Optics of GW detectors

1
Optics of GW detectors

• Jo van den Brand
• e-mail jo_at_nikhef.nl

2
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

3
General ideas

• Measure distance between 2 free falling masses
  using light
• h2DL/L (10-22)
• L 3 km ? DL 10-22 x 106 10-16 (10-3 fm)
• llight 1 mm
• Challenge use light and measure DL/l10-12
• How long can we make the arms?
• GW with f100 Hz ? lGW c/f3x108 km/s / 100 Hz
  3000 km
• Optimal would be lGW/4 1000 km
• Need to bounce light 1000 km / 3 km 300 times
• How to increase length of arms?
• Use Fabri-Perot cavity (now F50), then
  DL/l10-10
• Measure phase shift Df dfx-dfy 4pLBh/le
  10.(3 km).200.10-22/10-610-9 rad

L - DL
4
General ideas

• Power needed
• PD measures light intensity
• Amount of power determines precision of phase
  measurement Df weDt of incoming wave train
  (phase f 2pft)
• Measure the phase by averaging the PD intensity
  over a long period of time Tperiod GW/2 1/(2f)
• Total energy in light beam EI0.1/(2f)hbar.Ngwe
• Due to Poisson distributed arrival times of the
  photons we have DNg SqrtNg
• Thus, DE DNg .hbar. we and Dt DE
  (Df/we).SqrtNg. hbar. we gthbar
• We find Df gt 1/ SqrtNg ? Ng gt 1/(Df)2 1018
  photons
• Power needed I0 Ng. hbar. we .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 40

5
Cavities

• Fabri-Perot cavity (optical resonator)
• Reflectivity of input mirror -0.96908
• Finesse 50
• FSR 50 kHz
• Power
• Storage time
• Cavity pole

6
Cavity pole
7
Overcoupled cavities (r1 - r2 lt 0)

• On resonance 2kLnp
• Sensitivity to length changes
• Note amplification factor
• Note that amplitude of reflected light is phase
  shifted by 90o
• Reflected light is mostly unchanged Eref2
• Imagine that dL is varying with frequency fGW
• Loose sensitivity for fGWgtfpole

8
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 dL of cavity

9
Reflection locking
Modulation
Demodulation
10
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

11
Gaussian beams
P complex phase q complex beam parameter
12
Higher-order modes
13
Input-mode cleaner
14
Applications Anderson technique
15
Summary

• Some of the optical aspects
• Simulate with Finesse
• Frequency stabilization
• Presentation
• Control issues
• Presentation