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Design of Three-Dimensional, Path Length Matched Optical Waveguides COPYRIGHT AND USE OF THIS THESIS This thesis must be used in accordance with the provisions of the Copyright Act 1968. Reproduction of material protected by copyright may be an infringement of copyright and copyright owners may be entitled to take legal action against persons who infringe their copyright. Section 51 (2) of the Copyright Act permits an authorized officer of a university library or archives to provide a copy (by communication or otherwise) of an unpublished thesis kept in the library or archives, to a person who satisfies the authorized officer that he or she requires the reproduction for the purposes of research or study. The Copyright Act grants the creator of a work a number of moral rights, specifically the right of attribution, the right against false attribution and the right of integrity. You may infringe the author’s moral rights if you: - fail to acknowledge the author of this thesis if you quote sections from the work - attribute this thesis to another author - subjec t this thesis to derogatory treatment which may prejudice the author’s reputation For further information contact the University’s Director of Copyright Services sydney.edu.au/copyright Master’s Thesis Ned Charles Design of Three-Dimensional, Path Length Matched Optical Waveguides Arbitrary Design of Three-Dimensional, Path Length Matched Waveguides Abstract A method for designing physically path length matched, three-dimensional photonic circuits is described. These waveguides, with arbitrary endpoints, were fabricated via the femtosecond laser direct-write technique. The focus is specifically on the case where all waveguides are uniquely routed from the input to output; a problem which has not been addressed to date and allows for the waveguides to be used in interferometric measurements. Two iterative design methods were created for path length matched waveguides with adequate separation in three dimensions and minimized curvature. These algorithms could be used to calculate predicted radius of curvature, bend and transition loss in the waveguides, with results confirmed by computer simulation methods. Demonstrations via interferometric methods show that the fabricated circuits were indeed optically path length matched to within 45 μm which is well within the coherence length required for typical applications, including astronomical measurements. Acknowledgements This thesis wouldn’t be complete without the acknowledgement of my colleagues who helped me tremendously along the way. Thanks to Nem Jovanovic at Macquarie University for helping coordinate all the design, fabrication work and testing, and also for feedback on my paper and thesis. Thanks to Paul Stewart for letting me bounce ideas, keeping the lab running in top form and for putting up with my occasional cursing while sharing an office. To my advisor Peter Tuthill, for doing a thorough review of this thesis, contributing edits to it, and for coordinating the Dragonfly project. To my co-advisor, John O’Byrne, for all of the feedback despite coming late to the process, and for also reviewing and contributing edits to this thesis. To Barnaby Norris, for helping make all of the data analysis happen and for good advice on portions of the design process. I’d also like to thank two others at Macquarie University - Simon Gross for his expertise in the fabrication of the waveguides and Mick Withford for valuable feedback on our results. Also, a special thanks to Jon Lawrence at the AAO, who got the direct write waveguide design off to running start so I could pick up where he left off. Statement of Student Contribution The first section in this thesis is the introduction and is a review of existing relevant technologies and is mostly the work of others and cited appropriately. The theory section is also cited appropriately, however the review of the design requirements of the project was compiled by myself and based on a review by the Dragonfly team. The third section with the design of the waveguides using a cubic spline and developing all the software algorithms is my work, except for portions of the code that are cited appropriately. An extra acknowledgement is made to Jon Lawrence (at Macquarie University at the time) for originating the design using a type of spline for the concept. The concept of the sidestep design was created by the Dragonfly team and 2 Arbitrary Design of Three-Dimensional, Path Length Matched Waveguides implemented by myself. The circular arc design in Section 5 was suggested by my advisor, Peter Tuthill, but implemented by myself. The next two sections rely heavily on the theoretical calculations made by Snyder and Love in their important textbook and are cited appropriately. The power throughput and loss testing was all performed by myself and programmed in Python. The RSoft testing in Section 8 was all performed by myself. The right angle chip was designed by my colleague Nemanja Jovanovic from Macquarie University and appropriately acknowledged. The analysis of the path length from the interferomentric fringe data was performed by Barnaby Norris and Peter Tuthill. The conclusions were written by myself. The Python code in the appendix was all written by myself, except for particular algorithms which were borrowed and acknowledged. All waveguides were fabricated by Simon Gross at Macquarie University along with design help from Nemanja Jovanovic who also contributed many hours grinding and polishing all of the chip designs. I would like to acknowledge the help of my advisors, Peter Tuthill and John O’Byrne, for making edits to this thesis. I certify that this report contains work carried out by myself, except where otherwise acknowledged. Signed……………………………………………………………… Date: 27 April 2012 3 Arbitrary Design of Three-Dimensional, Path Length Matched Waveguides Table of Contents 1. Introduction .............................................................................................................. 7 1.1 Dragonfly ............................................................................................................ 9 2. Theory .................................................................................................................... 12 2.1 Optical Waveguides ......................................................................................... 12 2.2 Interferometry ................................................................................................... 12 2.3 Aperture Masking and Closure Phases ............................................................ 14 2.4 Single-Mode Waveguides ................................................................................ 15 2.4.1 Direct Write Waveguides ........................................................................... 15 2.5 Simulations of Optical Waveguides .................................................................. 16 2.6 Design Requirements ....................................................................................... 17 2.6.1 Path Length Matching of Waveguides ....................................................... 17 2.6.2 Positioning Input and Output Coordinates ................................................. 18 2.6.3 Orthogonal Endpoints ................................................................................ 18 2.6.4 Continuity of Waveguides .......................................................................... 19 2.6.5 Waveguide Curvature ................................................................................ 20 2.6.6 Spatial Separation of Waveguides ............................................................. 20 2.6.7 Physical Chip Write Depth ......................................................................... 21 2.6.8 Waveguides crossing vertically .................................................................. 22 3. Design of Three-Dimensional Waveguides ............................................................ 23 3.1 Physical Design of the Remapper .................................................................... 23 3.1.1 The Interpolating Cubic Spline ................................................................... 24 3.1.2 Using the cubic spline to construct a waveguide ....................................... 25 3.1.3 Path Length Matching Multiple Waveguides .............................................. 29 3.2 Algorithm to Calculate Path Length of a Curve ................................................ 31 3.3 Translating a Two-Dimensional Spline Curve into Three Dimensions .............. 32 3.4 Spatial Separation of Waveguides ................................................................... 33 3.4.1 Determining Proximity between Neighboring Waveguides ........................ 34 3.4.2 Adjusting the Curves to Meet Proximity Requirements .............................. 35 3.4.3 Spatially Aligning Waveguides ................................................................... 37 3.5 Determining Radius of Curvature ..................................................................... 39 4 Arbitrary Design of Three-Dimensional, Path Length Matched Waveguides 4. Sidestep Design ..................................................................................................... 42 4.1 Adding a Lateral Sidestep to Avoid Interference .............................................. 43 4.2 Proximity Challenges ....................................................................................... 44 4.2.1 An Additional Lead-In Straight Section ...................................................... 44
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