## 3 Results and Discussion
Figure 4: Spectral dependence of the TPA signal, denoting the corrected amplitude of the AC function (\(V_{pulse\_duration\_corrected}\)) (**a**) for the GaP detector measured in 20–30 nm wavelength steps across the 730–970 nm range, (**b**) for the GaAsP detector measured in 50 nm steps across the 685–1300 nm range, and (**c**) for the Si detector measured in 5 nm steps across the 1170–1300 nm range. Figure 4b shows the spectral dependence of the TPA signal for the GaAsP detector measured in 50 nm steps across the 685-1300 nm range. The spectral TPA response shows smoother variations and is consistent with the movement of the linear absorption curve of the GaAsP PD, revealing an asymmetric shape similar to a right-angled triangle. The peak of the TPA signal near 1200 nm coincides with the peak of the linear response at 600 nm, showing a 10-fold TPA signal strength difference between 685 and 1200 nm. This agrees with the fact that there is a near 10-fold sensitivity difference between 340 nm (\(\approx\)0.04 A/W) and 600 nm (\(\approx\)0.3 A/W). Notably, the TPA response of the GaAsP PD from a visible wavelength to a 1200 nm NIR wavelength tends to increase steadily, albeit differently from the previous results of [PERSON] et al. [1]. Although the linear sensitivity (\(\approx\)0.25 A/W) of GaAsP at 650 nm exceeds the sensitivity (\(\approx\)0.18 A/W) at 475 nm, the TPA signal strength is reversed--that is, the TPA signals near longer wavelengths (e.g., 1300 nm) rapidly decrease compared to those at the peak wavelength (i.e., 1200 nm). This may be related to several shallow defect/trap levels near the band edges with a low density of states, which might be created during the PD manufacturing process [32; 33]. Such imperfections/impurities in semiconductor PDs can distort and even extend to the linear response of PDs near a longer wavelength than the peak response. This is a general tendency for most semiconductor PDs. Figure 4c shows the spectral dependence of a TPA signal for the Si detector at 10 dB gain with a 3.3 MHz bandwidth measured in 5 nm steps across a narrow 1170-1300 nm range. Since the Si PD has a linear response with high peak sensitivity (\(\approx\)0.7 A/W) near 970 nm, the gain setting of the Si detector can be reduced to 10 dB, and still exhibits a TPA signal as high as a few hundred millivolts. Over the broad wavelength region from the response peak at 970 to 1060 nm and higher (\(\approx\)1100 nm), the Si PD exhibits sensitivity as high as \(\sim\)0.1-0.3 A/W, which is comparable to and even exceeds the peak sensitivities of GaP and GaAsP PDs. This makes the Si detector exhibit a high background-voltage rise, with the TPA signals weakening for short wavelength excitations below \(<\)1170 nm owing to strong direct absorption. The TPA signals are slightly scattered and variable because of the high TPA efficiency, with the detector position being sensitive to the shortest pulse width up to 200 fs over this wavelength region. However, a steadily increasing trend toward longer wavelengths from the red line is evident. The TPA response over a 1170-1300 nm range corresponds to the linear spectral response between wavelengths of 585 nm (\(\approx\)0.25 A/W sensitivity) and 650 nm (\(\approx\)0.38 A/W); however, it only shares a narrow spectral domain within an entire linear response region as narrow as 400-1100 nm. Even if the spectral region is relatively narrow, the steadily increasing TPA response resembles the corresponding steadily increasing linear spectral response.