Low-loss Grating for Coupling to a High-Finesse Cavity R. Schnabel, A. Bunkowski, O. Burmeister, P. Beyersdorf, T. Clausnitzer*, E. B. Kley*, A. Tünnermann*, K. Danzmann Institut für Atom- und Molekülphysik, Universität Hannover Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), *Institut für Angewandte Physik, Universität Jena LIGO-G Z

Aspen, , Roman Schnabel 2 Is it possible to couple light to a cavity without transmission? 1 st Order Littrow Laser m=0 m=-1 2 nd Order Littrow Laser m=-2 m=-1 m=0 Laser

Aspen, , Roman Schnabel 3 Is it possible to couple light to a cavity without transmission? 1 st Order Littrow Laser m=0 m=-1 Deep grating structure for high diffraction efficiencies

Aspen, , Roman Schnabel 4 Is it possible to couple light to a cavity without transmission? 2 nd Order Littrow Laser m=-2 m=-1 m=0 Advantage: Cavity finesse is limited by specular reflectivity (>99.99% seems possible) Low diffraction efficiency Shallow structures Low scattering loss

Aspen, , Roman Schnabel 5 Coupler / 2 nd Order Littrow Grating equation: for d=1450 nm (grating period),  =1064 nm, |m|=2. Shallow grating (40 to 50nm) structure with HR stack on top  in   Suggested design values for coupling amplitudes:    = 99%,    = 1%,     as small as possible,    (0°)=98%, no transmission at all, low loss

Aspen, , Roman Schnabel 6 Coupler / 2 nd Order Littrow Grating equation: for d=1450 nm (grating period),  =1064 nm, |m|=2. Shallow grating (40 to 50nm) structure with HR stack on top  in   Measured (+measurement inferred) values for coupling amplitudes:    ≈ 99.4%,    ≈ 0.58%,    ≈ 0.005%,    (0°) ≈ 98.8%, Overall ≈ 0.04%

Aspen, , Roman Schnabel 7 Measured (+measurement inferred) values for coupling amplitudes:    ≈ 99.4%,    ≈ 0.58%,    ≈ 0.005%,    (0°) ≈ 98.8%, Overall ≈ 0.04% Coupler / 2 nd Order Littrow Grating equation: for d=1450 nm (grating period),  =1064 nm, |m|=2. Shallow grating (40 to 50nm) structure with HR stack on top  in   A 3-port coupler!

Aspen, , Roman Schnabel 8 Coupler / 2 nd Order Littrow Grating equation: for d=1450 nm (grating period),  =1064 nm, |m|=2.  in   From   >0,   >0 and time reversal consideration one can deduce   >0! What is the lowest   possible? Measured (+measurement inferred) values for coupling amplitudes:    ≈ 99.4%,    ≈ 0.58%,    ≈ 0.005%,    (0°) ≈ 98.8%, Overall ≈ 0.04% A 3-port coupler!

Aspen, , Roman Schnabel 9 FP-Cavity: Coupled 2 nd Order Littrow Cavity free spectral range Finesse: F=400 A. Bunkowski et al., Opt. Lett. 29, 2342, (2004)    ≈ 0.58%,   (0°)≈ 98.8%, Overall 0.04%

Aspen, , Roman Schnabel 10 Coupling Relations of the 2-Port (transmissive) Beamsplitter a1a1 a2a2 b1b1 b2b2 or a i,b i : complex field amplitudes

Aspen, , Roman Schnabel 11 Coupling Relations of the 3-Port (reflective) Beamsplitter and a1a1 a2a2 b1b1 b3b3 a3a3 b2b2  in  

Aspen, , Roman Schnabel 12 Coupling Relations of the 3-Port (reflective) Beamsplitter and a1a1 a2a2 b1b1 b3b3 a3a3 b2b2

Aspen, , Roman Schnabel 13 3-Port Coupled FP Cavity a 1 =1 c1c1 c3c3 c2c2

Aspen, , Roman Schnabel 14   =   min  c1c1 c3c3 c2c2   >   min  c1c1 c3c3 c2c2 3-Port Coupled FP Cavity a 1 =1 c1c1 c3c3 c2c2

Aspen, , Roman Schnabel 15 3-Port Coupled FP Cavity a 1 =1 c1c1 c3c3 c2c2 Gratings with minimum  2 provide a dark port (c 3 =0) for a tuned cavity and enables power recycling.

Aspen, , Roman Schnabel 16 Summary A low loss reflective coupler to a cavity of Finesse 400 has been demonstrated. Phase relations of the three-port coupler are understood. Our results show that low efficiency, 3- port gratings are very promissing for high power interferometers.

Aspen, , Roman Schnabel 17 All-reflective Grating IFO Proposed by R. Drever

Aspen, , Roman Schnabel 18 3-Port Coupled FP Cavity a 1 =1 c1c1 c3c3 c2c2