Square shaped flat-top beam in refractive beam shapers

Transcription

1 Squar shapd flat-tp bam in rfractiv bam shaprs Alxandr Laskin a, Vadim Laskin a, Alksi Ostrun b a AdlOptica GmbH, Rudwr Chauss 29, Brlin, Grmany b St. Ptrsburg Natinal Rsarch Univrsity f Infrmatin Tchnlgis, Mchanics and Optics, Krnvrkskiy pr, 49, , St.Ptrsburg, Russia, ABSTRACT Lsslss transfrmatin f rund Gaussian t squar shapd flat-tp cllimatd bam is imprtant in building highpwr slid stat lasr systms t imprv ptical pumping r amplificatin. Thr ar industrial micrmachining applicatins lik scribing, display rpair, which prfrmanc is imprvd whn a squar shapd spt with unifrm intnsity is cratd. Prvd bam shaping slutins t ths tchniqus ar rfractiv fild mapping bam shaprs having sm imprtant faturs: flatnss f utput phas frnt, small utput divrgnc, high transmittanc, xtndd dpth f fild, pratin with TEM 00 and multimd lasrs. Usual apprach t dsign rfractiv bam shaprs implis that input and utput bams hav rund crss-sctin, thrfr th nly way t crat a squar shapd utput bam is using a squar mask, which lads t ssntial lsss. Whn an input lasr bam is linarly plarizd it is suggstd t gnrat squar shapd flat-tp utput by applying bam shapr lnss frm birfringnt matrials r by using additinal birfringnt cmpnnts. Du t birfringnc thr is intrducd phas rtardatin in bam parts and is ralizd a squar shapd intrfrnc pattrn at th bam shapr utput. Ralizatin f this apprach rquirs small phas rtardatin, thrfr wak birfringnc ffct is nugh and birfringnt ptical cmpnnts, prating in cnvrgnt r divrgnt bams, can b mad frm rfractiv matrials, which crystal ptical axis is paralll t ptical axis f ntir bam shapr ptical systm. Thr will b cnsidrd dsign faturs f bam shaprs crating squar shapd flat-tp bams. Exampls f ral implmntatins and xprimntal rsults will b prsntd as wll. Kywrds: bam shaping, flat-tp, tp hat, micrmachining, amplificatin, MOPA lasr, ptical pumping, ultra-shrt puls lasr. 1. INTRODUCTION Almst lsslss intnsity transfrmatin frm Gaussian t flat-tp distributin with saving th flatnss f a bam phas frnt is a wll-knwn fatur f rfractiv fild mapping bam shaprs 1-5 usd in varius industrial and scintific applicatins. Opratin principl f ths dvics prsums applying smth ptical surfacs, zr abrratin f a wav frnt, and mst ftn amrphus rfractiv matrials lik fusd silica, ptical glasss ar applid. Thrfr, typically th bams at th rfractiv bam shapr input and utput hav circular symmtry, th mthd f bam shaping dsn t dpnds n plarizatin f input bam and has n influnc n plarizatin prprtis f a bam. Thr ar sm intrsting ptical ffcts whn lnss f a bam shapr ar mad frm birfringnt matrials, fr xampl ptical crystals lik quartz r sapphir, and an input lasr bam is plarizd, fr xampl linarly plarizd that is typical fr mdrn ultra-shrt puls lasrs. By chsing lns thicknss it is pssibl cntrl th phas rtardatin btwn th wavs f diffrnt plarizatin and achiv intrfrnc ffcts whil bam prpagatin in lnss. This apprach givs n mr mans t cntrl intnsity distributin f utput bam and maks it pssibl t prvid lsslss transfrmatin f a rund Gaussian input bam t a squar shapd utput flat-tp bam. This articl dscribs basic principls and imprtant faturs f rfractiv bam shaprs, thrtical dscriptin f apprach t crat squar shapd flat-tp bams and xprimntal xampls.

2 2.1 Dsign basics f bam shaprs Th dsign principls f rfractiv bam shaprs f fild mapping typ, lik Shapr, ar wll-knwn and dscribd in th litratur 1-5. Mst ftn ths dvics ar implmntd as tlscpic systms with tw ptical cmpnnts, it is implid that wav frnts at input and utput ar flat, th transfrmatin f irradianc prfil frm Gaussian t unifrm is ralizd in a cntrlld mannr, by accurat intrducing f wav abrratin by th first cmpnnt and furthr its cmpnsatin by th scnd n, Fig.1, tp. Thus, th rsulting cllimatd utput bam has unifrm irradianc and flat wav frnt; it is charactrizd by lw divrgnc almst th sam lik n f th input bam. In thr wrds, th fild mapprs transfrm th irradianc distributin withut dtriratin f th bam cnsistncy and withut incrasing f bam divrgnc. Shrtly th main faturs f rfractiv fild mapprs ar: - rfractiv ptical systms transfrming Gaussian t flat-tp (unifrm) irradianc distributin; - transfrmatin thrugh cntrlld phas frnt manipulatin 1 st cmpnnt intrducs sphrical abrratin rquird t r-distribut th nrgy, thn 2 nd cmpnnt cmpnsats th abrratin; - utput bam is fr f abrratins, phas prfil is maintaind flat, hnc, lw utput divrgnc; - TEM 00 and multimd bams applid; - cllimatd utput bam; - rsulting bam prfil is stabl vr larg distanc; - implmntatins as tlscpic r cllimating ptical systms; 2. THEORETICAL CONSIDERATIONS Figur 1 Rfractiv fild mapping bam shapr Shapr Figur 2. Exprimntal intnsity prfils: Lft Input TEM 00 bam, Right - aftr th Shapr - achrmatic ptical dsign, hnc th bam shaping is prvidd fr a crtain spctral rang simultanusly; - Galilan dsign, n intrnal fcusing. Exampl f bam shaping fr Nd:YAG lasr is prsntd in Fig Prpagatin f light in birfringnt matrials Faturs f prpagatin f plarizd light in birfringnt matrials is vry gd dscribd in litratur 6,7,8. Fr th purpss f furthr cnsidratins w prsnt in Fig.3 layuts f wavs prpagatin in psitiv (fr xampl quartz) and ngativ (fr xampl sapphir) whn ptical axis f an ptical cmpnnt is paralll t th crystal ptical axis. Th birfringnc in such rciprcal axs rintatin is rlativly wak; hwvr it is nugh t intrduc a ncssary rtardatin f phas frnts and, hnc, raliz intrfrnc ffcts whn input bam is plarizd, fr xampl linarly plarizd.

3 Figur 3 Prpagatin f light wavs in cas whn crystal ptical axis is paralll t ptical axis f ptical systm 8. Variabls usd: n n n= n - n n ~ rdinary rfractiv indx, xtrardinary rfractiv indx, diffrnc f rfractiv indxs, psitiv fr psitiv crystals, incidnc angl, variabl xtrardinary rfractiv indx, dpnds n incidnc angl. Extrardinary rfractiv indx by frmula 8 n ~ in cnsidrd cas varis fr diffrnt incidnc angl, this dpndnc is dscribd n~ n n (1) n sin n cs Optical matrials usd in dsigns f bam shaprs, lik quartz (SiO 2 ) r sapphir (Al 2 O 3 ), ar charactrizd by wak birfringnc, fr xampl fr Al 2 O 3 at 1064 nm n = , n = , hnc, n = Thrfr, it is pssibl t rduc cmplxity f Eq. (1) using Taylr sris xpansin; mathmatical transfrmatins giv mr cmpact xprssin 2 n ~ n nsin (2) Cmparisn f xact and apprximat valus f n ~ calculatd using Eqs. (1), (2) fr varying frm 0 t 90 shws that apprximatin rrr dsn t xcd %, - this is accptabl in practical calculatins, thus, th Eq. (2) can b usd in withut limitatins fr matrials lik Al 2 O 3 r SiO Phas rtardatin in cnvrgnt/divrgnt bam Analysis f plarizatin ffcts happning with divrgnt r cnvrgnt bams whil prpagating in ptical lmnts frm birfringnt matrials is imprtant fr prpr dsigning f a bam shaping systm. Rays f such bams hav variabl angls, and it is imprtant t valuat phas rtardatin f rdinary and xtrardinary wavs happning whil variabl incidnc angls. This tpic is discussd in litratur 6,7,8, lt s valuat ptical path diffrnc (OPD) btwn rays crrspnding t rdinary and xtrardinary wavs in frm bing cnvnint fr furthr analysis f intrfrnc ffcts. It is suggstd t cnsidr a simplifid cas f a plat frm a psitiv uniaxial crystal, fr xampl quartz, which crystal ptical axis is paralll t ptical axis f whl systm, Fig. 4.

4 Figur 4 T analysis f phas rtardatin in cnvrgnt/divrgnt bams. Frm ptical layut prsntd in Fig.4 lft, n can writ fllwing st f quatins n ~ sin ' sin n sin ' sin ~ t t cs' (3) ~ t t cs ' whr t ~ is plat thicknss, t and ~ t ~ ar path lngths insid th plat, and ~ ar aprtur angls insid th plat, indics and rlat, crrspndingly, t rdinary and xtrardinary rays. Th OPD btwn rdinary and xtrardinary phas frnts can b writtn as OPD n~ ~ t n ~ t t tg ' tg ' sin (4) Cnsidring us f wak birfringnc matrials, lik SiO 2 r Al 2 O 3, and typical incidnc angls nt xcding 20, it is pssibl t simplify Eqs. (3) and (4) using Taylr sris xpansins and nglcting high rdr trms n² and sin 4, thn th Eq. (4) can b rducd t xprssin 2 OPD 2tnsin (5) Evidntly, th OPD is ngligibl at small incidnc angls but can rach ssntial valus fr big aprtur angls, i.. thr is variabl OPD dpnding n a ray hight n an ptical cmpnnt. Bcaus f variabl phas rtardatin th bam aftr th birfringnt ptical cmpnnt is charactrizd by variabl plarizatin stat at diffrnt ray hights that dpnds als n plarizatin spcificatins f input bam.

5 3. CREATING SQUARE-SHAPED OUTPUT BEAM Lt s cnsidr prpagatin f cnvrgnt bam thrugh a plat accrding t layut in Fig.4 lft, supps th light is linarly plarizd and plarizatin plan is paralll t Y axis as shwn in Fig.4 right, and crystal ptical axis is paralll t th systm ptical axis. Basing n dscriptin 6,7,8 f light prpagatin in birfringnt matrials n can dfin faturs f diffrnt parts f th bam passd thrugh th plat: (a) th plan cntaining ptical axis and Y axis (Y plan): plarizatin plan f a bam and crystal ptical axis ar paralll and nrmals t wav frnt ar inclind at incidnc angl with rspct t th crystal ptical axis, thrfr variabl angl lads t variatin f rfractiv indx n ~ f xtrardinary wav, birfringnc ffct is mst strng in that plan; (b) th plan cntaining ptical axis and X axis (X plan): birfringnt ffct dsn t appar, sinc nrmals t wav frnt stay prpndicular with rspct t th crystal ptical axis, s rfractiv indx stays cnstant and quals n ; (c) intrmdiat plans cntaining ptical axis and dirctins btwn Y and X axs: birfringnc ffct appars, variatin f rfractiv indx f xtrardinary wav is lss strng than in cas (a). Supps th plat thicknss t is chsn in such a way that fr a particular incidnc angl in Y plan th OPD quals light wavlngth, it is wll-knwn 6,7,8 that this cnditin crrspnds t intrfrnc maximum. Thrfr, intnsity in Y plan will hav maximum, th sam will b in X plan whr OPD is zr, whil in th plan tiltd at 45 t X and Y plans thr will b bsrvd intrfrnc minimum. Fr a cnvrgnt bam th incidnc angl is variabl, it dpnds n a ray hight at th ntranc surfac f th plat, thrfr thr will b variabl OPD fr diffrnt ray hights in diffrnt plans f analysis and, hnc, variabl and rathr cmplicatd intrfrnc pattrn. As will b shwn in nxt chaptr it is pssibl t ptimiz paramtrs f ptical systm in rdr t prvid a squar shapd utput bam. Lt s cnsidr an xampl: - = 1064 nm, - a plat frm SiO 1064 nm n = , n = , hnc, n = , - cnvrgnt lasr bam, - maximum aprtur angl 10, i.. ~170 mrad. Fr th cas OPD = n can calculat using Eq.(5) th plat thicknss, in ur cas t 2 mm; vidntly, such a plat can b asily manufacturd t prvid lsslss transfrmatin f a rund cnvrgnt bam with linar plarizatin t a bam with squar shap. An imprtant fatur f this bam shaping mthd is changing f plarizatin stat f a bam, sinc th utput bam will hav rathr cmplicatd pattrn f rintatins f plarizatin axs fr ach ray. This isn t a prblm in varius tchnlgis f lasr matrial prcssing; hwvr this ffct is unwishd in applicatins lik pwr amplificatin in MOPA dsigns whr kping unchangd plarizatin is rquird. On f slutins can b ralizd in frm f tw birfringnt plats mad frm diffrnt matrials: psitiv crystal lik quartz and ngativ crystal lik sapphir. Bth birfringnt crystals hav similar abslut valus f n but diffrnt signs: fr SiO 2 and fr Al 2 O 3, hr th data ar givn fr = 1064 nm. On plat can b installd bfr an amplifir crystal, and scnd plat aftr th amplifir; sur it is ncssary t raliz pratin f bth plats in cnvrgnt r divrgnt bams using additinal lnss. Lnss f th fild mapping bam shaprs hav curvd surfacs, nvrthlss dscribd ffct f changing th bam shap du t wak birfringnc is similar t n in a plat, and in cas f lw NA ptical cmpnnts f a bam shapr it is pssibl t apply abv cnsidrd frmulas fr apprximat calculatins and valuatins.

6 4. EXPERIMENTAL RESULTS Th apprach f lsslss transfrmatin f a rund linarly plarizd cnvrgnt bam t a squar shapd bam was ralizd in a vrsin f a rfractiv fild mapping bam shapr Shapr 12_12_HP, Fig. 5. Tw lnss f th dvic wr mad frm sapphir, which crystal ptical axs cincid with ptical axis f ntir systm, th lns thicknsss ar 1.3 mm. Accrding t th bam shapr dsign maximum incidnc angl dsn t xcd 8, thrfr frmulas cnsidrd in chaptr 2 can b applid fr valuatin f OPD. Calculating using Eq.(5) f ttal OPD fr bth lnss and maximum Figur 5 Viw f Shapr 12_12_HP. incidnc angl givs valu OPD ttal 0,79µm. In cas f 1064 nm lasr this crrspnds t apprximatly 0.74 (r /1.34) fr Y plan accrding t Fig. 4. Sinc maximum OPD ttal in Y plan is lss than = 1064 nm intnsity variatin btwn X plan and Y plan is nt strng, nvrthlss it is pssibl t bsrv similar t squar shap f th bam aftr th Shapr, - masurd input and utput prfils ar prsntd in Fig. 6, hr input bam is linarly plarizd, vrtical plarizatin dirctin. Th lnss mad frm sapphir hav psitiv ptical pwr, thrfr thir thicknss is gtting smallr at priphry whr, in cntrary, th incidnc angl is incrasd, hnc, thr xists crtain cmpnsatin f birfringnc ffct that lads t smthr variatin f OPD and, what is imprtant in applicatins lik MOPA lasrs, smth spt dgs. Implmnting th bam shapr frm birfringnt lnss maks it pssibl t cmbin tw functins: intnsity rdistributin frm Gaussian t flat-tp and bam shap transfrmatin frm rund t squar. And applying matrials f wak birfringnc, fr xampl uniaxial crystals with rintatin f crystal ptical axis paralll t a bam shapr ptical axis, maks it pssibl t avid ssntial influnc n a bam structur and disturbanc f its phas frnt, which is imprtant fr fild mapping bam shaping ptics. As discussd in chaptr 3, utput bam is charactrizd by cmplicatd pattrn f rintatins f plarizatin axs fr ach ray f a bam. T analys plarizatin faturs f utput bam n can apply a plarizr installd aftr th bam shapr. Masurd intnsity distributin aftr a Glan- Taylr prism as a plarizr installd aftr th Shapr is prsntd in Fig. 7, right. This xprimnt cnfirms cmplicatd utput bam structur frm th pint f viw f plarizatin stat in diffrnt bam zns. T hmgniz th plarizatin structur it is pssibl t apply a plat mad frm a crystal f ppsit birfringnc sign and usd in cnvrgnt bam. Figur 6 Exprimntal intnsity prfils using a Shapr with lnss frm birfringnt crystals: lft input TEM 00 bam, right squar-shapd flat-tp utput. Figur 7 Exprimntal intnsity prfils whn using a bam shapr with lnss mad frm birfringnt matrials: lft squar-shapd flat-tp utput bam, right plarizr (Glan-Taylr prism) aftr Shapr.

7 5. CONCLUSION Th task f transfrmatin f linarly plarizd bam frm rund t squar-shapd can b slvd by ptical lmnts mad frm birfringnt crystals. T raliz transfrmatin with minimizd influnc n a wav frnt f a bam it is suggstd t apply matrials with wak birfringnc, which crystal ptical axis is paralll t systm ptical axis. On f practical slutins can b implmntd in frm f a plat in divrgnt r cnvrgnt bam. Whn applying birfringnt lnss in a rfractiv fild mapping bam shapr it is pssibl t raliz transfrmatin f rund Gaussian bam t a squar-shapd bam unifrm intnsity distributin. 6. REFERENCES [1] Dicky, F. M., [Lasr Bam Shaping: Thry and Tchniqus, Scnd Editin], CRC Prss, Bca Ratn, (2014). [2] Hffnagl, J. A., Jffrsn, C. M., Dsign and prfrmanc f a rfractiv ptical systm that cnvrts a Gaussian t a flattp bam, Appl. Opt. vl. 39, (2000). [3] Shaly, D.L., Hffnagl, J.A., Asphric Optics fr Lasr Bam Shaping, [Encyclpdia f Optical Enginring], Taylr & Francis (2006). [4] Kruzr, J. L. Chrnt light ptical systm yilding an utput bam f dsird intnsity distributin at a dsird quiphas surfac. US Patnt , (1969). [5] Laskin, A. Achrmatic rfractiv bam shaping ptics fr brad spctrum lasr applicatins Prc. SPIE 7430, Papr (2009). [6] Brn, M., Wlf E., [Principls f Optics], Cambridg Univrsity Prss, Cambridg, (1999). [7] Smith, W.J., [Mdrn Optical Enginring], McGraw-Hill, Nw Yrk, (2000). [8] Yariv, A., [Optical Wavs in Crystals], Jhn Wily & Sns, Nw Yrk, (1984).