## 2 Materials and Methods  
We adopted a GaP photoconductive amplifier (PDA25K, Thorlabs, Newton, NJ, USA) as a photoconductive detector, to implement a solid and an autocorrelator for the readout of a real-time autocorrelation stamp without an additional amplifier. The GaAsP and Si photoconductive detectors were prepared by replacing the GaP PD with GaAsP (G1115, Hamamatsu, Japan) and Si (PDA100, Thorlabs, Newton, NJ, USA) PDs. This photodetector features a low-offset output, low noise, and an adjustable transimpedance amplifier to control the gain up to 70 dB. The light source was a commercial tunable laser, InSight X3 (Spectra-Physics, Milpitas, CA, USA), which could provide pulses with durations of less than 120 fs at an 80 MHz repetition rate and a broad tuning range of 680-1300 nm.  
Figure 1 shows the actual setup configuration for autocorrelation (12 \(\times\) 16 inch\({}^{2}\)). It follows a Michelson interferometer, as in conventional ACs equipped with a photoconductive detector. The pulse from the laser system was separated into two pulses by a 50:50 beam splitter (BS) with low group delay dispersion (GDD). They traveled to gold mirrors M1 and M2. The pulses reflected from M1 and M2 were noncollinearly overlapped and tightly focused on the surface of the detector using an off-axis parabolic silver mirror. A woofer was installed at the end of the reflection arm to undergo a delay scan and was operated by a 5 Hz sinusoidal wave from a home-built 30-watt power amplifier driven by the analog output terminal signal of the data acquisition card (NI USB DAQ 6356, 1.25 MS/s).  
To obtain an accurate time step, we used a linear encoder (MS 15 TTL, RSF Electronik, Austria) with a resolution of 0.1 \(\upmu\)m (0.67 fs \(<\) 1 fs) next to the fast-moving slider with retro-reflecting mirror M1. To evaluate the power dependence of the detector's photoconductivity, the laser light from the laser system was adjusted using a neutral density (ND) filter at the initial location of the autocorrelator. To confirm the wavelength dependence of TPA, wavelengths from 680 nm to 1300 nm were measured at intervals of 5 nm with the same laser power. By adjusting the variable beam attenuator, whose position was fixed in front of the incident autocorrelator, the intensity of the excitation light incident on the three semiconductor PDs was set to the same conditions. In the autocorrelator shown in Figure 1, since the TPA-based semiconductor PD was replaceable, three types were changed in turn, and then, mounted again. Since the distance of the replaced PD was changed, the distance of the parabolic mirror was finely adjusted so that the peak voltage signal of the pulse was maximized. Through this, the distance between the photodetector and the parabolic mirror was kept constant. During each tuning at 5 nm intervals, there was no change in the alignment of the autocorrelator and the incident excitation light. The output voltage from the detector was acquired and collected using a home-built LabVIEW application, in which the pulse width from each AC trace was fitted by assuming a Gaussian or sech-pulse shape. Most gain switching for the photoconductive detectors was maintained at a 30 dB setting to secure an adequately fast bandwidth; a transimpedance gain of 2.38 \(\times\) 104 V/A was achieved at a low output impedance load (50 \(\Omega\)) [28].