Optics of GW detectors Jo van den Brand e-mail: [email protected].

15
Optics of GW detectors Jo van den Brand e-mail: [email protected]

Transcript of Optics of GW detectors Jo van den Brand e-mail: [email protected].

Page 1: Optics of GW detectors Jo van den Brand e-mail: jo@nikhef.nl.

Optics of GW detectors

Jo van den Brand

e-mail: [email protected]

Page 2: Optics of GW detectors Jo van den Brand e-mail: jo@nikhef.nl.

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Introduction

• General ideas

• Cavities

• Reflection locking (Pound-Drever technique)

• Transmission locking (Schnupp asymmetry)

• Paraxial approximation

• Gaussian beams

• Higher-order modes

• Input-mode cleaner

• Mode matching

• Anderson technique for alignment

Page 3: Optics of GW detectors Jo van den Brand e-mail: jo@nikhef.nl.

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General ideas

Measure distance between 2 free falling masses using light

– h=2L/L (~10-22)

– L= 3 km L ~10-22 x 106 ~10-16 (=10-3 fm)

– light ~ 1 m

– Challenge: use light and measure L/~10-12

How long can we make the arms?

– GW with f~100 Hz GW ~c/f=3x108 km/s / 100 Hz = 3000 km

– Optimal would be GW/4 ~ 1000 km

– Need to bounce light 1000 km / 3 km ~ 300 times

How to increase length of arms?– Use Fabri-Perot cavity (now F=50), then L/~10-10

– Measure phase shift xy LBhe ~ 10.(3 km).200.10-22/10-6=10-9 rad

L + L

L + L

L - L

Page 4: Optics of GW detectors Jo van den Brand e-mail: jo@nikhef.nl.

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General ideas

Power needed

– PD measures light intensity

– Amount of power determines precision of phase measurement et of incoming wave train (phase ft)

– Measure the phase by averaging the PD intensity over a long period of time Tperiod GW/2 = 1/(2f)

– Total energy in light beam E=I0.1/(2f)=hbar.Ne

– Due to Poisson distributed arrival times of the photons we have N= Sqrt[N]

– Thus, E= N .hbar. e and t E= (e).Sqrt[N]. hbar. e >hbar

– We find Sqrt[N] N= 1018 photons

– Power needed I0 = Nhbar. e .2f ~ 100 W

Power is obtained through power-recycling mirror

– Operate PD on dark fringe

– Position PR in phase with incoming light

– GW signal goes into PD!

– Laser 5 W, recycling factor ~40L + L

L - L

Page 5: Optics of GW detectors Jo van den Brand e-mail: jo@nikhef.nl.

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Cavities

Fabri-Perot cavity (optical resonator)

Reflectivity of input mirror: -0.96908

Finesse = 50

FSR = 50 kHz

Power

Storage time

Cavity pole

-6 -4 -2 2 4 6

10

20

30

40

50

60

70

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Cavity pole

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Overcoupled cavities (r1 - r2 < 0)

On resonance 2kL=n Sensitivity to length changes

Note amplification factor

Note that amplitude of reflected light is phase shifted by 90o

Reflected light is mostly unchanged |Eref|2

Imagine that L is varying with frequency fGW

Loose sensitivity for fGW>fpole

Lik

rrrr

E

E

E

E

resonanceinc

ref

inc

ref 21

121

21

Amplification factor(bounce number)

fcLie Lffci 41)(4

Page 8: Optics of GW detectors Jo van den Brand e-mail: jo@nikhef.nl.

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Reflection locking – Pound Drever locking

Dark port intensity goes quadratic with GW phase shift.

How do we get a linear response?

Note, that the carrier light gets p phase shift due to over-coupled cavity.

RFPD sees beats between carrier and sidebands.

Beats contain information about carrier light in the cavity

Phase of carrier is sensitive to L of cavity

Laser EOM

3 x 1014 Hz

20 MHzFaraday isolator

carrier

L

sideband

RFFD

Page 9: Optics of GW detectors Jo van den Brand e-mail: jo@nikhef.nl.

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Reflection locking

Demodulation

Modulation

Page 10: Optics of GW detectors Jo van den Brand e-mail: jo@nikhef.nl.

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Transmission locking

Schnupp locking is used to control Michelson d.o.f.

– Make dark port dark and bright port bright

– Not intended to keep cavities in resonance

– Requires that sideband (reference) light comes out the dark port

Page 11: Optics of GW detectors Jo van den Brand e-mail: jo@nikhef.nl.

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Gaussian beams

P – complex phaseq – complex beam parameter

Page 12: Optics of GW detectors Jo van den Brand e-mail: jo@nikhef.nl.

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Higher-order modes

Page 13: Optics of GW detectors Jo van den Brand e-mail: jo@nikhef.nl.

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Input-mode cleaner

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Applications – Anderson technique

Page 15: Optics of GW detectors Jo van den Brand e-mail: jo@nikhef.nl.

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Summary

Some of the optical aspects

– Simulate with Finesse

Frequency stabilization

– Presentation

Control issues

– Presentation