Khuếch Đại Laser

I HC QUC GIA TP.H CH MINH

TRNG I HC KHOA HC T NHIN

KHOA KHOA HC VT LIU

B MN VT LIU NANO & MNG MNG

--------------------------------

Hunh ng Khoa 1019248

Trng Minh Hiu 1019237

Trn Ngc nh 1019215

ti:

BM KHUCH I LASER

SEMINAR PHOTONICS

Ch n ng nh i M ng ng

CN B HNG DN:

ThS. Ng Hi ng

----------------------------------

TP H CH MINH 2013

2

MC LC

Trang ph ba .......................................................................................................................... 1

Mc lc..................................................................................................................................... 2

I. GII THIU V KHUCH I LASER ...................................................................... 3

II. L THUYT V KHUCH I LASER ..................................................................... 6

1. Mc nng ng ca h ng t. Bc x t pht v bc x kch thch ................... 6

1.1 Bc x t pht ............................................................................................................... 8

1.2 Bc x kch thch .......................................................................................................... 8

2. Mi rng m o ln. .......................................................................................... 9

3. ng v bng hng. .................................................................................................. 11

3.1 H s tng ..................................................................................................................... 11

3.2 tng .......................................................................................................................... 14

3.3 Bng thng .................................................................................................................... 14

4. S tr pha ....................................................................................................................... 15

III. BM KHUCH I LASER ........................................................................................ 18

1. Phng rnh c ....................................................................................................... 18

1.1 Phng trnh tc trong h khng c bc x khuch i .......................................... 20

1.2 Phng trnh tc trong h c bc x khuch i ..................................................... 22

2. Cu to ca mt my pht laser ................................................................................... 24

2.1 Mi trng hot cht (gain medium) .......................................................................... 25

2.2 Bung cng hng ....................................................................................................... 26

2.3 B phn kch thch hay bm......................................................................................... 26

3. Nguyn l pht bc x laser .......................................................................................... 26

4. S b kh ch i laser .......................................................................................... 28

4.1 S bm bn mc ..................................................................................................... 28

4.2 S bm ba mc ....................................................................................................... 32

IV. BI TP P DNG.............................................................................................35

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I. GII THIU V KHUCH I LASER

A coherent optical amplifier l mt b khuch i quang ng pha, l mt thit b

lm tng bin ca mt di quang duy tr cc pha ca n. Nu nh sng vo l khch

i tia n sc th sng ra vn s l tia n sc vi tn s khng i. Bin u ra s

tng so vi u vo trong khi pha vn khng i hay thay i mt lng c nh.

Ngc li b khuch i quang khng ng pha (incoherent optical amplifier) lm

tng cng ca sng quang hc m khng duy tr pha ca n.

Khch i quang lin tc c vai tr quan trng trong mt s ng dng. V d bao

gm nhng ng dng ca xung quang hc yu nh i qua ng si quang di v to

xung c cng cao nh yu cu cho cc ng dng ca tia laser. Hn na n quan

trng trong vic hiu cc nguyn tc hot ng c bn ca khch i quang.

Nguyn tc c bn t c khch i nh sng lin tc l nh sng khch i

phi pht khch thch bc x hay cn gi l laser. Kch thch pht x l mt photon ri

khi mc to ra nguyn t c nng lng cao hn c chuyn i t mc nng

lng thp trong qu trnh pht x mt photon c mode dao ng nh lc u, l

mt photon c cng tn s, hng v phn cc nh lc u. hai nguyn kch

thch pht x thm hai photon v tip tc kch thch phn x nhng vn gi c

nhng tnh cht ban u. Kt qu l nh sng c khuch i lin tc. Bi v kch

thch pht x xy ra ch khi nng lng photon gn bng nng lng nguyn t chuyn

tip. Qu trnh c hn ch di tn s c xc nh bi rng di nguyn t.

Khuch i laser c mt khc vi khch i dng in. Khuch i dng in da

trn nhng thit b m c nhng thay i nh c xen vo dng in hay p th dn

n tc dng in mnh hn, v d cc in t v l trng trong trasistor trng

(FET) hay transistor lng cc. iu chnh khuch i in t s dng cc mch cng

4

hng (v d t dn v cun cm) hoc hp cng hng (metal cavities ) gii hn

mc tng khuch i trong dng th tn s c ch n. Ngc li nguyn t, phn

t v trng thi rn khuch i laser da trn s khc bit cc mc nng lng c

php ca n chn cc tn s chnh .trn thc t nhng cng hng t nhin

la chn cc tn s hot ng v rng di ca thit b. B cng hng quang

thng c dng cung cp iu chnh cc tn s ph.

nh sng c truyn qua vt cht trong trng thi cn bng nhit b suy gim.

l bi v s hp th mt ln cc nguyn t trong mc nng lng thp l ph bin

hn s kch thch pht x bi mt nguyn t thp trn mc nng lng cao. Mt

thnh phn thit yu t c s khuch i laser l s xut hin ln cc nguyn t

trn mc nng lng cao hn so vi mc thp, y l trng thi khng cn bng.

t c chim o ngc yu cu ngun nng lng phi kch thch c cc

nguyn t mc nng lng cao. Mc d c trnh by trong chng ny l phn

in t v mc in t nhng tn gi ny c hiu rng hn nh mi trng hot

ng v mc nng lng laser.

Nhng tnh cht l tng ca quang hc hay khuch i in t lin tc c trnh

by trong hnh I.0-2 (a). N l mt h thng tng tuyn tnh bin ca tn hin vo c

nh, khuch i tng. th hnh sin sng ra c tn s ging sng vo nhng c bin

ln hn. S tng khuch i l tng l tn s khng i bn trong khuch i

rng di quang.

5

Hnh I.0-1: Khuch i laser. Ngun nng lng bn ngoi (pump) kch thch

hot ng ca di quang (th hin s thu cc nguyn t ),lm cho mt nguyn

t b o ngc. Photon tng tc vi nguyn t khi kch thch bc x nhiu hn

so vi s hp th th di quang hot ng nh khuch i ng pha (coherent

amplifier).

Hnh I.0-2: (a) Khuch i tuyn tnh l tng . Lm tng bin ca sng ti

(tn s nm bn trong di) bi h s tng khng i ,pha thay i tuyn tnh . (b)

Khuch i thc l loi khuch i c tng v pha thay i theo phng trnh

ca tn s , c lm r khi sng vo c gi tri ln th sng ra s c bo ha v

khuch i u ra l khng tuyn tnh.

6

B khuch i c tng v pha thay i khng ph thuc vo tn s trong hnh

I.0-2 (b). tng v pha thay i xc nh theo b khuch i hm chuyn. Khi khch

i u vo ln, th khch i nhn chung c bo ha, mt dng ca trng thi

khng tuyn tnh l u ra khng tng t l vi u vo. Hay ni cch l u ra c

bo ha, iu ha cc thnh phn bn trong u ra.

B khuch i v vy c th c nhng tnh cht sau :

- tng .

- Bng thng.

- Thay i pha.

- Ngun.

- Khng tuyn tnh v tng bo ha.

- Tp m.

Trong chng ny chng ta tho lun mt s tnh cht c a ra trn. Trong

phn II ni v l thuyt khch i laser c xy dng thng qua tng khuch i,

ph bng thng, s thay i pha. Cc c ch hot ng ca ngun bm t c

mt o ngc c ni trong phn III.

II. L THUYT KHUCH I LASER

1. Mc nng ng ca h ng t. Bc x t pht v bc x kch thch

Trong in t c in, khuch i v pht sng in t da trn c s ng nng

ca in t (n in t ,listron, manhetron). Trong in t hc lng t, khuch i

v pht sng in t da trn c s bin i ni nng ca ngyn t, phn t, ion

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T c hc lng t ta bit rng , ni nng ca ht l lng t , tc l c th c mt

lot gi tr nng lng xc nh , gin on m trong vt l gi l trng thi nng lng

hay mc nng lng . Mc nng lng thp nht (ni nng ca ht nh nht ) c gi

l mc c bn. Cc mc cn li ng vi ni nng cao hn c gi l mc kch thch.

Khi ngi ta ni: ht chuyn t mt mc nng lng ny sang mc nng lng

khc, th iu c ngha l ni nng ca ht bin i mt lng bng hiu nng

lng ca hai mc nng lng . Khi chuyn ln mc nng lng cao hn th ht s

hp th nng lng, cn chuyn xung mc thp hn th ht s trao nng lng.

Nhng dch chuyn c th xy ra vi bc x hay hp th lng t bc x in

t.

Theo Einstein , nu h trng thi cn bng nhit ng vi mi trng xung quang

th c th xy ra 3 loi chuyn di gia cc mc nng lng l hp th ,bc x t pht

v bc x kch thch (cm ng).

Hnh II.1.1 Minh ha cc qu trnh hp th, bc x t pht v bc x kch

thch (theo th t t tri sang phi ).

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1.1. Bc x t pht

Hy gi thuyt rng ht c hai trng thi (mc) nng lng (1) v (2) ,tng ng

vi gi tr ni nng l 1W v 2W , trong 2W > 1W , tc l mc nng lng (2) nm

cao hn mc (1). Nu ht ang mc nng lng cao hn (2) th c th dch chuyn

xung mc nng lng thp hn (1) ng thi bc x lng t hv = 2W - 1W ngay c

khi khng c tc dng ca trng in t bn ngoi. Bc x gi l bc x t pht.

Khi dch chuyn t pht ,cc ht khc nhau s bc x khng ng thi v c lp

nhau, v vy pha ca photon bc x khng lin quan vi nhau. Hn th na hng

truyn ca photon bc x v phn cc ca n u mang c trng ngu nhin, cn tn

s ca n s dao ng trong khong no , c xc nh bi h thc bt nh. Nh

vy bc x t pht khng nh hng, khng phn cc v khng n sc.

1.2. Bc x kch thch

Dch chuyn ca ht t mc nng lng cao xung mc nng lng thp s xy ra

nhanh hn khi c tc dng ca trng in t bn ngoi, tc l trng in t c kh

nng tng xc sut bc x lng t ca ht. Bc x b sung c gi l bc x

kch thch (hay bc x cm ng).

Bc x kch thch c nhng tnh cht c bit quan trng: tn s, phn cc, hng

truyn trng lng t ca n v ca trng in t ngoi l trng nhau.

Hnh II.1-2 Cc dch chuyn hp

th, bc x v bc x cm ng v

cc h s c trng cho xc sut

chuyn dch.

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Ngoi bc x t pht v bc x cm ng, h ht c th hp th cng hng. Ht

mc nng lng thp (1), di tc dng ca trng in t ngoi c th ln mc nng

lng cao hn (2), ng thi hp th lng t hv = 2W - 1W . Trng hp ny ngi ta

gi l hp th cng hng, hay n gin l hp th.

2. Mi rng m o ln

Nu mt mi trng hot tnh c hai mc nng lng 1E v 2E ta c th kch thch

mt s nguyn t chuyn t trng thi c mc nng lng 1E sang mc nng lng 2E ,

kt qu l 1N s gim v 2N tng dn. Tuy nhin, khi 2N tng th xc sut xy ra qu

trnh pht x cng tng, ngha l qu trnh nguyn t chuyn t trng thi kch thch v

trng thi c bn tng v lm 2N gim. Cui cng h s t ti trng thi cn bng m

khng th to ra mi trng 2 1N N , hay h lng t vi hai mc nng lng 1E v

2E khng th to ra mi trng c mt o ln.

to mt o ln, khi ngi ta to ra mi trng hot tnh trong nguyn

t s c 3 (hoc 4) mc nng lng 1E , 2E v 3E sao cho thi gian sng nguyn t

mc 3E rt nh so vi thi gian sng mc 2E . Bng phng php bm quang hc

hoc bm in, ngi ta kch thch cc nguyn t chuyn t trng thi c nng lng

1E ln mc nng lng 3E . V thi gian sng ca nguyn t mc 3E nh hn nhiu

Hnh II.2-1 S v cc dch

chuyn i vi h hai mc

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so vi thi gian sng mc 2E nn nguyn t nhanh chng chuyn v mc 2E . Kt

qu l ta t c trng thi mt o ln vi 2 1N N .

Hnh II.2-2 S v dch chuyn trong h lng t 3 mc (tri) v 4 mc

(tri).

Mt chm nh sng n sc phng c hng z vi tn s v , in trng

(z) Re ( )exp( 2 )E z j vt , c bin E(z), cng 2

( ) ( ) / 2I z E z , mt dng

photon ( ) ( ) /z I z hv (dng photon trn mt n v din tch ) s tng tc vi cc

nguyn t mi trng, cung cp cc nguyn t ca mi trng c hai mc nng lng

cc mc nng lng khc gn nhau c mc nng lng photon l hv . S cc nguyn

t trn mt n v th tch mc nng lng thp v cao ln lt c gi tr tng ng

l 1N v 2N . Sng c khuch i vi h s tng ( )v (trn mt n v chiu di ) v

tri qua mt s thay i pha ( )v (trn mt n v chiu di ). Chng ta s tho lun

xc nh biu hin trong ( )v v ( )v . Khi ( )v dng tng ng vi qu trnh

khuch i , ( )v m tng ng vi qu trnh suy gim.

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3. ng v bng hng

C ba hnh thc tng tc gia photon v in t c ni n trong chng 13.

Nu in t di mc nng lng thp, photon c th b hp th. Nu in t trn

mc nng lng cao photon th cp s c pht ra bi qu trnh kch thch bc x.

Hai qu trnh ny dn n tng ng vi s suy gim hay s khch i. Hnh thc

tng tc th ba ca photon v in t l bc x t pht, trong qu trnh ny in t

trn mc nng lng cao t pht ra mt photon c lp trong s c mt ca photon

khc, s c nhc n trong phn khuch i tp m.

Mt xc sut ( 1s ) l mt nguyn t khng b kch thch hp th mt photon

khc. Ta c cng thc:

w ( )i v

Trong 2( ) / 8 ( )spv t g v l mt trng thi nng lng bin i ph thuc

theo tn s v , ( )g v l hm th hin hnh dng, spt l thi gian sng, bc sng ca

nh sng trong di. Mt xc sut trong kch thch bc x ging nh trong qu trnh

hp th.

3.1 H s tng

Mt trung bnh ca photon hp th ( s photon trong mt n v thi gian trong

mt n v th tch ) l 1WiN . Tng t, mt cc photon c lp c to ra sau qu

trnh kch thch bc x l 2WiN . V vy , s cc photon c to ra trn mt n v th

tch s bng WiN , trong 2 1N N N y l chnh lch mt in t. thun

tin, N c gi n gin l s chnh lch in t. Nu N dng th tn ti mt o

(1)

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ln, to ra di quang khuch i v mt dng photon tng. Nu N m th to ra di

quang suy gim v mt dng photon gim. Nu N=0 th di khng i.

Khi photon nh hng theo hng ti z th photon b kch thch pht x cng nh

hng theo hng z. u ra ca bm c chim o ngc (N>0) khi mt dng

photon ( )z tng theo hng ti z. V photon tip tc kch thch bc x nn s pht

trin bt k v tr z no l t l thun vi b chim ti v tr . V vy ( )z tng

theo hm s m.

chng minh qu trnh ny mt cch r rng , ta xem xt mt s gia tng theo

hnh tr ca chiu di dz v n v din tch. Nu ( )z v ( ) ( )z d z l mt

thng lng dng photon i vo v i ra trong gia tng hnh tr tng ng, th ( )d z

s l mt thng lng dng photon c pht ra t bn trong hnh tr. S gia tng

s photon ny (s photon trn mt n v din tch trong mt n v thi gian ) ( )d z

n gin l s photon tng ln trn mt n v thi gian trn n v th tch, iNW , nhn

vi chiu di ca ng tr dz:

Wid N dz (2)

Hnh II.3-1 Mt thng lng dng photon (photon / 2cm s ) vo mt gia

tng tr c cha cc nguyn t b kch thch tng n d sau khong cch dz.

13

T cng thc (1) v (2) ta c phng trinh vi phn:

( )( ) ( )

( )

d zv z

d z

(3)

Trong :

H s ( )v th hin s tng ca mt dng photon trn n v chiu di ca di

quang. Gii phng trnh (3) ta c:

( ) (0)exp ( )z v z (5)

Vi cng quang ( ) ( )I z hv z , phng trnh (5) c th vit theo I(z)

( ) (0)exp (v)zI z I (6)

V vy cng c th ni ( )v tng cng trn mt n v chiu di ca di

quang.

H s tng khuch i ( )v t l thun vi chim 2 1N N N . D N c cho l

dng trong cc v d cung cp trn, c th ly i s cho bt k gi tr no ca N.

Trong trng hp khng c mt o ln hay N m ( 2 1N N ) v h s tng cng m.

Khi di quang s suy gim (him gp hn so vi s khuch i ) nh sng s nh

hng theo hng z, tng theo m s ca phng trnh:

( ) (0)exp[- ( ) ]z v z

2

( ) N (v) N8 sp

vt

(4)

H s tng

14

Trong h s suy gim ( ) (v) N (v)v trong mi trng cn bng nhit

v vy khng th cung cp cho b khuch i laser.

3.2 tng

Trong tng tc c tng chiu di l d (Trong hnh II.3-1),tng h s tng khuch

i laser G(v) c xc nh theo t s ca mt thng lng photon u ra trn

cho mt thng lng photon u vo G(v) = (d) / (0) do :

3.3 Bng thng

Ty thuc vo h s tng ( )v da trn tn s ca nh sng v cha trong n v t l

vi hm hnh dng g(v). Sau cng l hm theo rng v gia cc nguyn t cng

hng vi tn s 0 2 1( ) /v E E h ,vi 2E v 1E l cc nng lng ca nguyn t. V

th, khuch i laser l mt thit b cng hng, vi tn s cng hng v bng thng

c xc nh bi hm hnh dng ca nguyn t chuyn tip. l v s kch thch

bc x v hp th c iu chnh bi nguyn t chuyn tip. rng v c tnh

theo n vi tn s (Hz) hoc n v bc sng (nm). rng ny c thay th bng

2 2( / ) ( / ) ( / )o o o oc v c v v c v . V th vi rng v =1THz ti o =0.6m s

tng ng vi =1.2nm.

Nu hm hnh dng c phng trnh :

2 2

/ 2( )

( ) ( / 2)o

vg v

v v v

(8)

Th h s tng Lorentzian vi cng rng.

( ) exp[ ( ) ]G v v d (7)

tng khuch i

15

2

2 2

( / 2)( ) ( )

( ) ( / 2)o

o

vv v

v v v

(9)

Vi 2 2( ) N( / 4 )o spv t v l h s tng ti tn s trung tm ov .

Hnh II.3-2 H s tng ( )v ca hnh dng ng lorentzian cng hng

khuch i laser.

4. S tr pha.

S khuch i v lan truyn ph thuc vo tn s. tr pha nh hng bi s

khuch i laser c th nh ngha bng cch xem xt s nh hng ca gii hn vt

cht ca in trng vi nh sng hn l cng hay mt photon.

H s lch pha ( ) ( s tr pha trn mt n v di ca mi trng khuch i)

lin quan ti h s khuch i ( ) bng chuyn i Heilbert.

Ti tt c tn s ( ) ch cho ra duy nht mt ( ). Mt nh sng v bin

sng ca trng biu th qua cng thc: I(z) = |E(z)|2/2. Vi I(z) = I(0) exp[( )z]

Bin sng trng bng: E(z) = E(0) exp[

( )z] exp[-j ( )z] (10)

16

Ta c bin sng ti z + z l:

(11)

Sau khi dng khai trin taylor cho hm m ta c s tng ca in trng:

V n tha mn phng trnh:

(12)

S tng khuch i c th c xem nh tuyn tnh vi bin l E(z) v E(z)/z.

Hm truyn qua c dng nh sau:

(13)

V s tng khuch i l mt h vt l nn n c h qu. Nhng phn thc v o

ca hm truyn qua ca h thng tuyn tnh lin quan ti chuyn di Hilbert theo -

( ) l s bin i ca

( ) do hm khuch i lch pha ph thuc vo h s

tng ca n.

H s tr pha tng ng h s tng theo hm Lorentzian Lineshape l:

17

H s tng l ln nht v h s tr pha l 0 ti ni cng hng. H s tr pha l m

khi di s cng hng v dng khi trn vi hm Lorentizian line-shape,c

minh ho hnh II.4-1 bn di.

III. BM KHUCH I LASER

S dng ngoi lc cung cp nng lng cho khuch i tn hiu vo. Bm cung

cp nng lng thng qua b truyn ng kch thch electron trong nguyn t, t

nguyn t c trng thi tht ti nguyn t c trng thi cao. lm c iu ny bm

cn phi cung cp mt lng N = N2 N1>0.

Tuy nhin, b truyn ng ca bm thng dng s ph thuc vo mc nng

lng bm c th bng: quang hc (n flash, laser), bng nng lng in ( e-beam,

Hnh II.4-1 H s tr pha v h

s tng vi hm Lorentizian line-

shape

(14)

H s tr pha

(Lorentzian

Lineshape)

18

i-beam, qua mt kh c nng lng, hoc a vo mt nng lng) hoc bng phng

php ha hc ( nhit hoc mt phn ng m sn phm trng thi kch thch.

Vi sng lin tc (continuous-wave) t l ca s kch thch v s tn ti khc nhau

ca cc mc nng lng phi cn bn duy tr trng thi cn bng qu trnh nghch

o t mc 2 1.

1. Phng rnh c

Phng trnh biu th tc thay i mt N1 v N2 l kt qu ca bm cng nh

qu trnh bc x v khng bc x ca thay i c gi l phng trnh tc - rate

equation.

iu kin cn bng nhit khng tn ti v s la chn ngoi lc t bn ngoi l mt

qu trnh.

Da vo hnh III.1-1 xem mc 1 v 2 c thi gian sng ( lifetime) l 1 v 2 cho

php chuyn xung mc thp hn. Thi gian sng ca mc 2 c hai gi tr - mt c

lin quan n phn r t 2 1 ( 21), v mt lin quan n s phn r t mc 2 xung

tt c cc mc thp hn ( 20). T tt c cc dng phn r c th, tc chuyn tip

ton phn l tng ca cc tc chuyn tip thnh phn. V tc l t l nghch ca

s phn r (decay) nn nghch o ca thi gian phn hy c thm vo:

(15)

C nhiu dng phn r do thi gian sng ton phn gim i (v d nh ta lm

qu trnh phn r nhanh hn). Bn cnh cc thnh phn bc x c th pht x t pht

(hng s thi gian tsp ) trong 21, thnh phn khng bc x tham gia vo nr (pht sinh,

19

t mt v va chm ca in t vi cc bc tng ca cc vng cha, do dn n

mt suy gim mt in t), dn n:

(16)

Nu mt h khng c tc ng bm ging nh minh ho hnh III.1-1 c th t

ti trng thi n nh, s mt in t N1 v N2 s b trit tiu bi h qu ca tt c

cc electron sau cng phn r n mc nng lng thp hn.

Mt in t trng thi n nh ca mc 1 v 2 c th c duy tr, tuy nhin,

nu nng lng ca mc di mc 2 vn ang b kch thch bi tc ng bm

(pumping) v mt in t sau cng ca mc 2 c th hin r rng hn hnh

III.1-2. Bm lm cho nhng nguyn t c electron ngoi mc 1 v 2 ra khi mc 1

v vo mc 2, c h s R1 v R2 ( trn 1 n v th tch trn giy) , lm cho mc 1 v 2

t c nhiu trng thi n nh ( mt khc 0).

Chng ta tin hnh vit cc phng trnh tc cho h thng ny c trong trng

hp khng c v c s hin din ca bc x khuch i (bc x cng hng vi

chuyn tip 2 1).

Hnh III.1-1 Mc nng lng 1

& 2 v thi gian phn r ca

chng.

20

1.1. Phng trnh tc trong h khng c bc x khuch i

Phng trnh tng mt in t ca mc 1 v 2 pht sinh t bm v phn ra l:

Hnh III.1-2 Nng lng mc 1

v 2 xung quanh mc nng

lng cao hn v thp hn vi

s c mt ca bm.

Hnh III.1-3 Mc nng lng 1

& 2 v thi gian phn r ca

chng. Vi s c mt ca bm,

mt ca mc 2 tng vi h s

R2 v mc 1 gim vi h s R1.

(17)

(18)

21

Di iu kin trng thi n nh (dN1/dt = dN2/dt = 0), ta gii phng trnh

(17) v (18) rt ra c N1 v N2 v xc nh s chnh lch mt in t N = N2

N1. Kt qu l:

Vi N0 i din cho chnh lch mt in t N khi khng c khuch i bc x.

Theo phn trn, h s tng cn c chnh lch mt in t ln, tc l N0 c gi tr

ln. Phng trnh (19) cho thy iu ny c th t c bng cch:

R1 v R2 ln.

2 c gi tr ln ( nhng tsp nh hng ti 2 thng qua 21 phi c gi tr nh

tc bc x chuyn tip ln).

1 nh nu R1< ( 2/ 21) R2.

Cc l lun vt l lm c s cho nhng iu kin ny hp l. Mc cao cn c

bm mnh v phn r chm n duy tr c mt ca mnh. Mc thp hn nn

c gin tip bm mnh n b tr nhanh mt in t. Mt cch l tng, ta c

21 tsp 20 nn 2 tsp, v 1 tsp. Theo nhng iu kin , phng trnh (19)

c vit n gin li l:

(20)

Khi khng c depumping (x bm) (R1 = 0), hay khi R1 (tsp/ 1) R2, do cng

thc c n gin ho thnh:

(19)

Chnh lch mt in t trng thi

n nh khng c khuch i bc x.

(21)

22

1.2. Phng trnh tc trong h c bc x khuch i

Khi c bc x gn tn s cng hng (resonance frequency) 0 , to iu kin cho

vic chuyn tip gia mc 2 sang mc 1 din ra thng qua bc x kch thch cng nh

l s hp th. Nhng qu trnh ny c m t bi mt xc sut Wi = .

Phng trnh tc (17) v (18) phi c m rng bao gm nguyn nhn ca s

mt i mt in t v tng trong c hai mc:

Mt in t ca mc 2 gim xung bi pht x kch thch (cm ng) t mc 2

n mc 1 v c tng ln bi s hp th t mc 1 ti mc 2. S gp phn pht bc

x t pht c bao gm trong 21.

Hnh III.1-4 Mt in t N1 v N2 (cm-3

s-1) ca cc in t trong nng

lng mc 1 v 2 c quyt nh bi ba qu trnh: s phn r ( ti tc 1/ 1 v

(22)

(23)

23

1/ 2, theo th t, bao gm cc tc ng ca s pht bc x t pht), x bm v s

bm ( ti tc theo th t l R1 v R2), v s hp th v pht x kch thch (cm

ng) (ti tc W1 vi hng s thi gian tng ng W-1

i ).

Di iu kin trng thi n nh (dN1/dt = dN2/dt =0), gii phng trnh (22) v

(23) rt ra N1 v N2, v s chnh lch v mt N = N2 N1. Kt qu l:

Trong : N0 l s chnh lch mt in t di iu kin trng thi n nh khi

s c mt ca bc x khuch i. Thi gian c trng s lun dng bi 2 21,

c biu din:

Khi khng c bc x khuch i, Wi = 0 v th theo biu thc (24) ta c N=N0 nh

mong i. Bi v s l dng, s chnh lch mt in t di iu kin trng thi n

nh nu c bc x khuch i lun l mt gi tr tuyt i nh hn trng hp khng

c bc x khuch i, |N| |N0|. Nu bc x yu th sWi 1, chng ta c th

ly N N0. V bc x khuch i tr nn mnh hn, Wi tng ln nn cui cng N 0

bt k tn hiu ban u ca N0, c minh ho trong hnh III.1-5. iu ny xut hin

bi v pht x kch thch v s hp th chi phi s tng tc khi Wi rt ln v mt

xc sut ca chng c th bng nhau. Hin nhin rng, thm ch mi bc x mnh

(24)

S chnh lch mt in t di iu

kin trng thi n nh khi c Amplifier

Radiation bc x khuch i.

(25)

Hng s thi gian bo ho

24

cng khng th bin i s chnh lch mt in t m thnh dng cng nh

ngc li. Lng s ng vai tr l mt hng s thi gian bo ha,nh hnh III.1-5

2. Cu to ca mt my pht laser

Laser my pht lng t cng quang hc gm 3 b phn chnh:

- Mi trng hot cht (gain medium)

- Bung cng hng

- B phn kch thch

Hnh III.1-5 S suy gim ca

chnh lch mt trong iu

kin trng thi n nh N = N2

N1 bi v tc ca s hp

th v pht x kch thch Wi

tng ln. Khi Wi =1/ s, N gim

xung bi mt yu t ca 2 t

gi tr ca n khi Wi = 0.

25

2.1 Mi trng hot cht (gain medium)

Mi trng hot cht l mi trng vt cht c kh nng khuch i nh sng i

qua n. Trong mi trng hot cht cha rt nhiu in t c cu trc nng lng sao

cho c th tm c trong t nht l ba mc nng lng hoc bn mc nng lng

to mt o ln. Hot cht gm:

i. Hot cht l cht kh i vi Laser kh.

- Kh n nguyn t: ArI, XeI, NeI.

- Ion kh n nguyn t: ArII, KrII..

- Kh phn t: CO2, CO, N2..

- Hn hp kh n nguyn t: He Ne

- Hn hp kh phn t: CO2 N2 He, CO N2 H2O

ii. Hot cht l cht rn i vi Laser rn

- Tinh th hay thy tinh c pha trn thm cc ion nguyn t him:

Eu3+

, Cr3+. Laser ruby: Cr3+ pha tp vo tinh th Al2O3.

iii. Hot cht l bn dn i vi Laser bn dn: GaAs, PbS, PbTe

iv. Hot cht l cht lng i vi Laser lng: Pereridin Eu (BA)4 ha tan trong

dung mi ru ethol + methol v pha tp thm ion nguyn t him Eu3+,

Nd3+

26

2.2 Bung cng hng

Bung cng hng l b phn m bo qu trnh phn hi ngc quang hc dng.

Mt bung cng hng gm 2 gng phn x, mt gng c h s phn x rt cao

100% v gng cn li c h s phn x thp hn khong 95% tia laser thot ra

ngoi. Mt trong cc gng c th c thay bng lng knh hay cch t.

Bung cng hng c vai tr l lm cho bc x do mi trng hat cht pht ra c

th truyn qua mi trng hat cht nhiu ln bc x ny c khuch i nhiu

ln.

2.3 B phn kch thch hay bm

Bm cung cp nng lng to s nghch o tch ly trong hai mc nng

lng no ca mi trng hat cht v duy tr s hat ng ca laser. Bao gm:

Kch thch bng nh sng bm quang hc.

Kch thch bng va chm in t: nng lng in t c gia tc trong in

trng c truyn cho cc nguyn t trong mi trng hat cht thng qua

qu trnh va chm.

3. Nguyn l pht bc x Laser

Chng ta ch tin hnh qu trnh pht ra bc x laser khi c cc iu kin:

Cn c mt mi trng hot tnh.

Dng cc phng php bm lm cho mi trng tr thnh mi trng

c mt o ln.

Cn dng mt c cu khuch i bc x pht ra. C cu ny gi l bung

cng hng.

27

y chng ta xem xt c ch hot ng ca bung cng hng. Khi cc in t

c a vo mi trng hot cht qua cc phng php bm s b bc x t pht hay

bc x kch thch gia cc mc nng lng, do to nn hiu ng thc bc x cm

ng.

Cc bc x cm ng ny s c phn hi qua li bng cch phn x qua hai gng

ca bung cng hng.

Hnh III.3-1 Bung cng hng ca my pht Laser Ruby

Hnh III.3-2 Hiu ng thc

bc x cm ng

Hnh III.3-3 Cc bc

x cm ng b phn x

qua gng

28

Cc photon cm ng b phn hi qua li trong mi trng hot cht bi hai gng

ca bung cng hng s c mt phn nh thot ra,do thit k mt trong hai gng c

phn x 95% khng phn x hon ton cc photon. Cc photon thot ra ny ng

pha v c nh hng ging nhau to nn chm laser pht ra.

4. S b khuch i laser

Chng ta tin hnh kim tra c th s bm bn cp v ba cp c s dng

t c mt mt o ln. Cc mc ch ca cc cch sp xp ny l lm cho vic

s dng mt qu trnh kch thch lm tng s lng ca cc nguyn t tch lu mc 2

trong khi gim s lng tch lu mc 1.

4.1 S bm bn mc

Trong s sp xp ny, th hin trong hnh III.4-1, mc 1 nm trn trng thi c bn

(c ch nh l mc nng lng thp nht; mc 0). Trong trng thi cn bng nhit,

mc 1 s hu nh khng c in t vi iu kin E1 KT. Qu trnh bm kch

thch cc in t t mc 0 n mt mc nng lng (hoc tp hp cc mc nng

lng) nm trn mc 2, chng ta gi mc nng lng ny l mc 3. Do mc 3 c thi

gian sng ngn nn in t s phn r trc tip xung trng thi c bn theo cch bc

x v pht ra photon cm ng. Nhng do mc 2 c nng lng thp hn nn in t s

Hnh III.3-4 Chm laser

pht ra

29

nhy (khng c bc x) ti mc 2, t y in t c th phn r xung mc nng

lng 1 thng qua qu trnh bc x t pht, trong nng lng d ra thu c nh s

pht photon c bc sng di hn bc sng kch thch. Mc 2 c thi gian sng lu

di, do n tch ly mt in t, trong khi mc 1 l ngn ngi nn n y

ra nguyn t, do mt mt o ln thit lp gia cc cp 2 v 1.y l iu

kin c s in t trn mc 2 nhiu hn mc 1.

Mt photon c mc nng lng tng ng vi s chnh lch gia mc 2 v 1th

n s kch thch cc in t mc 2 ri xung mc 1 v pht thm mt photon, photon

ny cng pha v hng vi photon ti (hin tng ny gi l bc x kch thch ca cc

photon). Bc x lm xut hin thm cc photon cng pha v cng hng vi cc

photon ti, iu ny c ngha l nh sng c khuch i to nn chm laser.

Hnh III.4-1 mc nng lng v tc phn r cho mt h thng bn mc.

Ngi ta cho rng t l bm vo cp 3, v ra khi mc 0, u ging nhau.

Mt ngun nng lng bn ngoi (v d, cc photon vi tn s E3/h) bm in t t

mc 0 n cp 3 vi tc R. Nu s phn r t cp 3 n cp 2 l nhanh, n c

th c xem l tc thi, trong trng hp tc bm in t vo mc 3 tng ng

30

vi bm vo mc 2, tc l R2 = R. Tuy nhin, trong cu hnh in t khng c s bm

vo cng nh ra ngoi mc 1, do R1 = 0. Nh vy, trong trng hp khng c bc

x khuch i (Wi = = 0), s khc bit mt in t trng thi n nh c a

ra bi biu thc (19) vi R1 = 0, tc l,

10 2

21

1N R

(26)

Trong hu ht cc h thng bm bn mc, cc in t phn r khng bc x trong

qu trnh chuyn i 2 1 l khng ng k (tsp nr) v 20 tsp 1 , do :

0 sp

s sp

N Rt

t

V do :

1

sp

sp i

RtN

t W

Ta gi thuyt rng tc bm R l c lp vi s chnh lch mt in t

(N = N2 - N1 ). iu ny khng phi l lun lun nh vy, tuy nhin, bi v mt tch

lu ca cc trng thi c bn v cp 3, tng ng Ng v N3, c lin quan n N1 v N2

bng:

1 2 3g aN N N N N (30)

Na l tng mt in t trong h thng, v l mt hng s. Nu bm bao gm mt

qu trnh chuyn tip gia trng thi c bn v cp 3 vi xc sut chuyn tip W,

(27)

(28)

(29)

31

R = (Ng - N 3)W. Nu mc 1 v 3 l tn ti trong thi gian ngn, sau N1 N3 0, v

Ng + N2 Na Ng Na - N2 Na - N.

Di nhng iu kin, tc bm c th c xp x nh:

aR N N W (31)

Trong cho thy rng tc bm l mt hm tuyn tnh gim ca s chnh lch

mt in t N v do r rng l khng c lp. iu ny pht sinh do s mt

o ln in t c thit lp gia cc mc 2 v 1 lm gim s lng ca cc in

t c sn c bm. Thay th biu thc (31) vo (29), v sp xp li cc iu kin, dn

n:

1

sp a

sp sp i

t N WN

t W t W

(32)

Cui cng, s chnh lch mt in t c th c vit di hnh thc chung ca

biu thc (24),

01

NN

Ws i

(33)

Nhng m by gi N0 v s, khng c th hin nh biu thc (27) v (28), m

c biu din di biu thc:

01

sp a

sp

t N W

t WN

(34)

V

32

1

sp

s

sp

t

t W

(35)

i vi bm yu (W 1/tsp), N0 tspNaW l t l vi mt xc sut bm chuyn

tip W, v s tsp , do biu thc (27) v (28) xut hin tr li. Tuy nhin, khi bm

tng sc mnh, N0 gim v cui cng l bo ha, trong khi s gim.

4.2 S bm ba mc

s bm ba cp, ngc li, s dng trng thi c bn (E1 = 0) nh mc laser

thp 1, nh m t trong hnh III.4-2. Mt ln na, mc th ba ph tr (c gi l

mc 3) l c tham gia vo v qu trnh chuyn tip 3 2 phn r nhanh chng

khng c s tch t ca mt in t cp 3. Trong khi , qu trnh chuyn tip

3 1 phn r chm ( 32 31) bm cung cp in t cho mt mc 2, l mc

laser cao hn. mc 2 c thi gian sng di v do tch ly mt in t. in t

c bm t mc 1 n mc 3 ( bng cch hp th nh sng tn s E3/h) vi tc

R; phn r nhanh (khng bc x) to iu kin cho bm cp 2 vi tc R2 = R. in

t b kch thch nhit ca mc 2 c gi s l khng ng k.

Ta d nhn thy rng di qu trnh chuyn tip 3 2 phn r nhanh, h thng ba

mc hin th trong hnh III.4-2 l mt trng hp c bit ca h thng th hin trong

hnh III.1-4 (vi iu kin l R l c lp ca N) vi cc thng s:

1 2R R R , 1 , 2 21 (36)

trnh nhng vn i s trong lin h vi cc gi tr 1 = , khng phi thay

th cc gi tr c bit vo biu thc (24) v (25), chng ta p dng cc thng s trn

33

tr li phng trnh tc ban u (22) v (23). Trong trng thi n nh, c hai

phng trnh cho ra cc kt qu tng t:

22 1

21

0 i iN

R N W N W

(37)

Hnh III.4-2 mc nng lng v tc phn r cho mt h thng ba mc.

Ngi ta cho rng t l bm vo cp 3 cng ging nh t l bm cp 1.

Khng th xc nh c hai N1 v N2 t mt phng trnh duy nht c lin quan vi

chng. Tuy nhin, kin thc v tng mt in t Na trong h thng ( mc 1,2,

v 3) quy nh mt iu kin h tr, m cho php xc nh N1 v N2. V 32 l rt ngn,

mc 3 vn gi c mt mt in t khng ng k trng thi n nh, tt c cc

in t c bm ln ngay lp tc phn r xung mc 2. Do ,

1 2 aN N N (38)

Biu thc trn cho php chng ta gii phng trnh (37) cho N1 v N2 v do

xc nh s chnh lch mt in t N = N2 - N1 v thi gian s bo ha. Kt qu c

th c c kt theo biu thcthng dng (24), N = N0 / (1 + sWi), by gi l:

0 212 aN R N (39)

212s (40)

34

Khi phn r khng bc x t mc 2 n mc 1 l khng ng k (tsp nr), 21 c

th c thay th bng tsp, v ri:

0 2 sp aN Rt N (41)

2s spt (42)

Chng ta quan tm n vic so snh cc phng trnh vi kt qu tng t nh

(27) v (28) cho mt s bm bn mc. t c mt mt o ln (N > 0 v do

N0 > 0) trong h thng ba mc i hi tc bm R tho R > Na/2tsp . Nh vy,

lm cho mt in t N2 bng N1 (tc l, N0 = 0) yu cu mt mt nng lng

bm ng k, vi E3Na/2tsp. Mt in t ln trng thi c bn ( l mc laser

thp nht) l mt tr ngi c sn t c mt s mt o ln trong mt h

thng bm ba mc v tr ngi ny c b qua trong mt h thng bm bn cp

(trong mc 1 l bnh thng trng v 1 ngn). Thi gian bo ha lin tc s tsp

cho s bm bn cp ch bng mt na cho s bm ba cp. V mt ln na, nh

trong hnh III.1-4, mt trng thi n nh o ngc tch lu khng th t c

bng cch trc tip bm quang hc gia cc cp 1 v 2.

S ph thuc ca tc bm R vo s chnh lch mt in t N c th c

a vo phn tch ca h thng bm ba cp bng cch vit R = (N1 - N3)W, N3 0, v

N1 =

(Na - N). T R

(Na - N)W.

Thay vo phng trnh chnh N = (2Rtsp - Na) / (1 + 2tspWi), v t chc li cc iu

kin, chng ta c th vit s chnh lch mt in t trong biu thc thc thng

dng l:

0

1 s i

NN

W

(43)

35

Nhng by gi vi:

0

1

1

a sp

sp

N t WN

t W

(44)

V

2

1

sp

s

sp

t

Wt

(45)

Nh trong s bm bn cp, N0 v s bo ha khi cc tn sut bm chuyn tip

W tng.

IV. BI TP P DNG

1. S suy gim v ng ca my pht laser ruby.

a. Xt mt tinh th ruby c hai mc nng lng song song vi bc sng

0 694,3nm ,vi rng lorent 330v GHz , thi gian sng 3spt ms ,

chit sut ca ruby n=1,76. Nu 22 31 2 10aN N N cm

. Xc nh mt

o ln 2 1N N N v h s suy gim 0( )v di iu kin cn bng nhit

T=300 K

b. Tnh mt o ln N bit h s tng 10( ) 0.5v cm ti tn s trung tm ?

c. Tnh di tinh th ruby khi c tng bng 4 ti tn s trung tm v

1

0( ) 0.5v cm ?

2. B q ang hc

Gi s rng tc bm R1 = 0 v R2 c cho bi nguyn t kch thch t

trng thi E = 0 ln mc 2 vi tn s nh sng l E2/h hp th bi kh nng

36

chuyn tip W. Gi s2 1sp spt and t hy chng minh rng trng thi cn

bng 1 0N v 0 2 spN R t . Nu N l tng mt in t ca mc 0, 1, v 2,

chng minh rng 2 0( 2 )WaR N N , do khc bit mt in t l

0 W / (1 2 W)a sp spN N t t

3. Nng ng b rong h thng b ba c v bn mc

a. Xc nh tn sut bm chuyn tip W cn thit t c chnh lch mt

in t bng 0 trong mt b khuch i laser ba mc va bn mc.

b. Nu tn sut bm chuyn tip W = 2/tsp trong h bm ba mc, v W =

1/2tsp trong h bm bn mc, chng minh N0 = Na/3.

Li gii :

1.

a. Ta c 2 2 1

1

exp( ) exp( ),N E E hv

N KT KT

vi 0

0

cv

34 8

9 34

6,625.10 .3.1069,12

694,3.10 .1,38.10 .300

hv hc

KT KT

69,12 302

1

0,958.10N

eN

2 1 2 0N N N

2 1 1 aN N N N N 22 3 28 310 10N cm m

2 228 10

0 0 2 2 3

( / ) (0,694 /1,76)( ) ( ) 10 3,98

4 4 3.330.10sp

nv v N m

t v

Vy h s suy gim 4 10( ) 3,98.10v m

b. 1 10( ) 0,5 50v cm m

37

22

0 0

4( ) ( )

4

sp

sp

t vv N N v

t v

25 31,254.10 /N atom m

c . Ta c 0( ) 500( ) 4 50 ln(4) ln(4) / 50

v dG v e e d d

d=0,02772m

2.

b chim ca 3 mc nng lng mc 2,mc 1 v mc c bn ln lt l 2N , 1N v

0N . Theo ta c 2 1 0 aN N N N

Gi thuyt 1 spt c ngha mc 1 c thi sng rt nh nn 1 0N

0 2aN N N (1)

V 2 spt 0 2 spN R t v 1R

Vi trng thi n nh 2 22

2

0 0dN N

Rdt

, 2 spt

H thng c bm c dch chuyn gia mc c bn v mc 2 ,v vy nn

2 0 2 0 2W W ( )Wi iR N N N N (2)

T (1) chng ta c 2g aN N N 2 2( 2 )WaR N N (3)

Chng ta c 0 2 ,spN R t

0 2( 2 )Wa spN N N t (4)

Ta c 0 2 1 2N N N N ( v 1 0N ) (5)

38

T (3) v (5) : 2 0( 2 )WaR N N

T (4) v (5): 0 0 0 0( 2 )Wt W 2a sp a sp spN N N N N t Wt N

Hay 0 02 Wsp a spN Wt N N t

0

W

(1 2 )

a sp

sp

N tN

Wt

(pcm)

3 .

Xt h bm ba mc:

a) p dng cng thc (44) ta c:

0

1

1

a sp

sp i

N t WN

t W

M N0 = 0 suy ra tspW 1 = 0 hay W = 1/tsp

b) Khi W = 2/tsp

Th vo cng thc (44) ta c 0(2 1)

1 2

aNN

.

Suy ra N0 = Na/3 (pcm)

Xt h bm bn mc:

a) p dng cng thc (34) ta c:

M N0 = 0 suy ra W = 0 do tsp v Na

b) Khi W = 1/2tsp

Th vo (34) ta c N0 = Na(1/2)/(1 + ) = Na/3

Vy s chnh lch mt in t trong h bm ba mc v bn mc bng nhau

th tn sut bm W ca h ba mc gp bn ln tn sut bm ca h bn mc.

39

TI LIU THAM KHO

Ting vi t

[1] Nguyn Hu Tr-Trn Tun (2002), Vt l laser, Nh xut bn i hc quc gia TP

H Ch Minh.

[2] Trn c Hn,Nguyn Minh Hin (2005), Quang ph nguyn t v ng dng, Nh

xut bn Gio dc

[3] Dng i Phng (2002), Quang ph phn t v ng dng, Nh xut bn i hc

quc gia TP H Ch Minh

Ting Anh

[4]B.E.A.Saleh-M.C.Teich, Fundamentals tals of photonics,Boston University