Download - Principles of Lasers
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ORAZIO SVELTO
PRINCIPLES of LASERS
F o u R T h E d i i N
TRANSIATJON FROM ENGHSIH b y D . N . K O S L O V , S . B . S O Z I N O V A N C I K . G . A D A M O V I C H ;
EdiTEdbyT. A . S H M A O N O V
SAINT-PETERSBURG M O S C O W KRASNODAR 2008
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2008
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32.86-5 3 43
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3 43 / . . . . . . 4-. .: , 2008. 720 : . ( . ). ISBN 978-5-8114-0844-3
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32.86-5
06-02-30013
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. . , . . , . . , . . ,
, 2008 ,
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, 2008 Translation from the Engl ish language edition:
Principles of Lasers, 4 t K e d . B y Orazio Svelto Copyright 1998 P lenum Publ ishing Corporation, being a part of Springer Science + Business Media
A l l Rights Reserved
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dt = - W l 2 # i , (1.1.6)
(dN1/dt)a 1 2 , a Nt 1. W12 , (1.1.5):
14 . .
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WL2 = G12F, (1.1.7)
a 1 2 ( ), .
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21 1 2 . X X ,
W21 = W12 , , a 2 1 = a i 2 * 1 2 gx- 2- ,
S 2 ^ 2 1 = l ^ l 2 > (1.1.8) ,
^ 2 1 = ^ 1 2 - (1.1.9) , ,
(. . 1.1): () 2 1, ; ()
2 -> 1, ; () , 1 - 2. , ,
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1 2 Nx N2 . z F (. 1.2), dF dz ( . 1.2)
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1. 15
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Nc = - [ InR X R 2 + 21n(l - )]/2. (1.2.3) (1.2.3) ,
= -In = -1(1 -
), (1.2.4) 2 = -1 2 = ( 1 - 2 ) , (1.2.46)
Y - - l n ( l - L ; ) , (1.2.4) 12 ( ). (1.2.4) (1.2.3)
Nc = y/al, (1.2.5)
1. 17
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Y = [2Y; + ( Y i + y 2 ) ] / 2 . .2.6)
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1. 19
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9 d ,
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1. 25
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. 1.8
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Dc , . Dc = 100 X = 1 . (1.4.1) Qd = - 2 , , , L = 100 , , D = Dc + 2QdL = 2QdL = 2 . ,
, D, , Dc.
I(P)a[(E1(t) + E2(t)]2, Ex(t) ,
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) = C[1 0sin(co* + ) + 2 0sin(co* + 2 )] 2 , , 10 20
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= (0 2 = 2() (., , . 1.6). , , () ) , ) . ,
< )> = [ 2 0 (sin 2 (* + )> + | 0 (sin 2 (* + 2 )> + +21020 (sin(co* + )sin(co* + 2))] = = [(?0 / 2 ) + ( | 0 / 2 ) + 1020((2 - ) ) ] .
, , ^*) 2(*),
(*) = \\fi(t) + kL1 2(*) = (0 + kL2, \ 2 , a L x L2 -
26 . .
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v|/ 1(f) \\f2(t) . , , (0 ~ 1(0> , , (cos (2 - )), , . :
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( ) Ip = 4P/nd2 = / ( /0 ) 2 .
= 4/(2)0) 2. (1.4.4)
(1.4.5)
28 - 0 -
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(1.4.4), 1
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D. 1
, D DL. :
Ip = n(NA)2B, (1.4.6)
NA = sin[tan~ 1()L/2/)] = (DL/2f) . (1.4.6) , .
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1. 29
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400 700 ). .
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1.3. 1 2 . 1.1 (2 - ), .
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1.5. ^ = ^ ^ 2 = 0,5, Lx = 1%. . I = 7,5 , = 2,8 10~1 9 2 , .
1.6. (X = 694 ) 1 . , ,
. ( 384 .)
1.7. , -, ( Labs, 107/109, 100 ) (X = 546 ) 95 / 2 . 1 (X = 514,5 ), -.
1. 31
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, ( ) .
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p v , v. p v : pvdv v v + dv. , p v :
P = / M v - (2.2.2)
Iv ,
, . , Jv p v, :
Iv = (c/4n)Pv, (2.2.3) , & . , Iv , p v, ,
, , v
. p v .
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2. 33
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. , v
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v. p v > ", , (2.2.3), II > / , . . 1 2. ,
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p v = p v . p v(v, )
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, (9 , z, t) :
V * E - i . 0 . O , (2.2.4)
V 2 , .
:
= 0, (2.2.5)
. 2.1
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34 . .
-
,
. , :
= (9 , z)E(t) (2.2.6) (2.2.6) (2.2.4),
V 2 u=J _ d?E
u 2 ' dt2 '
9 , z9 t,
,
, -k2. (9 9 z) E(t):
V 2 u = -fc2u, (2.2.7)
^ - = -(cnk)2E. (2.2.76) (2.2.76) :
= 0cos (* + ), (2.2.8) 0
co = cnk. (2.2.9) E(t) (2.2.8), (2.2.6) :
(9 9 z91) = 0(9 9 )/(* + ). (2.2.9) , (9 9 z)
(9 9 z)9 .
.
(2.2.7), , ,
(2.2.5). , :
= excoskxx suikyy sinkzz9 (2.2.10)
= eysmkxx cos kyy sinkzz9 (2.2.106) u2 = ezsinkxx sinkyy coskzz (2.2. 10B)
(2.2.7a) 9 9 29
:
k2+k2+k2=k2. (2.2.11) ,
(2.2.5). ,
2. 35
-
(2.2.10) , , = 0, = 0, z = 0. , , , z = 0, (2.2.5)
=
= 0, (2.2.10) (2.2.106) , , 2 = 0. (2.2.5) , :
19 . , , , z = L, (2.2.5)
=
= 09 (2.2.10) (2.2.106) , , 2 = 1 (2.2.12). Z, , ,
9 .
, 19 . , kx9 ky kz (2.2.12), , (2.2.9) (2.2.11), :
,
I, . , ,
9 2 .
,
, V = 0, , (2.2.10), exkx + eyky + e2k2 = 0. :
= 0, (2.2.14) , 9 z
9 2 kx9 ky kz . (2.2.14), ,
9 2
. , Z, ( ) , , (2.2.14), , .
. , \|/ ,
, , ,
, . . = ^; +
\|/. , Z, ,
.
iV(v), 0 v. , -
kx = ln/2a9 ky = /29 k2 = nn/L9
(2.2.12) (2.2.126) (2.2.12b)
(2.2.13)
36 . .
-
2n/L_
I > . . 1 . 1
k k* 0 2nv/cn. (2.2.12) , kx9 ky kz ,
,
. 2.2. kx9 ky kz ,
,
. ,
,
(/2, /2, /L). , k9 0 (2nv/cn)9 1/8 (2nv/cn)9 , (/2, /2, n/L). , , k , :
14 ( 2 \ 8 83 [
) grcv3-
. 2.2
,
. 2 .1.
.
iV(v) = 2
7 1
2 2 L
-V, (2.2.15)
V .
2.2.2. -
p v, pv ( 9 , ). pv = dN(v)/Vdv, (2.2.15) :
Pv 1 dN V dv
8 2 (2.2.16)
pv, p v
(), , . .:
Pv=pv{E). (2.2.17) () , . dp
2. 37
-
, + dE, dp = C exp [-(E/kT)]dE, ,
00 $Cexv[-(E/kT)]dE = l.
, () :
)Eexp[-(E/kT)]dE () = * = kT 4 1
00 jexv[-(E/kT)]dE
(2.2.16) (2.2.18) :
(2.2.18)
Pv = J
. (2.2.19)
-
-.
. , , (2.2.19) ,
(. (2.2.2)). , , , (2.2.3), Iv v 2 ,
, v > ( ). ,
.
,
X X . ,
hv, v , a h , . ,
, , .
,
v 0 , (2.2.18), :
= nhv, (2.2.20) . , ,
,
nhvexp[-(nhv/kT)] ^ exp(hv/kT)-l' ^ exn(hv/kT\-l' (2.2.21)
exp[-(rc/iv/A!T)] =0
38 . .
-
[ 1 6 / 3 ]
at
. 2.3 p v (v , )
v
[ 1 0 1 4 ]
(2.2.18). , hv < kT (2.2.21) (2.2.18). (2.2.16), (2.2.17) (2.2.21) :
_ 8 2 hv p v
3 e x p ( * v / * T ) - l ' (2.2.22)
,
, h 6,62 10" 3 4 . . 2,3 p v v .
,
= ^ 1 = * (2.2.23) w
hv exp(hv/kT)-l () . v = 4 10 1 4 , , hv 1 . 300 kT = (1/40) , (2.2.23) , () = ( - 40). , ,
.
0,
( 10 1 0 , . 7.1 . 7).
2.2.3.
,
, (2.2.20), , , . -
(2.2.18) (2.2.21), ,
.
(1904) , , ,
2. 39
-
. ,
(1927). , , [2] . ,
.
, ,
, v
. Ex(v, t) H^r, t) ,
(2.2.1),
V . , , ^ ( r , t) Hy(r, t) [2] . , Ex(r, t) y(r, t), , qx , , , .
,
qx . , , ,
qx9 . Ex(r, t) Hy(r9 i) ,
,
(2.2.4).
, ,
.
,
. ,
, , ,
, :
k , am . . ,
,
.
- , , kpx/29 ,
qx /2. , -
(2.2.24)
E = (kpl/2)Hql/2m), (2.2.25)
, ,
40 . .
-
,
\{\x{H2)/2)dV. , .
, ,
,
. ,
:
E = {l/2)hv + nh\, (2.2.26) .
,
. ,
, , (2.2.25),
qx, , , . ,
, , , (2.2.1),
.
. ,
,
( v) (2.2.26), (. (2.2.20)), , . ,
. ,
(. 2.2.1) ,
. ,
0 , . ,
(2.2.26) - , ,
, . 2.4. , , (2)9 (2) . .
, (hv/2) . (2.2.24)
E = (\pdv)-(hv/2)9 (2.2.27) , .
, -
(2)(2) , . ,
.
h\
hv
i hv/2 . 2.4
2. 41
-
2.3.
,
(. . ), (. . ). , (. . ) . .
,
, ,
, ,
. ,
( ) .
2 3 1
, ,
2 2, , , 1
(. . 1.1). , , :
(, t) = ^ / (2.3.1)
vi/ 2(r, t) = u2(r)exv[-j(E2/h)t], (2.3.16) u12(r) 1 2, - , ( ), h = h/2n. 2 - 1
:
= a^OVi + a2(t)^2, (2.3.2)
2 , . ,
\
\2 |2|2 , t 1 2. , - , :
k l 2 + k l 2 = i , ( 2 . . )
\
\2 |2|2. , ,
JLI. :
\x = -\e\y\2rdV, (2.3.4)
42 . .
-
; . (2.3.4) , , e|y| 2dV ,
dV , d\x = -(e\\\f |2 dV)r. (2.3.2) (2.3.4), (2.3.1) :
\ = [ |
|2| |2 dV + [ \2\2\2 |2 dV +
J
(2.3.5) + \ ^^^ exp j((o0t) + a[a2u{u2 exp[- j((o0t)] jlV,
* , 0 = (2 - Ex)/h. (2.3.5) , jli \iosc, 0, :
Pose = [2
^21 (0*)], (2.3.6) Re . 21
21 = \u2eruxdV. (2.3.7)
21 - , .
(2.3.6) , 2 1 08, 0,
^!, (2.3.7). , .
,
.
:
*W = cos(co0* + ) = [ exp (yo 0 OL
0 ,
, Re , ' , \'0 = 0('). 1
,
:
fi= 3 , (2.3.8) 12rce0cd
1 , , ,
,
, .
= [*] 1 / 2 , * , (. . *, * * , ).
2. 43
-
=| |=| 0 | , ,
. (2.3.8) , [i = 2\a1a2^i2i\y . . 2a1a2\i2i. , , :
=;\1\2\2\2, (2.3.9)
/ ,
1 6 3 2 (2.3.10)
~ 03 '
|jn| = |21| j i 2 1 . , ,
, ,
, ,
:
Tjf = (2.3.11)
= \1\21 + \2\22. (2.3.12) (2.3.3), (2.3.12) :
=
+ hv0\a2\2, (2.3.13) v 0 = (2 - Ex)/h .
(2.3.9), (2.3.10) (2.3.13) (2.3.11) :
d\a2 \ I % 121 "2 \2=~(1-1 2 \2) | 2 | 2 , (2.3.14)
xsp = hv0 / ' ,
3 / i sqC 3 (2.3.15) s p 16* 3v 3rc|uf '
( ) 2 ,
.
1 (2.3.15) :
1 - tanh
(2.3.16)
t0 , | 2 (0) | 2 . , (2.3.16)
1
. . .
44 . .
-
| 2 (0) | ; 1-tanh 2 (2.3.17) sp J _
| 2(0)| 2 ( , 1) t0. . 2.5 | 2()| 2 | 2 (0) | 2 = 0,96. , | 2 (0) | 2 t0 (2.3.16), . . . , , | 2 (0) | 2 = 0,8, | 2()| 2 -
. 2.5
| 2 () | 2
= xspPr/hv0.
;
-
. 2.5 , t = 0 0,8. | 2()| 2 (2.3.16). | 2()| 2, , (2.3.11) (2.3.13),
Pr = - hv0d\a2\2/dt. , = TspPr/hv0, . 2.5. , | 2()| 2 :
\a2(t)\2 = |a 2 (0) | 2 exp[-(f/x s ; , )] (2.3.18) |a 2 (0) | 2
-
,
( ) = 1 / :
1 6 3 ^ | 1 2 (2.39) 3he0c3
, Nt , ,
: N2(t) = Nt\a2(t)\2 N2(0) = AT f|a2(0)|2. (2.3.18) Nt9 : N2(t) = 2(0) (-t/i8p) (1.1.2), , .
2.3.2. -
-
,
, ,
.
, , |a 2 (0) | 2 = 1. (2.3.17) , t0 = . ,
. , |a 2 (0) | 2 = 1, | (0)| 2 = 0, (2.3.14) , d\a2\2/dt = 0. -, ,
(0) = 0 \xosc9 (2.3.6), . ,
, , .
. , ,
, \2\ 1 t = 0. ,
, |
|2, 1. (2.3.6) , , 0. (. . ) , 1. , \2\2 , .
, .
,
, :
1. \2\2 (2.3.16) , (. . \2\2 < 1) (. (2.3.18)).
2. (. . |a 2 (0) | 2 = 1), (), .
46 . .
-
,
[5, 6]: 1. ,
\2\2 ( --) . , (2.3.18) | 2 (0) | 2 .
2. 8 (2.3.15).
3.
=
- hv0d\a2\2/dt, 8.
, , --
-
(. . 2.5). 1 ,
.
,
-
.
.
(2.3.2), , .
,
. , ,
, ,
- , . ,
,
, .
, ,
. ,
. , ,
, .
= . , ,
,
- . , ,
1
, .
v 0 , .
,
, ( ) .
2. 47
-
2.2.3, (2) (2) ^ nj/ = ( ). ,
, , , -
. , ,
.
2.3.3.
(2.3.19) , , 0, , |] 0. , , ,
. ,
|| = 0, = 0, . , -
,
( ). .
, . . || = 0. |uj = |21|, (2.3.7) , , 2
, (. . ). 1 , (2.3.7) - , 2()() u2(-r)(-eY)ui(-r)dV. , ((-) = = ()) ((-) = -()), .
- , (2.3.7) , = 0. , (
, , 2 ), (2.3.7) - . , , || 0, .
, , -
,
( ) , ( , ). 2
1 , /() ( ), /(-) = ),
( ), /(-) = -/(). 2 ,
(. . , ) . , , , , .
48 . .
-
2.1.
.
,
, (2.3.19) X = c/v = 500 = , ( = 0,1 ). , = 108 "1 (. . xsp = 10 ). 105 , xsp = 1 . , (2.3.19) ,
.
,
,
.
, (, X ^ 5 ), ^ (10-100 ),
.
2.4.
, , ,
. ,
W12 W21 (. (1.1.4) (1.1.6)). , , , ,
. ,
, ,
, -
.
,
,
.
,
, .
2.4.1.
, t ^ 0 ,
(2.3.2) \
(0)\2=1\2(0)\2 = 0.
2. 49
-
/ '.
'
E(t, t) ( ), - ( ) . ^
:
(0, t) = E 0 s in (G )0 , (2.4.1) . ,
,
.
(2.4.1) ( ). ,
0.
, = -,
. ',
, :
' = = - E0sin cot. (2.4.2)
H'(t), . s 0,
. , t > 0 |aj(^)| 2 la^O)! 2 = 1, | 2(0| 2 . a2(t), , ,
,
,
t = 0.
| 2(0| 2> ^ , : \a2(t)\2 = ^ \ ^ 2 1 1 2 E2d(v-v0)t, (2.4.3)
v = /2, v 0 = 0/2, 5 - , 0 0 , |21| 21, (2.3.7). (2.4.3) , t > 0 |a 2 ( t) | 2 . ,
,
( ) W$ Wtf =d\a2\2 /dt, (2.4.4)
50 . .
-
(2.4.3):
H ? 2 a = ^ b 2 i l 2 - E o 2 8 ( v - v 0 ) . (2.4.5)
, , (2.4.4), ,
; sa ( . single atom ), W12.
, , t > 0 (2.3.2). , t > 0 08, (2.3.6). , ax(t) a2(t) , \08 . , , . .
(0) = 1 2(0) = 0, ,
. , ,
[3] . (2.4.5)
.
= 20*/2, (2.4.6)
, 0
,
w s = | 2 p 8 ( v-
V o )-
( 2-
4-
7 )
, W(2a - . , W = v v 0 W12 = v = v 0 , . . .
,
. ,
, v
( ) , v 0 , , . . ,
, v = v 0 .
( ), , ,
. ,
, ,
: (2.4.7) , 5-
2. 51
-
, v = v 0 # , . . , /
J8(v-v 0 )dv = l, g(y - v 0 ) , v v 0 , , . . ,
] * ( v - v 0 ) d v = l, :
_ 2 1 7iAv0 l + [ 2 ( v - v 0 ) / A v 0 ] 2 ' ( 2 ' 8 )
Av 0 - . , Wf2a :
Wsa - - 12 ~ 2
2
1^21 I 2 P g ( v - V o ) . (2.4.9) 3n 2s 0ft 2 [g(v - v 0 ) A v 0 ]
(v - v 0 ) / ( A v 0 / 2 ) . 2.6. (2.4.8) , , (FWHM . Full Width at Half Maximum ), Av 0 . g(v - v 0 ) v = v 0 ,
g(0) = 2/rcAv0 = 0,637/Av 0. (2.4.96) , (2.4.8), . . ,
(2.4.8) [3] .
W*g / .
/ = /, (2.4.10) A t e ( v - v 0 ) A v 0 ]
, (2.4.9) ,
H 2 i l 2 - t e ( v - v 0 ) . (2.4.11)
. 2.6
_ _ 2 2 _ _ 1 2 3ne0ch2
.
,
( (2.3.2) (2.3.1)) ' ( (2.4.2)) .
,
| 2()| 2
52 . .
-
|a i()l 2 (. ) . ,
| 2 (0)| 2 = 1 , , | 1 (0) | 2 = 0. ,
1 2. , ,
( ) Wfg (2.4.5) . (2.3.7) , | 1 2 = 2 1 |12| = |2|. ,
W^=W2f, (2.4.12) ,
(. (1.1.8)). , (2.4.9)
(2.4.11), :1
Wsa = - ^ \ ^ \ 2 p * ( v - v 0 ) , (2.4.13)
W" = - ^
2 ^ ( v - v 0 ) , (2.4.136)
= |12| = | | i 2 i l (2.4.12), W s a = W s a =W.
2.4.2.
(2.4.13) (2.3.19) , Wsa ||2. , , . ,
( )
2,
1 : 3 ( 2 . 4 . 3 ) , ( 2 . 4 . 5 ) , ( 2 . 4 . 7 ) , ( 2 . 4 . 9 ) ,
(2 .4 .11) , (2 .4 .13) (2 .4 .136) , ( ) . :
W(\. -So I2) =1 M I2 Eg
-
.
. , , W8a = 0, .
, , 1 2 .
, ,
.
,
,
, (2.4.11). ,
(- - ) . , ,
,
, .
We Wm. , :
,
. ,
.
, (2.4.5), We (^ 0) 2 (0)2, 0 ,
\ie .
, Wm ( jn m B 0 ) 2 ( 0 ) 2 , 0 , \
(3 ((3 == 9,27 10" 2 4 2 ) . , :
(We/Wm) = (0/$0)2 = (/$)2 = 10 5. (2.4.14) (2.4.14) , 0/0 = ( ), , = 0,05 . ,
.
2.4.3.
2.4.1
,
. Nt ,
.
54 . .
-
, v 0 ,
( ). Wh , :
Wh(v - v 0 ) = W*4v - v 0 ) . (2.4.15) , ,
, dN2/dt, :
(dN2/dt) = WhNt. (2.4.16) Wh , . . F = I/hv, oh:
Wh/F. (2.4.17) (2.4.13) (2.4.17) , ah
22 H 2 v ( v - v 0 ) .
(2.4.19)
3ne0ch^] ' * v ' * ' - (2.4.18) , ,
. 1.2, (2.4.16) (2.4.17), , 2 , (. ( 1
'2 ) )
' dF = -ahNtFdz. (2.4.19)
. , ,
, ,
(. 2.7). S ,
dz (. . 1.2) NtSdz, , aaNtSdz. (dF/F) dz , ,
. 2.7
S
(dF/F) = -(oaNtSdz/S). (2.4.20) (2.4.20) (2.4.19) ,
=
,
,
,
.
,
Vo v 0 ( ).
2. 55
-
g*(v'0 - v 0 ) , , dNt = Ntg*(v'0 - v0)dv'0 , VQ H V O +dvo. (2.4.16) d(dN2/dt)9 dNt9
d(dN2 /dt) = WhdNt = Wh (v - )Ntg * (v'0 - v 0 Wo> Wh(v-v'0) V Q .
(dN2/dt) = Nt \wh(v - )g *(v[> - v 0 Wo . (2.4.21) (2.4.21) (2.4.16) , Win9
= lwh(v-v'0)g*(vo-v0Wo. (2.4.22) (2.4.17) GIN GIN = Win/F. (2.4.22) F (2.4.17), :
-
(2.4.18) (2.4.23) :
2 2
2 v f t ( v - v o ) . 3ns0ch)r~> o t v w / ' (2.4.25)
(2.4.25) gt(v - v 0 ) ,
gt= lg*(x)g[(v-v0)-x]dx, (2.4.26)
^ = ( V Q - V 0 ) . 2 l n 2 (2.4.27)
A [ * ( v - v 0 ) A v * ]
[ ^ * ( v ~ v o ) ^ v o ] ( V - V 0 ) / ( A V Q / 2 ) . 2.8. , FWHM, (2.4.27) A V Q , v = v 0
,
(2.4.27), .
,
= GIN.
22 Sne0ch
|| 2 V ^ ( V - V Q ) . (2.4.29)
[^/2~
. 2.8
2. 57
-
W = GF :
W = 3 ^ ^ | 2 p ^ ( V - V o ) ' (2-4.30)
= (nil) = (nFhv/c) .
. (2.4.12) ,
(2.4.29) (2.4.30).
, (2.4.29) (||2, gt v 0 ) v . , (v - v 0 ) ,
.
. , ,
Nx iV 2, (2.4.19) :
dF = -G(N1 - N2)Fdz. (2.4.31) 1 (1.2.1), gi = g2. () .
,
OL = G(N1-N2). (2.4.32) Nx > iV 2 , , . (2.4.29), :
2 a =
3 ^ h ( N l - N M 2 v g ' ( v - V o ) - (2.4.33)
, ,
, , , .
,
. , (2.4.31) (2.4.32) :
dF = -aFdz. (2.4.34) , ,
I, [F(l)/F(0)] = exp(-aZ). , -
58 . .
-
.
, Nx N2, (2.4.32). , Nx N2 (1.2.2), NT = NX + N2H .
. , ,
1 . , , , 1 , , kT.
, N2> Nl9 , (2.4.32), , , ,
, .
gy :
; .
( ), [9] . , ,
,
.
.
, ,
.
, , p v
(2.2.22). , , , .
,
1 2 2 1.
21 12 ( ) , N{ N2 1 2. , :
g = a(N2-N1), (2.4.35)
2.4.4.
W21=B21p, .2 =
(2.4.36) (2.4.37)
AN* +B2lPvo = ^^ N{. (2.4.38)
2. 59
-
:
/ = exp(-/*v 0/kT). (2.4.39) (2.4.38) (2.4.39) ,
=
P v o Bi2exp(hv0/kT)-B21 * (2.4.40)
(2.4.40) (2.2.22), v = v 0 , :
1 2 = 2 1 = , (2.4.41) A Snhvln3 (2 4 42) B e 3 '
(2.4.41) , .
, (2.4.41) (2.4.12), . ,
(2.4.42) , .
(2.4.30), , .
pv
-
2.5.
, ,
.
. ,
, , -
.
. ,
,
.
(. . ) , .
, ,
gt(v - v 0 ) : 1. ,
.
v, .
(2.4.33) , vgt(v - v 0 ) . gt(v - v 0 ) , v 0 , , v0gt(v - v 0 ) . , gt(v - v 0 ) v .
2. ,
gt(v - v 0 ) , . , ,
- , .
,
, .
2.5.1.
.
, ,
. ., .
.
\\fx \|/2 (. (2.3.1)) . ,
\iosc (. (2.3.6)) . ,
2. 61
-
. 2.9
E(t), ,
.
(
10 7 . )
.
, ,
,
, \08. ,
, ,
. 2.9, . ,
. ,
v' v' 4- dV dp = pvdV, , , . . (2.4.7), :
92
d W l 2 = S n 2 o h 2 1^21 Pv 'S(v ' -V 0 )dv ' . (2.5.1)
(2.5.1) , :
Wl2=sXlh2^2112 j p v ' 8 ( v , - v o ) r f v ' . (2.5.2) pv :
p v >=ptf(v ' -v) f (2.5.3) (. (2.4.6)), g(v' - v) pv. , , = jp v dv' , (2.5.3) , g(V - v)
+ 0 0
f t f ( v ' - v ) d v ' = l . J (2.5.4)
-00 (2.5.3) (2.5.2) 8-, :
62 . .
-
2.4.1, , W12 5(v - v 0 ) (2.4.7) g(v - v 0 ) . , (2.5.4)
+00
J t f ( v - v o ) d V = l . (2.5.6) -00
g(v' - v ) .
(. 2 . 9 ) , , , . ,
= [(-/
) ] /
. (2.5.7) pxdx , + dx. ,
(2.5.7) , (). , ,
= o f c * = V (2.5.8)
, ,
.
, . 2 .9 ,
/>
, (2 .5 .7) . , , ,
.
^ ' - ) = 2 [ 1 + 4 1 ( , _ ) 2 ] . ( 2 . 5 . 9 )
(2.5.5) (2.5.9) v' v 0 . :
g ( v - v 0 ) = 2 T c 1 , (2.5.10)
. ,
(. . 2 . 6 ) , (2.4.8) , 2
,
Av 0 ,
0 = 1 / . (2.5.11)
2. 63
-
2.2. He-Ne .
.
= l/uth, I , vth , uth = (SkT/M)1/2, , / ,
, . Ne = 0,5 ( He-Ne ), (2.5.12), ^ 0,1
= 0,5, (2.5.11), Av 0 = 0,64 . , , , , Av 0 . ,
, (Av0/p) 1 / , Ne. , ,
, = V T c . , , v = 5 10 1 4 , 5 108. , . 2.9 ,
, .
2.3. Nd:YAG.
.
.
,
,
. . 2.10 Nd.YAG, . ( - 1 ) , ,
.
1 , 300
Av 0 = 4 1 = 120 Nd.YAG Av 0 = 11 1 = 330 .
.
1 v (. . - 1 )
w v/, ( / ) . , v v = cw.
( ) . = c/v = 1/w, ( 1 ) .
, :
(2.5.12)
64 . .
-
,
, .
. , , 2.3.2, , . .
, . ,
-
- .
, ,
. --
[10] , g(v - v 0 ) , (2.5.10)
2xsp, xsp . ,
,
(FWHM) Av0=l/2nxsp. (2.5.13)
, ,
, ,
exp(-t/xsp), ,
E(t) = exp(-t/2xsp) cos co0t. ( {E2(t)))9 (-/ 8 ),
.
,
E(t), , ,
(2.5.13).
2.4. .
Avnat . |] = , = 0,1 , X = 500 ( ), 2.1 , xsp = 10 . (2.5.13) Avnat = 16 . , Avnat, = 1/89 , vfj. ( - ).
2. 65
0 100 200 300
[ ]
. 2.10
,
,
N d : Y A G
-
2.5.2.
,
( ).
.
,
. - ,
, .
, ,
, , . ( .) ,
g*(v'0 - v 0 ) , . . (2.4.27). A V Q (FWHM) ,
, .
2.5. . N d 3 + . -
X = 1,05 AvJ = 5,4 , . . 40 Nd.YAG (. 2.3). , .
,
,
. , v
2 , 2 . -
, ,
, v' = v [ l - (u 2 /c ) ] , . , ,
2 > 0, v' < v, . , , v'
v 0 , . . v [ l - ( 2 / ) ] = v 0 . :
v = v 0 / [ l - ( u 2 / c ) ] , (2.5.14) : ,
, V Q ,
V o = v 0 / [ l - ( u 2 / c ) ] , (2.5.15)
66 . .
-
v 0 . ,
, ,
v V Q , . . v = V Q , (2.5.14) (2.5.15) , ,
, 2.5.
*(vo ~ v 0 ) , , pvdvz ,
2 2 + duz, :
1 / 2
*=[) (2.5.16)
|2|
-
2.1
1 - 1 0
5+10 / - 3 0 0 - 1
- 1 0 - 1
50 - 1
- 5 0 0 - 1 1-500 - 1
,
Avj Av 2 , Av = Av x + Av 2 . Av x Av 2 , Av = (Av 2 + Av | ) 1 / 2 . ,
.
, , , [11], -. , (, Ne), . .
. 2.1 .
,
xsp = 10 , , Avnat = 10 . , ,
isp = 1 , , Avnat = 1 , ,
.
, (
= 0,1 ) , , A v c = 1/ = 100 " 1. ,
; AvJ, , .
300 - 1 0,5 - 1 , , , Nd: Y A G .
2.6.
,
,
.
,
68 . .
-
.
, ,
, , :
1. . , ,
/ . ,
,
.
2. - .
, - , ,
, ,
, .
2.6.1.
[12], *
, :
*+-++ + , (2.6.1) *.
,
,
. (2.6.1) NB* ( ) :
dN -jf- = -kB*ANB*NA, ( 2.6.2)
NA , kB*A , .
, . . kB*A , , (, 0 2 ),
.
,
(, 238- He-Ne ). (2.6.2) :
Wnr=kB.ANA. (2.6.3) (2.6.2) (2.6.3) :
(dN2 ) = N2 (2.6.4) I dt J
'
2. 69
-
, , N2 ( ) *, - ,
, -
,
= (1/Wnr). , (2.6.2) , ,
(2.6.1), : + - * + - , (2.6.5)
( , ). , (2.6.2) :
(dNB. /dt) = -kB.ANB.NA + kBANBNA, (2.6.6) kBA , .
kBA kB*A, .
:
.
1 , (2.6.6)
:
kB.ANB.NA=kBANBNA. (2.6.7) :
NB* = NB (-2/kT), , . (2.6.7) :
* 2 =KBA exp(AE/kT), (2.6.8) , k (2.6.1) , (2.6.5). ,
kT. , (2.6.8), kB*A ^>kBA. , (2.6.8) , , ,
,
, -
, ,
, -
1 , 2.4.4 ,
,
.
70 . .
-
* * * *
. 2.11 ()
, ()
. ,
k ,
.
, ,
, . .
NB* NB, ^*^* ^ ^BANE, (2.6.6) (2.6.2). ,
(2.6.4) , > ,
.
(, (010) 0 2 ) , .
*
, (
1) : * + -> + * + , (2.6.9)
=
-
(. . 2.11). ,
[13]. ,
, (2.6.9) , , kT. .
1
( . ( 2 . 6 . 5 ) ) . ,
, ( . ( 2 . 6 . 1 ) ) , , ( . ( 2 . 6 . 9 ) ) . , , , -
.
2. 71
-
(, Ne He-Ne N 2 0 2 0 2 ). .
,
( , . 2.116): + *-> * +-. (2.6.10)
, , , ,
, , (. . = 0) , kB*A=kBA., ^ . ^ , (2.6.9) (2.6.10). , .
,
,
.
(NA* /NA) + ; ^ ) , (2.6.12) 1
vt ,
, ,
. , WNR
^IBL^-W N (2.6.13)
1 , , ,
, .
, , .
72 . .
-
, , -
,
. ,
v, Wnr Wnr= (-DAE/hv), ! ) , , , * .
,
= AE/hv , . . - .
, ,
,
.
WNROT . , ,
.
,
, ,
,
, (2.6.4),
. ,
, ,
9 2.5.1, . ,
,
. ,
, , ,
. , , ,
, ,
, ,
.
2 6 2
-
,
, -
, D, , , , .
.
[14] [15]. , ,
.
, ,
R .
2. 73
-
\xD, . [16] , , R, ( ), ED(t), , liD/4ns0R3.
ED(t, R), , |
.
:
Hcc\ED-a\k\iid-iia\/RZ. (2.6.14) ,
, \iD . ,
( ) .
,
, R, [14]:
(2.6.14)
8 ,
, gD ,
. , , , WDA W D A \\2, (2.6.14) W D A l u x ^ l u j 2 / ^ 6 * WDA (2.6.14) R~6, (1/
) (, 1/8 l u ^ l 2 , . (2.3.15)),
(,
|.
|2, . (2.4.29)). , (2.6.14) :
DA R (2.6.146)
R0
4
-|1/6
64 5
(2.6.146) R0 , -
. , (2.6.146) , , WDA = (1/8) R = R0, WDA = 1 0 - 6 ( 1 / T s / ) ) R = 10R0. R0 .
74 . .
-
. 2.12
- :
() , () -, () -.
, , -
- . ,
( D) , ,
(. 2.12). , ,
D. , -
D, -, , ,
. ,
i, . 2.126 (-). , . . AE2i = . , ,
, ,
(. 2.12). , - (. cooperative up-conversion), , . . 2 = A # 2 i -
- ,
, ND NA . (2.6.146) WDA R . , ,
, ,
R . ,
,
,
, ( ). , ,
2. 75
-
,
:
N2(t) = 2 (0)-[(* ) + C * 1 / 2 L (2.6.15)
,
. ,
.
2.7. Yb^-.Er3^'. [17]. Yb 3 +:Er 3 +: (. 9) - Y b 3 + ,
2 F 5 / 2 , 3 + ,
4 1 1 1 / 2 (. 2.13). , ,
Y b 3 + ,
3 +. , Y b 3 +
Y b 3 + , Yb 3 + -Er 3 + .
_
4
III.
N ; N ; :
. 2.13 - :
( ) Y b 3 + 3 + Yb:Er , () Nd:YAG -, () -
3 + .
2.8.
4F3/2 Nd:YAG.
4 F 3 / 2 Nd: YAG -. i . 2.126
4 I i 5 / 2 Nd 3 + (. 2.136). ,
4 1 9 / 2 ,
4 1 1 3 / 2 41 / 2 ( . 2.13, . . 2.15). (,
4 1 1 3 / 2 - 4 1 1 1 / 2 ) 2000 "1 (, ,
), . . 4 , YAG (~450 - 1 ) . Nd 3 + YAG 1 % .
76 . .
-
2.9. - 3+ [17]. , ,
3 + (. 2.13), -
.
3 +,
4 I i 3 / 2 ,
41 1 5 / 2,
4 1 9 / 2 .
41 1 3 / 2. -- ,
3 +,
4 I i 3 / 2 , , . . 50% .
2.6.3.
,
(2.6.4). ,
, N2 :
dN2_ (N2 N2) ~~{1 ^ 7 / (2.6.16)
(2.6.16) : dN2/dt = -(N2/x), (2.6.17)
1 1 ^ 1 - = - + (2.6.18)
N2(t) t , (2.6.17).
iV 2 (0 = ^ 2 ( 0 ) e x p - ( f A ) , (2.6.19) N2(0) t = 0. , , (2.6.16) N2/xr , . , ,
1 v 0 , t :
P(t) = N2(t)hv0V/Tn (2.6.20)
2. 77
-
V . (2.6.19) (2.6.20) : P(t) = [N2(0)hv0V/xr]exp-(t/T). (2.6.21)
,
,
, , ,
.
,
t = 0 N2(0), , (2.6.21), .
,
.
,
2. (2.6.21), :
N2(0)V / ,
, ,
,
, .
, ,
,
. ,
(2.6.18),
.
2.7.
, 1 2 . ,
.
. 2.14, , 1 2 g- 2 ~ > ( . . ), , . Nx N2 1 2, a Nu N2j - .
E2,g2,N2
2.14 ,
,
,
78 . . !
-
2.7.1.
.
, ,
;
} = N1 [ - ( 2 - ) / ] . (2.7.1) , , 1 , ;
=/8. (2.7.2) ,
}=/2. (2.7.26) (2.7.1) (2.7.2) :
=NZ(g2/g1)exp[-(E2-E1)/kT]. (2.7.3) ,
,
. ,
Nx N2; N2 i. ,
(2.7.4)
Wji , Wtj , (1 / )
. , Wjt Wtj (2.4.30), ||2 /, |p i ;| 2 | n y J 2 . , , (2.3.7). , \\itj\ (2.3.7),
ut, /- , 2 - .
,
Wy = WV}. (2.7.5) , ,
,
, , .
,
N2j = N2/g2y (2.7.6) # 1 * = # 1 / - (2.7.66)
2. 79
-
(2.7.6) (2.7.4), dN9 dt g2 gi J x
, (2.7.5),
1 =
. ^ . ^ ] . ^ (2.7.7)
8\ 82 8l g2
1 1 1 1
8l 82
1 _ 1 1 (2.7.9) #2
(2.7.7) , WN2/g2
WNi/gx
.
dF dz (. . 1.2)
dF = W -^]dz. (2.7.10) 82 Si)
2 1
1 2
2i = W/(g2F), (2.7.11) ci2 = W/(glF), (2.7.116)
, , ,
ft (N1/g1), (2.7.10), (2.7.11), : dF = gFdz, g
g = a2l(N2-N1&j. (2.7.14) , a 2i 1 2 (2.7.11) (2.7.116). Nx ^> N2 ( ), (2.7.13) a = a 1 2 iVi. , N2 Nt ( ), (2.7.14) g = a 2 1 N 2 .
80 . . 0
-
2.7.2.
, 2 1 g2 gx , , -
, ,
( ). , , , .
, ,
. (2.7.6) :
X2j = f2jN2, (2.7.15) Nu = fiiNl9 (2.7.156)
f2j (fu) 2 ( 1), j (0 . , , :
_ g2jexp-(E2j/kT)
tmg2mexI>-(E2m/kT) (2.7.16) 1
= guexp-(Eu/kT)
U 4 (2.7.166)
1 2
, a g2m gu . ,
(, I) 1 (, ) 2. (2.7.4)
J 1 1
(2.7.17) (2.7.15), (2.7.17)
(dN2/dt) = -W^N2 +W^Nt -(N2/x), (2.7.18) Wl9 W z ^, (1/)
W^ = f2mWml, (2.7.19) Wga=fiiWlm, (2.7.196)
(1/) = | \ | \ ( / 2 / / , ) . (2.7.19) 1 1
(2.7.18), dF dz
2. 81
-
dF^WZM-W&NJdz. (2.7.20)
Geml ofm
(2.7.19 ) Glm = Wlm/F oml = Wml/F I . , 1 ( ), Glm = Gml. , , (2.7.20) (2.7.21), :
: ( N2 > Nx) ,
. ,
N2 = 0 Nx = Nt, Nt , (2.7.22) :
alm=afmNt. (2.7.23) , Gfm , .
2.10. = 1,064 Nd:YAG. , Nd: YAG, . 2.15. 4 F 3 / 2 > 4 1 1 1 / 2 ( = = 1,064 ), , 4
/ 2 4 I I 3 / 2 (X = 1,32 ) 4 F 3 / 2 - 4 1 9 / 2 (X = 0,94 ). X = = 1,064 , = 2, 4 F 3 / 2 , I = 3, 41/2 ( R2 -> Y3). / 2 2 = N22/N2 = N22/(N2l + iV 2 2 ) , N22 N21 4 F 3 / 2 , N2 . , (2.7.3) N22 = N21exp -- (AE/kT)> . f22 f22 = 1/[1 + exp(AE/kT)]. = 84 1 kT = 208 "1 ( = 300 ) / 2 2 = 0,4. R2 > Y 3 2 3
=
6,5 10~19 2 [21]. 2 3 R2 ^ 3 (2.7.21), |3 = /2223 = 2,8 - 1 9 2.
oe
ml=W^l/F = f2maml, tn=Wl'k/F = fu
-
2.11. - .
2.16.
4 2 ;
42 ( = 730 * 800 ).
4 2
2, f2T ,
4 2 , f2T = N2T/(N2E + N2T), N2E N2T
.
N2T = N2Eexp -(AE/kT), . f2T = exp-(AE/kT)/[l + exp-(AE/kT)]. = 800 "1, = 208 ' 1 ( = 300 ) GTA = 4 10~19 2 X = 704 [22], , f2T = 2,1 10~2 = 0,8 ~ 2 0 2. f2T, .. ,
. ,
, f2T . ,
, 42 ->
4 2
(1/ = 1,5 105 - 1 (
= 6,6 ), 2 - 4 2 (1/) = 666,6 1 (
= 1,5 ). (2.7.19B) (1/) = (f2E/xE) + (f2T/xT), f2E = N2E/(N2E + N2T) = l-f2r ,
2.
(1/), , = 200 = 300 . ,
( 6,6 200 )
2,
, . , ,
, .
1,32
1,06 | 4 -
1 1 / 2 0,94
\ 9/2
1,064
= 84
J ^ 2 2 TTN* 21
0,946
. 2.15 ,
X = 1,064 N d : Y A G
= 800
.= 730-800
. 2.16 ,
2. 83
-
2.8.
( v 0 ) I v = v 0 . , .
, / , Nx N2 . N1 > N2 ( , Nx > N2), , WNl9 , WN2, . . 1 -> 2 , 2 -> 1. , / . .
2.8.1. :
(iV\ > N2) , .
N2 ,
(. 2.17) d^
= _ W ( N 2 _ N i ) _ ^
at (2.8.1)
N9
/\\
-^ WN, WN2 N2/x
. 2.17
/^ 1. :
Nx + N2 = Nt, (2.8.2) Nt . (2.8.1) ,
AN = Nt-N2. (2.8.3) (2.8.2) (2.8.3) Nt N2 AN Nt9 (2.8.1) :
dAN dt -AN( + 2w) + Nt.
, . . (dAN/dt) = 0, :
AN = l + 2Wx'
(2.8.4)
(2.8.5)
84 . .
-
AN ,
(dP/dV), = (hvWAN = m ^ r x , ( 2 . 8 . 6 )
, . . Wx > 1,
(dP/dV)s = (hv)Nt/2x. (2.8.7) (2.8.7) , (dP/dV)s, ,
, , ,
(Nt/2) .
(2.8.5) (2.8.6) . , (2.4.17) W
W = oI/hv, (2.8.8) .
(2.8.5) (2.8.6), (2.8.8), :
AN 1 (2.8.9)
I/Is
dP/dV (dP/dV)s~l + (I/Isy
Is = hv/2ax
(2.8.10)
(2.8.11) ,
.
(2.8.9). , I = Is , AN = Nt/2. v = v 0 , 18 . .
,
J .
, . 2.18,
v', / ' ,
.
,
[/(v)]
W W
. 2.18
v'
I'(v')
I v (/(v) I'(v'))
2. 85
-
.
(2.4.33) gt(v - v 0 ) g(v' - v 0 ) , v v'. - N1 - N2 = AN (2.8.9), :
=
0
0 = -
2 2 | u f i V , v ' ( v ' - v 0 )
(2.8.12)
(2.8.13) 3ne0ch v
( ). (2.8.12) (2.8.13) , I , .
,
g(V - v 0 ) . . 2.19 v' I/Is.
,
/ = I(t), .
, ,
.
,
AN , (2.8.4) \dAN/dt\
-
(2.8.14) () = Nt :
AN(t) = Nt exp (2.8.15) l-(2o/hv)jI(t)dt
(2.8.15) , t ():
t
r
-
t I I WN, WN2 N2/x
I
3 , iV 3
2,N2
. 2.20
,
. , 3 -> 2 1 -> g , NS = NX = 0.
N2 2:
(dN2/dt) = Rp- WN2 - ( 2 / ) , (2.8.21) Rp = WpNg , 3iNg . (. . dN2/dt = 0) Ng = Nt (2.8.21) :
1 + W V
(2.8.8), (2.8.22) : ^ 2 0 No
i + ( / / i s ) '
(2.8.22)
(2.8.23)
iV 2 0 = = RpT 2 (. . / = 0),
Is = hv/ax. (2.8.24) (2.8.24) (2.8.11) , Is , ,
. 2.17. - ,
. , AN .
, ,
. 2.18, v' , . (2.4.35)
= 0, (2.8.23), g :
g = (2.8.25)
g0 =
-
(2.8.25) (2.8.26) , , ,
g J, .
,
I(t). ,
(2.8.21) N2 . (2.8.23) 2 (2.8.25) , / . ,
,
2 Rp N2/x WN2. , :
(dN2/dt) = -(Gl/hv)N29 (2.8.27) (2.8.8). (2.8.27) :
N2(t) = JV20exp {- [(*) / J} , (2.8.28) N20 = Rp/ 2 , T(t) t (. (2.8.16)),
Ts = hv/a (2.8.29) .
(2.8.29) (2.8.17) , 8 ,
.
: g = g0exp { - [ ( 0 / . ] } , (2.8.30)
g0 = GN20 , (2.8.26). , ,
.
2.8.3.
,
,
(. 2.16 2.17 2, ). ,
, ,
(2.4.26). ,
2. 89
-
v'
. 2.21 ,
,
.
~
v o ) g ( v - V o )
. 2.22
v', ,
J(v') (
)
gt(v - v 0 ) g(v - V Q ) . ,
, . 2.21. , . 2.18, / ( v ) , V Q v. , I(v) .
, . 2.22 I(v). I(v) v. ,
, . 2.21, . . . ,
, , .
, . ,
,
.
2.3 .
, ,
.
,
, .
.
2.9.
90 . .
-
2.9.1.
, ,
, ,
, , .
, ,
,
. ,
( . [18]). , ,
, ,
.
-,
( (2.4.29), |p|2v - v ||2 ). .
2.9.2.
, ,
, ,
(, . amplified spontaneous emission ASE).
Q , ,
, (. 2.23). G = exp[a(iV2 - iVx)Z] , , ,
, Q ( 10 4 ). ,
,
(. 2.23),
Q, , , .
(R = 1) (. 2.236), .
.
,
D
1.
R=l
. 2.23
:
( ) , () .
2. 91
-
:
; , ; ; , , .
,
.
. 2.23. D
-
1,0
0,8
< 0,6
0,4
0,2
- 2 - 1 0 1 2 ( v - v 0 ) / A v 0
. 2.24
4 = 10' 10"; 10
I I M I L L
1 2 5 20 50 100 / s l 4 ^ " ) [ G l n G l i / 2 (2.9.3)
3/2 (2.9.36)
c^GlnG] 1 ' 2
.
, a Is = hv0/
-
, / Is. , , . 2.23, 4, . 1 = 18 G > 1 (2.9.3) (2.936) , :
G = 4 ^ . [ l n G ] i / 2 (2.9.4) 2
= | ^ 1 / 2 (2.9.46) . ,
(. 2.236), (2.9.4), G , G 2 , Q Q'. :
G 2 = i ^ [ l n G 2 - | i / 2 (2.9.5) 2
.
G 2 = 4ii G 2 ] 1 / 2 (2.9.56) 2
2.13, . ,
, Nd: YAG, D = 6 I = 10 , = 1,82, , . 2.23. (2.9.1) (0/4) = 2,25 10"4 . Nd: YAG , = 1, (2.9.4) , 4 T O G = 2,5 104, . . OpNthl = InG = 10,12. Nd:YAG 2,8- 10~19 2 (. 2.10), , Nth = 3,6 10 1 8 3. , . 2.236, (2.9.2) (0'/4) = 5,62 10~5 , (2.9.5) , G = 6,4 102, . . .
Nth = In G/apl = 2,3 10 1 8 3. ,
2 , Q
Q', . , , Q = 21 = 9,36 10"3 Q; =2
= 2,33 10 3 .
94 . .
-
. 2.26,
. 2.23 GpN2l, (Q/4n) = 10"4 , -
= 1. (2.9.3),
/ > Is- ,
, / < ,
,
. 2.23, . . (I/Is) = GpN2l/2.
,
, . .
[23].
,
. 2.236,
, -
, (. 10). ,
,
. ,
,
,
, ,
11, . . ,
,
1
. -
, -
/^J/' , , 3 + Y , Erbium-Doped Fiber Amplifier).
^
-
1550 .
100
. 2.26
J, / 8 ,
GpN2l
Q = 4 10~4
1 2- 95
-
2.10.
, . ,
,
, = a(v - v 0 ) .
(Av 0 ) . ,
, . ,
,
, 2.7. 2.2
, Av 0 ( AVQ )
.
6G , . ,
( 10" 1 3 2 ) A V Q ( ) ( ). ,
. ,
, Nd:YAG - , GP (10~ 2 0 ^ 10~ 1 9 2 ) , ( ), - . ,
( ), - 2.2
,
. [] [ ]
[]
H e - N e X = 0,6328 3 . 10 1 3 150 10~3 1,7
+ X = 0,5145 2,5 10- 1 3 6- 10- 3 1,7
N d 3 + : Y A G X = 1,064 2,8 - 1 9 230 120
N d 3 + : X = 1,054 4 10 2 0 300 5,4
6G
= 0,570 3,2 10- 1 6 5,5 10- 3 46
3 + : 1 2 0 4
= 0,704 0,8 l ( h 2 0 300 60 = 300
T i 3 + : A 1 2 0 3
= 0,790 4 . 10- 1 9 3,9 100 | | C r 3 + : L i S A F
= 0,845 5 10 2 0 67 84 | |
96 . .
-
. ,
, 6G, ,
10~1 6 2 ) , ,
.
, . 2.2, , ( 3 + :1 2 0 4 ) , (Ti 3 +:A1 2 0 3 ) CnLISAF (Cr 3 + :L iSrAlF 6 ) ,
. ,
( ), , Nd: Y A G , .
2.1. V = 1 3 , = 10 X = 600 .
2.2. p v ^, , pxdX X X + dX. ^ p v.
2.3.
X. ,
,
,
= hc/ky ( ), 5[1 - ( -* / ) ] = . .
2.4.
> . 2.3,
= 2,9 10"3 ( ).
= 6000 . ?
2.5. Rx (FWHM), 330 (. . 2.10). = 2,5 10~20 2 . ( = 1,76). , 3 ?
2.6. Nd: Y A G , Y 3 A 1 5 0 1 2 (- , Y A G ) , Y 3 + N d 3 + . N d 3 + 1%, . . 1% Y 3 + N d 3 + . Y A G 4,56 / 3 .
2. 97
-
N d 3 + , 412. ( ) , 134, 197, 311 848 - 1 . N d 3 + , 4 1 9 / 2 .
2.7. = 1,15
Av*0 = 9 108 . - 7 .
,
.
2.8. Sx -> S0 (. 9) 6G 0,87, 5 . Slt
2.9. X = 0,633 , , Avnat 20 , a Av c = 0,64 . ?
2.10. I .
2.11. Nd.YAG 6,3 7,5 .
1,06 = 2,8 10~19 2 , 1,82.
() (, , . . ). , ,
,
.
2.12. (. 8) ( 1,--4,4'-) .
(X = 0,6943 ) 8,1 10" 1 6 2. 22 . .
2.13. ( (2.6.9) (2.6.10)), , ( = 0) kB.A = hBA*, kB*A kBA. .
98 . .
-
2.14. , . 2.18, , J(v) 7(v). ,
:
a / v ( (0) . V o )
l + [ 2 ( v - v 0 ) / A v o ] 2 + ( / / / s o ) ' 0 (0) (J
-
1. R. Reif f, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, New York, 1965), Chap. 9.
2. W . Heitler, The Quantum Theory of Radiation, 3rd ed. (Oxford University Press, London, 1953), Sec. II. 9. . . M., 1956. . . 9.
3. . A. Lorentz, The Theory of Electrons, 2nd ed. (Dover, New York, 1952), Chap. III. . . . M.: .-. ., 1956. . .
4. J. A. Stratton, Electromagnetic Theory, 1st ed. (McGraw-Hill, New York, 1941), pp.431-438. .. . .-.: , 1948.
5. R. . PantellandH. . Puthoff, Fundamentals of Quantum Electronics (Wiley, New York, 1964), Chap. 6. P., . . .: , 1972. . 6.
6. W . Louisell, Radiation and Noise in Quantum Electronics (McGraw-Hill, New York, 1964), Chap. 6.
7. R. H. PantellandH. E. Puthoff, Fundamentals ofQuantum Electronics (Wiley, New York, 1964), pp. 40-41, 60, 62, and Appendix 4. P., . . .: , 1972. . 2 4.
8. R. . PantellandH. . Puthoff, Fundamentals of Quantum Electronics (Wiley, New York, 1964), Appendix 5. P., . . .: , 1972. 5.
9. A. Einstein, On the Quantum Theory of Radiation, Z. Phys. 18, 121 (1917). 10. W . Louisell, Radiation and Noise in Quantum Electronics (McGraw-Hill, New York,
1964), Chap. 5. . . .: , 1972. . 5.
11. . G. Kuhn, Atomic Spectra, 2nd ed. (Longmans, Green, London, 1969), Chap. VII. 12. Radiationless Transitions, ed. by F. J. Fong (Springer-Verlag, Berlin, 1976), Chap. 4. 13. . K. Rhodes and A. Szoke, Gaseous Lasers: Atomic, Molecular, Ionic in Laser Hand
book ed. by F. T. Arecchi and E. O. Schultz-DuBois (North Holland, Amsterdam, 1972), Vol. 1 pp. 265-324.
14. J. B. Birks, Photophysics of Aromatic Molecules (Wiley-Interscience, New York, 1970), Sec. 11.9.
15. D. L. Dexter, J. Chem. Phys. 21, 836 (1953). 16. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), Sec. 9.2.
.. . .: , 1965. . 9.2. 17. W . J. Miniscalco, Optical and Electronic Properties of Rare Earth Ions in Glasses, in
Rare Earth Doped Fiber Lasers and Amplifiers, ed.by M. J .F. Digonnet (Marcel Dekker, New York, 1993), Chap. 2.
18. T. Holstein, Imprisonment of Resonant Radiation in Gases, Phys. Rev. 72, 1212 (1947).
19. R. Arrathoon, Helium-Neon Lasers and the Positive Column in Lasers ed. by A. K. Le-vine and A. J. DeMaria (Marcel Dekker, New York, 1976), Tab. 2.
20. M. H. Dunn and J. N. Ross, The Argon Laser in Progress in Quantum Electronics, Vol. 4 ed. by J. H. Sanders and S. Stenholm (Pergamon Press, Oxford, 1977), Tab. 2.
21. W . F. Krupke, M. D. Shinn, J. E. Marion, J. A. Caird, S. E. Stokowski, Spectroscopic, Optical and Thermomechanical Properties of Neodymium- and Chromium-Doped Gadolinium Scandium Gallium Garnet, J. Opt. Soc.Am. 3, 102 (1986).
22. J. C. Walling, O. G. Peterson, J. P. Jennsen, R. C. Morris and E. W . O'Dell, Tunable Alexandrite Lasers, IEEE J. Quant. Electr. QE-16, 1302 (1980).
23. L. W . Casperson, Threshold Characteristics of Mirrorless Lasers, J.Appl. Phys. 48, 256(1977).
24. O. Svelto, S. Taccheo and C. Svelto, Analysis of Amplified Spontaneous Emission: Some Corrections to the Lyndford Formula. Optic. Comm. 149, 227-282 (1998).
100 . .
-
3
,
3 , ,
.
,
, ,
.
3.1.
, -
,
,
,
.
[1] .
3.1.1.
: (1)
; (2) Ev, ; (3)
, (4) . ,
. ^/ , ,
3. , 101
-
,
(
), (AEV) () .
ft2
* (3.1.1)
h = //2, , .
,
,
; ,
, / , ,
2/2. ,
2
Up R R0 Up = k0(R - R0)2/2 (. . 3.1). AEV :
, R
. 3.1
AEV = hv0 = h V 1/2
(3.1.2)
= 12/(1 + 2 ) . , ,
-11/2
(3.1.3) = 2ko
,
,
.
AEe = k0a2/2. (3.1.4)
2 k0 (3.1.1), (3.1.3) (3.1.4),
AEV = 2(//2. (3.1.5)
Er = h2J(J + 1) / 2 , J -
102 . .
-
.
, J = 0 J = 1,
= 22/2 =2(/)
,
( 3 . 1 . 1 ) . ( 3 . 1 . 5 ) AEr = (m/M)1/2AEv. ( 3 . 1 . 6 )
/ = 10~ 4 , ,
. ,
,
.
, (AEe/h), (AEv/h) (AEr/h) , , ( 2 5 - 5 0 ) 1 0 3 - 1 , 5 0 0 -3 0 0 0 - 1 1 - 2 0 - 1 .
, . ,
, ,
, --
,
R . ,
R. ( ), , JR , . 3 . 1 , 1 2 . (R > ) , , . R , .
,
, ,
R. , 1 . 3 .1 0 , .
R ,
,
. ,
(, R0). , , ,
. ,
R , , -
, .
,
R. , , , 1, ,
3. , 103
-
2 1
i/' = 0
3 R, R0. -
2 I^IIIZIZZZZZZZZI ^ -
,= 0 i? 0,
-
- -
.
3ZZZZZ R0 1 . -
. .2 -
, , . .
.
f_ . -
. -
,
" = 0 v" = 1 hv0, (3.1.2),
k0 . , ,
3.1 0, 1, 2, 3 . . , v = 0 , , ,
(hv0/2) . 1 2 , , . 3.1 , . 3.2, . 3.1 . , ,
v" = 3 1. . 3.1 , R , ' .
,
.
R0
. ,
, ,
.
.
, . 3.1, R ,
. , , SF 6 , (. 3.3), , . ,
. 3.3 ( ^ ) , R - . ,
3.3, SF 6 , -
104 . .
-
. 3.3 (, S F 6 ) . ,
( , [ 2 ] )
-f v' = l
. 3.4
,
.
,
-
-
,
U
.
,
. 3.1 ,
.
,
.
,
; (. . )
Er = BJ{J+l) (3.1.7) , h2/2I, / ,
. ,
3- , 105
-
, .
,
v" = 0 v' = 1 , . 3.4. , ,
; , J, . . [Er(J) - Er(J - 1)] = 2BJ.
3.1.2.
N(Ee, Ev, ) - , ,
N(Ee, EV9 ) gegvgrex? {-( + Ev + Er)/kT}9 (3.1.8) Ee, EvnEr , , a ge9 gvngr (. (2.7.3)). , 3.1.1, Ev/hc 1000 - 1 ,
EJhc .
kT/hc = 209 " 1 ( = 300 ) ,
9 Ev , kT. ,
, ,
.
1
, (3.1.7) (3.1.8),
40 J . 3.5
p(J)oc(2J+ l ) e x p [ - J ( J + l)/kT]. (3.1.9) (2J + 1) , J (2J + 1)- . , , = 0,5 " 1 kT/hc = 209 - 1 ( ), . 3.5 -
1 , , ,
. (, S F 6 )
1000 - 1 ( 100 - 1 ) ;
.
106 . .
-
(, ). , (3.1.9) (2J 4- 1) ( J = 0) , , J
(2J + 1)
= (2kT/B)i/2. (3.1.10) ,
.
3.1.3.
,
:
-
, ( ); - ;
-
(- ); - ;
, v" = 0, ( ); -- .
-
,
. ,
-, ,
(, ). ( . ) .
,
.
, ,
-,
. ,
" = 0 , 1 , . 3.6, 1 ,
. ,
v" > 0, .
3. , 107
-
2
1
uv(R) uv(R)
. ,
, - -
-'. -
,
"
v'
* \uv,uv,dR\2, (3.1.11)
, R
. 3.6
. v" = ,
, , ,
(3.1.11), , uv> uv. . 3.6 v' = 2. , , ,
,
, .
, , ( , . . ,
). , v' = 2.
R, ,
' = 2. , -
(- ) , . , -.
1 -
1 -
(, 2 ) . - ,
.
2
uv* uv-dR ; -.
108 . .
-
= 1 , .
v" = 0 v" = 1 (. . 3.2). , , v" = 1, v" = 2 (), v" = 0 (). ,
,
-. ,
= 1 . . 3.6 , , -
, Av = 2, 3 . ., , ( ).
, -
,
,
(3.1.9) (. . 3.5). , ,
.
AJ = 1 ( A J = J" - J\ J " H J' ). -
(, v" = 0 -> v" = 1 . 3.2), v 0 ,
(. 3.7). , , - A J = + 1 . - , v 0 ,
, (. . 3.4). , , -
A J = - 1 . (3.1.7), , 2B/h. 3.7 ,
. 3.7
.
,
v 0 .
: , -
AJ = + 1 , , -
J = - 1
- -
3. , 109
-
(. . 3.5). , -
(, ). AJ = 0;
v 0 (Q-). , (, , v' = 1 v" = 0 . 3.4) , , . 3.7, , .
3.1. 02 = 10,6 . 0001 -> 1000 (. , 0 2 10), v 0 , , v 0 = 960,8 "1 [20]. 0 2 = = 0,387 "1 [20], , (0001) (1000) . , -
E = hv0 + BJ'(Jf + 1) - BJ"(J" + 1) = hv0 - 2BJ", (3.1.12) , , J" . j ' m
(3.1.10). , 02 , .. = 450, J M A X = 19,6. 0 2 , J' J". , ,
, J' = 19 J' = 21. J' = 21, - J" = 22 ((22)-). (3.1.12) v = v 0 - (2BJ"/h) = 943,8 "1, X = (1/943,8) = 10,6 . , , v 0 , X = 1 / v 0 = 10,4 .
(3.1.12) , - Av = 2BAJ" = 4 = 1,55 1 .
3.2. 02 . 0 2 , ( (22)) X = 10,6 , , = 450 (. 3.1). 0 2 (2.5.28), = 5 0 . : , (2.5.18), A V Q ~ v 0 , 0 2 , He-Ne (. 2.7), , v 0 17 . , ,
, 0 2 , , He-Ne .
110 . .
-
3.3. 02 . 0 2 , , N 2 0 2 . ,
Av = 77,58(\|/02 + 0,73 - 4v|/N2 + 0,6) ^(/) 1/ 2 (. (2.5.12) (2.5.11)), , ,
( . .). , , ( = 15 . . C0 2:N 2:He 1:1:8) = 450 , Av = 40 . 3.2 , 0 2 . 0 2 ,
(. 10), .
,
. ,
.
A J = 1. , J J - 1.
, ,
- . -
AJ = 1 ,
. ,
v"
, ,
-. - -
, , A D = 1 A J = 1 .
A J = 1.
3.1.4.
, ,
(. . 3.6). , v' = 0 -
3. , 111
-
(, ). 1 ,
. v' = 0 - -
(, . . 3.6). ,
-. ,
,
CD . 3.6. (, ) v" = 0 (, , ). . 3.6 , .
.
-
. -
Av = 1 / = 1. ,
(. 3.1.1), : AJ = 1. , - , ,
,
(, xsp 1/vjj). ,
-
.
,
.
, 2.6.1, .
(. collisional deactivation) ( (2.6.1)) . ,
(, ) (, (0,1,0) 0 2 ; . 10). ,
.
1 , ,
, , .
(3 .1 .8 ) . .
112 . .
-
. 3.8
-
(. near-resonant energy transfer) (. (2.6.9) . 2 . ) ,
kT.
0 2 ,
(0,2,0) (0,1,0) (. 10). (. in
ternal conversion) -
(. . 3.8) . (. unimolecular decay), .
,
- ,
. , ,
. ,
. 3.6, , ( v' = 0 . 3.6), ( ).
, ,
.
,
v' = 0, , ,
.
3.2.
(. bulk semiconductors), . . ,
, . -
- (. quantum-confined semiconductors) , , , , ,
,
.
3. , 113
-
.
.
[3].
3.2.1.
-
,
[4] : }/() =
( ) [ ; ()] , (3.2.1) uk(r) , . (3.2.1) ,
.
, ( v . valence band), , , ( . conduction band). k, , . ,
. 3.9 k :
.
)
, ; ) * * - ^
^ ,
B f t J I
.
114 . ,
-
. 3.9.
,
, (. . 3.9), : h2h2
= ~ , (3.2.2) 2
= h2/[d2Ec/dk2]k=0 . Ev , , (. . 3.9), :
h2k2 E v =
fr^' (3.2.26) mv = h2/(d2Ev/dk2)k=0 . ,
,
,
(. 3.96). ' ,
, , :
E^=Eg+Ec, (3.2.3) El=-Ev, (3.2.36)
Eg , . .
kx, ky kz , , , . ., , ,
, z, (3.2.2) (3.2.3), k2 = k2 +k2 +k2.
,
.
,
Lx, Ly Lx, , ,
2. :
kt = (2nl/Lt), (3.2.4) i = , , z, / . , . 3.9
, .
,
. , ,
, 11 .
. .
2
, \\fx 2 . ,
3. , 115
-
d
> x E.
'2
X
> . 3.10 . 3.11
() ()
V i a V i b , d
-
N d
d . d ,
,
. -, , ,
,
, ,
- 19
.
vi/^ , 180 (. 3.10). ,
. ,
, d , ,
.
N , , , iV-
N . ,
,
2 , ,
(. 3.11). , N , N . N ,
.
, , (3.2.2) (3.2.3), (3.2.4), -
116 . .
-
. ,
= hk (, =
2/2), ,
Eg mv. , ,
k- , :
p = ftk. (3.2.5) , (3.2.2) (3.2.3)
, ,
k. , Si Ge, , .
IIIV, GaAs, InGaAs, AlGaAs InGaAsP. , GaAs
= 0,067 0 , 0 . , IIIV , ( hh . heavy holes) (mhh = 0,46m0 GaAs), ( lh . light holes) (mlh = 0,08m 0 GaAs) -- (. 3.12). , , , ,
,
.
,
,
, s- .
,
( 1 1
. 3.11), ,
-,
,
2 --
,
, .
,
,
- V , , k = .
-
. 3.12 : ,
-
I I I - V
3. , 117
-
-
- . (, GaAs = 0,34 ) kT (~ 0,028 ), - ,
. ,
3.2.2, . , ,
I I I - V .
3.2.2.
,
2.2.1, p(k), & &. . 2.2 , ,
kt, p(k) , . . 4nks/S9 , , (2n)3/LxLyL29 2, , . ,
p(k) = (ksV/Sn2), (3.2.6) V = LxLyL2 . , p(k), . . , k k k + dk, , (3.2.6),
, (3.2.7) , , , ,
, .
() . pcv(E)dE = pcv(k)dk, (3.2.2) :
1 2
in2 { h2
1 (2mv
3/2
() = ^ ^ ]'\ (3.2.8)
^ > = ^ ^ ) 3 / V - ( 3 - 2 - 8 )
,
Ev (. 3.9). , I I I - V mc
-
: -
3.2 3.
, .
,
. , . .
,
-, .
E'(k)> ( , , ), :
E'F , . , . 3.96, . (3.2.9), E' = E'F. , f(E'F) = l/2. ErF (3.2.9), -> 0. , f(E') = 1 'E'F. , = 0 , .
, EF . , > 0
3.2.3.1.
f(E') = l + exp[(E'-EF)/kT]9 (3.2.9)
. 3.13 ) ' k. ) f(E')
f 3. , 119
-
f(E') ' , . 3.136. , , Eg kT, , . .
.
, . 3.9 . 3.13 ,
. ,
,
.
. , - E'F ,
.
- E'F . ,
(~10 1 8 " 3) , .
,
.
3.2.3.2.
, () -
. ( , ~1 ) , ( ~ 1 , - ). , ,
,
.
fv fc . , fc fv (3.2.9). , , . 3.9, :
) = (3.2.10) , )
l + exp[(EC-EFc)/kT]
1 l + e x p [ ( F u - E v ) / k T ] 9 (3.2.106)
EFC EFV .
, EFC vlEFV fC(EC) fV(EV) , 3.146. ,
, , , -
UEV) =
120 . .
-
= . , . 3.14 = , ( ) , ( ). , ,
.
(3.2.10) , . 3.96. (3.2.3) (3.2.36), :
1
l + exv[(E'c-E'Fc)/kT] 1
(3.2.11)
A + exvKK-EkVW (3.2.116) , ,
,
. , EFc nEFv (3.2.11) , .
, ,
, Ne:
Ne= \Pc(Ec)fc(Ec)dEc. (3.2.12)
Nh , fv(Ev) = l-fv(Ev) ,
3- , 121
-
, , ! . (3.2.106) :
^{ E v } =
1 + [(- EFv )/kT]' (3.2.13) (3.2.13) , ,
. 3.14, , ,
(. (3.2.13) (3.2.10)).
. ,
Nh : 00
Nh = jpv(Ev)fv(Ev)dEv. (3.2.14)
, ,
- ,
, N. , , N, , ,
, (3.2.12) (3.2.14), Ne = Nh = N. , (3.2.12) (3.2.8) (3.2.10) :
00
Nc = 2(2nmckT/h2)3/2, = Ec/kT, a zF = EFc /kT. , (3.2.14) (3.2.86)
. 3.15 ) , I kT
N/Nc. , )
EF/kT iV G a A s
122 . .
-
(3.2.13) , (3.2.15). (3.2.15) , EFc /kT N/Nc, . 3.15. , .
3.4. GaAs.
= 0,0670 mv = mhh = 0,46m0 = 300 . Nc = = 4,12 10 1 7 - 3 ^ = (mv/mc)V2Nc = 7,41 10 1 8 "3, , (3.2.15), &NV .
N N/Nc , . 3.15, EFc /kT. .
EFJkT N GaAs, , GaAs, . 3.156.
3.2.4. :
v . ,
, , ,
1 (. (2.4.2)):
' = -, (3.2.16) = E(r, t) t. :
= 0 , - *), (3.2.17) kopt , = 2nv. v ^ Eg/h,
. 2{ , W, (.23) , :
W = g - | H S P 8 ( v - v 0 ) , < 3 - 2 8 > v 0 =
\ \=\jwl(-er'E0eik^-r)^vdv\2. (3.2.19) , \\fv (3.2.19) 1 2, (3.2.1).
1 , 2,
,
,
. ,
.
3. , 123
-
(3.2.18) (3.2.19) . 5- (3.2.18), , v = v 0 . ,
(Ei-E[) = hv, (3.2.20) .
, \\tv exp (jkv ) \|/ exp (ikc ), (3.2.19) ,