 Third-order pulse correlation ghost

A third-order pulse correlation ghost is a correlation lobe generated by a real feature in the nonlinear gate, appearing at a delay where no separate input pulse need exist. It is a property of the measurement's cross-correlation, not automatically an optical prepulse or optical postpulse.

The optical pulse temporal contrast article derives the separated-replica model $I(t)=g(t)+\epsilon g(t-d)$ for $d>0$, $0<\epsilon <1$ and nonoverlapping identical-shape pulses. In third-order intensity autocorrelation, the main, positive-delay and opposite-delay lobe weights are respectivelyThe physical delayed replica enters linearly when it meets the strong squared gate; its squared contribution to the gate creates the opposite-delay ghost. Lobe separation and negligible pulse overlap are assumptions of this simple decomposition.

For an original $\epsilon =0.04$, the real postpulse has four percent of the main intensity and equal duration. Normalized to the correlation's main peak, its lobe is $0.04/1.000064\approx 0.0399974$, while the ghost is $0.0016/1.000064\approx 0.00159990$. A feature at negative delay near that latter level does not establish a physical prepulse. The ghost-to-real-lobe ratio is exactly $0.04$ in this model. This ghost-level consistency test for a delayed pulse replica can check an interpretation, although an actual prepulse could also be present.

The historical correlator's inserted-etalon test supplies a controlled physical postpulse for checking the delay orientation.^[ref] Independent changes to the replica strength, or a reference with known temporal structure, test the ghost interpretation. Overlapping pulses, unequal shapes and instrument backgrounds require a richer model.