## 3 Results and Discussion  
In order to perform an effective measurement of the THz pulse, a phase-matching condition is required, i.e, whether the phase-matching condition in GaAs crystal is obtained in 0.1 THz and 1550 nm wavelength. The behavior of the THz refractive index of GaAs and the group refractive index as a function of the frequency (THz) is shown in Figure 3. The blue graph shows the refractive index of GaAs, and the red shows the group refractive index. The THz refractive index increases exponentially. Figure 3 shows that the refractive index of GaAs is overlapped to the group refractive index up to 6 THz, which means the GaAs crystals can obtain phase-matching up to 6 THz. Therefore, the phase-matching condition in GaAs crystal is obtained at 0.1 THz. The wavelength of the used laser should be appropriate to the THz radiation range to get phase matching in the GaAs crystal for the electro-optic process. The coherent length Lc as a function of laser wavelength concerning THz radiation is shown in Figure 4. The coherent length should be long as possible to make the electro-optic detection process effective. As the THz radiation increases, the coherent length decreases as shown in Figure 4. Figure 4 shows that the 1550 nm wavelength lasers can obtain the phase-matching condition in GaAs crystals for detection of 0.1 THz pulses. In order to demonstrate an improvement of the electro-optic detection method using GaAs crystals. The THz pulse was detected by two alternative methods: the electro-optic detector system and the Schottky diode detector. Millitech DXP-10 RPFW0 was used as a Schottky diode detector. The maximal safe input to the Schottky diode detector is 40 mW. Therefore the THz pulse was split by a power splitter. The Schottky diode detector receives approximately 30 dB less than the signal power, and the rest of the pulse power is transmitted to the elect  
Figure 3: THz refractive index of GaAs and group refractive index. Figure 5 shows a comparison between the free-space electro-optic detector and the Schottky diode detector. The schematic of the free-space electro-optic system detector is shown in Figure 1; in this experiment, there is no use of fiber coupling. The output signal is detected by a photodetector detector and amplified by an RF amplifier. The blue graph shows the Schottky diode detector. The red graph shows the free space electro-optic detector. Figure 5 shows that the electro-optic detector is close to the noise range and the Schottky diode detector is more clear and quiet. This noise is due to the distortion of the optical output signal in the free space. The output signal can be slightly improved by using a photodetector which has a high gain. The SNR of the free space electro-optic detector in this experiment is 13.9 dB. Although the electro-optic detector is noisy it has a similar response time to the Schottky detector. In order to evaluate the bandwidth improvement in the electro-optic detector, the time duration (\(\tau_{d}\)) of the detection pulse was measured in both of the detectors the Schottky diode and the electro-optic detector. The \(\tau_{d}\) of the electro-optic detector is bigger than the Schottky diode by 76.7 \(ps\). This indicates that the electro-optic detector has a larger bandwidth than the Schottky diode detector. Figure 4: coherence length with respect to THz frequency. Figure 5: THz pulse detection by free space electro-optic detector system. Figure 6 shows a comparison between the fiber-coupling electro-optic detector and the Schottky diode detector. The schematic experiment of the fiber-coupling electro-optic system detector is shown in Figure 2. The blue graph shows the Schottky diode detector. The red graph shows the fiber-coupling electro-optic system detector. Figure 6 shows that the electro-optic detector is more clear and quieter than the Schottky diode detector. Due to the EDFA amplifier and the 200 GHz filter, the laser beam was increased by 30 dB, and the noise around the frequency of the THz pulse was removed.