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

1. 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 17TH IEEE/LEOS Conference Puerto Rico, 7-11th November, 2004

2. Connector area Laser – Detector array Optical waveguides 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

3. b y Linear Taper Bend Taper y z c b c r z θ x a a The Bent Taper • In a “bent taper” the lateral dimension, a, tapers linearly with respect to angle, θ to the final width, b • In a “linear taper” the lateral dimension, a, tapers linearly with respect to the – z axis to the final width, b c x

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 > uo, ncladding > ncore. 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. z z Simulation Technique • 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 • BPM paraxial limitations are altered • Significant reduction of the simulation area/time (B) Transformed straight taper (A) Bent Taper A1 A2 R θ w

6. y z c c b r θ x a 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 Bent Taper VCSEL fundamental mode

7. VCSEL 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 Transmittance (dB) Field axial misalignment (μm)

8. VCSEL 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 Transmittance (dB) Field rotational misalignment (degrees) φ

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 Lateral offset FWHM (μm) Max. normalized power (dB) Solid lines: Bent taper Dashed lines: Linear taper Taper ratio (a/b) Solid line: Bent taper Dashed line: Linear taper Angular rotational FWHM (degrees) Taper ratio (a/b)

10. Conclusions • 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 FWHMθdegrades from 100 to 20 Acknowledgements • Xyratex Ltd. for financial support and useful discussion • Frank Tooley for useful discussion