非线性光学讲稿(4)
非线性光学讲稿(4)
非线性光学讲稿(4)
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§4.9 准相位匹配与光学超晶格<br />
非线性系数(光)栅<br />
国家自然科学基金委员会<br />
数理学部实验物理讲习班<br />
1 iGz<br />
deff<br />
= dqcosGz<br />
= dqe<br />
+ c.<br />
c.<br />
2<br />
dE 2 1 iω<br />
2 −iΔkq<br />
z<br />
= dqE1<br />
e<br />
dz 2 cn(<br />
2ω<br />
)<br />
dE1 1 iω<br />
∗ iΔkqz<br />
= dqE2<br />
E1<br />
e<br />
dz 2 cn(<br />
ω)<br />
Δ kq = Δk<br />
− G = k(<br />
2ω<br />
) − 2k(<br />
ω)<br />
− G<br />
Δk q = 0 → G = Δk<br />
= k(<br />
2ω<br />
) − 2k(<br />
ω)<br />
Λ g π π<br />
→ = = = lc<br />
2 G Δk<br />
I<br />
2ω<br />
eff<br />
d d eff eff deff<br />
P<br />
s<br />
0 c<br />
120<br />
− d − deff<br />
− deff<br />
l c<br />
z<br />
2l 3lc 4lc 5lc 6lc<br />
图 4.11<br />
a + b<br />
− d − d eff − d eff<br />
eff<br />
d eff d eff d eff<br />
有(光)栅参与的波矢匹配条件:<br />
k( 2ω<br />
) − 2k(<br />
ω)<br />
− G = 0 ▲对任意光学超晶格:<br />
m=<br />
+∞<br />
d ( z)<br />
= d ∑ A exp( iG z)<br />
eff<br />
m=<br />
−∞<br />
m<br />
m<br />
Λ<br />
=<br />
a b a b a b<br />
图 4.12<br />
Gm = 2πm / Λ k ( 2ω<br />
) − 2k(<br />
ω)<br />
= Gm<br />
z