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.