High Energy Laser Optics
نویسنده
چکیده
-This paper reviews br ief ly the theoretical understanding and properties of optical resonators. Starting from the theory of stable laser resonators, unstable resonators are discussed with emphasis on understanding the i r properties tha t ensure near diffraction limited performance of higb power lasers. The growing f i e ld of adaptive optics for laser transmission i s a lso examined as an added means of improving f a r f i e ld performance of a l a se r under adverse circumstances. The improvements obtained with active optics fo r turbulence and thermal blooming a r e given. INTRODUCTION. -The rapid development of lasers has introduced the need for specialized optics to exploit the capabil i t ies of th i s new source of coherent radiation. Of part icular in teres t here a re the optics related t o high power lasers which are necessary fo r high efficiency and good f a r f i e ld performance. Oftentimes the requirement of minimum beam divergence conflicts with the 1 imitations i n troduced by the nature of high-power l a se r cavit ies and propagation phenomena. The structure of osc i l l a to r cavit ies to overcome these l imitat ions, the search for optical materials, and design of mirrors and windows able to withstand the highpower densit ies of lasers represents formidable problems. In fac t , aerodynamic windows were introduced as a method of withstanding very high laser mwer i n wavelength regions for which there were no good optical materials available. High power lasers a re s t i l l being developed a t a f a s t r a t e and in recent years the' direction of these developments has tended to introduce new opt i ca l problems. For example, t he high power chemical l a se r i s one type of laser tha t i s continually evolving and as a resul t has introduced unique geometrical problems of the cavity involving the flow f ie ld . Then too, s a t u k t i o n power densit ies a re increasing and wavelengths a re shortening, which puts additional s t r a in on exist ing technology; new technologies are developing. There is considerable in teres t in f r ee electron lasers as e f f i c i en t high power l i g h t sources. Indications are tha t e f f i c i encies greater than 30% are possible provided cert a i n r e s t r i c t ive properties can be met with the electron beam and radiation f ie ld . Among the requirements are the need fo r extremely high radia12 2 t ion power densit ies ( 1 0 ~ ~ 1 0 w/cm ) fo r electron trapping and no e l e c t r i c f i e ld reversals on the electron beam axis. Unusual diffraction ef fec ts a re also present because of the small cross section of the gain medium. Such requirements and prhpert i e s will undoubtedlyaffectfuture resonator design. This paper'will t r y to review some of the'import an t aspects of optics for high energy systems and introduce some current subject material tha t will be of use t o the symposium attendee interested in continuous high power lasers. Problems pertaining to very high pulsed power lasers such as those used in l a se r fusion will not be covered in th i s paper. Since the f i e ld has grown enormously, a l l aspects of the optics of high energy lasers cannot be covered in a single paper. This paper covers only two topic areas. F i rs t t o be covered i s the theory of &stab1 e laser resonators a s these cavit ies permit the ef f ic ient u t i l iza t ion of large mode volumes while maintaining good f a r f i e ld performance. Even so, propagation ef fec ts which become especially important fo r high power lasers can l imi t severely beam irradiance a t a distance. Fortunately, adapt i v e optics i s an approach which helps to circumvent th i s problem.and.thi3.i~ the. second topic to Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980951 C9-372 JOURNAL DE PHYSIQUE be covered. By tak ing advantage o f the coherence p roper t ies o f the laser , a c t i v e o p t i c s has been used t o improve our a b i l i t y t o d e l i v e r a h igh i r r a diance beam under adverse circumstances. RESONATORS. -The l a s e r c a v i t y i s n o t simply a microwave cav i t y . The microwave c a v i t y i s a closed metal s t r u c t u r e a t which on ly c e r t a i n wavelengths resonate. General ly speaking, the dimensions o f the c a v i t y correspond t o these wavelengths. O f course, t h i s s i z e o f c a v i t y i s n o t use fu l ( t h e exception i s waveguide types which a re no t discussed here) f o r high power iasers having wavelengths on the order o f microns. The h igh power l a s e r c a v i t y i s l a r g e compared w i t h wavelength and operates i n a s l i g h t l y d i f f e r e n t way *than ord inary microwave c a v i t i e s . The o rd inary l a s e r c a v i t y does n o t determine t h e f r e quepcy p f the l s s e r ' i o much ( t h e c a v i t y dimension does determine the macrowave frequency) as the ga in media .does. Rather, i t serves t o discr iminate. among th$many pgssibl-e. frequencies' w i t h i n the gain bandw i d t h o f th'e malecular system. ,In so doing i t w i l l pyovide opeical feedbatk to'maintai'n the g iven osc i l la t io6.permi . tk ing h i g h l y .monqchromatic deams and, r hopefu l ly , cdn t ro l t h e o p t i c a l phase )cros; the beam f r o h t .so t h a t low beam divergence and h igh focus i n t e n s i t i e s a r e .possible. Stable C a j i t i e s , -As there i s a large.body o f 1 i t e r a t u r e ava i la l i l e on',stable reson8tor.s i: it i s the purpose:af t h i s sedt ion. t o in t roducp those features o f s t a b l e resonators which a r e h e l p f u l i n understan-. ' d ing the requirements d f high 'power l a s e r s only . Re-,, sonators can be c l a s s i f i e d as s t a b l e o r ,unstable, dipending on whether a ray i s trapped between the m i r r o r & o r not . ~i~ o p t i c ana lys is [I] shows t h a t t h e s t a b f l i t ; 'condi t ion" is 0 < (1 ~ / R ~ ) ( I L/R2) , <' l', where L ,is t h e d is tance betwe.en, the m i r r o r s and R1; R2 & f e r t o t h e rad ius o f curveture o f t h e m i r r o r s 1 and 2. If t h e value o f t h e product l i e s outs ide these numbers, the c a v i t y i s unstable. Because o f the repeated appearance o f these parameters and t h e i r importance, i t i s usefu l t o d e f i n e g1 = 1 L/R, and .g2 = 1 L/R2 so t h a t the cond i t i on simply reads 0 < g1g2 < 1. Any resonator can be represented as a p o i n t on a s t a b i l i t y diagram such as shown i n Fig. 1. Examples b f each type o f c a v i t y a r e shown. The shaded r e g i o n corresponds t o s t a b l e c a v i t i e s . Stable c a v i t i e s were used f i r s t and can be used f o r low o r high, ga in media. The beam q u a l i t y o f these c a v i t i e s may be measured by the divergence o f t h e beam i n the f g r f i e l d . Fig. 1 S t a b i l i t y Diagram By a p p l i c a t i o n o f the d i f f r a c t i o n i i n t e g r a l , i t i s known t h a t f a r f i e 1 d patte,rns, o f l a s e r beams are merely Four ier transforms d f t h i i r near f i e l d s [2]. General ly speaking, a .uniform f i e l d and pha:e outpu t o f a l a s e r produces the smallest, divergence,and '. , . maximum i n t e n s i t y i n t h e cen t ra l lobe. i n t$e fa? ' f ie.1 d [3] : For a c i r c u l a r . aper ture the we1 1knowh ,. A i r y p a t t e r n w i t h the angular w id th o f 2.44 x/d i s a ' r e s u l t [2]. If, however, there are ampl i tude,aid phase v a r i a t i o n s i n t h e near fiel'd, then the d ive r gence i s l a r g e r and the cen t ra l i n t e n s i t y i s reduced. Of, these, the phase d i s t r i b u t i o n i s the l a r . ger e f f e c t and i t i s t h i s f a c t o r t H a t must be made as uni form as poss ib le i n resonator , design. F:ig.2 shows schemat ica l ly the e f f e c t s o f ampli tude and phase v a r i a t i o n s across the beam. The s o l u t i o n o f t h e wave equation w i l l g i v e f i e l d ampli tude and phase t h a t i s necessar i td ~pre; d i c t o p t i c a l beam q u a l i t y . , For i n f i n i t e . s i z e m i r r o r s w i t h a un i fo rm ly passive inedium, matching ' the so lu t ions o f t h e wave equation f o r near ly ' plane waves gives a n a l y t i c r e s u l t s t h a t p r e d i c t t h e t ran sverse modes and frequency o f the l a s e r [I]. These r e s u l t s a re i n the form o f Hermite dr ~ ' a ~ u e r r e polynomials and can be found i n most t e x t s ah l a sers [4]. The c o r r e c t s o l u t i o n which 'may correspond t o a l i n e a r s u p e r p o ~ i t i o n o f many o f ,th.e ,polynomials i s determined by the boli$ary condi t ions. The important t h i n g t o n o t i c e i s , that the re i s a .sequence o f so lut ions, each more compli,cated than i t s predecessor. The fundamental mode' is.. a simple NEARFIELD FAR-FIELD I NEAR-FIELD NEARFIELD FAR FIELD INTENSITY PHASE INTENSITY L Fig. 2 E f f e c t o f Near F i e l d I n t e n s i t y and Phase D i s t r i b u t i o n on Far-F ie ld Pat tern guassian beam and t h i s mode i s r e a l l y what one aims f o r i n designing a s tab le l a s e r c a v i t y as i t produces the bes t qua1 i t y beam. These a r e the essen t ia l features o f s tab le cav i t i es , but, o f course, t o be usefu l some l i g h t must be ex t rac ted and one must consider t h e e f f e c t s o f f i n i t e m i r r o r size. M i r ro rs o f f i n i t e s i z e lead t o cated [I]. E s s e n t i a l l y one ca lcu la tes the f i e l d by analyz ing the steady s t a t e f i e l d d i s t r i b u t i o n t h a t can be sustained w i t h i n an empty resonator. This amounts t o c a l c u l a t i n g the f i e l d d i s t r i b u t i o n a t t h e second m i r r o r (2) from an assumed d i s t r i b u t i o n a t the f i r s t m i r r o r (1). The r e s u l t i n g d i s t r i b u t i o n can be obta ined v i a a n i n t e g r a l using the sca la r fo rmu la t ion o f Huygens' p r i n c i p l e [2,5]. Th is must be repeated, fo r t h e reverse case, i .e., from ( 2 ) t o (1) and u l t i m a t e l y a r r i v e a t t h e i n i t i a l d i s t r i b u t i o n . A f i e l d d i s t r i b u t i o n t h a t obeys t h i s condit i o n can be w r i t t e n as the i n t e g r a l equation where 9 i s the f i e l d d i s t r i b u t i o n , 6 i s the propaga t ion i n t e g r a l operator [2,31, and y i s t h e complex eigenvalue f o r the given mode. More e x p l i c i t l y , = (1-p)ei$, where $ = phase s h i f t and 6 = round t r i p power loss . Therefore 8 i s the output coupl i n g f r a c t i o n and g i s used t o determine t h e exact frequency o f t h e laser . Ear ly so lu t ions o f these o s c i l l a t o r s was g iven by Fox and L i where they showed t h a t c e r t a i n type resonators and low order modes have very low d i f f r a c t i v e losses [5]. Higher order modes have h igher losses and t h i s can be 'used as a means o f sel.ecting low o rder modes. A usefu l parameter i n descr ib ing t h e d i f f r a c t i o n e f f e c t s o f 2 t h i s problem i s t h e Fresnel number, N = a /hL,where a r e f e r s to: t h e rad ius of t h e m i r ro rs . F igure 3 ' shows how the losses vary w i t h N f o r the lowest o r der modes f o r a c a v i t y w i t h c i r c u l a r m i r r o r s having d i f f r a c t i o n losses and t h i s problem i s more compli-
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