Optics of GW detectors Jo van den Brand

LISA 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

LISA General ideas  Measure distance between 2 free falling masses using light – h=2  L/L (~ ) – L= 3 km   L ~ x 10 6 ~ (=10 -3 fm) – light ~ 1  m – Challenge: use light and measure  L/ ~  How long can we make the arms? – GW with f~100 Hz  GW ~c/f=3x10 8 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/ ~ – Measure phase shift  x  y  LBh  e ~ 10.(3 km) /10 -6 =10 -9 rad L +  L L -  L

LISA General ideas  Power needed – PD measures light intensity – Amount of power determines precision of phase measurement  e  t of incoming wave train (phase  ft) – Measure the phase by averaging the PD intensity over a long period of time T period GW /2 = 1/(2f) – Total energy in light beam E=I 0.1/(2f)=hbar.N   e – 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   = photons – Power needed I 0 = N  hbar.  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 ~40 L +  L L -  L

LISA Cavities  Fabri-Perot cavity (optical resonator)  Reflectivity of input mirror:  Finesse = 50  FSR = 50 kHz  Power  Storage time  Cavity pole

LISA Cavity pole

LISA Overcoupled cavities (r 1 - r 2 < 0)  On resonance 2kL=n   Sensitivity to length changes  Note amplification factor  Note that amplitude of reflected light is phase shifted by 90 o  Reflected light is mostly unchanged |E ref | 2  Imagine that  L is varying with frequency f GW  Loose sensitivity for f GW >f pole Amplification factor (bounce number)

LISA 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 LaserEOM 3 x Hz  20 MHz Faraday isolator carrier L sideband RFFD

LISA Reflection locking Demodulation Modulation

LISA 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

LISA Gaussian beams P – complex phase q – complex beam parameter

LISA Higher-order modes

LISA Input-mode cleaner

LISA Applications – Anderson technique

LISA Summary  Some of the optical aspects – Simulate with Finesse  Frequency stabilization – Presentation  Control issues – Presentation