Study Of The Local Mode Of Calcium-Fluoride Doped With Negative Hydrogen Ion With Intense Carbon-Dioxide Laser Lines

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Content 72-3784 LEE, Long C hi, 1940- ST U D Y O F T H E L O C A L M O D E O F CaF :H“ W IT H INTENSE C02 LASER LINES. 2 U n iv ersity o f Southern C a lifo r n ia , Ph.D., 1971 P h y sic s, sp ectroscop y r | University Microfilms, A X E R O X Company, Ann Arbor, Michigan -§■ ^ _ _____________________ THIS DISSERTATION HAS BE?N MICROFILMED EXACTLY AS RECEIVED STUDY OF THE LOCAL M ODE OF CaF2 tH WITH INTENSE CO2 LASER LINES t y Long C hi Lee A D i s s e r t a t i o n P r e s e n te d to th e FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA I n P a r t i a l F u l f i l l m e n t o f th e R e q u ire m e n ts f o r th e D egree DOCTOR OF PHILOSOPHY ( P h y s ic s ) Ju n e 1971 UNIVERSITY O F SOUTHERN CALIFORNIA TH E GRADUATE SCHOOL UNIVERSITY PARK LOS A NGELES. CALIFORNIA S 0 0 0 7 This dissertation, written by Long C hi Lee under the direction of Dissertation Com mittee, and approved by all its members, has been presented to and accepted by The Gradu ate School, in partial fulfillment of require ments of the degree of D O C T O R OF P H IL O S O P H Y n „,„ June 1971 DISSERTATION COMMITT Chairman PLEASE NOTE: Some Pages have i n d i s t i n c t p r i n t . Filmed as received. UNIVERSITY MICROFILMS TABLE OF CONTENTS f Page J |LIST OF FIGURES .............. v j |LIST OF TABLES ............................................................................................... v i i i [ABSTRACT .............................................................................................................. v i i i CHAPTER I . INTRODUCTION ................................................................................. 1 I I . A BRIEF REVIEW OF C02 LASERS .......................................... 5 A. The Mechanism L e a d in g t o P o p u la tio n I n v e r s io n ........................ 5 B. The L a s e r L in e s O bserv ed by V a rio u s W orkers ............ 6 C. I n s ta n ta n e o u s Power L e v e ls O b ta in e d by V a rio u s W orkers ................... 7 I I I . THE TUNABLE, PULSED-DISCHARGE, BUT NOT Q-SWITCHED C02 L A SER................................................. 8 A. S t r u c t u r e o f th e L a s e r 8 1 | i B. The Gas P r e s s u r e and th e P u ls e d - D isc h a rg e ............ 10 C. D e te c to r s .............. 10 i D. L a s e r P u ls e O u tp u t ................................................. 11 E . S im u lta n e o u s L a s e r A c tio n o f N20 . . . . . . . 11 IV. THE TUNABLE, Q-SWITCHED, PULSED-DISCHARGE j C02 LASER lk \ A. D esig n o f th e L a s e r ............. 14 B. S pectrum o f L in e s Found ........................... 14 C. Optimum Gas P r e s s u r e and C u r re n t . . . . . . . 15 D. L a s e r O u tp u t E n erg y V ersu s Time D elay . . 15 CHAPTER V. V I. V I I . I I V I I I . Page E. D u ra tio n o f th e O u tp u t P u ls e V ersu s Time D elay .......................... 20 ! F . E f f e c t s o f V a rio u s G ases ..................... 21 G. The D w ell Time .................................................... 24j H. The P rim in g E x p e rim e n t ....................................... 24j A BRIEF DESCRIPTION OF THE LOCAL M ODE OF CaF2 «H" ............................................................................................ 27 A. P re v io u s Work on H ydrogenated C alcium F l u o r i d e ................................................... 27 B. Review o f th e T h e o r e t i c a l Model ............... 29 SATURATION OF THE LOCAL M ODE OF CaF2 »H_ . . . . . . 33 A. E x p e rim e n ta l A rrangem ent ................ 33 i I B. E x p e rim e n ta l R e s u l ts ............... 33 C. T heory o f S a t u r a t i o n ......... 38 D. A n a ly s is o f th e E x p e rim e n ta l R e s u lts hy th e above T heory ............................................... 4 l STEPWISE EXCITATION .............................................................. 45 A. I n t r o d u c t i o n ................................................................ 45j B. E x p e rim e n ta l A r r a n g e m e n t ................ 45 C. E x p e rim e n ta l R e s u l ts and D is c u s s io n . . . . 45 i) S te p w is e E x c i t a t i o n .................................. 45 i i ) On P o l a r i z a t i o n ............. 49 i i i ) On L in e w id th .................. 51 ! iv ) T e s t on Two-Quantum A b s o rp tio n . . . 53| CONCLUSIONS .................................................................................. 54 iii t Page I APPENDIX................... 56 REFERENCES ........................................................................................................ 6l iv i LIST OF FIGURES j ‘F ig u re I 1. The L a s e r w ith a G r a tin g and th e S u p p ly f o r j a P u ls e d D is c h a r g e . The T rio d e i s P u ls e d by ! Change o f Both th e G rid P o t e n t i a l and th e | E f f e c t i v e C athode R e s i s t o r ............. J ! 2. The R e la ti v e O u tp u t Power and Time D elay i f o r D i f f e r e n t NQS L in e s .......................................................... I j 3. The E f f e c t o f V a ry in g D isc h a rg e P u ls e L en g th s on th e O p t i c a l P u ls e E n erg y ............................................... k. The L a s e r I n t e n s i t y v s . Time D elay f o r P - , R -b ra n c h e s o f ( 1 0°0 -0 0 1) B a n d ..................................... 5. The L a s e r I n t e n s i t y v s . Time D elay f o r P - and R -b ra n c h e s o f ( 0 2 ° 0 - 0 0 ° l) Band ...................................... 6 . Changes o f Shape i n th e O p t i c a l P u ls e w ith V a ry in g D elay T im es, D ata Taken on th e (0 2 °0 -0 0 °1 ) P (22) L in e ........................................................... ; 7» The E f f e c t o f V a ry in g P a r t i a l P r e s s u r e o f He, i N2 on th e O p tic a l P u ls e E n erg y V e rsu s Time D elay f o r T y p ic a l R o t a t i o n a l - V i b r a t i o n a l Components ......................................................................................... | 8 . ' The E f f e c t o f V a ry in g P a r t i a l P r e s s u r e o f H2 I on th e O p t i c a l P u ls e E n erg y V e rsu s Time D elay f o r T y p ic a l R o t a t i o n a l - V i b r a t i o n a l Components . . j 9 . S pectrum a t ~>20°K, A dopted from R e f. 1. T r a n s i t i o n s S tu d ie d i n S u c c e e d in g I I n v e s t i g a t i o n s a r e 1 i ) R e f. 1, I n f r a r e d A b s o r p tio n , L in e s a , c , e , f . i i ) R e f. i r , U n ia x ia l S t r e s s , L in e s a , | b , c , d . i i i ) R e f. 5> Raman S c a t t e r i n g , L in e s a , b , c . ' iv ) P r e s e n t Work, L in e s a , b ' , c ' t d*. I n s e t 1 O bserved R e la tiv e T r a n s m is s io n on 10°0 L in e s R(2), R(4), R( 6 ), R( 8), R(10), a t 90 K ....................................................... | 10. The A rran g em en t f o r th e S a t u r a t i o n E x p e rim e n t . . j F ig u re I 11. a) Above i O s c illo s c o p e T ra c e s Show ing N arrow ing o f T ra n s m itte d R (6 ) P u ls e R e la ti v e to I n c i d e n t P u ls e , a t 80°K. b) Below i P l o t s o f I 0u t V e rsu s I i n C o n s tru c te d from th e R is in g and from th e F a l l i n g | P o r tio n s o f th e P u ls e s above ........................... I j 12, l o u t A i n V e rsu s I i n . F i l l e d Sym bols a re D ata f o r 90®K, Where <«oi = 9 65.1 cm” 1 , W idth = j 1 .2 cm” 1 . Empty Sym bols a re D a ta a t 290°K, Where ^ o i ~ 9 5 7 .8 cm"1 , W idth = 8 . 7 cm” 1 . G iven L a s e r F r e q u e n c ie s f o r T r ia n g le s a re N ear th e R e s p e c tiv e P e a k sj Those f o r C i r c l e s a r e i n th e Wings ................................... ............................... 13. The A rrangem ent f o r th e Two Quantum E x c i t a t i o n E x p e rim e n t ...................................................................................... 14. Above : O s c illo s c o p e T ra c e s Show ing "F a st* and "Slow 1 ' E f f e c t s . Below i P l o t s v s . NQS F re q u e n c y . F u l l C urves Show th e F a s t E f f e c t t Dashed C urves Show th e Slow E f f e c t . . . . . . . . . . . . . . . . . . . . . . . . . . | j 15. W av efu n ctio n s f o r th e S te p w ise T r a n s i t i o n s . . . . I ; 16, The C o o rd in a te S ystem s Used to C a lc u la te L o c i o f F r a u n h o f e r D i f f r a c t i o n on a P la n e ! P e r p e n d ic u la r to th e Z e ro th O rd e r | D i f f r a c t i o n Ray............................................................................... i | 17. The L o c i o f F r a u n h o f e r D i f f r a c t i o n on a P la n e ! P e r p e n d i c u la r to th e Z e ro th O rd e r D i f f r a c t i o n j Ray w ith V a rio u s n A / d , z = l, Q = 20° .................... vi Page 3 6 i 37 46 48 521 I i i ! 58 | i 60 LIST OF TABLES QS L in e s E f f e c t e d by th e S p eeds o f M otor and by th e P rim in g o f NQS L in e s . P(2)- P (48) Means P ( 2 )f P(4), P ( 6 ) , • • • • *P(^8)i P( 2), P (4 8 ) Means P(2) and P (4 8 ) Only . . . Wave F u n c tio n s , S y m m etries, and P o s i t i o n s o f th e Lower V i b r a t i o n a l E n erg y L e v e ls o f an H“ Io n i n CaF2 • • ........................... I v i i ! ABSTRACT ! \ 1 Two i n te n s e COo l a s e r s were c o n s t r u c t e d f o r th e i j ^ i I s tu d y o f re s o n a n c e on th e sim p le v i b r a t o r CaF2 iH~. One i s j Q -sw itc h e d (QS), f o r th e p u rp o se o f s a t u r a t i o n o f th e | j j ifu n d a m e n ta l (n=0 to n=l). The se c o n d , n o n -Q -sw itc h e d | '(NQS), was b u i l t to p ro v id e a probe beam f o r s tu d y o f ! i ! !a b s o r p t io n c o n n e c tin g th e e x c i t e d l e v e l n = l to y e t h ig h e r n =2 e x c i t a t i o n s . The e a r l y p o r t i o n o f t h i s d i s s e r t a t i o n d e s c r ib e d i j c o n s t r u c t i o n o f th e l a s e r s and o b s e r v a tio n s upon t h e i r |o p e r a t i o n . B ecause o p e r a t io n on i n d i v i d u a l r e l a t i v e l y weak | l i n e s n e a r a band c e n t e r o f th e CO2 sy ste m was n eed ed f o r t h i s re s o n a n c e w ork, o u r l a s e r equipm ent i s v e ry h ig h ly j |d e v e lo p e d . NQS h o ld s th e r e c o r d f o r th e o p e r a t io n on 130 j ! i i v i b r a t i o n a l - r o t a t i o n a l l i n e s , s p a n n in g th e fre q u e n c y ra n g e 1 1 ;from 900 cm t o 1100 cm . QS o p e r a te d on 80 l i n e s , w hich; | ; i s a l s o p ro b a b ly a r e c o r d f o r t h i s k in d o f o p e r a t i o n . A d d i t io n a l QS l i n e s were p ro d u ced by "p rim in g " w ith weak j r a d i a t i o n from NQS. NQS g e n e r a t e s ro u g h ly 20 w a tt p u ls e s on s t r o n g l i n e s , o f d u r a t i o n ps, QS g e n e r a te s 20 kw p u ls e s on s t r o n g l i n e s , o f d u r a t i o n ~ 3 0 0 n s . ! F o c u sin g th e QS beam on a CaF2 *H“ sa m p le , we were : in d e e d a b le to s tu d y th e s a t u r a t i o n o f fu n d a m e n ta l ( n =0 to ;n=l). A sim p le th e o r y was d e v e lo p e d to f i t th e e x p e r im e n t- !a l d a ta on t r a n s m i s s io n v s . i n t e n s i t y . A v a lu e o f th e 1 • • * V l l l ! s a t u r a t i o n p a ra m e te r W was u se d to c a l c u l a t e t h e d e ca y tim e i i I i | . The v a lu e o b ta in e d (T^ = 11 p s e c ) a c c o u n ts f o r th e j | r e s i d u a l l i n e w i d t h a t low te m p e r a tu r e , i n a c c o rd a n c e w ith a p r i o r comment by H ayes, e t a l . The l in e s h a p e was c o n firm e d i I t o be hom ogeneous. When th e n -1 l e v e l p o p u la te d by a QS | beam p u l s e , a se c o n d e x c i t a t i o n ( n - l t o n~ 2 ) was o b se rv e d | | th ro u g h a b s o r p t i o n o f c e r t a i n NQS l i n e s . The n = l to n=2 j ! f r e q u e n c i e s a g re e w ith p r i o r c a l c u l a t i o n and o b s e r v a t i o n . W e a tte m p te d to d e m o n s tra te c e r t a i n e x p e c te d p o l a r i z a t i o n s e l e c t i o n r u l e s f o r t h r e e tw o - s te p p r o c e s s e s , b u t we fo u n d t h a t th e y do n o t h o ld . E v i d e n t l y , t h e r e i s a f a s t s c r a m b lin g among th e t h r e e d e g e n e ra te com ponents o f th e n = l j l e v e l b e fo r e th e seco n d a b s o r p t i o n . W e a t t r i b u t e t h i s | p o l a r i z a t i o n - s c r a m b l i n g to a p a r t o f th e p r o c e s s t o w hich i H ay es, e t a l . a t t r i b u t e d th e te m p e r a tu r e - d e p e n d e n t l i n e - j w id th . These in v o lv e e s s e n t i a l l y e l a s t i c s c a t t e r i n g o f j | th e r m a l- p h o n o n s . The l i n e w i d t h , o f t r a n s i t i o n from i ; n = l to n=2 , i s o b s e rv e d t o be th e sum o f th e fu n d a m e n ta l and th e s e c o n d -h a rm o n ic 1 in e w id th s , +AWq2 * CHAPTER I I INTRODUCTION I | T h ere a r e a num ber o f a t t r a c t i v e s p e c t r o s c o p i c p ro b lem s t o be s t u d i e d w ith t h e e x p l o i t a t i o n o f i n f r a r e d I gas l a s e r s a s s o u r c e s . W e have c o n s t r u c t e d two l a r g e COg l a s e r s and a p p l i e d them f o r th e s t u d y o f t h e l o c a l mode i n CaF2 iH“ . S u c c e s s f u l o p e r a t i o n o f s u c h l a s e r s h a s i n i t s e l f some g e n e r a l i n t e r e s t . I n r e c e n t y e a r s , t h e l o c a l v i b r a t i o n a l modes a s s o c i a t e d w ith t h e h y d ro g en d e f e c t s i n th e a l k a l i n e e a r t h f l u o r i d e s have b e e n s t u d i e d i n d e t a i l ( l - 5 ) . The a b s o r p t io n sp e c tru m o f CaP£ c o n t a i n i n g n e u t r a l h y d ro g e n atom s i n t h e i n t e r s t i t i a l s i t e h a s been s t u d i e d by Shamu, e t a l . ( 2 ) . The s p e c t r a o f h y d ro g e n a te d CaF2 c o n t a i n i n g r a r e - e a r t h io n s jhave b een i n v e s t i g a t e d by J o n e s , e t a l . ( 3). The v i b r a t i o n a l l o c a l modes o f th e h y d rid e io n H~ i n p u re CaT^t BaFgi land S rF g C U -c e n te rs ) have been s t u d i e d and d e s c r i b e d w ith an |a p p r o p r i a t e m odel by E l l i o t t , e t a l . ( l ) . F o r t h e sim p le r e s o n a n t sy s te m o f th e l o c a l mode i n CaF2 *H“ , some l e v e l s w hich a r e p r e d i c t e d by t h e m odel o f E l l i o t t , e t a l .. b u t w hich a r e n o t o b s e rv e d by s im p le i n f r a r e d a b s o r p t i o n , w ere i o b s e rv e d by s t r e s s - i n d u c e d i n f r a r e d a b s o r p t i o n ^ ) • More r e c e n t l y , a l s o , th e fu n d a m e n ta l and two se c o n d harm onic i i l e v e l s w ere o b s e rv e d by Raman s c a t t e r i n g ( 5 ) • 1 j I n g e n e r a l , t h e e x c u r s io n o f io n s i n c r e a s i n g l y i rem o te from th e l i g h t d e f e c t f a l l s o f f r a p i d l y ( 6 ) , P a r t i c u l a r l y when t h e d e f e c t i s v e r y l i g h t , t h e mode may be | d e s c r ib e d a p p ro x im a te ly as p e r i o d i c m o tio n o f th e d e f e c t io n a l o n e ( r i g i d l a t t i c e m o d e l). F o r CaFgiH” , th e H” io n , i w hich moves a b o u t a F ” s i t e , s e e s a p o t e n t i a l w e ll o f t e t r a h e d r a l sym m etry. The anharm onic te rm s a r e so s m a ll, when com pared w ith th e harm onic te rm , t h a t th e y c a n be c o n s id e r e d a s a p e r t u r b a t i o n . The n= l l e v e l has 1^ sym m etry. I t has a t h r e e - f o l d d e g e n e ra c y w hich i s n o t s p l i t by t h e p e r t u r b a t i o n . B ut t h e se c o n d harm onic l e v e l i s s p l i t i n t o t h r e e l e v e l s 1^ , F j , and P,, w ith o n e - , tw o -, and t h r e e - f o l d d e g e n e ra c y , r e s p e c t i v e l y . We a r e f o r t u n a t e i n s e v e r a l r e s p e c t s . Of th e v a r i o u s a l k a l i n e - e a r t h I I f l u o r i d e U c e n t e r s d e s c r ib e d by t h i s a n a l y t i c a l l y sim p le ! , t h e o r y , t h e CaF^ c a s e com bines th e f e a t u r e s i i ) s h a r p e s t a b s o r p t i o n l i n e s , i . e . r e s o n a n c e s o f h i g h e s t Q ( i n f a c t , j i th e CaF«iH“ fu n d a m e n ta l has t h e s m a l l e s t f r a c t i o n a l w id th ! | o f a l l l o c a l modes known), i i ) th e r e s o n a n c e s An= + 1 a r e | a l l w i t h i n th e c o v e ra g e o f th e COg l a s e r l i n e s . Thus t h i s sim p le r e s o n a n t sy ste m would a p p e a r t o le n d i t s e l f t o a v a r i e t y o f h i g h - i n t e n s i t y s t u d i e s su c h a s i i ) th e i | s a t u r a t i o n e f f e c t o f th e fu n d a m e n ta l mode, i i ) th e j I t r a n s i e n t e f f e c t s su c h a s n u t a t i o n , p u ls e b r e a k u p ,e t c . | i i i ) th e s te p w is e e x c i t a t i o n , p o s s i b l e v e r i f i c a t i o n o f s te p w is e s e l e c t i o n r u l e s . I n f a c t , we have b een a b le t o jstu d y s e v e r a l f e a t u r e s o f i ) and i i i ) , but not i i ) . ' The f o llo w in g m a tte r s w i l l be d is c u s s e d i | i ) C o n s tr u c tio n o f a t u n a b l e . p u l s e d - d i s c h a r g e , Q -sw itch ed COg l a s e r ( h e r e a f t e r ! QS) f o r s tu d y o f th e fu n d a m e n ta l t r a n s i t i o n o f th e l o c a l mode. W e w i l l c o n s i d e r a ! i num ber o f q u e s tio n s p e r t a i n i n g t o m ec h an ica l i j d e s ig n o f th e l a s e r , a n a l y s i s o f i t s o p e ra t i o n , and e x p e rim e n ts upon th e COg l a s e r i j medium w hich become p o s s i b l e . i i ) E x p e rim e n ta l o b s e r v a tio n o f t h e s a t u r a t i o n | e f f e c t o f th e fu n d a m e n ta l mode and a sim p le t h e o r y d e v e lo p e d t o f i t th e d a t a — t r a n s m is s io n v s , l a s e r i n t e n s i t y ( 8 ) . T h is work l e d to a n e s tim a te o f t h e d e ca y tim e o f n = l t o n=0 from th e s a t u r a t i o n p a ra m e te r W. I i i i ) C o n s tr u c tio n o f a t u n a b l e , p u l s e d - d is c h a r g e n o n -Q -sw itc h e d COg l a s e r ( h e r e a f t e r NQS) ! and s t u d i e s upon t h i s l a s e r i t s e l f . T h is l a s e r was b u i l t to make p o s s i b l e ite m i v ) • 1 | iv ) O b s e rv a tio n o f s t e p w i s e - e x c i t a t i o n w ith t h i s se co n d COg l a s e r * s e v e r a l i n t e r e s t i n g e f f e c t s w i l l be d e s c r i b e d . i W e c o n s i d e r t h i s an a t t r a c t i v e sy ste m f o r s t u d y , j e s s e n t i a l l y a te x tb o o k p ro b le m , b e c a u se i t i s w e l l - j (char a c t e r i zed by a f a i r l y s i m ple t h e o r y . I n f a m i l i a r t h e o r e t i c a l d i s c u s s i o n s o f t r a n s i t i o n s f o r n o n -d e g e n e ra te I two l e v e l s y s te m s , th e re s o n a n c e i s d e s c r ib e d by an |e x c i t a t i o n d ecay tim e T^, and by a p h ase c o h e re n c e tim e T2 , we w i l l se e t h a t th e CaF2 iH“ sy ste m h a s th e f e a t u r e o f an i j a d d i t i o n a l r e l a x a t i o n p ro c e s s — i t f o r g e t s th e p o l a r i z a - I I :t i o n o f an i n i t i a l e x c i t a t i o n . I t i s o u r b e l i e f t h a t j ™ & | |d e s c r i b e s t h i s p r o c e s s , a s w e ll as th e p h ase c o h e re n c e i | l o s s . 5 | CHAPTER II A BRIEF REVIEW OF COg LASERS A. THE MECHANISM LEADING TO POPULATION INVERSION The m o st im p o r ta n t m echanism f o r a C02 l a s e r t o jp ro d u ce a p o p u l a t i o n i n v e r s i o n i s t h e t r a n s f e r o f v i b r a t i o n a l e n e r g y from e x c i t e d Ng m o le c u le s i n t h e v = l s t a t e t o COg m o le c u le s (1 0) i N2 (v=1) + C02 (0 0 °0 ) — Ng(v=0) + C 0 g (0 0 °l) - 18 cm"1 F o r th e g as m ix tu r e s u s e d , w ith t o t a l p r e s s u r e ~ 1 0 t o r r , th e r e l a x a t i o n tim e f o r t h e t r a n s f e r i s l e s s t h a n a jisec ( 1 1 ) , S in c e a Ng m o le c u le h a s z e r o p e rm a n e n t d i p o le jmomemt, i t s v = l l e v e l h a s a lo n g v i b r a t i o n a l r e l a x a t i o n | Itime, a few m se c. The s t a t e (0 0 °1 ) o f C02 h a s a r e l a x a t i o n tim e l e s s t h a n a j i s e c ( l l ) . B u t, i n e q u i l i b r i u m w ith th e e x c i t e d N2 m o le c u le s , a ( 00° 1 ) p o p u l a t i o n c a n be s u s t a i n e d j few m se c • The lo w e r l a s e r l e v e l s (1 0 °0 ) and (0 2 °0 ) q u i c k l y em pty t o t h e ( 01° 0 ) s t a t e , and th e l a t t e r more s lo w ly goes i I i n t o c e n t e r - o f - m a s s m o tio n , so t h a t t h e r e i s a p a r t i a l ] |b o t t l e n e c k a t t h i s p o i n t . The r o l e o f h e liu m i s p r e f e r e n t i a l l y t o i n c r e a s e th e d e e x c i t a t i o n o f th e ( 01° 0 ) l e v e l , a s opposed t o t h e (0 0 °1 ) l e v e l . On t h e b a s i s o f d a t a a v a i l a b le from p r e v io u s w o r k ( l l ) , we e s t i m a t e t h a t th e s p e c i f i c j d e e x c i t a t i o n r a t e o f t h e (O l1©) l e v e l due t o h e liu m i s ^0 6 ■times f a s t e r th a n f o r t h e (0 0 ° 1 ) l e v e l* T h u s, w ith th e p r e s e n c e o f e x c i t e d Ng i n t h e v = l s t a t e , a p o p u l a t i o n o f t h e 00°1 l e v e l may p e r s i s t t h r e e o r d e r s o f m ag n itu d e l o n g e r t h a n th e lo w e r l e v e l s . B. THE LASER LINES OBSERVED BY VARIOUS WORKERS I n 196 4 , l a s e r a c t i o n i n COg g a s was r e p o r t e d by P a t e l e t a l .( 1 2 ) . P a t e l o b s e rv e d l a s e r o s c i l l a t i o n i n p u re COg by e m p lo y in g b o th d . c . and 1 jis p u ls e d i s c h a r g e s i n a g a s colum n 4 .5 m lo n g . He r e p o r t e d t h e o b s e r v a t i o n o f o p t i c a l m a se r a c t i o n i n th e P - b ra n c h r o t a t i o n a l t r a n s i t i o n s f o r a t o t a l o f 21 l i n e s i n t h e ( 00° 1- 1 0 ° 0 ) and ( 0 0 ° l - 02° 0 ) v i b r a t i o n a l b a n d s . I n 196 6 , M o e lle r and R ig d e n (1 3 )» |i n t r o d u c i n g a d i f f r a c t i o n g r a t i n g a t one end o f t h e r e s o n - i |a n t c a v i t y a s a w a v e l e n g t h - d i s c r i m i n a t i n g d e v ic e , fo u n d a ■ to ta l o f 103 COg l a s e r l i n e s f o r b o th P - and R -b ra n c h e s o f | !two v i b r a t i o n a l b a n d s . I n 1969* M eyer, P in s o n , R o s s e t t i i and B a r c h e w itz ( l4 ) u s i n g s i m i l a r g a s m i x t u r e s , b u t d . c . I | e x c i t a t i o n and a lc o h o l c i r c u l a t i o n t o c o o l th e w a ll i n a .2,4 m g a s colum n, fo u n d a t o t a l o f 112 COg l a s e r l i n e s on i |the two v i b r a t i o n a l b a n d s . I n o u r w ork, we have fo u n d a I t o t a l o f 130 l i n e s ( 9 ) . I n t h i s w ork, we em ployed a p u ls e d i { d is c h a rg e o f ~-100 ma a n d "'■'350 u s i n a 4 . 5 m g a s c o lu m n . 1 [The l a s e r tu b e was c o o le d t o n e a r z e ro d e g re e s c e n t i g r a d e . |F o r s tu d y o f t h e m axim al s e t o f l i n e s l a s i n g , pow er was jc o u p le d o u t s o l e l y th ro u g h th e z e r o o r d e r o f th e d i f f r a c - 7 t i o n g r a t i n g (F o r o u r CaF2 »H“ re s o n a n c e w ork, t h i s was g e o m e t r i c a l l y i n c o n v e n ie n t and a n o th e r o u tp u t was t a k e n th ro u g h a d i e l e c t r i c m i r r o r ) • C. INSTANTANEOUS POWER LEVELS OBTAINED BY VARIOUS WORKERS P a t e l (1 2 ) m ea su re d a c o n tin u o u s pow er o u tp u t o f a b o u t 1 m W f o r th e f i r s t COg l a s e r . M o e lle r and R ig d e n o b ta in e d a c o n tin u o u s power o f a b o u t ^W/m o f tu b e l e n g t h f o r a s t r o n g s i n g l e l i n e ( 1 3 ) ( w i t h a d i f f r a c t i o n g r a t i n g a t one end o f th e c a v i t y ) , and a b o u t 75 W/m o f tu b e le n g t h ( 1 5 ) f o r a m ultim ode l a s e r (w ith co n cav e m i r r o r s a t b o th en ds). E m ploying a r o t a t i n g m i r r o r , b u t w ith no l i n e - s e l e c t i o n d e v ic e , F ly n n , e t a l . ( l 6 ) fo u n d t h a t a 3 w a tt cw sy ste m j g iv e s a p u ls e o u tp u t o f p e ak pow er i n e x c e s s o f 10 kw and I p u ls e l e n g t h l e s s t h a n 100 n s . W ith o u r t u n a b l e . Q- s w itc h e d , p u l s e d - d i s c h a r g e COg l a s e r ( 7 ) , we o b t a i n p u l s e s ! o f <~20 kw p e ak pow er and r- 300 n s d u r a t i o n f o r s t r o n g i j r o t a t i o n a l l i n e s . T h e re have b e e n r e c e n t r e p o r t s o f g as i I J dynamic C0« l a s e r s g e n e r a t i n g c o n tin u o u s pow er l e v e l s o f ( | t h e o r d e r o f 100 k w (1 7 ). R e c e n tl y , B e a u lie u (1 8 ) h a s | d e v e lo p e d a COg l a s e r o p e r a te d a t a tm o s p h e ric p r e s s u r e , j He o b ta in e d p u l s e s o f 20 M w p e a k power and o f e n e r g y 2 i jo u le s ( t h u s r o u g h ly 100 n s d u r a t i o n ) w ith a 1- m e te r ! I d i s c h a r g e . To th e b e s t o f o u r k now ledge, n e i t h e r t h e g a s j | dynam ic l a s e r n o r t h e a tm o s p h e ric l a s e r h a s b een o p e r a t e d w ith a l i n e - s e l e c t i o n d e v ic e . | CHAPTER I I I ] I THE TUNABLE, PULSED-DISCHARGE, BUT NOT Q-SWITCHED CO« LASER I |A. STRUCTURE OF THE LASER ! j The l a s e r i s b u i l t upon a 16 f t s t e e l r a i l ( F i g , 1 ) , J |The b o re d ia m e te r i s t a p e r e d i n t h r e e s t e p s , t o accom m odate |the fu n d a m e n ta l modej the i , d . ' s a r e 22 mm, 27 mm, and | 32 mm. The l a s e r em ploys a t one end a c o n ca v e m i r r o r !w i t h in th e vacuum e n v e lo p e , and a t th e o t h e r end a B re w s te r i |window and a f l a t c i r c u l a r g r a t i n g . The m i r r o r h a s a 10 m e te r r a d i u s and r e f l e c t i v i t y ! i t i s a d i e l e c t r i c |m i r r o r on a Ge s u b s t r a t e , m a n u fa c tu re d by L a s e r O p t i c s , line. The 2" d ia m e te r g r a t i n g , B & L , Type 3 5 -5 3 -0 5 -8 9 0 i s a r e p l i c a c o a te d w i t h g o ld , b la z e d a t 37° w ith L i t t r o w wave l e n g t h 8 ji. A r e d Ne-He l a s e r was u se d t o a l i g n th e g r a t i n g . The g ro o v e s o f th e g r a t i n g a r e p e r p e n d i c u l a r t o t h e l a s e r jaxis. The g r a t i n g m ount, made by O r i e l O p tic s Corp., i s u se d t o v a r y t h e a n g le Q b etw een t h e n o rm al a x i s o f th e g r a t i n g and t h e l a s e r a x i s . The g r a t i n g r e t u r n s o f th e e n e rg y i n t o th e f i r s t o r d e r , b ack i n t o t h e l a s e r c a v i t y . i iThe o s c i l l a t i o n wave l e n g t h i s d e te rm in e d by t h e e q u a tio n I X= 2d s i n $ , where d i s th e g roo ve s p a c i n g . E i t h e r th e jco n cav e m i r r o r o r t h e z e r o t h o r d e r o f t h e g r a t i n g o r b o th , g r a t i n g B re w ste r window concave m ir r o r l a s e r o u tp u t . 25pfrJ= 15 kV MLEE64Y MLEEb^Y 10k -AAAA- 2N4240 25)lf fu s e 1 /1 6 A 2N^2^0 |----- |+45V t r i g g e r p u ls e fu s e 1/16 A F i g , 1. The l a s e r w ith a g r a t i n g and th e s u p p ly f o r a p u ls e d d i s c h a r g e . The t r i o d e i s p u ls e d by change o f b o th th e g r i d p o t e n t i a l and th e e f f e c t i v e c ath o d e r e s i s t e r . 10 may toe u se d f o r o u t p u t . The l a s e r tu b e was c o o le d t o n e a r z e ro d e g re e s c e n t i g r a d e toy c i r c u l a t i n g a c o o l i n g a g e n t j th r o u g h p l a s t i c t u b i n g w hich was a t t a c h e d a ro u n d th e l a s e r tu b e • B. THE GAS PRESSURE AND THE PULSED-DISCHARGE T h is l a s e r h as a f lo w in g g as s y s te m . The optimum p a r t i a l p r e s s u r e s a t e Pcc>2 = t o r r , P^^ = 2 .3 t o r r , pHe = 't o r r « The l a s e r h a s two d is c h a r g e s e c t i o n s . E ach s e c t i o n h a s a t r i o d e , M a c h le t MLEE 6k , a s shown i n F i g . 1 . A t r i g g e r p u ls e a p p l i e d t o th e g r i d o f th e t r i o d e g a te s t h e d is c h a r g e p u l s e . A t y p i c a l d is c h a r g e p u ls e was o f —350 jis l e n g t h and o f ^ 9 0 mA p e a k c u r r e n t* i t s r e p e t i t i o n r a t e o f 360 c p s was s y n c h ro n iz e d w ith t h e a . c . r i p p l e o f o u r f u ll- w a v e t h r e e - p h a s e .power s u p p l i e s . IC. DETECTORS Two p h o t o d e t e c t o r s were u se d t o s t u d y th e p u ls e jshape and th e r e l a t i v e i n t e n s i t y o f th e l a s e r o u t p u t . Two jc o ld dew ars w ere d e s ig n e d t o m ount GeiAu ( a t l i q u i d n i t r o - f gen te m p e r a tu r e ) and GetHg ( a t l i q u i d h y d ro g en te m p e r a tu r e ) j p h o t o d e t e c t o r s . E ach dew ar c a n m ount more th a n one d e t e c - jto r. The a v e ra g e pow er was e i t h e r m easu red toy a th e rm o - Ipile, o r d e te rm in e d by t h e change i n b o i l - o f f r a t e o f i ! l i q u i d n i t r o g e n when t h e l a s e r beam e n t e r e d a th u m b siz e d I l i q u i d n i t r o g e n dew ar. 1 1 D. LASER PULSE OUTPUT The l a s e r c a n tu n e o v e r t h e f r e q u e n c y ra n g e o f 900 cm”1 t o 1100 cm” '*'. We fo u n d a t o t a l o f 130 l i n e s —- P(2)-P(66) and R(0)-R(62) f o r b o th (1 0 ° 0 -0 0 ° 1 ) and ( 0 2 ° 0 - 0 0 ° 1 ) r o t a t i o n a l b a n d s . The r e l a t i v e pow er o u tp u t f o r d i f f e r e n t l i n e s i s p r o m in e n tly a f f e c t e d by t h e c h a r a c t e r i s t i c s o f th e g r a t i n g u s e d . The o u tp u t p u l s e l e n g t h i s c o r r e l a t e d w ith t h e d i s c h a r g e p u l s e ^350 jus l o n g . The p e ak pow er i s a ro u n d 20 w a tts f o r m o st o f t h e s t r o n g l i n e s . A w e l l - d e f i n e d r e l a t i o n s h i p b etw een t h e e n e rg y o u tp u t and t h e " tim e d e la y " on a l i n e was a l s o fo u n d ( F i g . 2 ) . The tim e d e la y i s d e f in e d a s t h e i n t e r v a l b e tw ee n t h e f r o n t edge i jof t h e e x c i t a t i o n p u l s e and t h e f i r s t a p p e a ra n c e o f i n f r a r e d [en erg y , Weak l i n e s , w h ich have r e l a t i v e l y slo w b u i ld u p , a p p e a r w ith d e la y s a p p ro c h in g 600 jisec ( s e e C h a p te r V I, s e c t i o n C f o r th e p r o b a b le m e c h a n ism )• E. SIMULTANEOUS LASER ACTION OF NgO Some l i n e s o t h e r t h a n t h e two p r i n c i p a l r o t a t i o n a l 1 b an d s o f COg a r e f o u n d . Such l i n e s o c c u r i n th e r a n g e s from P ( 8 ) t o P ( 6 6 ) and from R ( 6 ) t o R (18) o f th e (1 0 ° 0 -0 0 ° 1 ) | b a n d , and from P ( 6 ) t o P(l^) o f t h e ( 0 2 ° 0 - 0 0 ° l) band* The [ a d d itio n a l l i n e s am id t h e ( 1 0 ° 0- 00° 1 ) band seem t o be due t o t h e l a s e r a c t i o n o f NgO g a s a s r e p o r t e d by Sugiyam a and I n a b a ( 1 9 ) . The P (l) (1 0 ° 0 -0 0 ° 1 ) l i n e o f NgO i s c l o s e t o t h e tim e d e la y power a r b . u n i t 500 20 power — tim e d e la y 12 100 1060 1020 P( 20) P(60) R( 20) P( 20) P(60) F i g . 2. The r e l a t i v e o u tp u t power and tim e d e la y f o r d i f f e r e n t NQS l i n e s P (2 6) (1 0 ° 0 -0 0 ° 1 ) l i n e o f CC^. The o b s e rv e d a d d i t i o n a l l i n e s a r e c o n s i s t e n t w ith th e s p e c tru m o f th e NgO (1 0 ° 0 - 00°1) r o t a t i o n a l b a n d . The NgO l a s e r l i n e s from P ( l ) t o P(*H) and from R ( l ) t o R (51) o f (1 0 ° 0 -0 0 ° 1 ) r o t a t i o n a l band w ere o b s e r v e d , Meyer e t _ a l , (1*0 a l s o o b s e rv e d su c h a d d i t i o n a l l i n e s , b u t t h e y a t t r i b u t e d t h e s e l i n e s t o th e P b ra n c h o f t h e COg ( O l ^ l- l l ^ O ) v i b r a t i o n a l b a n d . The a d d i t i o n a l l i n e s amid P (6 ) t o P(1*0 o f (0 2 ° 0 -0 0 ° 1 ) band have f r e q u e n c i e s to o h ig h f o r th e NgO (1 0 ° 0 -0 0 ° 1 ) r o t a t i o n a l b a n d . W e c a n n o t i d e n t i f y them . j CHAPTER IV | | THE TUNABLE, Q-SWITCHED, PULSED-DISCHARGE C02 LASER I 1 |A. DESIGN OF THE LASER ! ! T h is l a s e r i s i d e n t i c a l t o th e p r e v io u s one, i n r e g a r d t o th e g as m ix tu re s u p p ly , th e d is c h a r g e sy ste m , and m ost o f th e m e c h a n ic a l p a r t s and d e t e c t o r s . B ut th e d i f f r a c t i o n g r a t i n g s p i n s a b o u t i t s sy m m e tric a l a x e s , l i k e a f l y w h e e l , t o a c h ie v e Q -s w itc h e d o p e r a t i o n . Only a t one p o i n t i n th e s p i n c y c le c an th e g r a t i n g c lo s e th e o p t i c a l r e s o n a t o r i t h i s i s when th e r u l i n g s a r e p e r p e n d i c u l a r to th e p la n e o f th e tu b e a x i s and th e g r a t i n g n o rm a l. Wave i l e n g t h s o f p o s s i b l e o p e r a t i o n a r e th e n s u b j e c t to th e u s u a l I j g r a t i n g e q u a t i o n . When th e g r a t i n g s p i n s , th e lo c u s o f th e ! i | f i r s t o r d e r o f d i f f r a c t i o n i s a c o n e - l i k e s u r f a c e (s e e th e : | |a p p e n d ix f o r a c o m p lete a n a l y s i s ) . The r e s o n a t o r l i n e u p i s j I c o m p le te ly t r i v i a l , b e c a u se a m in o r m is a lig n m e n t i n one o f i I jth e two c o o r d i n a te s o n ly ch an g e s th e p r e c i s e tim e o f th e |p u l s e , w h ile th e o t h e r c o o r d in a te d e te rm in e s th e l a s e r l i n e !— and t h e r e a r e no dead s p o ts b e tw ee n l i n e s . The s p i n i ! sp e e d o f th e g r a t i n g may be v a r i e d from 100 cp s to 650 c p s . B. SPECTRUM OF LINES FOUND j The l a s e r r o t a t i o n a l com ponents from J= 4 to J=^2 were o b s e rv e d on a l l f o u r b ra n c h e s — ( 1 0 ° 0 - 0 0 ° 1 ) , (0 2 ° 0 - lb 1 5 0 0 ° 1 )} P, R b ra n c h e s . W ith th e optimum g a s p r e s s u r e and I c u r r e n t , th e s t r o n g l i n e s , e . g , , P ( 2 0 ), have a v e ra g e i I pow ers o f a b o u t 2 W . The p u ls e l e n g t h , w hich depends on j ! i th e m o to r s p e e d , i s a b o u t J00 n s . A t y p i c a l peak power i s a b o u t 20 kw. C. OPTIMUM GAS PRESSURE AND CURRENT j As shown i n F i g . 3, th e l a s e r i n t e n s i t y i s t y p i c a l l y n o t s e n s i t i v e t o th e d is c h a r g e p u ls e l e n g t h w henever t h i s i s lo n g e r th a n 100 y jsec. The p a r t i a l p r e s s u r e s f o r th e s e d a ta a r e Pco2= 3 t o r r , Pne = 6*5 t o r r , Pjjg* 1 .5 t o r r . The c u r r e n t i s 90 mA. The "tim e d e la y " has been a d ju s te d to th e o p tim a l v a lu e o f 100 jasec, where we now d e f in e th e tim e d e la y a s th e i n t e r v a l from th e end o f th e d is c h a rg e p u ls e i | j t o th e b e g in n in g o f good a lig n m e n t (ju d g e d o n ly by th e ! I | !a p p e a ra n c e o f th e l a s e r o u tp u t p u l s e ) . [ A ll th e s e a re e s s e n t i a l l y o p tim a l v a lu e s ( f o r a i c o n v e n tio n a l low p r e s s u r e l a s e r ) , th o u g h some a re n o t | c r i t i c a l . F o r th e d a ta o f th e s u b s e q u e n t p a ra g r a p h s , th e |d is c h a r g e p u ls e le n g th was f i x e d a t 350 jis e c ( th e d is c h a r g e ! ! ! je x te n d s from -350 ^isec to z ero i n F i g . k -6 t se e b e lo w ). j |D. LASER OUTPUT ENERGY VERSUS TIME DELAY G e n e r a lly , o u r d a ta can be d is p la y e d a s p l o t s o f ! i o u tp u t e n e rg y v e r s u s tim e d e la y f o r v a r i o u s l i n e s , g as im ix tu r e s , c u r r e n t , e t c . F ig u r e s k, 5 show th e l a s e r 16 i 1 i n t e n s i t y a r b . u n i t 1 0 °0 -0 0 1 P (14) 10°0-00°1 R(20) .4 .5 ms d is c h a r g e p u ls e d u r a t i o n F i g . 3 . The e f f e c t o f v a r y i n g d is c h a r g e p u ls e l e n g t h s on th e o p t i c a l p u ls e e n e r g y . 1 7 (a ) p -b ra n c h i n t e n s i t y a r b . u n i t J=18 12 ms tim e d e la y (b) R -b ran ch i n t e n s i t y a r b . u n i t J=18 tim e d e la y F ig . 4 . The l a s e r i n t e n s i t y v s . tim e d e la y f o r P - , R- b ra n c h e s o f (1 0 ° 0 -0 0 ° 1 ) band. i n t e n s i t y a r b . u n i t P -b ra n c h J=18 12 - 3 ° m i n t e n s i t y 1 - a r b . u n i t (b) R -b ran c h J=18 12 i I j F ig , 5- The l a s e r i n t e n s i t y v s . tim e d e la y f o r P - and | R e b ran ch es o f 0 2 ° 0 -0 0 ° l band, 1 2 i n t e n s i t y a r b . u n i t \ - i n i t i a t i o n d u rin g d is c h a rg e 10 tim e d e la y - .1 5 ms 1.20 L tim e F ig , 6 , Changes o f shape i n th e o p t i c a l p u ls e w ith v a ry in g d e la y tim e s , d a ta ta k e n on th e 02°0-00 1 P (2 2) l i n e . VO 2 0 i n t e n s i t y v e rs u s tim e d e la y f o r d i f f e r e n t r o t a t i o n a l [com ponents o f e ac h b ra n c h . The m ost n o t i c e a b l e f e a t u r e o f t h i s fa m ily o f c u rv e s i s t h a t s t r o n g l i n e s s t i l l l a s e i w ith o u t e v id e n t s y s te m a tic d ecay ( b u t n o t w ith o u t some te m p o ra l s t r u c t u r e ) f o r tim e d e la y s f o r w hich weak l i n e s w i l l n o t l a s e a t a l l . Among weak l i n e s , a r o t a t i o n a l com ponent w ith a low J num ber seems t o l a s e somewhat lo n g e r th a n a com parable com ponent ( s i m i l a r max. power) w ith a h ig h J num ber. I t i s l i k e l y t h a t th e d e t a i l s o f th e s t r u c t u r e depend upon e f f e c t s o f v i b r a t i o n a l - r o t a t i o n a l r e l a x a t i o n . I t m ig h t be f e l t t h a t th e s t r u c t u r e i n F i g . ^ and 5 would be v e ry s e n s i t i v e to s m a ll v i b r a t i o n s i n th e r e s o n a t o r | geo m etry and t h a t l i t t l e g e n e r a l in f e r e n c e c o u ld be e x t r a c t e d from th e c u rv e s . However, we f i n d some u n if o r m i- |ty o v e r th e v a r io u s l i n e s o f b o th v i b r a t i o n s . The P -b ra n c h jli n e s a re a l l g e n e r a l l y s i m i l a r , w ith a l a t e ''bump". The j |R -b ran ch l i n e s a r e a g a in s i m i l a r , b u t th e l a t e bump i s now i •istro n g e r. A minimum a p p e a rs i n th e m id d le r e g i o n , so t h a t Ithe c u rv e s have th e a p p e a ra n c e o f a c a m e l's b a ck . i i |e . duration of the output pu l se versus t im e delay i As shown i n F ig , 6, th e d u r a t i o n o f th e o p t i c a l i ! | jpulse i s g r e a t e r when th e i n i t i a t i o n o f th e o p t i c a l p u ls e j I I jis d e la y e d th a n when i t i s a llo w e d t o i n i t i a t e b e fo r e th e ! jd isc h a rg e e x c i t a t i o n h a s been t e r m in a t e d . W e have c o n s i - 2 1 d e re d t h e o r e t i c a l a n a l y s i s a lo n g th e l i n e s o f th e work o f iLengyel and W agner(20), b u t t h e i r th e o r y ( d e v is e d f o r th e I jruby l a s e r ) assum es no f u r t h e r pum ping d u r in g th e o p t i c a l jp u ls e ; we f i n d no u n iq u e and s a t i s f a c t o r y e x p la n a t i o n o f jour d a t a , |F . EFFECTS OF VARIOUS GASES F i g s . 7 a , b show how th e p u ls e e n e rg y v e r s u s d e la y tim e c u rv e s change a s we add f i r s t , i n c r e a s i n g am ounts o f He ( w ith f i x e d Pc02= t o r r ) , th e n i n c r e a s i n g N2 ( w ith Pq02= 2 .5 t o r r , P ne= ^ .5 t o r r ) . W e f i n d t h a t th e a d d i t i o n o f N2 p ro d u c e s a m odest i n c r e a s e i n th e a v a i l a b l e p u ls e ien e rg y , b u t more n o ta b ly a s u b s t a n t i a l e x te n s i o n o f th e |p o s s ib le d e la y tim e (1 0 , 2 1 ). j As shown in F i g , 8, th e e f f e c t o f h y d ro g en on a s i n g l e r o t a t i o n a l com ponent was a l s o s t u d i e d . The l a s e r p u ls e pow er d e c r e a s e s r a p i d l y f o r i n c r e a s i n g d e la y tim e , more s e v e r e l y f o r i n c r e a s i n g H2 p r e s s u r e . W e a s c r i b e th e jdecrem ent o f th e l i f e t i m e to d e a c t i v a t i o n o f th e u p p e r l a s e r l e v e l by h y d ro g en . On th e o t h e r han d , i t was o b s e r ved t h a t th e a d d i t i o n o f v e ry s m a ll am ounts o f H2 c a u se d a i .sm a ll i n c r e a s e i n th e l a s e r p u ls e pow er, f o r s u i t a b l y s h o r t id e la y tim e s ( 2 2 ) . T h is i s due to th e d e a c t i v a t i o n o f th e I 'lo w e r l a s e r l e v e l by h y d ro g en . The p o i n t i s t h a t h y d ro g en i jr a p i d ly d e e x c it e s b o th th e u p p e r and th e lo w e r l e v e l s ; and t h e r e i s p r e f e r e n t i a l d e e x c i t a t i o n o f th e lo w e r l e v e l , b u t 22 (a) ‘ i n t e n s i t y - a r b . u n i t ■ J j*i !> i !n l i i i / 1 ' H - 0 2 ° 0 -0 0 ° l R(2*f) *. \ x - PC02 pHe ----------- 2 .5 1 .5 ------------2 .5 3 .3 -------- - 2 .5 6 .5 -------------2 .5 1 2 .7 \ \ V \ N ' \ \ I 1 I I I I I I f\ I I I I I \ l I l \ l [ 7 5 7 8 1T 2 \ 1 (i i n t e n s i t y a r b . u n i t 1 .6 2. (T ms tim e d e la y 2 ,5 6 .5 0 i i ----------2 .5 6 .5 1 .2 2 .5 6 .5 2.3 PC02 pHe PN2 \ \ ^ y 1 0 °0 -0 0 °1 R (20) \ \ i i i i i i i i i i\i i iv n i\ i i .8 1 .2 1 .6 ms tim e d e la y F i g , 7 . The e f f e c t o f v a r y in g p a r t i a l p r e s s u r e o f He, N« on th e o p t i c a l p u ls e e n e rg y v s . tim e d e la y f o r t y p i c a l r o t a t i o n a l - v i b r a t i o n a l co m p o n en ts. 23 10°0-00°1 R(20) il i n t e n s i t y — a r b . u n i t PC02 PHe p h2 3 .0 6 .5 0 3 .0 6 .5 A 5 3 .0 6 .5 ,6o 3 .0 6 .5 .90 3 .0 6 .5 1 .1 0 I I \ I I I l\ I I I 1 .2 176 2 / 0 ' tim e d e la y ms F ig . 8. The e f f e c t o f v a r y in g p a r t i a l p r e s s u r e o f H2 on th e o p t i c a l p u ls e e n e rg y v s . tim e d e la y f o r t y p i c a l r o t a t i o n a l - v i b r a t i o n a l co m p o n en ts. 24 th e p r e f e r e n c e i s n o t so s t r o n g a s f o r h e liu m . | G. THE DWELL TIME I T here i s a c e r t a i n " d w e ll tim e " T<j d u rin g w hich th e r e s o n a t o r l i n e u p i s a d e q u a te f o r h ig h Q ( f o r a l l th e s e r o t a t i n g - o p t i c s sc h e m e s). The l a s e r g as i n s i s t s upon a c e r t a i n tim e T^ f o r a m p l i f i c a t i o n o f a s i g n a l d e v e lo p in g from n o is e t o r e a c h a m e a su ra b le l e v e l , and f u r t h e r tim e Tp t o s a t u r a t e th e t r a n s i t i o n ( 2 3 ) . F o r a w e ll-fo rm e d p u ls e we r e q u i r e TD = Td + Tp , ^ 3 0 0 n s e c f o r a s t r o n g l i n e . L a s in g can ta k e p la c e w ith a c e r t a i n t o l e r a n c e a n g le ff>/2 from p e r f e c t a lig n m e n t, M ey erh o fer m easured <j>- 1 I |m rad (23). F o r th e g r a t i n g w ith a s p in n in g sp e e d o f 360 c p s , | jthe p r o j e c t i o n o f th e a n g u la r v e l o c i t y u) to an a x is jp e r p e n d ic u la r to th e l a s e r a x is i s 1.36 X 10-^ r a d / s e c . The j m e c h a n ic a l Q -s w itc h e d d w e ll tim e f o r su c h sp e ed i s 370 | i n s e c ; i t i s j u s t lo n g enough f o r s tr o n g l i n e s to l a s e , b u t n o t f o r weak l i n e s . T hus, QS g iv e s f a r fe w e r l i n e s (80 i n num ber) th a n NQS ( 1 3 0 ) . More l i n e s a r e o b se rv e d i f one slo w s down th e m o to r sp e e d to in c r e a s e th e d w e ll tim e , o r i f one in tr o d u c e s a s m a ll amount o f r a d i a t i o n from NQS j ( o p e r a t i n g on th e same l i n e ) t o "prim e" QS (s e e n e x t ‘ s e c t i o n ) . 1 1 H. THE "PRIMING" EXPERIMENT From th e o p e r a t io n o f NQS, we know t h a t th e d w e ll jtime r e q u i r e d f o r weak l i n e s i s much l o n g e r th a n t h a t f o r j js tro n g l i n e s (s e e F i g . 2 ) , The m e c h a n ic a l Q -sw ite h e d d w e ll Itime i s j u s t lo n g enough f o r s t r o n g l i n e s to l a s e . I f we |i n j e c t a s m a ll amount o f l a s e r e n e rg y i n t o th e QS c a v i t y , t h e tim e f o r b u ild u p t o a s i g n i f i c a n t l e v e l may be re d u c e d . | jThus, QS may be a b le to ru n on a d d i t i o n a l weak l i n e s . I n j p r i n c i p l e , c a r e s h o u ld be ta k e n t o o b t a i n c o in c id e n c e o f th e two l a s e r s ' d e t a i l e d f r e q u e n c i e s , and p e rh a p s o f o t h e r m a tc h in g p a r a m e te r s . W e to o k no d e l i b e r a t e m easures in th e s e r e g a r d s . N e v e r t h e l e s s , we d id o b se rv e su c h an e f f e c t . Some l i n e s w hich r a n w eakly i n th e Q -s w itc h e d l a s e r were a ls o en h an ced t o g iv e s u b s t a n t i a l l y l a r g e r p u l s e s . Those jlin e s e x te n d e d and en h an ced a re sum m arized i n T ab le I , I n jthe t a b l e , "QS l i n e s " r e f e r to th e QS l i n e s w hich e x p e r i e n ce d no e n ch an cem en t; th e m eanings o f th e o t h e r term s a re c l e a r . N ^ ^ ^ B r a n c h e s P (1 0 ° 0 -0 0 ° l) R (1 0 ° 0 -0 0 ° l) P (0 2 ° 0 -0 0 ° l) R ( 0 2 ° 0 - 0 0 ° l) R otating speeds of g r a t i n g w P M o o -3 - C V J QS l i n e s P (2 )-P (4 8 ) R (2 )-R (4 4 ) P (4 ) -P ( ^ 8 ) R ( 2 ) - R ( ^ ) enhanced l i n e s P (2 ) ,P ( 4 8 ) R (2 ),R (4 4 ) P (^ )» P (^ 8 ) R (2),R (4*0 a d d i t i o n a l l i n e s P (50) R (^ 6 )-R (5 0 ) P (2) P (5 0 )-P (5 ^ ) R (4 6 )fR(48) to P M o o V O QS l i n e s P(i|,)_P(420 R (2 )-R (^ 2 ) P ( 4 ) - P ( W R (4 )-R (4 2 ) enhanced l i n e s P ( ^ ) , P ( ^ ) R (2 ),R (^ 2 ) P ( ^ ) , P ( W R (4 ),R (4 2 ) a d d i t i o n a l l i n e s P(if6) R(il4) ,R (^6) P (^6) R(2) T ab le I . QS l i n e s e f f e c t e d by th e sp e e d s o f m o tor and by th e p rim in g o f NQS l i n e s . P (2 )-P (4 8 ) means P ( 2 ) f P (4)» P ( 6 ) ............... P ( W * P ( 2 ) ,P ( ^ 8 ) means P (2 ) and P (^ 8 ) o n ly . I CHAPTER V | ! A BRIEF DESCRIPTION OF THE LOCAL M ODE OF CaF2 iH” I A. PREVIOUS W O RK ON HYDROGENATED CALCIUM FLUORIDE j | I n 1962, H a ll and S c h u m ac h er(24) in tr o d u c e d h ydrogen j |atoms in to CaF2 by h eatin g pure CaF2 in the presence o f H 2 j |a n d m e t a l l i c A l. The c r y s t a l s were X -ra y e d , T h is c au se d I |th e hydrogen atoms to move from F“ s u b s titu tio n a l s i t e s to 1 i n t e r s t i t i a l s i t e s j the c r y s ta ls then appeared q u ite b lack . They in v e s tig a te d the e le c tr o n sp in resonance o f the d e fe c t hydrogen atom. In 19&3» Hayes e t a l .(2 5 ) reported the I measurement o f the in fra red ab sorp tion spectrum a sso c ia te d 1 ; ; 1 jw ith th e v i b r a t i o n o f th e h y d rid e io n i n CaF2 . They p r e p a r e d th e sam ple w ith th e m ethod o f H a ll and Schum acher, b u t X r a y i r r a d i a t i o n was n o t p e rfo rm e d . The h y d ro g e n a te d d e f e c t was a s s ig n e d t o th e s u b s t i t u t i o n a l s i t e o f th e ! flu o r in e io n . In 19^5* the same group, E l l i o t t e t a l . (1), com pleted the measurement o f the f i r s t fo u r allow ed (I"L) j j 1 ile v e l s . They a lso presented a th e o r e tic a l model to d escrib e t h is resonant system (F ig . 9)* L ater in the same jyear, Hayes e t a l . (26) observed the other two s t a te s o f the |n=2 le v e l p red icted by t h is m odel; the c r y s ta l was placed |under heavy s t r e s s so th a t ab sorp tion by the otherw ise lunobservable s t a te s was induced by admixture o f the nearby I | 1^ s t a t e s . T h e ir r e s u l t s were a l s o c o r r o b o r a te d i n some 28 cm (2) r-1 1 2912.2. 5 r4 2886.4. r . 2862.5- r",} 2825,6- ,n I T, 1943.6 r* 5 1919.8 r, 1894.1 1 .0 £ tn c o X v 8 3 10 . n \ 965.6 5 X » 6 1 , ; T I 6 <f r i 0 a b e d e f 0 F i g , 9 . S p ectru m a t^ -'2 0 oKl a d o p te d from r e f , 1, T r a n s tio n s s t u d i e d i n s u c c e e d in g i v e s t i g a t i o n s a re t i ) r e f . 1 , i n f r a r e d a b s o r p t i o n , l i n e s a , c , e , f . i i ) r e f . 4 . i r , u n i a x i a l s t r e s s , l i n e s a , b , c , d. i i i ) r e f , 5» Raman s c a t t e r i n g , l i n e s a , b , c . iv ) p r e s e n t w ork, l i n e s a , b ' r c ' , d* . 0 I n s e t i o b se rv e d r e l a t i v e t r a s m i s s i o n on 10 0 lin e $ R (2 ), R ( 4 ) , R ( 6 ) , R (8 ) , R (1 0 ), a t ~ 9 0 °K . 29 measure by Raman(5) and n eutron(2?) s c a tte r in g . R ecen tly , the i r ab so rp tio n sp e c tr a o f the lo c a liz e d v ib r a tio n o f an j i hydrogen atom on an i n t e r s t i t i a l s i t e fo r pure(2 ) and f o r r a r e -e a r th (3 ) doped CaF2 were a ls o measured. i B. REVIEW OF THE THEORETICAL MODEL i CaF2 has a fa ce cen tered cu b ic f lu o r it e str u c tu r e . | | iEach Ca io n i s s u r ro u n d e d by e i g h t f l u o r i d e s a t th e c o m e r s o f a cube and e v e ry se co n d cube o f f l u o r i d e s i s ++ em pty. The p o i n t sym m etry i s c u b ic , 0^* f o r b o th th e Ca io n s i t e and th e i n t e r s t i t i a l s i t e ( t h e s e b e lo n g to th e ++ v a c a n t p o s i t i o n s on th e Ca c u b ic l a t t i c e ) . The f l u o r i d e s have f o u r n e a r e s t - n e i g h b o u r Ca io n s a t th e c o m e r s o f a r e g u l a r t e t r a h e d r o n . The h y d rid e io n a t th e f l u o r i d e s i t e , t h e r e f o r e , w i l l se e a p o t e n t i a l w i l l o f t e t r a h e d r a l |sym m etry, Td . j I : I The l o c a l mode may be d e s c r i b e d a p p r o x im a te ly a s j p e r i o d i c m o tio n o f th e H" io n a lo n e . The r a t i o o f th e ! i displacem ent am plitudes between a s u b s tit u tio n a l d e fe c t ion o f mass M * and a n e ig h b o u r io n o f m ass Mp, i s t y p i c a l l y on th e o r d e r o f M '//M M _. ( 1 ) , where M i s th e mass o f th e io n | ^ Which i s r e p l a c e d by th e d e f e c t io n . F o r an H” io n i n th e |s u b s t i t i o n a l F s i t e , t h e r a t i o o f th e d is p la c e m e n t I ++ « a m p litu d e s b etw een Ca and H io n s i s a b o u t 3 \ | F o r th e o s c i l l a t i o n o f an H io n i n a s t a t i c t e t r a h e d r a l a n h arm o n ic w e l l, th e p o t e n t i a l f o r th e 3 0 d is p la c e m e n t o f t h e H~ io n from th e c e n t e r o f t h e c e l l h a s th e fo rm , j V * A r2 + Bxyz + C ^ x ^ + y ^ + z 1 *) + C g(y2 z 2+z^x^+ x^y^)+ ----- where t h e x - , y - , z - c o o r d i n a te s a r e a lo n g t h e s i d e s o f a u n i t c e l l . The i r sp e c tru m o f t h i s sy ste m i s q u i t e s i m i l a r |to one due t o a p e r f e c t harm onic o s c i l l a t o r , w hich shows t h a t t h e q u a d r a t i c , s p h e r i c a l l y sym m etric te rm g iv e s by f a r th e l a r g e s t c o n t r i b u t i o n t o t h e e n e r g i e s o f lo w - l y in g s t a t e s . T h u s, th e e f f e c t s o f th e an harm onic te rm s a r e sm a ll and t h e te rm s may be c o n s id e r e d a s p e r t u r b a t i o n s . On th e o t h e r h a n d , t h e s e te rm s c a u s e th e v a r i o u s A n- + 1 f r e q u e n c i e s t o be d i s t i n c t , w e ll o u t s i d e t h e i r l i n e w i d t h s . jThis i s q u i t e c o n v e n ie n t f o r o u r p u r p o s e s , s i n c e i t c a u s e s th e s e p r o c e s s e s t o be d i s t i n g u i s h a b l e . I n t h i s r e s p e c t , th e anharm onic te rm s a r e by no means n e g l i g i b l e . To be more s p e c i f i c , th e v i b r a t i o n a l s p e c tru m re s e m b le s t h a t o f a s p h e r i c a l l y sym m etric h arm o n ic o s c i l l a - j • I i t o r w ith u n ifo rm s p a c in g s h i/ i n th e v i c i n i t y o f 950 cm x , iln th e s p h e r i c a l harm on ic m o d e l(2 8 ), we have f o r n - 0 , a n s s t a t e (no d e g e n e ra c y )* f o r n = l , a p s t a t e ( t r i p l e degenerw ;acy)* n= 2, s+ d s t a t e s ( s i x f o l d ) * n=3» P+f ( t e n f o l d ) * e t c . B ecause o f t h e anharm onic p e r t u r b a t i o n , t h e d e g e n e r a c ie s | a r e b ro k e n and t h e c e n t e r - o f - g r a v i t y o f t h e s e v e r a l l e v e l s |o f an y g iv e n n i s s h i f t e d . The n = l l e v e l , w h ic h h a s JV j 5 [sym m etry, i s n o t s p l i t * t h e n=2 l e v e l i s s p l i t i n t o t h r e e l e v e l s w ith sy m m etries 1 ^ , and 1^, w hich have o n e -, tw o -, and t h r e e - f o l d d e g e n e r a c ie s , r e s p e c t i v e l y . These s t a t e s a r e sum m arized i n T ab le I I . The p e r tu r b e d e n e rg y , to f i r s t o r d e r i n th e q u a r t i c te rm s and t o seco n d o r d e r i n th e c u b ic te rm , r e l a t i v e to t h e u n p e rtu r b e d g ro u n d s t a t e , was f o u n d ( l ) to be E = nf>& + ( ^ 1C1-»^2c 2 ) ^ / 2M,^ ) 2- ^ B2ft2/ 2 ^ The c o n s t a n t s were d e te rm in e d by th e i r a b s o r p t io n sp e c tru m i Q,/C = 981 .1 cm"1 , B = 7 .8 ? X 1012 e rg /c m 3 , Ci = - 2 .3 2 X 1019 e rg /c m ^ , | C2 = -1 .0 1 X lO 1^ e rg /c m ^ | land th e i n t e g r a l c o n s t a n t s & ^ f o r d i f f e r e n t s t a t e s lare shown i n T ab le I I , | F i g . 9 shows th e t r a n s i t i o n s s t u d i e d i n v a r io u s i n v e s t i g a t i o n s . n Symmetry Wave F u n c tio n s n X ECcm"1 ) 0 1 |000> 9 3 1 0 i 5 lioo> 21 7 5 965.6 2 l ( | 200>+ |020> + |002> )//3 45 15 21 1894.1 2 3 ( |2 0 0 > -|0 2 0 > ) //5 ‘ 45 9 3 1943.6 2 5 |011> 33 15 13 1919.8 T ab le I I • Wave f u n c t i o n s , s y m m e trie s , and p o s i t i o n s o f th e lo w er v i b r a t i o n a l e n e rg y l e v e l s o f an H“ io n i n CaF2 « CHAPTER VI I | SATURATION OF THE LOCAL M ODE OF CaF2 *H“ j I i A. EXPERIMENTAL ARRANGEMENT The e x p e rim e n t i s a rr a n g e d a s shown i n F ig . 10. j Sam ples were p re p a r e d by th e m ethod o f H a ll and Schuma- c h e r ( 2 4 ) . T hree h o le s in a m ovable c o ld f i n g e r were c o v e re d r e s p e c t i v e l y by a pure CaF2 sa m p le , by a CaF2 »H“ sa m p le , and by n o th in g . Two BaF2 l e n s e s ( f = 62 mm) p la c e d a s dew ar windows f o c u s th e beam on th e sam ple and r e c o l l i - mate a f t e r i t . W e em ployed a c h o p p e r w i t h in th e l a s e r c a v i t y to re d u c e th e p u ls e r a t e from 360 cps to 20 c p s, i n o r d e r to re d u c e th e tim e -a v e ra g e th e rm a l lo a d a t th e c r y s t a l s . I t was d r i v e n s y n c h ro n o u s ly w ith th e d is c h a rg e j |p u l s e . A m onochrom ator was u se d to i d e n t i f y l a s e r l i n e s . | j A th e rm o p ile was u se d to d e te rm in e th e a v e ra g e power, and i j ;two GeiAu d e t e c t o r s were u se d to s tu d y th e p u ls e sh a p e s o f I ! j th e l a s e r o u tp u t from th e z e r o t h o r d e r o f th e g r a t i n g s and from th e concave m i r r o r . The t r a n s m i t t e d i n t e n s i t y th ro u g h th e t h r e e p o r t s o f th e c o ld f i n g e r (one by one, by moving th e f i n g e r ) a re com pared f o r v a r i o u s l y a t t e n u a t e d power i l e v e l s . i IB. EXPERIMENTAL RESULTS A t room te m p e r a tu r e , th e a b s o r p t i o n peak f o r th e 3 3 m o to r Ge s u b s tr a t e d m ir r o r g r a t i n g Q -sw itch ed C02 l a s e r m ir r o r B re w ster window m on och rom ator ’ m ir r o r Ge iAu d e t e c t o r I V o ltag e s i g n a l to o s c illo s c o p e Sample CaF2 *H“ and CaF2 on a m ovable c o ld f i n g e r (3 h o le s ) F ig . 10, The a rran g em en t f o r th e s a t u r a t i o n e x p e rim e n t. 3 5 jfu n d am en ta l i s a t P (^ ) (1 0 °0 -0 0 °1 ) (957*8 cirT'*'), This jfre q u e n c y , and some o f th e o t h e r A n = + 1 f r e q u e n c i e s , l i e i ' O O n e a r th e band c e n t e r f o r th e (10 0-00 1) v i b r a t i o n . As a c o n se q u e n c e , th e C02 l a s e r l i n e s h e re a r e r e l a t i v e l y weak. jT his c ir c u m s ta n c e , i n f a c t , f o r c e d us to d e v e lo p th e | I p r e v io u s " d e s c r ib e d " l a s e r d e s ig n s f o r m axim al g a in and jm inim al l o s s j t h i s i n t u r n l e d to th e o b s e r v a t i o n o f th e jre c o rd num ber o f 130 l i n e s l a s i n g . N e v e r t h e l e s s , P (^ ) re m a in s a weak l i n e f o r QS. T h e r e f o r e , i n o u r s tu d y o f s a t u r a t i o n , we have u s e d i n s t e a d th e s t r o n g e r l i n e s P (6 ) and P ( 8 ) , ( 1 0 ° 0 -0 0 ° 1 ) ( 9 5 6 .2 , 95^*5 cm * ) , w hich a re s t i l l w i t h in th e l in e w i d t h a t t h i s te m p e r a tu r e . The a b s o r p t io n peak c o in c id e s c l o s e l y w ith th e R ^ ) l i n e a t a c o n v e n ie n t jte m p e ra tu re ~ 90°K, n e a r th e b o i l i n g p o i n t o f l i q u i d oxygen. ! jBelow l i q u i d n i t r o g e n te m p e r a tu re (7 7 °K ), how ever, i t ia s y m p to tic a lly a p p ro a c h e s th e l i n e R(6). The r e l a t i v e ! t r a n s m i s s io n f o r v a r io u s l i n e s n e a r th e fu n d a m e n ta l, i s jshown i n th e i n s e r t o f F i g . 9 . Undoped CaF2 sam p les o f l i d e n t i c a l t h ic k n e s s show a c o n s t a n t t r a n s m i s s i o n ^ 90$ . I The tran sm itted p u lse a f t e r the CaF2 *H - was compared Iwith the p ulse from the zeroth order o f the g ra tin g and jdisplayed on an o s c illo s c o p e (T ektronix Type 556), as shown i jin F ig , 1 1 a. As a sim p le d e m o n s tra tio n o f s a t u r a t i o n , i t j jshows te m p o ra l n a rro w in g o f th e t r a n s m i t t e d p u ls e r e l a t i v e to th e i n c i d e n t p u l s e . F i g . l i b d i s p l a y s g ra p h s c o n s t r u c t - 36 pulse after CaF« :H 2 0 0 ns/cm F i g , 11, a) Abovei o s c i l l o s c o p e t r a c e s show ing n a rr o w in g o f t r a n s m i t t e d R(6) p u ls e . r e l a t i v e to i n c i d e n t p u l s e , a t '-*'80 K, b ) Below* p l o t s o f I q v s , I i n c o n s t r u c t e d from th e r i s i n g and from th e f a l l i n g p o r t i o n s o f th e p u ls e a b o v e . PERCENT 3 7 4 0 3 0 20 4 0 3 0 20 6 0 50 4 0 l r i r i r -I 9 5 4 .5 cm _ jo — to — o — _- o-------x r o - o ° — 956.2 cm-' _ - A - ~ ---------- _ - 4 9 6 6 .5 cm"' ____ — - • ~ • . 2.2 c 2.0 • — H 1.4 1 .0 RELATIVE I- in F i g . 12. I 0/ l i n vs-. I i n . F i l l e d sym bols a re d a t a f o r 9®°Kj , where Wq.,= 9 65.1 cm- ! , w id th A = 1.2 cm- ! . Empty sym bols a re d a ta a t 290°K, where Wq i =9 5 7 ,8 cm- ! , w id th A = 8 ,7 cm- ! . G iven l a s e r f r e q u e n c i e s f o r t r i a n g l e s a re n e a r th e r e s p e c t i v e p e a k s ; th o s e f o r c i r c l e s a re i n th e w in g s. ed from p o i n ts on 11a, to i n v e s t i g a t e w h e th e r th e t r a n s jm itte d i n t e n s i t y i s i ) s o l e l y a f u n c t i o n o f th e i n s t a n t a n eo u s i n c i d e n t i n t e n s i t y , c o rre s p o n d in g to s a t u r a t i o n (su c h e f f e c t s w i l l he r e f e r r e d to a s " f a s t " ) * o r i i ) d e p e n d e n t upon th e h i s t o r y — p resu m ab ly upon th e i n t e g r a l o v e r p r e v io u s i n t e n s i t i e s j t h i s m ig h t be ta k e n a s a th e r m a l e f f e c t (•'s lo w " ). Both s o r t s o f e f f e c t a re c l e a r l y p r e s e n t j i j jbut s a t u r a t i o n i s th e dom inant one o t h e r th a n f o r l a t e p o r t i o n s o f th e p u l s e , where th e slow e f f e c t o b v io u s ly d o m in a te s . i I n F ig . 12 we p l o t th e t r a n s m i s s io n I o u t / ^ i n v s * * in a t d i f f e r e n t te m p e r a tu r e s . T h is f i g u r e a l s o d e m o n s tra te s I s a t u r a t i o n . The c u rv e s p l o t t e d a re f i t by a sim p le th e o r y |(se e n e x t s e c t i o n ) , I t j i jc. THEORY OF SATURATION | C o n s id e rin g a s t r o n g CO2 l a s e r beam a t th e fu n d a m e n ta l fre q u e n c y fo c u s e d upon a CaF2 »H~, we a d o p t th e r a t e I j j ie q u a tio n s , jpj- = - Wi (N0 - % ) + ^ Nj. where |Nq i s th e c o n c e n tr a ti o n o f l o c a l mode a t th e ground s t a t e ! and N^ a t th e n = l s t a t e , 1 |Ti i s th e decay tim e from n = l to n=0, I | 39 i 2 jWi = i m i I g ( W “ ^ l o ) i s in d u c e d a b s o r p t io n r a t e , i|^ i \p Q1 = 0 . 1 x 10> = i s th e t r a n s i t i o n d ip o le moment, 11 i s th e l a s e r i n t e n s i t y a t f r e q u e n c y q j , |q i s th e e f f e c t i v e c h a rg e o f th e H“ io n , j ! t2_1 | g(CU~a#i r .) = —----------------- 5--------s— i s th e n o rm a liz e d L o re n tz | 10 * [ ; ( u - w1 0 ) 2+ t 2- 2 ] lin e s h a p e f u n c t i o n , I i W10 i s th e r e s o n a n t f re q u e n c y b etw een s t a t e s ( 1 ) and ( 0 ) , j | a n d , T2 » w hich w i l l a p p ro a c h t o T^ when t h e te m p e ra tu re a p p ro a c h e s 0°K ( d i s c u s s i o n b e lo w ), i s th e l i f e - t i m e o f I | th e n = l l e v e l . | The r e l a x a t i o n tim e s a re o f th e o r d e r o f a few p s e c , |b u t th e l a s e r d u r a t i o n i s *-400 n s , so t h a t th e p o p u la tio n j . d i s t r i b u t i o n i s b a s i c a l l y one o f s t e a d y - s t a t e d u rin g th e j l a s e r p u ls e , i . e . dN0 dNi L e t N -t;0-t be th e t o t a l c o n c e n t r a t i o n o f th e l o c a l 'modes i n s t a t e s ( 0 ) and ( 1 ) , i . e . = N0 + Nl t th e n wiTl | N1 1 + The l a s e r i n t e n s i t y a b so rb e d by H“ io n s i n th e | i n t e r v a l A x i s j A h I = - t la ;W i (N0 - N^AX . o r 4° A u i _ ^ w l ^ o i l 2 T2 N to 1 : 1 ________ A * fi c -2 8 7 r ^Olt 2 -1 ( 01- O ^0 ) + T2 + — ------ T ^ g T h is r e s u l t i s i d e n t i c a l t o a n e q u a t io n d e r iv e d from a d e n s i t y m a tr ix t r e a t m e n t by F a i n an d K h a n in (2 9 ), D e f in in g some new q u a n t i t i e s t o em p h asize th e i n t e n s i t y , r a t h e r th a n t h e fr e q u e n c y d e p e n d e n c e , we have A h1 _ A h1 A x 1+WI , where 2 7Tq2T2N-fc0t _ ^ i s th e a b s o r p t i o n c o e f f i c i e n t McCl + ( M - W 10)2T22] due t o H” io n s i n th e l i m i t o f low l a s e r i n t e n s i t y , and ^7Tq2T1T2 W = -r o— 5“ i s "the s a t u r a t i o n p a r a m e te r . * wi o MCCi+ ( w - w1 0 ) 2t 2z 3 i | I f we ta k e C L ^ t o be th e a b s o r p t i o n c o e f f i c i e n t due t o th e i j l a t t i c e o f p u re CaFgi th e n th e n e t a b s o r p t i o n o f l a s e r j i n t e n s i t y p e r u n i t l e n g t h w i l l be ! A l „ , „ . ®H__\ t ' £ x L T+WI ;A f t e r i n t e g r a t i o n , we g e t / „ - b -b e „ v a(R e - 1) WIi n = — - bc~ ’ where j R - e D e D C ja = b ~ a l / aK» c ” R = i o u t ^ i n * !I ou^. i s th e l a s e r i n t e n s i t y a f t e r th e CaFgiH” c r y s t a l o f l e n g t h L , and I I i n i s th e l a s e r i n t e n s i t y r e a c h i n g th e sa m p le . The c o n s t a n t s O f L and CfH can be m easured by th e ^ a b so rp tio n o f a weak beam, i . e . i i I a LL = - i n R f o r p u re CaF2 » = - I n R - OjL f o r CaF2 *H” , T hus, th e e x p e r im e n ta l curve R v s , I ^ n can be f i t by a s i n g l e p a ra m e te r WI^n (m ax). a „ 27T q2T2 D e f in in g <T = = -------------------------- -— — , we have " t o t M0& + < " l o ) T2 3 2 ) ^ = 1 1 i “ iow /<r L a t e r we w i l l se e e v id e n t t h a t t h e r e i s a v e ry f a s t s c ra m b lin g among th e t h r e e d e g e n e ra te com ponents o f th e n=l l e v e l . The above argum ent m ust be m o d ifie d ! th e r e s u l t i s t h a t th e f a c t o r o f i s changed to 2 , By d e te r m in a tio n o f !W from th e s a t u r a t i o n c u rv e , and o f (T from p re v io u s w ork, |as d e s c r ib e d b e lo w (2 ), th e n T^ can be c a l c u l a t e d . j |d . ANALYSIS OF THE EXPERIMENTAL RESULTS BY THE ABOVE ! THEORY j — 1 — 1 A t room te m p e r a tu r e , O fL = 4 .5 6 cm" = 4 4 . 7 cm” , ! land WI^n (max) = .152 f o r l i n e P ( 6)* a t l i q u i d oxygen i te m p e r a tu re (c h o s e n b e ca u se t h i s p l a c e s a l i n e c lo s e to th e -1 -1 I p e a k ) , Cf^ = 2 .7 7 cm » a H = *75 cm , and Wl£n (max) = .357 i |f o r l i n e R (4 ). Our e s t im a t e o f I ^ n (max) i s v e r y rou g h i jb ecau se th e s p o t d ia m e te r d i s p o o r ly known. T ak in g d=80 | p.m and a maximum power r e a c h in g th e sam ple o f 3 kw, we f i n d ............................ i+2 , I i n (max) = 6 .0 X 10? w a tt/c m 2 . The s a t u r a t i o n p a ra m e te r wj th e n i s 2 .5 X 10“ ^ cm2/ w a t t a t room te m p e r a t u r e , and -9 2 / 6 .0 X 10 7 cm / w a t t a t l i q u i d oxygen t e m p e r a t u r e . Our s u c c e s s i n d e s c r i b i n g th e s a t u r a t i o n in t h i s s im p le f a s h i o r le n d s s u p p o r t t o o u r b e l i e f t h a t t h e l in e s h a p e i s homo gen eo u s . Shamu e t a l .( 2 ) m easu red th e i n t e g r a t e d i n t e n s i t y o f th e se c o n d h a rm o n ic a s f 20 H(27rC)’' 1d % 2 = 68 cm” 2 And E l l i o t t e t a l . ( l ) m ea su re d th e r a t i o o f th e fu n d a m e n ta l t o th e se c o n d h arm onic a s / l « H d% l / = 2 3 + 3 I T h u s, th e i n t e g r a t e d i n t e n s i t y o f t h e fu n d a m e n ta l ! i f o r Shamu*s sam ple was i i f 1a ii( z m ) ~ 1&a01 = 156b cm” 2 ! 1 A ssum ing t h a t th e l in e s h a p e i s L o r e n t z i a n , th e n f o r ! th e fu n d a m e n ta l j ®H(p e a k ) = 832 cm” 1 ^ where th e fu n d a m e n ta l l i n e w i d t h i s A = 1 .2 cm” f o r 90°K . i ( The d e f e c t c o n c e n t r a t i o n o f th e Shamu*s sam ple was o n o ! d e te rm in e d by n e u tr o n s c a t t e r i n g t o be n= 10 /cm -5. T hus, ! th e p e ak c r o s s s e c t i o n d e te rm in e d from O'- O /n i s I O' = 8.3 X 10” 18 cm2 . ; peak j The c o n c e n t r a t i o n o f th e one o f o u r sa m p le s u n d e r d i s c u s s i o n i s a p p ro x im a te ly H 175 lg .3 N+ + = -=------- = ----------------- T-o = 2 .0 X 10 7 cm . t o t p eak 8 .3 X 10“ 18 w here th e fre q u e n c y o f th e R (^) l i n e i s ta k e n t o be a t th e p eak o f th e l o c a l mode a b s o r p t i o n . One may n o te t h a t , e v en a p a r t from a s tu d y o f s a t u r a t i o n , th e r e l a t i v e l y lo w -p o w er ( W I « 1 ) m easurem ent o f CtH n e c e s s a r y f o r t h i s p u rp o se w ould be v e ry d i f f i c u l t w ith a c o n v e n tio n a l s o u r c e . T h is pro b lem a r o s e f o r Shamu, i n f a c t , and c a u se d him t o s tu d y th e se c o n d h a rm o n ic a b s o r p t i o n r a t h e r th a n t h a t o f th e fu n d a m e n ta l (s e e a b o v e ). F o r a v i b r a t o r o f known fr e q u e n c y an d m ass t o g iv e o u r t T p g ^ v a l u e , th e e f f e c t i v e c h a rg e * w ould n e c e s s a r i l y be q = y/<r mHCA/¥ T if - .18 e . i ; 1 S u b t i t u t i n g th e v a lu e o f W and O’p e ak i n t o e q u a t io n ■ ( 2 ) , we have T1 = 11 p s e c , j The q u a n t i t a t i v e u n c e r t a i n t i e s a r e l a r g e , b u t th e ' im p lie d d e ca y w id th (hom ogeneous, o b v io u s ly ) c h e c k s w e ll i I w ith th e r e s i d u a l w id th * ( t h e l i n e w i d t h a t z e ro te m p e ra - tt i t u r e ) - .7 cm” and w ith th e a s s e r t i o n by Hayes e t a l .( 2 5 ) ♦The v a lu e o f c r i s p r o p o r t i o n a l to q t th u s i f one ch o se a <rp e a ij v a lu e a p p r o p r i a t e to th e known f r e q u e n c y OJq i » m ass mp, an a a u n i t c h a rg e e , one w ould i n f e r a v a lu e o f Ti so l a r g e a s t o be i n c o n s i s t e n t w ith t h e o b s e rv e d r e s i d u a l l i n e w i d t h . t h a t th e r e s i d u a l w id th i s due to d e c a y . They a l s o s t a t e d t h a t th e " te m p e r a tu re -d e p e n d e n t e f f e c t s (o n lin e w i d t h ) f o llo w from th e i n t e r a c t i o n o f l o c a l i z e d modes w ith th e band m odes. The w id th o f th e l i n e s a r i s e s from p r o c e s s e s iin w hich phonons a r e s c a t t e r e d o f f th e d e f e c t w ith o u t a J |change i n i t s v i b r a t i o n a l s t a t e " ( b u t w ith ra n d o m iz a tio n o f |p h a s e i e v i d e n t l y a l s o o f p o l a r i z a t i o n — se e n e x t C h a p t e r ) . CHAPTER V II STEPWISE EXCITATION A. INTRODUCTION The p o s i t i o n s o f t h e n = 2 l e v e l s o f t h e l o c a l mode w ere o b s e rv e d by s te p w is e e x c i t a t i o n . OS was u se d t o p o p u la te th e n = 1 l e v e l . NQS was u se d th e n t o o b s e rv e th e n * = 1 t o n = 2 a b s o r p t i o n . The p o s i t i o n s o f t h e n « 2 l e v e l s were d e te rm in e d by t h e sum o f th e s e two r e s o n a n t f r e q u e n c i e s ( s u b j e c t t o some l a t e r c o n s i d e r a t i o n s on fr e q u e n c y a d d i t i v i t y ) . B. EXPERIMENTAL ARRANGEMENT ! As shown i n F i g . 13» th e d e w ar, th e s a m p le , and t h e ! d e t e c t o r sy ste m a rra n g e m e n t was t h e same a s i n t h e s a t u r a - ' t i o n e x p e r im e n t. B oth l a s e r s were m e c h a n ic a lly chopped ; t o 2o p u l s e s / s e c . t o m in im iz e h e a t i n g o f th e s a m p le . The | sam ple was g lu e d i n f r o n t o f a h o le o f 20 m il d ia m e te r on I i | a c o ld f i n g e r . B oth l a s e r s w ere a d j u s t e d t o i l l u m i n a t e a common s p o t (fro m d i s t i n c t c o n e s o f s o l i d a n g le ) on t h e I s a m p le . The tim in g f o r b o th l a s e r s was a d j u s t e d so t h a t i | t h e OS p u ls e l a y w i t h i n t h e NQS p u l s e . I | | C. EXPERIMENTAL RESULTS AND DISCUSSION i ) STEPWISE EXCITATION ^ 5 ch o p p er Q -s w itc h e d COg l a s e r n o n -Q -sw itc h ed CO2 l a s e r Ge jAu d e t e c t o r m onochrom ator v o lta g e s i g n a l to o s c i ll o s c o p e t r i g g e r Ge«Au — ] d e t e c t o r ! v o lta g e s i g n a l to o s c i ll o s c o p e sam ple CaF2 »H- on a c o ld f i n g e r o f dewar F i g . 13. The a rra n g e m e n t f o r th e s te p w is e e x c i t a t i o n e x p e rim e n t. | ~ ........ ^7 j | The e x p e rim e n t was done a t l i q u i d n i t r o g e n and a t J I l i q u i d h eliu m t e m p e r a tu r e s . When th e n 2 5 ! l e v e l was pumped |by th e QS l i n e R(4) (9 6 ^ .7 7 cm- *) o r by R(6) (966,25 cm- * ) , I jth e in d u c e d a b s o r p t io n o f NQS p u ls e s was s t u d i e d f o r each |l i n e o f th e (1 0 °0 -0 0 °1 ) ban d . F o r th e s e v a r i o u s NQS I f r e q u e n c i e s , th e chan ges o f t r a n s m i t t e d i n t e n s i t y c a u se d by a p u ls e from QS a r e d e p ic te d i n F i g . l ^ . T here i s a "slo w ” |com ponent o f a b s o r p t io n ( p e r s i s t s a few p s e c ) f o r f r e q u e n c i e s i n th e w ing o f th e fu n d a m e n ta l, a sy m m etric to th e low - fre q u e n c y s i d e . W e t e n t a t i v e l y a t t r i b u t e t h i s to a sim p le ] i n c r e a s e o f l in e w i d t h w ith r i s i n g te m p e r a tu r e , so t h a t a NQS fre q u e n c y i n th e w ing e n c o u n te r s a d d i t i o n a l a b s o r p t io n . T h is th e r m a lly - in d u c e d i n c r e a s e o f a b s o r p t i o n c o rre s p o n d s to a te m p e r a tu re r i s e to a t m ost 120°K. More p ro m in e n t and I imore i n t e r e s t i n g i s th e s te p w is e a b s o r p t i o n , n = l t o n=2j | t h i s i s a " f a s t ” e f f e c t , f a i t h f u l to th e te m p o ra l shape o f th e QS p u ls e . A t l i q u i d n i t r o g e n te m p e r a tu r e , th e NQS beam ;was a b so rb e d on l i n e s P (3 6 )(9 2 9 ,0 2 c m " 1 ) - P (^ O )(9 2 ^ .9 7 cm ” i ) , jP (6 ) (9 5 6 .1 9 cm"1 ) - P ( 10) (9 5 2 .8 8 cm"1 ) , and R(20) (975*93 cm- 1 )-R (2 6 ) (9 7 9 .7 1 cm"1 ) . These t h r e e g ro u p s b e lo n g to th e lin e s h a p e s f o r th e l e v e l s P p r e s - ! j p e c t i v e l y . A t l i q u i d h e liu m te m p e r a tu r e , th e l in e w i d t h s 1 a r e n a rro w e r. The NQS beam was a b so rb e d o n ly f o r l i n e s !P (36 ) — P ( 3 8 ), P ( 8 ) - P ( 1 0 ), and R (2 2 )-R (2 4 ). j j Each o f th e t h r e e n=2 l e v e l s o f E l l i o t t e t a l . (1) jwas in d e e d o b se rv e d i n s te p w is e a b s o r p t i o n , a t th e e n e rg y Q _ or- o co G O < A y \ A/ 20°K QS R(6) A J L > . '■ x v 20°K QS R(4) - a ; _________ A / 80°K QS R(6) 60 50 38 J VALUE |o 4 22 50 | I I I I i I I I I I I I I I I I I II I I I I I I I I I I ^ I I I I I Ml I 1111 |l IIIII111{ lIlIM | 900 920 940 cm-i 960 980 1000 I ---------------- P BRANCH---------—J 1 --------- R BRANCH— 1 F ig , 1^. Above* o s c i ll o s c o p e t r a c e s show ing ''f a s t " and "slow " e f f e c t s . Below* p l o t s v s , NQS fre q u e n c y . F u l l c u rv e s show th e f a s t e f f e c t } d ashed c u rv e s show th e slow e f f e c t . •£ - 0 3 2*9 d e te rm in e d i n th e p r i o r w ork. T h a t i s , th e f r e q u e n c i e s 'a d d , cu01 + t ^ i 2 =<**0 2 # i n e a c h c a s e . T h is i s p e rh a p s l e s s ;t r i v i a l th a n i t seem s. T here m ig h t o c c u r r e l a x a t i o n o f th e j v i c i n a l l a t t i c e io n s a f t e r e x c i t a t i o n o f th e H“ to n = l, w ith a c o n s e q u e n t change o f <^12 f o r 'tlie n e w ly -d e fin e d j " v e r t i c a l " t r a n s i t i o n s . The p o i n t i s t h a t we have a v e ry I good c a se o f a l o c a l e x c i t a t i o n w eakly c o u p le d to l a t t i c e j jphonons. From R e f, 1 we have q u i t e d i s t i n c t "no-phonon" l i n e s ( d o m in a n t), "o n e-p h o n o n " l i n e s (w e a k ), and " m u lt i - phonon" l i n e s ( n o t o b s e r v e d ) . Our n = l t o n=2 l i n e s , a s w e ll a s th e fu n d a m e n ta l, a r e n o -p h o n o n l i n e s , c h a r a c t e r i s t i c o f a sy ste m in c a p a b le o f r e l a x a t i o n . j I i i ) ON POLARIZATION | Our n a iv e e x p e c t a t i o n was t h a t , w ith o u r B rew ster-w in d o w l a s e r s , we c o u ld c o n firm p o l a r i z a t i o n s e l e c t i o n r u l e s i n s te p w is e e x c i t a t i o n . S uppose t h a t we d r i v e ft#Q£ w ith Ex r a d i a t i o n from QS, th e n w ith d i f f e r e n t p o l a r i z a t i o n s o f NQS s tu d y th e n=2 1^ l e v e l f o r s te p w is e !e x c i t a t i o n . T h is n=2 mode i s l a r g e l y l i k e x y j one s h o u ld ! i |f i n d a n u l l e f f e c t i f Ex i s u s e d a g a in f o r NQS. B r i e f l y , Ex *Ey— * r 5 only* EX*EX— * r i f | one f i n d s e a c h l i n e i n e a c h p o l a r i z a t i o n I T here seems t o ibe f a s t " s c ra m b lin g " b e tw een th e t h r e e com ponents o f th e jn=l l e v e l b e fo r e th e se c o n d a b s o r p t i o n . W e a t t r i b u t e t h i s t o phonons s c a t t e r e d from th e 1-3 o n ly . E x p e r im e n ta lly d e f e c t w ith o u t a change from th e n = l l e v e l ( b u t th e p o l a r i z a t i o n may be c h a n g e d ). T h is i s c o n ta in e d among th e p r o c e s s e s to w hich Hayes a t t r i b u t e s l o s s o f p h a se c o h eren c e i le a d i n g to a te m p e ra tu re - d e p e n d e n t e x c e s s w id th beyond th e i r e s i d u a l w id th (T -0 ) d e te rm in e d by decay ( T ^ ). As s t a t e d by E l l i o t t * e t a l . ( 1 ) , th e te m p e r a tu re - d e p e n d e n t e x c e s s i 8 -1 l in e w i d t h can be e x p re s s e d a s A 0 ^ = 3 .2 X 10 T ' cm , A t 5 6 °K, th e te m p e r a tu re -d e p e n d e n t l in e w i d t h w i l l be ,k5 cm"'1 ', th e same a s th e r e s i d u a l l in e w i d t h (T^ - 11 p s e c ) . The r a t e f o r th e p o l a r i z a t i o n s c ra m b lin g sh o u ld be e q u a l to th e r a t e o f phase d i s r u p t i o n , to w i t h in a n u m e ric a l f a c t - j I i o r o f th e o r d e r o f u n i t y . Thus th e r e l a x a t i o n s c ra m b lin g j I i tim e s h o u ld be i n th e o r d e r o f a few p s e c , w hich i s in d e e d ! i v e r y f a s t com pared w ith th e d u r a t i o n o f th e QS l a s e r p u ls e , i I*-*300 n s , I I W e a tte m p te d " f r e e z e - o u t '1 o f th e r e s p o n s i b l e phonons ! i ' |w ith l i q u i d h e liu m , b u t th e s c ra m b lin g re m a in s . The t e s t -p ro b ab ly i s s p o i l e d by th e QS p u ls e h e a t in g e f f e c t . | j | L e t us assume f o r arg u m en t t h a t th e t h r e e n=l ! j d e g e n e ra c y s t a t e s sc ram b le so r a p i d l y t h a t th e y rem a in i ! ' ! e q u a l ly p o p u la te d r e g a r d l e s s o f th e QS p o l a r i z a t i o n . On j t h i s h y p o th e s is , th e r e l a t i v e r a t e s o f a b s o r p t io n on th e t h r e e n = l to n=2 t r a n s i t i o n s f o r any s p e c i f i c e l e c t r i c p o l a r i z a t i o n , s a y Ex , a r e g iv e n e s s e n t i a l l y by th e sq u a re o f th e m a tr ix e le m e n ts . I n d e t a i l , one m ust sum th e r a t e s l o v e r th e d e g e n e ra te com ponents o f t h e n=2 l e v e l . The I c a l c u l a t i o n i s s t r a i g h t f o r w a r d ( s e e F i g . 1 5 ) . D e n o tin g i t h e s e r a t e s o r i n t e n s i t i e s o f n = l to n=2 a b s o r p t i o n by W^, ! W^, W 5 ( f o r r i f r 3§ 1 ^ ) , we c a n d i s p l a y t h e r a t i o s a s | W x t 1W 5 = 1 1 2 1 3 . A m e a n in g fu l t r i a l h e re r e q u i r e s t h a t th e two l a s e r s j have a common s p o t , o r a t l e a s t t h a t th e o v e r l a p be th e same a s we t r y th e f r e q u e n c i e s f o r I \ , F j , F j . W e o b s e rv e t h a t th e i n d u c e d - a b s o r p t i o n s t r e n g t h f o r th e X s t a t e i s in d e e d a lw a y s th e s t r o n g e s t o n e , b u t th e r a t i o , 1 1 2 i 3 , i s n o t c o n s i s t e n t l y v e r i f i e d . W e a t t r i b u t e t h i s t o th e o v e r la p p ro b le m . 1 i i i ) ON LINEWIDTH ! W e ta k e th e w id th o f th e n==l s t a t e t o be g iv e n [b y th e m easurem ent o f E l l i o t t , e t a l . ( 1 ) . th e l i n e w i d t h A a ,01 o f th e fu n d a m e n ta l. S i m i l a r l y , th e w id th o f th e n=2 j j r*3 s t a t e i s ta k e n from t h e i r s e c o n d -h a rm o n ic l i n e w i d t h | A W02 d e te r m i n a ti o n . I n t h e o r y , we s h o u ld f i n d f o r th e j I s te p w is e p r o c e s s , 2= + ^ w02 ^ 0 )« The ol3Served ! 1 — 1 — 1 — 1 ! w id th s a r e r e s p e c t i v e l y a b o u t 3 cm , 1 cm , and 1 .5 cm . I T h is i s e s s e n t i a l l y s a t i s f a c t o r y . A c t u a l l y i t i s p o s s i b l e | t h a t o u r w id th A W i 2 has b een i n c r e a s e d som ewhat by h e a t i n g : due to th e QS l a s e r p u l s e . The t e s t i s th u s n o t a l t o g e t h e r i f I I c o n c l u s i v e » b u t o u r f e e l i n g i s t h a t t h i s b ro a d e n in g i s r [s m a ll and t h a t th e t e s t i s m e a n in g f u l. j ( |200>-|020> ) / / 2 , (2 |002>-|200>-|02G> )//% |011>, | 101>,| 110> | (| 200> +|020>+/0 0 2 > )//3 ! i i i i c ' I NQS » E |ioo>, loio>,|ooi> ! I I I I I Q S — ------- J . 1000> F ig . 15. W av e fu n c tio n s f o r th e S te p w ise T r a n s i t i o n s , iv ) TEST O N TW O -Q UANTUM ABSORPTION W e have made r a t h e r s e n s i t i v e t e s t s f o r e f f e c t s ' o f th e c h o ic e o f QS fre q u e n c y u se d to d r iv e th e fu n d a m e n ta l I jupon th e a p p a r e n t p o s i t i o n s o f th e s e c o n d - s te p r e s o n a n c e s . j |Any inhom ogeneous component o f th e lin e s h a p e c o u ld p ro d u ce su c h a s e f f e c t . Two NQS f r e q u e n c i e s , one on e a c h wing o f a s te p w is e r e s o n a n c e , a re com pared f o r th e i n t e n s i t y o f a b s o r p t io n — f i r s t QS on one wing o f th e fu n d a m e n ta l, and th e n on th e o t h e r . No su ch s h i f t i s d i s c e m a b l e . W ith th e fre q u e n c y o f QS w e ll-re m o v e d fromGU01, we s o u g h t NQS a b s o r p t io n a s th e sum o f th e two l a s e r f r e q u e n c i e s p a s s e d th ro u g h an "this a ls o g iv e s a n u l l r e s u l t . CHAPTER VIII l | i CONCLUSIONS j ! 1 ; 1 7 i The QS o u tp u t w ith a f o c u s e d f l u x d e n s i t y '■'-6 X 1 0 ' t 1 ? | w a tt/c m s u f f i c e s to s a t u r a t e th e fu n d a m e n ta l f o r ^ 6 0 j d e p th i n t o th e c r y s t a l a t ^ 90°K, The e x p e r im e n ta l c u rv e J i o f t r a n s m i s s i o n v s . i n c i d e n t l a s e r i n t e n s i t y i s f i t hy a I j !sim p le t h e o r y w ith a d ju s tm e n t o f a s i n g l e s a t u r a t i o n I p a ra m e te r W. T h is a llo w s c a l c u l a t i o n o f th e d e ca y tim e | Ti = 11 p s e c . T h is i n t u r n a c c o u n ts ro u g h ly f o r th e o b s e r v e d r e s i d u a l l i n e w i d t h a t low te m p e r a tu r e a s th e l i m i t e d - l i f e t i m e w id th , i n a c c o rd a n c e w ith a comment by Hayes e t a l . ( 2 5 ) . | The s te p w is e e x c i t a t i o n e x p e rim e n t was s u c c e s s f u l l y i [perform ed by th e o b s e r v a t i o n o f in d u c e d a b s o r p t i o n o f o u r j |NQS beam. E ach o f th e t h r e e n=2 l e v e l s o f E l l i o t t e t a l . ( l ) i s c o n firm e d by th e s te p w is e e x c i t a t i o n a s th e sum o f l a s e r f r e q u e n c i e s . The l o c a l mode i s w eakly c o u p le d t o th e phonori land i s w e ll d i s c r i b e d by a r i g i d - l a t t i c e m odel. The j l i n e s h a p e was v e r i f i e d t o be hom ogeneous. j F o r e a c h o f th e n=2 l e v e l s , th e in d u c e d a b s o r p t i o n ] o f th e NQS beam i s in d e p e n d e n t o f th e r e l a t i v e p o l a r i z a t i o n s ' I iof th e l a s e r s . T h is e f f e c t i s a t t r i b u t e d t o f a s t " s c ra m - j i i " i j jb lin g " among th e t h r e e d e g e n e ra te n = l 1 ^ s t a t e s p r i o r t o the; jsecond a b s o r p t i o n . T h is s c r a m b lin g i s a t t r i b u t e d t o a p a r t | 5k I o f p r o c e s s e s o f e l a s t i c phonon s c a t t e r i n g which i s |a s s o c i a t e d w ith T2 . I I i I i APPENDIX 56 [ APPENDIX i | A c c o rd in g to th e F r e s n e l - K i r c h h o f f d i f f r a c t i o n i l ! i n t e g r a l ( 3 1 ) , th e com plex a m p litu d e a t th e o b s e r v a t i o n i I |p o i n t p w i l l be U (p) = - f f ± ------------ [ > o s ( z ' , r ) - c o s ( z * ,s)]]dS 2 \ Sf sr Where th e z 1 a x i s i s a lo n g th e n o rm al o f th e g r a t i n g , and j a i l o t h e r n o t a t i o n i s d e f in e d i n r e f e r e n c e (3 1 ) o r shown in F i g . 16. I n t e g r a t i o n o v e r th e l a s e r s p o t a r e a S on th e g r a t i n g g iv e s th e a n g u la r lo c u s o f d i f f r a c t i o n r a y s o f o r d e r n a s th e i n t e r s e c t i o n o f th e c o n es ^ = s i n £ sLn<j> and = - s i n # c o s <f}+ 2 2 2 \ A * | w here r - ( x ' + y ' + z* )% A i s th e w a v e le n g th , d i s j th e g ro o v e s p a c in g , and Q i s th e a n g le b etw een th e l a s e r ; a x i s and th e z ' a x i s . The c o o r d i n a te sy ste m ( x Q , y , z ') , I w hich h a s th e l a s e r a x i s on th e x 0 z* p l a n e , i s f i x e d i n s p a c e * . The c o o r d i n a te sy ste m ( x ^ y ^ z ' ) h a s th e y* a x i s p a r a l l e l to th e g ro o v e s o f th e g r a t i n g . < /> i s th e a n g le j *The c o o r d i n a te sy ste m w h ich we r e g a r d a s " f i x e d " a c t u a l l y change i f a w a v e le n g th a d ju s tm e n t i s made* th e j p r e s e n t a n a l y s i s d e a l s o n ly w ith t h e s p in n in g m o tio n , so t h e s e a r e ta k e n a s f i x e d . z e r o th o r d e r th e i n c i d e n t l a s e r g r a t i n g g ro o v e ► y l a s e r s p o t a r e a S (f> S cu t F i g . 16. The c o o r d i n a te sy ste m s u s e d to c a l c u l a t e l o c i o f F r a u n h o f e r d i f f r a c t i o n on a p la n e p e r p e n d i c u l a r t o th e z e r o t h o r d e r d i f f r a c t i o n r a y . [betw een XqZ ' p la n e and x * z ' p la n e . Each c o o r d in a te sy ste m | [ is r ig h t- h a n d e d and h a s th e c e n t e r o f th e l a s e r a r e a on th e i g r a t i n g a s i t s o r i g i n . T ra n sfo rm in g ( x ^ y ' j Z 1) c o o r d in a te s (m oving sy ste m ) to ( x Q ,y ,z ') ( f i x e d sy ste m ) and th e n to ( x , y , z ) ( a l s o f i x e d ) , f o r w hich th e z a x i s i s p a r a l l e l to th e z e ro — o r d e r o f d i f f r a c t i o n , th e n th e two cones above a r e r e p r e s e n t e d by - c o s# s i n ^ | j + s i n # s i = s i n # s i n<j> - c o s ^ ^ c o s # cos< £^ + s i n ^ ^ - s i n # c o s = - s i n # co s4* + n X d 2 2 2 where r = ( x +y + z ) I f th e g r a t i n g r o t a t e s w ith a n g u la r v e l o c i t y C tl , th e n 4* = & t . E li m in a t in g 0 from th e e q u a tio n s , we g e t th e !lo c u s on th e p la n e p e r p e n d i c u l a r to th e z e ro — o r d e r d i f f r a c t i o n r a y , a t z = c o n s t . , to be j , x c o s g - z s i n g + s l n o ) 2+ / . ( n X ) 2 r r 2 d i [Taking # = 2 0 °, z - 1, th e f a m ily o f l o c i w ith v a r i o u s [n X /d a re shown i n F ig u r e 17. A 6328 £ He-Ne l a s e r , u s e d | [fo r l i n e u p , g iv e s a v i v i d q u a l i t a t i v e c o n f ir m a tio n o f t h i s [ p a tte r n . nA /d = ,7866 — 1.6 - .6 - . 4 - 1.6 - A - 1.2 — 6 - - 1.0 - - 1 .4 F ig . 17. The l o c i o f F r a u n h o f e r d i f f r a c t i o n on a p la n e p e r p e n d i c u l a r to th e z e r o t h o r d e r d i f f r a c t i o n r a y w ith v a r io u s n A /d , T ak in g z = l t 0 = 2 0 ° . 6 1 REFERENCES i | 1 > , R. J . E l l i o t t , W. H ayes, G. D, J o n e s , H. F . M acD onald, Co T . S e n n e t t , P r o c . R oy. S o c . 289 A. 1 (1965)* 2 . R. E . Shamu, W. M. H artm ann and E . L. Y a s a i t i s , P h y s. | R ev. 1 2 0 , 822 (1 9 6 8 ). ! 3» G. D. J o n e s , S . P e le d , S . Rosenwaks and S . Y a t s i v , j P h y s . R ev. 1 8 2 , 353 ( 1 9 6 9 ) . 1 4 , W. H ayes and H. F . M acD onald, P r o c . Roy. S o c . 297 A. 503 ( 1 9 6 7 ). 5* R. T . H a r le y , J . A. H a r r in g to n an d C. T . W alk er, B u l l . j Am. P h y s . S o c . 1 2 , 297 ( 1 9 7 0 ) . ! 6 . E . W. M o n tro ll and R. B. P o t t s , P h y s . R ev. 1 0 0 . 5^5 | ( 1 9 5 5 ) . i 7 . L . C. L e e , M a rtin G u n d ersen and W. L . F a u s t , O p tic s C o m m u n icatio n s, 1 , 291 ( 1970 ) . ! 8 . L . C. Lee and W. L . F a u s t , P h y s . R ev. L e t t e r s , 2 6 , 648 ( 1 9 7 1 ). 9 . L . C . Lee and W. L . F a u s t , O p tic s C o m m u n icatio n s, 2 , 111 ( 1 9 7 0). ! 1 0 . C. K. N. P a t e l , P h y s , R e v , L e t t e r s , 1 2 , 617 (1 9 6 * 0 . 1 1 . C. B. M oore, R . E . Wood, B. L . Hu and J . T . Y a rd le y , J . Chem. P h y s . 4 6 , 4222 ( 1967 ) . 1 2 . C. K. N. P a t e l , W. L . F a u s t and R . A. M c F a rla n e , B u l l . I Am. P h y s . S o c . £ , 500 (1 9 6 4 )1 C. K. N. P a t e l , P h y s . j R e v . 136 A. 118? (1 9 6 4 ). j 1 3 . G. M o lle r and J . D. R ig d e n , A p p l. P h y s. L e t t e r s 8 , I 69 ( 1 9 6 6 ) . ! 1 4 . C. M eyer, P . P in s o n , C. R o s s e t t i and P . B a rc h e w itz , " S t a b i l i s a t i o n en P u is s a n c e d 'u n L a s e r a Gas C a rb o - n iq u e Monode e t M o n o ch ro m atiq u e", t o be p u b l i s h e d . ! 1 5 . J . D. R ig d en and G, M o e lle r , IEEE J , o f Q, E l e c t r o n i c s V o l. QE-2, 365 (1 9 6 6 ). 1 6 . G, W, F ly n n , L , 0 . H o c k e r, A. J a v a n , M. A. K ovacs and C. K. R h o d es, IEEE J . o f Q. E l e c t r o n i c s V o l. QE-2, 378 ( 1 9 6 6 ) . 17. 18. 19. 20. 2 1 . 2 2 . 23. 24. 25. 2 6 . 27. 2 8. 29. 3 0. 31. 62 E . T. G e rry , B u l l. Am. P h y s. S o c. lj>, 563 (1970) 1 A. E. H i l l , A p p l. 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Creator Lee, Long Chi (author)

Core Title Study Of The Local Mode Of Calcium-Fluoride Doped With Negative Hydrogen Ion With Intense Carbon-Dioxide Laser Lines

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Degree Doctor of Philosophy

Degree Program physics

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

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Language English

Advisor Faust, Walter L. (committee chair), Hurrell, John P. (committee member), Marburger, John H. (committee member), Porto, Sergio P.S. (committee member), Spitzer, William G. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-544295

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Rights Lee, Long Chi

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University of Southern California Dissertations and Theses