## 3 Results and Discussion  
Figure 2 shows the sequential process of extracting pulse characteristics from the readout of an AC trace based on TPA, measured using a GaAsP detector at a transimpedance gain of 30 dB, for hundreds of femtosecond pulses, with a moderate power of 300 mW, from an Insight X3 oscillator. Figure 2a shows a real-time readout of an AC trace at a 5 Hz rate across the entire \(\pm\)10 ps time delay. Figure 2b shows a fitted pulse width of 430 fs, and the amplitude of the time-delay-corrected autocorrelation trace is assumed to have a Gaussian shape from the AC trace based on TPA, measured using femtosecond pulses at an 800 nm center wavelength for GaAsP PDs. Inside the femtosecond laser (Insight X3), there was an extra-cavity GDD setup outside the oscillator to control the pulse width and deliver the shortest pulses at a particular center wavelength, to meet the demands of specific applications. The AC function for a coherent light source yields a peak-to-background ratio of 2:0, while the ratio can be increased to 8:1 for the IAC function [23; 29]. Most semiconductor PDs have intrinsic sharp bandgaps; however, owing to their material inhomogeneity, their linear absorption bands exhibit smooth response curves over a limited wavelength range across their inherent bandgaps--such as the spectral response curves over the 300-680 nm range of GaAsP PDs. The introduction of impurities into compound semiconductors results in the creation of additional energy levels within the material's band structure. These impurity levels, depending on the type of dopant (III or V), are commonly found in close proximity to the valence or conduction band edge [30]. Figure 1: Real-time readout autocorrelator with a photoconductive detector to obtain TPA signals. M1 and M2 are retro-reflecting gold mirrors with a 50:50 beam splitter (BS). The focal length of the parabolic mirror and the off-axis silver mirror is 25 mm. For delay scans, a woofer is used between two separated pulses. A linear encoder is used for accurate time-step movement of the retroreflector. However, the impurities of semiconductor PDs extend the linear response of the PD detector and exhibit considerable linear absorption, enhancing the background DC voltage of AC traces for long wavelengths above the bound of the linear response of a PD--for example, 680 nm for a GaAsP PD. These direct absorptions outside the linear PD  
Figure 2: Subsequent processes of extracting pulse characteristics: (**a**) Readout of the AC trace at a 5 Hz refresh rate collected using a home-built LabVIEW application. (**b**) AC traces collected and fitted to the intensity AC function using Gaussian-assumed pulses, and the pulse width and amplitude of the intensity AC function. Here, the amplitude of the AC function is corrected by the squared ratio of the fitted pulse width at 800 nm to the shortest pulse width at 1300 nm, as shown in (c). (c) Variation in the pulse width with center wavelength tuning of the femtosecond laser from 680 to 1300 nm in steps of 50 nm. response are detrimental and a primary challenge for two-photon measurements using semiconductor PDs. As direct absorption due to impurity levels is rare and relatively weak at wavelengths far outside the linear response--to eliminate these unwanted linear contributions for various PDs--we normalized and fitted each AC trace such that the background DC signal strength was zero. Figure 2c shows the measured and fitted full-width-half-maximum of pulse width from the AC traces for input pulses from the Insight X3 cavity, tuned at center wavelengths of 680 to 1300 nm in steps of 50 nm. The measured and fitted pulse widths vary from \(\sim\)800 to \(\sim\)220 fs as the center wavelength increases, indicating that the extra-cavity GDD setup outside the oscillator is unbalanced for proper GDD compensation, and the output pulses are all severely chirped and partially GDD-compensated at the longest wavelength near 1300 nm.