Charles H. Townes

C H A R L ES H . T O W N E S

Pro d uction of coherent ra diation by ato ms an d molec ules

Nobel Lect ure, Dece mber 11, 1964

Fr o m th e ti m e w h e n m a n first sa w th e s u nli g ht u ntil v er y re c e ntl y, th e li g ht which he has used has co me do minantly fro m spontaneous e mission, like the rando m e mission of incandescent sources. So have most other types of electr o m a g n eti c r a di ati o n - i nfr ar e d, ultr a vi ol et, or g a m m a r a ys. T h e m a xi m u m r a di ati o n i nt e nsiti es, or s p e cifi c all y t h e p o w er r a di at e d p er u nit ar e a p er u nit s oli d a n gl e p er u nit fr e q u e n c y b a n d wi dt h, h a v e b e e n c o ntr oll e d b y Pl a n c k’s black-body la w for radiation fr o m h ot o bj e cts. T his s ets a n u p p er li mit o n r a di ati o n i nt e nsit y - a li mit w hi c h i n cr e as es wit h i n cr e asi n g t e m p er at ur e, b ut w e h a v e h a d a v ail a bl e te m p er at ur es of o nl y a fe w te ns of t h o us a n ds or p ossi bl y a f e w milli o ns of d e gr e es. R a di o w a v es h a v e b e e n diff er e nt. A n d, p er h a ps wit h o ut o ur r e ali zi n g it, e v e n m u c h of o ur thi n ki n g a b o ut ra di o w a v es h as b e e n diff er e nt, in s pit e of Max well’s de monstration before their discovery that the equations governing r a di o w a v es ar e i d e nti c al wit h t h os e f or li g ht. T h e bl a c k- b o d y l a w m a d e r a di o w a v es s o w e a k t h at e missi o n fr o m h ot o bj e cts c o ul d n ot, f or a l o n g ti m e, h a v e been even detected. Hence their discovery by Hertz and the great use of radio waves depended on the availability of quite different types of sources - oscillators and a mplifiers for which the idea of te mperature and black-body radiation even see ms rather out of place. For exa mple, if we express the radiation i nt e nsit y of a m o d er n el e ctr o ni c os cill at or i n t er ms of t e m p er at ur e, it will t y pi c all y b e in th e ra n g e 1 0 1 0 t o 1 0 3 0 degrees Kelvin. These t wo regi mes, radio electronics and optics, have no w co me much clo- s er t o g et h er i n t h e fi el d k n o w n as q u a nt u m el e ctr o ni cs, a n d h a v e le nt e a c h ot h er i nt er esti n g i nsi g hts a n d p o w erf ul t e c h ni q u es. The develop ment of radar sti mulated many i mportant applications of electronics to scientific proble ms, and what occupied me in particular during the l at e 1 9 4 0’s w as mi cr o w a v e s p e ctr os c o p y, t h e st u d y of i nt er a cti o ns b et w e e n micro waves and molecules. Fro m this research, considerable infor mation c o ul d b e o bt ai n e d a b o ut m ol e c ul ar, at o mi c, a n d n u cl e ar str u ct ur e. F or its s u c c ess, c o h er e nt mi cr o w a v e os cill at ors w er e cr u ci al in all o wi n g a p o w erf ul P R O D U C T I O N O F C O H E R E N T R A D I A T I O N 5 9 hi g h-r es ol uti o n te c h ni q u e. C o ns e q u e ntl y it w as i m p ort a nt f or s p e ctr os c o p y, as well as for so me other purposes, to extend their range of operation to wave- l e n gt hs s h ort er t h a n t h e k n o w n li mit of el e ctr o ni c os cill at ors, w hi c h w as n e ar

I milli m et er. H ar m o ni c g e n er ati o n a n d s o m e s p e ci al te c h ni q u es all o w e d i n- t er esti n g, t h o u g h r at h er sl o w, pr o gr ess. T h e b asi c pr o bl e m wit h el e ctr o ni c a m plifi ers or os cill at ors s e e m e d t o b e t h at i n e vit a bl y s o m e p art of t h e d e vi c e w hi c h re q uir e d c ar ef ul a n d c o ntr oll e d c o nstr u cti o n h a d to b e a b o ut as s m all as t h e w a v el e n gt h g e n er at e d. T his s et a li mit t o c o nstr u cti o n of o p er a bl e d e- vi c es 1 . It w as t his e x p eri m e nt al diffi c ult y w hi c h s e e m e d i n e vit a bl y t o s e p ar at e t h e te c h ni q u es w hi c h w er e a p pli c a bl e i n t h e ra di o re gi o n fr o m t h os e a p pli- cable to the shorter waves of infrared or optical radiation. W h y n ot us e th e at o mi c a n d m ol e c ul ar os cill at ors alr e a d y b uilt f or us b y n at ur e ? T his h a d b e e n o n e r e c urri n g t h e m e w hi c h w as r e p e at e dl y r ej e ct e d. T h er m o d y n a mi c ar g u m e nts tell us, in a d diti o n to th e bl a c k- b o d y la w of ra- di ati o n, t h at t h e i nt er a cti o n b et w e e n el e ctr o m a g n eti c w a v es a n d m att er at a n y t e m p er at ur e * c a n n ot pr o d u c e a m plifi c ati o n, f or r a di ati o n at t h e t e m- p er at ur e of m att er c a n n ot b e m a d e m or e i nt e ns e b y i nt er a cti o n of t h e t w o wit h o ut vi ol ati n g t h e s e c o n d l a w. B ut alr e a d y b y 1 9 1 7, Ei nst ei n h a d f ol- l o w e d t h er m o d y n a mi c ar g u m e nts f urt h er t o e x a mi n e i n s o m e d et ail t h e n a- ture of interactions bet ween electro magnetic waves and a quantu m- mechan- i c al s yst e m. A n d a r e vi e w of his c o n cl usi o ns al m ost i m m e di at el y s u g g ests a w a y i n w hi c h at o ms or m ol e c ul es c a n i n f a ct a m plif y. T h e rat e of c h a n g e of el e ctr o m a g n eti c e n er g y c o nfi n e d in a re gi o n w h er e it int er a cts wit h a gr o u p of m ol e c ul es m ust, fr o m Ei nst ei n’s w or k, h a v e th e for m

w here N a a n d N b are the nu mbers of molecules in the upper and lo wer of t wo q u a nt u m st at es, w hi c h w e ass u m e f or si m pli cit y t o b e n o n d e g e n er at e (t h at is, si n gl e). A a n d B ar e c o nst a nts, a n d th us th e first a n d se c o n d ter ms re pr es e nt spontaneous e mission and absorption, respectively. The third ter m represents e mission fro m the upper state produced by the presence of a radiation inten- sit y I, a n d is h e n c e c all e d sti m ul at e d e missi o n. At e q uili bri u m, w h e n

B’

* Stri ctl y s p e a ki n g, at a n y p ositi ve te mperature. Negative absolute te mperatures can b e d efi n e d as will b e n ot e d b el o w. 6 0 1964 C H ARLES H. T O W NES R at h er si m pl e furt h er th er m o d y n a mi c re as o ni n g s h o ws th at B’ = B a n d gi v es t h e r ati o A/ B. W hil e B olt z m a n n’s la w at a n y te mperature T, it is i m m e di at el y cl e ar fr o m E q n. 1 t h at if will al w a ys b e p ositi v e a n d th us th e ra di ati o n a m plifi e d. T his c o n diti o n is of c o urs e o n e of n o n e q uili bri u m for th e gr o u p of m ol e c ul es, a n d it h e n c e s u c c essf ull y o b vi at es t h e li mits s et b y bl a c k- b o d y r a di ati o n. T h e c o n diti o n is als o s o m eti m es d es cri b e d as p o p ul ati o n in v ersi o n, or as a n e g ati v e te m p er at ur e 2 , si n c e i n B olt z m a n n’s l a w it m a y b e o bt ai n e d b y ass u mi n g a n e g ati v e a bs ol ut e te mperature. T h er m o d y n a mi c e q uili bri u m b et w e e n t w o st at es of a gr o u p of at o ms re- q uir es n ot o nl y a B olt z m a n n rel ati o n = als o a ra n d o m n ess of p h as es of th e w a v e f u n cti o ns f or th e at o ms. I n cl assi c al ter ms, this m e a ns th at, if t h e at o mi c el e ctr o ns ar e os cill ati n g i n e a c h at o m, t h er e m ust n ot b e a c orr e- l ati o n in th eir p h as es if th e e ntir e gr o u p c a n b e d es cri b e d as in te m p er at ur e e q uili bri u m. Ei nst ei n’s r el ati o n ( E q n. 1) i n fa ct ass u m e d th at th e p h as es ar e r a n d o m. A n d, if t h e y ar e n ot, w e h a v e a n ot h er c o n diti o n w hi c h will all o w t h e at o ms t o a m plif y el e ctr o m a g n eti c w a v es, e v e n w h e n This represents a second type of loophole in the li mits set by the black-body la w and ther mo- d y n a mi c e q uili bri u m, a n d o n e w hi c h c a n als o b e us e d al o n e or i n c o nj u n cti o n wit h t h e first i n or d er t o pr o d u c e a m plifi c ati o n. Ther modyna mic argu ments can be pushed further to sho w that sti mulated e missi o n ( or a bs or pti o n) is c o h er e nt wit h th e sti m ul ati n g ra di ati o n. T h at is, the energy delivered by the molecular syste ms has the sa me field distribution a n d fr e q u e n c y as th e sti m ul ati n g ra di ati o n a n d h e n c e a c o nst a nt ( p ossi bl y z er o) p h as e diff er e n c e. T his c a n als o b e s h o w n s o m e w h at m or e e x pli citl y b y a q u a n- tu m- mechanical calculation of the transition process. Sti m ul at e d e missi o n re c ei v e d littl e att e nti o n fr o m e x p eri m e nt alists d uri n g t h e 1 9 2 0’s a n d 1 9 3 0’s w h e n at o mi c a n d m ol e c ul ar s p e ctr os c o p y w er e of c e ntr al i nt er est t o m a n y p h ysi cists. L at er, i n t h e 1 9 4 0’s, e x p eri m e nts to d e m o nstr at e sti m ul at e d e missi o n w er e at le ast dis c uss e d inf or m all y a n d w er e o n th e mi n ds of se v er al ra di o s p e ctr os c o- pists, i n cl u di n g m ys elf. B ut t h e y s e e m e d o nl y r at h er diffi c ult d e m o nstr ati o ns a n d n ot q uit e w ort h w hil e. I n t h e b e a utif ul 1 9 5 0 paper of La mb and Rether- f or d o n t h e fi n e str u ct ur e of h y dr o g e n 3 t h er e is a s p e cifi c bri ef n ot e a b o ut " n e g ati v e a bs or pti o n" wit h re v ers al of p o p ul ati o n. A n d a y e ar lat er P ur c ell and Pound 4 p u blis h e d t h eir stri ki n g d e m o nstr ati o n of p o p ul ati o n i n v ersi o n a n d sti m ul at e d e missi o n. As a m att er of f a ct, p o p ul ati o n i n v ersi o n a n d its effects on radiation had already sho wn up in a so me what less accented for m in P R O D U C T I O N O F C O H E R E N T R A D I A T I O N 6 1 the resonance experi ments of Bloch 5 a n d ot h ers. B ut all t h es e eff e cts w er e s o s mall that any a mplification was s wa mped by losses due to other co mpeting pr o c ess es, a n d th eir us e f or a m plifi c ati o n se e ms n ot to h a v e b e e n seri o usl y c o n- sidered until the work of Basov and Prokhorov 6 , Weber 7 , and of Gordon, Zeiger, and To wnes 8, 9 i n t h e e arl y 1 9 5 0’ s. M y o w n p arti c ul ar int er est c a m e a b o ut fr o m th e re ali z ati o n th at pr o b a bl y only through the use of molecular or ato mic resonances could coherent oscillators for very short waves be made, and the sudden discovery in 1 9 5 1 of a p arti c ul ar s c h e m e * w hi c h s e e m e d t o r e all y off er t h e p ossi bilit y of s u bst a nti al g e n er ati o n of s h ort w a v es b y m ol e c ul ar a m plifi c ati o n.

Basic Maser Pri nciples

The crucial require ment for generation, which was also recognized by Basov a n d Pr o k h or o v, w as t o pr o d u c e p ositi v e fe e d b a c k b y s o m e res o n a nt cir c uit a n d t o e ns ur e t h at t h e g ai n i n e n er g y aff or d e d t h e w a v e b y sti m ul at e d m ol e c u- lar transitions was greater than the circuit losses. Consider a resonant micro- w a v e ca vit y wit h c o n d u cti n g w alls, a v ol u m e V, a n d a q u alit y f a ct or Q. T h e l att er is d efi n e d b y t h e f a ct t h at p o w er l ost b e c a us e of r esist a n c e i n t h e w alls is

E 2 V v

4 Q w here is the electric field strength in the mode averaged over the volu me a n d v is t h e fr e q u e n c y. If a m ol e c ul e i n a n e x cit e d st at e is pl a c e d in a p arti c ul ar fi el d of str e n gt h E, the rate of transfer of energy to the field is

when the field’s frequency coincides with the resonance frequency v bet ween t h e t w o m ol e c ul ar st at es. H er e m is a di p ol e m atri x el e m e nt f or t h e m ol e c ul ar tr a nsiti o n a n d D n is t h e wi dt h of t h e m ol e c ul ar r es o n a n c e at h alf m a xi m u m (if

a L or e nt z li n e s h a p e is ass u m e d). H e n c e for N b m ol e c ul es in th e u p p er st at e

a n d N a in the lo wer state the po wer given the field in the cavity is 6 2 1 9 6 4 C H A R L E S H. T O W N E S If th e m ol e c ul es ar e distri b ut e d u nif or ml y thr o u g h o ut th e c a vit y, E 2 m ust b e averaged over the volu me. For the net po wer gain to be positive, then,

T his gi v es t h e t hr es h ol d c o n diti o n f or b uil d u p of os cill ati o ns i n t h e c a vit y

There is by no w an enor mous variety of ways in which the threshold condi- ti o n c a n b e m et, a n d s o m e of t h e m ar e stri ki n gl y si m pl e. B ut t h e s yst e m w hi c h first see med to give an i m mediate hope of such an oscillator involved a bea m of a m m o ni a m ol e c ul es e nt eri n g a r es o n a nt c a vit y, as s h o w n i n Fi g. 1 . T h e

Fi g. 1. T h e a m m o ni a (bea m-ty pe) maser. Molec ules diff use fro m the so urce into a fo- c uss er w h er e t h e e x cit e d m ol e c ul es ( o p e n cir cl es) ar e f o c us e d i nt o a c a vit y a n d m ol e c ul es i n t he gr o u n d state (s oli d circles) are rejecte d. A s ufficie nt n u m ber of excite d m olec ules will i niti at e a n os cill ati n g el e ctr o m a g n eti c fi el d i n t h e c a vit y, w hi c h is e mitt e d as t h e o ut- p ut micro waves. Beca use of energy given to the fiel d, so me molec ules ret urn to the gr o u n d st at e t o w ar d t h e e n d of t h eir tr a nsit t hr o u g h t h e c a vit y.

transition used was the well-kno wn inversion transition of a m monia at 2 3, 8 7 0 Mc/sec. A "focuser", involving inho mogeneous electric fields, tends to re move molecules in the ground state fro m the bea m and to focus molecules in the excited state along the axis of the bea m and into the cavity, thus ensuring P R O D U C T I O N O F C O H E R E N T R A D I A T I O N 6 3 t h at P. G or d o n pl a y e d a cr u ci al r ol e i n m a ki n g o p er a bl e t h e first s u c h s yst e m i n 1 9 5 4, aft er 2, 5 years of experi mental work 9, 1 0 , a n d H. J. Z ei g er w as a v al u a bl e c oll e a g u e i n t h e first y e ar of w or k a n d e arl y d esi g ns. W e c all e d this general type of syste m the maser, an acrony m for m icro wave a m pli c ati o n b y sti m ul at e d e missi o n of radiation. The idea has been successfully extended to such a variety of devices and frequencies that it is probably well to generalize the na me - perhaps to mean m ol e c ul ar a m plifi c ati o n b y sti m ul at e d e missi o n of ra di ati o n. B ut in th e ra di o-fr e q u e n c y ra n g e it is s o m eti m es c all e d th e ras er, a n d f or li g ht t h e t er m laser is convenient and co m monly used. Maser a mplification is the key process in the ne w field kno wn as quantu m electronics - that is, electronics in which pheno mena of a specifically quantu m- mechanical n at ur e pl a y a pr o mi n e nt r ol e. It is w ell k n o w n t h at a n a m plifi er c a n us u all y b e m a d e i nt o a n os cill at or, or vi c e v ers a, wit h r el ati v el y mi n or m o difi c ati o ns. B ut it w as o nl y aft er e x p eri- mental work on the maser was started that we realized this type of a mplifier is exceedingly noise-free. The general reason for lo w noise can be stated si m- pl y. T h e m ol e c ul es th e ms el v es ar e u n c h ar g e d s o th at th eir m oti o ns, in c o n- trast to motions of electrons through vacuu m tube a mplifiers, produce no u n w a nt e d el e ctr o m a g n eti c si g n als. H e n c e a si g n al i ntr o d u c e d i nt o t h e res o- n a nt c a vit y c o m p et es o nl y wit h w h at e v er t h er m al n ois e is i n t h e c a vit y as t h e r es ult of t h er m al r a di ati o n fr o m t h e c a vit y w alls, a n d wit h s p o nt a n e o us e missi o n fr o m th e e x cit e d m ol e c ul es. S p o nt a n e o us e missi o n c a n b e re g ar d e d f or t his p ur p os e as t h at sti m ul at e d b y a fl u ct u ati n g fi el d of e n er g y Si nce f or mi cr o w a v es i n a c a vit y at r o o m t e m p er at ur e, t h e t h er m al r a di a- ti o n i n t h e c a vit y is m u c h m or e i m p ort a nt t h a n s p o nt a n e o us e missi o n. It is t h e n o nl y t h e t h er m al ra di ati o n pr es e nt w hi c h s ets t h e li mit t o b a c k gr o u n d n ois e, si n c e it is a m plifi e d pr e cis el y as is t h e si g n al. T h e a b o v e dis c ussi o n als o s h o ws th at, if th e c a vit y is at 0° K a n d n o e xtr a n e- o us n ois e e nt ers t h e c a vit y wit h t h e i n p ut si g n al, t h e li miti n g n ois e fl u ct u ati o n is d et er mi n e d b y th e s p o nt a n e o us e missi o n, w hi c h is e q ui v al e nt to o nl y o n e q u a nt u m of e n er g y i n t h e c a vit y. It c a n b e s h o w n, i n fa ct, t h at m as ers c a n yi el d th e m ost p erf e ct a m plifi c ati o n all o w e d b y th e u n c ert ai nt y pri n ci pl e. The motion of an electro magnetic wave is analogous to that of a mechan- i c al h ar m o ni c os cill at or, t h e el e ctri c a n d m a g n eti c fi el ds c orr es p o n di n g t o position and mo mentu m of the oscillator. Hence the quantu m- mechanical uncertainty principle produces an uncertainty in the si multaneous deter mina- ti o n of t h e el e ctri c a n d m a g n eti c fi el ds i n a w a v e, or e q ui v al e ntl y i n d et er mination of the total energy and phase of the wave. Thus one can sho w that, to 6 4 1 9 6 4 C H A R L E S H . T O W N E S the extent that phase of an electro magnetic wave can be defined by a quan- t u m- m e c h a ni c al o p er at or, t h er e is a n u n c ert ai nt y rel ati o n 1 1

( 3) Here D n is the uncertainty in the nu mber of photons in the wave, and Df is t h e uncertainty in phase measured in radians. Any a mplifier which gives so me representation of the phase and energy of a n i n p ut w a v e i n its o ut p ut m ust, t h e n, n e c ess aril y i n v ol v e u n c ert ai nti es or fl u ct u ati o ns i n i nt e nsit y. C o nsi d er, f or e x a m pl e, a n i d e al m as er a m plifi er c o m- p os e d of a lar g e n u m b er of m ol e c ul es in th e u p p er st at e int er a cti n g wit h a n i niti al el e ctr o m a g n eti c w a v e, w hi c h is c o nsi d er e d th e si g n al. Aft er s o m e p e- ri o d of ti m e, t h e el e ctr o m a g n eti c w a v e will h a v e gr o w n t o s u c h m a g nit u d e that it contains a very large nu mber of quanta and hence its phase and energy can be measured by classical means. By using the expected or average gain and p h as e r el ati o n b et w e e n t h e fi n al ελεχτροµ αγνετιχ w a v e a n d t h e i niti al si g n al t h e m as er a m plifi er th us all o ws a m e as ur e m e nt of th e initi al w a v e. A calculation by well-established quantu m- mechanical techniques of the relation bet ween input and output waves sho ws that this measure ment of the input wave leaves an uncertainty just equal to the mini mu m required by the u n c ert ai nt y pri n ci pl e 1 1 . F urt h er m or e, th e pr o d u ct D E D H of u n c ert ai nti es in t h e el e ctri c a n d m a g n eti c fi el ds h as t h e mi ni m u m v al u e all o w e d w hil e at t h e is mi ni mi z e d. T h e u n c ert ai nt y i n n u m b er n of q u a nt a i n t h e i niti al w a v e is a n d i n p h as e it is s o t h at

The phase has real meaning, ho wever, only when there are as many as several q u a nt a, i n w hi c h c as e d t h e mi ni m u m all o w e d b y E q n. 3. T h e b a c k- gr o u n d n ois e, w hi c h is pr es e nt wit h n o i n p ut si g n al ( n = o), is s e e n t o b e e q ui v- al e nt t o a si n gl e q u a nt u m n = of i n p ut si g n al. A s o m e w h at l ess i d e al m as er mi g ht b e m a d e of a n d m ol e c ul es i n t h e u p p er a n d lo w er st at es, res p e cti v el y, all int er a cti n g wit h th e in p ut si g n al. I n t his c as e fl u ct u ati o ns ar e in cr e as e d b y th e rati o If t h e a m plifi er P R O D U C T I O N O F C O H E R E N T R A D I A T I O N 6 5 h as a c o nti n u o us i n p ut si g n al, a c o nti n u o us a m plifi e d o ut p ut, a n d a b a n d wi dt h f or a m plifi c ati o n D n, t h e n ois e p o w er o ut p ut ca n b e s h o w n to b e e q ui v al e nt to that produced by an input signal 1 2

The noise po wer N is custo marily described in ter ms of the noise te mperature of t h e a m plifi er, d efi n e d b y N = Thus the mini mu m noise te mpera- t ur e all o w e d b y q u a nt u m m e c h a ni cs is th at f or a m as er wit h I , w hi c h is

( 4)

This is equivalent to the mini mu m energy uncertainty indicated above of one q u a nt u m ( A n = I). I n t h e mi cr o w a v e r e gi o n, gi v e n b y E q n. 4 is a p pr o xi- m at el y 1 °, w h er e as th e b est ot h er mi cr o w a v e a m plifi ers w h e n m as er a m plifi ers w er e first b ei n g d e v el o p e d h a d n ois e fl u ct u ati o ns a b o ut 1 0 0 0 ti m es gr e at er. It is int er esti n g to c o m p ar e a n id e al m as er as a d et e ct or wit h a p erf e ct p h ot o- detector, such as a y-ray counter. The y-ray counter can detect a single pho- t o n wit h al m ost n o f als e si g n als, w h er e as a m as er m ust al w a ys h a v e a p ossi bl e false signal of about one photon. But the photodetector gives no infor mation about the phase of the signal; it only counts quanta, which is why the uncer- t ai nt y pri n ci pl e all o ws Unfortunately, there are no perfect photo- d et e ct ors in th e mi cr o w a v e or ra di o re gi o ns, s o th at th e m as er is o ur b est a v ail- able detector for these waves. T h e s a m e fr e e d o m fr o m n ois e w hi c h m a k es t h e m as er a g o o d a m plifi er h el ps m a k e it a stri ki n gl y g o o d s o ur c e of m o n o c hr o m ati c r a di ati o n si n c e, w h e n th e thr es h ol d c o n diti o n is f ulfill e d a n d th e m as er os cill at es, th e lo w n ois e i mplies a mini mu m of rando m frequency fluctuations. Consider no w a maser oscillator consisting of a group of excited molecules i n a r es o n a nt c a vit y. L et t h e m ol e c ul ar tr a nsiti o n fr e q u e n c y b e its h alf wi dt h at h alf- m a xi m u m a n d th e res o n a nt- c a vit y fr e q u e n c y b e wit h a h alf If a n d differ by much less than t h e radiation produced by the oscillation can be sho wn to occur at a frequency 1 3

( 5) 6 6 1 9 6 4 C H A R L E S H . T O W N E S w h er e t h e q u alit y f a ct ors a n d ar e a n d r es p e cti v el y. T h us if th e m ol e c ul ar res o n a n c e is m u c h s h ar p er th a n th at of th e c a vit y, as in the a m monia-bea m maser > t h e fr e q u e n c y of os cill ati o n is 1 0

If t h e c a vit y is t u n e d s o t h at is s m all, t h e n t h e fr e q u e n c y of os cill ati o n c oi n ci d es v er y cl os el y wit h th e n at ur al m ol e c ul ar fr e q u e n c y and one has an al m ost c o nst a nt fr e q u e n c y os cill at or b as e d o n a m ol e c ul ar m oti o n, a s o- c all e d at o mi c cl o c k. The frequency ν is not precisely defined or measurable because of noise fluc- t u ati o ns, w hi c h pr o d u c e ra n d o m p h as e fl u ct u ati o ns of th e w a v e. I n fa ct, th e m as er is ess e nti all y li k e a p ositi v e f e e d b a c k a m plifi er w hi c h a m plifi es w h at- ever noise source happens to be present and thereby produces a more or less st e a d y os cill ati o n. If or is high, and the a mplifier gain is very large, then the band width of the syste m beco mes exceedingly s mall. But it is never zero, n or is th e fr e q u e n c y e v er pr e cis el y d efi n e d. T h e a v er a g e d e vi ati o n in fr e q u e n c y fr o m E q n. 5 w hi c h th es e p h as e fl u ct u ati o ns pr o d u c e w h e n a v er a g e d o v er a ti m e t i s I 4

w here

P is th e p o w er g e n er at e d b y th e os cill at or, a n d is the effective energy in the s o ur c e of fl u ct u ati o ns. W h er e h v i n a c a vit y at t e m p er at ur e T a n d resonant frequency ν, the effective energy co mes fro m ther mal noise and If th e n ois e fl u ct u ati o ns c o m e fr o m s p o nt a n e o us e missi o n, as th e y d o w h e n

It is als o us ef ul t o st at e t h e s p e ctr al wi dt h of t h e r a di ati o n e mitt e d fr o m a maser oscillator, as well as the precision to which the frequency can be deter- mi n e d. T h e h alf wi dt h of t h e s p e ctr al distri b uti o n is a g ai n d et er mi n e d b y t h e s a m e n ois e fl u ct u ati o n a n d is gi v e n b y 1 0, 1 5, 1 6 P R O D U C T I O N O F C O H E R E N T R A D I A T I O N 6 7

w h er e D n, W n , a n d P ar e t h e s a m e as i n E q n. 7. T his wi dt hs is t y pi c all y s o s m all in maser oscillators that they provide by far the most monochro matic sources of r a di ati o n a v ail a bl e at t h eir fr e q u e n ci es.

Maser Clocks a nd A mplifiers

Alt h o u g h t h e a m m o ni a b e a m-t y p e m as er w as a bl e t o d e m o nstr at e t h e l o w- n ois e a m plifi c ati o n w hi c h w as pr e di ct e d 1 7, its e xtr e m el y n arr o w b a n d- wi dt h makes it and other bea m-type masers more useful as a very monochro matic source of electro magnetic waves than as an a mplifier. For the original maser, t h e p o w er o ut p ut P w as a b o ut 1 0 - 9 W att, a n d t h e res o n a n c e wi dt h D n a b o ut 2 kil o c y cl es, as d et er mi n e d b y t h e le n gt h of ti m e r e q uir e d f or t h e b e a m of m ol e c ul es to p ass thr o u g h th e c a vit y. Si n c e th e fr e q u e n c y of os cill ati o n v is 2 3, 8 7 4 m e g a c yl c es, t h e fr a cti o n al s p e ctr al wi dt h, a c c or di n g t o E q n. 8, is

δ / ν 1 0 ≈- 1 4 . I n a ti m e t = 1 0 0 s e c o n ds, E q n. 7 s h o ws t h at t h e fr e q u e n c y c a n b e s p e cifi e d t o a fr a cti o n al pr e cisi o n e/ n = 2 ·1 0 - 1 4 , and of course the precision increases for longer ti mes proportionally to As a c o nst a nt-fr e q u e n c y os cill at or or pr e cis e at o mi c cl o c k, h o w e v er, t h e a m m o ni a m as er h as a n a d diti o n al pr o bl e m w hi c h is n ot s o f u n d a m e nt al, b ut w hi c h s ets a li mit o n l o n g- t er m st a bilit y. T his c o m es fr o m l o n g-t er m drifts, p arti c ul arl y of t h e c a vit y t e m p er at ur e, w hi c h v ar y v,. T h es e v ari ati o ns c a n b e s e e n, fr o m E q n. 6, t o « p ull » n. Variations of this type have li mited the long- t er m st a bilit y’ * of a m m o ni a m as ers t o fr a cti o n al v ari ati o ns of a b o ut 1 0- 1 1 ; t his still re pr es e nts a re m ar k a bl y g o o d cl o c k. A b e a m-t y p e m as er usi n g th e h y p erfi n e str u ct ur e tr a nsiti o n in th e gr o u n d st at e of h y dr o g e n, w hi c h is at 1 4 2 0 m e g a c y cl es, h as re c e ntl y b e e n d e v el o p e d by Goldenberg, Kleppner, and Ra msey 1 9 . I n t his c as e, t h e e x cit e d at o ms b o u n c e m a n y ti m es fr o m gl ass w alls in th e c a vit y, a n d th er e b y a res o n a n c e wi dt h as s m all as I cycle per second is achieved. Present designs of the hydro- g e n m as er yi el d a n os cill at or wit h l o n g-t er m fr a cti o n al v ari ati o ns n o lar g er t h a n a b o ut 1 0 - 1 3 . This syste m see ms likely to produce our best available clock or ti m e st a n d ar d. M as ers of r e as o n a bl y wi d e utilit y as a m plifi ers c a m e i nt o vi e w wit h t h e r e ali z ati o n t h at c ert ai n s oli ds c o nt ai ni n g p ar a m a g n eti c i m p uriti es all o w e d at- t ai n m e nt of th e m as er thr es h ol d c o n diti o n 2 0 . Micro wave resonances of para- m a g n eti c at o ms i n s oli ds, or i n li q ui ds, h a d b e e n st u di e d f or s o m e ti m e, a n d m a n y of t h eir pr o p erti es w er e alr e a d y w ell k n o w n. T h e wi dt hs of t h es e re- 6 8 1 9 6 4 C H A R L E S H. T O W N E S s o n a n c es v ar y wit h m at eri als a n d wit h i m p urit y c o n c e ntr ati o n fr o m a s m all fr a cti o n of a m e g a c y cl e to m a n y h u n dr e ds of m e g a c y cl es, a n d th eir fr e q u e n- ci es d e p e n d o n a p pli e d m a g n eti c fi el d str e n gt hs, s o th at th e y ar e e asil y tu n a bl e. Thus they offer for maser a mplifiers a choice of a considerable range of band- wi dt h, a n d a c o nti n u o us ra n g e of fr e q u e n ci es. A p ar a m a g n eti c at o m of s pi n ½ has t wo energy levels which, when placed i n a m a g n eti c fi el d, ar e s e p ar at e d b y a n a m o u nt us u all y of a b o ut v = 2. 8 H M c. H er e H is the field in gauss, and fro m this it is clear that most of the micro wave frequency range can be covered by magnetic fields of nor mal magnitudes. The first para magnetic masers suggested involved i mpurity ato ms of this type i n cr yst als of sili c o n or g er m a ni u m. R el a x ati o n b et w e e n th e t w o st at es w as sl o w e n o u g h i n t h es e c as es t h at a s uffi ci e nt p o p ul ati o n i n v ersi o n c o ul d b e achieved 2 0 . Ho wever, before very long a very much more convenient sche me for using para magnetic resonances was proposed by Bloe mbergen 2 1 , t h e s o- c all e d t hr e e-l e v el s oli d-st at e m as er. T his s yst e m all o w e d c o nti n u o us i n v ersi o n of p o p ul ati o n, a n d h e n c e c o nti n u o us a m plifi c ati o n, w hi c h w as v er y a w k- w ar d to o bt ai n in th e pr e vi o us t w o-l e v el s yst e m. Para magnetic ato ms with an angular mo mentu m due to electron spin S gr e at er th a n I h a v e + 1 l e v els w hi c h ar e d e g e n er at e w h e n th e at o m is in fr e e s p a c e. B ut t h es e l e v els m a y b e s plit b y " cr yst alli n e fi el ds", or i nt er a cti o n

2 + Fi g. 2. E ner g y le vels of Cr i n r u b y wit h a p arti c ul ar cr yst alli n e ori e nt ati o n i n a m a g n eti c fiel d of 3900 oerste ds. For a t hree-level maser, 23.1 k Mc (23.1 ·1 0 3 M C ) is t he fre q ue nc y of t h e p u m pi n g fi el d a n d 9. 4 k M c is t h e fr e q u e n c y of a m plifi c ati o n or os cill ati o n. P R O D U C T I O N O F C O H E R E N T R A D I A T I O N 6 9 with neighboring ato ms if the ato ms are i mbedded in a solid, and frequently the splittings lie in the micro wave range. The energy levels of such a syste m, i n v ol vi n g a s pi n of 3/ 2 a n d f o ur l e v els, c a n b e as i n di c at e d i n Fi g. 2 when the s yst e m is in a m a g n eti c fi el d. If a s uffi ci e ntl y lar g e el e ctr o m a g n eti c w a v e of frequency v 1 3 (the transition frequency bet ween levels 1 a n d 3) is a p pli e d, t h e population of these t wo levels can be equalized or « saturated ». In this case, the r ati o of t h e p o p ul ati o n of l e v el 2 t o t h at of l e v el 1 or 3 under steady conditions

T 1 2 2 3

1 2 2 3 H er e T is t h e t e m p er at ur e of t h e cr yst al c o nt ai ni n g t h e i m p uriti es, a n d and are the ti mes for relaxation bet ween the states I a n d 2 or 2 a n d 3, res p e c- ti v el y. F or h v 1 a n d as occurs at very lo w te mperatures or at or di n ar y te m p er at ur es if t h e le v els ar e s e p ar at e d b y o pti c al fr e q u e n ci es,

T 1 2

T 2 3 W he n h v a n d h v w hi c h is m or e c o m m o nl y th e cas e for micro waves,

( 9)

T h us if

there is an inversion of population bet ween levels 2 a n d I, or if,

there is an inversion of population bet ween levels 3 and 2, si n c e th e p o p ul a- ti o ns n 3 a n d n h a v e b e e n e q u ali z e d b y t h e « p u m pi n g » r a di ati o n. E q u ati o n 9 is ess e nti all y t h e r es ult o bt ai n e d b y Bl o e m b er g e n 2 1 , who also suggested several pro mising para magnetic materials which might be used. Basov and Prok- 7 0 1 9 6 4 C H A R L E S H. T O W N E S horov had already proposed a rather si milar three-level « pu mping » sche me f or a p pli c ati o n to a m ol e c ul ar b e a m s yst e m 2 2 . The first successful para magnetic maser of this general type was obtained b y S c o vil et al. 2 3 , usi n g a rar e- e art h i o n i n a w at er-s ol u bl e cr yst al. B ut, b e- f or e l o n g, ot h er m or e s uit a bl e cr yst als s u c h as r u b y 2 4 (chro miu m ions in

Al 2 O 3 ) beca me more or less standard and have provided a mplifiers of re- m ar k a bl e s e nsiti vit y f or r a di o astr o n o m y, f or s at ellit e c o m m u ni c ati o n, a n d for co m munication with space probes 2 5 . They have considerably i mproved the potentialities of radio astrono my, and have already led to so me ne w dis- coveries 2 6, 2 7 . T h es e s yst e ms g e n er all y r e q uir e c o oli n g wit h li q ui d h eli u m, w hi c h is a t e c h n ol o gi c al diffi c ult y t h at s o m e d a y m a y b e o b vi at e d. B ut ot h er- wise they represent rather serviceable and convenient a mplifiers. A m as er a m plifi er of mi cr o w a v es c a n rat h er e asil y b e b uilt w hi c h h as a theoretical noise te mperature as lo w as 1° or 2° K, and experi mental measure- m e nts h a v e c o nfir m e d t his fi g ur e 2 8 . H o w e v er, s u c h a lo w n ois e le v el is n ot easy to measure because al most any measure ment involves attach ment of i n p ut a n d o ut p ut cir c uits w hi c h ar e at te m p er at ur es m u c h hi g h er t h a n 1° K, a n d w hi c h r a di at e s o m e a d diti o n al n ois e i nt o t h e a m plifi er. T h e l o w est o v er all noise te mperature so far reported for an entire receiving syste m 2 9 using a maser a m plifi er is a b o ut 1 0° K. T his r e pr es e nts a b o ut 1 0 0 ti m es t h e s e nsiti vit y of mi cr o w a v e a m plifi ers b uilt b ef or e in v e nti o n of th e m as er. B ut m as ers h a v e sti m ul at e d ot h er a m plifi er w or k, a n d s o m e p ar a m etri c a m plifi ers, usi n g m or e or less classical properties of materials rather than quantu m electronics, no w h a v e se nsiti viti es wit hi n a fa ct or of a b o ut 5 of this fi g ur e.

Optical ad I nfrared Masers, or Lasers

U ntil a b o ut 1 9 5 7, the coherent generation of frequencies higher than those w hi c h c o ul d b e o bt ai n e d fr o m el e ctr o ni c os cill at ors still h a d n ot b e e n dir e ctl y attacked, although several sche mes using molecular-bea m masers for the far- infrared were exa mined fro m ti me to ti me. This lack of attention to what had been an original goal of the maser ca me about partly because the preli minary st a g es, i n cl u di n g mi cr o w a v e os cill at ors, l o w- n ois e a m plifi ers, a n d t h eir us e i n v ari o us s ci e ntifi c e x p eri m e nts, h a d pr o v e d s o i nt er esti n g t h at t h e y dis- tr a ct e d att e nti o n fr o m t h e hi g h-fr e q u e n c y p ossi biliti es. B ut j oi nt w or k wit h A. L. S c h a wl o w 3 0 , b e gi n ni n g at a b o ut t his ti m e, h el p e d o p e n t h e w a y f or f airl y r a pi d a n d i nt er esti n g d e v el o p m e nt of m as er os cill at ors P R O D U C T I O N O F C O H E R E N T R A D I A T I O N 7 1 i n th e far-i nfr ar e d, o pti c al, a n d ultr a vi ol et re gi o ns - as m u c h as 1 0 0 0 ti m es hi g h er in fr e q u e n c y th a n a n y c o h er e nt s o ur c es of ra di ati o n pr e vi o usl y a v ail- able. It is masers in these regions of the spectru m, frequently called lasers (light a m plifi c ati o n b y sti m ul at e d e missi o n of ra di ati o n), w hi c h h a v e p er h a ps pr o- vi d e d t h e m ost stri ki n g n e w s ci e ntifi c t o ols a n d r es ults. I m p ort a nt as p e cts of t his w or k w er e cl e ar d e m o nstr ati o ns t h at t h er e ar e pr a cti c al s yst e ms w hi c h c a n m e et th e thr es h ol d c o n diti o n of os cill ati o n, a n d th at p arti c ul ar res o n at or d esi g ns all o w t h e os cill ati o ns t o b e c o nfi n e d t o c ert ai n s p e cifi c a n d d esir a bl e m o d es. T h e r es o n at or a n al y z e d w as c o m p os e d si m pl y of t w o p ar all el mirrors-the well-kno wn Fabry- Perot interfero meter, but ofspecial di mensions. For light waves, the wavelength is so short that any macroscopic resonator c o nstr u ct e d m ust h a v e di m e nsi o ns t h at ar e lar g e c o m p ar e d wit h t h e w a v e- l e n gt h. I n t his c as e, t h e el e ctr o m a g n eti c fi el d m a y t o s o m e r e as o n a bl e a p- proxi mation be considered to travel in straight lines and be reflected fro m the w alls of th e res o n at or. T h e thr es h ol d c o n diti o n m a y b e writt e n

- - V t w here t is t h e d e c a y ti m e f or t h e li g ht i n a c a vit y ofr efl e cti n g w alls a n d v ol u m e V. If the light has a rando m path in the cavity, the decay ti me can be expressed g e n er all y i n t er ms of t h e r efl e cti o n c o effi ci e nt r of t h e w alls, t h e v ol u m e V, t h e w all ar e a A, a n d t h e v el o cit y of li g ht c,

3 0 H e n c e E q n. I O beco mes

v V It c a n b e s e e n t h at t his criti c al c o n diti o n is al m ost i n d e p e n d e nt of fr e q u e n c y if th e fr a cti o n al li n e wi dt h d o es n ot c h a n g e wit h fr e q u e n c y (as, f or e x- a m pl e, in th e D o p pl er eff e ct). T h e refl e cti o n c o effi ci e nt a n d di p ol e m o m e nt m atri x el e m e nt m are not particularly dependent on frequency over the range i n q u esti o n. H e n c e, if th e criti c al c o n diti o n c a n b e m et for o n e fr e q u e n c y, it can probably be met over the entire range fro m the far-infrared to the ultra- vi ol et. T h er e is a pr o bl e m wit h a res o n at or w hi c h is lar g e c o m p ar e d to a w a v e- l e n gt h i n t h at t h er e ar e m a n y m o d es. H e n c e, u nl ess t h e m o d es i n w hi c h os cill a- 7 2 1 9 6 4 C H A R L E S H . T O W N E S ti o ns o c c ur ar e s u c c essf ull y c o ntr oll e d, t h e el e ctr o m a g n eti c fi el d m a y b uil d u p si m ult a n e o usl y i n m a n y m o d es a n d at m a n y fr e q u e n ci es. T h e t ot al n u m b er of m o d es i n a c a vit y wit h fr e q u e n ci es w hi c h li e wit hi n t h e li n e wi dt h D n of t h e at o mi c m ol e c ul ar res o n a n c e is

9 3 or a b o ut 1 0 f or a c a vit y v ol u m e of I c m , a frequency in the optical region, a n d or di n ar y at o mi c li n e wi dt hs. B ut f ort u n at el y t h e p ossi bilit y of os cill ati o n c a n b e eli mi n at e d f or m ost of t h es e m o d es. T wo s mall parallel mirrors separated by a distance much larger than their di a m et er will all o w a b e a m of li g ht tr a v eli n g al o n g th e a xis joi ni n g th e m to tr a v el b a c k a n d f ort h m a n y ti m es. F or s u c h a b e a m, th e d e c a y ti m e t is L/ c (I - r), w here L is the mirror separation and r the reflectivity. Hence the thres- h ol d c o n diti o n is

h c (I

T his ass u m es t h at diffr a cti o n l oss es ar e n e gli gi bl e. A b e a m of li g ht w hi c h is n ot tr a v eli n g i n a dir e cti o n p ar all el t o t h e a xis will dis a p p e ar fr o m t h e v ol u m e b et w e e n t h e mirr ors m u c h m or e r a pi dl y. H e n c e t h e t hr es h ol d c o n diti o n f or off- a xis b e a ms will r e q uir e a p pr e ci a bl y m or e e x cit e d at o ms t h a n t h at f or a xi al b e a ms, a n d th e c o n diti o n f or os cill ati o n c a n b e m et f or th e latt er wit h o ut a b uil d- u p of e n er g y i n off- a xis li g ht w a v es. M a n y f e at ur es of t h e m o d es f or t h e el e ctr o m a g n eti c w a v e b et w e e n t w o square, plane, parallel mirrors of di mension D a n d s e p ar ati o n L c a n b e a p- proxi mately described as those in a rectangular box of these di mensions, al- t h o u g h th e b o u n d ar y c o n diti o ns o n th e e n cl os e d si d es of th e « b o x » ar e of c o urs e s o m e w h at diff er e nt. T h e r es o n a nt w a v el e n gt hs of s u c h a r e gi o n f or waves traveling back and forth in a nearly axial direction are 3 0

w here q, a n d s ar e i nt e g ers, a n d q, q. More precise exa mination of t h e m o d es re q uir es d et ail e d n u m eri c al c al c ul ati o n 3 1 . F or a pr e cis el y a xi al di- r e cti o n, r = s = o, a n d t h e m o d es ar e s e p ar at e d b y a fr e q u e n c y c/ 2 L. If t his fr e q u e n c y is s o m e w h at gr e at er th a n th e at o mi c li n e wi dt h D n, t h e n o nl y o n e a xi al m o d e c a n os cill at e at a ti m e. T h e a xi al w a v e h as a n a n g ul ar wi dt h d u e t o P R O D U C T I O N O F C O H E R E N T R A D I A T I O N 7 3 diffr a cti o n of a b o ut a n d, if t his is c o m p ar a bl e wit h t h e a n gl e D/ L, then all off- a xis m o d es ( r or s o) are appreciably more lossy than are the axial o n es, a n d th eir os cill ati o ns ar e s u p pr ess e d. If o n e of t h e mirr ors is p arti all y tr a ns p ar e nt, s o m e of t h e li g ht es c a p es fr o m t h e a xi al m o d e in a n a p pr o xi m at el y pl a n e w a v e a n d wit h a n a n g ul ar di v er- g e n c e, a p pr o xi m at el y d et er mi n e d b y diffr a cti o n. A nu mber of modified resonator designs have been popular and useful in optical masers, in particular ones based on the confocal Fabry- Perot in- t erf er o m et er. H o w e v er, t h e pl a n e- p ar all el c as e s e e ms t o off er t h e si m pl est m e a ns of s el e cti n g a n i n di vi d u al m o d e. Although a nu mber of types of ato mic syste ms and excitation see med pr o misi n g i n 1 9 5 8 as b as es f or o pti c al m as ers, o pti c al e x cit ati o n of t h e al k ali vapors lent itself to the most co mplete analysis and planning for an operable oscillator. One such syste m has been sho wn to oscillate as expected 3 2 ; b ut t h e alkali vapors are no longer of great interest, because other syste ms which were at t h e ti m e m u c h less pr e di ct a bl e h a v e t ur n e d o ut t o b e c o nsi d er a bl y m or e us ef ul. T h e first o p er ati n g l as er, a s yst e m i n v ol vi n g o pti c al e x cit ati o n of t h e c hr o- mi u m io ns in r u b y a n d yi el di n g re d li g ht, w as d e m o nstr at e d b y M ai m a n in 1960 3 3 . H e t o o k w h at s e e m e d at first a r at h er diffi c ult r o ut e of i n v erti n g t h e population bet ween the ground state and excited states of the chro miu m ion. T his t e c h ni q u e r e q uir es t h at at l e ast h alf of t h e v er y l ar g e n u m b er of at o ms i n t h e gr o u n d st at e m ust b e e x cit e d i n or d er t o h a v e t h e p ossi bilit y of a p o p ul a- ti o n i n v ersi o n. I n t h e c as e of t w o n or m all y u n p o p ul at e d at o mi c st at es, t h e total a mount of excitation required is much less. Ho wever, Mai man succeeded h a n ds o m el y i n e x citi n g m or e t h a n h alf t h e c hr o mi u m i o ns i n a r u b y wit h c hr o mi u m c o n c e ntr ati o n of a b o ut 1 /2000 b y a p pl yi n g a v er y int e ns e p uls e of li g ht fr o m a fl as h t u b e. T his t y p e of s yst e m is ill ustr at e d s c h e m ati c all y i n Fi g. 3. Success i m mediately yielded a very-high-energy maser oscillation because, t o g et p o p ul ati o n i n v ersi o n at all, a l ar g e a m o u nt of e n er g y m ust b e st or e d i n t h e e x cit e d at o mi c st at es. S urf a c es of t h e r u b y s er v e d as t h e r efl e cti n g mirr ors. C olli ns et al. 3 4 q ui c kl y d e m o nstr at e d th at th e r u b y las er s h o w e d m a n y of th e c h ar a ct eristi cs pr e di ct e d f or s u c h a n os cill at or. T h e r u b y las er is o p er at e d n or m all y o nl y i n p uls es, b e c a us e of t h e hi g h p o w er r e q uir e d t o r e a c h t hr es h ol d, a n d e mits i nt e ns e b ursts of r e d li g ht at p o w er le v els b et w e e n a b o ut 1 kil o w att a n d 1 0 0 m e g a w atts. It h as gi v e n ris e t o a w h ol e f a mil y of l as ers i n v ol vi n g i m p uriti es i n v ari o us cr yst als of gl ass es, and covering frequencies fro m the near infrared into the optical region. 7 4 1 9 6 4 C H A R L E S H . T O W N E S

FLAS H T UBE

Fi g. 3. S c h e m ati c di a gr a m of a r u b y ( o pti c all y excited solid-state) laser. When the gas fl as h t u b e is a cti v at e d, el e ctr o m a g n eti c os cill ati o ns o c c ur wit hi n t h e r u b y r o d, a n d s o m e of these light waves are e mitte d in a bea m thro ugh one partially reflecting en d of the ro d.

N ot v er y lo n g aft er th e r u b y las er w as d e v el o p e d, Ja v a n, B e n n ett a n d H erri ott 3 5 o bt ai n e d m as er os cill ati o ns fr o m n e o n at o ms e x cit e d b y c ollisi o ns of the second kind with metastable heliu m, in accordance with an idea previous- l y p ut f or w ar d b y J a v a n 3 6 . T his s yst e m, ill ustr at e d in Fi g. 4, re q uir es o nl y a g as e o us dis c h ar g e thr o u g h a tu b e c o nt ai ni n g a mi xt ur e of h eli u m a n d n e o n at l o w pr ess ur e, a n d t w o r efl e ct ors at t h e e n ds of t h e t u b e. It os cill at es at t h e

Fig.4. Sc he matic diagra m of a heli u m- neo n (gas disc harge) laser. Electrical excitatio n c a n i niti at e a st e a d y m as er os cill ati o n, r es ulti n g i n a n e mitt e d li g ht b e a m fr o m eit h er e n d of t he gas disc har ge, w here t here are reflecti n g mirrors. P R O D U C T I O N O F C O H E R E N T R A D I A T I O N 7 5 r el ati v el y l o w p o w er of a b o ut 1 milli w att, b ut a p pr o a c h es i d e al c o n diti o ns much more closely than the ruby syste m, and affords a continuous source of i nfr ar e d r a di ati o n of gr e at p urit y a n d dir e cti vit y. The technique of gaseous excitation by electrical discharge has also led to a lar g e f a mil y of las ers, pr o d u ci n g h u n dr e ds of diff er e nt fr e q u e n ci es fr o m many different gases which range fro m wavelengths as long as a fe w tenths of 1 milli m et er d o w n int o th e ultr a vi ol et. F or s o m e s yst e ms, a h e a v y dis c h ar g e p uls e in th e g as is n e e d e d. Ot h ers, p arti c ul arl y s o m e of th e infr ar e d fr e q u e n ci es i n rar e g as es, os cill at e s o re a dil y th at it se e ms pr o b a bl e th at w e h a v e h a d las ers a c ci d e nt all y all al o n g. V er y li k el y s o m e n e o n or ot h er r ar e- g as el e ctri c si g ns h a v e b e e n pr o d u ci n g m as er os cill ati o ns at infr ar e d w a v el e n gt hs, w hi c h h a v e gone unnoticed because the infrared could not escape fro m the glass neon t u b es. S o m e of t h es e os cill ati o n fr e q u e n ci es r e pr es e nt at o mi c tr a nsiti o ns w hi c h w er e pr e vi o usl y u n d et e ct e d; f or ot h ers, th e tr a nsiti o n h as n ot y et e v e n b e e n i d e ntifi e d. Another class of lasers was initiated through the discovery 3 7 t h at a p- n j u nc- tion of the se miconductor galliu m arsenide through which a current is passed c a n e mit n e ar-i nfr ar e d li g ht fr o m r e c o m bi n ati o n pr o c ess es wit h v er y hi g h effi ci e n c y. H all et al. 3 8 o bt ai n e d t h e first m as er os cill ati o ns wit h s u c h a s yst e m, wit h li g ht tr a v eli n g p ar all el to th e ju n cti o n a n d refl e ct e d b a c k a n d f ort h b e- t w e e n t h e f a c es of t h e s m all g alli u m ars e ni d e cr yst al. His r es ults w er e p ar all el e d or f oll o w e d i m m e di at el y, h o w e v er, b y si mil ar w or k i n t w o ot h er la b or at o- ri es 3 9, 4 0 . T his t y p e of l as er, ill ustr at e d i n Fi g. 5, is of t h e g e n er al si z e a n d c ost of a tr a nsist or. It c a n b e m a d e t o os cill at e si m pl y b y p ass a g e of a n el e ctri c c urr e nt, a n d i n s o m e c as es t h e r a di ati o n e mitt e d r e pr es e nts m or e t h a n 5 0 p er c e nt of t h e i n p ut el e ctri c al e n er g y - a n effi ci e n c y gr e at er th a n th at of ot h er m a n- m a d e li g ht s o ur c es. T h er e q ui c kl y d e v el o p e d a lar g e fa mil y of se mi c o n d u ct or las ers, s o m e in- v ol vi n g j u n cti o ns a n d, re c e ntl y, s o m e usi n g e x cit ati o n b y a n e xt er n al b e a m of el e ctr o ns 4 1 . They range in wavelength fro m about 1 0 mi cr o ns, in th e infr a- r e d, t o t h e c e nt er of t h e visi bl e r e gi o n. Nor mal Ra man scattering can be regarded as spontaneous e mission fro m a virt u al st at e, as i n di c at e d i n Fi g. 6. Ass o ci at e d wit h a n y s u c h s p o nt a n e o us e missi o n t h er e m ust b e, i n a c c or d a n c e wit h Ei nst ei n’s r el ati o ns, a sti m ul at e d e missi o n. J a v a n sho wed 4 2 t h e pri n ci pl es i n v ol v e d i n usi n g t his sti m ul at e d e missi o n f or a R a m a n m as er. W h at is r e q uir e d is si m pl y a lar g e e n o u g h n u m b er of m ol e c ul ar s yst e ms w hi c h ar e s uffi ci e ntl y str o n gl y e x cit e d b y r a di ati o n of frequency greater than so me Ra man-allo wed transition. 7 6 1 9 6 4 C H A R L E S H . T O W N E S

SILVE R RIBB O N

SILVE R- G OL D EVAP ORATED STRIPE ( MICR OALL OYED)

Fig. 5. Sc he matic diagra m of a galli u m arse ni de (i njectio n, or se mico n d uctor) laser. A s mall voltage a p plie d bet wee n t he silver ribbo n a n d t he molyb de n u m disc ca n pro d uce maser oscillatio ns wit h res ulti n g e missio n of co here nt i nfrare d ra diatio n.

O n e mi g ht c o nsi d er t h e p o p ul ati o n of t h e virt u al l e v el i n a R a m a n maser (s e e Fi g. 6) t o b e gr e at er t h a n t h at of t h e first e x cit e d st at e, s o t h at t h er e is n o p o p ul ati o n i n v ersi o n. O n t h e ot h er h a n d t h e i niti al st at e, w hi c h is t h e gr o u n d st at e, n e e ds to b e m or e p o p ul at e d th a n th e first e x cit e d st at e. O n e ca n q uit e properly consider the a mplification process as a para metric one with the m ol e c ul ar fr e q u e n c y as i dl er, or as d u e t o a mi xt ur e of gr o u n d a n d e x cit e d states in which there is phase coherence bet ween the various molecules. This is t h e s e c o n d t y p e of l o o p h ol e t hr o u g h t h e bl a c k- b o d y r a di ati o n l a w m e n- tioned earlier. The a m monia-bea m maser itself illustrates the case of a mplifi- c ati o n wit h o ut th e n e c essit y of p o p ul ati o n in v ersi o n. As th e a m m o ni a m ol e- cules progress through the cavity and beco me predo minantly in the ground st at e r at h er t h a n t h e e x cit e d st at e, t h e y c o nti n u e t o a m plif y b e c a us e t h eir os cil- lations are correlated in phase with each other, and have the appropriate phase wit h res p e ct t o t h e el e ctr o m a g n eti c w a v e. Ra man masers were first de monstrate d by Woodbury a n d N g 4 3 a s t h e r e- s ult of e x cit ati o n of v ari o us li q ui d m ol e c ul es wit h a v er y i nt e ns e b e a m fr o m a pulsed laser. They too have no w many versions, giving frequencies which 7 7

Fi g. 6. Re prese ntatio n of e nergy levels i n a Ra ma n maser. T his syste m rese mbles q ual- it ati v el y a t hr e e-l e v el m as er, o n e of t h e le v els b ei n g « virt u all y », or n ot c haracteristic of t h e m ol e c ul e w h e n n o fi el d is pr es e nt. diff er fr o m t h e ori gi n al dri vi n g m as er b e a m b y s o m e s m all i nt e g er ti m es a m ol e c ul ar- vi br ati o n al fr e q u e n c y. T h eir a cti o n h as b e e n c o nsi d er a bl y e xt e n d- ed by Terhune 4 4 a n d tr e at e d i n a n u m b er of t h e or eti c al p a p ers 4 2, 4 5 .

Prese nt Perfor ma nce of Lasers

Where no w do we stand in achieving the various theoretical expectations for perfor mance of masers? First, consider the general extension of the frequency range where we have coherent a mplifiers and oscillators. This has been increased by a factor of s o m e w h at m or e th a n 1 0 0 0; th er e ar e still a d diti o n al s p e ctr al re gi o ns w h er e s u c h t e c h ni q u es n e e d t o b e d e v el o p e d, b ut t h e p a c e h as b e e n q uit e r a pi d i n t h e l ast fe w y e ars. M as er os cill ati o ns in th e infr ar e d, o pti c al, a n d ultr a vi ol et regions have no w been obtained in many ways and appear easy; n e w e x cit ati o n m e c h a nis ms a n d s yst e ms ar e c o nti n u all y tur ni n g u p. T h er e ar e still t w o fr e- q u e n c y re gi o ns, h o w e v er, w h er e s u c h s o ur c es of ra di ati o n ar e rar e or n o n- e xist e nt. O n e is i n t h e s u b milli m et er r e gi o n or f ar-i nfr ar e d. T h e r e gi o n h as, i n a sense, no w been crossed and conquered by maser oscillators. But techniques in this spectral region are still rudi mentary, and the frequency coverage with 7 8 1964 C H ARLES H. T O W NES m as ers is s p ott y. Pr es u m a bl y f urt h er w or k will all o w i nt er esti n g e x pl or ati o ns i n t his r e gi o n a n d a v er y fr uitf ul, hi g h-r es ol uti o n s p e ctr os c o p y. Another region where coherent oscillators have not yet been developed is t h at of still s h ort er w a v el e n gt hs str et c hi n g i n d efi nit el y b e y o n d t h e n e ar- ultr a- vi ol et, w h er e t h e first s u c h os cill at ors ar e n o w a v ail a bl e. It c a n b e s h o w n t h at a r at h er s e v er e a n d f u n d a m e nt al li mit ati o n e xists as o n e pr o c e e ds t o s h ort er wavelengths because of the continually increasing nu mber of electro magnetic modes in a given volu me and the faster and faster dissipation of energy into the m by spontaneous e mission. C o nsi d er a c a vit y res o n at or of fi x e d v ol u m e, fi x e d- w all refl e cti vit y, a n d fixed-fractional frequency- width ∆ v/ v. Meeting the threshold condition ( Eqn. II) i n s u c h a res o n at or r e q uir es t h at t h er e is p o w er w hi c h i n cr e as es as v 4 , r a di at e d b y s p o nt a n e o us e missi o n i nt o all m o d es of t h e s yst e m 3 0 . I n t h e o pti c al r e gi o n t his dissi p at e d p o w er f or t y pi c al c o n diti o ns, w h er e as at 5 0 å n gstr ö ms, i n t h e s oft X-r a y r e gi o n, it w o ul d b e a b o ut 1 0 5 watts. The threshold condition w o ul d t h e n b e v er y diffi c ult t o m ai nt ai n. B ut, b y t h e s a m e t o k e n, if it is maintained, the coherent X-ray bea m produced would contain many kilo watts of p o w er. It s e e ms re as o n a bl e t o e x p e ct, o n t his b asis, t h at m as ers will b e developed to wavelengths so me what belo w 1 000 ångströ ms, but that maser os cill ati o ns i n t h e X-r a y r e gi o n will b e v er y m u c h m or e diffi c ult. Secondly, let us exa mine the monochro maticity which has been achieved. For the a m monia-bea m maser, the variation of micro wave oscillations was s h o w n e x p eri m e nt all y t o a gr e e wit h t h e t h e or eti c al e x pr essi o n ( E q n. 7) wit hi n the experi mental precision of about 50 percent. This was done by beating t wo independent a m monia oscillators together and exa mining their relative phase v ari ati o ns 4 6 . A si mil ar pr o c e d ur e c a n b e c arri e d o ut f or t w o o pti c al os cill at ors b y mixing their t wo light bea ms together in a photocell and detecting the beat fr e q u e n c y. H o w e v er, t h e t e c h ni c al diffi c ulti es i n o bt ai ni n g t h e or eti c al p erf or m a n c e ar e r at h er m or e d e m a n di n g t h a n i n t h e c as e of t h e a m m o ni a m as er. E q u ati o n 8 f or a t y pi c al h eli u m- n e o n l as er pr e di cts a fr e q u e n c y s pr e a d of a b o ut 1 0 - 2 cycle per second, or a fraction 3·10 - 1 7 of t h e os cill ati o n fr e q u e n c y of 3·1 0 1 4 cycles per second. Al m ost all m as ers s o f ar os cill ati n g i n t h e o pti c al or n e ar-i nfr ar e d r e gi o n r e- q uir e a s h ar p er r es o n a n c e, or hi g h er Q, of t h e c a vit y t h a n of t h e at o mi c r es- onance. Hence the frequency of oscillation is pri marily deter mined, fro m Eqn. 5 by the cavity resonance. The frequency of oscillation thus depends on the separation L bet ween mirrors, since fro m Eqn. 12 v = q c/ 2 L, w h er e q is P R O D U C T I O N O F C O H E R E N T R A D I A T I O N 7 9 so me i nteger. If, t he n, t he ra diate d freq ue ncies are to have a fractio nal ba n d- wi dt h of a b o ut 3 · 1 0 - 17 , such as would co me fro m funda mental noise accord- i n g t o E q n. 8, t h e mirr or s e p ar ati o n m ust n ot v ar y b y m or e t h a n t his fr a cti o n al a m o u nt. F or a mirr or se parati o n of I m et er, t h e m oti o n all o w e d w o ul d b e l ess t h a n 3 · 1 0 - 1 3 c e nti m et er - a d e m a n di n g r e q uir e m e nt! If t h e mirr or s e p ar ati o n is h el d c o nst a nt b y c yli n dri c al r o ds, L m ust still v ar y as a res ult of ther mal excitation of the lo west freq uency-stretching mo des of t h e r o ds. T his gi v es a n a d diti o n al fl u ct u ati o n w hi c h is us u all y l ar g er t h a n t h at fro m spontaneous e mission. It pro duces a fractional motion 4 7

w h er e T is t h e t e m p er at ur e, V t h e v ol u m e of t h e s e p ar at ors, a n d Y t h eir Young’s modulus. In or der to exa mine the monochro maticity of lasers, t wo heliu m-neon syste ms were carefully shock- mounte d in an acoustically insulate d wine cellar of a n u n o c c u pi e d a n d is ol at e d h o us e s o t h at a c o usti c vi br ati o ns w o ul d b e mi ni- mi z e d 4 7 . T heir pairs of mirrors were se parate d b y hea v y i n var ro ds a bo ut 60 c e nti m et ers l o n g. F or t his c as e, t h e li miti n g t h e or eti c al fl u ct u ati o ns s et b y ther mal motions of the ro ds corres pon de d to fractional freq uency variations of 5 .1 0 - 1 5 , or a freq uency fl uct uation of 2 cycles per secon d. Light fro m each laser was se nt i nto a p hoto detector, a n d t he beat fre q ue nc y exa mi ne d electro n- ically. U n der goo d co n ditio ns free fro m aco ustic dist urba nces or t her mal tra nsie nts i n t he i nvar s pacers, t his ex peri me nt s ho we d t hat variatio ns i n t he laser freq uencies over perio ds of a fe w secon ds were less than 20 cycles per s e c o n d, or a b o ut o n e p art i n 1 0 1 3 . T his w as t e n ti m es t h e li mit of t h er m al fl uct uations, b ut corres pon de d to detection of motions of the t wo mirrors as s m all as 5 ·1 0 - 1 2 centi meter, a di mension co m parable with n uclear dia meters. Pres u mably, with great care, one can obtain res ults still nearer to the theo- r eti c al v al u es. The narro west ato mic s pectral lines have wi dths of the or der of 10 8 c y cl es per secon d, so that the laser meas ure d was more monochro matic than earlier light so urces by a factor of abo ut 1 0 6 . Li g ht of t his t y p e c a n i nt erf er e wit h itself after traveli ng a dista nce of abo ut 10 000 kilo meters. He nce it co ul d i n pri nci ple meas ure c ha n ges i n s uc h a lar ge dista nce t o a precisi o n of o ne wa ve- le ngt h of lig ht, if t here were a ny o ptical pat h so co nsta nt. I nterfere nce work has bee n do ne i n several laboratories wit h laser lig ht over dista nces of a fe w h u n dre d meters, w hic h does not re q uire q uite s uc h s pecial eli mi natio n of aco ustic or ot her dist urba nces. 8 0 1 9 6 4 C H A R L E S H . T O W N E S

A t hir d pro pert y of laser li g ht w hic h is of i nterest is its directi vit y, or t he s pacial co here nce across t he bea m. As i n dicate d abo ve, certai n mo des of oscillatio n s ho ul d re prese nt a p proxi mately a pla ne wave of cross sectio n co m para- bl e wit h t h e mirr or di a m et er D. T he heli u m- neo n maser see ms to easily allo w a dj ust ment so that s uch a mo de of oscillation occ urs, an d its bea m has been sho wn 3 5, 4 8 to ha ve nearl y t he ex pecte d di ver ge nce d u e t o diffr a cti o n. The s pacial coherence or planarity of a laser bea m i m plies that the entire b e a m c a n b e f o c us e d b y a mi cr os c o p e t o a r e gi o n as s m all as a b o ut or t he resolving po wer of the microsco pe. Si milarly, it may be trans mitte d thro ugh a telescope in a bea m whose angular width is si mply deter mined by the angular resol ution of the telesco pe, an d hence m uch less than the ang ular divergence as the bea m e merges fro m a s mall laser. The entire energy is originally create d in the i deal laser in a single mo de; it can be trans mitte d into other si ngle mo des by o ptical syste ms wit ho ut violati ng t he well-k no w n brig ht- ness la ws of o ptics. This brings us to a fo urth i m portant pro perty, the intensity or brightness which can be achieve d by maser techniq ues. As in dicate d initially, once one h as t h e p ossi bilit y of c o h er e nt a m plifi c ati o n, t h er e is n o fir m li mit t o i nt e nsit y b e c a us e e q uili bri u m t h er m o d y n a mi cs a n d Pl a n c k’s l a w n o l o n g er ar e c o n- tr olli n g. T h e o nl y li mit is s et b y t h e a v ail a bl e e n er g y i n p ut, h e at dissi p ati o n, a n d size of t he a p parat us use d. If o nl y t h e 1 milli watt of po wer e mitte d by a heli u m-neon laser is foc use d by a goo d lens, the po wer density beco mes high beca use the cross-sectional ar e a of t h e f o c us e d s p ot w o ul d b e o nl y a b o ut T his gi ves a p o wer de nsit y of 4 .1 0 5 Watt /c m 2 . The effective te m perat ure of s uch a bea m, beca use of its m o n o c hr o m ati cit y, is als o r at h er hi g h - a b o ut 1 0 1 9 ° K for t he lig ht of 20-cycle per-second band width. The p ulse d syste ms, s uch as r uby lasers in partic ular, e mit m uch greater po wer, although they do not quite approach the li mits of coherence which t h e g as e o us s yst e ms d o. R u b y l as ers e mit a f e w t e nt hs of a j o ul e t o a f e w h u n- dre d jo ules of e ner g y i n p ulses fro m a bo ut 10 - 3 seco n d to 10 - 8 seco n d i n length. The po wer can th us be as great as 10 9 Watts or m ore. Effecti ve te m- perat ures of t he ra diatio n are of t he or der 10 2 3 ° K. T h e a ct u al li mit of p o w er d e nsit y will g e n er all y b e s et b y t h e li mit of li g ht i nt e nsit y o pti c al m at eri als c a n sta n d wit ho ut brea ka ge or io nizatio n. Po wer of 10 9 Watts foc use d to a s pot 1 0 - 2 milli meter i n dia meter pro d uces a n electric fiel d stre ngt h i n t he o ptical wave of abo ut 10 9 Volt /c m, which is in the range of fiel ds by which valence el e ctr o ns ar e h el d i n at o ms. H e n c e t his p o w er i o ni z es a n d disr u pts all m at eri al. P R O D U C T I O N O F C O H E R E N T R A D I A T I O N 8 1

T he ra diatio n press ure also beco mes lar ge, bei n g a bo ut 10 1 2 dyne/c m 2 , or 1 0 6 at m os p heres, at s uc h a f ocal p oi nt.

So me Applicatio ns of Lasers

It is cl e ar t h at li g ht i n m or e i d e al a n d i n m or e i nt e ns e f or m, w hi c h m as er t e c h- niques have pro duce d, can be expecte d to fin d application in wi de an d nu- mero us areas of tec h nolo g y a n d of scie nce si m pl y beca use we fi n d o ur prese nt tec h ni q ues of pro d uci ng a n d co ntrolli ng lig ht alrea dy so wi dely a p plie d. Most of t hese a p plicatio ns are still a hea d of us, a n d t here is not ti me to treat here e ve n t hose w hic h are alrea d y be gi n ni n g to de velo p. I s hall o nl y me ntio n t h at i n t e c h n ol o g y l as ers h a v e b e e n p ut t o w or k i n s u c h di v ers e ar e as as r a d ar, s ur g er y, w el di n g, s ur v e yi n g, a n d mi cr os c o p y. A littl e m or e s p a c e will b e devote d here to disc ussi ng t hree broa d areas of scie nce to w hic h o ptical, i n- frare d, a n d ultra violet masers are ex pecte d to co ntrib ute. Masers see m to pro vi de t he most precise tec h ni q ues for meas ure me nt of t he t wo funda mental di mensions of ti me and length. Over short periods of ti me maser oscillators clearly give t he most oscillatio ns; for lo nger ti mes t he hy- dr o ge n maser als o see ms t o pr o vi de t he m ost precise cl oc k yet a vaila ble. Li g ht fro m o ptical masers allo ws ne w precisio n i n t he meas ure me nt of dista nce, a n d alrea dy see ms capable of i mproving o ur stan dar d of length. This ne w precisio n s u g gests i nteresti n g ex peri me nts o n certai n f u n da me ntal pro perties of o ur s p a c e, as w ell as t h e a p pli c ati o n of hi g h er pr e cisi o n t o a v ari et y of p h ysi c al eff e cts. S o f ar, e x p eri m e nts h a v e b e e n d o n e t o i m pr o v e t h e pr e cisi o n wit h w hic h t he Lore ntz tra nsfor matio n ca n be ex peri me ntally verifie d 4 9, 5 0 . It a p- p e ars t h at i m pr o v e d pr e cisi o n i n m e as ur e m e nt of t h e s p e e d of li g ht c a n als o b e ex pecte d. If we look so me dista nce i n t he f ut ure, it see ms clear t hat t he tec h- niq ues of q ua nt u m electro nics will allo w direct meas ure me nt of t he freq ue ncy of li g ht, r at h er t h a n o nl y its w a v el e n gt h. T his c a n b e a c c o m plis h e d b y g e n er a- tion of har monics of a ra dio freq uency, a m plification of the ne w freq uency, a n d f urt her ge neratio n of har mo nics u ntil t he ra dio regio n is li nke d wit h o p- tical freq uencies. This sho ul d event ually allo w meas ure ment of the velocity of li g ht, c , t o w h at e v er pr e cisi o n w e d efi n e ti m e a n d l e n gt h. Or, it will all o w the eli mination of se parate stan dar ds of ti me an d of length beca use c ti m es a sta n dar d ti me will defi ne a sta n dar d le ngt h wit h more precisio n t ha n we ca n no w ac hieve. T he po wer of s pectrosco py s ho ul d be co nsi derably i ncrease d by use of 8 2 1 9 6 4 C H A R L E S H . T O W N E S masers. In particular, these very monochro matic sources can very much i m- prove spectroscopic resolution an d thus allo w more detaile d exa mination of t he str uct ure of ato ms, molec ules, or soli ds. T his a dva nce ca n be partic ularly striki ng i n t he i nfrare d a n d far-i nfrare d, w here prese nt resol utio n is far less than the wi dths of ato mic or molecular lines. Alrea dy so me high-resolution s pectrosco py has bee n do ne wit h lasers 5 1 , 5 2 a n d still m or e i nt er esti n g w or k of t his ge neral ty pe ca n be ex pecte d before lo ng. A thir d interesting fiel d for which lasers are i m portant has e merge d as a fiel d al most e ntirely beca use of t he existe nce of lasers, a n d is t he area w here scie ntific researc h has so far bee n most active. T his is w hat is us ually calle d no nli near o ptics 5 3 , 5 4 although it includes so me pheno mena which might not previo usly have bee n describe d i n t his way. We have bee n acc usto me d i n t he past to disc ussi ng t he progress of lig ht t hro ug h a passive o ptical material of more-ore-less fixe d pro perties. B ut, i n t he i nte nse laser bea ms no w available, interactions bet ween the light an d the o ptical me di u m are s ufficiently large that pro perties of the me di u m can no longer be regar de d as fixe d. The me di- u m dist orts, it m olec ules vi brate, a n d p olarizati o n of electr o ns i n its at o ms n o l o n g er r es p o n ds li n e arl y t o t h e a p pli e d fi el d. O n e m ust n o w als o c o nsi d er t h e dyna mics mediu m, and interactions bet ween their t wo motions. So me of the ne w pheno mena observe d are multiple-quanta absorption, which makes absorption depend on i nt e n sit y 5 5 , 5 6 , har mo nic ge neratio n i n o ptical materials a n d mi xi n g of li g ht fr e q u e n ci es 57-60 , excitati o n of c o here nt m olec ular vi bra- tions an d sti m ulate d Ra man effects 42-45 , a n d sti m ulate d Brillo ui n scatter- i n g 6 1 , 6 2 . O nly t he last t wo of t hese will be disc usse d, partly beca use t hey bear o n still a not her ki n d of maser, o ne w hic h ge nerates p ho no ns.

The Phonon Maser

A c o usti c w a v es f oll o w e q u ati o ns t h at ar e of t h e s a m e g e n er al f or m as t h e e q uatio ns of lig ht a n d ma nifest ma ny of t he sa me p he no me na. A n aco ustic wave can pro d uce an ato mic or molec ular excitation, or receive energy fro m it by eit her s po nta neo us or sti m ulate d e missio n. He nce, o ne may ex pect maser a cti o n f or a c o usti c w a v es if a s yst e m c a n b e f o u n d i n w hi c h m ol e c ul es ar e s ufficie ntl y co u ple d to a n aco ustic fiel d a n d a p pro priate excitatio n ca n be o b- taine d to meet the threshol d con dition. The first s uch syste ms s uggeste d in- v ol v e d i n v ersi o n of t h e s pi n st at es of i m p uriti es i n a cr yst al i n w a ys si mil ar t o those use d for soli d-state electro magnetic masers 6 3 . A syste m of t his ty pe has P R O D U C T I O N O F C O H E R E N T R A D I A T I O N 8 3 bee n s ho w n to o perate as ex pecte d 6 4 . Ho wever, a more generally applicable tec h ni q ue see ms t o be Brill o ui n scatteri n g a n d its cl ose ass ociate Ra ma n scattering, which utilize phase correlation rather than po p ulation inversion to pro- d uce a m plification. This process can also be vie we d as para metric a m plifica- ti o n. Li g ht m a y b e sc att er e d b y t h e tr ai n of cr ests a n d tr o u g hs i n a n a c o usti c w a v e m u c h as b y a gr ati n g. Si n c e t h e w a v e is m o vi n g, t h e s c att eri n g i n v ol v es a D o p pl er s hift. T h e n et r es ult, first a n al y z e d b y Brill o ui n 6 5 , is t h at t h e s c att er e d lig ht is s hifte d i n freq ue ncy fro m t he freq ue ncy of t h e ori gi n al b e a m b y a n a mount

v = ( 1 3) w h er e v a n d c are t he p hase velocities of so u n d a n d of lig ht, res pectively, i n t he m e di u m, a n d θ is t h e s c att eri n g a n gl e. T h e e n er g y l ost, h v, is gi v e n t o t h e scatteri ng aco ustic wa ve of fre q ue ncy v . If t h e li g ht is of s uffi ci e nt i nt e nsit y, it ca n t h us gi ve e nergy to t he aco ustic fiel d faster t ha n it is lost a n d f ulfill a t hres h- ol d c o n diti o n w hi c h all o ws t h e a c o usti c e n er g y t o b uil d u p st e a dil y. F or t h e v er y hi g h a c o usti c fr e q u e n ci es ( 1 0 9 t o 1 0 1 0 c / s e c) i m pli e d b y E q n. 1 3 w h e n θ is n ot v er y s m all, t h e l oss es ar e us u all y s o lar g e t h at i nt er esti n g a m plification cannot be achieve d with or dinary light. B ut, with laser bea ms of h un- dre ds of mega watts per sq uare centi meter, it is q uite feasible to pro d uce an i nte nse b uil d- u p of ac o ustic wa ves b y t his pr ocess of sti m ulate d Brill o ui n scatteri n g 6 1 , 6 2 - so i nte nse, i n fact, t hat t he aco ustic e ner g y ca n crac k glass or q uartz. T his gi ves a met ho d of pro d uci ng a n d st u dyi ng t he be ha vior of very- hi g h-fr e q u e n c y a c o usti c w a v es i n al m ost a n y m at eri al w hi c h will tr a ns mit li g ht - a p ossi bilit y w hi c h w as pr e vi o usl y n ot s o cl e arl y a v ail a bl e. Brillo ui n scatteri n g b y s po nta neo us e missio n has bee n st u die d for so me ti me. B ut the intense monochro matic light of lasers allo ws no w m uch greater pr e cisi o n i n w or k wit h t his t e c h ni q u e 5 2 a n d it too is yiel di n g i nteresti n g i nfor- matio n o n t he pro pagatio n of hy perso nic wa ves i n materials. T h er e is n o fir m li mit t o t h e a c o usti c fr e q u e n ci es w hi c h c a n b e pr o d u c e d b y sti m ulate d e mission, even tho ugh Eqn.13 in dicates a kin d of li mit, for θ = π, of c. B ut i n t h e o pti c al br a n c h of a c o usti c w a v es t h e p h as e v el o cit y v c a n be very high. In fact, sti m ulate d Ra man scattering, or the Ra man maser men- tio ne d briefly above, re prese nts excitatio n of t he o ptical bra nc hes of aco ustic s pectra, a n d ge nerates co here nt molec ular oscillatio ns. Q ua nt u m-electro nic tec h niq ues ca n t h us allo w i nteresti ng ne w ways to ge nerate a n d ex plore most of t he aco ustic s pectr u m as well as m uc h of t he electro mag netic do mai n. 8 4 1 9 6 4 C H A R L E S H . T O W N E S Concluding Re marks

I n a fe w years t his brief re port will no lo nger be of m uc h i nterest beca use it will be o ut date d a n d s u perse de d, exce pt for so me matters of ge neral pri nci ple or of hist ori c al i nt er est. B ut, h a p pil y, it will b e r e pl a c e d b y f urt h er stri ki n g progress and i mproved results. We can look for ward to another decade of rapid develo p me nt i n t he fiel d of q ua nt u m electro nics - ne w devices a n d u ns us pecte d facets of t he fiel d, i m pro ve d ra nge a n d perfor ma nce of masers, a n d exte nsi ve a p plication to science an d to technology. It see ms abo ut ti me no w for masers an d lasers to beco me every day tools of science, an d for the ex ploratory work which has de monstrate d so many ne w possibilities to be increasingly re placed by much more finished, more syste matic, and more penetrating appli- c ati o ns. It is t his st a g e of q u a nt u m el e ctr o ni cs w hi c h s h o ul d yi el d t h e r e al be nefits ma de a vailable b y t he ne w met ho ds of deali n g wit h ra diatio n.

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