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

Transcription

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-G Z

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

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

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

5 Coupler / nd Order Littrow Grating equation: mλ sinθin + sinθm = d θ = 47. in,litt for d=1450 nm (grating period), λ =1064 nm, m =. Suggested design values for coupling amplitudes: in η 1 η η 0 η 0 =99%, η 1 =1%, η as small as possible, ρ (0 )=98%, no transmission at all, low loss Shallow grating (40 to 50nm) structure with HR stack on top 5

6 Coupler / nd Order Littrow Grating equation: mλ sinθin + sinθm = d θ = 47. in,litt for d=1450 nm (grating period), λ =1064 nm, m =. Measured (+measurement inferred) values for coupling amplitudes: in η 1 η η 0 η %, η %, η 0.005%, ρ (0 ) 98.8%, Overall loss@0 0.04% Shallow grating (40 to 50nm) structure with HR stack on top 6

7 Coupler / nd Order Littrow Grating equation: mλ sinθin + sinθm = d θ = 47. in,litt for d=1450 nm (grating period), λ =1064 nm, m =. Measured (+measurement inferred) values for coupling amplitudes: in η 1 η η 0 η %, η %, η 0.005%, ρ (0 ) 98.8%, Overall loss@0 0.04% A 3-port coupler! Shallow grating (40 to 50nm) structure with HR stack on top 7

8 Coupler / nd Order Littrow Grating equation: mλ sinθin + sinθm = d θ = 47. in,litt for d=1450 nm (grating period), λ =1064 nm, m =. Measured (+measurement inferred) values for coupling amplitudes: in η 1 η η 0 η %, η %, A 3-port coupler! η 0.005%, ρ (0 ) 98.8%, Overall loss@0 0.04% From η 1 >0, η 1 >0 and time reversal consideration one can deduce η >0! What is the lowest η possible? 8

9 FP-Cavity: Coupled nd Order Littrow Cavity free spectral range Finesse: F=400 η %, ρ (0 ) 98.8%, Overall loss@0 0.04% A. Bunkowski et al., Opt. Lett. 9, 34, (004) 9

10 Coupling Relations of the -Port (transmissive) Beamsplitter a 1 a b 1 b a i,b i : complex field amplitudes b 1 b = S 11 S 1 a 1, S 1 S a T S T * p S p =Ι S T p = ρ τ τ ρ or T S p = ρ iτ iτ ρ 10

11 Coupling Relations of the 3-Port (reflective) Beamsplitter a a 1 b b 1 b 3 a 3 in η 1 η η 0 b 1 b b 3 η e iφ η 1 e iφ η 0 e iφ 0 = η 1 e iφ 1 ρ 0 e iφ 0 η 1 e iφ 1 η 0 e iφ 0 η 1 e iφ 1 η e iφ a 1 a a 3, T * S 3 p S T 3 p =Ι ρ 0 + η 1 =1 η 0 + η 1 + η =1 and ( 1 ρ 0 ) ( η 1+ ρ 0) 11

12 a 1 Coupling Relations of the 3-Port (reflective) Beamsplitter a φ 0 = 0 b a 3 φ 1 = 1/ ( )arccos ( η 1 η 0 )/ρ 0 η 0 b 1 b 3 φ = arccos[ η ( 1 /η η )] 0 [ ( )] b 1 b b 3 η e iφ η 1 e iφ η 0 e iφ 0 = η 1 e iφ 1 ρ 0 e iφ 0 η 1 e iφ 1 η 0 e iφ 0 η 1 e iφ 1 η e iφ a 1 a a 3, T * S 3 p S T 3 p =Ι ρ 0 + η 1 =1 η 0 + η 1 + η =1 and ( 1 ρ 0 ) η 1+ ρ 0 ( ) 1

13 3-Port Coupled FP Cavity a 1 =1 c c 1 c 3 d = c 1 c c 3 = T 1 S 3p c exp(iφ) 0 c 1 = η exp(iφ ) + η 1 exp[ i(φ 1 + φ) ]d c = η 1 exp(iφ 1 )d c 3 = η 0 + η 1 exp[ i(φ 1 + φ) ]d 1 ρ 0 exp iφ ( ), 13

14 3-Port Coupled FP Cavity a 1 =1 c c 1 c 3 ρ 0 ρ 0 η = η,min c 1 c 3 c η > η,min c 1 c 3 c 14

15 3-Port Coupled FP Cavity a 1 =1 c c 1 c 3 Gratings with minimum η provide a dark port (c 3 =0) for a tuned cavity and enables power recycling. 15

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. 16

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

18 3-Port Coupled FP Cavity a 1 =1 c c 1 c 3 18