Anti-Reflection Coating of Large-Format Lenses for Sub-Mm Applications
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Anti-reflection coating of large-format lenses for sub-mm applications Peter C. Hargrave Cardiff University, Department of Physics & Astronomy, 5 The Parade, Cardiff CF24 3AA, UK [email protected] Giorgio Savini Department of Physics and Astronomy, University College London, Gower Street, London CF24 3AA, UK ABSTRACT We have recently developed a repeatable and reliable technique for anti-reflection coating large lenses, suitable for use at sub-mm wavelengths. Small lenses have been coated using this technique, and are currently flying on-board Herschel- SPIRE and Planck-HFI. We have recently coated much larger, highly-curved lenses (up to 380 mm diameter) for the EBEX and Polarbear cosmic microwave background (CMB) experiments. In this paper, we present details of the coating technique, experimental results of coated samples, and comparison of the results to theoretical predictions. We also present an indication of their technology readiness level (TRL) for future space applications such as B-Pol. Keywords: sub-mm, lens, anti-reflection, coating, optics, telescope 1. INTRODUCTION There is increasing need to employ refractive optical components in millimetre (mm) and submillimetre (sub-mm) optical systems. This is particularly true for experiments designed to detect the B-mode signal from the polarization of the cosmic microwave background. In order to reach the sensitivity goals of such experiments, it is unlikely that a Gregorian reflector and feedhorn system alone, such as used on Planck [1], will have enough throughput. To achieve higher focal plane area utilization, the individual pixels must be smaller, leading to a higher edge taper. This problem has traditionally been addressed in mm and sub-mm systems by the use of a reflective cold Lyot stop, created with re- imaging optics. Many of the new generation of focal plane detector array technologies also require a flat, telecentric field, also created with re-imaging optics. As throughput grows and f-number shrinks, re-imaging optics with reflectors becomes more difficult because of the limited amount of space for folded beams to clear obstructions. Cold lenses are the natural solution, but they come with a set of their own problems. Several experiments which employ cold re-imaging lenses coupled to a Gregorian telescope have already been deployed (ACT, SPT, GBT) or are nearing deployment (POLARBEAR and EBEX [2]). Additionally, the BICEP and BICEP2 [3] experiments employ solely refractive optics. However, these systems are still in the initial operational phase, and the full polarization performance has yet to be determined. Future CMB-polarization satellite missions have been proposed (EPICS, CMB-Pol, B-Pol) which make use of several refractive telescopes, each telescope optimised over a narrow frequency band. This optical configuration should provide low aberrations and polarization for a large focal plane and large field of view. Additionally, it should provide minimal beam imperfections, such as differential ellipticity, differential beam width and differential gain. But there are many uncertainties over the performance modelling of such systems. Reflections in optical systems cause loss and lead to systematic effects. For typical plastic lenses, reflections can be >10% at each surface. Reflections can be >30% for silicon substrates. Additionally, reflection from lenses causes polarized ghosting which must be reduced. These effects can be greatly reduced by the use of anti-reflection (AR) coatings. This paper describes a new technique for applying broadband mm and sub-mm anti-reflection coating layers to large, highly-curved lens substrates. Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy V, edited by Wayne S. Holland, Jonas Zmuidzinas, Proc. of SPIE Vol. 7741, 77410S © 2010 SPIE · CCC code: 0277-786X/10/$18 · doi: 10.1117/12.856919 Proc. of SPIE Vol. 7741 77410S-1 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 09/02/2014 Terms of Use: http://spiedl.org/terms 2. ANTI-REFLECTION COATING THEORY AND TECHNIQUES 2.1 Theory and design For a slab of dielectric material of index of refraction ns, without AR coatings the reflective loss is given by 2 ª()1- ns º R … » (1) ()1+ ns ¼ at each surface at normal incidence. For silicon (ns=3.4), R is 30%. The application of anti-reflection coating on a flat slab of dielectric substrate, with a given index of refraction ns follows two very simple guidelines. The first is to ensure that a coating material with an optical index of refraction nc is available, where nc ns at the same frequency at which ns is measured. The second requirement is to make sure that it is possible to obtain, manufacture or engineer the thickness of the coating material such that its resulting thickness is one quarter of the required transmission wavelength within the material. These simple theoretical requirements don’t always translate as easily into the real world, where materials are available with a limited range of index of refraction, which limits choice of materials and application. Moreover, a number of secondary requirements, which do not concern optical design directly, need to be taken into account which are highly relevant to the success of the application. For instance, if the coated lens needs to be cooled, then thermal expansion coefficients of the substrate and coating should be matched as closely as possible if the system is to survive cryogenic cycling. The nature of anti-reflection coatings can be very different depending on the wavelength that the coating is optimised for. As in this work we are focussing on coatings for large optical elements to be used at sub-mm to mm wavelengths, we will discuss only issues relevant to such materials. Lens and coating material design considerations Design considerations when choosing the lens substrate and coating materials should include:- x Thermal conductivity of substrate material. If the lens component is of large diameter and is to be used cold, then radiative heating of the lens needs to be controlled by the use of thermal IR blocking filters. x Availability of suitable coating materials. The range of materials with a suitable refractive index to match a certain substrate material is limited. The choice may be further limited by the form and thermo-mechanical properties of that coating material. x Machineability of substrate material. x Intrinsic birefringence of the substrate material. x Stress-induced birefringence caused by cooling to cryogenic temperatures. x Transmission losses in the substrate material. The waveband of the experiment obviously limits this choice. Typical material data for suitable materials for use in the mm and sub-mm range are shown in Table 1. It should be borne in mind that these material parameters will vary as a function of temperature and as a function of frequency. More detailed material information can be found in Lamb (1996) [4]. Coating thickness and index Unlike optical and near infrared coatings, where deposition is obtained with layers which are deposited through evaporation or sputtering, the thickness required at these large wavelengths makes it more practical to employ layers of material that are available at thickness values close to the required quarter-wavelength in the material (few hundreds of microns). A suitable coating material must meet the requirements on refractive index for matching to the substrate, but also be flexible and ductile enough to allow it to be laminated to a curved substrate. The theoretical ideal value for the required thickness can not always be exactly coincident with the available values of coating material thickness, or can deviate slightly from the achieved thickness after application due to the bonding Proc. of SPIE Vol. 7741 77410S-2 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 09/02/2014 Terms of Use: http://spiedl.org/terms process. Similarly, the index of refraction is unlikely to be an exact match to the theoretically required value indicated above, or will have a wavelength dependence that will unlikely match the above relation at all wavelengths. For these reasons, modelling the efficiency of the anti-reflection coating becomes necessary, and a wavelength dependent transmission line code has been produced in order to predict the performance of the coating prior to its application. This allows for a tuned design of the coating in question, allowing us to choose in some cases slightly different thickness for the two sides of the lens when the exact required value happens to be in between two readily available values, or when the lens is required to work in a spectral range larger than a small interval around a given wavelength. Typically this is required when a band width >30% is desired. After the coating is applied, spectroscopic measurements of the optical element will allow the recovery of the exact optical parameters by comparing with variations on the original simulation. Spectroscopic measurements are straightforward for a flat slab, and can be done with a lens too providing that either a small aperture at the centre is used, or that the comparison be made with an identical uncoated lens. Table 1. Dielectric properties of materials suitable for mm and sub-mm lenses and coatings. Material Index n Loss tangent (150GHz), tan d Silicon 3.42 2.2 x 10-4 Sapphire 3.07 / 3.40 2.3 / 1.2 x 10-4 TMM 10i 3.13 TMM 10 3.03 TMM 6 2.55 TMM 4 2.12 TMM 3 1.81 Quartz 1.87 0.001 Cirlex® 1.84 0.008 Stycast 1266 1.68 0.023 HDPE 1.54 3 x 10-4 LDPE 1.51 3 x 10-4 Polypropylene 1.50 6.5 x 10-4 PTFE 1.44 3 x 10-4 Porous PTFE 1.2 Coating thermo-mechanics A serious design consideration for coating lenses to be used at cryogenic temperatures is that, as far as possible, the thermal expansion coefficients of the substrate material and coating material should be closely matched, if the system is to survive multiple thermal cycles.