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Low-loss Grating for Coupling to a High-Finesse Cavity

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

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Low-loss Grating for Coupling to a High-Finesse Cavity

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  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-G050051-00-Z

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

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

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

  5. h1 in h2 h0 Shallow grating (40 to 50nm) structure with HR stack on top Coupler / 2nd Order Littrow Grating equation: for d=1450 nm (grating period), l =1064 nm, |m|=2. Suggested design values for coupling amplitudes: h02=99%, h12=1%, h22as small as possible, r2(0°)=98%, no transmission at all, low loss

  6. h1 in h2 h0 Coupler / 2nd Order Littrow Grating equation: for d=1450 nm (grating period), l =1064 nm, |m|=2. Measured (+measurement inferred) values for coupling amplitudes: h02≈99.4%, h12≈0.58%, h22 ≈0.005%, r2(0°) ≈98.8%, Overall loss@0° ≈0.04% Shallow grating (40 to 50nm) structure with HR stack on top

  7. h1 in h2 h0 A 3-port coupler! Coupler / 2nd Order Littrow Grating equation: for d=1450 nm (grating period), l =1064 nm, |m|=2. Measured (+measurement inferred) values for coupling amplitudes: h02≈99.4%, h12≈0.58%, h22 ≈0.005%, r2(0°) ≈98.8%, Overall loss@0° ≈0.04% Shallow grating (40 to 50nm) structure with HR stack on top

  8. h1 in h2 h0 A 3-port coupler! Coupler / 2nd Order Littrow Grating equation: for d=1450 nm (grating period), l =1064 nm, |m|=2. Measured (+measurement inferred) values for coupling amplitudes: h02≈99.4%, h12≈0.58%, h22 ≈0.005%, r2(0°) ≈98.8%, Overall loss@0° ≈0.04% From h1>0, h-1>0 and time reversal consideration one can deduce h2>0! What is the lowest h2 possible?

  9. Cavity free spectral range Finesse: F=400 FP-Cavity: Coupled 2nd Order Littrow h12≈0.58%, r2(0°)≈98.8%, Overall loss@0°≈0.04% A. Bunkowski et al., Opt. Lett. 29, 2342, (2004)

  10. a2 a1 b1 b2 Coupling Relations of the 2-Port (transmissive) Beamsplitter ai ,bi : complex field amplitudes or

  11. h1 in a2 b2 a3 a1 h2 h0 b1 b3 Coupling Relations of the 3-Port (reflective) Beamsplitter and

  12. a2 b2 a3 a1 b1 b3 Coupling Relations of the 3-Port (reflective) Beamsplitter and

  13. a1=1 c2 c1 c3 3-Port Coupled FP Cavity

  14. a1=1 c2 r02 r02 c1 c3 c1 c1 h2 = h2,min h2 > h2,min c3 c3 c2 c2 3-Port Coupled FP Cavity

  15. a1=1 c2 c1 c3 3-Port Coupled FP Cavity Gratings with minimum h2 provide a dark port (c3=0) for a tuned cavity and enables power recycling.

  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.

  17. All-reflective Grating IFO Proposed by R. Drever

  18. a1=1 c2 c1 c3 3-Port Coupled FP Cavity

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