On waveplate polarimeters for high precision CMB and mm astronomy measurements Maria Salatino Physics Department “Sapienza Università di Roma” Rencontres de Moriond, La Thuile, 13 th -20 th March 2010

cosmological + cosmological + astrophysical signals astrophysical signals Rotating Half Wave Plate (HWP) + fixed polarizer components temperatures; non ideal parameters; internal reflections; reflections between components POLARIZEDDETECTEDSIGNAL new description of the HWP Summary of the presentation optimization experimental setup (temperatures of distinct components, bkg...) B-POL,SPIDER,EBEX... Mueller formalism Assumptions PILOT

Principle of operation: rotating HWP followed by a fixed polarizer The HWP polarimeter: ideal behavior ideal behavior HWP polarizer detector with Stokes + Mueller matrix formalism

Ongoing and future polarization experiments BPOL PILOT SPIDER BRAIN EBEX LSPE QUBIC

HWP polarizer detector The HWP polarimeter: real behavior T POL 1.Temperatures of the components + background emission of polarized radiations If they were constant, given typical temperatures of CMBP experiments optical devices,….. T BKG

they would add simply an offset contribution but…

HWP polarizer detector The HWP polarimeter: real behavior T POL 2.Non ideal parameters (absorbing coefficients, HWP refraction indeces,...) Spectral dependence of the absorbing coefficients (Savini et al., 2006) a x, a y ≠ 0,1 n e ( ), n o ( ) T BKG

THE MUELLER FORMALISM rotating HWP or QWP 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.

frequency incidence wave; d thickness crystal  c speed of light  n e  extraordinary refraction index  n o  ordinary refraction index   characteristic impedence of the medium input and output wave In vacuum THE ADACHI FORMALISM Advantages: Spectral dependence of  (Savini G. et al., Applied Optics, 2006) (Adachi S. et al., 1960)

OPTICALLY ACTIVE MULTIPLE REFLECTIONS (OAMR) (OAMR) Ingredients: dielectric reflection; optical action HWP; spectral dependence Adachi; Fresnel equations for an anisotropic medium. 2 output waves from the HWP: the reflected and transmitted component. air HWP A new Mueller matrix for the transmitted field by a HWP and for the reflected one; Complicate expression, function of n e  n o   (Salatino M. et al., in preparation)

ideal HWP real HWP

HWP polarizer detector The HWP polarimeter: real behavior T POL 3. Internal reflections a x, a y ≠ 0,1 (Salatino M. et al., in preparation) birefringency + multiple reflections OAMR 1 plate -> complete solution + new Mueller matrix 2 or more plates -> approximate solutions T BKG

HWP polarizer detector The HWP polarimeter: real behavior T POL 4. Reflections between components emission of polarized radiations a x, a y ≠ 0,1 Normal incidence Input: monochromatic wave Non monochromatic waves -> small circular polarization (few % S 1 ) T BKG

Detected signal due to CMB only Lambda CDM model + T/S=0.1 expected signal: K Real HWP (absorption + OAMR) Similar signal amplitude but different height of the peaks (2theta component) Ideal HWP Signal when staring at a given pixel, while HWP rotates Real HWP

POL -> Cos(2 theta) BKG-> Cos(2 theta) 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. e=1% 150 GHz Total

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. Spurious 10 m 2  CMB 0.6  2  +4  Spurious 0.3  2  Total signal dominated by HWP 2  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. out in 22 2 

NON LINEARITIES Greater effect on S 1 with respect to S 2, limits on the bkg

HWP WITH ANTI REFLECTION COATING HWP The efficiency of the polarimeter increases by a factor > 2. 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! Naive model WORK INPROGRESS

Possible solution… HWP detector arrays HWP detector + pol arrays Reduction of the detected emission reflected from the HWP + polarized emission with different phases

He tank secondary mirror polarizer 124 cm 70 cm vapor cooled shields fiberglass cylinders tertiary mirror Polarized Instrument for Long Wavelenght Observation of the Tenuous interstellar medium Targets: cirrus clouds at high Galactic latitudes, Galactic plane 1st flight Kiruna (Sweden) ? Off-axis telescope (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 (Salatino et al., 2008) HWP at 4K

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  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.