N O NLI NEAR OPTICS A N D SPECTR OSC OPY Nobel lect ure, 8 Dece mber, 1981 b y NICOLAAS BLOE MBERGE N Harvar d University, Division of A p plie d Sciences, Ca mbri dge, Massach usetts 02138, US A T he develo p me nt of masers a n d lasers has bee n revie we d i n t he 1964 Nobel lect ures by To w nes (1) a n d by Baso v (2) a n d Prok horo v (3). T hey ha ve sketche d the evol ution of the laser fro m their pre decessors, the micro wave bea m a n d s oli d state masers. Lasers are s o urces of c o here nt li g ht, c haracterize d b y a hi g h de gree of mo noc hro maticit y, hi g h directio nalit y a n d hi g h i nte nsit y or bri g ht n ess. T o ill ustr at e t his l ast pr o p ert y, c o nsi d er a s m all r u b y l as er wit h a n acti ve vol u me of o ne 1 cc. I n t he Q-s witc he d mo de it ca n e mit a bo ut l0 1 8 p hoto ns at 694 n m wa vele ngt h i n abo ut l0 - 8 sec. Beca use t he bea m is diffracti o n li mite d, it ca n rea dil y be f oc use d o nt o a n area of l0 - 6 c m 2 , a b o ut te n o ptical wavele ngt hs i n dia meter. T he res ulti ng peak fl ux de nsity is l0 1 3 watts /c m*. W hereas 0.1 Jo ule is a s mall a mo u nt of e nergy, e q ual to t hat co ns u me d b y a 100 watt li g ht b ulb, or to t he heat pro d uce d b y a h u ma n bo d y, eac h o ne-t ho usa n dt h of a seco n d, t he po wer fl ux de nsity of 10 tera watts /c m 2 i s a weso me. It ca n be gras pe d by noti ng t hat t he total po wer pro d uce d by all electric ge nerati n g stati o ns o n eart h is a b o ut o ne tera watt. ( T he affix "tera" is derive d fro m t he Greek = mo nstrosity, not fro m t he Lati n “terra”!) I n d e e d, fr o m P o y nti n g’s v e ct or it f oll o ws t h at t h e li g ht a m plit u d e at t h e f o c al s pot wo ul d reac h l0 8 v olts / c m, c o m p ar a bl e t o t h e el e ctri c fi el d i nt er n al t o t h e ato ms a n d molec ules res po nsi ble for t he bi n di n g of vale nce electro ns. T hese are literall y p ulle d o ut of t heir or bits i n m ulti p hoto n t u n neli n g processes, a n d a n y material will be c o n verte d t o a hi g hl y i o nize d de nse plas ma at t hese fl ux d e nsiti es. It is cl e ar t h at t h e f a mili ar n oti o n of a li n e ar o pti c al r es p o ns e wit h a co nsta nt i n dex of refractio n, i.e., a n i n d uce d polarizatio n pro portio nal to t he a m plit u de of t he lig ht fiel d, s ho ul d be dro p pe d alrea dy at m uc h less extre me i nte nsities. T here is a no nli nearity i n t he co nstit uti ve relatio ns hi p w hic h may b e e x p a n d e d i n t er ms of a p o w er s eri es i n t h e el e ctri c fi el d c o m p o n e nts. Pi = . S uc h no nli nearities ha ve bee n fa miliar at lo wer fre q ue ncies for o ver a ce nt ur y. For exa m ple, po wer a n d a u dio e ngi neers k ne w abo ut t he no nli near relatio ns hi p bet wee n mag netic fiel d a n d i n d uctio n, B = µ( H) H, i n tra nsfor mers a n d sole- noi ds containing iron. Wavefor m distortion res ults (4). S uch nonlinear phe- no me na at o ptical fre q ue ncies are q uite stri ki n g a n d ca n rea dil y be calc ulate d N. Bloe mbergen 1 3 by co mbi ni ng t he no nli near co nstit utive relatio n (1) wit h Max well’s eq uatio ns. I n t he first deca de of t his ce nt ur y L ore ntz (5) calc ulate d χ ( 1) wit h t he electr o n mo dele d as a har mo nic oscillator. If he ha d a d mitte d so me a n har mo nicity, he co ul d ha ve de velo pe d t he fiel d of no nli near o ptics se ve nt y years a go. It was, ho wever, not ex peri me ntally accessible at t hat ti me, a n d Lore ntz lacke d t he sti m ulatio n fro m sti m ulate d e missio n of ra diatio n. N o nli n e ar eff e cts ar e ess e nti al f or t h e o p er ati o n of l as ers. Wit h d y e l as ers it is possible to cover t he ra nge of wavele ngt hs fro m 350-950 n m co nti n uo usly, i ncl u di n g t he e ntire visible s pectr u m. A variet y of no nli near processes, i ncl u d- ing har monic generation, para metric do wn conversion an d the sti m ulate d Ra ma n effects exte n d t he ra nge for co here nt so urces t hro ug ho ut t he i nfrare d a n d i nto t he vac u u m ultra violet. T h us t he fiel d of no nli near laser s pectrosco py co ul d be de velo pe d ra pi dly d uri ng t he past t wo deca des, ai de d co nsi derably by pre vio us i n vestigatio ns of relate d p he no me na at ra diofre q ue ncies. It is, t here- fore, a p pro priate to start t his revie w by recalli ng so me no nli near p he no me na first dis c o v er e d i n t h e fi el d of m a g n eti c r es o n a n c e. N O NLI NE AR PREC URS ORS I N M A G NETIC RES O N A NCE As a gra d uate st u de nt of Professor E. M. P urcell at Har var d U ni versit y, I st u die d relaxatio n p he no me na of n uclear mag netic reso na nce i n soli ds, liq ui ds a n d g as es. A r a di ofr e q u e n c y fi el d at r es o n a n c e t e n ds t o e q u ali z e t h e p o p ul ati o n of t w o s pi n l e v els, w hil e a r el a x ati o n m e c h a nis m tri es t o m ai nt ai n a p o p ul ati o n differe nce, corres po n di ng to t he Boltz ma n n distrib utio n at t he te m perat ure of t he ot her degrees of free do m i n t he sa m ple. T he re d uctio n i n po p ulatio n differe nce is calle d sat uratio n.