Parametric Effects in aParametric Effects in aMacroscopic Optical CavityMacroscopic Optical Cavity

Sascha Schediwyschediwy@physics.uwa.edu.au

AIGO WorkshopThursday 6th October

Optical SpringOptical Spring

CirculatingPower

l

cFSR

2

)2( 22 LRc

PF circ

rad

Frequency

Q reduction Q increase

Q Increase - Parametric GainQ Increase - Parametric Gain

Niobium ResonatorNiobium Resonator

Cavity Properties Niobium Qm = 1.562 (8)*105

fmech = 780 Hz

meff = 32.3 g

l = 0.10 m

Proxy Mirrors R = 0.98 F = 155 roc = 10.0 m

Super Mirrors R ~ 0.99968 (rated: 0.9994+) F ~ 9800 (rated: 5200+) roc = 1.0 m

60°C

Yacca Gum PropertiesYacca Gum Properties

viscous at 80°C+ reversible bonds dissolves in alcohol relatively low loss Q ~ 100

70°C80°C90°C

Yacca Gum BondingYacca Gum Bonding

Experimental DesignExperimental Design

3525

temp mirror 1

temp mirror 2

key:objectposition (mm)beam power (%)optical loss (%)

Optical Error Signal RingdownOptical Error Signal Ringdown

Ringdown Linear Fit

time (s) time (s)

(experimental results)

Q Factors

0.60

0.62

0.64

0.66

0.68

0.70

0.72

0.74

0.76

0.78

0.80

779.

68 -

3

779.

68 -

4

779.

68 -

5

779.

68 -

6

779.

68 -

7

779.

68 -

8

779.

68 -

9

Ave

rage

Mode Frequency (Hz)

Qu

alit

y F

acto

r (1

0^5)

Quality Factor Quality Factor

Q = 0.700 ± 0.002 x105

Proxy Mirror Q ModificationProxy Mirror Q Modification

Mechanical Q

Quality Factor (-)

F[rad] (N)

k[opt] (N/m)

Modified Q

Super Mirror Q ModificationSuper Mirror Q Modification

F[rad] (N)

k[opt] (N/m)

(Hz)

(Hz)

(Hz)

Quality Factor (-)

Laser Maximum

Damage Threshold Limited

Mechanical Q

Parametric Instability TranquilisationParametric Instability Tranquilisation

Model proposed by:

Braginsky & Vyatchanin

(Phys. Lett. A 293 (2002) 228-234)

Any Question?Any Question?

Q Modification / Optical Spring Const.Q Modification / Optical Spring Const.

2232

181

1

21

11024

cR

fRlRRc

fPlk

offset

offsetinputopt

1

32543

2

21

8121

40961

Rc

flRfcm

lfP

QQ

offsetmecheff

offsetinput

mechalt

Circulating PowerCirculating Power

Cavity Properties Rayleigh Range / Beam Waist

R1 = R2 = 1.0 m

L = 0.1 m

Spot Size at Mirror ( z = 0.05 m )

2

20

22 z

zzR

1

20

11 z

zzR

20

22

22 4

2

1

2zR

Rz

20

21

21 4

2

1

2zR

Rz

4

20

LLRz

mz

w 400 10716.2

mz

zwzw 4

2

00 10787.21)(

mz 2179.00

24

282

10767.7

10767.7)(

cm

mzw

Circulating PowerCirculating Power

Newport Supermirrors Damage Threshold:

Maximum Circulating Power:

Maximum Input Power R1 = R2 > 99.94%

T1 > 0.06%

242 10767.7)( cmzw

2/1000 cmWDT

WP Maxcirc 7767.0)(

)(

1

2

21)(

1MaxcircMaxin P

T

RRP

mW

P Maxcirc

466.0

0006.0 )(

Radiation Pressure ForceRadiation Pressure Force

Radiation pressure force for FP Cavity

)2( 22 LRc

PF circ

rad

≈ unity

inx

irad P

eRRc

TLRF 24

21

122

1

)2(

inx

icirc P

eRR

TP 24

21

1

1

dx

xFdk rad

opt

)(

inx

iopt P

ceRR

TLR

dx

dk 24

21

122

1

)2(

21 iCx

opteB

A

dx

dk

let:c

PTLRA in122 )2(

21RRB

4

C

Optical Spring ConstantOptical Spring Constant

21 iCx

opteB

A

dx

dk

21 BeeB

A

dx

dk

iCxiCxopt

substitute ABC back

221 BCxBCos

A

dx

dkopt

2221

sin2

BCxBCos

CxABCkopt

2

2121

21221

4cos21

4sin28

xRRRR

xRRLRT

c

Pk in

opt

2

2121

21221

4cos21

4sin28

cflRRRR

cflRRLRT

c

Pk

offset

offsetinopt

in x space

in f space

mWP Maxin 466.0)(

Cavity AlignmentCavity Alignment

–ωm ωm

““Low Q” / “High Q”Low Q” / “High Q”

FWHM

FWHM

–ωm ωm

Low Q – when the bandwidth is larger than ωm

High Q – when the bandwidth is smaller than ωm