On waveplate polarimeters for high precision CMB and mm astronomy measurements Maria Salatino Physics Department “Sapienza Università di Roma” Rencontres de Moriond, La Thuile, 13th-20th March 2010 Summary of the presentation cosmological + astrophysical signals Rotating Half Wave Plate (HWP) + fixed polarizer Mueller formalism components temperatures; non ideal parameters; internal reflections; reflections between components B-POL, SPIDER, EBEX... PILOT POLARIZED DETECTED SIGNAL new description of the HWP Assumptions optimization experimental setup (temperatures of distinct components, bkg ...) The HWP polarimeter: ideal behavior HWP Principle of operation: rotating HWP followed by a fixed polarizer polarizer hor Wdet ( ) D [ M pol M HW P ( )] Sin S det TRAS, ideal 1 ( ) [ S 0 S1 cos 4 S 2 sin 4 ] 2 with detector t Stokes + Mueller matrix formalism SPIDER Ongoing and future polarization experiments QUBIC BPOL EBEX LSPE BRAIN PILOT The HWP polarimeter: real behavior TBKG 1. Temperatures of the components + background HWP polarizer TPOL emission of polarized radiations If they were constant, given typical temperatures of CMBP experiments optical devices,….. detector they would add simply an offset contribution but… The HWP polarimeter: real behavior TBKG 2. HWP ax , ay ≠ 0,1 ne(n), no(n) polarizer detector TPOL Non ideal parameters (absorbing coefficients, HWP refraction indeces, ...) Spectral dependence of the absorbing coefficients (Savini et al., 2006) THE MUELLER FORMALISM rotating HWP or QWP 1 0 0 0 0 0 1 0 0 Cos() 0 Sin() Cos() 0 0 -Sin () S0 S1 S 2 S 3 sapphire HWP Advantages: simple description for the radiation detected by a polarimeter Drawbacks: independence by the incidence angle; doesn’t depend on the frequency; assumption: 100% transmitted radiation. THE ADACHI FORMALISM (Adachi S. et al., 1960) (k e ko ) j Sin(k e d) Cos(k e d) j Sin( ke d ) Cos(k d) e ηe 0 0 0 0 2π ν d (ne no ) c 0 0 Cos(k o d) jSin( 0 jηo Sin(k o d) Cos(k o d) 0 ko d ) ηo Advantages: Spectral dependence of no (n ) 3.053 4.7 104 ν 2.2 1010 ν 2 1.11012 ν 3 ne (n ) 3.387 1.3 10 ν 5 (Savini G. et al., Applied Optics, 2006) n d c ne no frequency incidence wave; thickness crystal; speed of light; extraordinary refraction index; ordinary refraction index. characteristic impedence of the medium Ex Hy E y H x input and output wave In vacuum ηo ηe 1 H x Ex H y Ey air HWP air OPTICALLY ACTIVE MULTIPLE REFLECTIONS (OAMR) Ingredients: dielectric reflection; optical action HWP; spectral dependence Adachi; Fresnel equations for an anisotropic medium. A new Mueller matrix for the transmitted field by a HWP and for the reflected one; Complicate expression, function of ne , no , 2 output waves from the HWP: the reflected and transmitted component. (Salatino M. et al., in preparation) 1. 0. 0. 0. 0. 0. 1. 0. 0. - 1 . 0. 0. ideal HWP 0. 0. 0. - 1. 0.737 0.008 0. 0. 0.008 0.737 0. 0. 0. 0. - 0.737 0.028 real HWP 0. 0. - 0.028 - 0.737 The HWP polarimeter: real behavior TBKG 3. Internal reflections HWP ax , ay ≠ 0,1 polarizer TPOL birefringency + multiple reflections detector OAMR 1 plate -> complete solution + new Mueller matrix 2 or more plates -> approximate solutions (Salatino M. et al., in preparation) The HWP polarimeter: real behavior TBKG 4. Reflections between components HWP ax , ay ≠ 0,1 emission of polarized radiations TPOL polarizer Normal incidence Input: monochromatic wave Non monochromatic waves -> small circular polarization (few % S1) detector Detected signal due to CMB only Lambda CDM model + T/S=0.1 expected signal: 10-7 K Signal when staring at a given pixel, while HWP rotates Real HWP (absorption + OAMR) Similar signal amplitude but different height of the peaks (2theta component) e=1% 150 GHz BKG-> Cos(2 theta) POL -> Cos(2 theta) Total The radiation reflected by the HWP produces a cos(2*theta) which contaminates the CMBP Stokes parameters. Necessity of cooling down the polarizer and to reduce the background. CMB 0.6 mK @ 2+4 Spurious 10 mK @ 2 Spurious 0.3 mK @ 2 Total signal dominated by HWP emission @ 2 The result of the addition of the modulated emission of BKG and Pol depends on the relative angle between the CMBP polarization angle and the orientation of the wire grid. Can we separate it ? NON LINEARITIES The disturbance signals at 2theta (produced by unpolarized background, waveplate emission and reflected polarizer emission) are easily separated from the sky signal at 4theta. However if they are too large they challenge the linearity of the detectors and the dynamic range of the data acquisition system. Bolometers become non linear and start to saturate so that a pure 2 theta signal acquires a 4theta component. 2 out in 24.. NON LINEARITIES Greater effect on S1 with respect to S2, limits on the bkg HWP WITH ANTI REFLECTION COATING Naive model The efficiency of the polarimeter increases by a factor > 2. HWP The spurious signal reflected by the HWP is reduced by at least one order of magnitude. However here there could be a component modulated at 4 theta; which would be extremely dangerous! Possible solution… HWP HWP Reduction of the detected emission reflected from the HWP + polarized emission with different phases detector arrays detector + pol arrays 1st flight Kiruna (Sweden) Off-axis telescope (70 cm) He tank polarizer fiberglass cylinders 124 cm Targets: cirrus clouds at high Galactic latitudes, Galactic plane vapor cooled shields Polarized Instrument for Long Wavelenght Observation of the Tenuous interstellar medium ? secondary mirror tertiary mirror 70 cm The PILOT Cryogenic Waveplate Rotator innovative MECHANICAL SYSTEM driven by a DC motor running at room temperature the control of its position is assured by a 3-bit optical encoder fed by optical fibers HWP at 4K (Salatino et al., 2008) CONCLUSIONS AND FUTURE DEVELOPMENTS (1/2) A study of the sistematics introduced in a CMBP polarimeter has been done taking into account the emission of the polarizer and the unpolarized radiative background; both the thermal emission of the polarizer and the unpolarized bkg are modulated at 2; this has been done by means of a new description of the HWP which takes into account multiple reflections, the transmitted and reflected fields inside an anisotropic medium, …. the non linear behavior of the bolometers introduces a 4 component -> constraints on the bkg; possible dangerous signals at 4 can be reduced with 1 polarizer per bolometer; in the PILOT experiment a DC motor running at room temperature will rotate the HWP at 4K. CONCLUSIONS AND FUTURE DEVELOPMENTS (2/2) The HWP description has been done with some assumptions: normal incidence ; input monochromatic wave; no ARC. Future work: slant incidence -> effect of the mixing of extraordinary and ordinary ray on the incoming ray; input non monochromatic wave; full model ARC ; achromatic HWP (multi-plates) with multi-layer ARCs. -------------------------------------------------------Full simulation of a balloon/ satellite experiment -> multi-pixel analysis of these sistematics.