## 3 Results and Discussion
The amplifier gain bandwidth product in our detector is 25 MHz, and its bandwidth at 40 dB gain is reduced to 100 kHz [28], which is sufficient to resolve the fast-oscillating components in IAC with a rise time of \(<\)10 \(\upmu\)s [27]. Figure 3b shows the corrected amplitude of the AC function for the GaP detector held to a 20-30 dB gain at three wavelengths--that is, 680, 860, and 970 nm. It is similar to that of the GaAsP detector, and its behavior can be understood within a linear response range of 150-550 nm. However, the TPA signal at 970 nm is noticeably lower than expected, with the TPA signal at 30 dB gain being too weak to enable the measurement of the pulse width at wavelengths longer than 970 nm. This is because the photodiode's responsivity varies according to the wavelength of laser light. Figure 3c shows the corrected amplitude of the AC function, which is as high as approximately 1 V for the Si detector held to a 0 dB gain at three wavelengths--that is, 1165, 1230, and 1300 nm. Since the Si PD detector delivers the highest TPA signals, it shows sufficient strength even with a gain of 0 dB. TPA signals at shorter wavelengths than 1165 nm are too weak for measuring the pulse width because of the background DC  
Figure 3: Corrected amplitude of the AC function, denoting the TPA signal response (**a**) for the GaAsP detector at three wavelengths—that is, 685, 900, and 1300 nm; (**b**) for the GaP detector at three wavelengths—that is, 680, 860, and 970 nm; and (**c**) for the Si detector at three wavelengths—that is, 1165, 1230, and 1300 nm. The three wavelengths are represented by serial numbers. level enhanced by strong direct absorption. The TPA signals tend to grow toward the direction of longer wavelengths, from 1165 nm to a maximum of 1300 nm. Moreover, the standard Si PD has the widest and highest linear responses among known PDs, covering a 350-1100 nm wavelength range, indicating that the TPA for Si PDs is feasible for an 1165-2200 nm wavelength range. For a detailed investigation of the spectral response of TPA signals for photoconductive detectors, we examined the spectral dependence of the above PDs over the spectral domain, which provided the exact TPA measurements, as verified in Figure 3.  
As described in Figure 3, the TPA signal in Figure 4 denotes the amplitude of the intensity AC function (\(V_{peak\_corrected}\)) corrected by the squared ratio of the pulse width at a particular wavelength to the shortest pulse width, fitted from the collected TPA trace for each detector. Figure 4a shows the spectral dependence of the TPA signal (sensitivity, response) over just the 730-970 nm range for the GaP detector at a 30 dB gain with a 300 kHz bandwidth. The blue circles denote the TPA signals (\(V_{peak\_corrected}\)) with voltage scale measured using the 20-30 nm wavelength steps. The red line represents a guideline representing a rough average value. Although the data are slightly scattered and deviated, the spectral response of TPA is similar to the linear absorption response trace of the GaP PD, as shown by the red line. The highest TPA signal of approximately 1 V at 860 nm is consistent with the peak at 430 nm of the linear response curve of the GaP PD. With the peak TPA response at 860 nm, the TPA signals moving toward longer wavelengths are rapidly reduced compared to those for shorter wavelengths. This is similar to the asymmetric linear absorption curve of the GaP PD, which exhibits a rapidly decreasing slope at the longer wavelength side lobe. It is evident that the TPA signal of the AC function on the 30 dB gain setting is reduced to be sufficiently weak to be barely distinguishable at 970 nm; however, it recovers with sufficient strength, more easily extracting the pulse width at higher gain settings than at 30 dB. Notably, a higher gain setting causes the bandwidth to reduce, with the 30/40 dB gain setting being the permissible margin to fully resolve rapidly oscillating fringes in the IAC trace [27].