Vai trò của hiệu ứng tạo hốc và sự phụ thuộc thời gian trong hoạt động của LASER chứa vật liệu hấp thụ bão hoà

Trong ban luan an nay, chung toi sU dung gan dung h^ phUdng trinh toe dg de nghien ciju hoat dpng cua LSA vdi buong cong hUdng Pabry-perot co do md rong khong dong nhat la chu yeu.. Cac

Bo giao due va dao tao Truong dai lipc Tong hap Ha ncn

vO TUAN LAM

I T R O CUA HIEU UNG TAO HOC VA SU PHU THUQC

HOI G I A N T R O N G H O A T D Q N G CUA LASER CHUA

VAT LIEU HAP THU BAO HOA

Cluiyen nglianh : Quaiig lioc

Ma hieii : 1.02.18

Liian an Pho tien si khoa hoc Toan-Ly

tJgirai liunng dhn klioa hoc : Pho giao su Tien sT

Dinli Viin Iloang

lla no! - 1993 ^

Myc Lvc

Trang

Md dau ^ Childng I: Anh hUdng cua hi|u -ing t^c hoc trong LSA vdi 5

buong c^ng hUdng Fabry-Perot va hi^n tUtpng liidng on c^nh quar^g Y.QC

.1- Hi^n t\10n£ lUdng on dinh guang hgc va cac hi^u Ung 5

vat ly phi tuyen trong LSA

ChUdng II: Cac d^c trUng cua LSA vdi buong cgng huong IS

Fabry-Perot 1- Ke phtiong trlnh cd ban 1^'

2 - Anh hUdng cua hi^u ilng t^c hoc trong ho^t cipng ddn 23

mode cua laser

2.1- D|LC trUng ciidng dq) mode 24

2.1.1- Toe d^ bdm nang lU';;^ng d hai ngan la khiong dbi 25

2.1.2- Toe dr- bdiL nang luv^n£ ngan khuyech d^,i hhong 25

o »i." i.-'ac "crun^ c u c n g u-^ iriooe

0.1, j ^ iGC: Gp odrn r^ang lU^jng o n a i n ^ a r , a-a jiriong G^^'J

3.2.2- Toe dp bdir, nang lUgng ngan khuyech d^i khong 51

•deu

3.3- D6 rgng' cua trUdng laser biie x^ 53

GhUdng III: Ki^n tuging hon lo^in quang trong ho^t dpng 58

khong d^ahg cua LSA 3.1- Ho^t deng khong dung cua h^ LSA trong che dg ddn SI

MO ^"'- u r\ u

Trong nhUng nam gan day, trong llnh vrlc nghien CLIU ve laser, cac nha khoa hoc chu y nhieu den laser co chUa v|Lt li^u hap thu bao hoa ( laser with saturable absorber, viet tat la LSA ) LSA ra ddi t\i nhUng nam 60 cua thap ky nay A.SZOKE [ 116 1 la ngudi dau tien da phat hien ra hieu <ing,

phi tuyen ludng on dinh quang hoc ( Optical bistability viet tat la OB ), Tu do mdt hu6ng ung dyng mdi trong quang hoc phi tuven ra deli Cac cong trinh nghien ciju ve LSA xuat hien ngay cang nhieu nham muc dich giai thich va khai thac cac tinh chat vat ly ly thu cua loai laser nay Vdi LSA ngxJdi ta con tim ra nhieu hi^u ung phi tuyen khac : hon loan quang '' chaos ') , phan nhanh ( bifurcation i, tao xung c\lc ngan -

-Co ba phiiong phap Ly thuyer- chinh de i;iai quvet bai toan quang hvc cua LSA

Phudng phap thU nhat la phudng phap ban co ciien Trong phUdns pha.p nay tr^idng dUoc xem la trudng co dien tuan theo cac phudng trinh dien dong lUc Maxwell, con he nguyen tu cua moi tri.tdng tuan theo cac nguyen ly cua cd hoc lUdng tU Saloma va Stenhom [107,108] cung mot so tac gia khac [32,331 da sU dung phUdng phap Lamb trong trUdng yeu vcJi laser co md rong khong dong nhat trong hoat dong cua ddn mode

PhUdng phap thU hai de giai bai toan LSA la phUdng phap lugng tu Trong phUdng phap nay ca trUdng va h^ nguyen tU

^6i truSng deu tuan theo cac nguyen ly cua cd hpc lU<Jng tU, Lugiato va Mandel [84] da bUdc dau nghien c{iu he LSA v6i moi trUdng md rgng dong nhathoat dong d che do ddn mode bang phUdng phap lu^ng tU

PhUdng phap thU ba dUdc nghien cUu la DhUdng phap gan dung he phudng trinh toe do Cac tae gia [10-13] xay dUng cac phUdng trinh mo ta sU thay doi theo thdi gian so photon

trong buong cgng hudng, sU thay doi hieu tich luy d cac mUc nang lUdng trong cac moi trUdng khuech dai va hap thu theo cac thong so cua moi trudng nhu : bdm khuech dai, he so tich thoat, do md rong vach nguyen tU

De xay dung he phudng trinh toe do ngUdi ta thUcJng sU dun.g hai phUdng phap khac nhau : true tiep hoi=LC gian tiep PhUdng phap trUe tiep la xac dinh phUdng trinh tren ed sd nhUng qua trinh vat ly anh hUdng den sU bien doi eua moi trudng phi tuyen va anh sang RoLand va MuLLer [97]

va cae tac gia da sU dung phUdng phap nay khi nghien cilu Laser da mode vdi md rong dong nhat PhUdng phap suv ,gan dung til he cac phudng trinh la phUdng phap xac dinh phudng trinh tec d$ mgt each gian tiep, d trUdng hOv nay no nhU mot cong :*u de cu r.he hoa ly thuyet Tren cd sd ba phUdng phap nay nhieu tac gia da nghien cUu sU sU hoat dong cua LSA vdi mo hinh 2 mUc hay 4 mue nang lueng eho cac ngan khuyech ilai va hap thu voi buong cong hUdng dang vong hay buong cong huong Fabry-peroi: Tuy nhien, trong cac tai lieu cong bo, hau het la nghien eUu vdi Laser co md rong dong nhat la chu yeu Con Laser vdi md rong khong dong nhat dUdc nhien cUu chu yeu voi orudn.g hop don mode Phan Ngoe Ha [10] nghien eUu vdi Laser khi vdi buong cong hUdng dang vong Trong ban luan an nay, chung toi sU dung gan dung h^ phUdng trinh toe dg de nghien cij(u hoat dpng cua LSA vdi buong cong hUdng Pabry-perot co do md rong khong dong nhat

la chu yeu Cac van de dat ra eho luan an la nghien cilu dac trUng cUdng do bue xa va dieu kien xuat hien lUdng on dinh quang hoe trong cac LSA vdi buong cong hUdng Fabry-perot Qua do, xet vai tro eua hieu Ung tao hoc doi vdi hoat dong cua LSA Chung toi tim hieu anh hUdng cua d^ md rong khong dong nhat den dac trUng eUdng do bijlc x^i va dieu ki^n xuat hien OB

De nghien cilu dae trUng' cUcJng do mode bi-tc xa, chung toi xet hoat dong cua LSA trong che do ddn mode va da mode

Ban luan an nay gom 3 ehUdng :

ChUdns I : ChUdng nay gom hai phan

Phan 1 gidi thieu qua mot so hieu Ung phi tuyen t.rong LSA va trinh bay hien tUdng lUdng on dinh quang hoc v6i cd che va dieu ki^n xuat hien Trong phan nay co dUa vao mot so ket qua thUc nghiem hien tUdng lUdng on dinh ma chung toi quan sat dUdc khi tien hanh thi nghiem v6i Laser khi Ar

Phan 2 gidi thieu vai tro eiia hieu itng tao hoc trong hoat dong eua LSA vdi buong cong hUdng Fabry-perot

ChUdng II : Gom ba phan

Phan dau khao sat Laser khi ehUa vat lieu hap thu bao hoa trong buong cong hudng Fabry-peroi: vdi mo hinh hai muc nang iUdng De mo ta hoat dong eua he, chung ~6i su dung phUong phap he phUdng trinh toe do, vdi phudng phap nay, chung toi xay dung dugc he phuong trinh dae "crung c\ldng do mode cua laser khi eiing nhU sU thay doi hieu do tich luy d cac ngan khuech dai va hap thu Tiep theo chung toi si dua he phudng trinh dac trung ve d^ng thuan tien eho tinh toan

Phan thu hai khao sat hoat dong cua LSA vdi che do ddn mode qua viee xac dinh dae 'rUng eudng do mode d trang thai dilng Tiep theo nghien euu vai tro cua hieu ung tao hoc trong LSA vdi buong cong hUdng Fabry-perot qua viec khao sat sU bien doi eudng do bue xa khi thay doi vi tri cac ngan khuech dai va hap thu trong buong cong hUdng Hi|n tUcpng lUdng on dinh quang hoe va dieu kien xuat hien OB dude de cap tdi trong trUdng hdp cu the

• Phan thu ba khao sat hoat dong eua LSA d one do da mode khi thay doi toe do bdm nang lUdng moi trUdng khuech dai khong chi CO hien tUdng lUdng on dinh ma eon co hien tUdng

da on dinh xuat hien Moi quan he giUa eUdng do mode phat

va do rong trUdng bUe xa dUde xac lap

ChUdng III: Khao sat hoat dong khong dung eua he LSA chu yeu vdi buong cong hUdng dang vong Nghien cdu sU phu thuoc th6i gian eua cUdng do mode phat va hieu do tich luy cua hai

4

-moi trUong He phudng trinh toe do dUdc giai bang phUdng phapsotren cd sd thuat toan Runge Kutta ap dung chg cac trUdng hdp ddn mode va da mode Vdi che do da mode, hoat dong cua he trd nen hon lo^n sau trang thai dilng, hi^n tUOng hon lo^n quang xuat hien

Phan cuoi cung la ket luan, phu luc va tai li^u tham khao Ban luan an nay cd ban dUdc hoan thanh tai bo mon quang pho khoa vat ly trUdng dai hoc Tong hop Ha noi va dUdc bo sung tai to vat ly dai cUdng va cae qua trinh truyen song khoa ^/at ly trUdng d.ai hoc Tong hdp Matxcdva

Cac ket qua eua luan an da dUde bao cao d cac xemina tai

bo mon quang pho khoa vat ly trudng dai hoc Tong hdp Ha noi, tai hoi nghi vat ly ly thuyet toan quoc Ian thil 12,13 [5,6], tai hoi nghi quoc te mang ten Ernsrabe Ian thU nhat tai Jena-CHDC Due va hoi nghi quoc te ve nhung xu hUdng phat trien trong dien tu hoc lUdng tu d Bucares-Rumani[49,50] va

da dUdc cong bo d cae tap chi trong nUdc [4,5] va tap chi d nUdc ngoai [13]

, ,Nhan dip nay chung toi xin bay to long biet dn sau sac doi vdi pho Giao sU, Tien si Dinh Van Hoang- ngUdi hUdng dan khoa hoc- aa tan tinh giup dd chung toi hoan thanh ban luan an

Toi cung xin bay to long biet dn sau sac doi vdi pho Giao

sU Krindash rdai hoe Tong hdp Matxccjva) , pho Giao sU Vu NhU CUdng, pho Tien si Trinh Dinh Chien da tan tinh diu dat

va CO nhieu y kien co gia tri de chinh ly va hoan chinh luan an

Chung toi xin chan thanh cam dn cac Giao sU,can.b6 giang day bo mon quang pho Dai hoe Tong Hdp Ha Noi co nhieu y kien quy bau khi thUc hien de tai

Chung toi cung xin chan thanh cam dn ban chu nhiem khoa vat ly va cac ban dong nghiep xa gan da tao dieu kien vat

chat va tinh than oho chung toi hoan thanh luan an nay

ChUdng I: ANH HUONG CUA HI?U L/NG TAG HOC TRONG LSA v6l

BUONG CONG HUONG FABRY-PEROT VA HI?N TUONG LUdNG ON DINH QUANG HQC

1-Hi^n tUdng lUOng on dinh auans hnn va cac hJeu (Ang vat ]y ph-i tuven trong LSA

Laser chUa vat lieu hap thu bao hoa fLSA) trong nhUng nam gan day da trd thanh moi quan tam Idn eua cac nha vat ly ly thuyet va thue nghiem Cac nha nghien eUu da thu dUde mot loat cac hien tUdng ly thu va md ra hu6ng (ing dung mdi trong cac nghanh quang pho hoc Laser Cac hien tUdng nay cung nhU Ung dung cua ehung da dude Phan Mgoc Ha, Tr.an Thi Thu Ha [2, 3] trinh bay trong ban luan an eua minh 0 day ehung toi chi nhac lai nhUng net chinh va gi6i thifu mot so cone trinh trong nhUng nam gan day eo lien :3uan t6i chung Cac hifu ring

phi tuyen lien quan T:di LSA la:

1.1 Su bien dieu do pham chat tiiiu doug (Passive Qswitching- viet tat la PQS)

Day la mot trong nhUng hien tUdng dac trUng eua LSA Theo cac nha nghien cUu [14,13], chat hap thu bao hoa la moi trUdng co he so hap thy ty 1§ nghich vdi cUdng do anh sang tdi- Khi eUdng do bUe xa tdi nho thi he so hap thu l6n nen bUc xa tU dong va buc xa cam Ung sinh ra hau nhU bi hap thu het, hoat dong Laser eoi nhU bi cam Khi eUdng do bile

xa tdi v6 cung Idn thi he so hap thu trd nen nho Luc do sU bAo hoa va hien tUdng tay trang ( bleaching) cua chat hap thu xuat hien, anh sang di qua chat hap thu hau nhU khong bi hap thu Nang lUdng dudc tich tu til trUdc bUe xa thanh mot xung Ly thuyet chung ve hien tUdng dUdc Szabo va Stein nghien cUu [115] cac tac gi4 [36,37,42,105,117] khi nhien euu PQS trong Laser- CO2 da tim ra dieu kien xuat hien xung PQS lien quan tdi toe do tich thoat dao dong cua moi trUdng khuech dai va hap thu Co the xem them ve hien tUdng nay

trong cae cong trinh gan d-ay [24^28 , 51, 77 , 99 , 115 ] r

^ 2 Hien tUdng hon loan guana

Khi nghien cUu tinh khong on dinh trong LSA, cac nha vat

ly thay xuat hien hien tUdng hon loan quang, hieu lina nay dUdc Mrugala,Peplowski [96] va Antoranz,velarde[22] quan sat dau tien Hien tudn^ hon loan quang da dudc nghien cuu trong Laser CO2 [45,73] va Laser ban dan [75] Cac tac gia

da eho thay dieu kien xuat hien hien tUdng nay lien quan tdi ap xuat hdi bao hoa 1 doi vdi Laser khi ) va thdi gian song cua cae phan tU mang trong mien phun va mien khong dUde phun ( doi vdi Laser ban dan ) co the tham khao them trong cac cong trinh [9,40,43,46,63,67,72,73,96]

1.3 Hien tUdng phan nhanh

Khi nghien cUu he LSA cac nha nghien cilu [ 47,55 j nhan thay rang e6 su thay doi lien tiep trang th.ai cua he khi

d ieu kh i'^n cae rham so cua mo i ^ ruen^3 "c ron g bi.iong cong hUdng Dembinski Mandeir47] va Srneux [55,56] da budc dau

mo ta gian do phan nhanh cua laser Ta biet LSA co loi the hdn laser thong thUdng (la laser khong ehUa vat lieu hap thu bao hoa) d eho eo the dieu khien dUde hai tham 36 dong thdi, do la bcm nang Ludng moi truong khuyech dai va hap thu He phudng trinh LSA eo hai kha nang phan nhanh ke tiep nhau theo thdi gian Hudng phan nhanh dau tien itng vdi khoang thdi gian khi cUdng do bien doi tU "zezo" den trang thai CO eUdng do bien doi tuan hoan cheo thdi gian HUdng phan nhanh thU hai bien doi tU trang thai eo eudng do bien doi tuan hoan sang trang thai dUng Cac cong trinh [23,44 9*4] cung de cap tdi hien tUdng nay

1.4 Hien tUdng lUdng on dinh auang hoc:

Ludng on dinh quang hoc la hien tUdng truyen hai tr^ng thai anh sang on dinh khi chi c6 mot trang thai anh sang t6i Hien tUdng nay xuat hien trong cae laser ehita vat lieu hap thu bao hoa va trong cae buong cong hUdng thy dgng (khong ehUa moi trUdng khuyech dai) chUa day cac nguyen tU hap thu Hien tUong OB dUde Szdke [116] phat hien Ian dau

- 7

tien vao nam 1969 TU do OB trd thanh mot trong* nhung hif^u Ung chinh trong hoat dong eua LSA, dUde nhieu nha vat ly [107,97,10] quan tarn nghien cUu do nhung ilng dung mdi me cua no trong cac llnh vuc

Nghien eUu dieu kien xuat hien OB la van de kha ly thu,co hai yeu to lien quan tdi dieu kien xuat hien OB la rtinh phi tuyen cua moi trUdng tUdng tac vdi trUdng dien tU va nang lUdng hoi dUdng ( feed back i khi ngtion nang lUdng hoi dudng

la hoan toan quang hoe ( all optical ) , tUc la bile xa d moi trucJng phi tuyen la do bue xa laser eua chinh buong cong hUdng cung cap Thiet bi nay dude goi la tU t^i (Intrinsic) Khi nguon nang ludng hoi dUong la do mot the hieu ben ngoai dat vao tinh the cung cap de tao thanh tinh phi tuyen nhan t^io, thiet bi nhu r.he goi la ngoai lai (hybrid) [ 104]

He tu tai quang hoe dUdc tao thanh tit ba loai vat chat : phan tu,nguyen tu t\i do TnB], moi truong kerr, [94], chat ran chat ban dan [19,20]

He ngc-^i lai quang hoc dudc Smitb va Tunnex" [114] nghien cUu Ian dau tien Cae ong chieu buc xa laser He-Ne qua buong cong hudng eo dat tinh the dien quang KDP lam bien dieu dcp pham chat moi truoni^ trong buong cong huong, the hieu 200v dUdc dat len tinh the de tao tinh phi tuyen, khi quan sat bile xa ra cae tac gia da thu dude hieu Ung OB

Moloney [93] da chUng to rang he LSA vdi buong cong hUdng dang vong co the xuat hien OB khi thdi gian bUc xa di het mot vong trong buong cong hUdng Idn hdn thdi gian tai hdp eua he nguyen tu moi trUdng

Muiier [97] eho rang dieu kien de xuat hi^n lUdng on dinh trong cae he LSA vdi md rong dong nhat chiem Uu the thi chat hap thu phai bao hoa nhanh hdn so v6i chat khuyech dai

V6i laser khi thi md rong dong nhat chiem Uu the,Phan Ngoe Ha [10], Vo DUc LUdng [12] neu len vai tro quan trong cua he so tich thoat cua hai moi trUdng De eo OB thi ap suat ngan khuyech dai phai Idn hdn ngan hap thu Bang

s

phUdng phap he phudng trinh toe do, e.ae tac gia d^ t m h dUde nang lUdng can thiet d loi vao de co the nhan dude hai gia tri ngang luong d loi ra

Kawaguchi [75] da nhien cUu hien tudng OE trong laser ban dan dang phun loai doi.Ong thay rang, khi thdi gian song eua cac phan tU tai trong mien duoc phun vao trong mien khong dUde phun xap xi"' bang nhau thi lUdng on dinh xu^t hien Co the xem hien tUdng OB trong laser ban dan trong cac cong trinh [102,81]

Nhu tren ta da biet, hieu Ung lUdng on dinh quang hoe co hai loai : OB do hap thu va OB do tan sac Khi ehieu anh sang vao vat chaT: dat trong buong cong " hUdng thi co hai hieu ung xay ra dong "chdi ; hap thu va tan sac Neu tan so anh sang tdi cong hudng" mot each chinh xac voi tan so dieh ehuven cua nguven tU thi sU tan sac khong dong vai tro quan trong Ngudc Lai neu hieu so tan so eua bUe xa tdi v,a t.an

so hap thu nguyen tu Idn den mUe c6 the bo qua hap thu thi

ta CO luong on dinh tan sac

OB hap thu xuat hien khi chat hap thu trd nen bao hoa Ssoke [116] la ng^.ldi dau tien phat hien ra hieu ung nay Ong tien h.anh "chi nghiem nhu sau: tren duong di cua laser CO2 ( vdi bUdc song • 10, 6>im ) co dat buong cong hUdng Fabry-perot ehUa day chat khi SFs va ap suat cua no eo the thay doi nhd he bdm chan khong, tac gia mo ta trUdng dien til bang ly thuyet ban co dien, khi moi trudng hap thu bao hoa thi he so hap thu ti le nghich vdi eUdng do bile xa tdi trong buong cong hUdng Do phu thuoc vao he so hap thu nen d trang thai diing trUdng dien tU co hai gia tri : gia tri mat cong hUdng khi he so hap thu Idn, va gia tri cong hUdng khi

he so hap thu nho Liic do trUdng bile xa truyen qua tang len dot ngot va hau nhU 100% anh sang dUdc truyen qua chat hap thu Nhu vay ta thay rang do sU phu thuoc cua he so hap thu vao cUdng do bite xa ma dudng cong dac trUng loi ra la dudng cong tre Do la lUdng on dinh do hap thu Co the xem them

SU giai thich cd che tao thanh vong tre trong cong trinh eua

9

-Lugiato [84] OB hap thu dUde nghien eitu ly thuyet bang phUdng phap ban co dien [108] va phUdng phap he phUdng trinh toe do [97], OB hap thu trong cac laser khi [107], laser mau [97], laser ban dan [751 da dUdc xet den chi tiet Cae nha thUe nghiem da nghien eUu hien tUdng OB hap thu bang each dat chat hap thu SFs, CHsOH, CHsF trong buong cgng hUdng dang vong [10] cua laser khi CO2

LUdng on dinh do tan sac xuat hien do tinh phi tuyen eua moi trUdng Tinh phi tuyen -he hien d eho cae dai litdng dac trUng eho moi trUdng nhii eh let suat phu thuoc" vao cUdng do bile xa Lugiaro da giai thich bang ly thuyet hien tUdng OB tan sac trong moi trudng Kerr [84,85] Gia sU co mot vat chat phi tuyen co chiet suat no dudc chUa day buong cong hUdng Do truyen qua eua moi trUdng theo dinh nghia cua Born va Woff [34] la ty 36 giUa cudng do anh san.e truyen qua

I T va cUdngdo anh sang -oi Iv :

0 day F = 4R / T vdi R ^ T = 1, R - do phan xa

J := 2nnoL (^/2'' la do lech pha khi anh sang di het mot chu trinh trong buong cong hucJng, x la bUdc song bUc xa , L la ehieu dai buong cong hUdng Khi $ = 2 n N ( N la so nguyen ) thi sU truyen qua la toan phan (T=l) Tii bieii thilc cua *? ta thay rang de truyen qua la toan phan ta co the thay doi chiet suat cua moi trUdng Khi co bile xa tdi vao moi trUdng phi tuyen thi chiet suat moi trUdng se bien doi theo eUdng

dd bUc xa Ta co chiet suat phu thuoc vao eUdng do dUdi dang :

n (I) = no + nl (1.2),

V6i no- chiet suat ban dau khi chua c& bile x§ ,n la h^

so phu thutpc vao tinh chat m.oi trudng, Khi eo bile xa t&i thi

•

cUcJng do anh sang trong buong eong hUdng I se tang va '5 cung

Gibbs [60] la ngUdi dau tien dUa ra thiet bi OB tan sac Thiet bi nay gom mot buong

cong hUdng chiia day vat

chat phi tuyen la hdi Na va

Laser mau eong suat cd 50 mw

ehieu v.ao buong eong hUdng

nay Buc xa loi CO dang

nhu hinh 1.1, do chiet suat

hdi Ma phu thuoc vao cUdng do

buc xa toi cua L.aser mau ma

hien tudng ludng • n llnh

xuat hien Cac cong t r i n h

nghien cuu 'JB "an sac co

the xem trong [53,55,57,60] Hinh 1.1- Pi cong suat vao

p2 cong suat ra Sau day ehung toi trinh bay mot so ket qua thUe nghiem hien tUdng lUdng on dinh quang hoc tan sac ma chung toi quan sat dUde khi tien hanh thi nghiem v6i laser khi Ar

Sd do quan sat thUe nghiem dUdc bo tri theo hinh ve (1.2)

i

Hinh 1.2 sd do quan sat thUc nghiem

Trong do : A- laser Ar hoat dong trong che do lien tuc vdi cong suat khoang 1 mw ,B- thau ki.lih hoi tu vdi tieu cvL

f =6em C- cuvet chUa rUdu pha iot vdi nong do thap, D

- 11 - ,

- man quan sat bUc tranh giao thoa eua chum tia ,^- thiet bi

do cong suat chum tia buc xa, F - Kinh hien vi qukn sat

sU chuyen dong cua chat mau trong cuvet

Bile xa cua laser khi Ar qua thau kinh se hoi ty tfi tam cuvet mau.Do tac dung nhiet eua bUe xa ,vung chat long tai tam cuvet se nong len.Ta co sy phan bo khong gian ve nhiet

do trong dung d^-ch: nhiet dg t^i cac diem khac nhau se khac nhau Chiet suat eua moi trUdng thay dbi theo nhiet do, bdi vay n la ham phu thuoc vao v^ tri quan sat Til [ 34] ta co the viet :

Trong do :

^ = i,8.10-^(dq)'' , A T = T(r;-l, y(},' T„

at

la nhiet do chat long khi chua eo bUe 'xa tdi va T(r)la nhiet

do tai diem quan sat each tam hoi tu vdi khoang each la r Khi bUe xa tdi cuvet tang len t^hi do chenh lech nhiet do AT cang Idn TU '' 1.3 > ta thay rang chiet suat moi trudng se giam dan va nho nhat tai tam hoi tu, do vay bUc xa laser di qua cuvet se khuc xa ve hai phia Luc n^y cuvet m.au eo tac dung nhu mot thau kinh phan ky.Biic tranh phan ky cua chum tia bUc xa quan (sat tren man D ) dUde ghi lai tren hinh (1.3) khi cong suat loi vao P-.- eon nho (P=20mw - trUdng hdp a) bile tranh la mot eham sang tron Tang P-y cham sang do to len va xuat hien cac vong tron dong tam ftrUdng hdp b ) Tiep tuc tang Pv thi cac vong tron nay se xuat hien them rlhieu ( trudng hdp c ) TU (1.3) ta thay cae tia sang gan 'tam hoi tu se khiic xa manh hdn cac tia sang d xa tam ,do d6 cac tia sang nay se gap nhau va giao thoa tao nen cac vong tron dong tam • •

Khi eong suat Pv- dat t6i gia tri tdi han (P^^ =150 mw) bUc tranh cac vong tron dong tam dot ngot bien mat , thay vao do la cac vung sang nhU hinh ve (1.3 i Luc nay eudng do

•loi ra dot ngot giam.Khi giam cong suat loi vao, cUdng ao

'' '^9^^^BB^B

Hmh 13 H(nh 3nK phan ki" ctia cUlm, lia USER

1 9

loi ra •::un,^ khong trd ve gia tri ban dau Ta chu duc^c dudng

Gong tre tren ninh fl.4)

(y/^^)

Hinh 1.4—Su ohu thuoe I R ( ?—)

Ngoai ra chung toi cung khao sat sU bien doi cua eUdng do

bUc xa ra khi thay del nong do duns dich hoac do day !!:uvet

cung nhu su phu thuoc thoi gian cua hien tudng lucng on

dinh quang hoc tan sac.Co the xem chi tiet trong ohu luc (5)

Tren day la mot sd eong trinh nghien eUu heat dong cua

LSA Cae tae gi.a da dua ra dieu kien ton tai, ed che va cac

van de lien quan tdi cac hifu ilng phi tuyen xay ra trong

hoat dong cua LSA trong LSA con nhieu van de phai nghien

cilu nhu khao sat cae van de lien quan tdi diem chuyen tiep

[78,791 dac trung eUdng do bile xa trong trang thai khong

ditng [70] anh hUdng sU thang giang pha [71] mot trong

nhUng hUdng nghien ^Uu hien nay la khao sat sU ^hay doi cua

he LSA khi mot trong nhUng thaon so moi trUdng bien doi theo

thdi gian [54,56]

Laser chua vat lieu hap thu bao hoa dong vai tro quan

trong trong ky thuat bdi nhung Ung dung mdi me cua no TrUdc

het phai ke den sU dong gop trong phUdng phap pho laser : tao

xung cUc ngan, do nhay tach vach hap thu -hien tudn,^ OB

CO y nghia Idn trong viee ilng dung vao may tinh quang hoe

nhu tao nen cac yeu to logic va b9 nh6 quang hoe, cae yeu

to " va " va "hoac" , Khi nghien eUu LoA vdi buong cong hUdng Fabry-perot ta

khong the bo qua anh hUdng cua hieu Ung tao hoc Day l^a mot trong nhUng net dae trUng eua buong eong hUdng loai nay

TrUdc khi di vao trinh bay noi dung cua luan an ehung toi se gidi thieu so qua ve vai tro eua hieu ^ing tao hoc

trong hoat dong cua LSA voi buong cong hUdng Fabry - perot

2 anh bUdng eua hi*fu Ung t;^o hoe ( hdi-? burning 'gffeatl Trong hoat dong cua laser chua vat 11*^11 hap thu bao hoa,ta

biet trong buong cong hUdng Fabery - perot trUdng phan bo khong dong nhat Tuy theo tUng loai gUdng cong hUdng [17] ma

nang lUdng eua trUdng tap trung thanh cac eUc dai va cUc

tieu Khi ta dat cac ngan khuech dai va hap thu trong buong

cong hUdng thi cUdng do mode phat ra cung bien thien theo

sU thay doi cua trUdng fi,

tao hoc trong hoat dong eua cae he LSA Vai

chinh la anh hUdng cua hieu Ung

:ro eua hieu ing nay the hien d eho eUdng do mode phat ra phu thuoc vao

vi tri eua c.e.c ngan khuech d.ai va hap thu dat ^i-ong buong cong hilong [97] , mkz khac no con phu ehuoc vao *an so mode

phat [107 ]

A.^2dke [116] da nghien eUu hoat dong cua he LSA vdi buong

cong hUdng Fabery - perot.DUa tren ly thuyet ban co dien ong

da xay dUng dUdc phuong trinh truyen song v6i sU "Chay- doi

eua vec td cudng do dien -DrUdng Song di lai trong buong eong hUdng nen cudng do dien trUdng tai tilng gUdng la cung

khac nhau Ta eo the mo ta trUdng trong buong cong hUdng

Trong do : 7 va V la do phan xa va do truyen qua eua trUdng o( la he so hap thu Nghiem eua he phUdng trinh tren chinh la gia tri trUong khi cong hUdng vdi dao dong nguyen til moi trUdng trong buong eong hudng Tuy nhien tac gia cung ehUa neu ro anh hUdng eua hieu Ung tao hoc

Muller [97] da xet vai trd cua hieu Ung do trong laser co

md rong dong nhat la noi bat (chu yeu xet vdi laser mau ) de

mo ta hoat dong cua he LSA, tac gia da xay dUng he phUdng trinh toe do mo ta sU thay ddi theo thdi gian eua sd photon nghich dao do tich luy d cae ngan khuech dai va hap thu De thay dude vai tro cua hieu itng tao hoc tac gia da thay ddi vi tri cua cac ngan khuech dai va hap thu Ddi vdi laser thildng ("khong chua mdi trUdng hap thu ^ thi ty le cUdng do mode phat gan ngudng trong buong cong hUdng Fabry

- perot v.a buong eong huong loai vong la 2/3 sd di co sU khac nhau nay la do kha nang bao hoa khac nhau cua tUng loai buong eong huong Khi chat hap thu dat gan gudng va chat khuech dai d giua buong cong hUdng thi kha nang bao hoa de hdn so vdi truong hdP ngUde lai Mile do bao hoa cung anh hUdng len sxi eanh tranh mode do do no cung xae dinh sd mode dao dong Hien tUdng lUdng dn dinh ehi xuat hien khi chat hap thu de bao hoa hdn so vdi chat khuech dai

Do hieu Ung tao hoc ma dudng cong tre trong cae trUdng hdp khac nhau ( khi thay ddi vi tri cac ngan ) se khac nhau ro ret Dieu nay the hien ro tren hinh (1.5)

Muller cung dua ra dieu

kien xuat hien OB ddi vdi

tilng trUdng hdp cu the Khi

ca hai moi trUdng dat giUa

buong cong hUdng thi dieu

kien xuat hien OB la:

P>Pmin =1 + k/^to

S^'pbo w-iori^xa

Trong do P la ty le ti^n^ Iv't/pt^ ^rn,

eUdng do bao hoa moi trudng Hinh 1.5 a.Ca hai ngan dat khuech dai va hap thu , K-dac giUa buong eong hUdng trUng eho thdi gian song cua b.Ca hai ngan dat gan gUdng phoron trong buong cong hudng

^•b dae trung eho nang lUdng bdm hap thu Khi moi tritdng hap thu da^ gan gUdng va moi trudng khuyech dai ''la'

cong hudng, dieu kien xuat hien OB la:

f

-Trong do Po la tan sd chuyen ddi giUa hai mile nang lUdng ( Po = ( Es -El )/h ) , c - van toe anh sang Song diing trong buong cong hUdng Fabry- perot vdi tan sd p bao gom hai hu&ng

(di va ve ) NhU vay luc do xay ra tUdng tac trUctng dien til vdi hai nhom phan tU chuyen dong ngUdc ehieu nhau vdi v=Ln toe V Khi bi^e xa thi h^m phan bd dd tich luy d cac miic tren theo van toe co hai "hoc" Khi ^ =>^o thi hai hoc se trung nhau Dd la hien tUdng lambdip Nhu vay cong xuat phat cua laser tai ^ ~^o se nho hdn so vdi eong :':uat phat tai

y < >>o hoac P > 9o nhu hinh (1.6)

Saloma va Stenholm [107]

md ta hoat dong cua laser

khi '/oi chat hap thu bao

eua lampdip dUde giai

thich trong thuyet nhieu

loan cua eua Lisitsyn va

Chebotaev [41] Su khac

nhau dd bao hea trong

e.ae ngan khuech dai va

hap thu dUa den tao nen

cac "hoc" t-ai tan sd

cong hildng vdi dd rong

mien nang lUdng bdm tUdng

Ung Tren hinh (1.7) eho

thay sU phu thuoe eUdng

dd 1 vao do lech cong

hUdng A =: o-(j/ku khi

thay ddi bom hap thu va cd

Sinh bdm khuyech dai

Tin. hinh ve ta thay rang

dieu kien de xuat hien

lambdip la dao ham bac 2

cua 1(A) phai ddi dau tai

A = 0 Tac gia da tim ra dUdc gidi han bdm hap thu de nhan lambdip trong md rong khong dong nhat Tran Thi Thu Ha [3] nghien cUu LSA vdi buong cong hUdng dang vong bang ly thuyet

tri khac nhau

>ft . 17

ban cd dien Qu.a nghien eiiu sit phu thuoe ham bdm hap.thu vao eu6ng do I vdi nhung gia tri d^ lech eong hUdng khao nhau Tac gia thay rang khac vdi dudng dac trung do Saloma va Stenholm'tim ra trong trUdng hdp song dUng , d day eac dUdng dac trung khong cat nhau , do vay lambdip khong xuat hien tren diidng dac trUng cuong dd vao do lech eong hUdng Tran Thi Thu Ha da ket luan rang hieu Ung tao hoe khong anh hudng den dieu kien xuat hien va mien hoat dong eua OB Cd the tham khao them vai trd cua hieu Ung tao hoc trong eac edng trinh [31,35,48,52,92,98]

Trong nghien eUu LSA ,cac nha vat ly da su dung chu yeu hai phudng phap : he phudng trinh toe dd va ly thuyet ban cd dien PhUdng phap ban cd dien dUa tren ly thuvet lamb khdns dua ra sU phu thuoe tudng minh cu.a cuong dd vao cao tham sd mdi trUdng.Rieng phucng phap he phudns trinh tdc do la phudng phap rat phu hop vo lai toan L.bH vi no cno eac ket qua tudng minh eho den nay van con dude sU dung phd bien

de nghien cuu ly thuyet ve LSA

Trong cac tai lieu cong bd hau het nghien cUu ve laser eo

md rong dong nhat Rieng laser co md rong khong dong nhat,sU nghien cUu ehi eo the xem nhU la bUoe dau Phan Ngoe Ha [10]

da giai quyet bai toan LSA vdi md rong khong dong nhat trong laser vdng

Trong ban luan an nay ehung tdi nghien cilu LSA vdi buong edng hUdng Fabry-perot dita tren phUdng phap gan dung he phUdng trinh tdc dd Tim hieu hoat dong LSA vdi md rong khong dong nhat se gop phan vao su phat trien ly thuyet ve LSA

"(i :t'X

: oi.fi.H.^s ; , 0 !

v.U//f53

j

13

-ChUdng II GAG DAG TRUt^G CUA LSA v6l BUONG CQNG HUdNG

FABRY - PEROT

?.1 HE PHrJONG TRINH CCl BAN

Hoat dong cua laser chUa vat lieu hap thu bao hoa trong buong edng hUdng Fabry-perot dUde trinh bay theo sd dd d hinh (2.1)

i V

^

i- -5

Kinh 2.1 od do ho^t d')na ciia laser chua vat li^u hap

thu bao hoa vdi buong edng hudng Fabry-perot

Trong so do gom hai gUdng cong hudng, giUa hai gUdng la hai ngan Ngan A oh(\a. chat co tinh khuech d^i anh sang va ngan B ehita vat lieu hap thu bao hoa Khi co bUc xa laser trong buong cong hUdng, song anh sang se di lai giUa hai gUdng c^ng hUdng Qua ngan A thi bue xa dude khuech dai len,

va qua ngan 3 biie xa se giam di do hap thu Buc xa laser d day cd the la bile :<a ddn mode hoac da mode de md ta hoat dong cua laser ehUa vat lieu hap thu bao hoa trong buong e^ng hUdng Fabry - perot, ta sit dung phUdng phap gan diing he phUdng trinh tdc do Vdi phUdng phap nay chung toi se xay dung dUde he phUdng trinh dae trUng eudng dg mode cua laser khi, ciing nhU hieu dg tich luy d cac ngan khuech dai va hap thu

Sd pho ton va he so mat mat trong budng cong hUdng cua mode thil j la nj va He sd mat mat cua tUng mode phv thuoc vao sU tan sac tren eac gUdng va tinh chat cua tiing gUdng cy

the Trong md rong vach nguyen tit, moi mode vdi tan sd i^^j lien ket vdi eac nhom nguyen til ed cung do md rong dong nhat r nhUng khac nhau tan sd d tam ^^ He sd tich thoat d mile tren trong cae ngan khuech dai va hap thu la ^a va iSt> Cac he sd nay lien he vdi nhau bdi bleu thue :

0 day 5 ^^ ^^ ^^ lien he dg bao hoa, dac trUng eho cd che dan den sit thay ddi tich thoat d hai ngan NhU ta da biet trong Laser khi,do tich thoat lien quan toi ap suat cua tUng ngan, do vay he sd bieu hien do chenh lech ap suat giUa hai ngan Neu ap rcuat ngan khuech dai Idn hdn ap suat ngan hap' thu thi ngan khuech dai eo dd bao hoa Idn hon, khi

dd 0< ^ <^ - Khi % >1 ta co trUong hdp ngUdc lai Theo cae tae gia [97] thi hien tUdng liidng dn dinh quang hoe :<ay ra

ro nhat vdi cac laser chua vat lieu hap thu bao hoa khi mdi trUdng hap thu de bao hoa hdn so vdi mdi trudng khuech dai 3di vay trong bai toan nay ta ehi xet chu yeu tritdng hop 0< ^<1 Theo phUdng phap he phUdng tinh tdc dd [10,97] ta eo the md ta sU thay ddi theo thdi gian sd photon nj , hieu do tich luy d cac ngan khuech dai N^A^L va ngan hap thu N^-b theo cae phrldng trinh sau:

- [ H^%in^i-nm.z,/L)Az

^N/co, ^ 5 ^ _ N / R V r-^i^^'n-^fTTm^-x/L)

0 day, 3 la he sd Enstein, mo ta xac :<uat chuyefi rdi eUdng bile giUa cac mile nang lUdng

md ta do md rong dong nhat eua cac nhdm nguyen tU cd tan sd tam iJ^ Ta biet trong laser khi md rong khdng dong nhat chiem Uu the nen 7. trons (2.1) noi len sit dong sop eua tat

^/u>^ = i^Ro

s'-^ 4 K - - S I J

Trong dd Ro la nang lUdng bdm tai mode tam i^o va Z la do

md rong khong dong nhat Ta thay nang lUdng bdm tap trung d mode tam va giam dan ra cac mode ben eanh So hang 1 trong tong (nj + 1 ) d (2.1) dac trung eho bUc x a tU dong dong vai tro nho be trong eUdng dd bite xa laser, Tuy nhien no dong

v a i trd quan trong trong viec phat bile xa ban d a u

So hang sin ( nmjs/L ) trong (2.2) vk (2.3) dac trUng eho SU phu thuoc eUdng do mode thu j vao vi tri khdng gian theo true z (true eua buong eong hUdng ) , 1 , L la ehieu dai

•

eua cae nean va budng edng hUdng ,m.i la so nguyen thoa man

21

dieu kien cong huen-g 'Cua mode thU j •

m j Xj = 2L

Vdi Xj la bude song eua mode thu j

So vdi cac luan an trUdc [2,3] trong he phUdng trinh (2.1,2.2,2.3) eo xuat hien them sd hang sin ( TT^JZ/L ) NhU vay SU thay doi so photon cua mode thu j khdng ehi phu thuoc vao nang lucng bom ma con phu thuoc vao vi tri cua ngan khuech •rial va hap thu trong buong edng hUdng Day la sU khac biet giua budng edng hUdng dang vdng va buong eong hUdng Fabry - perot

Tit he phuong trinh ed ban ta thay sd photon mode thu j la

nj dUde sinh ra khi di qua mdi truong khuech dai va bi giam

di do mat mat trong buong cong hUdng cung nhu bi hap thu khi qua mdi ".ritdng hap thu bao hoa

Tons Z tr^-^ns f 2.2 ' va (2.3) chi sit dons gop eua tat ca cae mode "rona: bue r-ca laser :

Trons bai toan nay eac mode d day la mode doc

Chung r,oi se chuyen he phuong trinh co ban ( 2.1, 2.2,2.3; ve dang khac nhau thuan tien eho viec tinh toan Khai trien ham dac trUng eho sU phu thuoc eitdng do mode vao

vi tri cua eac ngan trong budng edng huong

sin ! rtmj2/L ) = — L 1 - cos (2TTm,i2:/L * 1

Ta nhan thay rang hieu do tich luy mdi trudng khuech dai M^a la ham bien thien nhanh so vdi ham cos ( 2TTmjz/L )nen

ta CO the bien doi :

TUdng tu nhu vay vdi hieu dg tleh luy moi trUdng hap thu:

Dat Qj=njB/^ dai lUdng dae trung eho eUdng do mode thit j

thay (2.4) va (2.5 i vao ( 2 1,2 2 , 2 3 ) Liic dd he phUdng trinh

ed ban con lai' la:

^jjcs^ va e/yJC^^:> bleu thi eho hieu dd tich luy d hai ngan

khuech dai va hap thu ha va hb dac tritng eho sU phu thuoc cUdng do mode vao vi tri cac ngan trong buong cong hUdng De

xet dac trUng eUdng dd mode, ta se giai he phUdng trinh ed

ban (2.6, 2 7 , 2 8 ) trong trang thai diing khi laser hoat dong

d che do ddn mode va da mode, luc dd:

Thay (2.10) va (2.11) vao phUdng trinh (2.6) thu dUdc

-K^i

6 day - (T = >*^ , <r= ^^y^ j ^ ^ trung eho tham sd bdm khuech dai va hap thu. So hang B/^ trong tong ( Q.j -^ tV^ ) dac trUng eho bue xa tu dong

PhUdng trinh i2.12 ) la phudng trinh cd ban eho hoat dong eua laser ehUa vat lieu hap thu bao hoa trong che dd dung

No eho phep chung t:di nghien cUu dac trUng eudng do mode phu thuoc vao cac tham sd mdi trUdng hap thu va khuech dai Tuy nhien cc hai tham sd quyet dinh dae tinh cua laser la nang lUdng bom mdi truong khuech dai ^ A va hap thu (Tb Tren cd so

dd chung tdi xet hoat dong eua LSA trong hai trUdng hdp :

- P>* 3, = ronst ' tuc (Ta = const ' : nang lucng bom khuech dai la nhu nhau vdi cae mode

- IV^ iai ham sd ( tile tr^ la ham sd ) : nang lUOng bdm khuech dai la khdng deu theo cac mode

^ 2- km HTJtTNG CUA HlgU (MG TAO HOC TRONG HOAT DONG DC^N

MODE CUA LASER

• % '"

- Khi laser hoat dong d che do ddn mode ,trong phUdng

trlnh (2.12) se khdng ed tong theo so mode phat theo k ma ehi con lai tong theo sd nhdm nguyen tit u vdi tan so tam w^

Do dich chuyen cac tan so tam (o^ la lien tucnen tong theo >L

trong (2.12) dudc chuyen thknh tich phan theo tan so w nhd he thitc sau : •

4

Trong do 2/^t la he so chuan hoa vdi £ la do md rong

khdng dong nhat cua v^ch b(ic :c.=i„ Dd md rong Doppler, khi do tii phUdng trinh i2.12) ta eo

*• 0 C

^â ^ ^

:r O

d day oc _ 1/^

Tuy thuoc ^"ao che do bdm <r^,(Tir ma chung ta co the xac

dinh dudc dai j.uong dae trUng cuong do bue xa Cxho trUdng hdp tong quat CO tinh den bite xa tu 'dons Ve mat v nghia vat ly bite xa tu dong cni 'rT'jng 5op mot phan nho be vao cUcng do bUc

xa ma chu yen l.a do dich chuyen cuong buc Boi vay, de eho đn gian truce hệ ta bo qua sd hang—trong ^2.14) dac tritng eho bue xa tu dong

2.1 Dac trung cuons đ mode

Khi bo qua bUc rca tu dong thi philong trinh f 2 14 ' trd thanh

M-^f[7:^ kx.siA\xij

C-t.-rs;

Chiing ta nhan thay dai iUdng dac trUng Qj phu thuoc vao cac tham sd bdm ifs. ^(ri, tham sd tich thoat oc Bai toan duoc khao sat chii yeu trong hai trudng hdp hoat dong cua he LSA vdi sU ph4n b6 bdm nang luong la deu eho cac mode ira,rb

=Const) va vdi bdm phan bo khong deu theo cac mode ( chling han bdm khuech dai ?han bo theo dang ham Lorentz vdi c4c mode )

- 25

?.1.1 Toe dd bem nkn<i lUdng d hai ngan la khdng ddi

Do (Ta va (T-b la hang so nen ta cd the dUa ehung r& ngoai

dau tich phan ,tinh eac gia tri tich phan (theo phu luc 1)

phUdng trinh (3.1.3) sau khi tinh toan eon lai la

Ta cc the viet (2.13) dUdi dang sau :

Qj G ( Qj ,<r3,,r ,e, ) - 0

Trong dd :G (Qj , 0"=^ ,r , 6 )goi la ham khuech dai ed dang

^v5;(^u.Oj+^)^^ zvz(o<)x^Q^ t-i/'^-i

Ham nay co dang nhu ham khuech dai do Saloma va Stenholm

[107] tim dUde bang phudns phap ban cd dien

H = - - i

(r + A)% (^I-^ i) v^

Trong do >t va Tit dac trung eho nana lUdng bdm moi trUdng

khuech dai va hap thu ( tUdng Ung vdi <r=, va 0"^ ) va I la

eudng do trudng dien tU (tUdng ung voi eUdng dd mode Qj )

Dang bien ddi eua ham khuech dai G phu thuoe vao cudng

do mode Q,^ vdi cae gia tri bdm hap thu khac nhau (T^ dUdc the

hien tren hinh (2.2)

- 26

''^.<^K<%<^y,

:?> Q;

Hinh 2.2 Su phu thuoc G (Q.i * vol cae gia

tri ''to khac nhau

Theo hinh ve ta thav khi khdng eo bdm hap thu Ty^ ~ 0 thi ha.m khuech dai ty le nghich vdi cUdng dd bUc :<a Q j Dudng cong t a * giam ddn dieu khi bUe xa tang Khi bdm hap thu (TTO bat dau tang len thi dang ham bat dau ciing thay ddi G Idn ed dang khac nhau vdi cae gia tri ^r-^ khac nhau ( dudng eong b,c,d) Khi tr-'o =: tr^a ta thay rang G {Q.:^ ) - 0 tai hai gia tri dUdng dong thdi eua eUdng do bUc xa.Liie do lUdng dn dinh xuat hien Cac diem D va E la cac diem dn dinh, diem C

la diem khdng dn dinh

Bay gid chung ta tiep tuc giai phUdng trinh (2.14) de tim dang tudng minh ciia dai lUdng dac trUng cUdng do bile xa Qj

Xet bai -toan d phan ngUdng phat, tUe la eoi nhU Qj<<l, ta

cd the khai, trien gan diing ham trong dau can

Qji - 0

Tren hinh (2.3) eho ta thay sU phu thuoc cudng do mode phat ra 'o).j theo nang lUdng bdm khuech dai (TV la mdt ham tuyen tinh, gidng nhu ddi vdi laser thong thudng (la laser khdng chita vat lieu hap thu bao hoa )

a-

Hinh 2.3 Su phu thuoc Q^j ( (T^, ) vdi oc - 1

Su phu thuoe dac trUng eudng do mode theo do md rong

- "'R

khdng doug nhat dUde bieu hien tren hi,

tri bdm khac nhau

•vol c a e SIa

cr;<^i<^j

p ^ rhfi Chfi •=

Hinh 2.4 - Su phu thude Q,i ' ^ i , (T = CT^L - <r>^

Tu hinh ve '2.4 ) ta thay ran^ cung met tee dd bdm, eUdng

dd bile :<a la Idn neu dd md rong Doppler la nho

Khi dd tich thoat e hai ngan la khac nhau ( '•< ^ 1 ) ta

eo da^:- truna cUdng dd mode tim duoc nhu o ( 2.20 > ta biet khi hei ngan khuech -lai hap thu ehua hai chat khi khac nhau hay ehua cung mdt chat khi nhung vdi ap suat khac nhau-thi he sd tich thoat d hai nganla se khac nhau, thong thUdng ngUdi ta sU dung LSA eo eiing mdt chat khi d hai ng.an nhUng vdi ap suat khao nhau, khi do oc the hien dd chenh lech ap suat giiia hai ngan, hay la he sd lien he ':td bao hoa giiia chung

2.1.2 Toe do bdm nana lUdng d ngan khuech dai khdng deu Gia sU rang bdm khuech dai phan bd theo dang ham Lorentz

2

(^.Jiz)

d d-ay Ro la dai lUdng dac trUng eho eudng dd bdm tai mode tam t^o, £ -do md rong khdng dong nhat vach bile xa NhU vay ham bom khuech dai tap trung d mode tam va giam dan ra eac mode d ben eanh

Thav (2.22^ vao phUdng trinh i2.14) ta thu dude

Tinh cae gia tri tich ohan ' theo ?hu Lwc I'

Thay vao (2.23) ca duoc

d L - <5: f ^^'"^'^ ^^^^^ I = o (^ -2^;

T r o n g :Io o'i = , :iac t r U n g e.no bdm k h u e c h ciai '"='' -r^^*''

tam Sio va

rrv

Xet hoat dong LSA 1 g^n ngUdng phat Q.i •.< 1 luc dd

ta eo the khai trien gan lung cae bieu thue i-ron^ r-an, khi

do (2.24) trd thanh

Nhu vay nghiem eua (2.25) la dac trUng cUdng dd mode khi laser phat ddn mode voi bdm khuech dai theo phan bd Lerentz PhUdng trinh (2.25) ludn ton tai khac nghiem

Q.ji - 0

va Qj2.3 = l^'^'uKi C ' ^ ' ^ - ^ ) - ^(kx-^^K^) i

Trong do nghiem Q:;c tUdng Ung vdi dau -^ va nghiem Qj3 tuong ung voi dau - trong (2.26) sU phu thuoc cuong do buc :^a '^ji vao toe -ild bdm khuech 'lai <ro the hien tren hinh • 2.5 ;

r r e n h i n h \' 4 -:I o a n a b t \\ d n g u n 3; r o i n ? h 1 e m ^ • " • • • 2 '•' a •: o a r. ^o e

30

T- T < - 1 »-i r-y 1 ^^ ,—,• ' r '*' "i 1^ o" ''T "• 3 rri ' A ^

H i n h 2 5 - 3u p h u t h u o c '-^' -i < (r=i -^ -' : a. i

Ta they ii.tdng on riinh rcay ra trong vung d -^an iinb hypecpol ve phia ^o '"ana, iae trUng eUong -io mode khi bom la ham so theo i 2.26) kn.ac voi dac trung cudng do moee khi bom la hana so theo •.2.20; o chd trong ':2.26) them so hang

m 'Jac trung eho phan ed nang luong theo "jac mode, khi ci

-il-^ tbi m-: luc do • Z 16 ^ va i 2.20 • trun^ nbBu i ii^'de t-nav

la '^an tam )

Ta biet trcn.2 phue.ng trinh ( 2 14) sd hang 0/?f trong tens (Qci+d/*^^ dac trung eho buc xa tu dong De tinh :Iae trung eudng do mode Qj eo "inn den bUe :<:a tU dong, ta giai phudng tri.nh (2.14) dang day du tUdng tu nhu o (2.1) ehung toi ian lUdt :<et hoat dong rua LSA khi bdm phan bd deu eho cae mode va khi bdm phan bo khdng deu ! theo dang ham lorentt ) 2.2.1 Toe do bdm nana ludng o hai nsan 15 khdn.^ idi

Vi bdm phan bd deu theo cac mode nen ta eo the dua a"^ va o-b ra ngoai dau tich phan d phUdng trinh •2 14 ) sau khi tich den eac gia tri tich phan phUdng trinh (2.L4i eon lai

l a

^-(^-7),ir[ (^K^ <X<fi,h4,

(KQ: + ly^^ (<^ Ki Qj + -i) VA Xet l a s e r >inat dr.n% gan n g U d n g (Q^ << 1 ) , k h a i t r i e n -Han

d i i n g ham t r o n g c a n "a t h u d u d c

Ta eoi ^-Uona do mode On can tim eo dang

Trong do ; ^6'2. tUdng Ung vdi Qj2 va J is tiiong Ung vdi

Q -^:^- trong (2.29) nhU vay khi tinh den buc :<a tu dcng thi cUdng do mode tim dUdc chinh la cUdng dd khi chUa tinh ien bUe :<a tu dong eong them mot sd hang bd chinh :':ae dinh V i

so bo v;;hinh nay la kha nho eho nen buc r-ca tU dong khdng eo anh hUdng dang ke tdi cUdng do mode, dieu nav eun^ phu hdo vdi gia thiet ban dau eua ehung tdi ou phu thude iae trun^^

•

cUdng do mode Q.:j theo bom khuech dai •iTuoe chi re tren hin.n

-J-ff Hinh (2.6)- 3u phu thuoc Q.7 ( >'=\ ' vdi tr.^ - 19 oc -4

Ta thav xuat hien lUeng eong tre nhu eac tac^ gia f 11, 121 tim •:Tude,doan de tuon'? ung vdi ngiem Q.71 , :Toa.n ?.b tuer.^ u.n:? '/•O i ns"iem ''•Jr ' 'z^ 'rioan be Tuen5" un 15; '.' ~ i n zhien"^ ' i e '-'c i eac tham 30 m.di trudng la r = 4'"^ , 6 -1700 <x r: 4 ,<r^,-, =19 Tu hinh ve ta thay khi thay dc i bom khueen dai voi eac ~heng so mdi trudng ho'^ ly ; he ?o ^ich thoat, bem ngan hap thu, do md rong ddng nhat thi dUdng dac trung cuong dd mode loi ra

la dUdng eong tre, eac gia tri tuons ung vdi Qj2 trong dUdng eong tre la gia tri on d m h , eon eac gia tri tUdng i.tng vdi Qj3 la khdng dn dinh, no ehi xuat hien khi cac tham sd vat

ly mdi trUong thoa man dieu kien lUdng Dn rlinh auang hoc ma

ta khao sat d phan sau nay

2^.1i,.2 Toe do bdm nang lUdng n&kn khueeh dai khdng deu

Gia sU ham bdm khuech dai tuan theo phan be Lerent" thav lia tri ham bdm R.^ - Rof(€) vao phudng t:rinh i2.14) tinh toan eac gia tri tich phan theo phu lue 1, sau khi bien doi tudng tu nhu tren ta tnu dudc

Ta se giai phUdng trinh ^•2.30) theo phudng ohap, nhiei.i

l o a n , dhc t r u n g eudng do mode Q.i k h i bom khu-rch.a ii -.n^^n^

-'7,3 \/ai tro eua hieu ^ins tao hoe ddi vdi hien tudn.g luong

on dinh ouang hoc trong LSA vdi buong cong huoag Fabry perot

-Nhu ta da biet trong hoat dong ciia laser chua vat lieu hap thu bao hoa thi hien tUdng lUdng dn dinh quang hoc chiem mdt vai tro kha quan trong LUdng dn dinh quang hoc la khi ed mdt trang thai anh sang tdi thi co hai trang thai anh sang dn dinh d loi ra De nhan dUdc hieu itng lUdng on cJinh quang hoc ddi hoi he LSA phai hoat ddng trong nhilng dieu kien thich hdp ciia cac tham sd dac trUng eho hai mdi trudng khuech dai laser va hap thu bao hoa sao eho buc xa loi ra ludn ludn ton tai hai gia tri on dinh Viec lua chon cac tham sd dae trUng eho hai mdi trUdng ciia LSA i tUc la xae dinh dieu kien xuat hien hieu Ung OB ) la mot edng viec can thiet khi nghien cilu hieu Ung lUdng on dinh quang hoc trong hoat ddng eua LSA

0 pha-n tren ehung ca da :-:ac dinh duoc aac truiig cuong •.id

mode trong che dd Laser pnat don mode.Cac dai ludng nay la

nhitng ham phu thude vao tham so vat ly mdi trUdng Tim dieu

kien de eho eac nghiem '^.i eung thUc va dUong ddng thoi do

chinh la dieu kien lUdng dn dinh quang hoc

2,3 I f)i^ii kien xuat hien ludng on dinh guang hoc

Ta biet trong phan f2.1) hoat dong laser chUa vat lieu

hap thu bao hoa d che do ddn mode, co cUdng do bUc xa thoa

man phUdng trinh

QjG(Q.i ,<r.a,r ,£ i - 0 <2.32) Trong dd ham Gi'Qj,"-.^, ) la ham khuech dai ed dang-

<T(^j.r.,08 ) = ^^-^- ^"'^^

4,vTf/uc3:^^y^ cll/l(xfHQj- ri)'/^

PhUdng trlnh i2.32) thoa man khi Q.j - 0 hoac G(Q.i, ^e.,

) = 0 khi Qj?i 0 ham G(Qj , ('., j se eo gia tri dUdng hoac am tuy theo tdc do bom cua hai ngan khuech dai. <r^ va

hap thu <rb Tren hinh (2.2) ta nhan thay khi (Tb = 0 thi ham

G giam d6n dieu khi Qj tang , khi do chi co mdt nghiem diing,

khi bat dau ed bdm hap thu thi dang ham G thay doi theo cac

dang b,c,d De di tim dieu kien lUdng dn dinh chung ta se

tim dieu kien de de ham G co hai nghiem Q^-j dUdng dong thdi

Xet dao ham cua ham khuech clai G theo Qj , ta co

^ ^"S; 4Vi^<^fH<3j+i)Vi ^a(ka aj+j.)y^

Tuy theo ty le t6c do bdm r^/r^ ma Q.IG C O the dUdng

hoac am Qja dUdng khi toe do bdm thoa man dieu kien

a.}4;

MhU vay tai gia tri Q.j - Qj-:^ ham G ^dat gia tri cUc dai

Bdi vay dieu kien xuat hien ludng dn dinh la :

G(o,cra,r,£ ) < 0 (^35.^

va G(QjG, <r^,r ,£ j y 0

Dieu kien nay trung vdi dieu kien thu dUdc eua Saloma

Stelholm Tuy theo gia tri thong so mdi trUdng ma dieu kien

(2.35) dUdc thoa man Tren bang 1 trinh bay eac gia tri eua

ham G(Qj ^ vdi eac gia tri bdm hap thu khac nhau r^ tren cd sd

laser khi He-Ne vdi cac gia tri sau :H/^ = 10 , ^^ - 10 s

Theo bang 1 thi Qjo la gia tri eUdng dd thich hdp de tai

do ham G ed gia tri cUc dai Ta thay tai gia tri (r\D = 26

va <r^ - 242 thi ham Gf Qj ,(ra.,r , ^: ) thoa man dieu kien

(2.35), nhu vay khi dd hieu Ung lUdng on dinh xuat hien

Tren bang 2 trinh bay cac gia tri cua hkm G vdi eac gia

tri bdm khuech dai <r^ tren cd sd eac thong so vat ly thUc

nghiem laser khi He- Ne va (T^ =40

n a n g lUdng, bom moi t r u o n g k h u e c h dai va h a p thu la <r=,.'(Tb =

Trong phSn naV chung tdi xae dinh dilu kien xu^t hien

OB b^ng hai PhUdng phap : Tim diSu kien ve nghiem cua phUdng trinh xac dinh cUdng dd mode va phudng phap ap dung tieu cfhuan Routh- Hurwitz [llOJ

2.3.P!.a f)ieu ki^n ye nghi^ry]

T^ Phan (2.1) ta Ji xac dinh dudc nghiem Q, khi tinh d^n bUc xa tu ddng la :

Q ft4-(^'^a - °<^<'~0