 Third-order intensity autocorrelation

A third-order intensity autocorrelation measures the delay-dependent intensity productThe name counts three intensity factors. A physical implementation can use two second-order nonlinear processes: second-harmonic generation creates a gate proportional to $I^2$, and sum-frequency generation mixes it with a delayed fundamental replica. It therefore need not use a third-order material susceptibility. The historical device spatially encoded delay in crossing beams and imaged the sum-frequency signal onto a charge-coupled device.^[ref]

An original Gaussian calculation illustrates response width. Set $I(t)=I_0{e}^{-t^2/(2{\sigma }^2)}$. Completing the square in the integral givesHence the third-order correlation width of a Gaussian pulse obeys ${\tau }_3=\sqrt{3/2}{\tau }_I$ for intensity full widths at half maximum. A $90\mathrm{fs}$ correlation width would imply ${\tau }_I\approx 73.5\mathrm{fs}$ within this ideal Gaussian model. The square-root-of-two conversion appropriate to second-order Gaussian intensity autocorrelation would be different.

For a general pulse, $A_3(\tau )$ need not equal $A_3(-\tau )$; this asymmetry can distinguish a delayed feature from an earlier one. It is still a cross-correlation with a finite-width nonlinear gate, rather than a direct reading of $I(\tau )$. The existing optical pulse temporal contrast derivation shows how a delayed weak replica also produces an opposite-delay third-order pulse correlation ghost.

Characterize phase matching, beam overlap, spatial uniformity and the temporal response before interpreting a narrow feature. Scaling the input intensity by $k$ scales this ideal signal by $k^3$, so input fluctuations also matter. The measured trace does not uniquely reconstruct an arbitrary complex optical electric field.