Question

Is the conversion efficiency of second harmonic generation the same for sum frequency generation?

Answer 1

HEYA!!

The answer is : -

Generally speaking, and making the naive assumption that phase-matching has a minimal effect on the produced intensity, the power emitted at a frequency ω3=ω1+ω2 in sum-frequency generation using pumps at frequencies ω1 and ω2 is given by

Pω3=η(ω1,ω2)Pω1Pω2,

i.e. it is proportional to the product of the intensity of the two pumps; within that formalism, second-harmonic generation can be seen as the degenerate process with ω1=ω2=ω, so that the produced intensity

P2ω=η(ω,ω)P2ω

is quadratic in the pump's intensity.

Note, however, that the efficiency is generally a function of the pump frequencies, and the equality

η(ω,ω)=?η(ω+Δ,ω−Δ)

is never guaranteed. This might occasionally hold if you're very far away from any resonances, but typically the two efficiencies (essentially stand-ins for the nonlinear susceptibility) are never required to be equal.

Answer 2

Efficiency of Short-Pulse Type-I Second-Harmonic Generation With Simultaneous Spatial Walk-Off, Temporal Walk-Off, and Pump Depletion Haifeng Wang and Andrew.