LASER FREQUENCY STABILIZATION BY SATURATED ABSORPTION

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LASER FREQUENCY STABILIZATION BY SATURATED ABSORPTION

A. Brillet, P. Cérez

To cite this version:

A. Brillet, P. Cérez. LASER FREQUENCY STABILIZATION BY SATURATED ABSORPTION.

Journal de Physique Colloques, 1981, 42 (C8), pp.C8-73-C8-82. �10.1051/jphyscol:1981809�. �jpa-

00221704�

JOURNAL DE PHYSIQUE

Colloque C8, supplément au n° 12, Tome 42, décembre 1981 page C8-73

LASER FREQUENCY STABILIZATION BY SATURATED ABSORPTION

A. B r i l l e t and P. Cerez

Laboratoire de l'Horloge Atomique, Equipe de Recherche du CNRS, associée à l'Université Paris-Sud, Bât. 221, Université Paris-Sud, 91405 Orsay, France

A b s t r a c t . - This paper summarizes the metrological r e s u l t s available about s a t u r a t e d absorption s t a b i l i z e d l a s e r s . After r e c a l l i n g t h e i r fundamental l i m i t a t i o n s / we describe the p r e s e n t s t a t e of the a r t of the most important l a s e r s : CO_ a t 10.6 )jro, He-Ne a t 3.39 urn ,and v i s i b l e iodine s t a b i l i z e d s y s - tems. We show t h a t there i s a r e a l need for improved performances, and t h a t we now have a l l the t o o l s necessary t o f u l f i l l t h i s need.

1. I n t r o d u c t i o n . - During the l a s t decade, hundreds of papers ( s p e c u l a t i v e , t h e o r e - t i c a l and experimental) have been published concerning s a t u r a t e d absprption and o p t i c a l frequency s t a n d a r d s , and a l l the metrology l a b o r a t o r i e s have b u i l t and s t u - died t h e i r own He-Ne or CO or argon s t a b i l i z e d l a s e r s . About 20 more papers p r e - sented a t t h i s Symposium r e l a t e the l a t e s t t h e o r e t i c a l and experimental developments i n t h i s f i e l d . We thought i t could be useful to brush a coarse p i c t u r e of the p r e - sent s t a t e of the a r t i n order t o help the p o t e n t i a l user in understanding what can be r e a l l y expected from a s a t u r a t e d absorption s t a b i l i z e d l a s e r . We w i l l also t r y t o compare the achievements with the p r e s e n t and future needs, hoping t o stimulate some more e f f o r t s from the l a s e r people. The performances of the various standards w i l l be described by the usual q u a n t i t i e s : accuracy, r e p r o d u c i b i l i t y and s t a b i l i t y , defined by the Allan variance. We w i l l s p e c i a l l y emphasize the d i s t i n c t i o n between the r e p r o d u c i b i l i t y , which can be measured by comparing standards from d i f f e r e n t l a b o r a t o r i e s , and r e p e a t a b i l i t y , which concerns one standard, or a s e r i e s of s i m i l a r standards o r i g i n a t i n g from the same l a b o r a t o r y . This happens t o be necessary since the intercomparisons of d i f f e r e n t o p t i c a l standards show t h a t t h e " r e p r o d u c i b i l i t y "

estimates given by a l l the authors were usually too o p t i m i s t i c by an order of ma- gnitude.

After a rapid d e s c r i p t i o n of the more or l e s s fundamental l i m i t a t i o n s which are common t o a l l s a t u r a t e d absorption frequency s t a b i l i z e d l a s e r s , we w i l l consider the experimental r e a l i z a t i o n s , with s p e c i a l emphasis on the I s t a b i l i z e d systems in the v i s i b l e , the CH. s t a b i l i z e d systems a t 3.39 Mm and the COZ systems a t 10 pm. We w i l l f i n a l l y compare t h e i r performances with the present and future needs.

2. Line s h i f t s and asymmetries i n s a t u r a t e d a b s o r p t i o n . - In f l a t space, the conser- vation of the energy-momentum quadrivector leads t o the following formula for the resonant emission and absorption frequencies of a two-level atom of v e l o c i t y v, mass m and frequency s p l i t t i n g 0) , with respect t o an electromagnetic wave propagating along the x d i r e c t i o n :

(1)

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981809

C8-74 JOURNAL DE PHYSIQUE

This formula c o n t a i n s a l l t h e problems of t h e s a t u r a t e d a b s o r p t i o n t e c h n i q u e , i f we n e g l e c t l i g h t s h i f t s , Zeeman o r S t a r k s h i f t s and t h e g r a v i t a t i o m a l r e d s h i f t .

A. I n f l u e n c e of c o l l i s i o n s . - The time dependence o f w h a s been i n t r o d u c e d h e r e t o symbolize t h e p e r t u r b a t i o n of t h e atomic energy l e v e f s by c o l l i s i o n s w i t h o t h e r atoms. T h i s i s n o t r e a l l y a fundamental e f f e c t , b u t it i s i m p o r t a n t s i n c e i t i s known t h a t c o l l i s i o n n a l s h i f t and broadening have a non l i n e a r p r e s s u r e depen- dence i n s a t u r a t e d a b s o r p t i o n ( ' l 2 ) which f o r b i d d e n s t h e e x t r a p o l a t i o n s t o zero- p r e s s u r e and limits t h e accuracy although t h i s problem i s now w e l l understood theo- r e t i c a l l y . On t h e o t h e r hand, i n t h e low p r e s s u r e , h i g h r e s o l u t i o n c a s e , t h e p r e s - s u r e s h i f t s g e t very s m a l l , because t h e main e f f e c t becomes t h e v e l o c i t y change o f t h e molecule, which r e s u l t s i n broadening b u t n o s h i f t . I n methane a t 3.39 pm, t h e p r e s s u r e s h i f t i s o n l y 5 l ~ - ' ~ / m ~ o r r ( 3 ) , and very low v a l u e s were a l s o observed i n i o d i n e i n t h e v i s i b l e ( 4 , 5 ) .

So, t h e d i r e c t i n f l u e n c e o f c o l l i s i o n s can b e made n e g l i g i b l e a s concerns t h e r e p r o d u c i b i l i t y , and a l s o t h e accuracy, f o r gas p r e s s u r e s i n t h e s u b - m i l l i t o r r range.

B. Geometrical e f f e c t s . - --- I n t h e i d e a l c a s e of i n f i n i t e p l a n e waves propa- g a t i n g a l o n g t h e x d i r e c t i o n , t h e s a t u r g t e d a b s o r p t i o n technique completely sup- p r e s s e s t h e f i r s t - o r d e r Doppler s h i f t (A). I n t h e p r a c t i c a l case o f f i n i t e Gaussian

, *.

waves one g e t s a broadening, and, e v e n t u e l l y , a s h i f t ' " I , i f t h e 2 counterpropaga- t i n g waves have unequal i n t e n s i t i e s and i f t h e absorbing medium i s n o t s y m e t r i c a l r e l a t i v e t o t h e w a i s t . This"wavefront c u r v a t u r e s h i f t " i s probably n e g l i g i b l e i n a l l i n t e r n a l c e l l systems although it h a s . never been f u l l y e v a l u a t e d i n t h a t case.

I t i s a l s o n e g l i g i b l e i n a l l t h e h i g h r e s o l u t i o n d e v i c e s u s i n g expanded beams.

:, C. Q u a d r a t i c D0~e;J.r e f f e c t . - The q u a d r a t i c Doppler e f f e c t i s a r e d s h i f t v -

(- 7 ) . Its o r d e r o f magnitude f o r t h e most probable v e l o c i t y o f a Boltzmann &is- 2 cA

KT , t h a t i s : - 1.72 10-l2 f o r CH a t 3.39 p, - ^1.08

t r i b u t i o n a t T

i s - w- ---;; 4

u

mc -13

10'13 f o r OsO, a t 10.6 pm, and - 1.08 10 f o r I , , a t 300' K. Its temperature dependence isY- 5.7 I O - ~ ~ O K - ' f o r CH4 ( 3 ) , and l e s s ;or t h e h e a v i e r molecules, s o i t does n o t s e r i o u s l y l i m i t t h e r e p r o d u c i b i l i t b u t i t i s n e c e s s a r y t o e v a l u a t e it p r e c i s e l y i n o r d e r t o reach an accuracy of I n t h e low s a t u r a t i o n l i m i t , Ch.J.

Bord6 ( 7 ) could g i v e an a n a l y t i c a l e x p r e s s i o n f o r t h e l i n e s h a p e i n s a t u r a t e d absorp- t i o n , i n c l u d i n g t h e q u a d r a t i c Doppler e f f e c t and t h e beam geometry. The i m p o r t a n t r e s u l t i s t h a t t h e q u a d r a t i c Doppler e f f e c t causes power dependent, a s w e l l as reso- l u t i o n dependent asymmetry and s h i f t of t h e resonance l i n e . This e f f e c t h a s been demonstrated i n a s p e c t a c u l a r way by Barger ( * ) , i n a calcium beam. T h i s seems t o forbidden t h e use o f l i g h t molecules i n h i g h accuracy work, u n l e s s one can c o o l them o r o p e r a t e a v e l o c i t y s e l e c t i o n .

D. Recoil ef_fe_ht.- The importance o f t h e f o u r t h term i n eq. ( 1 ) , t h e r e c o i l e f f e c t h a s been p o i n t e d o u t b y Kol 'Chenko e t a 1 (')', a s soon i n 1968. I n s a t u r a - t e d a b s o r p t i o n l i n e s , it produces a s p l i t t i n g 6 = 1 - 3 3 lo-' ' 1 M-I where 1 is t h e wavelength i n microns and M i s t h e molecular weight. The value o f t h i s s p l i t -

-12

t i n g i s 2.45 lo-" ^{i n CHI,} 4 10-l3 i n Os04 and 8.3 10 m 12. I n most c a s e s , t h i s s p l i t t i n g i s n o t r e s o l v e d , and it r e s u l t s an i n a c c u r a c y from t h e f a c t of t h e two components o f t h e d o u b l e t have unequal i n t e n s i t i e s i f t h e r e l a x a t i o n r a t e s o f t h e two atomic l e v e l s a r e d i f f e r e n t . More d e t a i l e d t h e o r e t i c a l s t u d i e s show t h a t t h e

s p l i t t i n g becomes s m a l l e r t h a n 6 when power broadening o c c u r s ( 1 0 ~ 1 1 ~ 1 2 ) ~ h ~ i ~ r e s u l t s a r e confirmed b y experimental a a t a ( 8 f 1 3 ) . I n t h e case of p u r e t r a n s i t

broadening, t h e e f f e c t i v e r e l a x a t i o n r a t e s o f t h e two l e v e l a r e given by t h e i n -

v e r s e o f t h e t r a n s i t time : t h e y a r e e q u a l and t h e r e i s no s h i f t due t o t h e r e c o i l .

Another i n t e r e s t i n g case happens a t h i g h e r p r e s s u r e , where t h e r a t i o o f t h e ampli3-

tudes o f t h e two components becomes p r e s s u r e independent. High r e p r o d u c i b i l i t y can

be o b t a i n e d i n t h a t c a s e , b u t t h e accuracy i s l i m i t e d .

Considering t h e above problems, it seems t h a t u l t r a h i g h r e s o l u t i o n i s n o t compatible w i t h high accuracy, u n l e s s t h e atoms a r e cooled. On t h e o t h e r hand, t h e a r t i c i f i a l broadening s o u r c e s may induce s h i f t s ( c o l l i s i o n s , t r a n s i t t i m e ) . A very good compromise may be t h e c a s e of t h e I 2 molecule i n a low p r e s s u r e c e l l o r a beam. For w e l l chosen t r a n s i t i o n s , t h e l l n e w i d t h i s l i f e t i m e - l i m i t e d t o about 50 kHz (Q =

I

s o t h a t t h e r e c o i l e f f e c t can be d e s c r i b e d a c c u r a t e 1 ; t h e quadra- t i c Doppler e f f e c t i s weak enough, compared t o t h e l i n e w i d t h , t o prozuce o n l y a s h i f t and no asymmetry. The l i g h t beam w a i s t s i z e needs o n l y be a few m i l i m e t e r s t o avoid any g e o m e t r i c a l e f f e c t .

A f t e r t h i s paragraph, whose main g o a l was t o remember o r d e r s o f magnitude and t o give t h e r e f e r e n c e s o f some i m p o r t a n t t h e o r e t i c a l c o n t r i b u t i o n s , l e t us t r y t o understand t h e e x p e r i m e n t a l i s t ' s problems.

3. Experimental r e s u l t s . - The m e t r o l o g i c a l d a t a a v a i l a b l e today concern mainly t h e following systems :

- s t a b i l i z a t i o n t o I2 h y p e r f i n e components i n t h e v i s i b l e . The b e s t documen- t e d and most widely developped s t a b i l i z e d l a s e r i s + t h e He-Ne w i t h an i n t e r n a l I2 c e l l a t 633 nm. The most performant ones a r e t h e A l a s e r and He-Ne l a s e r s t a b i - l i z e d on e x t e r n a l c e l l s a t 515 and 612 nm.

- ^He-Ne-CH4 systems a t 3.39 um.

- ^CO l a s e r s locked by s a t u r a t e d a b s o r p t i o n i n Os04 and SF6 and by s a t u r a t e d fluorescence2 i n CO

E x c e l l e n t stabilities have been o b t a i n e d w i t h t h e He-Xe l a s e r a t 3.51 Um, locked on 2' H CO ( I 4 ) b u t t h i s system i s n o t much documented y e t .

2

A. S _ t a b i l i z a t i o n by s a t u r a t e d - ~ ~ o _ ~ t i o n i n iodine.- The i o d i n e molecule 1271 has a very r i c h a b s o r p t i o n spectrum i n t h e v i s i b l e , which c o n t a i n s about 50 080 s t r o n g l i n e s between 15 000 and 20 000 cm-l. Each of t h e s e l i n e s h a s an h y p e r f i n e s t r u c t u r e 900 MHz wide f e a t u r i n g 15 o r 21 main components. The weakly r a d i o a c t i v e 1 2 9 ~ has a s i m i l a r i l y dense spectrum, w i t h d i f f e r e r h h y p e r f i n e s t r u c - t u r e s because o f 2 t h e d i f f e r e n t n u c l e a r s p i n (9/2 i n s t e a d 5/21. The l i f e t i m e s o f t h e e x c i t e d l e v e l s corresponding t o t h e s e t r a n s i t i o n s vary between 0.3 U s f o r h i g h l y p r e d i s s o c i a t e d l e v e l s and t e n o f microseconds f o r t h e low Franck-Condon l e v e l s which l i e n e a r t h e d i s s o c i a t i o n l i m i t , s o t h e Q f a c t o r corresponding t o t h e n a t u r a l l i n e - width v a r i e s bstween 10' and 10". ~t r e s u l t s t h a t any l a s e r e m i t t i n g between 5000 and 6500 A , w i t h a t u n a b i l i t y o f 1 GHz o r more, w i l l probably c o i n c i d e i n f r e - quency with some o f t h e s e h y p e r f i n e components. T h i s f a c t h a s been used t o frequency s t a b i l i z e argon and krypton l a s e r s a t d i f f e r e n t wavelengths ( I 5 16) and He-Ne l a s e r s

a t 633 ⁽ 18)

( I 7 ) and 612 nm .

Let us f i r s t d e s c r i b e t h e achievements and t h e l i m i t a t i o n s o f t h e b e s t known system, t h e He-Ne l a s e r w i t h an i n t e r n a l i o d i n e c e l l a t 633 nm.

1 ) I n t e r n a l c e l l systems.

Since t h e f i r s t o b s e r v a t i o n of s a t u r a t e d a b s o r p t i o n of t h e R(127)6-3 l i n e of 1271 by Hanes and Dahlstrom

2 ( I 7 ) with a He-Ne l a s e r a t 633 nm, a l l t h e wavelength

metrology l a b s i n t h e world have b u i l t s i m i l a r systems and t h e y use i t , now, i n s t e a d of t h e krypton lamp, f o r most a p p l i c a t i o n s . A k i n d o f " s t a n d a r d " s e t - u p h a s e s t a b l i - shed by h i m s e l f : t h e t y p i c a l system i s a 40 cm long c a v i t y , c o n t a i n i n g a 10 cm i o - d i n e c e l l whose p r e s s u r e i s f i x e d around 100 mTorr w i t h a c o l d f i n g e r a t 1S0C and a 20 cm long He-Ne g a i n c e l l . S i n g l e frequency o p e r a t i o n r e s u l t s from t h e s h o r t l e n g t h and from t h e i n t r a c a v i t y a b s o r p t i o n l o s s e s . T r a n s v e r s e modes a r e e l i m i n a t e d by d i f f r a c t i o n l o s s e s due t o t h e s m a l l diameter o f the He-Ne t u b e ( 1.1 mm t y p i c a l l y ) .

The s a t u r a t e d a b s o r p t i o n s i g n a l s have a c o n t r a s t of 2 and a width of 5 MHz (FWHM). Because of t h e s l a t e d background due t o t h e He-Ne g a i n c u r v e , i t i s neces- s a r y t o use a 3rd harmonic d e t e c t i o n (19), t h e optimum modulation amplitude b e i n g 7 MHz p. t o p. Such systems have now been b u i l t i n about 15 d i f f e r e n t c o u n t r i e s (20 to 32) and probably more t h a n 50 l a b o r a t o r i e s use i t now a s a r e f e r e n c e f o r wavelength metrology o r h i g h r e s o l u t i o n spectroscopy.

During t h e f i r s t y e a r s (1970-76) , ^{t h e main} e f f o r t was p u t on t h e improvement

of t h e servo-loop e l e c t r o n i c s : t h e weak c o n t r a s t of t h e s a t u r a t e d a b s o r p t i o n s i g n a l s

C8-7 6 JOURNAL DE PHYSIQUE

r d ask f o r low n o i s e and low o f f s e t s e r v o loops. Furthermore, t h e use o f t h e 3 h a r - monic d e t e c t i o n p u t s s t r i n g e n t l i m i t s on t h e t o l e r a b l e harmonic d i s t o r s i o n s o f t h e frequency modulation (33 1.

BY 1975, most o f t h e l a b o r a t o r i e s agreed upon a s t a b i l i t y of about 2 10-13 f o r T > 100 s , probably l i m i t e d by f l u c t u a t i o n s o f t h e i o d i n e p r e s s u r e (- 1 MHz/Torr), and a r e p e a t i b i l i t y o f 1 t o 2 p a r t s i n lo1'. Everybody was unhappy w i t h t h e weak c o n t r a s t , and w i t h t h e broad l i n e s , which s h o u l d have been 10 times narrower, ac- cording t o t h e l i f e t i m e measurements (341of t h e e x c i t e d l e v e l , b u t , s t r a n g e l y enough, nobody h a d t r i e d t o modelize t h e p h y s i c a l system. The t h e o r e t i c a l b a s i s was a v a i l a - b l e (35) , b u t t h e d i f f i c u l t y was t o e v a l u a t e all t h e r e l e v a n t parameters. The quan- t i t a t i v e model we made i n 1976 (36)allowed us g e t a good d e s c r i p t i o n o f t h e c o n t r a s t and width of t h e s i g n a l s and o f t h e i r v a r i a t i o n w i t h t h e i o d i n e p r e s s u r e . I t r e s u l - t e d from t h i s model t h a t t h e c o n t r a s t would be improved by a f a c t o r o f t e n when h e a t i n g t h e I c e l l t o 200°C, a t c o n s t a n t p r e s s u r e , which was r a p i d l y v e r i f i e d e e- r i m e n t a l l y ( 3 3 3 8 ) , allowing one t o improve t h e short-term s t a b i l i t y o f t h e

But t h e e l a b o r a t i o n o f t h i s model a l s o t a u g h t u s about t h e l i m i t a t i o n s o f i n t e r n a l c e l l d e v i c e s : t h e main one i s t h a t i n simple He-Ne-I2 systems, it i s n o t p o s s i b l e t o reach a narrow l i n e w i d t h , because, when d e c r e a s i n g t h e i o d i n e p r e s s u r e , one i n c r e a s e s t h e power broadening. This could be avoided o n l y by expanding t h e beam i n t h e i o d i n e c e l l , which i s d i f f i c u l t w i t h such a low g a i n l a s e r , o r by running i t very c l o s e t o t h r e s h o l d , which would b e very n o i s y , and anyway very uneasy t o con- t r o l and t o use. Although it d e s c r i b e s c o r r e c t l y t h e c o n t r a s t and width o f t h e l i n e s , t h i s model does n o t i n c l u d e t h e causes o f asymmetries and s h i f t s , which go- vern t h e r e p r o d u c i b i l i t y of t h e l a s e r s .

Apart from t h e s t u d i e s made i n each l a b . , t h e problem of r e p r o d u c i b i l i t y h a s been p a r t i c u l a r l y s t u d i e d by t h e B. I .P.M. group, through t h e numerous intercompa- r i s o n t h e y made w i t h o t h e r l a b o r a t o r i e s (23140) . This work p o i n t e d o u t two pro- blems ; t h e f i r s t one i s t r i v i a l and concerns t h e p u r i t y o f t h e i o d i n e : any non condensable vapor, p r e s e n t i n t h e i o d i n e c e l l w i t h a p r e s s u r e of 0.05 T o r r o r more, can produce a s h i f t a s l a r g e a s 100 kHz (2 1 0 - l ~ ) , w i t h o u t a f f e c t i n g i n a n o t i c e a - b l e way t h e l i n e w i d t h o r c o n t r a s t of t h e s i g n a l i n an i n t e r n a l c e l l system. SO, i t i s n e c e s s a r y t o be a b l e t o check t h e absence of a f o r e i g n vapor e i t h e r by u s i n g t h e Hanle e f f e c t ( 4 l ) o r by a d i r e c t f l u o r e s c e n c e l i t e f i m e measurement from a long l i v e d s t a t e . The second problem i s an asymmetry o f t h e l i n e s , which r e s u l t s i n a modulation s h i f t o f - 5 kHz/MHz. Among t h e p o s s i b l e o r i g i n s o f t h i s e f f e c t , one can imagine t h e f o l l o w i n g :

a) Asymetric "Fano l i n e s h a p e " r e s u l t i n g from t h e I p r e d i s s o c i a t i o n : accor- d i n g t o a t h e o r e t i c a l e v a l u a t i o n ( 4 2 ) t h i s e f f e c t s h o u l d be t o o small. 2

b) harmonic d i s t o r s i o n s coming from t h e s a t u r a t e d d i s p e r s i o n e f f e c t ( f r e - quency p u l l i n g ) ( 4 3 ) would a l s o be t o o small.

C )

frequency dependent d i f f r a c t i o n l o s s e s due t o t h e gas-lens e f f e c t (44 t o 46)

because o f t h e r a d i a l i n t e n s i t y dependence o f t h e g a u s s i a n beam, t h e i o d i n e c e l l may s l i g h t l y focus o r defocus t h e beam according t o t h e s i g n o f t h e frequency de- t u n i n g r e l a t i v e t o t h e n e a r e s t h y p e r f i n e component. I f t h e d i f f r a c t i o n l o s s e s a r e s i g n i f i c a n t , t h i s e f f e c t w i l l superimpose a d i s p e r s i o n shaped power v a r i a t i o n upon t h e s a t u r a t e d a b s o r p t i o n s i g n a l , producing a l i n e asymmetry. I n He-Ne l a s e r s , a d i f f r a c t i o n l o s s of 2 - 5 % r e s u l t s from t h e s m a l l diameter o f t h e g a i n c e l l , and t h i s e f f e c t may be r e l a t i v e l y important. U n f o r t u n a t e l y , it i s d i f f i c u l t t o e v a l u a t e i t , s i n c e i t s amplitude and even i t s s i g n may change w i t h t h e c a v i t y geometry.

A r e c e n t computation of t h i s e f f e c t made by one of us (P.C.), on t h e b a s i s o f Le F l o c h ' s model(46) shows t h a t , i n a t y p i c a l He-Ne I2 system, it can produce modu- l a t i o n s h i f t s a s l a r g e as a few ~ H Z / M H Z , b u t w i t h a s i g n a p p o s i t e t o what h a s been g e n e r a l l y observed. I t i s p o s s i b l e t h a t t h i s d i f f r a c t i o n l o s s e f f e c t may be compen- s a t e d by t h e f a c t t h a t t h e number of a c t i v e Ne atoms i s a l s o changed by t h e beam geometry m o d i f i c a t i o n .

d) t h e asymmetry due t o wavefront c u r v a t u r e . Once a g a i n , a c o a r s e e v a l u a t i o n ( 4 7 ) p r e d i c t s a n e g l i g i b l e e f f e c t , b u t t h e e f f e c t h a s n e v e r been c a r e f u l l y e v a l u a t e d

i n an i n t e r n a l c e l l system.

e ) modulation and e l e c t r o n i c d i s t o r s i o n s : t h e p r e s e n c e o f 2 nd harmonic dis-

t o r s i o n i n t h e frequency modulation o f t h e l a s e r w i t h a r a t e o f 0.5 t o 1 % would b e

s u f f i c i e n t t o e x p l a i n t h e modulation s h i f t s ( 4 8 ) . Rut s i n c e t h e i r s i g n i s t h e same

f o r a l l l a s e r s , t h e phase o f t h i s second harmonic d i s t o r s i o n s h o u l d be t h e same.

*is i s u n l i k e l y , u n l e s s t h e d i s t o r s i o n comes from an h y s t e r e s i s e f f e c t common t o a l l P.Z.T. The measurements which have been made of t h e PZT d i s t o r s i o n s (45,

47) seem t o r u l e o u t t h i s p o s s i b i l i t y .

I n t h e s e i n t e r n a l c e l l systems, a l l t h e parameters o f t h e g a i n and t h e absorp- t i o n c e l l s , t h e c a v i t y geometry and l o s s e s , and t h e modulation amplitude have t o b e taken i n t o account s i m u l t a n e o u s l y i n o r d e r t o make a r e a l i s t i c e v a l u a t i o n of t h e above e f f e c t s . Furthermore, it i s extremely d i f f i c u l t t o make any s i g n i f i c a n t expe- r i m e n t a l t e s t i s o l a t i n g one o f t h e s e e f f e c t s , s i n c e all t h e parameters a r e coupled.

For i n s t a n c e , i f one t r i e s t o i s o l a t e t h e " d i f f r a c t i o n l o s s e s - gas-lens" e f f e c t by adding a p i n h o l e i n s i d e t h e l a s e r c a v i t y , h e w i l l simultaneously modify t h e l i g h t i n t e n s i t y , and t h e n t h e power broadening, and t h e n t h e r a t i o o f t h e modulation am- p l i t u d e t o t h e homogeneous width. A frequency s h i f t w i l l r e s u l t whatever t h e e f - f e c t a , b , c , d o r e i s r e s p o n s i b l e f o r t h e asymmetry, and no u s a b l e i n f o r m a t i o n can be o b t a i n e d .

W e t h i n k it i s wise t o conclude t h a t t h e s e l a s e r a r e u s e f u l and r e l i a b l e s t a n - dards a t t h e p r e c i s i o n l e v e l o f 1 p a r t i n provided t h e o p e r a t i n g c o n d i t i o n s a r e c l o s e t o t h e "standard" d e v i c e d e s c r i b e d above. Even i f t h e asymmetry was ex- p l a i n e d , i t would b e i l l u s o r y t o hope f o r 1 p a r t i n loi1, because it would r e q u i r e t h e s p e c i f i c a t i o n o f t o o many o p e r a t i n g parameters w i t h t o o h i g h a p r e c i s i o n .

The above c o n s i d e r a t i o n s a r e a l s o v a l i d f o r i n t e r n a l c e l l A + s t a b i l i z e d l a - s e r s and He-Ne l a s e r s a t 612 nm, w i t h o n l y s l i g h t d i f f e r e n c e s . The obvious way t o improve t h e s i t u a t i o n i s t o use an e x t e r n a l c e l l system. This i s u n f o r t u n a t e l y d i f - f i c u l t a t 633 nm, because t h e R(127) 11-6 l i n e i s a weak one, b u t i t h a s been done a t 515 and 612 nm ( 4 ~ 4 9 ) .

2) E x t e r n a l c e l l systems.

A) Argon l a s e r s a t 515 nm.- This system h a s been s t u d i e d by Carny ( 4 ) and Spieweck (5DJ.-%e-IodIne-iinessat 515 nm a r e i n t e r e s t i n g because t h e y a r e s t r o n g and p o t e n t i a l l y narrow. Using expanded l a s e r beams i n a low p r e s s u r e I2 c e l l , Carny ob- t a i n e d a l i n e w i d t h of 70 kHz, c l o s e t h e n a t u r a l l i n e w i d t h . He r e p o r t e d a s t a b i l i t y of 5 10-14 f o r r = 100 s , and a r e p e a t a b i l i t y o f 1.5 10-12, l i m i t e d by t h e l a s e r beams geometry and alignment. He a l s o demonstrated t h e p o s s i b i l i t y of u s i n g Doppler g e n e r a t e d l e v e l c r c s s i n g s , which have t h e advantage o f b e i n g f r e e o f r e c o i l s p l i t - t i n g , b u t t h e drawbacks o f being weaker t h a t t h e main l i n e s and s e n s i t i v e t o l i g h t - s h i f t s .

1271

B ) He-Ne l a s e r a t 612 nm.- The R(47) 9-2 and P(48) 11-3 l i n e s a t 612 nm a r e s t r o n g enough t o g i v e good s i g n a l s i n an e x t e r n a l c e l l , b u t t h e He-Ne l a s e r a t 612 nm i s r a t h e r weak (300 WW t y p i c a l l y ) . So, we chose t o enhance t h e s a t u r a t e d ab- s o r p t i o n s i g n a l s by p u t t i n g t h e I2 c e l l i n s i d e a high f i n e s s e (100) Fabry P e r o t r e s o n a t o r , whose r e s o n a n t frequency i s s e r v o locked t o t h e l a s e r frequency (51).

The m u l t i p a s s e f f e c t i n t h e Fabry P e r o t g r e a t l y i n c r e a s e s t h e c o n t r a s t , s o t h a t it i s p o s s i b l e t o use low i o d i n e p r e s s u r e s ( 3 m o r r ) and t o o b t a i n narrow l i n e w i d t h s

(200 kHz) and l a r g e S/N r a t i o . The Fabry P e r o t c a v i t y , i n c l u d i n g a t e l e s c o p e , de- f i n e s a wide beam, of h i g h g e o m e t r i c a l q u a l i t y , t h e two c o u n t e r p r o p a g a t i n g waves being self-matched. These c o n d i t i o n s a r e h i g h l y s u i t a b l e f o r m e t r o l o g i c a l a p p l i c a - t i o n s . A f i r s t comparison o f two s i m i l a r systems allowed us t o demonstrate l o n g term s t a b i l i t y (r > 100 s) of 2 10-13 and a r e p e a t i b i l i t y o f 6 10-l3 (300 H z ) , un- f o r t u n a t e l y l i m i t e d by e l e c t r o n i c o f f s e t s .

We could v e r i f y t h e h i g h symmetry o f t h e l i n e s from t h e absence of modulation s h i f t , and we were n o t a b l e t o measure any power s h i f t w i t h i n t h e r e s o l u t i o n o f 6 10-13, s o we can s t i l l e x p e c t some improvements. We t h i n k t h i s technique could b e u s e f u l i n conjunction w i t h o t h e r l a s e r s (argon, dye o r o p t i c a l l y pumped Na2,Li2.. .

l a s e r s ) , p r o v i d i n g a r e f e r e n c e g r i d i n t h e v i s i b l e w i t h a r e p r o d u c i b i l i t y o f o r b e t t e r .

C) ;h_~-H_e_-Ne CH4 system a t 3.39 Wm.- The He-Ne l a s e r a t 3.39 pm s t a b i l i z e d on t h e F ( 2 ) component of t h e P ( 7 ) l i n e of t h e v, branch of C H A i s one of t h e most important systems f o r h i s t o r i c a l r e a s o n s , b e c i u s e it was uszd by Barger and all'^^),

who f i r s t demonstrated t h e f e a s i b i l i t y o f hi9h performance o p t i c a l frequency s t a n -

JOURNAL DE PHYSIQUE

d a r d s , and f o r p r a c t i c a l r e a s o n s , because it l i e s i n t h i s narrow p a r t of t h e spec- trum where b o t h wavelength and frequency can p r e s e n t l y be measured w i t h h i g h p r e c i - s i o n . T h i s i s why i t was used f o r t h e d e t e r m i n a t i o n of t h e v e l o c i t y o f l i g h t ( 5 3 2

The work o f Barger and H a l l was followed by many s t u d i e s i n d i f f e r e n t coun- t r i e s . Most of t h e m e t r o l o g i c a l s t u d i e s ( e v a l u a t i o n o f s t a b i l i t y and r e p e a t i b i l i t y ) were made w i t h simple i n t e r n a l c e l l systems (54,55,561 5 7 ) , while more fundamental s t u d i e s were undertaken, mainly a t JILA ( H a l l and co-workers) and Novosibirsk

(Chebotayev and co-workers) , i n o r d e r t o i n c r e a s e t h e r e s o l u t i o n and t o reach t h e fundamental limits. Other groups from USSR s t u d i e d d i f f e r e n t ways o f improving t h e c o n t r a s t of t h e CH4 resonance v i a mode competition i n l i n e a r o r r i n g l a s e r c a v i t i e s

(58,591 . C o n t r a s t s o f up t o 80 % have been o b t a i n e d , i n t h a t wayr w i t h a l i n e w i d t h of 100 kHz o r l e s s , which l e a d s t o a p o t e n t i a l s t a b i l i t y o f 10-15/Jr. The frequency p u l l i n g of t h e l a s e r , due t o s a t u r a t e d d i s p e r s i o n h a s a l s o i n v e s t i g a t e d and used f o r l o c k i n g t h e l a s e r s (59,431 .

The most s i g n i f i c a n t r e s u l t s from t h e viewpoint of metrology a r e t h e f o l l o - wing : t h e simple i n t e r n a l c e l l systems t y p i c a l l y show a s t a b i l i t y o f I O - ' ~ / / T and a r e p e a t i b i l i t y o f 1-2 10-11. They e x h i b i t a power s h i f t and a l i n e asymmetry a t h i g h i n t e n s i t y ; b o t h can be e x p l a i n e d by t h e presence of h y p e r f i n e s t r u c t u r e o f t h e

~ ~ ( 2 ) l i n e c6O), which i s n o t r e s o l v e d i n t h e s e systems, b u t h a s been c l e a r l y r e s o l - ved by H a l l and Borde (61), and l a t e r by o t h e r groups (59162) .This h y p e r f i n e spec- trum c o n t a i n 3 main components w i t h a s p a c i n g of = 11 kHz p l u s 3 weaker ones and some S o p p l e r g e n e r a t e d l e v e l c r o s s i n g s . Even a t t h e h i g h e s t r e s o l u t i o n ( 1 kHz) ob- t a i n e d by H a l l and Borde, a l l t h e components a r e n o t completely r e s o l v e d . Every s t a b i l i z e d l a s e r u s i n g t h e F 2 ( 2 ) l i n e i s locked "somewhere" i n t h e middle o f t h i s h y p e r f i n e s t r u c t u r e , and t h e l o c k i n g p o i n t v a r i e s w i t h t h e r e s o l u t i o n and t h e l i g h t i n t e n s i t y , because t h e r e l a t i v e i n t e n s i t i e s o f t h e h y p e r f i n e components and t h e D.G.L.C. have d i f f e r e n t s a t u r a t i o n parameters. These e f f e c t s can b e computed i n o r d e r t o e v a l u a t e t h e power s h i f t and l i n e asymmetry o f a given e x p e r i m e n t a l set-up.

Bagaev and Chebotayev (3)could f i n d some s p e c i f i c c o n d i t i o n s i n which t h e frequency of t h e i r l a s e r s i s n o t t o o much dependent on power and modulation parameters. Using two i d e n t i c a l l a s e r s f u n c t i o n n i n g i n t h e s e w e l l d e f i n e d c o n d i t i o n s , t h e y could reach a s t a b i l i t y o f 5 10-l5 f o r T = 100 s , and a r e p e a t i b i l i t y o f 3 10-14. I t i s p o s s i b l e t h a t a s i m i l a r l a s e r b u i l t independently i n a n o t h e r l a b o r a t o r y would con-

f i r m a r e p r o d u c i b i l i t y of - 10-l3, b u t t h e n e c e s s i t y o f s p e c i f y i n g a l l t h e o p e r a t i n g c o n d i t i o n s i n o r d e r t o g e t a good r e p r o d u c i b i l i t y i s n o t a very s a t i s f a c t o r y s i t u a - t i o n , although t h e r e i s a l r e a d y a p r e c e d e n t , w i t h t h e krypton lamp.

The obvious way t o overcome t h e H.F.S. problem i s t o use t h e E - l i n e o f CH which l i e s 3 GHz t o t h e r e d o f t h e F 2 ( ' ) , and h a s no s t r u c t u r e . I n 1975, we showed 4, t h a t i t was n o t d i f f i c u l t t o t u n e t h e 0-Ne g a i n curve w ' t h a magnetic f i e l d Of .18 T e s l a i n o r d e r t o observe t h e E-line. The g a i n on t h e 0' and T components i s e a s i l y quenched w i t h a CH B r a b s o r p t i o n . More r e c e n t l y , Koshelyaevskii e t a 1 (64) made a deeper s t u d y o f t h e m e t r o l o g i c a l p r o p e r t i e s of E-line s t a b i l i z e d He-Ne l a s e r s . 3 A s expected, t h e power s h i f t and l i n e asymmetry a r e much weaker t h a n w i t h t h e F 2 ( 2 ) l i n e . They could observe an asymmetry r e l a t e d t o d i f f r a c t i o n l o s s e s . This problem was s o l v e d by i n c r e a s i n g t h e g a i n c e l l d i a m e t e r , and t h e y o b t a i n e d a r e p e a t i b i l i t y o f 5 10-13 with a simple system ( 6 5 ) . T h e i r l i n e s h a p e i s very s y m e t r i c a l , b u t t h e r e remains a weak power s h i f t , which i s probably due t o t h e q u a d r a t i c Doppler e f f e c t . I t seems t h a t t h i s fundamental e f f e c t w i l l l i m i t t h e r e p r o d u c i b i l i t y and accuracy of CH4 s t a b i l i z e d l a s e r s t o about 1 p a r t i n 1013, a t l e a s t when one u s e s a c e l l . Another cause o f power s h i f t i n a c e l l is t h e coupling of power broadening w i t h non- l i n e a r c o l l i s i o n a l s h i f t and b r o a d e n i n g ( 6 6 ) .

I t is d i f f i c u l t t o understand why t h e E-line i s n o t y e t of g e n e r a l use i n CH4

s t a b i l i z e d l a s e r s . The main reason i s probably t h a t t h e r e p e a t i b i l i t y o f 2 10-11

o b t a i n e d w i t h t h e F2 ( 2 ) systems was c o n s i d e r e d a s b e i n g "good enough" f o r their ap-

p l i c a t i o n s i n frequency s y n t h e s i s chains and i n wavelength measurements. Unfortuna-

t e l y , i n t e r c o m p a r i s o n s have been made i n 1976 between a few CH4 s t a b i l i z e d l a s e r s

from NPL, BIPM and PTB ( 5 7 ) , whose c o n c l u s i o n s a r e t h a t , when used i n s i m i l a r condi-

t i o n s , t h e l a s e r s under t e s t where capable of a r e p r o d u c i b i l i t y o f f 2 b u t

t h a t s h i f t s a s l a r g e as 1.2 10-lo could b e observed, e s p e c i a l l y when one o f t h e

l a s e r s was locked by t h e s a t u r a t e d d i s p e r s i o n t e c h n i q u e i n s t e a d o f s a t u r a t e d absorp-

Furthermore, t h e r e i s now a r e a l need t o improve t h e r e p r o d u c i b i l i t y and accu- r a c y o f 3.39 u m s t a b i l i z e d l a s e r s , s i n c e t h e VNIIFTRI group was r e c e n t l y a b l e t o measure t h e frequency o f an He-Ne CH4 l a s e r by comparison w i t h t h e Cs clock f r e - quency, t h e whole frequency s y n t h e s i s chain b e i n g phase-locked(67). The measurement p r e c i s i o n was t h e n l i m i t e d o n l y by t h e C s clock accuracy, and t h e v a l u e t h e y g o t f o r t h e F2 ( 2 ) l i n e frequency i s :

V - ⁼ 88 376 181 603.4 kHz FL ( 2 ) -11

w i t h an e r r o r b a r of + 1.4 kHz (1.5 10 ) corresponding t o t h e CH4 s t a b i l i z e d

l a s e r r e p e a t i b i l i t y . -

The l a c k o f r e p r o d u c i b i l i t y o f t h e " ~ e - ~ e - F ~ ( 2 ) l i n e " system i s probably r e s - p o n s i b l e f o r t h e 10 kHz disagreement between t h i s measurement and p r e v i o u s o n e s ( 6 8 ) .

D) CO,, s t a b i l i z e d l a s e r ? . - The CO s t a b i l i z e d l a s e r s a t 10.6 pm, l i k e t h e 3.39 pm He-Ne l a s e r s , played an importang r o l e i n t h e measurements o f t h e v e l o c i t y of l i g h t (69,70) , and a r e an e s s e n t i a l p a r t of t h e frequency s y n t h e s i s c h a i n s . The e x p e r i m e n t a l i s t s working on CO s t a b i l i z e d l a s e r s have taken 2 main d i r e c t i o n s :

a) t h e f i r s t one i s t h e s t d i b i l i z a t i o n by s a t u r a t e d f l u o r e s c e n c e i n C0 ₂ (71) .

This technique h a s been extremely u s e f u l i n t h e frequency s y n t h e s i s c h a i n s and f o r c a l i b r a t i o n o f t h e i n f r a r e d spectrum. I t p r o v i d e s a convenient r e f e r e n c e f o r each CO o r N 0 l a s e r l i n e . U n f o r t u n a t e l y , one h a s t o f i n d a d i f f i c u l t compromise between

2 2

p r e s s u r e broadening and S/N r a t i o , which l i m i t e d t h e s t a b i l i t y t o 10-12 about, and the r e p r o d u c i b i l i t y t o 5 kHz (1.5 10-10). T h i s technique i s then a l i t t l e b i t obso- l e t e now, i n r e g a r d t o t h e measurement p r e c i s i o n of t h e phase locked frequency syn- t h e s i s chains.

b) much more promising were t h e s a t u r a t e d a b s o r p t i o n experiments i n SF and Os04 r e p o r t e d f o r t h e f i r s t time i n ( 7 2 ) and (73). Most of t h e work r e a l i z e d on b e s e mo- l e c u l e s up tonow h a s been s p e c t r o s c o p i c a l more than m e t r o l o g i c a l ( 7 4 ~ 7 5 ) , b u t e x c e l - l e n t s t a b i l i t i e s (5 f o r 10 s ) have a l r e a d y been o b t a i n & (76) . The SF mole- c u l a r l i n e s have narrow h y p e r f i n e s t r u c t u r e s , which a r e u s u a l l y n o t r e s o l v e 9 , and which l i m i t t h e r e p r o d u c i b i l i t y t o a few kHz ⁽ j u s t l i k e i n t h e CH - F2 ( 2 )

l i n e case. The l g 2 0s0 molecule i s f a r more i n t e r e s t i n g f o r metrology, s f n c e it h a s no h y p e r f i n e s t r u c t u r e and, a l s o , because it i s very heavy, s o t h e q u a d r a t i c Doppler and r e c o i l e f f e c t s a r e weak.

U l t r a h i g h r e s o l u t i o n experiments a r e i n p r o g r e s s a t LPL ( V i l l e t a n e u s e ) which should r e s u l t soon i n a l i n e w i d t h much s m a l l e r t h a n 1 kHz ( 3 (77). It would be s u r p r i s i n g i f t h e r e s u l t i n g r e r o d u c i b i l i t y was worse t h a n b u t up t o now, no r e s u l t b e t t e r t h a n 3 10-lP h a s been r e p o r t e d a t 10.6 p.

4. Conclusions. - O p t i c a l frequency s t a n d a r d s were c o n s i d e r e d as extremely promi- s i n g i n 1970, on t h e simple b a s i s t h a t much h i g h e r l i n e Q ' s could b e o b t a i n e d i n t h e o p t i c a l range t h a n i n t h e microwave range, l e a d i n g t o much b e t t e r s t a b i l i t i e s . T h i s p a r t of t h e c o n t r a c t h a s been p a r t i a l l y r e a l i z e d , s i n c e t h e b e s t CH4 o r SF6 o r I

2 s t a b i l i z e d l a s e r s a l r e a d y have a b e t t e r s h o r t - t e r m s t a b i l i t y t h a n a l l t h e microwave s t a n d a r d s . But t h e g o a l of improving r e p r o d u c i b i l i t y and accuracy h a s n o t been achieved. We s e e many reasons f o r t h a t :

a ) non l i n e a r spectroscopy b r i n g s t h e h i g h - r e s o l u t i o n c a p a b i l i t y , b u t a l s o a l o t of new problems, which were n o t r e a l i z e d i n 1970. They a r e now w e l l understood theo- r e t i c a l l y , b u t t h e y a r e d i f f i c u l t t o overcome e x p e r i m e n t a l l y a t a 1 l e v e l b e t t e r than 10-13 - 10-14.

b) more t r i v i a l problems, l i k e unresolved h y p e r f i n e s t r u c t u r e s r e s u l t from a wrong choice of t h e r e f e r e n c e l i n e . The use of 1 9 2 0 s ~ molecules and of t h e E-line o f CH

should s t r a i g h t e n t h i s s i t u a t i o n . 4 4

C )

t h e r e p e a t i b i l i t i e s o f +_ ² lo-" achieved a t 3.39 pm and 633 nm a s soon a s

1973, were considered a s "good enough" f o r most a p p l i c a t i o n s . T h i s may have slowed

down t h e enthusiasm of many f o r working towards b e t t e r m e t r o l o g i c a l performances :

i n most l a b o r a t o r i e s , frequency s t a b i l i z e d l a s e r s were n o t s t u d i e d f o r themselves,

b u t t h e y were used a s t o o l s f o r w e l l d e f i n e d a p p l i c a t i o n s , such a s l e n g t h measure-

ments, frequency s y n t h e s i s , high r e s o l u t i o n s p e c t r o s c o p y , measurement o f t h e Rydberg

C8-80 JOUPJAL DE PHYSIQUE

c o n s t a n t , geophysics, r e l a t i v i t y , a l l s u b j e c t s w h i c h o f t e n s e e m m o r e r e w a r d i n g than p u r e m e t r o l o g y .

H o p e f u l l y , " g o o d e n o u g h " i n n o t a l o n g - l i v e d s t a t e m e n t i n physics : the s u c - c e s s f u l l operation of a phase-locked frequency s y n t h e s i s chain a s k s f o r CO and 3 . 3 9 p ' H e - N e lasers h a v i n g a r e p r o d u c i b i l i t y of 10-14, w h i c h could be U s e % as secon- dary standards a l l o w i n g the e x t e n s i o n of the s y n t h e s i s up t o the v i s i b l e w i t h t h i s h i g h accuracy, w i t h o u t the n e e d of o p e r a t i n g the w h o l e c h a i n s i m u l t a n e o u s l y .

T h e r e are other reasons f o r i m p r o v i n g t h e v i s i b l e standards : the m e a s u r e m e n t s of t h e R y d b e r g c o n s t a n t n o w approach the l i m i t w e r e t h e i r accuracy is l i m i t e d by t h e He-Ne-I2 laser r e p r o d u c i b i l i t y ( 7 8 ) . T h e n e w h i g h r e s o l u t i o n f r e q u e n c y m e t e r

proposed by J. S n y d e r could provide t h e " l a m b d a m e t e r s " w i t h a r e s o l u t i o n of 1 0 - ~ ~ ( ~ 9 ) w h i c h should r e s u l t i n a n i m p r o v e m e n t of t h e i r a c c u r a c y t o the 10-l1 l e v e l .

S i n c e w e n o w have the n e e d s , a n d t h e adequate t o o l s , w e can hope i t w i l l n o t take t e n m o r e y e a r s before w e can see s o m e t r u e o p t i c a l f r e q u e n c y s t a n d a r d s .

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