TAP CHI KHOA HOC & CONG NGHE I j ^ ™?!'.P_^^j.".'jf:£H'_™
Journal of Science and Technology 4(13) (2014) 8-13
Tao xung anh sang trang bang laser femto giay va scJi quang tinh the
Supercontinuum Generation by Femtosecond Laser and Photonic Crystal Fiber
Biii Yen D u y ^ Huynh Ngoc Linh PhlIc^ng^ Nguyen Thi Thu Ngan^, Le Cong Nhan^
Nguyin Ngoc Hieu^
"Dai hoc Sai Gon, 273 An Duong Vuong. Thanh phd Hd Chi Minh, Viet Nam Sai Gon University, 273 An Duong Vuong street. Ho Chi Minh city. Vietnam ''Vien Nghiin ciiu vd Phdl trien Cong nghe cao. Dai hoc Duy Tan, K7/25 Quang Trung. Da Nang Viet Nam
Institute of Research and Development, Duy Tan University, K7/25 Quang Trung street. Da Nang Vietnam
Tom tat
Xung anh sang irSng da duoc lao ra bang each phong lia laser femto giay vao sdi quang linh the. NhiJ vao cau triic mitrf met cua .sdi, xung la.serdu'dc nen trong mot tiel dien nho gay nen hien lUdng m^ rong pho thanh xung anh sang trang Ihon^
qua hang loat cac hieu iJng quang hoc phi tuyen bae ba nhU: tu bien dieu pha, biln dieu cheo pha, Iron lan bon birdc sonE tan xa Raman cam ling-.Trong bai bao nay, chiing toi Irinh bay ket qua thf nghiem va nhOng chi tiet ki thuat lien quandef qui trinh lao xung anh sang tring.
Tii khoa: Anh sang tring, laser femto giay, sdi quang tinh the Abstract
Supercontinuum pulse are produced in photonic crystal fibers under femtosecond laser injection. Thank to the microstruc- tured silica of fiber, laser pulses are compressed in a small section leading to uttrabroad spectra of light, which is called supercontinuum. through a series of third-order nonlinear effects such as: self phase modulation, cross phase modulation, four-wave mixing, stimulated Raman scattering... In this paper, we present experimental results and the technical details related to the process of creating supercontinuum pulse.
Keywords: Supercontinuum, femtosecond laser, photonic crystal fiber
©2014 Ban quyen thuoc Dai hoc Duy Tin
1. Gidi thieu mdi u-udng phi tuyen. Trong khoang 30 nam trS lai day, sU phat trien manh me cua laser femto Hien tUdng md rong pho ciia chiim tia laser, 8'3y [21 da cho ra cac xung laser vdi cong sual tiJt nguon sang gkn nhU dan sac thanh nguon '^'"'^ ^at Idn nen cac hien lUdng quang hoc phi sang trang (supercontinum: SC), da dUdc quan ^"y^" <^i^dc tao ra mot each de dang hdn. Hien sat lan dau tien trong mdi trUdng niidc vao nam "^y- nguon anh sang trang d dang xung ciic ngan 1970 [1]. Hieu ling vat ly nay la ket qua cua <5^dc ling dung ritnhieu trong cac kl thuat quaiij sir tUdng tac gitia mot cudng do laser manh vdi pho, y sinh, xut ly hinh anh... [3]. Su phat trier
£mai7j;lcnliaiiayalioo.fr(Le Cong Nhan), h i e u i m « d u y t a n . e d u . v i i (Nguyen Ngoc Hieu)
Bui Yen Duy va cang su/ Tap chi Khoa hpc vd Cong nghe - Dai hpc Duy Tan 4(13) (2014) 8-13 cua cac sdi quang hoc tinh the (Photonic Crystel
Fibers: PCF) [4], til nam 1996, da md ra hUdng mdi cho viec phat trien cac nguon sang SC. Diem dac biet d PCF la cac yeu t6 tan s5c va phi tuyin cd the diSu chinh dUdc thong qua each thiet ke cau true ciia sdi. Tinh chat nay cho phep tao ra SC blng nhiing nguon laser cong suat thap. Tao xung anh sang trang la mot qua trinh phiic hdp gifla cac y^u td tan sac va nhieu higu ting quang hoc phi tuySn, cd nguon goc phi tuyen bae ba, nhU:
tu bien dieu pha, bien dieu cheo pha, tron bon song, tan xa cam ling Raman, hien tUdng soli- ton... [1, 5, 6]. Su phiJc hdp cac hieu ling quang hoc nay gSy ra sif md rong pho cue Idn, cd the len tr^n 1000 nm. Vat lieu tao ra sdi PCF thudng la thuy tinh hoac thuy tinh pha tap nen mdi trUdng cd tfnh d^ng hudng, vi vay, hau nhif khdng cd su tham gia cua cac hidu ling quang phi tuyen bae hai. Tuy vao mtic dfch ting dung ma cac yeu clu ve tinh chat cua xung anh sang trang cd the khac nhau. T\iy nhien, phan Idn cac yeu clu dat ra cho xung anh sang trSng la pho phai rong, hinh dang pho phai on djnh, dp thang giang ve cUdng do phai toi thieu... Viec tao ra cac xung anh sang trSng bang sdi PCF vdi cac tinh chat vat ly cd the kiem soat dUdc la van con nhieu van de can nghien ciiu, ca iy thuyet lan thUc nghiem [5].
Tren the gidi, hiTdng nghien ciiu ve SC tao bdi PCF dUdc phat trien manh tif nam 1996 sau khi sdi PCF ra ddi. Hien nay, nhdm diing dau trong hirdng nghien ciiu nay dUdc di6u hanh bdi GS. J.
M. Dudly, Dai hoc Franche - Comte [5,6]. Ngoai ra con cd mot so trung tam chuy6n nghien cii!u va san xuat sdi PCF, vi du nhu trung tam nghien ciiu Xlim, dai hpc Limoge.
6 Viet Nam, cd the do con han che ve thiet bj thi nghiem nen chUa cd nhdm nao nghien ciiu ve SC tao bdi PCF mac du dSy la mot lanh vuc rat dtfdc quan tam bdi cpng ddng quang hpc tren th6 gidi trong suot ba thap ki qua. Chinh vi vay ma ngoai muc dfch gidi thieu kt thuat tao anh sang trang dang xung cue ngan, bai bao nay con hUdng den pho bien kien thiJc v^ laser femto giay va sdi PCF.
2. Laser va dac diem cua laser xung ngan Laser (Light Amplification by Stimulated Emission of Radiation) boat dong dUa tren nguyen ly khuylch dai cudng dp anh sang nhd vao hien titdng phat xa cam ling. Hien tUdng nay da dUdc Albert Einstein dUa ra gia thuyet va dang tren tap chi Physikalische Zeitschrift vao nam 1917. Tuy nhien de quan sat diidc bang thUc nghiem thi phai chd tdi sit phat minh, vao nhiing nam 1954 -1955, cua cac nha vSt li ngUdi Nga (Basov, Prokhnov) va ngUdi MT (Towns). Ho da che tao ra nhflng may khuyen dai sdng dien tCt dau tien vdi mdi trUdng boat tfnh la khf amo- niac NH4. Do cac may nay phat sdng dien tC(
vdi budc sdng cd pm nen thdi do difdc gpi ten la MASER (Microwave Amplification by Stimu- lated Emission of Radiation). Mac dij v$y, laser dau tien ra ddi khong phai do hp che tao ma la T. Maiman, nha vat li ngUdi MI, lam viec tai vien nghien ciiu Hughes. Vao nam 1960, Maiman da tao ra may laser dau tien, sii dung mdi trUdng boat tinh la chit ran Ruby, phat sdng anh sang trong vung quang pho kha kien 0,69 /im. Tii nam 1960 trd di, hang loat laser khac nhau da ra ddi.
De ddn gian trong each gpi ten, chung thUdng dupe phan chia theo nhdm dUa vao tfnh chat vat If ciia mdi trUdng boat tfnh: ran, long, khf, ban dSn, sdi quang hpc... Hoac dua vao phUdng phap kfch thi'ch: quang hpc, hoa hpc, dien... Hoac dUa vao dac tfnh biic xa laser (ddng anh sang phat ra): lien tuc hay xung. Trong each phan chia cuoi cung, hai nhdm laser nay co mot su khac biet rat Idn v6 mat cong suat. Laser xung thudng cd cong suat trung binh thap hdn so vdi laser lien tuc, nhung cong suat dinh cua mdi xung la rat cao. Bdi vi toan bp nang lUdng cua xung chi tap trung trong mot khoang thdi gian ngan. Vi du nhif trtfdng hdp laser femto giay, chi can mot nang lUdng xung rat be vao khoang 1 ;/J va thdi gian xung khoang 50 fs thi cong suSt dinh ciia xung len tdi 20 GW. Nhd dp Idn ciia cong suat dinh nen viec tao ra cac hien tUdng quang hpc phi tuyen hay tham chi mdi trUdng plasma la ral d6 doi vdi laser xung. Ben canh dd, cong suat trung binh thap cija laser xung ciing la mot ldi thi nfla, no cho phep tranh dUdc cac hieu ting nhiet. Can lUu y them mot diem khac biet niia v6 tfnh chat pho
Bui Yen Duy vd cpng sU/Tap chi Khoa hpc vd Cong nghe - Dai hoc Duy Tan 4(13) (2014) 8-13
giiia laser lien tuc va laser xung ngan, nSu nhU pho cua laser lien tuc la ddn dc thi pho ciia laser xung ngin luon cd mot dp rong nhat dinh. Thdi gian xung va dp rong pho cd sU lien he vdi nhau thong qua nguyen ly bat djnh vS thdi gian - nang lUdng, ArAv> 1/2 [2]. Nhu vay, deed the tao ra nhiing xung cang ngan thi dp rong pho phai cang Idn.
Hinh 1. Anh chup mat ck ngang cua sdi PCF bang kinh hien vi dien ifi. (a) sdi phi ludng chiel, (b) sdi lir<3ng chiet.
Vat lieu Silica ditdc hien thi bang mau xam con cac \6 khong khi thi dUdc hien thi bang mau den.
3. Sdi quang tinh the
Sdi quang tinh the (Photonic Cristal Fiber:
PCF), sdi quang cd cau trdc micro hay sdi quang • cd cau triic 16... la nhiJng ten gpi danh cho nhdm cac sdi quang dUdc che tao dUa tren sU sap xep tuan hoan: cau triic Id trdng micro met bao bpc bdi silica (thuy tinh). Cach sap x6p nay cho phep nen anh sang trong cau triic ciia sdi va dan truyen anh sang trong ldi silica (sdi quang vdi ldi chiet suat cao) hay dan truyen anh sang trong ldi khdng khf (sdi quang vdi ldi chiet suat thap) [I, 4-6], Trong nghien ciiu nay, chiing tdi s^ dung cac loai sdi PCF dUdc cung cip bdi phong thi nghiem Xlim cua Dai hpc Limoge va nhdm nghien ciiu ciia Dai hpc Franche - Comte, cpng hoa Phap.
DSy la cac loai sdi cd ldi chiSt suit cao, dUdc che tao bang each tap hdp cac 6ng thuy tinh lai thanh bd rdi ket hdp nung - keo vdi di6u kien nhiet dp nung va loc dp keo ludn on dinh [1], CSu true mat cat ngang cua cac sdi PCF nay dUdc trinh bay tren hinh 1. Sdi thii nhSt cd cau triic loi ddi xiing (a), edn sdi thii hai thi cd cau triic ldi bat ddi xiing (b). Dac diem nay cho phep sdi PCF thii nhat khong cd U'nh ludng chiet con sdi PCF thii hai thi cd tinh Ittdng chilt, nhd vao sU bat
doi xiing ve chiet suat do yeu to hinh hpc gay ra.
Hai kieu sdi PCF nay dai dien cho hai the loai dac trUng nhat cua cac sdi PCF ma ta thUdng gap tren thi trUdng sdi quang phi tuySn. Ph^n than cua sai la mot mang ludi tuan hoan micro met gom cac 16 trong chiia khdng khf dUdc bao bpc bdi thiiy tinh, la vat lieu phi kim cd tfnh dang hUdng. 0 giiia phan than xuat hien mot ldi pha vd trat tif tain hoan, vi trf nay ddng vai tro loi cua PCF.
Sdi PCF phi ludng chiet cd mot loi tron dUcfc bao bpc bdi nhiing 16 khdng khf cd dudng kinh trung binh d = 1,8 fim. Cac lo trong nay nim each nhau mot bUdc trung binh khoang A = 2,26 fim. NhU vay, ty le d/A la 0,796. Ty le nay cd nghia ring dp phi tuy6n cua sdi la cao va siJ din truySn sang cd tinh chSt lUdng mode [7]. Sdi PCF nay cd hai mode truyen sang d ldi: mode cd ban LpQ] va mode bae nhSt LP] |. Ddi vdi mode cd ban LFQI. cUdng dp sang phan bd theo khong gian cd dang gan vdi phan bo Gauss, con mode bae nhat L/*n thi lai cd sU phan bo cUdng do theo dang hai Gauss. Dudng tan sac ciia modecd ban cd mot gia tri tan sac bang khdng (zero dis- persion wavelength: ZDW) tai 814 nm, trong khi dudng tan sac ciia mode bae nhat lay hai gia tri ZDW tai 650 nm va 1050 nm. Dieu do lam xuat hien hai vung pho ma d dd PCF cd tan sac binh thudng. Cau triic tan sac nay cho phep tao ra cac sdng tan sac trong vCing kha kiln va trong viing hong ngoai neu bdm bang xung laser co bUdc sdng nam trong viang tan sac bat binh thUdng cua sdi PCF [8]. Trong trudng hdp nay, su md rong pho la hieu qua hdn bdi cd sU tUdng tac vdi soliton [5, 6, 8], dUdc hinh thanh trong viang tan sac bat thudng, cho phep cac sdng tan sac m6 rong ve phfa vung budc sdng ngan va vijng bUdc sdng dai. Ngoai vkn de din truyen sdng trong loi, mot s6 vi tri tren vach ngan ciia than sdi ciing co the truy6n sang vdi cung nguyen h', truyin sang bdi khiic xa toan phan. Trong trUdng hdp nay, cac vach ngan ddng vai tro la ldi con cac thanh phan xung quanh ddng vai trd la than. SiJ ih truyen anh sang trong cac vach ngan thudng la ddn mode bdi dudng kfnh cua vach ngan la du nhd. Can luu y la chi nhflng vach ngan cd dildng kinh Idn hdn budc sdng anh sang dupe dan truyen mdi cd kha nang nay.
Bui Yen Dityvd cpng sU/Tap chi Khoa hpc vd Cong nghe - Dai hoc Duy Tan 4(13) (2014) 8-13 Sdi PCF ludng chiet cd loi hinh eli'p dUdc bao
bpc bdi hai Id khong khf Idn, dUdng kfnh lan lUdt la 3,3 va 3,6 ^im. Phan than la mot mang ludi tuSn hoan cac Id nho cd dUdng kinh trung binh d = l,S fim vdi khoang each giiia cac 16 la A = 2,6 fim. Ty le d/A la 0,71. SU khac biet ve dudng kfnh ciia hai Id Idn ben canh ldi lam gia tang tfnh chit lUdng chiSt ciia ldi elfp. Dp lUdng chiet vl pha va ve nhdm lan lUdt la B^ = 2.10"^
va B^ = 3.10"^, dieu nay dan tdi mot sU phu thudc manh vao tfnh chat tan sac theo true cua PCF. Phan ldi cd the dSn truyen anh sang bang bon mode: hai mode co ban LPQ\x,LPo\y va hai mode bae nhltLPiijt. LP\iy Vi tri ZDW ciia bon mode nay lan lUdt nam d cac bUdc sdng 827,866, 757, 764 nm [12]. (3 day, x va y lan lUdt la U-uc nhanh va true cham ciia sdi PCF. Dien tich thUc ciia mode cd ban dUdc Udc tinh la 4,9/im^ doi vdi btidc sdng 850 nm, va 5,3;im^ cho bUdc sdng 1064 nm [12]. Uu diem cua sdi PCF lUdng chiet la kha nang bao toan tinh phan cite anh sang hoac tao ra SC phan cue thang [9-11 ]. TUdng tu nhu sdi PCF phi lUdng chiet, cac vach ngan cua than cung cd the dSn truyen anh sang. NhU vay viec tao SC vdi sdi PCF ludng chiet cung cd the thUc hien dUdc d trong phan than cua sdi.
Doi vdi tat ca cac mode dSn truyin trong hai loai PCF nay, cac dUdng tan sac cd ZDW tap trung xung quanh bUde sdng 800 nm. NhU vay, sU md rong pho ciia SC se hieu qua neu nhi/ PCF dUdc bdm bdi nhiing xung laser cd ban cd bUdc sdng d lan can va idn hdn 800 nm. Nghia la phai bdm trong viing tan sac bat binh thudng, ndi ma thudng cd hien tUdng soliton xuit hien nhd sU lan truyen cua cac budc sdng ngan nhanh hdn ciia cac budc sdng dai.
4. Thi nghiem tao xung anh sang trang bang laser femto giay va sdi quang tinh the
Thi nghiem tao xung anh sang trang bang laser femto giay va sdi quang tinh the da dUdc chiing tdi trien khai tai Vien Vat ly va Hoa hpc Vlit Ii6u d Strasbourg, cpng hoa Phap (hinh 2).
Trong thi nghiem nay, sdi PCF co chieu dai 6 mm dupe dat trong mot ranh nhd cua de sat va dupe giii bdi mot mSu nam cham dat phfa tren.
Viec phdng tia laser vao sdi PCF dUdc thUc hien thong qua mot dau kfnh hien vi, cd dp phdng dai 60X. "Riy nhien, theo khao sat blng thUc nghifem ciia chiing ldi thi than kfnh hien vi cd dd phdng dai trong khoang tfl 28X den 40X la toi Uu nhat.
Dau kfnh hien vi dupc dat tren mot he thong dich chuyen XYZ. Cdng suat laser phdng vao sdi PCF la 60 mW, bUdc sdng trung tam la 840 nm, nam d viing pho hong ngoai gan. Ong vdi tSn so xung la 27 Hz thi nang lUdng xung vao cd 2,2 nJ. Trong thUc te, viec mat mat nang lUdng do phan xa tai ht mat phan each d dau vao la rat cao, thUdng len tdi 50\% , nen nang lUdng di vao sdi PCF ehi khoang 1,1 nJ. Ci dau ra, be mat sdi PCF ddng vai trd nhu mot nguon sang diem nen anh sang ciia SC phat ra dudi dang sdng cau. Cac sdng cau nay dupe chuyen thanh sdng phang bdi mot gUdng cSu cd lieu cU 2 cm dat phfa sau d5u ra cua sdi PCF. Hinh anh SC dUdc hiing tren man cho ta thay anh sang cua viang kha kien. NhU vay, su tUdng tac giCa xung laser ya sdi PCF da md rong pho tii hong ngoai xuong kha kien.
Hinh 2. Tao xung anh sang trang bang each phong tia laser femto giay vao sdi quang tinh the.
Ve mat nguyen ly, chiing tdi minh hoa thf nghiem tao SC bSng PCF tren hinh 3. Xung laser cd ban, cd pho hep vdi hudng phan ciic dUdc kiem soat bang ban niia budc sdng, dUdc dUa vao sdi PCF bang dau hdi tu cua than ki'nh hien vi.
Nhd cau triic micro met cua PCF, nang lUdng dUdc nen trong mot tiet dien cd vai ^m^. Do vay, mat dp nang lUdng trd nen rat cao va dUdc giam gifl trong cSu triic cua sdi PCF trong qua trinh lan
Bui Yen Duy vd cpng su/Tap chi Khoa hpc vd Cong nghe - Dai hpc Duy Tan 4(13) (2014) 8-13 truyen. Mat dp nang lUdng cao va dUde duy tri
trong qua trinh lan truyen lam gia tang cac tiTdng tac phi myen gay ra sU md rong pho [5,6]. Day la diem khac biet so vdi phUdng phap truyen thong, tao SC bang each hoi tu chiim laser vao cac mdi trUdng phi tuyIn bae ba, cac mdi trUdng nay cd the la chat ran, chat long hoac chat khi...[l]. Sau diem hdi tu, chum laser bi phan ky nen mat do quang hpc khdng con du cao cho viec duy tri cac hieu ling phi tuyen gay md rong pho. Chfnh vi vay, thf nghiem tao SC bang phUdng phap truyen thdng phai cin tdi nhiing he laser khuech dai cd cdng suat cao, con vdi sdi PCF thi chi can mot buong cdng hUdng cdng suSt nhd la du nang lifdng [3].
cd, nhiet... De cd the phdng tia laser vao sdi PCT thi budc diu tien la dieu chinh theo phUdng Z, diem hoi tu sau thau kfnh phai rdi diing be mat ciia sdi PCF. Sau day la dieu chinh hai phUtJng X, Y de tia laser diidc phong vao ldi. Vi6c dieu chinh vi trf d§u vao cd the quan sat dUdc trUc tiep nhi lap them he thdng phdng dai anh trudc scli PCF, hinh 3. Vdi he thong nay, vj trf dau vao ciia xung laser hoan toan dUdc kiem soat. Dieu nay cho phep quySt djnh viec tao SC vdi loi sdi hay vdi vach ngan. Ngoai ra, trong trudng hdp chieu xung laser cd ban vao loi PCF thi ta ciing kilm soat dupc van de tao SC, vdi mode ed ban hay vdi mode bae nhat. Hinh 4 trinh bay hai mode tao b3i sdi quang phi ludng chiet (A), va hai mode tao bdi sdi quang ludng chiet (B).
s
M,•u>^i
Hmh 3. Sd do lao xung anh sang trdng bang each bdm xung laser vao s^i PCF. W, va M2 la cac gUdng, ,t/2 la ban nfla budc sdng, 28X la thau kfnh hien vi, XYZ la true djch chuyen theo ba chilu, PCF la sdi quang tinh the.
Ve van de an toan, can lUu y ring laser xung ngan dUdc xep vao hang nguy hiem bae 4, la hang nguy hiem nhat, dac biet doi vdi mat. Vi vay ngUdi lam thuc nghiem phai ludn mang kinh bao hp va quan sat tia laser qua cac hnh kifin nhU: camera hong ngoai, giiy huynh quang h^p thu hai photon... Trong thf nghiem nay, chiing tdi quan sat tin hieu, de thUc hien cac thao tac dieu chinh, qua man hinh cua may tinh bang, bdi cam- era ciia may tfnh bang cd dp nhay cao trong viing pho hong ngoai gan.
Ve mat ky thuat, viec dUa xung laser vao dau cua sdi PCF la mot budc thao tac rat nhay cam. Vi cau triic ciia ldi PCF la r^t nhd, vao cd I - 2 pm, nen viec dUa xung laser vao phai dUdc thiet ke tren mot he thong on djnh, cd dp dich chuyen dUdi 0,5 fim va iranh dupc cac dao dong
Hinh 4. Su phan bo ctfiJng do iheo khong gian ciia cac mode khac nhau. (A) Hai mode tao bdi sdi quang phi lu9iig chiet, (B) hai mode tao b3i sdi quang lirflng chiet.
Tit ket qua hinh 4, ta nhan thay rang sU phan bo SC theo khdng gian phu thuoc ca vao dang hinh hpc cua ldi lin bsic cua mode dUn truyen.
Trong trUdng hdp dan truyen bang mode bSc nhit thi cUdng dp sang SC dupc phan bo theo hai ham Gauss. DiSu nay the hien rat ro trong hinh chup vdi su giam cudng dp sang cua vi tri dUdng trung tSm.
5. Ket luan
Trong nghien cflu nay chiing toi da xay diing thi nghiem phdng tia laser femto giay vao scfi PCF va da tao thanh cdng xung anh sang trang.
Chiing tdi da phan tich vai tro cau triic cua sdi PCF va tfnh chat tan sac ciia mode dSn truyen (dac biet la vi tri ZDW) trong viec duy U-i cac hieu ling phi tuyen. De cd the tao dildc SC thi budc sdng cua laser phai nam trong viing tan sac bat thudng hoac tai vi tri ISn cSn vdi ZDW.
Ve thao tac ky thuat, chung toi da dua ra sd dc
Biii Yen Duy vd cpng su / Tap chi Khoa hpc vd Cong nghe - Dai hoc Duy Tan 4(13) (2014) 8-13 nguyen ly cung vdi qui trinh phdng tia laser vao
ldi sdi PCF, nham dam bao an toan thf nghiem va han che nhflng khd khan do dp nhay cd hpc gay
l^i lieu tham khao
[1] G.P Agrawal, Nonlinear Fiber Optics, Academic Press, San Diego. 2(K)1.
[2] C. Rulliere, Femtosecond Laser Pulses, Springer, Berlin, 2010.
[3] J. Leonard, N.Lecong, J.P Likforman, O. Cregut. S.
Haacke, P.Viaie, P. Leproux, and V.Couderc, Broad- band ultrafkst spectroscopy using a photonic crystal fiber: application to the photophysics of malachite green. Optics express, 15 (2007) 1624-1629.
[4] P. Russell, Photonic crystal fibers, Science, 299 (2003) 358-362.
[5] J. M. Dudley, G. Genty, and S. Coen, Supereontin- uum generation in photonic crystal fiber, Rev. Mod.
Phys. 78 (2006) 1135-1184.
[6] J. M. Dudly, J.R. Taylor, Supercontinuum generation in optical fibers, Cambridge University Press, Cam- bridge, 2010.
[7] R. K. Sinha and S. K. Varshney, Dispersion proper- ties of photonic crystal fibers. Opt. Lett. 37 (2003) 129-132.
[8] J. K. Ranka, R. S, Windeler, and A. J. Stentz, Visi- ble continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 8(M) nm.
Opt, Lett. 25 (2000) 25-27.
[9] A Ortigosa-Blanch, J. C. Knight, W. J. Wadsworth, J. Arriaga, B. J. Mangan, T. A. Birks. and P St. J.
Russell, Highly birefringent photonic crystal fibers.
Opt. Lett. 25 (2000) 1325-1327.
[10] T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knud- sen. A. BJarklev. J. R. Jensen, and H. Simonsen, Highly birefringent index-guiding photonic crystal fibers. IEEE Photonics Techno!. Lett. 13 (2001) 588- 590.
[11] K. Suzuki, H. Kubota, S. Kawanishi, M. Tanaka.
and M. Fujila. Optical properties of a low-loss polarization-maintaining photonic crystal fiber. Opt.
Exp. 9(2001)676-680.
[12] J. P. Diez, Single-pulsed supercontiuum generation in millimeter pieces of a birefringent microstruc- tured silica fiber under femtosecond laser injection.
Master Thesis in Photonics, Escola Tescnica Super- rior d'Enginyeria de Telecomunicaeio' de Barcelona, 2009.
