1. ©UCL 2004 17 TH IEEE/LEOS Conference Puerto Rico, 7-11 th November, 2004 Multimode Laterally Tapered Bent Waveguide Ioannis Papakonstantinou, David R. Selviah and F. Anibal Fernandez Department of Electronic and Electrical Engineering University College London Outline Research Motivation Modelling Approach Results - Discussion

2. ©UCL 2004 2 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

3. ©UCL 2004 3 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 z x Linear Taper In a “linear taper” the lateral dimension, a, tapers linearly with respect to the – z axis to the final width, b

4. ©UCL 2004 4 ≡ 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 > u o, n cladding > n core. A bend is always lossy Index in the core is asymmetric resulting to asymmetric modes Solid line: Index of transformed guide Dashed line: Step-index guide

5. ©UCL 2004 5 Simulation Technique (A) Bent Taper (B) Transformed straight taper z z 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 A2A2 A1A1

6. ©UCL 2004 6 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 n core = 1.54, n cladding = 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

7. ©UCL 2004 7 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 Transmittance (dB) Field axial misalignment (μm)

8. ©UCL 2004 8 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 Transmittance (dB) Field rotational misalignment (degrees)

9. ©UCL 2004 9 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) Lateral offset FWHM (μm) Max. normalized power (dB) Angular rotational FWHM (degrees) Solid lines: Bent taper Dashed lines: Linear taper Solid line: Bent taper Dashed line: Linear taper

10. ©UCL 2004 10 Conclusions Acknowledgements Bent taper simulations using FD-BPM revealed: As taper ratio varies from 1 < a/b < 25 lateral misalignment FWHM x degrades from 50 μm down to 7 μm Proportionally angular misalignment FWHM θ degrades from 10 0 to 2 0 Xyratex Ltd. for financial support and useful discussion Frank Tooley for useful discussion