Optical pulse temporal contrast ($C(t)=P_{\max }/P(t)$)

Optical pulse temporal contrast compares a pulse's peak with weaker light at another time. For a radiant power trace with peak $P_{\max }>0$, explicitly choose either the peak-to-local ratio $C(t)=P_{\max }/P(t)$ or its inverse $r(t)=P(t)/P_{\max }$. The first is at least one where the local power is positive; the second lies between zero and one. With a fixed transverse beam shape, the same ratio can be formed from light intensity. If the beam shape changes with time, specify the spatial sampling instead of identifying local intensity and total power.

A plateau at $10^{-3}$ of the peak has $r=10^{-3}$ and $C=1000$. Expressing this power ratio as optical contrast in decibels givesFor an amplitude ratio $A$ whose power ratio is $A^2$, the same definition gives $10{\log }_{10}(A^2)=20{\log }_{10}A$. Contrast also needs a delay or time range: an optical prepulse, an optical postpulse and a long optical pulse pedestal can have the same relative height but different positions and laser pulse energies. The pedestal energy fraction additionally requires integration over the contribution's duration.

A useful nonlinear measurement is third-order intensity autocorrelation. In an ideal instantaneous model, an input light intensity $I(t)$ generates a second-harmonic gate proportional to $I^2(t)$. Sum-frequency generation with a delayed fundamental replica gives a recorded signal proportional toThe instrument measures this cross-correlation, rather than simply reading $I(\tau )$. Finite gate width, phase matching, spatial overlap and detector response enter the interpretation.

The1998/99 instrument of J. Collier and colleagues used second-harmonic generation, a Wollaston prism and an optical biprism to form crossing fundamental and harmonic beams. A second crystal generated the sum-frequency signal, imaged through optical filters onto a charge-coupled device. Position encoded delay. An inserted glass etalon produced a delayed replica near $1.5\times 10^{-3}$ of the main signal, recorded on one side of the correlation peak. Figure4 combines window settings shifted with etalons.^[ref]

An independent ideal calculation explains both the asymmetry and a possible third-order pulse correlation ghost. Let $I(t)=g(t)+\epsilon g(t-d)$ represent two identical-shape pulses with well-separated supports and correlation lobes, with the second weaker and delayed. Squaring introduces no overlap term. If $A_g(\tau )=\int g^2(t)g(t+\tau )dt$, expansion givesThe delayed replica produces a lobe of relative order $\epsilon$, while the opposite-delay ghost has order ${\epsilon }^2$. For $\epsilon =0.01$, the scales are about $10^{-2}$ and $10^{-4}$ respectively. These values are predictions of the stated ideal model. Assigning every small correlation feature directly to a separate input pulse would miss this distinction.

A nondetection below the measurement floor establishes a bound under a detection model, rather than demonstrating that no light exists there. Finite dynamic range, detector baseline subtraction, delay coverage and resolution should accompany a reported contrast trace. The Sequoia manufacturer likewise distinguishes optical temporal resolution from the scan step; making that step smaller does not alone narrow the optical response.^[ref]

Optical contrast in decibels expresses a specified ratio logarithmically. For peak-to-local radiant power contrast $C=P_{\max }/P(t)>0$,The inverse convention $r=P(t)/P_{\max }$ gives $10{\log }_{10}r=-L$. State the convention and the time of the weak feature. A $60\mathrm{dB}$ peak-to-feature contrast means one million to one in power, not in field amplitude.

An original readout example uses a linear photodetector whose baseline-corrected output is proportional to optical power. A main reading of $0.80\mathrm{V}$ and weak-feature reading of $80\mu \mathrm{V}$ imply $C=10^4$ and $L=40\mathrm{dB}$. Applying $20{\log }_{10}$ to those readings would incorrectly report $80\mathrm{dB}$: the electrical signal represents power, not optical wave amplitude.

If instead a measurement is proportional to an optical field amplitude $A$, with the same impedance and spatial normalization for both fields, power is proportional to $|A{|}^2$. ThenA field-amplitude ratio of $100$ and a power ratio of $10^4$ therefore express the same $40\mathrm{dB}$ contrast. The correct multiplier follows the measurement model, not whether the readout unit happens to be volts.

Contrast does not specify pedestal energy fraction, optical prepulse duration or delay coverage. The Sequoia primary sheet specifies dynamic range, scan range and optical temporal resolution separately.^[ref] A signal beneath a known measurement floor supports a contrast bound within that window; subtracting an uncertain background does not establish unlimited contrast.