M. De RosaINOA, LENS, INFN

F. MarinUniversity of Florence, LENS, INFN

F. MarinoINFN

O. Arcizet, M. Pinard, A. Heidmann Laboratoire Kastler Brossel, Paris

Experimental investigation of dynamic Photothermal Effect

ILIAS STREGA T2 – 2005 Meeting Palma de Mallorca

Photothermal effect Photon absorption

Local heating

Thermal expansion

Depends on: •laser power impinging on the mirrors•absorption coefficient•material: - thermal expansion

- thermal conductivity and capacitance

•temperature (through the above parameters)•mirror size and shape/suspension•beam waist•detection frequency

Photothermal effect Photon absorption

Local heating

Thermal expansion

Depends on: •laser power impinging on the mirrors•absorption coefficient•material: - thermal expansion

- thermal conductivity and capacitance

•temperature (through the above parameters)•mirror size and shape/suspension•beam waist•detection frequency

Mirror half space approximationBraginsky et al., Phys. Lett. A 264, 1 (1999)Cerdonio et al., Phys. Rev. D 63, 082003 (2001)

L = L0 K(/c)

P abs0 κπ

α σ)(1L

w2

s

c κ2

c

02222

22

)π

1K

2

)(i)((

u

dvduvuvu

eu

-3 -2 -1 0 1 2 3-6

-5

-4

-3

-2

-1

0

1

log

( K

()

)

log()

1/

: thermal expansion coefficient: Poisson ratiok: thermal conductivitycs: volumetric thermal capacitancew: beam waist

-3 -2 -1 0 1 2 3

-6

-5

-4

-3

-2

-1

0

1

log

( K

()

)

log()

Mirror half space approximationBraginsky et al., Phys. Lett. A 264, 1 (1999)Cerdonio et al., Phys. Rev. D 63, 082003 (2001)

L = L0 K(/c)

P abs0 κπ

α σ)(1L

w2

s

c κ2

c

02222

22

)π

1K

2

)(i)((

u

dvduvuvu

eu

: thermal expansion coefficient: Poisson ratiok: thermal conductivitycs: volumetric thermal capacitancew: beam waist

Logarithmic divergence !Size effects?Coatings ?

Calculatedc (Hz)

Fused silica Sapphire

w/2 300K 1K 300K 1K

10mm 0.0015 4.8 0.02 19000

0.1mm15 48000 200 1.9·108

• Cut-off depending on the mirror shape and suspension (heat

dispersion

• Large timescale and size spread necessity of accurate and

verified model over a complete frequency range)

Frequencyservo loop

Laser EOM1O.I.BS

PD1 QW

PBS

13.3 MHz

PD2

QWPBS

PD4

Cavity servo loopAOM

EOM2

C1

C2

PD3

Oscilloscope+

PC

Reference

cavity

Probed Cavities

Spacer Zerodur Aluminum

L (mm) 200 7.1

Waist (mm) 0.370 0.073

c (Hz) 2.2 57

Finesse 38000 40000

Mirrors substrate: Fused SilicaCoatings: SiO2/Ta2O5

Long cavity

a) half-infinite mirrorb) finite size effectsc) coating effect

IMPROVED MODEL

Low frequency: finite size effectHigh frequency: coating effect

One-dimensional model

= FS + coat

Short cavity

Frequency scaling with

waist as predicted

Phase at high frequency: to

be improved (coating depth

comparable with waist)

Setup of high-finesse cavitiesSetup of high-finesse cavities

Mirrors made by J.M. Mackowski Input mirror T = 20 ppm, total losses < 10 ppm

Compact cavity: L = 0.2 mm

Cavity finesse = 230 000, input power > 3 mW

Test at cryogenic temperatureTest at cryogenic temperature

Cavity assembled in copper rings for thermal conductivity

Cryogenic facility with mechanical isolation from the helium tank

Observation of first optical resonances at low temperature

Upgrade of a bar with optical readout for cryogenic

operation

Conclusions

•beam waist dependence of cut-off frequency is verified

•finite size effects at low frequency

•coating effects at high frequency

•improvement of the half-infinite mirror model including finite size and coating effect (material properties)

•low-temperature setups under construction

•mirrors based on a silicon wafer currently being coated at the Laboratoire des Matériaux Avancés in Lyon

Solving the windmills noise problem...