, , .
, .
ω
E1 = E10cos(ωt k1z), (7.12)
2ω: E2 = E20cos(2ωt k2z), (7.13)
:
u1=/nw=w /k1 u2=/n2w=2w /k2. (7.14)
nw≠n2w, , , u1 ≠u2.
(7.15) k1≠k2, ,
2 k1-k2=Δk (7.15)
Δk .
z, , : A2w(z)=(2A/Δk)sin(Δkz/2), (7.16)
, : l=p/Δk=l/4(nw -n2w), (7.17)
l=(2p/w) - . , , l1 Dn10-2, l25.
.7.3.
.7.3. . |
, .
z>>l, (7.16). , : Δk=0, k2=2k1. (7.18)
(7.18) , .
. , ( ) , , .. . (no>ne) w 2w.
7.4., , qc Z, w 2w
..: nw=n2we. (7.19)
.7.4. w 2ω. |
(7.19) . . , q - . , ne(q)=nen/[n2-(n2-ne2)cos2q]1/2, (7.20)
|
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n0 ne - w.
(7.20) .
. (7.11) , . , cos(wt-k) qE03. , , , q . . D w :
D=e0eE=e0e0 cos(wt - k)=[1+c+3/4qE02]e00os(wt-k) (7.21)
, , : e =n2=e + e202 (7.22)
e=1+c, e2=3/4q. e202<<e, (7.22) : n= n0 +n2E2 (7.23)
n0=e1/2. , . n2E2 , . . e ( n) , , 02. .
(7.23) , , . , n2E2. n2>0 . , , .
, , . , n2>0 , , , .. . , . n2E2, , , - , , . , , ( ) .
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. n2>0 (.7.5). n0=e1/2, : n=n0+n2E2. , , ; , a . , β0 : β0=arccos[n0/(n0+n2E2)] (7.24)
.7.5. . |
β>β0 , β<β0 . , ( ) , β :
β=0,61λ0/n02a (7.25)
, β0 β. β0<β , , . β0=β ; . , . . (7.24) (7.25), , (7.24) . : β2/2=n2E2/n0;
P=λ20(1,22)2/256n2. (7.26)
β0>β , , P>P (.7.6.). . Ÿ , (7.26). R=ka2/2 ≈ a/β, (7.26), β0=β :
R=a/2 ≡R. (7.27)
R, , .
.7.6.
.
. 20% . , . .
, , , , , ( , ) E1 E2 (.7.7., ). , .
.7.7. : ) ω0; ) ω1; ) ω2 ω3..
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, . , .
, I . z - , :
, , (7.28)
γ - .
(7.28) , , : .
, ω1 ω2. I10 I20 - , : (7.29)
(7.28) , I1 I2. , I10 > I20, : ,
, (7.30)
I10 >>I20, I1 . : I1≈I10,, I2=I20exp(-Kz). (7.31)
, ω1=ω2 = ω. (7.28) : , (7.32)
, : . (7.33)
:
(7.34)
(7.34) , γ . (7.34) , γ , .
, , : , (7.35)
n2=ε11/2ε21/2, - q, N , Mfi w1 w2 (.7.7), ri rf - i f.
. 7.8. |i> |f > |s>. |
, γ q, .