# Potential of Liquid-Crystal Materials for Millimeter-Wave Application
## 2 Measurement of Complex Refractive Indices in Millimeter Wave
### Evaluation of Refractive Index and Absorption Coefficient  
Figure 3 shows a typical measured time waveform appearing on the oscilloscope. The periodic dip waves were observed according to the LD light pulse irradiation and one of them is shown, where the LD pulse repetition is defined at 100 Hz by the external oscillator. The interference between the MMWs reflected at the optical short and at the right-sideend caused a dipping-waveform intensity response. It was observed that the interference disappeared about 50 us after the LD pulse irradiation, which was determined by the diffusion and recombination phenomena of photo carriers because the laser pulse width was much shorter (100 ns) than the response time. The baseline of the response waveform shows the MMW intensity level reflected from the right-side edge of the CPW without the LD light irradiation, which is much larger than the dip depth of the time waveform. This situation is difficult to understand from Figure 3, because the wave is observed under the alternating current (AC) coupling mode. The interference wave generally became smaller than the baseline level, and only the  
Figure 1: Millimeter-wave (MMW) propagation model on the coplanar waveguide (CPW). LD: laser diode. Figure 2: Reflection MMW measurement system. ATT: Attenuator. dipping wave form was observed. This was probably caused by some absorption phenomenon due to the optical short, which may work not only as a reflector, but also as an absorber of MMW. The interference effect appeared at the dipping part in the time waveform; thus, we measured the depth change of the dipping wave as a function of the LD light irradiation position, as shown in Figure 4. It was observed that the depth changed periodically according to the position, which is caused by the MMW propagation path length change between the interference MMWs. The period corresponds to the waveguide wavelength; thus, the refractive index of the waveguide material can be determined from the wavelength. The absorption coefficient can be determined from the decreasing rate of the dipping depth as a function of the propagation length, if we assume the simple Lambert-Beer law for the dip depth dependency. The interference phenomena could be clearly observed only aroundthe shorter distance position from the contact probe, and it became difficult to observe when the propagation length of the reflected MMW by the optical short became longer. This was probably caused by the significant intensity difference between the interference waves, where the reflected MMW by the optical short was much smaller than that reflected from the right-side end. The reflectance of the optical short must be increased to improve the measurement accuracy by optimizing the CPW, wavelength of the LD, and so on. Table 1 presents the evaluation results of the refractive index and absorption coefficient of the Si substrate using the measurement data in Figure 4. The waveguide wavelength can be directly measured from the periodicity in Figure 4, and the effective refractive index was calculated in comparison with the  
Figure 4: Dip depth property as a function of propagation length of the MMW reflected by the optical short. Figure 3: Typical measurement waveform appearing according to the irradiation of a laser diode (LD) pulse. vacuum wavelength. The permittivity was calculated from the refractive index, because the refractive index is simply related to relative permittivity in high-frequency regions like MMW. The obtained permittivity was almost the same as that with the mean value of an intrinsic Si semiconductor and air, because the propagating MMW experienced permittivity similarly for both substrate and air. On the other hand, the absorption coefficient was larger than the commonly known value for Si semiconductors. There is almost no absorption by air; thus, the absorption of the CPW comes from the Si substrate.