DEMANDS ON LASER PURITY IN AN INTERFEROMETRIC GRAVITATIONAL WAVE DETECTOR

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DEMANDS ON LASER PURITY IN AN

INTERFEROMETRIC GRAVITATIONAL WAVE DETECTOR

A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, H. Billing, K. Maischberger

To cite this version:

A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, H. Billing, et al.. DEMANDS ON LASER PU-

RITY IN AN INTERFEROMETRIC GRAVITATIONAL WAVE DETECTOR. Journal de Physique

Colloques, 1981, 42 (C8), pp.C8-451-C8-459. �10.1051/jphyscol:1981851�. �jpa-00221747�

JOURNAL DE PHYSIQUE

CoZZoque C8, suppZ6ment au n012, Tome 42, dgcembre 1981 page ^C8-451

DEMANDS ON LASER PURITY IN AN INTERFEROMETRIC GRAVITATIONAL WAVE DETECTOR

A. ~ G d i g e r , R. S c h i l l i n g , L. Schnupp, W. Winkler, H. B i l l i n g and K. Maischberger

Max-PZanck- I n s t i t u t ftir Physik und Astrophysik, I n s t i t u t far Astrophysik, 0-8046 Garching bei MUnchen, Karl-SchwarzschiZd-Strasse 1, F.R.G.

A b s t r a c t

I n t h e s i g n a l frequency window (500 t o 3000 H Z ) i n s i d e which t h e Michelson i n t e r f e r o m e t e r i s t o d e t e c t g r a v i t a t i o n a l r a d i a t i o n , i t must a t l e a s t be a b l e t o r e s o l v e to-' of a f r i n g e . This r e q u i r e s a l a s e r i l l u m i n a t i o n o f extremely high p u r i t y . Noise c o n t r i b u t i o n s due t o l a s e r f l u c t u a t i o n s i n power and i n beam geometry can be k e p t s u f f i c i e n t l y s m a l l by p r o p e r c o n t r o l of t h e o p e r a t i n g p o i n t , and by t h e use of a mode-selective r e s o n a t o r .

The s t r o n g demands on frequency s t a b i l i t y a r i s e from two d e f i c i e n c i e s o f t h e i n t e r f e r o m e t e r : ( i ) a r e s i d u a l path d i f f e r e n c e between t h e two arms r e q u i r e s 60 < 5*10-~ H a / m ; ( i i ) t h e i n t e r f e r e n c e of s c a t t e r e d l i g h t with t h e main beam, with l a r g e path d i f f e r e n c e s AL, may r e q u i r e 69 < ^3.10-~

A r a t h e r c o n v e n t i o n a l frequency c o n t r o l ( w i t h feedback t o t h e l a s e r c a v i t y ) i s expected t o a l l o w 60 < 3 . 1 0 - ~ HZ//&. A t o t a l l y independent second c o n t r o l loop u s e s the! i n t e r f e r o m e t e r arms a s r e f e r e n c e , and c o r r e c t s t h e l i g h t phase (and t h u s t h e frequency) with a Pockels c e l l , a f t e r t h e l i g h t h a s l e f t t h e l a s e r . A s t a b i l i t y o f 69 < He/i= may e v e n t u a l l y be p o s s i b l e . The n o i s e due t o s c a t t e r e d l i g h t may be reduced f u r t h e r by a scheme of breaking t h e coherence between s c a t t e r e d l i g h t and main beam.

1 . LASM INTERFEROMETER AS GRAVITATIONAL WAVE DETECTOR

T h i s conference i s devoted t o t h e measurement and s t a n d a r d i z a t i o n o f f r e - q u e n c i e s , w i t h a c c u r a c i e s t h a t a r e almost u n b e l i e v a b l e . I w i l l t a l k about an a p p l i c a t i o n - a l a s e r i n t e r f e r o m e t e r t o d e t e c t g r a v i t a t i o n a l waves - i n which t h e prime emphasis i s on s e n s i t i v i t y r a t h e r than on accuracy. But i t w i l l soon become c l e a r t h a t i n o r d e r t o a c h i e v e t h e d e s i r e d s e n s i t i v i t y , t h e l a s e r i l l u m i n a t i o n must have a degree of p u r i t y t h a t i s q u i t e comparable t o t h e demands i n frequency metrology, and we may b e n e f i t tremendously from t h e p r o g r e s s achieved t h e r e .

Laser i n t e r f e r o m e t e r s t o d e t e c t g r a v i t a t i o n a l waves a r e now bein i n v e s t i g a t e d i n - s e v e r a l l a b o r a t o r i e s . A f t e r pioneering work a t Hughes L a b o r a t o r i e s f l ] and a t I I T L2J, s i m i l a r a c t i v i t i e s were s t a r t e d by groups i n Munich [3, 4) and Glasgow 15) and r e c e n t l y a t Caltech 16); r e l a t e d i n v e s t i g a t i o n s a r e under way a t Novosibirsk [75.

1.1 G r a v i t a t i o n a l Waves

G r a v i t a t i o n a l r a d i a t i o n would m a n i f e s t i t s e l f a s an a l t e r n a t i n g s t r a i n i n space, with o p p o s i t e s i g n s i n t h e two orthogonal d i r e c t i o n s t r a n s v e r s e t o t h e d i r e c t i o n o f propagation. A Michelson i n t e r f e r o m e t e r (Fig. I), w i t h its two orthogonal arms, i s an i d e a l antenna f o r s u c h - r a d i a t i o n . The expected s t r a i n s a r e , however, extremely small. Typical e s t i m a t e s L8J (perhaps even somewhat on t h e o p t i m i s t i c s i d e , [ 9 ] ) a r e s t r a i n s 6L/L o f t h e o r d e r 10-18 f o r supernovae e v e n t s i n our g a l a x y , which, however, o c c u r o n l y a few times p e r c e n t u r y . Event r a t e s o f , s a y , one a week could be ex- pected i f supernovae i n t h e Virgo c l u s t e r could be d e t e c t e d , but they would have s t r a i n s of a s l i t t l e a s o r l e s s .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981851

JOURNAL DE PHYSIQUE

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The mere d e t e c t i o n of g r a v i t a t i o n a l waves would be a g o a l worth s t r i v i n g f o r , a s a f u r t h e r v e r i f i c a t i o n of g e n e r a l r e l a t i v i t y . But even more v a l u a b l e would be t h e chance t o observe t h e m i l l i s e c o n d processes d u r i n g s t e l l a r c o l l a p s e , f o r e v e r hidden t o v i s u a l o b s e r v a t i o n .

1.2 S i g n a l Frequencies of G r a v i t a t i o n a l Waves

Our s e a r c h f o r g r a v i t a t i o n a l waves h a s chances o f s u c c e s s o n l y i n a l i m i t e d frequency range i n t h e kHz r e g i o n , s a y from 500 t o 3000 Hz: g r a v i t a t i o n a l r a d i a t i o n i s expected t o d e c r e a s e r a p i d l y a t f r e q u e n c i e s above a few kHz, and towards low f r e q u e n c i e s t h e s t e e p r i s e o f almost a l l n o i s e c o n t r i b u t i o n s s e t s a l i m i t a t a few hundred Hz.

A s o u r i n t e r e s t i s c e n t e r e d mainly on a frequency range n o t i n c l u d i n g zero and slow d r i f t s , we p r e f e r t o e x p r e s s t h e n o i s e c o n t r i b u t i o n s by t h e i r s p e c t r a l d e n s i t i e s r a t h e r than by i n t e g r a l measures such a s Allan v a r i a n c e o r l i n e width. We w i l l r e p r e s e n t a s t o c h a s t i c v a r i a b l e q ( t ) by t h e l i n e a r measure d ( f ) , r e l a t e d t o t h e (two-sided) power s p e c t r a l d e n s i t y s q ( f ) by ~ ( f ) = . I f q ( t ) h a s t h e dimension m , t h e n ~ ( f ) h a s t h e dimension m/& .

1.3 Length of O p t i c a l Path

The s t r a i n s e n s i t i v i t y o f t h e i n t e r f e r o m e t e r i n c r e a s e s with i n c r e a s i n g o p t i c a l p a t h L, up t o an optimum l e n g t h L o f h a l f t h e wavelength o f t h e g r a v i t a t i o n a l wave, f o r i n s t a n c e 150 km f o r a 1 kHz s i g n a l . Even with such extremely long p a t h s L i n t h e i n t e r f e r o m e t e r , t h e v a r i a t i o n 6L due t o a g r a v i t a t i o n a l s t r a i n of would be o n l y I 5 1 0 m. Our i n t e r f e r o m e t e r , i l l u m i n a t e d with t h e green l i n e of an argon l a s e r ( A = 0 . 5 1 4 - 1 0 - ~ m), would have t o be a b l e t o d e t e c t phase d i f f e r e n c e s 6$ = 2a6L/X of a s l i t t l e a s 2 . 1 0 - ~ r a d , o r 3 . 1 0 - ~ O of a f r i n g e .

The r e q u i r e d long t o t a l p a t h s L can be r e a l i z e d with m u l t i - r e f l e c t i o n schemes, f o r i n s t a n c e with o p t i c a l d e l a y - l i n e s , a s i n d i c a t e d i n Fig. 1. The number N of r e f l e c t i o n s i s l i m i t e d t o a few hundred by c o n s i d e r a t i o n s o f r e f l e c t a n c e l o s s e s and m i r r o r s i z e . With N = 300, we would need a m i r r o r d i s t a n c e (= arm l e n g t h ) of L = 500 m t o a r r i v e a t L = N - L

150 km. I n our p r e s e n t p r o t o t y p e , t h e m i r r o r d i s t a n c e is !L = 3.05 m, and with N = 138 bounces we have a t o t a l path of 420 m.

I n an a l t e r n a t i v e approach 163, u s i n g Fabry-Perot r e s o n a t o r s i n s t e a d of t h e

d e l a y - l i n e s , t h e i n t e g e r N would have t o be r e p l a c e d by NF, a f a c t o r c l o s e l y r e l a t e d

t o t h e f i n e s s e F

n p / ( l - p 2 ) of t h e c a v i t y , with p 2 t h e r e f l e c t a n c e o f t h e c a v i t y

m i r r o r s . Typical v a l u e s f o r N F would range from 50 t o s e v e r a l hundred.

1.4 Shot Noise Limit

A quantum t h e o r e t i c a l l i m i t f o r t h e s e n s i t i v i t y i s g i v e n by t h e s h o t n o i s e of t h e photo c u r r e n t , e q u i v a l e n t t o f l u c t u a t i o n s i n phase d i f f e r e n c e 6 4 t h a t can be expressed by t h e ( l i n e a r ) s p e c t r a l d e n s i t y

-

where h i s t h e Planck c o n s t a n t , c t h e speed of l i g h t , P t h e l i g h t power a v a i l a b l e a t t h e i n t e r f e r o m e t e r o u t p u t , and q t h e quantum e f f i c i e n c y of t h e p h o t o d i o d e ( s ) . The b e s t combinations of X and W a r e provided by argon i o n l a s e r s . With commercially a x a i l a b l e s i n g l e mode powers o f 2 W , and an o v e r a l l l o s s o f 0.4, one would have

64,h = 1 rad/& . ^{We w i l l} take t h i s a s o u r r e a l i s t i c s e n s i t i v i t y g o a l .

With o u r s i g n a l band width o f 2.5 kHz, t h i s is about a f a c t o r o f 25 above our e v e n t u a l g o a l (Virgo c l u s t e r ) . More powerful l a s e r s a r e one hope f o r t h e f u t u r e , and t h e r e a r e o t h e r p r o p o s a l s aiming a t a b e t t e r u t i l i z a t i o n of t h e a v a i l a b l e l a s e r power ("squeezed s t a t e s " LlOJ; " r e c y c l i n g " i l l ] ) . A t any r a t e , t h e s h o t n o i s e l i m i t s f o r t o d a y ' s l a s e r s would e a s i l y a l l o w t h e d e t e c t i o n of supernovae i n o u r own galaxy.

2. LASER NOISE

The n a t u r a l p u r i t y of a l a s e r is by f a r n o t s u f f i c i e n t t o allow t h e d e s i r e d s e n s i t i v i t y cff ,h of our i n t e r f e r o m e t e r . What t h e demands a r e i n our p a r t i c u l a r a p p l i c a t i o n w i l l be d i s c u s s e d i n t h i s c h a p t e r . The non-ideal behavior o f a l a s e r can m a n i f e s t i t s e l f a s f l u c t u a t i o n i n l a s e r power, i n beam geometry, and i n l a s e r f r e - quency. These t h r e e n o i s e s o u r c e s have i n common t h a t they become a p p a r e n t o n l y when accompanied by a p p r o p r i a t e asymmetries i n t h e i n t e r f e r o m e t e r . The frequency n o i s e w i l l t u r n o u t t o be t h e toughest problem, and t h e most r e l e v a n t a t t h i s conference, and so a f u r t h e r c h a p t e r w i l l be devoted t o t h e techniques o f c o n t r o l l i n g i t .

2.1 Power F l u c t u a t i o n s

F l u c t u a t i o n s i n t h e i n c i d e n t l i g h t power P w i l l , o f c o u r s e , become a p p a r e n t i n t h e o u t p u t c u r r e n t s of t h e photo d i o d e s ( F i g . 1 ) . A p l o t o f t h e r e l a t i v e power f l u c t u a t i o n s 6P/P i s shown i n Fig. 2 . They a r e t y p i c a l l y o f t h e o r d e r I O - ~ / ~ Z i n our frequency range of i n t e r e s t .

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C8-454 JOURNAL DE PHYSIQUE

The Michelson i n t e r f e r o m e t e r l e n d s i t s e l f t o applying a n u l l i n g technique, by which t h e e f f e c t s of power f l u c t u a t i o n s can be s t r o n g l y suppressed. One common method is t o measure the d i f f e r e n c e i n t h e photo c u r r e n t s , and one has t o o p e r a t e near a p o i n t o f equal c u r r e n t s i n t h e two diodes D+ and D-. The o t h e r method, t h e one we have implemented, i s t o use a phase modulation i n one arm and o p e r a t e near t h e i n t e r f e r e n c e minimum, monitoring it with o n l y one diode (D-). I n both c a s e s , f l u c - t u a t i o n s &/P i n t h e l a s e r power e n t e r o n l y according t o t h e q u a s i s t a t i c d e v i a t i o n 6LoP/i from t h e i d e a l o p e r a t i n g point.

A mechanical s e r v o loop, a c t i n g on t h e d i s t a n t m i r r o r s , c o n t r o l s t h e slow v a r i a t i o n s i n path l e n g t h d i f f e r e n c e (up t o , s a y , 30 Hz), and t h e high frequency d e v i a t i o n s a r e c o r r e c t e d o p t i c a l l y with a Pockels c e l l . The Pockels c e l l v o l t a g e a l s o r e p r e s e n t s t h e s i g n a l t o be analyzed f o r g r a v i t a t i o n a l events. The mechanical and t h e o p t i c a l s e r v o loops reduce t h e d e v i a t i o n s 6LOp t o something l i k e 10'' o f a wave l e n g t h , and s o t h e e f f e c t o f power f l u c t u a t i o n s is s u f f i c i e n t l y suppressed.

2.2 F l u c t u a t i o n s i n Beam Geometry

F l u c t u a t i o n s i n t h e geometry of t h e i l l u m i n a t i n g l a s e r beam w i l l i n t r o d u c e s p u r i o u s s i g n a l s i f t h e wavefronts o f t h e two outgoing beams a r e not p e r f e c t l y matched. I t i s e a s i l y seen, f o r i n s t a n c e , t h a t a t i l t , due t o a misaligned beam s p l i t t e r , would make t h e i n t e r f e r o m e t e r s e n s i t i v e t o a l a t e r a l j i t t e r o f t h e beam.

The l a t e r a l j i t t e r x has been measured with p o s i t i o n s e n s i t i v e photo diodes [4];

Fig. 3 shows a p l o t of i t s s p e c t r a l d e n s i t y ~ ( f ) . The amplitudes a r e very small compared with t h e beam width 2w (of about 1 mm), and t h i s allows a r e p r e s e n t a t i o n o f t h e n e a r l y gaussian beam by a fundamental mode TEM,,, contaminated with t r a n s v e r s e modes TEMm o f non-zero o r d e r m+n. The l a t e r a l j i t t e r is described a s an admixture Of a mode of o r d e r 1, having a (time varying) amplitude a ( t ) = 0.8 x(t)/w. An admixture o f modes o f o r d e r 2 would r e p r e s e n t p u l s a t i o n s 6~ i n beam width, which a l s o have been observed, and which lead t o spurious i n t e r f e r o m e t e r s i g n a l s i f t h e two i n t e r f e r i n g wave f r o n t s a r e mismatched i n t h e i r curvatures.

The mode r e p r e s e n t a t i o n of t h e f l u c t u a t i o n s i n beam geometry a l r e a d y s u g g e s t s t h e proper therapy: t h e beam i s made t o pass through a n o p t i c a l c a v i t y t h a t is tuned s o i t has maximum transmission o f t h e fundamental mode, but suppresses t h e t r a n s v e r s e modes, by a f a c t o r r e l a t e d t o t h e f i n e s s e o f t h e c a v i t y [13]. By implementing such a

"mode cleaner" we have been a b l e t o suppress t h e n o i s e due t o beam f l u c t u a t i o n s .

2.7 Frequency F l u c t u a t i o n s

The upper t r a c e of Fig. 4 shows t h e n a t u r a l frequency j i t t e r o f o u r ~ r + l a s e r , a f t e r some mechanical improvements had been implemented [4]. I n s i d e our frequency window we have s p e c t r a l d e n s i t i e s between 10 and 100

& .

There a r e s e v e r a l types of mismatches between t h e two i n t e r f e r o m e t e r arms by which frequency f l u c t u a t i o n s bv can be turned i n t o spurious s i g n a l s St.

Path Difference: It i s by no means impossible t o o p e r a t e t h e i n t e r f e r o m e t e r i n the "white" f r i n g e , i . e . with a r e s i d u a l path d i f f e r e n c e U < ~ / 2 . Due, however, t o i n e v i t a b l e d i f f e r e n c e s i n t h e m i r r o r c u r v a t u r e s , a good matching of t h e two outgoing wave f r o n t s may r e q u i r e o p e r a t i o n with r a t h e r l a r g e path o f f s e t s AL. We do not know t o what e x t e n t one can a d j u s t t h e m i r r o r c u r v a t u r e s , by applying a p p r o p r i a t e bending f o r c e s t o t h e mirrors.

To be on t h e s a f e s i d e , l e t u s assume t h a t i n a f i n a l c o n f i g u r a t i o n we have t o l i v e with a AL o f a s much a s 1 m. To a r r i v e a t t h e d e s i r e d s e n s i t i v i t t h e f r e - quency f l u c t u a t i o n s i n o u r frequency range should not exceed 5*10* Hz/ k . ^{When we}

compare t h i s with t h e free-running noise o f o u r ~ r + l a s e r (Fig. 4, upper t r a c e ) , we

s e e t h a t an improvement i n frequency s t a b i l i t y by a t l e a s t 3 powers of t e n is

required.

Fig. 4 Frequency j i t t e r 6J.

Free-running (upper t r a c e ) , and wzth f i r s t stage of frequency s t a b i l i z a t i o n

f lower trace).

S c a t t e r e d Light: An even more s t r i n g e n t demand a r i s e s from t h e e x i s t e n c e o f s c a t t e r e d l i g h t , which, due t o i t s n a t u r e , cannot be expected t o show much cor- r e l a t i o n i n t h e two arms. The s c a t t e r i n g a t o u r o p t i c a l s u r f a c e s , p a r t i c u l a r l y a t t h e d e l a y l i n e m i r r o r s , h a s been i n v e s t i g a t e d r e c e n t l y by Walter Winkler [14]. One f i n d s - a whole s e r i e s o f "echoes", w i t h d i f f e r e n t "delays" ALs, = 2m.R between t h e s c a t t e r e d l i g h t and t h e main beam, depending on how many r e t u r n t r i p s 2% were skipped (m < 0 ) , o r r e p e a t e d ( m > 0 ) . by t h e s c a t t e r e d l i g h t . A schematic diagram of t h e s e c o n t r i b u t i o n s i s shown i n Fig. 5.

The s t r o n g "echo" a t -N (= -138) r e s u l t s from s c a t t e r a t t h e Pockels c e l l b e f o r e t h e beam even e n t e r s t h e d e l a y l i n e ; o t h e r major c o n t r i b u t i o n s ( a t N , 2 N , e t c . ) r e p r e s e n t a d d i t i o n a l f u l l round t r i p s o f t h e s c a t t e r e d l i g h t i n t h e d e l a y l i n e . The f r a c t i o n o f l i g h t s c a t t e r e d , and t h e n f i n d i n g i t s way t o t h e photo diode t o i n t e r f e r e with t h e main beam, h a s been e s t a b l i s h e d t o be i n t h e o r d e r of i n power, o r o = 10-4 i n amplitude. The i n s e r t i n F i g 5 shows how t h e v e c t o r 8 superimposes on t h e main beam, with a phase $ = 2aALSc/1 t h a t i s a very l a r g e number, and t h a t changes very . r a p i d l y with a change i n frequency:

2aALSc

61

6 ~ .

C

To keep t h e phase e r r o r 60 = ~.cos$.631 i n t h e r e s u l t i n g f i e l d v e c t o r below o u r s h o t n o i s e l i m i t , a 150-km i n t e r f e r o m e t e r would r e q u i r e t h e frequency t o vary by no more than 63 = 3 . 1 0 - ~ H Z / ~ = ( o r 6</v = 0 . 5 . 1 0 - ~ ~ / & ) . So h e r e we want an improve- ment i n frequency s t a b i l i t y by a t l e a s t 4 powers o f t e n .

Fig. 5 Scattered l i g h t contributions i n our interferometer, us. "delay length" 2mR

with respect t o main beam. Insert: Scattered l i g h t of r e l a t i v e arrplitude o,

and of phase @, superinposing on main beam.

C8-456 JOURNAL DE PHYSIQUE

Finesse: Before we discuss how such a frequency control might be accomplished, let us briefly look at the requirements in the alternative approach of using two orthogonal Fabry-Perot interferometers. To suppress noise due to power fluctuations, the interferometer has to be operated at equal photo currents. The sensitivity of each Fabry-Perot to frequency fluctuations is proportional to its finesse F, and the difference signal, expressed as a phase error, might be represented by

.. _ 2TTL AF

As one can see, the requirements are even higher than those due to scattered light, unless one succeeds in matching the finesses of the two arms to better than AF/F = 10"*, the value of a.

3. FREQUENCY CONTROL

We have heard at this conference of several very powerful methods to stabilize the frequency of a laser. Again let me point out that in our application we are not so much concerned with long-term stability; however, inside our frequency window of interest (500...3000 H z ) , we want a suppression of the frequency fluctuations down to such extremely small spectral densities as 10"

Hz//Hz. The concept of our frequency control is, in some respects, modelled after these particular needs.

3.1 Feedback to the Laser Cavity

A first step toward the high noise suppression is a rather conventional feedback to the laser cavity (Fig. 6 ) . An optical resonator, evacuated to reduce statistical pressure fluctuations, is used as frequency reference. The amplified error signal is fed back to the laser in two ways. The high frequency part is applied to an intra- cavity Pockels cell (PC), whereas the low frequency portion, with its large dynamic swings, can only be handled by the piezo (PZT) driving the output mirror.

With a commercial resonator (TROPEL), a reduction of the frequency noise down to 1 Hz//Hz was achieved (Fig. 4, lower trace). Karl Maischberger has just implemented a new resonator having larger mirror spacing (25 cm), using a heavy Zerodur spacer for improved mechanical and thermal stability. This, together with an upgrading of the electronics, has reduced th'. frequency noise to 1.5-10

Hz/ vfizT With better mirror coatings, and perhaps a further extension of the length, values of \0~

Hz/v^te^

seem achievable. This is, however, still somewhat short of our goal of 3«10"

Hz/vUS".

Fig. 6 Frequently control, by feedback to the laser cavity. High frequency part: to

intracavity Pockels cell; low frequency part: to piezo drive of mirrors

3.2 Phase C o n t r o l Loop

A d e c i s i v e f u r t h e r improvement i s expected from t h e second s t a g e o f feedback c o n t r o l t h a t i s c u r r e n t l y being implemented by Roland S c h i l l i n g 1141. The e s s e n t i a l components c a n be found i n Fig. 7. One u t i l i z e s t h e i n t e r f e r o m e t e r i t s e l f , w i t h i t s l o n g o p t i c a l p a t h L, a s a v e r y s e n s i t i v e f r e q u e n c y measuring d e v i c e , by l e t t i n g one ( o r both) o f t h e o u t g o i n g beams i n t e r f e r e w i t h t h e undelayed l i g h t o f t h e incoming beam. T h i s i s s i m i l a r t o a scheme proposed f o r t h e Fabry-Perot i n t e r f e r o m e t e r [6].

The d e c i s i v e l y new f e a t u r e i s t h a t t h e r e s u l t i n g e r r o r s i g n a l i s n o t fed back t o t h e l a s e r , b u t i s used t o d r i v e a Pockels c e l l t h a t c o r r e c t s t h e phase (and t h u s t h e frequency) a f t e r t h e l i g h t h a s l e f t t h e l a s e r c a v i t y . The two s t a g e s o f f r e q u e n c y c o n t r o l a r e t h u s c o m p l e t e l y decoupled, and each can b e s e p a r a t e l y optimized. T h e i r n o i s e s u p p r e s s i o n f a c t o r s a r e m u l t i p l i e d .

Phase Control

Fig. 7 Phase control loop (dashed l i n e s ) . Interferometer arms used a s frequency reference; high frequency part o f error signal corrected by Pockels c e l l ; low frequency part corrected mechanically (mirror d i s t a n c e ) .

A s a P o c k e l s c e l l a l l o w s o n l y a l i m i t e d phase swing, t h e low f r e q u e n c y p o r t i o n o f t h e e r r o r s i g n a l is used t o c o r r e c t m e c h a n i c a l l y t h e m i r r o r p o s i t i o n s . The r e s u l t i s t h a t t h e m i r r o r d i s t a n c e s R, e x p r e s s e d i n wavelengths A , remain c o n s t a n t , and t h i s i s p r e c i s e l y what h a s t o b e done t o s u p p r e s s t h e n o i s e due t o s c a t t e r e d l i g h t . T h e r e f o r e , we a r e j u s t i f i e d t o use t h e e r r o r s i g n a l f o r judging what we have accom- p l i s h e d ( f o r o u r a p p l i c a t i o n ) .

With a r a t h e r crude p r e l i m i n a r y s e t - u p t h e f e a s i b i l i t y o f t h e concept h a s been

proved. The e r r o r s i g n a l , w i t h and w i t h o u t t h e second s t a g e o f c o n t r o l , i s shown i n

Fig. 8. An a r t i f i c i a l l y i n t r o d u c e d modulation, a t 4 kHz, e x h i b i t s t h e expected n o i s e

s u p p r e s s i o n by one power o f t e n . The s u p p r e s s i o n o f t h e n o i s e f l o o r is n o t q u i t e a s

good, f o r r e a s o n s y e t t o be analyzed. We have observed t h a t d r i v i n g t h e P o c k e l s c e l l

produces, a s a s i d e e f f e c t , r a t h e r s t r o n g v a r i a t i o n s i n beam geometry. These, i n

t u r n , g i v e a c o n t r i b u t i o n t o t h e e r r o r s i g n a l , which t h e feedback l o o p t r i e s t o

compensate by a s p u r i o u s s h i f t i n frequency. With a p r o p e r d e s i g n , and by p l a c i n g

t h e mode c l e a n e r a f t e r t h e P o c k e l s c e l l , we hope t o e l i m i n a t e t h i s d i f f i c u l t y .

JOURNAL DE PHYSIQUE

F i g . 8 S t a b i l i z a t i o n of l a s e r frequency;

upper t r a c e : o n l y f i r s t c o n t r o l loop, lower t r a c e : both c o n t r o l s t u r n e d on.

( E r r o r s i g n a l )

3 . 3 Breaking t h e Coherence

A t t h e end of the t a l k , I w i l l mention a p o s s i b i l i t y t o cope with o u r s c a t t e r e d l i g h t problem i n a way t h a t must seem l i k e blasphemy a t t h i s conference. Do n o t a l l our d i f f i c u l t i e s with t h e s c a t t e r e d l i g h t stem from t h e f a c t t h a t - d e s p i t e i t s huge path d i f f e r e n c e - i t i s s t i l l coherent'with t h e main beam? And does t h i s not mean t h a t t h e constancy o f our frequency is t o o good? I n a way t h i s i s r e a l l y t h e case.

By adding a frequency modulation ( o f c o u r s e w e l l o u t s i d e o u r frequency window) one can break t h e coherence between main beam and s c a t t e r e d l i g h t , whereas t h e i n t e r - f e r e n c e between t h e two main beams i s p r a c t i c a l l y unaffected.

One such method h a s been d e s c r i b e d and implemented by Roland S c h i l l i n g [15], and only q u i t e r e c e n t l y we have heard from Alain B r i l l e t t h a t t h e y had used a s i m i l a r ' method some y e a r s ago i n a d i f f e r e n t c o n t e x t L16J. The d i f f i c u l t y i n o u r a p p l i c a t i o n i s t h a t we want t o suppress simultaneously t h e d i f f e r e n t "echoes" of Fig. 5.

A simple harmonic phase modulation '4 = 8 - s i n m of t h e incoming beam a l l o w s us t o c a n c e l o u t t h e e f f e c t s of a s u b s e t of t h e s e echoes, i f t h e phase swing 0 and t h e modulation frequency 52 a r e p r o p e r l y chosen. With t h e a d d i t i o n of f u r t h e r p e r i o d i c components i n t h e modulation, a l a r g e r number o f t h e echoes can be suppressed, b u t t h e s u p p r e s s i o n w i l l no l o n g e r be a f u l l c a n c e l l a t i o n .

In a d i f f e r e n t approach, one could modulate t h e l a s e r frequency with broad band n o i s e ( a t h i g h f r e q u e n c i e s , s a y from 1 MHz upward). The s u p p r e s s i o n of t h e s c a t t e r e d l i g h t n o i s e w i l l be a f u n c t i o n of t h e r m s modulation phase swing and t h e modulation band width. Both must be very h i g h t o produce a p p r e c i a b l e e f f e c t s .

4. CONCLUSION

A f t e r t h i s h e r e t i c d i g r e s s i o n on reducing our i n t e r f e r o m e t e r n o i s e by adding

n o i s e t o t h e l a s e r frequency, l e t me remind you t h a t t h i s a f f e c t s only t h e n o i s e due

t o s c a t t e r e d l i g h t . F o r t h e main e f f e c t o f a r e s i d u a l path d i f f e r e n c e AL between t h e

two main beams, t h e r a t h e r s t r i n g e n t demand remains, o f keeping t h e frequency j i t t e r

down t o , s a y , 6u < 5 - 1 0 -2 Hz/&, perhaps even < 2.10-~ Be/dHz, f o r experiments i n t h e

d i s t a n t f u t u r e . Again, i t must be mentioned t h a t t h i s high p u r i t y i s required only

i n s i d e our frequency window between 500 and 3000 Hz. We a r e c o n f i d e n t t h a t such a

high degree of frequency s t a b i l i z a t i o n is within t h e realm of p o s s i b i l i t y , even with

r a t h e r conventional t e c h n i q u e s , but i t w i l l be an u p h i l l b a t t l e , each improvement by

a n o t h e r f a c t o r of t e n becoming more d i f f i c u l t . T h i s conference has n o t nourished any

i l l u s i o n s t h a t t h e d e s i r e d p u r i t y o f l a s e r behaviour might f a l l i n t o our l a p s .

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