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1. D. Gargas et al, Imaging Single ZnO Vertical Nanowire Laser Cavities Using UV-laser Scanning Confocal Microscopy, J. Am. Chem. Soc. 131, 2125 (2009)
2. G. Grinblat et al, High-Efficiency Second Harmonic Generation from a Single Hybrid ZnO Nanowire/Au Plasmonic Nano-Oligomer, Nano Lett. 14, 6660 (2014)
3. X. Wen et al, Cavity-enhanced frequency doubling from 795nm to 397.5nm ultra-violet coherent radiation with PPKTP crystals in the low pump power regime, Opt. Express 22, 32293 (2014)
4. S. Alharthi et al, 1300 nm optically pumped quantum dot spin vertical external-cavity surface-emitting laser, Appl. Phys. Lett. 107, 151109 (2015)
期末论文要求：首先，总结文献，此部分不超过一页纸；其次，结合课程学过的知识，做相关调研，分析文献。12 月 31 日 10 点 -10 点 30分，交纸质版至教室。我的邮箱： zhangyong@nju.edu.cn
10Nonlinear Optics
EPED r
00 EP
0
1r
......1 2)3()2()1( EEnonr
......)( 3)3(2)2()1(0 EEEPnon
......)3()2()1( PPP
kjzyxkjijki EEP
,,,
)2(0
)2(lkj
zyxlkjijkli EEEP
,,,,
)3(0
)3(
Nonlinear susceptibility tensor
22002
1)( xmxU
)()( 230
200 xCmxm
dxdUxF
tEtE sin)( 0
tEtP 220
)2(0
)2( sin)(
)2cos1(21)( 2
0)2(
0)2( tEtP
The Physical origin of optical nonlinearities
......41
31 4
403
30 xCmxCm
)(230
20002
2
0 teExCmxmdtdxm
dtxdm
)(21cos)( 00
tti eeEtEtE
.).(21)( 2
21 cceXeXtx titi
.).(21.).2(
4
.).(21)24(
.).(21)(
0
021
221
3
22
20
2
120
2
ccemeEcceXXeXC
cceXi
cEceXi
tititi
ti
ti
Oscillator model:
im
eEX)(
122
00
01
P
)()(.).(21
),(),(
01 tEcceXNe
tNextP
ti
])[(2)( 22
000
2
imNe
042
)24( 21
3220
2 XCXi
)24(2 220
213
2
i
XCX
2043
22030
220
2220
20
20
23
2)2()(
)24()(2
EeN
Cm
iimEeC
2)2(0
22 )(.).(
21
),2(),2(
tEcceXNe
tNextP
ti
32
20
230)2( )2()(
eNCm
2)2(
0)2( )()( tEtP
Non-resonant nonlinearitiesSecond-order nonlinearities ((2)) -- Nonlinear frequency mixing
])cos()[cos(21
coscos)(
212121)2(
0
2211)2(
0)2(
ttEE
tEtEtP
21
21
diff
sum
Optical frequency conversion(Second Harmonic generation)
= 2 - 21= 0 k = k2
-2k 1 = 0
Energy conservation
Momentum conservation k
Birefringence Phase Match (BPM)
Phase matching 2
0)2( )(tEP
LnLp
dij
Lp+Ln X
Y
Z
m
xiGm
meKdxd 33)(X
mGm2
np LL
QPM Condition: k=(k2-2k )-Gm=0
Overview of third-order phenomena
tEtEtEtP 332211)3(
0)3( coscoscos)(
3214
)(21cos titi eet
• Frequency tripling
• The optical Kerr effect and the nonlinear rafractive index ( degeneate four-wave mixing)
Phase match problem
No phase match problem
r
nonr E 2)3()1(1
20
020
)3(
00
2)3(
0
21
21
2
2)(
nEcIIcn
nnEn
nr
rr
020
)3(
220 ,)(
cnnInnIn
(K: Kerr constant)
2KEn
• Stimulated Raman scattering