rθ maps the bent taper to a straight taper

• The effective index of the structure is tilted in comparison with the usual step index guide

• The slope of the tilt depends on the radius of curvature

• For u > uo, ncladding > ncore. A bend is always lossy

• Index in the core is asymmetric resulting to asymmetric modes

2

2

222

2

2

222

4

11)()(

o

y

ooeff krkr

R

krnrn

ou

Solid line: Index of transformed guideDashed line: Step-index guide

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Simulation Technique

(A) Bent Taper (B) Transformed straight taper

)cos1(1

2

R

w

A

A

zz

• FD – BPM

• 3D – Mesh of 0.1 μm × 0.1 μm and 1 μm axial step

• (1,1) Padé Coefficients

• Full TBC boundary conditions

Benefits by using the transform with BPM

A. BPM paraxial limitations are altered

B. Significant reduction of the simulation area/time

θ

w

R

A2A1

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Physical Parameters• Channel waveguide with

initial dimensions a = 50 μm, c = 50 μm

• Dimension b varies from 25 μm to 2 μm

• Variable taper ratio (a/b): 2 < a/b < 25

• ncore = 1.54, ncladding = 1.5107. N.A = 0.3

• R > 20 mm to minimize bend losses

• Material intrinsic losses and scattering losses all ignored

• Launching field: Gaussian 7 μm 1/e width, TE – polarised, λ = 850 nm

VCSEL fundamental mode

z

y

x

c

c

a

b

θ r

Bent Taper

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Lateral Misalignment• Input Gaussian field is

translated along the x-axis

• Position 0 is at the centre of the guide

• Maximum transmittance NOT when the source is centred to the guide

• Coupling is better towards the outer side of the bend

• This is due to the asymmetric nature of the modes inside the bend VCSEL

Tra

nsm

ittan

ce (

dB)

Field axial misalignment (μm)

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φ

Angular Misalignment• Input field is positioned at

the maximum position on the x - axis

• Then it is rotated on the xz - plane

• As the taper ratio increases losses increase

• For < 3 dB losses we can tolerate just a few degrees of misalignment in any case

• Therefore angular misalignment might be more critical than translational

VCSEL

Tra

nsm

ittan

ce (

dB)

Field rotational misalignment (degrees)

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Comparison with Linear Tapers• FWHM of the lateral and

rotational misalignment graphs for bent and linear tapers are compared

• Linear tapers show higher insertion loss but better lateral misalignment tolerance

• Bent tapers show better angular misalignment tolerance

• All FWHM degrade as taper ratios increase

Taper ratio (a/b)

Taper ratio (a/b)

Late

ral

offs

et FWHM

(μ

m)

Max

. no

rmal

ized

pow

er (

dB)

Ang

ular

rot

atio

nal

FWHM

(de

gre

es)

Solid lines: Bent taperDashed lines: Linear taper

Solid line: Bent taperDashed line: Linear taper

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Conclusions

Acknowledgements

• Bent taper simulations using FD-BPM revealed:

• As taper ratio varies from 1 < a/b < 25 lateral misalignment FWHMx degrades from 50 μm down to 7 μm

• Proportionally angular misalignment FWHMθ degrades from 100 to 20

•Xyratex Ltd. for financial support and useful discussion

•Frank Tooley for useful discussion