On waveplate polarimeters for

high precision CMB and

mm astronomy measurementsMaria Salatino

Physics Department “Sapienza Università di Roma”

Rencontres de Moriond, La Thuile, 13th-20th March 2010

cosmological +cosmological + astrophysical signalsastrophysical signals

Rotating Half Wave PlateRotating Half Wave Plate(HWP) + fixed polarizer(HWP) + fixed polarizer

components temperatures;components temperatures;non ideal parameters;non ideal parameters;internal reflections;internal reflections;reflections between componentsreflections between components

POLARIZEDPOLARIZEDDETECTEDDETECTEDSIGNALSIGNAL

new description of the HWP

SummarySummary of the of thepresentationpresentation

optimizationoptimizationexperimental setupexperimental setup(temperatures of(temperatures ofdistinct components, distinct components, bkg ...)bkg ...)

B-POL,B-POL,SPIDER,SPIDER,EBEX...EBEX...

Mueller formalism

Assumptions

PILOT

Principle of operation: rotating HWP followed

by a fixed polarizer

The HWP polarimeter:The HWP polarimeter: ideal behaviorideal behavior

HWP

]4sin4cos[2

1)(

)]([)(

210det

idealTRAS,

det

SSSS

SMMDW inHWPhorpol

polarizer

detector

t with

Stokes + Mueller matrix formalism

Ongoing and future polarization experiments

BPOL

PILOT

SPIDER

BRAINEBEX LSPE

QUBIC

HWP

polarizer

detector

The HWP polarimeter: real behaviorThe HWP polarimeter: real behavior

TPOL

1. Temperatures of the components + background

emission of polarized radiations

If they were constant, given typical temperatures ofCMBP experiments optical devices,…..

TBKG

they would add simply an offset contribution but…

HWP

polarizer

detector

The HWP polarimeter: real behaviorThe HWP polarimeter: real behavior

TPOL

2. Non ideal parameters (absorbing coefficients, HWP refraction indeces, ...)

Spectral dependence of theabsorbing coefficients(Savini et al., 2006)

ax , ay ≠ 0,1ne(), no()

TBKG

THE MUELLER FORMALISMTHE MUELLER FORMALISM

rotating HWP or QWP

sapphire HWP

3

2

1

0

00

00

0010

0001

S

S

S

S

) () Cos Sin(

) () -Sin Cos(

Advantages: simple description for the radiation detected by a polarimeter

Drawbacks: independence by the incidence angle; doesn’t depend on the frequencyassumption: 100% transmitted radiation.

)n(nc

π ν d)k(k oeoe

2 frequency incidence wave;d thickness crystalc speed of lightneextraordinary refraction indexnoordinary refraction index

x

y

y

x

oo

o

ooo

ee

e

ee

H

E

H

E

d)(k) Cosη

dk jSin(

d)Sin(kjηd) Cos(k

d) ) Cos(kη

dkj Sin(

d) Sin(kd) jCos(k

00

00

00

00 characteristic impedence of the medium

input and output waveIn vacuum

1 eo ηη

xx EH yy EH

THE ADACHI FORMALISM THE ADACHI FORMALISM

Advantages:Spectral dependence of

ν..n

ν.ν.ν..n

e

o

5

3122104

10313873)(

1011102210740533)(

(Savini G. et al., Applied Optics, 2006)

(Adachi S. et al., 1960)

OPTICALLY ACTIVEOPTICALLY ACTIVEMULTIPLE REFLECTIONSMULTIPLE 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 transmittedcomponent.

air

air

HWP

A new Mueller matrix for the transmittedfield by a HWP and for the reflected one;

Complicate expression, function of neno

(Salatino M. et al., in preparation)

0.737- 0.028 0. 0.

0.028- 0.737- 0. 0.

0. 0. 0.737 0.008

0. 0. 0.008 0.737

1.- 0. 0. 0.

0. . 1- 0. 0.

0. 0. 1. 0.

0. 0. 0. 1.

ideal HWP real HWP

HWP

polarizer

detector

The HWP polarimeter: real behaviorThe HWP polarimeter: real behavior

TPOL

3. Internal reflections

ax , ay ≠ 0,1

(Salatino M. et al., in preparation)

birefringency +multiple reflections

OAMR

1 plate -> complete solution + new Mueller matrix2 or more plates -> approximate solutions

TBKG

HWP

polarizer

detector

The HWP polarimeter: real behaviorThe HWP polarimeter: real behavior

TPOL

4. Reflections between components

emission of polarized radiations

ax , ay ≠ 0,1

Normal incidenceInput: monochromatic wave

Non monochromatic waves ->small circular polarization (few % S1)

TBKG

Detected signal due to CMB onlyLambda CDM model + T/S=0.1expected signal: 10-7 K

Real HWP (absorption + OAMR)Similar signal amplitude butdifferent height of the peaks(2theta component)

Ideal HWP Signal when staring at a given pixel, while HWP rotates

Real HW

P

POL ->Cos(2 theta)

BKG->Cos(2 theta)

The radiation reflected by the HWP produces a cos(2*theta) which contaminatesthe 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.

Spurious10 mK @ 2

CMB0.6 K @ 2+4

Spurious0.3 K @ 2

Total signal dominated by HWP emission@ 2

Can we separate it ?

NON LINEARITIESThe 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 thedetectors 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

NON LINEARITIES

Greater effect on S1 with respect to S2,limits on the bkg

HWP WITH ANTI REFLECTION COATING

HWP

The efficiency of the polarimeter increasesby a factor > 2.

The spurious signal reflected by the HWP isreduced by at least one order ofmagnitude.

However here there could be a component modulated at 4 theta; which would be extremely dangerous!

Naive model

WORK IN

PROGRESS

PROGRESS

Possible solution…

HWP

detector arrays

HWP

detector + pol arrays

Reduction of the detected emission reflected from the HWP +polarized emissionwith differentphases

He tank

secondarymirror

polarizer

124

cm

70 cm

vapo

r co

oled

shi

elds

fiber

glas

s cy

linde

rs

tertiarymirror

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.