Analysis of Quasi-Optical Components for Far-Infrared Astronomy Presented by Paul Kelly, B.Sc. A thesis submitted for Degree of Master of Science Department of Experimental Physics NUI Maynooth Co. Kildare Ireland May 2014 Head of Department Professor J. A. Murphy Research Supervisor Dr. Créidhe O'Sullivan Contents Contents ........................................................................................................................ i Abstract ....................................................................................................................... v Acknowledgements .................................................................................................... vi Chapter 1 Introduction .............................................................................................. 1 1.1 Introduction to Terahertz / Submillimetre Astronomy ........................................... 1 1.2 The Big Bang and the CMB ................................................................................... 4 1.2.1 The Big Bang ........................................................................................ 4 1.2.2 The Cosmic Microwave Background .................................................... 5 1.2.3 Temperature Anisotropies in the CMB ................................................. 6 1.2.4 CMB Polarization ................................................................................ 10 1.2.5 CMB Instrument Types ....................................................................... 13 1.2.6 CMB Experiments ............................................................................... 15 1.3 Other Terahertz Applications ............................................................................... 18 1.4 Summary and Thesis Outline ............................................................................... 21 Chapter 2 Techniques For Modelling Horn Antennas ......................................... 22 2.1 Introduction .......................................................................................................... 22 2.2 Waveguides .......................................................................................................... 22 2.2.1 Solutions to Maxwell's Equations in Waveguides .............................. 22 2.2.2 Rectangular Waveguides ..................................................................... 28 2.2.3 Cylindrical Waveguides ...................................................................... 32 i 2.3 Corrugated Horns ................................................................................................. 41 2.4 CST Studio Suite .................................................................................................. 44 2.4.1 CST Solver .......................................................................................... 47 2.4.2 CST Setup ........................................................................................... 48 2.4.3 Advantages & Disadvantages.............................................................. 50 2.5 Scatter Matrix Method .......................................................................................... 51 Advantages & Disadvantages....................................................................... 53 2.6 Far-Field Beam Patterns ....................................................................................... 54 2.7 Summary .............................................................................................................. 55 Chapter 3 Improvements to Scatter ....................................................................... 56 3.1 Introduction .......................................................................................................... 56 3.2 Specification of horn geometries for Scatter ........................................................ 56 3.3 Matrix Inversion ................................................................................................... 57 3.4 The Pseudoinverse ................................................................................................ 58 3.4.1 Calculating the Pseudoinverse of a Matrix in C .................................. 60 3.5 Examples Utilizing the Pseudoinverse Code ........................................................ 67 3.5.1 The 857-GHz Planck Horn .................................................................. 67 3.5.2 Small Gaps in Platelet Horns .............................................................. 68 3.6 Summary .............................................................................................................. 69 Chapter 4 Analysis of Platelet Horn Arrays for QUBIC ...................................... 71 4.1 Introduction .......................................................................................................... 71 4.2 QUBIC .................................................................................................................. 71 ii 4.2.1 Instrumental Set Up ............................................................................. 72 4.3 Platelet Formed horns ........................................................................................... 74 4.3.1 Advantages and Disadvantages of Platelet Feed Horn Arrays ............ 75 4.3.2 Adding a Thick Plate for Stability....................................................... 75 4.3.3 Adding a Thick Plate (simulations with CST) .................................... 77 4.3.4 Adding a Thick Plate (simulations with CST) .................................... 79 4.3.5 Experimental results ............................................................................ 81 4.3.6 Gaps between platelets ........................................................................ 88 4.3.7 Random Variations to Corrugations .................................................... 92 4.4 Summary .............................................................................................................. 96 Chapter 5 Analysis of Electroformed Corrugated Horns for the Planck Telescope ................................................................................................................... 98 5.1 Introduction .......................................................................................................... 98 5.2 Planck ................................................................................................................... 98 5.2.1 Instrumental set up .............................................................................. 98 5.3 Electroformed Horns .......................................................................................... 100 5.4 Analysis of Electroformed Horns ....................................................................... 101 5.4.1 Filled Corrugated Horn ..................................................................... 102 5.4.2 Damaged Corrugated Horn ............................................................... 113 5.4.3 Comparison between Filled and Damaged Horn .............................. 122 5.4.4 Partially Filled Corrugated Horn ....................................................... 124 5.4.5 Partially Damaged Corrugated Horn ................................................. 128 iii 5.5 Summary ............................................................................................................ 130 Chapter 6 Conclusions ........................................................................................... 132 6.1 Conclusion .......................................................................................................... 132 6.2 Author’s Contribution ........................................................................................ 136 Works Cited ............................................................................................................ 138 Appendix A ............................................................................................................. 144 Appendix B .............................................................................................................. 147 iv Abstract This thesis is concerned with the development and analysis of quasi-optical components used in experiments to measure of the CMB in the terahertz and submillimetre wavebands. I have concentrated on corrugated horn structures in the Planck and QUBIC experiments. A precise analysis of the electromagnetic and optical performance of such instruments is required if they are to reach the sensitivity goals required. The analysis of these components was done through computer simulations and experimentation. There were a number of techniques used to model the horns. These techniques were implemented in NUI Maynooth's in-house simulation code 'Scatter' and a commercial software package known as CST. They were used to predict the beam pattern of corrugated horns including the effects of likely manufacturing errors. NUI Maynooth's Vector Network Analyser was used to confirm the results obtained by the simulations. The results in this thesis show that variations in corrugated horn made with the efectroforming technique could result in significant degraded performance but that small gaps between the metal sheets in platelet arrays are acceptable. v Acknowledgements First of all I would like to thank my supervisor Dr. Créidhe O’Sullivan for her advice and commitment throughout this masters project, for always being helpful and patient, and for providing me with the opportunity to perform this research.