___________________________________________________ DESIGN AND ANALYSIS OF A QUASI-OPTICAL BEAM COMBINER FOR THE QUBIC CMB INTERFEROMETER ___________________________________________________ David G. Bennett B.Sc. Research Supervisor: Dr. Créidhe O'Sullivan Head of Department: Prof. J.A. Murphy A thesis submitted for the degree of Doctor of Philosophy Sub-mm Optics Research Group Department of Experimental Physics National University of Ireland, Maynooth Co. Kildare Ireland 9th July 2014 Contents 1 The Cosmic Microwave Background 8 1.1 A signal from the early Universe . 8 1.2 A brief history of CMB observations . 9 1.3 Modern Cosmology and the CMB . 12 1.3.1 The Big Bang and the expanding Universe . 12 1.3.2 CMB temperature power spectra . 14 1.3.3 Primary temperature anisotropies . 18 1.3.4 Secondary anisotropies . 19 1.3.5 CMB Polarization . 21 1.3.6 The CMB and Inflation . 27 1.4 Recent CMB experiments . 28 1.5 The CMB and the cosmological parameters . 29 1.6 Conclusions . 33 2 QUBIC: An Experiment designed to measure CMB B-mode polarization 35 2.1 Introducing QUBIC . 35 2.2 Interferometry . 35 2.2.1 Interferometers in astronomy . 35 2.2.2 Radio receivers . 37 2.2.3 Additive Bolometric Interferometry . 39 2.3 The QUBIC experiment . 41 2.3.1 QUBIC specifications . 42 2.4 Phase Shifting and equivalent baselines . 49 2.5 Quasi optical analysis techniques . 55 2.5.1 Methods for the optical modeling of CMB experiments . 55 2.5.2 Geometrical optics . 58 2 2.5.3 Physical optics (PO) . 59 2.5.4 Quasi optics . 62 2.5.5 Fourier optics . 66 2.5.6 Modeling lenses . 68 2.6 Thesis outline . 70 2.7 Conclusions . 70 3 Dual reflectors for bolometric Fizeau interferometers 72 3.1 The Optical Combiner for QUBIC . 72 3.1.1 Focal Systems . 73 3.1.2 Performance of a Telescopic Combiner . 75 3.1.3 Disadvantages of lenses of QUBIC . 77 3.1.4 Disadvantages of on-axis reflector designs for QUBIC. 78 3.1.5 Cassegrain versus Gregorian . 80 3.2 Dual reflectors . 80 3.2.1 The geometry off-axis dual reflectors . 81 3.2.2 Designing off-axis dual reflectors . 81 3.2.3 Beam distortion in dual reflectors . 84 3.3 Compensated dual reflectors . 89 3.3.1 Summary of off-axis dual reflectors for implementation in a CMB Fizeau interferometer . 126 3.3.2 Comparison of crossed reflectors for short focal length systems . 129 3.4 Alternative geometries for the combiner in a QUBIC-type experiment . 136 3.4.1 Fold mirror and a crossed Cassegrain dual reflector . 136 3.4.2 Fold mirror and a GCC examined using equivalent baselines . 140 3.4.3 GCC dual reflector and a concave hyperboloid . 144 3.5 Conclusions . 146 4 Optical Combiners for QUBIC 149 4.1 Possible optical combiners for QUBIC . 149 4.1.1 Introduction . 149 4.1.2 General crossed Cassegrain (GCC) . 151 4.1.3 Compensated Gregorian (CG) . 157 4.1.4 Constraints on the mirror dimension in the GCC and CG . 161 4.2 Effect of changes in QUBIC requirements . 162 3 4.2.1 Adjustment to combiners . 163 4.2.2 Zemax optimization to generate Telecentric combiners . 169 4.2.3 Off-axis parabolas . 175 4.2.4 Details of the geometry of the dual reflectors . 184 4.3 Power coupled to the bolometers . 185 4.4 Leakage concerns in a general crossed Cassegrain (GCC). 198 4.5 Conclusions . 200 5 Lens Design 201 5.1 Gaussian beam telescope and CATR combination . 201 5.1.1 Using Zemax to model the fringe patterns generated by a Gaus- sian beam telescope and CATR combiner . 205 5.2 Fully refractive combiner for QUBIC . 208 5.2.1 Telecentric lens combiners. 208 5.2.2 Gaussian and Cooke Triplet designs . 216 5.2.3 Symmetric double lenses that ignore field curvature. 220 5.3 Analysis of refracting combiners . 224 5.3.1 Using Zemax to model the fringe patterns generated by a lens combiner . 224 5.4 Conclusions . 227 6 QUBIC2.0 228 6.1 Introduction . 228 6.2 QUBIC2.0 . 228 6.2.1 Problems with the QUBIC design . 228 6.2.2 Modulating the sky polarization using a rotating half wave plate 235 6.2.3 QUBIC2.0 as a dirty imager . 240 6.2.4 Calibration techniques . 246 6.2.5 Cyrostat upgrades . 249 6.2.6 Remaining issues . 252 6.3 QUBIC2.0 optical combiner . 253 6.3.1 Analysis of optical combiners . 255 6.3.2 PSF of reflector combiners . 255 6.3.3 PSF of lens combiners . 259 6.4 Loss of sensitivity caused by optical combiners . 263 4 6.5 Conclusions . 266 7 Birefringence in CMB Polarimeters 267 7.1 Introduction . 267 7.2 A brief summary of QUaD . 267 7.2.1 The QUaD polarimeter . 267 7.2.2 QUaD model in Zemax . 271 7.2.3 Introduction to birefringence. 271 7.3 Investigation of possible birefringence in QUaD . 274 7.3.1 Using Zemax to investigate birefringence in QUaD . 274 7.4 Optimizations to identify QUaD crystal axes . 293 7.5 Zemax optimizations . 293 7.5.1 Displacements due to optimized crystal axes. 293 7.5.2 Results obtained by randomizing the crystal axis . 300 7.6 Birefringence in QUBIC lens combiners. 301 7.7 Conclusions . 303 8 Conclusions 307 Appendices 326 5 Acknowledgments There are quite simply no words that can express my gratitude to my supervisor Dr. Cr´eidheO'Sullivan. Also to quantify my thanks to Prof. Anthony Murphy and the NUIM Experimental Physics department will require a logarithmic scale. I am deeply grateful to my parents, brother, grandparents and my family. And finally many thanks to my friends and colleagues, both new and old. And finally a special thanks to Lee and Dave who saved the entire day at the last minute !!! Abstract In winter 2009 a number of physicists met in Paris to discuss the prospect of ob- serving the CMB B-mode polarization using a novel technique called bolometric in- terferometry. This was the first meeting of what would later become the QUBIC collaboration. In this thesis we discuss the scientific reasons for CMB observation, we present a detailed explanation of how QUBIC will use bolometric interferometry to measure CMB polarization and in particular we discuss the author's contribution to the project. As part of the sub-mm optics research group in the National University of Ireland Maynooth the author was charged with the design and modeling of the optics that would focus the beam from the sky onto the bolometric detectors. This thesis describes various types of reflecting and refracting optics that were investigated. The results we present are useful not only for the QUBIC instrument, but for the design of imaging experiments in general. Detection of CMB B-mode polarization is one of the supreme goals of modern cosmo- logy. The faintness of this signal, combined with the interferometric observing tech- nique, places extreme performance specifications on the QUBIC optics. Fortunately, as we shall show, there are types of well-known reflecting and refracting telescopes that are suitable for QUBIC. In this thesis I propose a design for the quasi-optical combiner that will perform as required. 1 The Cosmic Microwave Background Between the idea And the reality Between the motion And the act T. S. Eliot 1.1 A signal from the early Universe The Cosmic Microwave Background (CMB) is a highly red-shifted thermal radiation signal from the early Universe. From its initial prediction and detection to current attempts to map its polarization the CMB has profoundly deepened our understand- ing of the Universe. To date the CMB has the most accurately measured black body spectrum in nature. Its black body spectrum corresponds to a temperature of T = 2:7 K and it is responsible for a \glow" across the cosmos not associated with a stellar or galactic source. Initially thought to be spurious systemic noise, the CMB has al- lowed us to quantify the curvature of space time as well as ordinary and dark-matter densities. A plethora of scientific knowledge has emerged from the quantification of CMB temperature anisotropies. Detection of CMB polarization is expected to her- ald a new era of understanding of inflationary cosmology. In this chapter we briefly discuss the characteristics of the Microwave Background from its origin to its tem- perature and polarization spectrum. We also present the case for the further study of the CMB concluding with the importance of detecting the extremely faint B-mode polarization. 8 1.2 A brief history of CMB observations For almost 50 years cosmologists have made remarkable attempts to observe the CMB with greater and greater sensitivity. These efforts culminated in May 2009 with the launch of ESA's Planck satellite [1]. Like many scientific milestones the initial discov- ery of the CMB was purely accidental. Predicted by Alpher, Gamov and Hermann in 1947 [2] as a consequence of a Freidmann-Lema^ıtreUniverse it lay undetected until 1965 when two radio astronomers (Penzias and Willson) encountered excess noise in a well calibrated horn antenna. The signal causing this noise appeared isotropic and they estimated that it corresponded to a temperature of 3.5 ± 1.0 K. Following dis- cussions with various other researchers the noise was linked with the relic black body radiation predicted by Alpher and Herman. In 1965 two papers were published that would dramatically influence the course of far infrared astronomy over the next 50 years. The first by Penzias and Wilson detailed their observations [3].