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Khuếch Đại Laser
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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
3
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
7
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 ).
8
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.
9
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
10
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.
11
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)
12
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