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 HannoverMax-Planck-Institut für Gravitationsphysik

(Albert-Einstein-Institut),*Institut für Angewandte Physik, Universität Jena

LIGO-G050051-00-Z

2Aspen, 21.01.2005, Roman Schnabel

Is it possible to couple light to a cavity without transmission?

1st Order Littrow

Laser

m=0m=-1

2nd Order Littrow

Laser m=-2m=-1

m=0

Laser

3Aspen, 21.01.2005, Roman Schnabel

Is it possible to couple light to a cavity without transmission?

1st Order Littrow

Laser

m=0m=-1

Deep grating structure for high diffraction efficiencies

4Aspen, 21.01.2005, Roman Schnabel

Is it possible to couple light to a cavity without transmission?

2nd Order Littrow

Laser m=-2m=-1

m=0

Advantage: • Cavity finesse is limited by specular reflectivity (>99.99% seems possible)• Low diffraction efficiency• Shallow structures• Low scattering loss

5Aspen, 21.01.2005, Roman Schnabel

Coupler / 2nd Order Littrow

Grating equation:

for d=1450 nm (grating period),=1064 nm, |m|=2.

2.47

sinsin

,Littin

min d

m

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

6Aspen, 21.01.2005, Roman Schnabel

Coupler / 2nd Order Littrow

Grating equation:

for d=1450 nm (grating period),=1064 nm, |m|=2.

2.47

sinsin

,Littin

min d

m

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%

7Aspen, 21.01.2005, Roman Schnabel

Measured (+measurement inferred) values for coupling amplitudes:

≈ 99.4%,

≈ 0.58%,

≈ 0.005%,

(0°) ≈ 98.8%,Overall loss@0° ≈ 0.04%

Coupler / 2nd Order Littrow

Grating equation:

for d=1450 nm (grating period),=1064 nm, |m|=2.

2.47

sinsin

,Littin

min d

m

Shallow grating (40 to 50nm) structure with HR stack on top

in

A 3-port coupler!

8Aspen, 21.01.2005, Roman Schnabel

Coupler / 2nd Order Littrow

Grating equation:

for d=1450 nm (grating period),=1064 nm, |m|=2.

2.47

sinsin

,Littin

min d

m

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!

9Aspen, 21.01.2005, Roman Schnabel

FP-Cavity: Coupled 2nd Order Littrow

Cavity free spectral rangeFinesse: F=400

A. Bunkowski et al., Opt. Lett. 29, 2342, (2004)

≈ 0.58%,

(0°)≈ 98.8%,Overall loss@0°≈ 0.04%

10Aspen, 21.01.2005, Roman Schnabel

Coupling Relations of the 2-Port (transmissive) Beamsplitter

a1 a2

b1 b2

b1

b2

S11 S12

S21 S22

a1

a2

,

5S 2 p

*5

S 2 p

5

S 2 p

5S 2p

ii

or

ai ,bi : complex field amplitudes

11Aspen, 21.01.2005, Roman Schnabel

Coupling Relations of the 3-Port (reflective) Beamsplitter

b1

b2

b3

2ei2 1e

i2 0ei0

1ei1 0e

i0 1ei1

0ei0 1e

i1 2ei2

a1

a2

a3

,5

S 3p*

5S 3 p

0

2 212 1

02 1

2 22 1

1 0 2

2 1 0

2and

a1

a2

b1 b3

a3

b2

in

12Aspen, 21.01.2005, Roman Schnabel

Coupling Relations of the 3-Port (reflective) Beamsplitter

and

a1

a2

b1 b3

a3

b2

0 0

1 1/2 arccos 12 20

2 / 200 2 arccos 1

2 / 220

b1

b2

b3

2ei2 1e

i2 0ei0

1ei1 0e

i0 1ei1

0ei0 1e

i1 2ei2

a1

a2

a3

,5

S 3p*

5S 3 p

0

2 212 1

02 1

2 22 1

1 0 2

2 1 0

2

13Aspen, 21.01.2005, Roman Schnabel

3-Port Coupled FP Cavity

c1

c2

c3

5S 3p

1

c2 exp(2i)

0

,

c1 2 exp(i2) 12 exp 2i(1 ) d

c2 1 exp(i1)d

c3 0 12 exp 2i(1 ) d

d 1

0 exp 2i

a1=1

c1 c3

c2

14Aspen, 21.01.2005, Roman Schnabel

= min

c1

c3

c2

> min

c1

c3

c2

3-Port Coupled FP Cavity a1=1

c1 c3

c2

15Aspen, 21.01.2005, Roman Schnabel

3-Port Coupled FP Cavity a1=1

c1 c3

c2

Gratings with minimum 2 provide a dark port (c3=0) for a tuned cavity and enables power recycling.

16Aspen, 21.01.2005, Roman Schnabel

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.

17Aspen, 21.01.2005, Roman Schnabel

All-reflective Grating IFO

Proposed by R. Drever

18Aspen, 21.01.2005, Roman Schnabel

3-Port Coupled FP Cavity a1=1

c1 c3

c2