refractive index of silica aerogel: uniformity and...

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Refractive index of silica aerogel:

uniformity and dispersion law

Tito BellunatoINFN Sezione di Milano–Bicocca

RICH 2007 Trieste – October 18th, 2007

Outline

• Silica aerogel

– Physical and optical properties

• Refractive index measurement

– Minimum deflection

• Refractive index uniformity

– Laser deflection: monochromatic

– Charged particle beam: Cherenkov spectrum

• Wide spectrum dispersion measurement

– UV lamp + Monochromator

RICH 2007 Trieste – October 18th, 2007 2 Tito Bellunato

Silica Aerogel

– Silica aerogel is a linked network of SiO2

nanocrystals, 2 − 5 nm in diameter.

– Tunable density ( ρ ∼ 0.15 g/cm3) → tunable

refractive index n

– We tested tiles with dimension 200 × 200 × 50

mm3 and n ' 1.03 produced by the Boreskov

Institute in Novosibirsk.

The refractive index is measured with

the minimum deviation method. Ne-He Laser

Filters L

x

CCD

Aerogel

Φθout

Turning Table

θin

n =

sin

„

Φ + θout

2

«

sin

„

Φ

2

«


Refractive Index Inhomogeneity

– The refractive index of aerogel depends on the

density according to n(λ) = 1 + k(λ)ρ with

k ' 0.21 at λ = 400 nm

– local density fluctuations lead to variations of

the refractive index within the tile

– these variations contribute to the θC Cherenkov

angle accuracy

Two methods developed to evaluate the homogeneity

– laser beam deflection

– Cherenkov angle measurement

LHCb requirement:

Max variation σ(n − 1)/(n − 1) < 1%

corresponding to σi(θC) ' 1.17 mrad

when σtot(θC) ' 2.6 mrad



Electromagnetic radiation bends if there is a refractive

index gradient transverse to the direction of propagation

t

Aerogel block

δ

He-Ne Laser

∆z

CCDy

L

Laser Beam Method

Assuming parallel faces for the tile,

the deviation angle δ is proportional

to the refractive index gradient

dn

dy' n

δ(y)

t⇒ ∆n(y) =

n

t

Z y

y0

δ(y)dy



Laser Aerogel CCD camera

Y axis

Sample measurement with

gradient towards the sides:

100 × 100 × 41 mm3

0

0.05

0.1

0.15

0.2

x 10-2

0 20 40 60 80 100

Y (mm)

∆n(y

)

A=0.9558C=0.0060 µm4/cm

– fast feed–back method

– one wavelength at a time can be monitored

– extrapolation to the full wavelength range

σ(n − 1)/(n − 1) ∼ 1.3%


APACHE

Aerogel Photographic Analysis by CHerenkov Emission

� table–top RICH detector with b/w film as photon detector

� 500 MeV electrons from the DAΦNE Beam Test Facility in Frascati

� scanning the beam entrance point along the aerogel surface

N2

Film

Aerogel

Mirror

e- beam

Photons

Aerogel Holder

Spherical MirrorFilm

Beampipe

Aerogel200 × 200 × 50 mm3


APACHE

– Cherenkov ring width dominated by

chromaticity n = n(λ)

aerogel ring

N2 ring

GEANT4


APACHE

– Cherenkov ring width dominated by

chromaticity n = n(λ)

aerogel ring

N2 ring

DATA


APACHE

– 25 entrance points measured (a 200 × 200 × 50 mm3 tile tested)

– retracking algorithm to build the distribution of reconstructed θC

– resolution: ∼ 0.3 mrad, including systematics (GEANT4)


APACHE





APACHE




0

500

1000

1500

2000

2500

3000

x 10 3

0 0.05 0.1 0.15 0.2 0.25 0.3

θC (rad)

Ligh

t Int

ensit

yA=0.9558C=0.0060 µm4/cm


APACHE




0

500

1000

1500

2000

2500

3000

x 10 3

0 0.05 0.1 0.15 0.2 0.25 0.3

θC (rad)

Ligh

t Int

ensit

yA=0.9558C=0.0060 µm4/cm

Surface plot of n − n̄

02468

101214161820

0 2 4 6 8 10 12 14 16 18 20

-0.4

-0.2

0

0.2

0.4

x 10-3

X (cm)

Y (c

m)

σ(n − 1)/(n − 1) = (0.76 ± 0.01)%

The very promising results from the APACHE runs show that large transverse size

aerogel tiles now available comply with the homogeneity requirements of LHCbRICH 2007 Trieste – October 18th, 2007 13 Tito Bellunato

Dispersion law

– Chromatic dispersion is often the source of the dominant contribution to σθ

in RICH detectors with silica aerogel as radiator

– A correct parameterisation of n(λ) is essential for a realistic simulation of the

detector and a more performing pattern recognition

– There are several heuristic models, based on the Lorentz-Lorenz law:

n2− 1

n2 + 2= cf (Eγ) with c =

4πa30ρNA

3M

– f(Eγ) can be parameterised in terms of a multi–pole Sellmeier function as:

f (E) =N∑

j=1

Fj

E2j − E2

γ


Dispersion - Setup

Usual prism method with some important modifications:

– A UV lamp coupled to a monochromator provides a monochromatic source,

an objective allows to have parallel rays at the output

– The refracted beam stops on a fine mesh screen

– Centre of gravity of the spot is calculated taking a picture of the screen with

a digital camera

– Measurements taken at fixed angle instead of minimal deviation condition,

hard to find at short wavelengths

We were able to take data in the range 350–700 nm, well matched to the spectrum

of detected photons from the aerogel in LHCb.

Below 350 nm the transmission of the objective is too poor.


Dispersion

– A one–pole Sellmeier function fits well the data

– Two superimposed poles are found in a two–poles fit

As a function of λ:

n2(λ) − 1 =a0λ

2

λ2− λ2

0

The pole is found at 83.2 nm. The den-

sity dependent coefficient is consistent

with the one calculated from the mea-

sured density of the aerogel sample.Wavelength (nm)

300 350 400 450 500 550 600 650 700 750

Refra

ctive

Inde

x

1.0280

1.0282

1.0284

1.0286

1.0288

1.0290

1.0292

1.0294

1.0296

/ ndf 2χ 5.534 / 15 0a 4.383e-05± 0.05639 0λ 1.246± 83.22

/ ndf 2χ 5.534 / 15 0a 4.383e-05± 0.05639 0λ 1.246± 83.22

Dispersion Law


Comparison of different parameterisations

The esperimental points are compared to various parameterisations, all properly

scaled to match the laser measurement n(632.8 nm) = 1.0282.

The same n(λ) laws are compared in simulations.– n1 is the unphysical approximation

n=constant.

– n2 is the fitted one–pole Sellmeier

function

– n3 is the curve derived from SiO2

data (the stars) and the Clausius–

Mossotti equation for binary mix-

tures.

– n4 is a two–pole Sellmeier function

for the aerogel used in the LHCb sim-

ulation

Wavelength (nm)300 350 400 450 500 550 600 650 700 750

Refra

ctive

Inde

x

1.0280

1.0285

1.0290

1.0295

1.0300

1.0305

1.0310

n(632.8)=1.02823

1n

2n

3n

4n

Dispersion Law


MonteCarlo analysis

The APACHE simulation package has been run four times, each time with a dif-

ferent ni(λ), as previously defined. The results are summarized in the table below.

The plot shows the log–scale distribution of the reconstructed Cherenkov angle for

the constant n and the one–pole Sellmeier.

Mean Cherenkov angle θC and sin-

gle photon resolution σθ (mrad)

for 10 GeV/c pions.

θC (mrad) σθ (mrad)

n1 234.3 0.5

n2 236.3 2.8

n3 236.1 2.0

n4 236.4 3.5Cherenkov Angle (rad)

0.22 0.23 0.24 0.25 0.26 0.27

Entri

es

10

210

310

410

510

1n

2n

CθReconstructed Cherenkov Angle


Conclusions

– Complete characterization of the aerogel for the LHCb experiment

– It has been verified both with measurement at fixed λ and with a dedicated

Cherenkov detector that the material is well inside the specifications for the

homogeneity of the refractive index σ(n − 1)/(n − 1) < 1%

– The refractive index has been measured in the range 350 to 700 nm and a

one–pole Sellmeier function fits the data very well

– This information is essential for the simulation and the performance of an

aerogel–based RICH detector


refractive index of silica aerogel: uniformity and...

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