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Phase Mismatch in SHG in Nonlinear Optics

​
ω
Δφ
Phase mismatching is an important aspect of second harmonic generation (SHG) in nonlinear optics. The second harmonic wave
cos(2ωx)
is generated at one place and its original phase is 0. Another harmonic wave
cos(2ωx+Δφ)
is generated at another place and its original phase is
Δφ
. When
Δφ=0
,
cos(2ωx)+cos(2ωx+Δφ)
is largest. When
Δφ=π
, the sum is 0. Therefore, the length
L
C
=π/(
k
2ω
-2
k
ω
)
is defined as the optimum length in SHG.
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