Numerical Treatment of short Laser Pulse Compression in transient stimulated Brillouin Scattering

Transcription

1 Nolar Aalyss: Modllg ad Corol Vls IMI v.7 No. 3-9 Nmrcal Tram of shor asr Pls Comprsso ras smlad Brllo carg A. Dm v V. Grdasas O. Vrblvsaa Is of Physcs avaorų 3 8 Vls haa aldm@l.m.l Vyaas Mags Uvrsy Vlos Kaas haa [v.grdasas o.vrblvsaa]@gmf.vd.l cvd:.4. Accpd: 4.4. Absrac sls of mrcal vsgao of h comprsso procss of shor plss drg ssally osaoary B ar prsd ag o acco h dffraco ad focsg of h racg lgh bams ad h f oscllao prod ad lfm of hyprsod wavs olar mda. Kywords: shor lasr pls ras smlad scarg comprsso Irodco Drg smlad Brllo scarg (B) of shor lasr plss a opmm focsg codos ffc pls comprsso ad grao of os plss wh drao sb-aoscod [ ] ad v pcoscod [3 4] rags s possbl. B pls comprssors ar wdly sd owadays powrfl lasr sysms [4-]. Thrfor dald aalyss of ffccy of scarg ad spao-mporal srcr of h scard plss dpdg po h rgy h shap ad h drao of h pmp plss h focsg gomry ad physcal paramrs of h 3

2 B mda s of gra rs. Alhogh amps ar sll bg mad o vsga aalycally h prcpls of comprsso sg graly smplfd qaos of bacward B h approxmao of plawavs of sy ad ag o acco h so-calld wav osaoary oly [] clso of h maral osaoary o h rsarch s possbl by mrcal mhods oly. c h xprmally achvd draos of h comprssd plss T ar smallr o oly ha h lfm T of h hyprsod wavs dcd h procss of h smlad scarg b also ha hr oscllao prod T B as wll [-5] amog ohr hgs h scod paral drvav wh rspc o m shold b prsrvd h maral qao for h complx ampld of hyprsod oscllaos [-7]. Howvr mos wors dalg wh h pls comprsso osaoary B h ram s lmd o prsrvg h frs drvav ad h rm dscrbg h dcay of hyprsod oscllaos. Oly rlavly rc wor [8] ao was draw aga o h cssy o prsrv h scod drvav wh aalyg h possbly o comprss h os plss o draos shorr ha h prod of h hyprsod oscllaos sg h pla-wav approxmao for aalyss of h comprsso rgm [7]. A h sam m for corrc dscrpo of h xprmal rsls s cssary prcpl o xplor h so-calld grao rgm of h os radao from lvl of h dsrbd os of spoaos scarg of h focsd radao [-6]. I s q aral o a o acco sgfca varao (of h ordr of ms) of h rasvrs ss of h pmp bam ad h os bam achvd h B comprsso procsss by xpadg h flds o h srs of agrr- Gassa mods [-6 9] whch has b do alrady for q som m. Bsds a paralll calclao algorhm has b mplmd [] 4

3 sg h xpaso o h agrr-gassa mods. Thrfor h sams of h ahors of rc wors [ ] ha a fd hrdmsoal modl compassg fally all h aspcs of B parclarly h osaoary ad h rasvrs ffcs has b crad hs wors oly loos v mor srprsg. I shold b od ha oly h frs mporal drvav s a o acco h maral qao hs wors ad h agrr- Gassa mod xpaso s also sd for dscrpo of dsrbo of focsd axally-symmrc flds. Bsds hs wors ra oly h wllow pr-comprsso of h ladg dg of h plss drg h osaoary scarg rgm rahr ha h comprsso rgm. Th ma sbsac howvr s ha hs wors cocld followg h wors dalg wh h saoary B focsd axally-symmrc bams [3 4] whr h agrr-gassa mod xpaso was also appld ha h rasvrs dmsos of h os bam xcd h s of h pmp bam bgg from h focal was ad p o h x from h cll h rgm of grao from h os lvl of spoaos scarg. Ths rsls coradc hos obad or prvos wors [3-65]. Thrfor hs wor a ovl algorhm for mrcal solo of qaos of srogly osaoary B focsd bams was dvlopd (who applcao of h agrr-gassa mod xpaso) ad mrcal vsgao of comprsso dyamcs of shor lasr plss was prformd whr h ma mphass was o h chags of covrso ffccy ad qaly of h os bams as h rgy of h pmp plss grow ad h dpdcs of h spao-mporal characrscs of h comprssd os plss po h lfms ad prods of hyprsod oscllaos. 5

4 Eqaos of srogly osaoary B wh focsd bams Th ma par of a B comprssor (g. ) s a log cv wh glass facs coag lqd or gasos Brllo mdm. Th crclarly polard collmad lasr bam wh rads w s focsd by a ls wh focal lgh sch a way ha h bam was s locad sd h cv. If h lgh Z s clos or largr o half h spaal lgh of h lasr pls sd h g. Th opcal schm of a B comprssor cll v ad h covrgc agl of h focsd bam sd h T cv s chos appropraly a shor os pls (grad a h was from h os of spoaos scarg) s ffcly amplfd d o B whl propagag agas h lasr pls. I hs way os plss ar grad h comprssor whos drao s smallr by a comprsso rao T T ha ha of h cd lasr pls ad N hr rgy xcds h lvl of half or v mor h al rgy of h 6

5 lasr pls. Afr ravrsg h polarao dcoplg sysm cossg of qarr- wav pla λ 4 ad dlcrc polarr P h os plss x from h B- comprssor ad propaga hrogh h daphragm wh rads D. Th lasr ad h os opcal wavs ad h sod wav propagag alog h cll (Z axs) rac h B procss: E E ( c..) c ( Z T ) A ( Z T ) ( Z ω T ) ( c..) c ( Z ωt ) ( Z T ) A ( Z T ) ( c. c. ) (a) (b) ~ ( ) ( ) ( qz ΩT ρ Z T U Z T ). (c) Hr T s h mporal coorda ( X Y ) spaal coordas A amplds of hs wavs ad Z ar h A ad U ar h slowly varyg complx q ar hr wavmbrs ω ω Ω ω ω ar hr cyclc frqcs. To dscrb h olar raco of h wavs cas wh h os pls drao s shorr o oly ha h sod wav lfm T b also shorr ha s prod T B srogly osaoary B qaos of cyldrcal bams for slowly varyg amplds of lasr os ad sod wavs coag h scod drvav h sod wav qao ad h rms dscrbg h flc of Krr olary of rfraco dx of h mdm wr sd [-8]: 7

6 v A T A Z A γ 4ρ ω AU c ( A A ) A (a) v A T A Z A γ 4ρ A U * ω c ( A A ) A (b) T B γ q 4π Ω U U U U A A T T T * T T 6π U f. (c) whr s rasvrs aplaca γ s h lcrosrco coffc ρ s h prrbd dsy of h olar mdm v ar h grop vlocs of h lasr ad h os wavs h mdm ar h rfraco dcs for h lasr ad h os bam s h olar rfraco dx U f s h ampld of h hrmal flcaos of h mdm. I was assmd ha h rsoac codo qv Ω holds h B grao rgm wh drvg (c). Th doma of h solo of Eqs. () s T Tm Z m whr T m s h m rval drg whch h comprsso procss s cosdrd s h lgh of h mdm alog h wav propagao drco m s h dsac from h lasr bam axs o h bodary of h mdm alog h drco rasvrs o h bam axs. Th al codos of Eqs. () ar: ( Z T ) 8 A U ( Z T ) T U f. Th bodary codos ar A ( Z T ) A ( m Z T ) ( Z T) ad A ( Z T ) A ( T ) s h al lasr pls of ow ampld. Eqaos () wr sd ormald form for mrcal solo. c h damr of h bam focsd o h cv s may ms (by A

7 9 a facor of ad mor) smallr a h bam was ha s damr a h rac o h cll h adapv rasformao of h rasvrs coorda proposd f. [6] was sd: ( ) ( ) ( ) ) ( / / Z Z Z Z ρ (3) whr Z s h dsac from h rac o h mdm o h lasr bam was w Z s h aylgh lgh ad w s h bam rads a h was. Afr applyg h rasformao (3) h ormald srogly osaoary B qaos rad as follows: () ( ) ( ) ( ) r r r r 4 µ ρ µ ( ) o η Γ (4a) () ( ) ( ) ( ) r r r r 4 µ ρ µ ( ) o * η Γ (4b) f B * 4 τ τ π τ. (4c) whr T T v T Z / r ar ormald dpd varabls whr ( ) m Z Z ( ) 4 xp r A A µ ( ) 4 xp r A A µ ar h slowly

8 varyg complx amplds of h lasr ad h os wavs ormald o h characrsc ampld A Z Z U U s h ormald sod wav ampld µ ( ) τ B T B v s h ormald sod wav prod τ T v s h ormald sod wav lfm Γ gi v 4T s h coffc of h olar coplg ω γ TB ( g s h B amplfcao coffc v s h vlocy of 3 ρ c v hyprsod I c A 8π ) η 8π I c λ s h olary coffc of h rfraco dx f s h ormald ampld of hrmal flcaos of h mdm. Th lms of varao of h ormald varabls ar: r whr m m Tmv. 3 Nmrcal mhod or mrcal solo of Eq. (4) h spl sp mhod was sd whos schm s prsd o g.. Th ssc of hs mhod s g. Th schm of h mrcal mhod NT N T m

9 dvso of smlaos wav dffraco ad procsss of olar raco o coscv sqc.i s assmd ha vry dscr m sp h dffraco (D) h focsg () h Brllo olary (BN) ad h Krr olary (KN) a plac sqally. I ordr o cras h accracy of h mhod o h scod ordr h symmrcal schm [7] s sd whr h mod procsss ar appld rvrs ordr for coscv m sps. Dffraco sp. I hs sp h qaos of wav propagao ad dffraco ar bg solvd for h amplds of h lasr ad h os wavs: µ ρ µ ρ () r r r r () r r r r (5a). (5b) Th f-dffrc mhod s appld. Th grd wh cosa sp alog h axs ad crasg dsy oward h bam axs alog h r coorda s sd h doma r : N Z αy α N Z r ( ) ( ) N ; y r ; r N ; α. Th vals of h amplds a h grd ods ( r ) ( r ) wr calclad sg h followg mplc fdffrc schm [8]:

10 µ ρ ( ).5 Λ ( β ) β ) (6a) µ Λ (.5 ) ρ ( β ) β ). (6b) I was assmd hr ha.5. 5 ad h coffc β ca assm h vals from h rval β. Wh β w hav a complly mplc schm ad cas β. 5 h Cra-Ncholso schm. Th followg f-dffrc approxmao was sd for h rasvrs aplaca: Λ r.5 r.5 r.5 r.5 r (7) whr r r r.5 r r. rom h bodary codos.5 r N. Th bacsbso algorhm [8] was sd for solo of h s of h lar algbrac qaos. ocsg sp. Th followg qaos ar solvd hs sp: ( r 4 ) ( ) µ ( ) ( r 4 ) ( ) µ ( ) (8a). (8b)

11 3 Th xac solos of hs qaos ar: ( ) ( ) ( ) r µ xp (9a) ( ) ( ) ( ) r µ xp. (9b) Brllo olary. Th followg s of qaos s solvd: o Γ (a) o Γ (b) f g * 4 τ τ π τ. (c) Th prdcor-corrcor mhod proposd ad aalyd [9 3] s sd: ( ) f p * (a) p Γ (b)

12 4 * p Γ (c) * f (d) g g y y y y y y τ πτ τ π τ. () Krr olary. Th followg s of qaos s solvd for dscrpo of raco of h opcal wavs d o rfraco dx olary: ( ) η (a) ( ) η. (b) Th xac solo of hs qaos s: ( ) [ ] η xp (3a) ( ) [ ] η xp. (3b)

13 Th horcal accracy of h abov dscssd symmrcal spl-sp mhod s ( r ) wh h sp s r cos. Drg h smlao h calclao accracy was bg chcd by vrfyg h cosrvao of h oal rgy of h opcal wavs so ha h rgy dvao wold o xcd svral prcs. Accracy of solo of h lar dffraco problm was smad by comparg h mrcal solo wh h ow xac solo for h Gassa bam. Accracy of h oal solo of h olar problm was smad by drmg by how mch h solo chags wh h sp or r s rdcd wc. 4 Modllg rsls Th ormald qaos (4) ad h abov dscssd mrcal spl sp mhod was appld for modlg of comprsso of lasr plss wh wavlgh of λ.64 µm ad h vlop wh a spr ladg dg: r ( r ) xp xp ατ ( ) ατ w (4) (hr h cosa α.45 τ s h pls drao a half h maxmm sy lvl w s h lasr bam rads a / of h maxmm ampld) a h opmm focsg codos for h cass wh h draos of h p lasr pls ar T s ( W.4 cm 9 cm) ad T s ( W.9 cm 9 cm) h Brllo mdm whos paramrs ar as follows: h sod wav rlaxao m T.4 s ad h prod T B.75 s rfraco dx.7 h ga coffc g cm/w whch corrspods o h mdm C-75 5

14 [34]. I shold b od ha for dffr draos of h pmp plss h lghs of h cvs sd wr also dffr ( T s - 5 cm T. 68 s ad T s - 3 cm T. 37 s) hrfor h ormalao ms T v wr dffr as wll. Thrfor h os plss havg h sam ormald draos mgh hav dffr draos absol s. rs h dpdcs of h rgc rflco coffc rm r m H ( r) rdr H ( r) rdr (5) whr H () r I ( r d h rgy dss of h lasr ad ) h os plss a h rac pla of h olar mdm draos a half h maxmm τ P of h ormald powr vlops of h os pls P s r m ( ) ( r ) π rdr (6) ad draos a half h maxmm τ I of h ormald sy vlop a h bam axs I ( r ) ( r ) ad h os bam qaly paramrs M ( ) ad M ( ) po h paramrs of h cd lasr plss wr vsgad. or characrao of h bam 6

15 qaly h wdly sd lasr bam qaly paramr M ha characrs h bam dvrgc h far o compard o ha of h dal Gassa bam of h sam rads [767] was sd. or h dal Gassa bam M ad for all ohr bams M >. or h ow rasvrs ampld dsrbo ( r ) h bam qaly paramr vals ar calclad sg h followg xprsso [67]: M 3 () rdr r dr r dr rdr (7) r 4 r Th rasvrs ampld dsrbo of a pls s chagg m hrfor h qaly paramr s a fco of m M () ha characrs h bam qaly a vry mom m. or characrao of h r pls h powr-wghd P () mavragd qaly paramr [6] r / M M ( ) P ( ) d P ( d ) (8) was sd. Th dvlopd sofwar provdd h possbly o rcord ad aaly h vals of ( r m ) ad ( r m) a mbr of plas. g. 3 prss h hr-dmsoal dsrbo ad sols of h sqar of h modls of h complx ampld of h os pls a h x ( ) from h B cll. I s s ha h comprssd pls has a rahr complx characrsc spao-mporal srcr [679] coag off-axs sb-plss h ralg par of h pls. Thr spaal 7

16 ad mporal sparao mas possbl o xrac by mas of a smpl daphragm (g. ) h ma sb-pls whos drao s ssally shorr ha h gral drao of h r pls. Th pls qaly dgradao s drmd by a complx spaomporal dyamcs of h os pls bldp ha s clarly rflcd by h sy vlop ad s sols of h os pls. I s s ha as h os plss of so shor drao bld p h prologd ralg dg of h pls s sgfcaly dsord ad a rg-shapd srcr mrgs. Thrfor h qaly of h pls dcrass cosdrably (g. 4a) ad a pa blds p a h cr of h ar fld rgy dsy dsrbo (g. 4b). Th rgy dsy dsrbo a h far fld s clos o Gassa (g. 4b). Th dpdcs of h os pls draos τ P ad τ I h qaly paramr ad h rflco coffc po h cd lasr pls rgy wr vsgad. Th rsls ar prsd o g. 5. As s from g. 4 h mporal shap of h os plss has gral a srcr comprsg a mbr of sb-plss. Th scod ad sbsq sb-plss appar h mporal shap of h plss of saaos powr v wh h B hrshold s xcdd oly slghly (g. 5a). Th frs mos s pa s always sparad from h followg os by a sag whr h powr s lss ha half of h pa powr. As was s from g. 3 hs axal pa s spaally sparad from h sbsq off-axs powr pas hrfor hy ca b prcpl dsgshd. Thrfor s rasoabl o rodc h drao of h frs sb-pls oly τ P ( ) ad h oal drao of h pls of h () saaos powr a half h maxmm lvl τ P. I ca b s ha h draos of h frs powr sb-plsτ ad of h sy a h bam axs τ I dcras moooosly as h lasr pls rgy crass () P 8

17 () (g. 5a). Th maxmm comprsso (h rao τ τ P ad τ τ I ) for () h 8 mj rgy s mor ha 3. Dcras of h ovrall drao τ P s somwha smallr b sll sffcly ocabl (~ ms). As h lasr pls rgy crass h os pls rgy crass moooosly as wll (g. 5b). Th maxmm rflco coffc xcds 75%. or hgh rgs a sarao of h comprsso ad h rflco coffc ca b obsrvd. As h lasr pls rgy crass h qaly paramr M of h os pls crass (g. 5b).. s qaly dgrads sgfcaly. ar was vsgad how h comprsso procss s flcd by h sod wav prod. I has b drmd ha as h sod wav prod dcrass mor s rgy rasfr from h lasr pls o h os pls s achvd shorr drao ad br pls qaly ar obad. Comparso of h os pls powr ad sy vlops o g. 6 dmosras ha cras of h prod rsls srogly modlad ad prologd ralg dg of h pls alhogh h modlao h cral par of h bam rmas wa. Thrfor h modlao of h ralg dg ca b rdcd br pls qaly ad shorr drao τ P clos o τ I ca b achvd by propaga g h os pls hrogh a daphragm whos rads D s mch smallr ha w (g. 7). Th modlg rsls dmosra ha afr h os plss propaga hrogh a daphragm whos rads s w / 4 hr drao s oly 56 ps wh h lasr plss of s drao ar bg comprssd (g. 7b). Howvr a cosdrabl par of h os pls rgy s los (86% hs cas) d o small damr of h daphragm compard o h cd lasr bam damr; hrfor frhr amplfcao of hs plss s cssary. 9

18 (r) r g.3. pao-mporal srcr of comprssd os plss a h x of Bcll for h p lasr pls wh rgy E mj drao T s hyprsod wav prod TB.75 s ad s lfm T.4 s.

19 3..5 (a) P() I(r) M () P() I(r) M () W (r ) W (r f) W (r ) W (r ) W (r f) (b) r g.4. Tmporal dpdcs a) of sy o h bam axs I ( r ) h powr P () ad facor M () of h os pls a h cll op ad b) r r rasvrs dsrbos of h rgy dsy W ( ) ad os ( ) plss a h p ad op of h cll ad a h focal pla of h focsg ls W ( r f ) a h p lasr pls rgy E 8 mj h drao T s ad h hyprsod wav prod TB.75 s ad lfm T.4 s. W

20 .4 (a) /τ τ I /τ τ P () ().3.. τ P () /τ τ P () /τ τ I /τ E mj. <M >.5..5 <M > (b) E mj g.5. Th dpdcs a) of rlav draos (a half h maxmm) of h comprssd os plss sy a h bam axs τ I / τ ad by saaos () () powr of h frs pa oly τ P / τ ad of h r pls τ P / τ ad b) of h avragd propagao facor M ad h rgy covrso ffccy o h p lasr pls rgy E a h drao T s wh h hyprsod wav prod TB.75 s ad lfm T.4 s.

21 P() (a..) 3 τ B /τ.5 τ B /τ.75 τ B /τ.5 (a) I(r) (a..) (b) τ B /τ.5 τ B /τ.75 τ B /τ g.6. Tmporal dpdcs a) of h saaos powr P () ad b) of h I r of h os pls a h cll op po h hyprsod wav prod T B a h p lasr pls rgy E mj h drao T s ad cosa lfm T.4 s. sy o h bam axs ( ) 3

22 . P() (a) τ B /τ.5 D /w.5 E( D )/E( m )4% D /w.6 E( D )/E( m )59% D /w. E( D )/E( m )98% P() (b) τ B /τ.5 D /w.5 E( D )/E( m )% D /w.6 E( D )/E( m )54% D /w. E( D )/E( m )98% g.7. Th vlops of h saaos powr P () of os plss propagad hrogh daphragms of dffr rad ad h hyprsod prod T B a h p lasr pls rgy E mj h drao T s bam was w.9 cm ad lfm T.4 s. 4

23 Ivsgao of how h comprsso s flcd by Krr olary of h rfraco dx of h mdm has show ha h rflco coffc chags sgfcaly b h os pls drao crass a hgh rgs of lasr pls alhogh h drao a h bam axs dcrass bcas h mos s cral par of h pls s bg focsd mos sharply. Th qaly of h cral par of h pls dgrads o a larg x hrfor h qaly of h r pls dgrads mor srogly as wll. 5 Coclso A ovl algorhm s proposd hs wor for mrcal aalyss of ssally osaoary B focsd bams. Th algorhm s basd o a cra rasformao of varabls ha mas possbl o apply h sadard f-dffrc mhods also for sharply focsd lgh bams. Ulao of h spl sp ad h prdcor-corrcor mhods abl o a o acco h focsg h dffraco ad h olars of varos physcal ar of srogly osaoary B a form mar. Th dvlopd calclao algorhm prmd o vsga h rgc ffccy of h B comprsso procss of shor lasr plss cas wh hr al drao s comparabl by a ordr of magd wh h lfms ad h oscllao prods of h hyprsod phoos. Th prsd rsls dmosra ha sparao of h cral ar-axal par of h os plss mas possbl o achv h draos of h os plss praccally h pcoscod rag ad h comprsso ra xcdg 3 ms. I shold b od ha cas wh h hrshold s sgfcaly () xcdd also h ovrall pls drao τ P s o lmd h focsd bams by h half-prod of h hyprsod as s cas of h pla- 5

24 wav approxmao [8]. Howvr hs cas h qaly of h comprssd plss dgrads sgfcaly (p o M ( ) ~ ). frcs. Byals.. Dm v A.. Koso E.K. ormao of sbaoscod plss by smlad Brllo scarg of radao from a pls-prodc YAG:Nd lasr ov. J. Qam Elcro. 5 p Nshv D. Vlchv I. Maws W.A. Hogrvors W. Ubachs W. B pls comprsso o ps a compac sgl-cll sp Appl. Phys. B. 68 p Bls. Dm v A. ad Mrasas E. Ivsgao of possbls of ffcv B comprsso of aoscod pls o ps haa Phys. J. 39 p Kwahara K. Taahash E. Masmoo Y. Kao. ad Owadao Y. hor-pls grao by sarad Kr lasr amplfcao of a sp os pls prodcd by wo-sp smlad Brllo scarg J. Op. oc. Am. B 7 p Bls. Dm v A.. Koso E.K. ad Mrasas E. mlad-brllo-scarg comprsso of plss from a Nd:YAG lasr wh a shor cavy ad masrm of h oradav rlaxao m of h lowr acv lvl Qam Elcrocs 5 p Bls. Dm v A. Koso E. Mrasas E. Čgs. ad Karyė G. "Nmrcal aalyss ad xprmal vsgao of bam qaly of B-comprssors wh mlpass Nd:YAG amplfr" Proc. PIE 77 p

25 7. Bls. Vacasas. Dm v A. Ivaasas. Koso E. Mrasas E.ad adžūas M. Nmrcal aalyss ad xprmal vsgao of grao B-comprsso ad amplfcao of shor plss of Nd:YAG lasr Ivsya ossso Aadm Na r. ch. 6 p ( ssa) 8. A.Dmv Ivsgaos of dyamcs of sold-sa lasrs wh pls comprsso NONINEA POCEE. Modllg ad corol Vls MII p ( haa) 9. Tmor V.V. hlovs E.I. Nmrcal modllg of lasr wh B-mrror Kvaovaya Elroa 3 p. 3-8 ( ssa). Dm v A. Bls. Koso E. Mrasas E. Navaas. old-sa lasrs wh pls comprsso by ras smlad Brllo ad ama scarg. Proc.PIE 445 p Bab V. Mocofasc A. Vlad V.I. Dam M.J. Aalycal ram of lasr- pls comprsso smlad Brllo scarg J. Op. oc. Am. B 6 p Bls.. Grdasas V.V. Dm v A.. Koso E.K. Cgs.Y. mlad Madlsam-Brllo scarg comprsso of os plss focsd Gass bams from YAG:Nd lasr... 6(5) p ; Allro Prss Ic. [ov. Phys. Collco] p Byals.. Grdasas V.V. Dm v A.. Koso E.K. Cgs.Y. ad hba M.. pac-m srcr of plss from cascad dcd-scarg comprssors Bll of h Acadmy of ccs of h U Phys. sr. 55() p Kbč V. Hamal K. Prochaa I. Bls. Grdasas V. Dm v A. Nd:YAP lasr pls comprsso by hr-sag 7

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