= Third-order pulse correlation ghost
A \b[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 $I(t)=g(t)+\varepsilon g(t-d)$ for $d>0$, $0<\varepsilon<1$ and nonoverlapping identical-shape pulses. In <third-order intensity autocorrelation>, the main, positive-delay and opposite-delay lobe weights are respectively
$$
1+\varepsilon^3,\qquad \varepsilon,\qquad \varepsilon^2.
$$
The 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 $\varepsilon=0.04$, the real postpulse has four percent of the main intensity and equal duration. Normalized to the correlation's main peak, its lobe is $0.04/1.000064\approx0.0399974$, while the ghost is $0.0016/1.000064\approx0.00159990$. 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.
\Image[/third-order-correlation-postpulse-ghost.png]
{title=A real optical postpulse creates an opposite-delay ghost in an ideal third-order intensity autocorrelation}
{description=Original compact triangular intensity profiles with a delayed replica at4ps and relative peak0.04. Direct numerical correlation produces the opposite-delay lobe near0.0016; the optical profile has no pulse there. Each panel is normalized to its own maximum.}
{source=third-order-correlation-postpulse-ghost.py}
The historical correlator's inserted-etalon test supplies a controlled physical postpulse for checking the delay orientation.<A Single Shot 3rd Order Cross-Correlator for Pulse Contrast and Pulse Shape Measurements by J. Collier and others>[printedp195, Results and Figure4]{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.
Back to article page
