1.

Introduction

The terahertz (THz) region lies between the microwave and infrared zones of the electromagnetic spectrum, with the frequency ranging from 0.1 to 10 THz.^1,2 In the past two decades, THz science and technology have been developed tremendously due to impressive improvements of ultrafast optoelectronics and low-dimensional semiconductor technology. The applications of THz technology have been extended to security,³ pharmaceutical sciences,⁴ nondestructive evaluation (NDE),^5,6 and many others. Carbon-fiber-reinforced plastic (CFRP) laminates are useful composite materials. Because of their high stiffness and strength, they are commonly used wherever a high strength-to-weight ratio and rigidity are required such as in aerospace, automotive, civil engineering, sporting goods, and so on. The wide utilization of CFRP composites calls for correspondingly advanced methods and technologies for detecting their defects and flaws, especially in NDE.^7,8 The current standard NDE technologies for CFRP are ultrasonic-based⁹ and x-ray-based^10,11 testing and imaging methods, which have advantages and limitations. For instance, close contact with a test sample is required for ultrasonic testing, and harmful radiation must be involved in x-ray methods.

In recent years, THz technology has received increasing interest and attention as a potential NDE method for CFRP due to its unique features such as penetrability with respect to nonpolar materials, low-photon-energy radiation, and spectroscopic fingerprinting ability.^12–14 Many studies have been reported regarding NDE for CFRP by using THz technologies. Redo-Sanchez and Karpowicz¹⁵ and Karpowicz and Dawes¹⁶ applied THz continuous and pulsed wave technology in reflection mode to detect burn damage of CFRP. Im et al.^17,18 and Park and Im¹⁹ investigated the electrical field characterization in conducting carbon fiber. Additionally, a reflective THz time-domain spectroscopy (TDS) system was utilized to evaluate polyphenylene sulfide CFRP solid laminate with different angles of orientation of the carbon fibers. The THz scanning images showed the fiber orientation information therein and predicted the orientation of the ply. Yang et al.²⁰ detected the impact damages in CFRP specimens using millimeter waves of 65 to 67 GHz. When the electric field vector direction is parallel to the carbon fiber direction, reflection coefficients on the surface with and without damage were easily distinguished and damage detection is possible. Ospald et al.²¹ analyzed misprocessed coating layers on CFRP panels with high depth resolution. The coating misprocesses can be detected through changes in the propagation time of the reflected THz pulses that are induced by the different dielectric layers.

In the previous studies, the THz reflection properties of CFRP have been fully characterized. However, to our knowledge, there are few studies on the THz transmission properties of CFRP, especially for thin layers of CFRP. In this paper, THz reflection and transmission properties of unidirectional CFRP composites with different thicknesses (e.g., 140 to $550\mu \mathrm{m}$) are investigated systematically. It is found that the reflectivity and transmissivity of CFRP for THz radiation depend on the angle between the fiber direction and electric field direction. When the fiber direction is parallel to the electric field direction, the THz reflected power of CFRP is fairly close to that of an aluminum metal plate while the transmitted power is relatively low. When the fiber direction is perpendicular to the electric field direction, the THz reflected power of CFRP is about half of that from the aluminum metal plate while the transmitted power is the highest compared with other angles. When compared among different thicknesses in the through-transmission mode, CFRP composites exhibit an abnormal phenomenon in that the transmitted power of a 2-ply CFRP is distinctly greater than that of a 1-ply CFRP from 0.1 to 0.2 THz. The underlying reason is that the CFRP acts as a Fabry–Pérot cavity and the transmitted power is strengthened at the resonant frequency. Furthermore, the refractive index and absorption coefficient of CFRP composites are obtained in this paper.

The remainder of this paper is organized as follows. First, we describe the related theories about refractive index and electric field characterization of CFRP in Sec. 2. Section 3 introduces the CFRP samples used in our experiments. Next, we explain the THz TDS system from which data are presented in Sec. 4. The experimental results and discussion are given in Sec. 5. Finally, concluding remarks and a summary are presented in the last section.

2.

Theoretical Background

3.

Preparation of the CFRP Samples

In this study, unidirectional CFRP samples with different numbers of plies are prepared for investigation with pulsed THz radiation. These samples are 1-, 2-, 3-, and 4-ply, with corresponding thickness of 0.14, 0.31, 0.42, and 0.55 mm. All the samples used in our experiments consist of two parts: carbon fiber (67% volume) and epoxy resin (33% volume). The former gives CFRP its strength and rigidity, and the latter binds the carbon fibers together. In addition, the orientations of the carbon fibers in our samples are all the same. Figure 1 shows the optical images of the samples, clearly showing that the fibers’ orientation is unidirectional.

Fig. 1

The optical images of samples: (a) 1-ply, (b) 2-ply, (c) 3-ply, and (d) 4-ply.

4.

THz Time-Domain Spectroscopy

A commercially available THz TDS system T-Gauge 5000 from Advanced Photonix, Inc. is employed in this research.²⁴ Figure 2 shows a schematic diagram of the THz TDS system in the through-transmission and reflection mode. The THz TDS system begins with a Ti:Sapphire oscillator, which produces pulses of 1064 nm central wavelength, 80 fs duration, and 100 MHz repetition rate, with an average power of 20 mW. In the through-transmission mode, the transmitter and receiver are mounted on the spectroscopy rail to perform transmission spectroscopic measurements. In the reflection mode, the transmitter and receiver are coupled with the collinear adapter to perform as a collinear reflection transceiver. Due to the restriction of this unique THz TDS system configuration, it is not possible to perform simultaneous THz transmission and reflection measurements of the spectroscopic properties of CFRP samples. The main specifications/parameters of the system are as follows: a spectral range of 0.1 to 3.5 THz with a spectral resolution of 12.5 GHz, a signal-to-noise ratio of better than 70 dB at the lower frequency end, and about 30 dB at the high-frequency end, a time-domain range of 0 to 80 ps with 0.1 ps resolution, and a rapid scanning rate of 1 kHz.

Fig. 2

Schematic diagram of the THz TDS system in the through-transmission and reflection modes (M1–M7: mirrors; HDPE: high-density polyethylene; PCA: photoconductive antenna; TX: transmitter; and RX: receiver).

5.

Experimental Results and Discussion

5.1.

Results Obtained in the Reflection Mode

As the CFRP is highly anisotropic, the reflected power from the 1-ply CFRP exhibits a strong angular dependence as expected. The measurements were carried out at every 15 deg angle in our experiments. The angle of 0 deg represents the case that the fiber direction is parallel with the electric field direction (parallel polarization), whereas 90 deg corresponds to the case that the fiber direction is orthogonal to the electric field direction (perpendicular polarization). The total spectrointegrated reflected powers at different angles with a frequency range from 0.1 to 1 THz are calculated and are shown as the seven data points in Fig. 3. As can be seen from Fig. 3, the reflected power decreases as the angle increases from 0 to 90 deg. The seven points are fitted to the relation represented by Eq. (4), and the black curve in Fig. 3 is the final fitting curve. The fit result is $R=130.93*{\cos }^2\theta +169.8$ and the goodness-of-fit statistics is 99.67%. Through the high goodness of the fit, it is again verified experimentally that the reflectivity of CFRP indeed satisfies Eq. (4).

Fig. 3

Angular dependence of reflected power through 1-ply carbon-fiber-reinforced plastic (CFRP).

In our experiments, we compared the total reflected power from the 1-ply CFRP with that from a reference aluminum plate. The spectrointegrated reflected power from 0.1 to 1 THz of CFRP in the case of parallel polarization is 94.5%, relative to that of the reference, whereas it is 53.6% in the case of perpendicular polarization.

Based on the aforementioned observations, we have carried out a preliminary test of the THz reflection spectroscopic setup for imaging of a buried defect in the CFRP. The reflective imaging results of a CFRP sample with a Teflon artificial insert are shown in Fig. 4. The Teflon sheet ($50\times 10\times 0.2\mathrm{mm}$) was deliberately inserted between two single-ply unidirectional CFRP sheets ($100\times 100\times 0.14\mathrm{mm}$) through a hot-press process to simulate a foreign inclusion and/or an inter-ply delaminational defect. In the case of parallel polarization, the incident THz power is almost fully reflected by the first ply CFRP and the hidden defect cannot be detected, as seen in Fig. 4(b). THz waves can penetrate deeper into the CFRP composite and access more depth-related information for perpendicular polarization, such that the defect is readily visualized in Fig. 4(c) without any graphical filtering. After a simple textbook linear-contrast-enhancement processing of the image, the defect becomes much clearer, as shown in Fig. 4(d), which shows basically a diffraction-limited rendition of the hidden defect.

Fig. 4

The reflective imaging results of a Teflon artificial insert defect: (a) front side optical image, (b) THz power image in the parallel polarization mode at 0.075 THz, (c) THz power image in the perpendicular polarization mode at 0.075 THz, and (d) the result after a simple image enhancement process.

To fully realize the potential of THz imaging techniques in NDE/NDI of composite materials, it is obvious that much more effort needs to be conducted. At present, we are mainly focusing on thin-film coatings on CFRP composites and sandwiched structures involving thin layers of CFRP and dielectrics. The polarization direction of the THz radiation plays an important role in such THz imaging techniques of CFRP related composites, as demonstrated quite convincingly in Fig. 4.

5.2.

Results Obtained in the Through-Transmission Mode

Figure 5 shows the power transmission ratios of 1-ply CFRP measured at every 15 deg angle (the power spectrum after propagation through the CFRP sample divided by the power spectrum for the air). As can be seen from Fig. 5, THz waves can penetrate the most when the fiber direction is orthogonal with the electric field direction.

Fig. 5

The power transmission ratio of 1-ply CFRP at different angles.

The refractive index of CFRP with different angles and thicknesses calculated through the first approach is shown in Table 1. The formula to calculate the resolution of refractive index can be obtained through a derivative operation on Eq. (1), leading to

Eq. (5)

$${\mathrm{\Delta }}_{n_s}=\frac{V_{\text{air}}}{d}*{\mathrm{\Delta }}_t.$$

Table 1

The terahertz (THz) refractive index of carbon-fiber-reinforced plastic (CFRP).

Samples	Angle (deg)						Mean±STD
	90	75	60	45	30	15
1-ply	4.1957	4.3955	4.3955	4.1957	4.3955	4.5952	$4.3622\pm 0.1504$
2-ply	4.1389	4.0438	4.1389	3.9486	3.9486	4.0438	$4.0438\pm 0.0851$
3-ply	4.6466	4.5764	4.5764	4.5063	4.5764	4.5764	$4.5764\pm 0.0444$
4-ply	4.8376	4.9488	4.8932	4.8376	4.8376	4.8376	$4.8654\pm 0.0465$

The resolution of time delay in our system is 0.1 ps. According to Eq. (5), we estimate that the resolution of refractive index is 0.2143, 0.0968, 0.0714, and 0.0545 for 1-ply, 2-ply, 3-ply, and 4-ply, respectively. From Table 1, we see that the standard deviations of the measured refractive index are smaller than the theoretical resolution. Hence, we can conclude that within our measurement error, the refractive index of CFRP is a scalar quantity and does not depend on the fiber direction (the electrical conductivity of CFRP). As can be seen from Table 1, there are some variations in the refractive index for CFRP with different thicknesses. That is because CFRP samples are composite materials and the composition of carbon fiber and epoxy resin for CFRP with different thicknesses may vary slightly.

The frequency-dependent refractive index and absorption coefficient of 4-ply CFRP at different angles calculated through the second approach are separately shown in Figs. 6 and 7. We can see that the refractive index of 4-ply CFRP obtained by the second approach is basically consistent with the first approach, and similarly have no direct relationship with the angle between the fiber direction and electric field direction. Over the entire frequency range, the absorption coefficient gradually increases with frequency. In addition, it decreases as the angle increases from 15 to 90 deg. The increase of the angle from 15 to 90 deg entails the decrease of the electrical conductivity of CFRP (see our previous discussion). In other words, the absorption coefficient decreases with the electrical conductivity of CFRP, which agrees with the common knowledge that the absorption coefficient is proportional to the electrical conductivity.²⁵ Because the transmitted power of CFRP at 0 deg angle is relatively low, the THz pulse of CFRP is submerged in the noise, and as a result we can obtain accurate optical parameters with neither approach.

Fig. 6

The refractive index of 4-ply CFRP at different angles.

Fig. 7

The absorption coefficient of 4-ply CFRP at different angles.

Figure 8 is the power transmission ratios of CFRP with different thicknesses at a 90 deg angle. Generally speaking, the transmitted power decreases with the increase of sample thickness. However, there is an interesting anomaly in the frequency range from 0.1 to 0.2 THz in Fig. 8. The transmitted power of the 2-ply CFRP is significantly greater than that of the 1-ply CFRP. This is because that the CFRP acts as Fabry–Pérot cavity for the THz wave and all the resonant frequencies are quite obvious.²⁶ The optical path difference of two adjacent transmitted THz waves is given as

Eq. (6)

$$D=2nh\cos \alpha ,$$

where $n$ is the refractive index of the sample, $h$ is the sample thickness, and $\alpha$ is the incident angle. When $D=k\lambda$ ($k=1,2,3\dots$), the phases of all the transmitted THz waves are the same and the transmitted power is constructively strengthened.

Fig. 8

The power transmission ratio of CFRP with different thicknesses.

When THz wave is vertically incident, we can derive the resonant frequencies from the equation $D=2nh=k\lambda$ ($k=1,2,3\dots$)

Eq. (7)

$$f_k=k\frac{c}{2nh},\text{for}k=1,2,3,\dots .$$

This formula can predict all the peak positions where the transmitted power is strengthened. Table 2 gives the comparison between measured and calculated peak positions and we can see that the measured peak positions have a good agreement with those of the calculated values.

Table 2

The comparison between measured and calculated peak positions.

Samples	Refractive index	Thickness (mm)	K	Calculated resonant frequencies (THz)	Measured resonant frequencies (THz)	Relative error (%)
1-ply	4.1957	0.14	1	0.2551	0.2719	6.5857
2-ply	4.1389	0.31	1	0.1169	0.1189	1.7109
2-ply	4.1389	0.31	2	0.2338	0.2625	12.2754
3-ply	4.6466	0.42	2	0.1536	0.1500	2.3438
3-ply	4.6466	0.42	3	0.2304	0.2469	7.1615
4-ply	4.8376	0.55	2	0.1127	0.1156	2.5732
4-ply	4.8376	0.55	3	0.1690	0.1625	3.8462
4-ply	4.8376	0.55	4	0.2254	0.2500	10.9139

The transmitted THz power of CFRP at different frequencies is determined by both sample thickness and the Fabry–Perót effect. From 0.1 to 0.2 THz, the Fabry–Perót effect may play a major role, so when the resonant peaks occur, the transmitted THz power of a thicker CFRP could be larger than that of thinner CFRP within certain frequency ranges (e.g., $2\text{-}\mathrm{ply}>1\text{-}\mathrm{ply}$ and $4\text{-}\mathrm{ply}>3\mathrm{ply}$). When the frequency exceeds 0.2 THz, the thickness of the samples starts to become a leading factor, so the transmitted power decreases monotonously when the sample thickness increases.

6.

Conclusion

In conclusion, we have conducted a systematic investigation of THz reflection and transmission properties of unidirectional CFRP composites with thin-layer structures (i.e., 1- to 4-ply). Due to the strong anisotropy resulting from fiber orientation, the THz reflection and transmission properties of the CFRP samples are orientation-dependent. The THz reflection power reaches the highest value when the fiber direction is parallel to the THz electric field orientation and the lowest value under the condition of perpendicular polarization. These results are in good agreement with previous studies.^15–19 Concomitantly, the THz transmission power increases when the angle between the fiber and electric field directions increases from 0 deg to 90 deg, which has not been convincingly demonstrated to date. Furthermore, the optical parameters (e.g., refractive index and absorption coefficient) of CFRP composites are obtained in this paper. Interestingly, and perhaps technologically of importance, we found Fabry–Perót echoes in the transmitted power spectra, resulting from multiple internal reflections from the CFRP–air interfaces. Our investigation has achieved some interesting and useful results, but there are still limitations that must be overcome in the future. Based on this study, we note that CFRP composites have a prominent polarizing effect on THz waves and, as such, can be used to fabricate low-cost, flexible, and easy-to-use THz-polarization devices. Furthermore, the conductivity of CFRP hinders the penetration of THz wave into the samples, rendering it difficult to use THz technology to detect internal flaws of CFRP samples with over 1 mm thickness. On the other hand, it would be more advantageous to focus on research pertinent to thickness and defect inspection of dielectric and ceramic coatings on the surface of CFRPs, and thin CFRP–dielectric sandwiched structures in the reflection modality of THz imaging technology, for which the present study may serve as a precursor, and as such, it lays the foundation for future work along this direction.