1. 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-G050204-00-Z

2. LSC Meeting, 03/22/2005, Roman Schnabel LIGO-G050135-00-Z 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

3. LSC Meeting, 03/22/2005, Roman Schnabel LIGO-G050135-00-Z 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

4. LSC Meeting, 03/22/2005, Roman Schnabel LIGO-G050135-00-Z 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

5. LSC Meeting, 03/22/2005, Roman Schnabel LIGO-G050135-00-Z 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

6. LSC Meeting, 03/22/2005, Roman Schnabel LIGO-G050135-00-Z 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 loss@0° ≈ 0.04%

7. LSC Meeting, 03/22/2005, Roman Schnabel LIGO-G050135-00-Z 7 Measured (+measurement inferred) values for coupling amplitudes:    ≈ 99.4%,    ≈ 0.58%,    ≈ 0.005%,   (0°) ≈ 98.8%, Overall loss@0° ≈ 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  

8. LSC Meeting, 03/22/2005, Roman Schnabel LIGO-G050135-00-Z 8 FP-Cavity: Coupled 2 nd Order Littrow Cavity free spectral range Finesse: F=400 A. Bunkowski et al., Opt. Lett. 29, 2342, (2004)   (0°)≈ 98.8%,    ≈ 99.4%,    ≈ 0.58%,    ≈ 0.005%. A 3-port coupler!

9. LSC Meeting, 03/22/2005, Roman Schnabel LIGO-G050135-00-Z 9 Coupling Relations of the 2-Port (transmissive) Beamsplitter a1a1 a2a2 b1b1 b2b2 or a i,b i : complex field amplitudes

10. LSC Meeting, 03/22/2005, Roman Schnabel LIGO-G050135-00-Z 10 Coupling Relations of the 3-Port (reflective) Beamsplitter and a1a1 a2a2 b1b1 b3b3 a3a3 b2b2  in  

11. LSC Meeting, 03/22/2005, Roman Schnabel LIGO-G050135-00-Z 11 Coupling Relations of the 3-Port (reflective) Beamsplitter and a1a1 a2a2 b1b1 b3b3 a3a3 b2b2

12. LSC Meeting, 03/22/2005, Roman Schnabel LIGO-G050135-00-Z 12 3-Port Coupled FP Cavity a 1 =1 c1c1 c3c3 c2c2

13. LSC Meeting, 03/22/2005, Roman Schnabel LIGO-G050135-00-Z 13   =   min  c1c1 c3c3 c2c2   >   min  c1c1 c3c3 c2c2 3-Port Coupled FP Cavity a 1 =1 c1c1 c3c3 c2c2

14. LSC Meeting, 03/22/2005, Roman Schnabel LIGO-G050135-00-Z 14 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. A. Bunkowski et al., Opt. Lett. (2005), in press

15. LSC Meeting, 03/22/2005, Roman Schnabel LIGO-G050135-00-Z 15 3-Port Coupled FP Cavity a 1 =1 c1c1 c3c3 c2c2 Cavity length, t[s] Intensity port 1, U[V] c1c1

16. LSC Meeting, 03/22/2005, Roman Schnabel LIGO-G050135-00-Z 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 promising for high power interferometers.

17. LSC Meeting, 03/22/2005, Roman Schnabel LIGO-G050135-00-Z 17 New Document Number = LIGO-G050135-00-Z DocumentG050135-00-Z AuthorRoman Schnabel Document Date03/20/2005 CategoryG GroupZ TitleLow-loss Grating for Coupling to a High-Finesse Cavity

18. LSC Meeting, 03/22/2005, Roman Schnabel LIGO-G050135-00-Z 18 All-reflective Grating IFO Proposed by R. Drever

19. LSC Meeting, 03/22/2005, Roman Schnabel LIGO-G050135-00-Z 19 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 loss@0° ≈ 0.04% A 3-port coupler!

20. LSC Meeting, 03/22/2005, Roman Schnabel LIGO-G050135-00-Z 20 3-Port Coupled FP Cavity a 1 =1 c1c1 c3c3 c2c2