Design and operational characteristics of cw and KLM Ti : sapphire lasers with a symmetric Z-type cavity configuration
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(2) 348. 7²æ B 13² B 4^,. j 8ú. 2002. " r^ö Vº î~ . æz& jSÿ .(unper R ·, Kerr îj Û turbed refractive index) "~º z Vê ï8j ÒÏ¢ º &;~öBò æ ~ ¯R(transfer matrix) 5 j& Z-¶ ; êVö & q-2¢zV¢ '' > ® . ¾ Kerr îj Û"~ º ;{ z V~ æzº ï z Vf Ú¦êV ÂK Ô º &; ~öBº > ìV r^ö ²w z" êV z~ Ö(coupling)j 'z > ì . V¢B. öBº Kerr îö & 6 æ~ ¯R r Ò(negative distance)ö & &Ön(Gaussian) z *2~ Bvj Bn~& . O» öB VF O» º ¢>'æò, ÖF Ôf Ú¦êV ÂKj <º ³ Bê ÿ·öB êV z V¢ êÖ~ ¸f Ú¦êV ÂKj <º Î-ß ÿ·j * Kerr î~ æ~ ¯Rj áV *~ Kerr î 7öB~ z V¢ êÖ~¢ . V ¢B jF; î ÚöB zf 7»ö "7~ *2> ¶ F*öB~ *2O;j ò~º ÒÏzB q-2¢zV (renormalized q-parameter)¢ ê«~ ¶Ú-÷³j ~ º ^B¢ ¶F*ö & *2 C > ®b, Kerr. îj ~ v B~ >Z 2®f v B~ ï Þ WB êVº *f ?f O» b C >& ® . öBº æª Ò2Ú .&ö & Ïê¢ ¸ V *~ v B~ ï Þ, Kerr î æª Ò2 Ú Ö;, Ö;j ~ ®º v B~ JÏ Þ, . jV 5 *Ò¾ 3 j Ï~ Z-;~ &; .& êV¢ W~ ÂK ÎN ¸ 9f 2Ë&æ'j <º ³ Bê æª Ò2Ú .&¢ Jê B·~, Kerr. î 5 4-B~ Þ WB Z-;~ &; êVö & n;" KLMö & ' ªCj *~ ABCD » b æ~>º ÒÏzB q-2¢zV ¢ Ï~ Ú¦ êV .& ÂKö ~~º z Vf KLMj * n; , KLM ;ê 5 KLMj * ' " ?f 7 ' ßWj êÖ~ ¢ þ Ö"f jv ªC ~& . [8,17]. j òj & . VB, Kº Kerr 2¢zVB 8P π 2 K = ------- --- n 0 n 2 π λ. f ? ;~>, Pº êV ÂK 5 n º î~ F; .j ¾æÞ . 6 q-2¢zV¢ 0. 1 1 1--= Re --- + jIm --- 1 – K q q q′. [16]. [18]. [14,17]. [19]. [19]. [19,20]. ;~ &; .& êV ö & KLM. d 1 1 – ----- ---- = ------2q′ dz q′. (5). & >Ú 1/q~ ¶F *ö & *2 O;" ¢~~æ ¶Ú-÷³j ~º ^B¢ ¶F * *2 C > & ® . Huang ~ þ Ö" f ¢~>º 8j áV * ~, ; &Ë ; ¶(correction factor) α¢ Kerr 2¢zV ³ö Ò > ®, K~ ;~º K=P/P > ;F > ® . VB P f Kerr îöB z~ V æz& ì ê¯~º(self-trapping) Ú¦êV ÂK~ ªê ÂK b P =αλ /(8 π n n )& B . r, ªê ÂKö & ; ¶ α¢ ~æ P ≈ P ¸f ÂKö &Bê 'Ï > ® . â 1f v B~ JÏ Þ Òö Kerr î ¹ 4B ~ Þ WB Z-;~ .& êV¢ ¾æÞ . â öB M " M º ï Þ M " M º ÿ¢ .6Ò f¢ <º JÏ Þ, . n , ^ s .& î(6 º jF; . n ~ Kerr î) v JÏ Þ Òö ¹ ®b Þ~ 7¾'f 2θ . r, Ö(sagittal plane) 5 ¶J(tangential plane)~ .6Ò& '' f =f/cosθ 5 f = f cosθ >æ êV Úöº j6>N(astigmatism) & V ¢ ç~V * θº [20]. cr. cr. [18]. cr. 2. 0 2. cr. 1. 4. 2. 2. 3. 0. 2. s. [21]. t. –s( n – 1) n + 1 s ( n 0 – 1 ) ( n 0 + 1 ) 0 0 - + ---------------------------------------------θ = cos –1 ------------------------------------------- ⁄ 2 4 2 8 2. . 0. (4). f ? ÒÏz~. II. Z-. êV ÚöB~ KLMö & j *B~V *~ z ~ ê A f >ã ω &Ön z~ q-8j ÒÏ~, j F; . n Kerr î~ ^ dzö V ¶Ú-*ç æ z ∆φº. (3). 2. 2. 2fn0. 2. 2. 2. . 4f n 0. (6). & B . 6 M " M 5 M f M ~ Òº '' d " d , M öB Kerr î~ ã I(r, f ¦Ê V 'b &N)f M öB ã IIræ~ Ò¢ '' r 5 r ¢ r, M öB q-2¢zVº q =jy =jπω /λ B. . VB λº ¶F *öB~ 2Ë, ω f ÂK Þ 1. 2. 3. 4. 1. 2. 2. 3. 1. 2. 1. 1. 1. 2 1. 1. 2π 2 2 2 ∆φ = ------ n 2 A 0 exp ( – 2r ⁄ ω )dz λ 2 2π 2 2r ≈ ------ n 2 A0 1 – -------2- dz λ . (1). ω. f ? B .. [16]. H.A. Haus[19]. d 1 2 1 1 – ----- --- = ----2- + KIm --- q dz q q. f 1/q~ *2 O; (2). â 1. ^& s Kerr î" 4B~ Þ WB Z-;~ .& êV..
(3) Ó¢^ÔZ-;~ &; .& êV ¢ <º ³ Bê 5 Kerr-2® ºÁnº> . öB &Ön z >ãj ¾æÞ . r, M öB M ¢ ãF~ Iræ ê¯~º ABCD ¯R 5 IIöB M f M ¢ æ¾ IIræ ê¯ ~º ¢"(round trip) ¯Rf ''. M1. 1. =. 1 r1. C1 D1. 0 1. A2 B2. 1 r2. =. C2 D2. 1 0 1 2d 2 1 0 1 r2 – 1 ⁄ f 1 0 1 –1 ⁄ f 1 0 1. (7). 2 1. +. +. 2 2 a2 ( y1 ). 2. + a1 ( y1 ) + a0 = 0. 4. 3. 2. 1. 2. 1. 2. 1. 1. 4. 1. 4. 2 1. 1. I. 1 1 1 ------ = Re ---- + jIm ---- 1 – K q I q I qI ′ q1 C1 + D1 = ------------------------q1 A1 + B 1 2. – y 1 ( f – r ) + ( f – d ) ( rf + df – rd ) – jy 1 f 1 – K = -----------------------------------------------------------------------------------------------------------------2 2 2 y 1 ( f – r ) + ( rf + df – rd ). II. (9). 6 « IöB~ q '2¢zV¢ q ' =q' +s/n =q ' +L &ê j Ï~,  IIöB q ' æ~B  IIöB~ q ¢ áj > ® . VB, L=s/n º 7' ^ n º. î~ FÎ .j ¾æÞ . &W r^ö 1/q5 1/q ~ î > ¦ª z îÒ(beam waist) Vº ?, > ¦ª >ãf ¦^& >&& B . V¢B 1/q =-Re(1/q )+jIm(1/q )~ &êö ~B Jç y ò 2N O;b Bz>Ú I. 0. I. II. 0. II. 0. I. II. I. II. II. 2 1. 2 2. 2. a ( y1 ) + b ( y 1 ) + c = 0. 2. a = ( f – r ) ( L + 2r – 2f ) 2. 4. b = ( f – r ) ( rf + df – rd ) [ ( L + 2r ) ( d – f ) – 2df + f ] + Lf ( 1 – K ) 2. c = ( d – f ) ( rf + df – rd ) [ ( L + 2r ) ( d – f ) – 2df ] 2. 2. = ( d – f ) ( rf + df – rd ) [ L + 2r – 2df ⁄ ( d – f ) ]. & B . (10)j ¦V *ö Ôf jF; .j <¾ Ôf Ú¦êV ÂK K ≈ 0 ãÖj J~¶. r z Vº ç ·~ >æ K=0ö & y ~ F¢ º 2 1. 2 2df ( d – f ) ----------------- – ( L + 2r ) (d – f ) = --------------------------------------------------------------------L + 2r – 2f. (11). & B . ¢>'b Î-ßB .&º d>f æ êV~ n ;f 2f < (L+2r) < 2df / (d − f )6º 0<δ<[2df / (d−f )]-2f ¢ ò¢ . VB L+2r = s/n +2rf JÏ Þ ~ FÎ *Ï, δ = L+2r−2f ¢ n; 2¢zV ;~ . 6 n ;f a>0" c<0 ¢ r Wã~ (10)~ ¢>º y = [ ( b – 4ac ) – b ] ⁄ 2a ¦V > ®b n;f ac<0 öò jî¢ b -4ac>0¢ rê Wã . r, ac<0 f n;~ ~ ãê& δ > 0 >ê .~º K=0ö & " ÿ¢~, b − 4ac>0 f n; 2¢zV~ ç ãê¢ Ö; . y j ~ M " êV Ú~ ª~ * ~öB~ z >ãf ABCD»ö ~ êÖ > ® . ¯, M b¦V Ò z öB~ z Vº y(z)º y(z)=y [1+(z/ y ) ]& B . 2 1. 1⁄2. 2. 2. 2. 1. 1. 1. 1 2. 1. III.. (10). ~ ;& B . (10)~ ç> a, b 5 c¢ ~V *  IöB z~ *2 ¯Rj 'Ï~ b′ – jc′ 1 ------ = ----------------a′ qI ′. I. 0. 1–K 1 = ----- – j ----------------yI RI. II. 2. & >, II öB~ z îÒ Vº ?V r^ö q '" q'~ î > ¦ªj ?² ¹j > ®, ?f N>~ ç> ¢Ò Îb. 2 y 10. I. 1–K. a′b′ + L ( b′ + c′ ) + ja′c′ 1 -------- = --------------------------------------------------------------2 2 q II ′ b′ + c′. I. 2. 2. & Nj r > ® . 6  IIöB Kerr îj 澺 z~ *2 ¯Rj 'Ï~. 0. 1. 4. 2. (8). VB ê> a , a , a , a 5 a º Kerr î~ ^ > v B~ ABCD¯R~ º² j ¾æÞ . (8)~ º â 1~ êV ¢ r =r =r, d =d =d &; .& êV &Ú~ z× *ê . ¯, M ö B q-2¢zV q f &Wb ~ M öB q-2¢zV q f ?² >Ú q =q =jy =jπω / λ& B . V¢B Iö B q-2¢zVº F; æ~ ¯Rö ~ q f &>, I öB ÒÏzB q-2¢zV q 'f r" ? êÖB .. 2. b′ = – y 1 ( f – r ) + ( f – d ) ( rf + df – rd ). 2. 1. 2 3 a3( y1 ). 2. c′ = y 1 f. 1 0 1 d1 , –1 ⁄ f 1 0 1. 0 1. 2. a′ = y 1 ( f – r ) + ( rf + df – rd ). 4. & B . Kerr îj Û"~º q -2¢zVf IIöB ¶ Ú-¢~(self-consistence)& >V * jºb æ~~V *~ ÒÏzB q-2¢zV Bvj ÒÏ~ y ~ 4N O ;f r" ? . 2 4 a4 ( y1 ). & >, (9) ¦V. 2. 3. A1 B1. 349. ³ Bê 5 KLMB æª Ò2Ú .& ÂK ßW. ³ Bê æª Ò2Ú .&f ÂK ßW ³ Bê 2Ë&æ 5 KMLj * Z-;~ &; æ ª Ò2Ú .&~ êV ¢ â 2ö ¾æî . âöB êV ΢ ÷³ÊV * v B~ JÏ Þ 3.1.
(4) 350. 7²æ B 13² B 4^,. j 8ú. 2002. â 2. 2Ë&æ ³ Bê 5 KLMj * æª Ò2Ú . &~ êV. PR: Þ7 ²*V, L: ÷³2®, M , M : >ã 100 mm~ JÏ Þ, M : ÂK Þ, M : * >Ò Þ, BF: . jV, P , P : *Ò¾. 2. 1. 1. 3. 4. 2. f M ~ >ãf '' 100 mm, ²w 2Ë 514 öBº R"~ 800 nm~ Bê 2ËöBº >Ò~º ï z+B Þ . 6 .& î" JÏ Þ r^ö B~º j6>N(astigmatism)¢ ç~V * > ¢; 7¾'(2θ)j Fæ¢ ~, (6)ö ~ 9 mm Ö;j ÒÏ~ £ 23 & B . M º 800 nmöB >ÒN 97%( ³Bê ÿ·) 6º 90%(KLM ÿ·) z+B ï ÂK Þ M º 800 nmj 7b 9² z+B ï *>Ò Þ Îv Layer Tech.Ò B®j ÒÏ~&b, &; êV~ ã : ^¢ 85 cm ~ *Ú êV ^º £ 183 cm ;ê . ²w .&º 5 W ÂKj <º Ar-N .&(Coherent, Innova 90-6)¢ ÒÏ~&b Þ7 ²*V PR¢ Û Þ7 OËj 90 ²*Î ê .6Ò 125 mm~ ï "; 2® Lj Û ¦ÊV 'b îB æª Ò2Ú Ö;(Union Carbide Ò, Ti ³ê; 0.10 wt.%, çã; 6 mm, ^; 9 mm)b ÷³V . V¢B Ö;~ Nê&. Ö ¸² çß~ .& ÂK 5 n;W 6²>æ Ö; j ö ;ïb 6j ¶ÿ Nê .Vö ~ ÿ>º & Ïï *-ï'V(thermoelectric-cooler) *ö Ò & ææ& ;BB ;& ²* &Ë ²*& *ö ËO~ Ö;~ ÇOË Nê¢ Î"'b ï'~ ; Nê quenchingj ÛB" ÿö ;R Ï~ê ~& . BF º 2Ë&æj * 3 6-. jV, P 5 P º KLM B ê êV Ú~ ªÖj ç~ f ªÊ¢ áV * ã « *Ò¾(LakL21 Òî), Ö;j j v JÏ Þ, 2® 5 *Ò¾f KLMj * n;ö £² 7"~V * ~ ;&~² ÿ~º .¢(THK Ò) *ö J~~, î V¢ ¦O~ ÿ¢ »F çö ï¯ 6º >ç OËb ^ ; &Ë~ê Jê B·~& . â 3öº R"N 3%~ ÂK Þj ÒÏ 2Ë&æ ³ Bê æª Ò2Ú .&~ ÂK 5 2Ë&æ 'j ¾æî . âöBf ? ÂK VÞV ÎN 5 Bê ^W ²w ÂKf '' 31.3% 5 290 mW Ö ¸f ÎN" Ô f ^W8j &æ, 5 W~ Ar-N ²w ÂKöB & 1420 mW~ ï ÂKj <º . 6 5 W ²w ÂKö &~ 2Ë&æ 'ê 730 nm~908 nm Ö 9, 'ö B Îv 700 mW ç~ ÂKj ® . M2 nm. 3. o. 1. 4. o. 3+. 1. â 3. (a) Ar-N .&~ ²w ÂKö & ³ Bê 2Ë& æ æª Ò2Ú .&~ ïÂK(j¾ » 5 ¢ã >ç») 5 (b) 2Ë æzö V ÂK ßW(=» 5 J ã >ç»).. j * æª Ò2Ú .&f ÂK ßW j * æª Ò2Ú .&¢ ªC~V *~ öB êÖB Ö" " F; 5 jF; . '' n 5 ªê 5 Ü ; ¶ K ç> ¢ Ï~ Ö;~ ^& 9 mm &; ;~ 5 ~ .6Ò æª Ò2Ú .& êV¢ '~¶ â öº ¢Ú¾æ pj r êV : ^ ö &~ n; 2¢zV ö V M " öB~ z V¢ êÖ~ '' ¾æî. â ~ öBf ? ''~ êV : ^ö &~, ¢Ú¾æ pj r ÂK ÞöB~ z Vº n; 2¢zV ö B JÏ Þ Ò~ *Ï Ã& > ² 6²~, δ = 0¢ r Z&& >, êV~ : ^& Ã&> JÏ Þ Ò~ Ò& 66 6²j r > ®, d =75 cm, d =85 cm 5 d =95 cmö &~ z V 3.2 KLM KLM II =1.76 n2=3 10−20 m2W−1, α ≈ 5.35 [20] Pcr≈2.62 MW , M3 f=50 mm ZM2 . 4 KLM (K=0), (δ =L+2r−2f) d(=d1=d2) M2 . 4 (a) KLM (K=0). 0. 1. 2. â 4. ³ Bê æª Ò2Ú .&öB n; 2¢zVö & (a) M " (b) M öB z~ V. 1. 2.
(5) Ó¢^ÔZ-;~ &; .& êV ¢ <º ³ Bê 5 Kerr-2® ºÁnº> . & ' >º n; 2¢zV 8f '' δ = 7.15 mm, δ = 6.25 mm 5 δ = 5.55 mm& B . 6 n; '~ 7(δ ≈ 2.8 mm~ 3.6 mm)öBº ³ Bê ÿ·ö & z V& £ 1.0 mm ;ê ~ ?rj r > ® ¾ â 4~ (b)öBf ? JÏ Þ öB~ z Vº n; '~ ·ã &˶ Ò ¦ªöB Z&& > &Ë¶Ò ' KLMj ¢b Ò > ®º ' B . Þ, 7' Kerr Î"ö ~ ¶Ú êæ ÎNf Ú¦ êV .& ÂK~ æzö V z V~ æzN Ö; >æ, KLM ;ê(strength) Fº r" ? ;~B . [17]. 1 dw F = – ---- ------w dP. K=0. 8 π n 0 n 2 1 dy 2 - -------- -------= – ----------------2 2 αλ 4y dK. (12) K=0. F8 æ KLM ÎNê Ã&~, ÂK P(6º K)ö & B y j ª~ dy /dK = Lf ( y ) ⁄ ( b – 4ac) > ç ' . 6 ÂK ÞöB~ z Vº .&  Kö jf~æ ;~ .&ö &Bº ÂK Þ *ö ÒB¢ ã«~ KLMj áj > ìb, ?f Ö "º -ÒB¢ ÂK Þö ã«~º j&; .& êV ãÖ fº ÎB B . (12)öB yº &Ön z æ~j <º y ~ > ¯, dy ⁄ dK = ( dy ⁄ dy )( dy ⁄ dK ) æ F8j .& êV *Úö &~ êÖ > ® . â 5öº Z-;~ &; êV öB (12)¢ Ï~ êV Ú~ *~ zf n; 2¢zV δö V KLM ;ê F¢ êÖ~ ¾æî . r, zº ÂK Þ M b G ;B êV Ú~ Ò¢ ¾æÞ . â 5~ (a)öBf ? δ = 6.0 mm ;~, KLM ; êº z=30 cmöB¦V z=90 cm ÒöB jò~² æzj r > ® . â 5~ (b)º z=80 cmöB n; 2¢zV& Ã&ö V¢ KLM ;ê& Ã&j ", KLM ;ê & ·~ 8(F>0) >Ú KLM ¢Ú¾º n; 2¢zV~ º*º 3<δ <6.25 mm >, º ³ Bê ÿ· ê z × BB º*& Nj r > ® . KLM ;ê& IöB 2 1. 4 2 1. 2 1. 1⁄2. 2. [7,17]. 2. 1. 2. 2 1. 2 1. 351. &8j <V r^ö KLM ÿ·j áV *B I "¾ ö ÒB¢ ã« > ®b, ÒB &ö zj ¾¢ÚV * ªÖ *Ò¾~ ;6(apex)j ÒÏ >ê ® . ¯, *Ò¾~ ;6j &Ë M ¦" z=80 cm &² "7 B J~~, ~¾º ''~ ;6j z~ B >& ¦ ªj ¾¢â > ®ê J~~ z~ £ ΢ ¾¢ÚV *~ êV Úö >ç Òå(vertical slit)j ã«~º Î"f ÿ ¢ Î"¢ áj > ®Ú KLM ÿ·j áj > ® . r v *Ò¾ Ò~ Òº êV Ú~ 2N ªÖ(group velocity dispersion) 5 3N ªÖ(cubic phase) j ç~V * .& î ^, *Ò¾ Òî 5 Ú¦*Ò¾ Û" ^ j J~ ' ^ ²J ;R¢ ~, Ö"¢ â 6~ (a)f (b)ö ¾æî . â 6~ (a)º .& Bê 2Ëö V ^ 9 mm~ æª Ò2Ú Ö;öB B~º ·~ 2N ªÖj *Ò ¾ Òî~ Òö ~ r~ ªÖb j*® ç~V * *Ò¾ Ò¢ ¾æÞ © . r, z *Ò¾ Ú¦¢ Û" ~º Òº 3 mm ~ êÖ~& . âöBf ? æ ª Ò2Ú .&~ " Bê 2Ë 800 nmö &~ ' * Ò¾ Òî F2, LakL21, BK7 5 Fused silicaö & 2N ªÖj ç~V * Òº '' 29 cm, 38 cm, 59 cm 5 2. [22,23]. 1. â 5. (a) δ=6.0 mm ¢ r M öB G;B *~ zö & KLM ;ê(j¾ »" ¢ã >ç ») 5 (b) z=80 cmö B êÖB n; 2¢zVö & KLM ;ê(=»" J ã >ç »). 1. â 6. (a) *Ò¾ Òîö &~ 2Ë æzö V 2N ª Öj ç~V * *Ò¾ Ò 5 (b) æª Ò2Ú Ö;~ 2Ëö V 3N ªÖ8" *Ò¾ Òî~ 2Ëö V 3N ªÖ~ .&8..
(6) 352. 7²æ B 13² B 4^,. j 8ú. 2002. 79 cm ªj r > ® . â 6~ (b)º *Ò¾ö &~ 2Ëö V 3N ªÖ~ .&8j ¾æîb, 9 mm æ ª Ò2Ú Ö;~ 3N ªÖ8"~ v6 ¯, λ 5 l & ' ' 3N ªÖ j*® ç>º 2Ë 5 *Ò¾ Ò¢ ¾æ Þ . ' *Ò¾ Òî F2, LakL21, BK7 5 Fused silicaö &~ λ 5 l º '' 1010 nmf 11.5 cm, 884 nmf 20.6 cm, 879 nmf 36.3 cm 5 853 nmf 49.2 cm êÖ>Ú, 2N ª Ö"º Ò 800 nmöB 3N ªÖj j*® ç > ®º *Ò¾f ì æ 3N ªÖ8 ·f Fused silica Òî~ *Ò¾j ÒÏ~º © f ªÊ¢ áVö FÒj r > ® . Þ, ÒÏzB q-2¢zVº Ú¦êV ÂK P<P & > Wã~æ, ÏzB ÂK(P<P )ö V¢ Kerr î Úö Bf êV Ú~ ª~ *~öB~ z V¢ êÖ > ® . â 7ö êV :^& 85 cm &; êV öB Kerr î~ 7" M öB 80 cm ÎÚê *~öB~ Ïz B ÂK(normalized power)ö ~~º z V¢ êÖ~ ¾æî . â 7~ (a) ¦V z=80 cmöB z Vº ² 6² ~ êV ÂK 0.85 P "¾öB ²8 1.28 mm 7"j r > ®b, â 7~ (b)öBº Kerr î~ 7 öB êV ÂK 'öB 0.73 P ræ æö V¢ 25 µmö B 21 µmræ ¦#² æz~, ê self-trapping ~ Ö " /Ï® Ã&j r > ® . 6 z V~ æz ·, êV~ &W r^ö z îÒº î~ 7 ö *~~² B . V¢B Î-ßj Fæ~º FÒ ²w Îf êV Î~ Ö(coupling)j Ï~² > ®b, .& ÎNf êV ÂK 0.73P j >ÚBæ p º j&; êV z ¸ . Þ, -ÒB Î"º êV Úö ÒB(6º Òå) ¢ ç7 ã«~ ¢Ú¾º >, ¦Ú-ÒB Î"º ²w~º KLM .&öB ²w .& z Îf êV Î Ò~ Öb ¢Ú . 6 -ÒB Î"º op. op. p. p. cr. cr. 1. cr. cr. [8,17]. cr. [7,17]. â 8. KLM¢ * ²w . ²w zj êV Îf ÊV *~ ÷³¢ .. " ³ Bê ÿ·ö & êV {-¶ (round tripj ê~º >, ¦Ú-ÒB Î"º ²w ÎN " ³ Bê ÿ·ö & êV (gain)j ê . V¢B ÂK Îö &~ Ö ÎNj & ~ ÿ ö ã« ¶ j ² ~ Î-ß ÿ·j 'z > ®bæ ÎN ¸f KLM ÿ·j *F > ¦Ú -ÒB Î"¢ J¢ ~, ¢ *Bº Kerr î ³ö B ²w z 5 êV z V¢ êÖ¢ . â 8f KLMj * Z-;~ &; êV öB Kerr îö ÷³>º ²w 2® L" îj 6 º JÏ Þ M ~ ö ~ ²w ¢ ¾æÞ . r ²* z îÒ~ V& Ö;> ²* 2®~ .6Òf *~¢ êÖ > ® . âöB 2®f Þ~ ö ~ .6Ò¢ f ¢ ~ ²* 2®f Kerr î Ú~ ²* z îÒræ~ 7' ^¢ t¢ ~¶. r, ²w 2®~ «Ò ïöB~ ²w z V& 2ω , î Ú¦öB~ z îÒ¢ 2ω ¢ r, ABCD »j Ï~ KLM loss) KLM. 2. p. 0. p. A B = 1 1 – t ⁄ fp C D 0 1. (13). & B . 6 1/q =1/R -j/y , 1/q =(q C+D)/(q A+B)=1/R -j/y æ ²w zj ï2(R =á)¢ &; r, o. o. o. p. o. o. p. t = [ y0 ( yp – y0 ) ]. 1⁄2. 2. 2. , fp = ( y0 + t ) ⁄ t. (14). & B . VB y =nπω / λ, y =mπω / λ, n 5 mf ' ' Kerr î 5 ¶F*~ .j ¾æÞ . r, tº J Ï Þ" z îÒ Ò~ 7' ^ z ¢ ~æ ²w 2®º JÏ Þ 3(M 5 M )~ : ãö *~B ¢ . þö ÒÏB Ar-N ²w .&~ 2Ë λ=514.5 nm, ω =1.1 mm æ ω =10 µm ãÖ t≈f =8.91 cm & Nj r > ® . â 9öº ²w .&~ Kerr îöB~ z V 5 ¦ Ú-ÒB Î"¢ J~V * êV ÂKö & ~ Kerr î Ú¦ *~öB~ z V¢ '' ¾æî . â 9~ (a)¦V Ú¦êV ÂK P<0.73P ¸f ÂK Îö & z Vº ç Ôf ÂK Î~ z V ·, êV ÂK 0.73P Kerr î 7 ¦"öB~ z V& Ã&~V ·j r > ® . Ö"' b P=P öB zf V& æz~æ p ¢; Î * 0. 2 0. 2 p. p. 2. p. 2. 0. p. cr. â 7. (a) M öB 80 cm ÎÚê *~(¢ã >ç ») 5 (b) Kerr î~ 7(Jã >ç »)ö B ÏzB ÂKö ~~º z V. 1. p. 0. cr. cr.
(7) Ó¢^ÔZ-;~ &; .& êV ¢ <º ³ Bê 5 Kerr-2® ºÁnº> . â 9. Kerr î Ú~ *~ö V (a) ²w .& 5 (b) êV ÂK Pö & z V.. 353. â 11. KLMB æª Ò2Ú .&~ ªÊ , *»: 0.1 µs/div. *{»: 10 mV/div.. â 10. (a) Kerr î 7öB n; 2¢zV 8~ æzö V z~ V(j¾ »" ¢ã >ç»)f þöB Î-ß ¢Ú¾º*, (b) ²w .& ÂKö & KLMB æª Ò2Ú . & ÂK(=»" Jã >ç») 5 (c) KLM ¢Ú¾º n; 2¢zV *(ù: j¾ »).. 2N(self-trapping)j r > ® . Kerr î ÚöB ²w" êV z~ V& ·j> ªê ²w ÂKf Ôjæ Ö ÎNf z× ææ, ²w 2®~ .6Òf *~¢ '.® ;~ ²w z~ V¢ êV z~ V · ² ò > ® . 6 P<0.73P ö &, KLM Î~ V º Kerr î ÚöB ³ Bê ÿ· ç ·bæ ¦ Ú-ÒB Î"º ç Î-ß ÿ·j FÒ~² ò . â 10öº K=0.73¢ r n; 2¢zV 8~ æzö &~ Kerr î 7öB zV~ êÖ Ö"(a)f R"N 10% ÂK Þj ÒÏ~ ²w .&~ «Ò ÂKö & KLMB æª Ò2Ú .&~ ï ÂK(b) Ò KLM ¢Ú¾º n; 2¢zV *(c, ù)j '' ¾æî .. þ öB Jê B· Z-;~ &; êV ~ KLM æª Ò2Ú .&öB Î-ß ¢Ú¾º * â 5~ êÖ Ö"f ¾ ¢~j r > ® . 6 [24]. cr. â 12. (a) *S; ¶Úç&ê G; KMLB æª Ò2Ú .& ªÊ 5 (b) Ê¿Þ" >~.. â 10~ (b)¦V KLMB æª Ò2Ú~ ²w ^W8 5 ÂK~ VÞV ÎNf '' 2.8 W 5 16%, 5 W ² w ÂKöB & 550 mW~ ï ÂKj áj > ®î . â 11öº KLMB æª Ò2Ú .&~ ªÊ(pulse train)j J Êz* G;~ ¾æî . âöBf ? ªÊ >f Z-;~ &; êV ^(183 cm)ö &w.
(8) 354. 7²æ B 13² B 4^,. j 8ú. 2002. >º 82 MHz Ö n;B KLMB ªÊ¢ áj > ®î . â 12~ (a)öº KLMB Z-;~ &; æª Ò2 Ú .& êV Úö Ò~º ªÖ·(2N 5 3NªÖ)j .~ ªÊj *V *~ êV~ ã :ö LakL21 Òî~ *Ò¾ 3j ã«~ z~ *Ò¾j Û"~ º ^ 5 *Ò¾ Ò~ Ò¢ '' 3 mm 5 38 cm ~& j r, 0.1 mm vþ~ KDP jF; Ö;j Ï~ ¶Ú B· *S; ¶Úç&ê(interferometric autocorreator) G ; KMLB æª Ò2Ú .& ªÊj ¾æîb, â 12~ (b)öº KMLB æª Ò2Ú .&~ Ê¿ Þ" >~j G;~ ¾æî . â 12~ (a)öB J Êz* G;B ªÊ >~f 0.42 ms J Êz* ç~ ^¢ *S; ¶Úç&êö & æ~ º²¢ Ï~ ~Ö~ 63.5 fs/ms& >Ú B ªÊf £ 27 fs& B . ¾ 7RF ª7V(Ocean Optics Inc., Mo.S1000)¢ Ï ~ G; Ê¿Þ" >~f 7 2Ë 807 nmö &~ 33 nm G;>î, Ê¿Þ"b¦V êÖB æ~-ê (transform-limited) ªÊf 21 fs £*~ N¢ ®. . ©f ªÊ& ÂK Þj Û" r ªÖb ~ â 12~ (a)öBf ? ÆB ¦ªöB chirp ¢Ú¾V r ^, ÂK Þ ö ªÖ çj * *Ò¾ 3j Ï ~ chirp-free ªÊ¢ áj > ® . IV.. Ö . öBº æª Ò2Ú .&ö & Ïê¢ ¸ V *~ v B~ ï Þ, Kerr î æª Ò2 Ú Ö;, Ö;j ~9 ®º v B~ JÏ Þ, . jV 5 *Ò¾ 3 j Ï~ Z-;~ &; .& êV¢ W~ ÂK ÎN ¸ 9f 2Ë&æ 'j < º ³ Bê æª Ò2Ú .&¢ Jê~ B·~& . 6 KLM j Kerr î 5 4-B~ Þ WB Z-; ~ &; êVö &~ ABCD »b æ~>º Ò ÏzB-2¢zV¢ Ï~ ªC~ Kerr-2® Î-ß (KLM)j ¢bÊV * KLM ;ê 5 êV Î V& êV Ú~ *~, Ú¦êV .& ÂK 5 n; 2¢zV ö ~j {~&, ¢ " ~ KLMB æª Ò2Ú .&¢ B·~ ÂK ßW, ªÊ 5 Ê¿Þ" >~ j G;~&b, Ö"¢ º£~ r" ? . (1) ³Bê æª Ò2Ú .&~ ÂKö & VÞV ÎNf 31.3% .& Bê ^W²w ÂKf 290 mW 5 W~ Ar-N ²w .& ÂKö & & 1420 mW~ ï ÂKj áj > ®îb, 2Ë&æ 'f 730 nm~908 nmræ 700 mW ç~ ÂKj & . (2) Z-;~ &; .& êV öB KLM ÿ·ö & n; 2¢zV ' f ³Bê ÿ· ãÖ~ º* z B', KLM ;êº n;'~ &Ë¶Ò ¦"öB &8j < ¢. þ'b { > ®î . (3) Z-;~ &; .& ê Vº ¶Ú-ÒB Î"(self-aperturing effect)ö ~ ²w ÎN" KLM¢ ÿö áj > ®b, ²w ÎN ÿ. ö ÒB ã«ö & ¶ Ôj> FÒ KLM ·ÿ j áj > ®rj {~& . (4) êV Úö *Ò¾ 3j ã«~ ¶Ú ê æj ¢bÊ ³ê ªÖj ç~ B· KLMB æª Ò2Ú .& ÂK~ VÞV ÎN f 16% 5 W ²wöB & 550 mW~ ï ÂKj á j > ®î . 6 7 2Ë 807 nmöB Ê¿Þ" >~ 33 nm ªÊ > 82 MHz 27 fs~ n;B f ª Ê¢ áj > ®î . V¢B Z-;~ &; .& êV ¢ <º ³Bê 5 KLMB æª Ò2Ú .&º ÎN ¸j ö jî¢ £² B· > ®Ú PL, PR, ¢ò 5 *ª ª7 7ö Ïê& ¸j ©b 'B .. 6Ò~ & ¢^f 2000jê .J"&v jö ~ >¯> îb ö 6Ò ãî .. ^^ò [1] P. F. Moulton, “Spectroscopic and laser characteristics of Ti:Al2O3,” J. Opt. Soc. Am. B, vol. 3, no. 1, pp. 125-132, 1986. [2] J. Harrison, A. Finch, D. M. Rines, G. A. Rines, and P. F. Moulton, “Low-threshold, cw, all-soild-stste Ti:Al2O3 laser,” Opt. Lett., vol. 16, no. 8, pp. 581-583, 1991. [3] C. Zimmermann, V. Vuletic, A. Hemmerich, L. Ricci, and T. W. Hansch, “Design for a compact tunable Ti:sapphire laser,” Opt. Lett., vol. 20, no. 3, pp. 297-299, 1995. [4] A. J. Tiffany, I. T. McKinnie, and M. warrington, “Low-threshold, single-frequency, coupled cavity Ti:sapphire laser,” Appl. Opt., vol. 36, no. 21, pp. 4989-4992, 1997. [5] B. Pati and J. Borysow, “Single-mode tunable Ti:sapphire laser over a wide frequency range,” Appl. Opt., vol. 36, no. 36, pp. 9337-9341, 1997. [6] D. E. Spence, P. N. Kean, and W. Sibbett, “60-fsec pulse generation from a self-mode-locked Ti:sapphire laser,” Opt. Lett., vol. 16, no. 1, pp. 42-44, 1991. [7] P. F. Curley, Ch. Spielmann, T. Brabec, F. Krausz, E. Winter, and A. J. Schmidt, “Operation of a femtosecond Ti:sapphire solitary laser in the vicinity of zero group-delay dispersion,” Opt. Lett., vol. 18, no. 1, pp. 54-56, 1992. [8] T. Brabec, Ch. Spielmann, P. F. Curley, and F. Krausz, “Kerr lens mode locking,” Opt. Lett., vol. 18, no. 17, pp. 12921294, 1992. [9] J. L. A. Chilla and O. E. Martinez, “Spatial-temporal analysis of the self-mode-locked Ti: sapphire laser,” J. Opt. Soc. Am. B, vol. 10, no. 4, pp. 638-643, 1993. [10] I. D. Jung, F. X. Kartner, N. Matuscheck, D. H. Sutter, F. Morier-Genoud, G. Zhang, U. Keller, V. Scheuer, M. Tilsch, and T. Tschudi, “Self-starting 6.5-fs pulses from a Ti:sapphire laser,” Opt. Lett., vol. 22, no.13, pp. 1009-1011, 1997. [11] U. Morgner, F. X. Kartner, S. H. Cho, H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Sub-two-cycle pulses from a Kerr-lens mode-locked Ti:sapphire laser,” Opt. Lett., vol..
(9) Ó¢^ÔZ-;~ &; .& êV ¢ <º ³ Bê 5 Kerr-2® ºÁnº> 24, no. 6, pp. 411-413, 1999. [12] D. H. Shutter, G. Steinmeyer, L. Gallmann, N. Matushek, F. Morier-Genoud, and U. Keller, “Semiconductor saturableabsorber mirror assisted Kerr-lens mode-locked Ti:sapphire laser producing pulses in the two-cycle regime,” Opt. Lett., vol. 24, no. 9, pp. 631-633, 1999. , , , “Self-Mode-Locking Ti: [13] Sapphire ,” , 33 5 , pp. 536-543, 1993; , , , , , ,“ ,” , 5 4 , pp. 466-472, 1994; , , , , “Kerr Ti: sapphire 30 fs ,” , 35 6 , pp. 714-719, 1995; , , , , , , “40 ,” , 10 5 , pp. 430-438, 1999; , , , , “Kerr 10 fs ,” , 11 1 , pp. 43-46, 2000. [14] T. Brabec, Ch. Spielmann, P. E. Curley, and F. krausz, “Limits of pulse shortening in solitary lasers,” Opt. Lett., vol. 17, no. 10, pp. 748-750, 1992. [15] C.-P. Huang, M. T. Asaki, S. Backus, M. M. Murnane, and H. C. Kapteyn, “17-fs pulses from a self-mode-locked Ti: sapphire laser,” Opt. Lett., vol. 17, no. 18, pp. 1289-1291, 1992. [16] Kuei-Huei Lin and Wen-Feng Hsieh, “Analytical design of symmetrical Kerr-lens mode-locking laser cavities,” J. Opt.. º fÏï f× j Ï .&~ . ªÊ B îbÒ B ² ^ ;«& ¢; c^ ªÏ Ò; Ë&W æª Ò2Ú .&~ ¶ÚÎßö ~ . ªÊ~ B 7²æ B ² ^ NÏ^ ;'¢ Îc îbÒ 2® ÎßB .&öB ~~ . ªÊ B îbÒ B ² ^ ªÏ 'Æ V" f& Ò; Ë&W ÎÆ. ò ª Ê~ ÂK 2Ë&æ æª Ò2Ú .& 7 ²æ B ² ^ sã NÏ^ ; '¢ Îc 2® ÎßB æª Ò2Ú . &öB ~ ªÊ~ B 7²æ B ² ^. 355. Soc. Am. B, vol. 11, no. 5, pp. 737-741, 1994. [17] D. Georgiev, J. Herrmann, and U. Stamm, “Cavity design for optimum nonlinear absorption in Kerr-lens mode-locked solid-state lasers,” Opt. Commun., vol. 92, no. 4-6, pp. 368375, 1992. [18] Vittorio Magni, Giulio Cerullo, and Sandro De Silvestri, “Closed form gussian beam analysis of resonators containing a Kerr medium for femtosecond laser,” Opt. Commun., vol. 101, no. 5-6, pp. 365-370, 1993. [19] Hermann A. Haus, James G. Fujimoto, and Erich P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron., vol. 28, no. 10, pp. 2086-2096, 1992. [20] D. Huang, M. Ulman, L. H. Acioli, H. A. Haus, and J. G. Fujimoto, “Self-focusing-induced saturable loss for laser mode locking,” Opt. Lett., vol. 17, no. 7, pp. 511-513, 1992. [21] H. W. Kogelnik, E. P. Ippen, A. Dienes, and C. V. Shank, “Astigmatically compensated cavities for cw dye laser,” IEEE J. Quantumn Electron., vol. QE-8, no. 3, pp. 373-379, 1972. [22] R. L. Fork, O. E. Martinez, and J. P. Gordon, “Negative dispersion using pairs of prisms,” Opt. Lett., vol. 9, no. 5, pp. 150-152, 1984. [23] B. E. Lemoff and C. P. J. Barty, “Cubic-phase-free dispersion compensation in solid-stste ultrashort-pulse lasers,” Opt. Lett., vol. 18, no. 1, pp. 57-59, 1993. [24] F. Krausz, E. Winter, A. J. Schmidt, and A. Dienes, “Continuous wave thin plate Nd:glass laser,” IEEE J. Quantum Electron., vol. 26, no. 1, pp. 158-168, 1990.. Design and operational characteristics of cw and KLM Ti:sapphire lasers with a symmetric Z-type cavity configuration Han Tae Choo†, Bum Soo Ahn, Gyu Ug Kim, and Tae Dong Lee School of Natural Science, Kumoh National Institute of Technology, Kumi 730-701, KOREA † E-mail: [email protected]. Byoung Won Yoon Superconductor Group, Korea Research Institute of Standards and Science, Daejon 305-600, KOREA. (Received April 25, 2002, Revised manuscript received June 10, 2002). We have constructed a high efficiency and broad tunable cw Ti:sapphire laser with a four-mirror symmetric Z-type laser cavity to increase the laser usability. From theoretical analyses and experimental data for a symmetric Z-type laser cavity containing a Kerr medium, the cavity mode size and the Kerr-lens mode-locking (KLM) strength for KLM lasers can be confirmed as function of the position in the cavity, the intracavity laser power, and the stability parameter. As a result, the slope efficiency and the maximum average output power of cw Ti:sapphire laser at 5 W pumping power of Ar-ion laser were 31.3% and 1420 mW respectively. The tunablility was ranged from 730 nm to 908 nm with average output power above 700 mW. We obtained the KLM operation easily by self-aperturing effect in the Kerr medium and the slope efficiency and the maximum average output power of KLM Ti:sapphire laser was 16% and 550 mW respectively. The spectral bandwidth was 33 nm at the center wavelength of 807 nm and the pulse width was 27 fs with a repetition rate of 82 MHz. Classification codes: LO.070, LO.080, LO.090..
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