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Linear dichroism and birefringence spectra of bamboo and its use as a wave plate in the terahertz frequency region

Hiroya Ichikawa, Kei Takeya, and Saroj R. Tripathi

Open Access Open Access

Abstract

The applications of terahertz (THz) waves have been increasing rapidly in various fields, and there is a strong demand for efficient, robust, and low-cost optical components working in the terahertz frequency region. Bamboo, being one of the naturally occurring renewable resources, it has the potential to be used as an easily accessible and sustainable material for the fabrication of terahertz optical components. In this article, transmission mode terahertz time domain spectroscopy (THz-TDS) is used to investigate the terahertz properties, such as refractive index and absorption coefficient of three different species of bamboo in a frequency range from 200 GHz to 1 THz. Remarkable features such as birefringence and linear dichroism are observed, and the origin of these properties is primarily attributed to the orientation of fiber in the bamboo. The possibility of fabricating waveplates using bamboo is explored, and a quarter waveplate working in the sub-terahertz frequency region is demonstrated as a proof-of-principle. This wave plate can be used in terahertz sensing and imaging systems.

© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

The electromagnetic waves covering a frequency range from few hundreds of gigahertz (GHz) to few terahertz (THz) are known as terahertz waves [1]. The terahertz frequency region lies in between microwave and infrared region in the electromagnetic spectrum and the terahertz waves share some properties with both microwaves and infrared waves. Terahertz waves can penetrate through a wide variety of materials such as plastics, ceramic, cloths, and papers in a way similar to that of microwaves whereas they can propagate in a straight line like that of infrared waves [2]. Moreover, terahertz waves are strongly absorbed by polar liquids such as water making it possible to measure and monitor the moisture content in a wide range of construction materials and food products [3–5]. Some organic compounds such as illicit drugs, explosives and narcotics have unique spectral fingerprints in the terahertz region rendering them detectable based on the spectral imaging [6–9]. Besides this, terahertz waves are considered safe non-ionizing radiation for humans as the photon energy associated with the terahertz wave (For example, 1 THz = 4.1 meV) is not high enough to ionize the biomolecules [10]. Owing to these remarkable characteristics, terahertz waves can be used in various fields such as information and communication technology, non-destructive testing and analysis, homeland security, biomedicine, and pharmaceutical sciences [11–15].

One of the unique features of terahertz waves is their ability to penetrate various nonmetallic materials that are opaque in visible and infrared wave regions. This characteristic makes terahertz waves attractive in many areas of sensing and imaging of materials. In the past, transmittance, and reflectance of variety of materials such as textiles and clothing have been investigated in terahertz frequency region to identify fabrics and to remotely detect the weapons covered with cloths [16–17]. Furthermore, a wide range of construction materials such as woods, papers, polymers, wood-plastics composites, stones, and concrete were characterized using terahertz waves for their quality assessment [18–23]. Similarly, terahertz reflection characteristics of various building materials are also being studied to develop novel propagation channel models for terahertz communication systems. For example, polarization sensitive terahertz transmission and reflection properties of glass, plaster and multi-layer building materials such as window glass were measured to investigate the signal propagation characteristics in future wireless communication system operating at the frequencies above 100 GHz [24–26].

Along with these studies, researchers have been exploring the possibility to use various naturally occurring sustainable materials for the development of optical components working in the terahertz region. Natural stones such as dolomite, marble, and sandstone have been studied using THz-TDS and it was shown that these stones function as a terahertz lens when cut in an appropriate size and shape because of their suitable refractive index in the sub terahertz region [27]. Besides this, birefringence and diattenuation properties of wood and paper have been investigated and its was demonstrated that the birefringence properties are sufficient to construct low-cost half and quarter wave plates operating in the sub-terahertz frequency region [28–30]. Similar study on a stacked copy paper with an air gap in between the sheets as a waveplate has also been reported [31].

Despite the availability of terahertz properties of such naturally occurring materials, terahertz spectroscopic study of bamboo has not yet been carried out. Bamboo has excellent properties such as low-cost, flexibility, lightweight and high strength-to-weight ratio compared to wood and other plant materials [32]. Because of such reasons, bamboo is being used not only as a renewable and sustainable construction materials but also as a raw material for making textiles, sanitary materials, kitchenware, musical instruments, fiber reinforced composites and even ornaments such as earring and bracelets [33–34]. Therefore, the terahertz optical properties such as refractive index and absorption coefficient along with birefringence and linear dichroism of bamboo have both theoretical and practical significance. The theoretical significance comes from the fact that knowing terahertz properties can lead to better understanding of their mechanical strength, homogeneity, density profile and so on [35]. On the other hand, terahertz properties are of practical significance because they provide useful information to non-destructive and non-contact testing and evaluation of bamboo and bamboo products. Besides this, knowledge of terahertz properties of bamboo and bamboo-polymer composite become crucial while designing a low-cost optical component working in the terahertz frequency band similar to those reported using wood and wood-polymer composite. Moreover, reflection properties of bamboo along with other building materials is important while investigating the non-line of sight terahertz wave propagation in future communication systems.

The objective of this research is to obtain frequency dependent terahertz optical constants such as refractive index and absorption coefficient of three different bamboo species using terahertz time domain spectroscopy. Moreover, birefringence and linear dichroism of the bamboos in the terahertz frequency region will also be investigated. Besides this, the potential of bamboo to function as waveplates in terahertz frequency region will be explored. Finally, a quarter wave plate made of bamboo working in the sub-terahertz frequency region will be demonstrated as a proof-of-concept.

2. Measurement

2.1 Sample preparation

The bamboo culm is usually straight and cylindrical in shape with the longitudinal direction being the axis of symmetry. The bamboo is mainly composed of vascular bundles embedded in a parenchyma, and these bundles are non-uniformly distributed with higher concentration close to the outer wall. The superior mechanical properties of bamboo are primarily attributed to its unidirectionally oriented vascular bundles which consist of two metaxylem vessels, phloem, protoxylem attached fiber sheaths and fiber bundles [36], [37]. The orientation of the fiber makes bamboo a highly anisotropic natural composite material. The density of mature bamboo is usually high (about 0.65 g/cm3), which is much higher than that of low-density wood species, such as balsa, basswood, and poplar (normally 0.1 − 0.4 g/cm3) [38].

In our experiment, three different species of bamboo (Hachiku bamboo, Phyllostachys nigra; Madake bamboo, Phyllostachys bambusoides; Moso bamboo, Phyllostachys edulis) widely available in Japanese forests are obtained from local hardware store. The schematic diagram of the test sample extracted from the bamboo culm is shown in Fig. 1. Three samples were prepared from each bamboo species. The surface of these samples is polished to avoid scattering of the terahertz wave. Three samples are labelled as A, B and C and their photographs along with their enlarged images are shown in Fig. 2. The bamboo fibers distributed longitudinally along the culm are clearly visible from all enlarged photographs. The thicknesses of samples A, B and C are 2.15 mm, 2.15 mm and 2.00 mm respectively and the size of all samples is approximately 60 mm × 20 mm.

 figure: Fig. 1.

Fig. 1. Schematic diagram of the test sample extracted from the bamboo culm. The angle between the terahertz electric field and the visible bamboo fiber is denoted by θ.

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 figure: Fig. 2.

Fig. 2. Photographs of the samples used in the terahertz time domain spectroscopic measurement. (a) Hachiku bamboo (Phyllostachys nigra) (b) Madake bamboo (Phyllostachys bambusoides) and (c) Moso bamboo (Phyllostachys edulis).

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2.1 Terahertz time domain spectroscopy

We used a conventional terahertz time domain spectroscopy system in transmission mode to measure the optical constants such as refractive index and absorption coefficient of three bamboo samples [39–40]. This system consists of a compact femtosecond fiber laser (λ= 780 nm, pulse width < 100 fs, repetition frequency = 50 MHz, average power = 20 mW) and two low-temperature grown Gallium Arsenide (Lt-GaAs) photoconductive antennas as an emitter and a detector of terahertz wave. The femtosecond pulse generated by the laser is divided into two equal halves using beam splitter. The first half of the laser excites the emitter antenna whereas the second half of the laser beam travels through the optical delay stage and excites the detector antenna. The terahertz wave emitted by the antenna is first collimated by an off-axis parabolic mirror and then focused on the sample using another off-axis parabolic mirror. The terahertz wave transmitted through the sample is then again collimated and focused to the detector antenna using another pair of off-axis parabolic mirrors. We used step scanning mechanical delay stage to acquire terahertz time domain waveform. Each waveform consists of 1024 samples with the sampling time of 140 fs. The frequency resolution of the measurement system is approximately 24 GHz. Typical terahertz time domain spectroscopy system, time domain terahertz pulse and its intensity spectrum obtained from Fourier transformation are shown in Fig. 3(a), 3(b) and 3(c) respectively. The samples were measured at room temperature and normal atmospheric pressure. The sample under test was mounted on a rotatable holder which can be rotated 0 to 360 degrees to study the angle dependent terahertz properties. During the measurement, the samples were placed on a focused beam with a spot diameter of approximately 3 mm.

 figure: Fig. 3.

Fig. 3. (a) Terahertz time domain spectroscopy in transmission mode. (b) Terahertz time domain pulse measured using THz-TDS and (c) its intensity spectrum.

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2.2 Optical constant calculation

In a transmission mode terahertz time domain spectroscopy, determination of optical constants is accomplished by measuring a terahertz pulse transmitted through the sample under investigation (sample signal) and another pulse without placing anything in the path of the terahertz beam (reference signal). Let ESam(t) and ERef(t) are the time domain sample and reference signals, then their Fourier transformed spectra are written as ESam(ω)= |ESam(ω)| exp{iφSam(ω)} and ERef(ω)= |ERef(ω)| exp{iφRef(ω)} respectively, where iφSam(ω) and iφRef(ω) are sample and reference phase spectra respectively. Now, transmittance T(ω) of the sample is defined as the ratio of sample intensity spectrum ISam(ω) to reference intensity spectrum IRef(ω) written as

$$T\left( \omega \right) = \frac{{{{\left| {{E_{\textrm{sam}}}\left( \omega \right)} \right|}^2}}}{{{{\left| {{E_{\textrm{ref}}}\left( \omega \right)} \right|}^2}}} = \textrm{}\frac{{{I_{\textrm{sam}}}\left( \omega \right)}}{{{I_{\textrm{Ref}}}\left( \omega \right)}}$$

Next, the phase difference between the unwrapped phase spectra of ESam(ω) and ERef(ω) is calculated as

$$\Delta \varphi (\omega )= \textrm{}{\varphi _{\textrm{sam}}}(\omega )- \textrm{}{\varphi _{\textrm{ref}}}(\omega )$$

The ratio of sample spectrum to reference spectrum is equated to the theoretical equation as

$$\begin{aligned} \frac{{{{\tilde{E}}_S}\left( \omega \right)}}{{{{\tilde{E}}_R}\left( \omega \right)}} &= \sqrt {T\left( \omega \right)} exp\left[ {i\Delta \varphi \left( \omega \right)} \right],\\& = {t_{as}}.{t_{sa}}.\exp \left[ {\frac{{i\left( {\tilde{n}\left( \omega \right) - 1} \right)d\omega }}{c}} \right]. \end{aligned}$$
Where, c is the velocity of light, ω is angular frequency, d is sample thickness, tas and tsa are the Fresnel’s transmission coefficients for terahertz electric field from air to sample and sample to air respectively and their product is written as ${t_{as}}.{t_{sa}} = 4n(\omega ).{[{\tilde{n}(\omega )+ ik(\omega )} ]^{ - 2}}\textrm{}$ . When the terahertz wave is normally incident upon the sample, then the complex refractive index $\mathrm{\tilde{n}}(\omega )= n(\omega )+ ik(\omega )$ is obtained using the following equations with an approximation in Fresnel’s equation that of n >> k [40]
$$n(\omega )= 1 + \frac{c}{{d\omega }}\Delta \emptyset (\omega )$$
$$k(\omega )={-} \frac{c}{{2d\omega }}ln\left[ {T(\omega ){{\left\{ {\frac{{{{({n(\omega )+ 1} )}^2}}}{{4n(\omega )}}} \right\}}^2}} \right]$$
where d is the thickness of the sample under investigation. Finally, the absorption coefficient is computed using the following expression.
$$\mathrm{\alpha }(\omega )= 2\omega k(\omega )/c$$

3. Results

3.1 Refractive index and absorption coefficient

It was previously reported that some woods exhibit strong birefringence combined with linear dichroism (also called diattenuation) due to the repetitive fiber structure in a micrometer range [41,42]. Therefore, bamboo is also expected to show the birefringence as the bamboo fibers are aligned along the axis of the symmetry of the culm. We first investigated the time domain pulse of terahertz wave transmitted through the bamboo sample as a function of the angle between the orientation of the bamboo fiber and the polarization of terahertz pulse. Since the standard THz -TDS system emits and detects a linearly polarized terahertz pulse, it is necessary to rotate either a sample or a polarization of the incident terahertz pulse to measure the angle dependent transmitted terahertz pulse [43]. Therefore, here we choose to rotate the sample by mounting the sample in a rotating holder.

Figure 4 shows the time domain signals transmitted through the sample for different angle of orientation. The angle of orientation (θ) is defined as the angle between the terahertz electric field polarization and the visible bamboo fiber as shown in Fig. 1. Figure 4(a) shows three time-domain pulses transmitted through the sample for the three angles of orientation (θ) as 90°, 180° and 270° respectively. It is clear that the transmitted pulses are delayed due to the reduced propagation speed of the terahertz pulse inside the sample. The maximum delay of time domain pulse is observed when the sample is rotated from 90° to 180° and the pulse returned to its initial time when the sample is rotated to 270° as shown in Fig. 4(b). This demonstrates the birefringence property of bamboo sample. In order to further analyze the frequency domain birefringence and diattenuation properties, we performed the terahertz time domain spectroscopic measurement of all three bamboo samples.

 figure: Fig. 4.

Fig. 4. Angular dependence of the terahertz wave transmitted through the 2 mm thick bamboo sample. (a) Time domain terahertz pulses for three angles (90°, 180° and 270°) of fiber orientation with respect to terahertz electric field polarization. These time domain signals are vertically offset for clarity. (b) Terahertz time domain pulses with varying angle of orientation from 0° to 360°.

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Figure 5 shows the refractive index and absorption coefficient of the three samples in the frequency range of 200 GHz to 1 THz. For all three samples and for both orientation angles (θ = 0° and 90°), the refractive indexes remain rather frequency independent. Compared with the refractive indexes of sample A and C, the refractive indexes of sample B are relatively small which is possibly due to the different in their densities as it is known that the refractive index is influenced by sample density. We also examined the absorption coefficients of three samples. In contrast to the refractive indexes of these samples, the absorption coefficient increases considerably with the increase in frequency for both orientation angles (θ = 0° and 90°). In the case the sample C, the data are presented only up to 0.7 THz because of the low signal to noise ratio due to strong terahertz wave absorption [44]. The absorption coefficient of all samples shows considerable similarly. For example, the absorption coefficient for θ = 0°and 90° for samples A, B and C are 4.0 cm-1, 2.8 cm-1; 5.1 cm-1, 2.3 cm-1; 6.9 cm-1 and 3.7 cm-1 respectively at around 400 GHz.

 figure: Fig. 5.

Fig. 5. Refractive index and absorption coefficient of three different samples of bamboo. (a) Hachiku bamboo (b) Madake bamboo (c) Moso bamboo. The refractive indexes for θ = 0° and θ = 90° are shown by the yellow circle and blue cross sign respectively. Similarly, the absorption coefficients of all samples for θ = 0° and θ = 90° are shown by green triangle and red plus sign respectively. Both refractive index and absorption coefficient for sample C is shown only up to 0.65 THz because of low signal-to-noise ratio data due to the strong terahertz absorption at higher frequencies.

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3.2 Birefringence and linear dichroism

Next, we studied the birefringence and dichroism properties of these bamboo samples as shown in Fig. 6. Birefringence is the polarization dependent refractive index of a material, and it is written as Δn(ω) = n||(ω) – n⊥(ω) where, n|| is the refractive index of the bamboo with the terahertz electric field polarization parallel to the fiber orientation (θ = 0°) and, n⊥(ω) is the refractive index of the bamboo with the terahertz electric field polarization perpendicular to the orientation of the fiber (θ = 90°). Similarly, linear dichroism (LD) also known as diattenuation is the polarization dependent absorption of a material. It is mathematically written as LD(ω) = log T||(ω) – log T⊥(ω) where, T||(ω) and T⊥(ω) are the transmittances of the bamboo sample with the terahertz electric field polarization parallel and perpendicular respectively to the bamboo fiber.

 figure: Fig. 6.

Fig. 6. Birefringence and linear dichroism (LD) of three bamboo samples (a) Hachiku bamboo (b) Madake bamboo and (c) Moso bamboo. In all these figures, birefringence is shown by red triangle whereas linear dichroism is shown by blue cross sign.

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Bamboo is a complicated system and its terahertz properties such as refractive index and absorption coefficient depend upon various factors such as free and bound water, fiber orientation, density, and the cellulose microfibrils in bamboo [45]. The differences in the optical properties of the different species of bamboos are originated from these parameters. The birefringence in bamboo is due to the results of relative contribution from both form birefringence and intrinsic birefringence. Among these two, the form birefringence is the dominant one and it is due to presence of repetitive fibrous structure in the micrometer range and the orientation of fiber along the culm of the bamboo [46] whereas the cellulose in the bamboo is the source of the intrinsic birefringence [47]. On the other hand, the diattenuation is caused by of the terahertz wave extinction due to the difference in the terahertz wave polarization dependent scattering loss. Since the diameter of the fibers in the bamboo is in the range of few tens of micrometer, terahertz wave with its electric field parallel (θ = 0°) to the fiber scatter more strongly than the terahertz wave polarized perpendicular (θ= 90°) to fibers. The difference in the linear dichroism is attributed to the difference in polarization dependent loss due to the scattering of terahertz waves.

In this section, we have studied the polarization dependent terahertz optical properties such as refractive index and absorption coefficient of three widely available bamboo species in Japan using terahertz time domain spectroscopy in the frequency range of 200 GHz to 1 THz. These properties can provide useful information to understand the interaction of terahertz wave with bamboo and may help develop terahertz sensors to investigate the various bamboo parameters such as density, moisture content, fiber orientation and many more. Moreover, these properties can be utilized to fabricate a low-cost optical component working in the terahertz frequency region as discussed in the following section.

4. Waveplate fabrication

Terahertz optical constants such as refractive index and absorption coefficient along with birefringence of various materials such as stone, woods and sheets of paper have been measured. It has been suggested that these materials have sufficient birefringence to fabricate terahertz waveplates. Waveplates, also known as retarders, are used to change the polarization property of electromagnetic wave. Two types of waveplates, half wave and quarter waveplates are commonly used in optical measurement systems. When a linearly polarized light is incident on a birefringent dielectric slab at an angle of 45° to the optic axis, phase difference is introduced between the electric fields parallel and perpendicular to the optic axis. The phase difference Δφ(ω) is written as [48]

$$\Delta \varphi (\omega )= \frac{{2\pi fd\mathrm{\Delta }n(\omega )}}{{{c_0}}}$$
Where, f is the frequency, d is the thickness, Δn(ω) is the birefringence and c0 is the velocity of the light. Figure 7 shows the relationship between the frequency, phase difference and the wavelength when the thickness and mean birefringence are taken as 2.15 mm and 0.086 respectively. Here, the mean birefringence is calculated in the frequency range of 0.2–1 THz. The dielectric slab produces phase difference from 0 to π for frequency extending from 0 to 0.8 THz. The quarter wave plate produces a phase difference of π/2 between two electric fields, therefore it changes linearly polarized light to circularly polarized light. On the other hand, half wave plate produces a phase difference of π between two electric fields, it rotates a plane of polarization of a linearly polarized wave. In this particular case (d = 2.15 mm and Δn = 0.086), the bamboo piece functions as a quarter wave plate and half wave plate at around 405 GHz and 810 GHz since the phase differences are π/2 and π respectively in these frequencies.

 figure: Fig. 7.

Fig. 7. The relationship between frequency and phase difference for a dielectric slab. Here, birefringence (Δn) and thickness (d) of the sample are taken as 0.086 and 2.15 mm respectively.

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In order to investigate the half wave and quarter wave functionality of the bamboo sample, we measured the terahertz wave electric field transmitted through the 2.15 mm thick Hachiku bamboo (Sample A). Typically, terahertz time domain spectrometer produces a linearly polarized terahertz wave, and its polarization direction is determined by the orientation of the photoconductive antenna used to emit and detect the terahertz wave. In this measurement, we used the THz-TDS system as shown in the Fig. 3 where we used two wire grid polarizers to measure both horizontal (Ex) and vertical (Ey) components of the terahertz wave [49]. The sample under investigation is mounted on a rotatable holder and placed on the focus of the terahertz wave. The sample is rotated in such a way that the angles between the fiber orientation of the bamboo and the terahertz electric field become +45° and -45°. In these cases, the sample produces left and right circularly polarized light as it functions as a quarter wave plate at 405 GHz.

Figure 8(a) shows the horizontal and vertical components of terahertz electric field transmitted through the bamboo sample when the angle between fiber orientation and terahertz electric field is +45°. Figure 8(b) shows their respective amplitude spectra obtained using fast Fourier transformation and Fig. 8(c) shows the frequency dependent phase difference between these two electric fields. From these figures, it can be seen that the electric field amplitudes are equal in the frequency of 405 GHz. Moreover, the phase difference between these electric fields is approximately π/2 at this frequency. Since these are the two essential criteria that need to be satisfied in order to work a birefringent material as a quarter wave plate, the results shows that the bamboo sample functions as a quarter wave plate at 405 GHz. Here, it is worthwhile to note that the transmittance efficiency of this waveplate is around 15% at this frequency.

 figure: Fig. 8.

Fig. 8. Orthogonal components of terahertz time domain electric fields transmitted through the bamboo sample and their intensity and phase information. In this case the angle (θ) between terahertz electric field and bamboo fiber axis is -45°. (a) vertical and horizonal components of terahertz electric fields (b) their intensity spectra obtained from fast Fourier transformation and (c) the phase difference between vertical and horizontal component of terahertz electric field.

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Next, in order to investigate the purity of circularly polarized terahertz waves, we calculated the ellipticity of the terahertz wave transmitted through the sample using the Stokes polarization parameters as shown below [50]

$${S_0}(\omega )= \; {|{{E_x}(\omega )} |^2} + {|{{E_y}(\omega )} |^2}$$
$${S_1}(\omega )= \; {|{{E_x}(\omega )} |^2} - {|{{E_y}(\omega )} |^2}$$
$${S_2}(\omega )= \; 2|{{E_x}(\omega )} |\; |{{E_y}(\omega )} |\cos \{{\Delta \varphi (\omega )} \}$$
$${S_3}(\omega )= \; 2|{{E_x}(\omega )} |\; |{{E_y}(\omega )} |\sin \{{\Delta \varphi (\omega )} \}$$
Where, Ex(ω) and Ey(ω) are the electric field components and Δφ(ω) is their phase difference. The ellipticity of the terahertz wave transmitted through the sample is written as
$$\mathrm{\chi }(\omega )= \frac{{{S_3}(\omega )}}{{{S_0}(\omega )}} = \frac{{2|{{E_x}(\omega )} |\; |{{E_y}(\omega )} |\sin \{{\Delta \varphi (\omega )} \}}}{{{{|{{E_x}(\omega )} |}^2} + {{|{{E_y}(\omega )} |}^2}}}$$

The value of χ(ω) = -1 indicates the pure right-handed circularly polarized terahertz waves whereas χ(ω) = + 1 indicates the pure left-handed circularly polarized terahertz wave. For the purely circularly polarized terahertz wave Ex (ω) = Ey (ω). Therefore, the ellipticity of terahertz wave is written by substituting the value of Δφ(ω) from Eq. (7) in Eq. (12) as

$${\chi }\left( \omega \right) = \sin \left\{ {\Delta \varphi \left( \omega \right)} \right\} = sin\left\{ {\frac{{2\pi fd{\Delta }n}}{{{c_0}}}} \right\}.$$

Figure 9 shows the theoretical and experimental values of ellipticities of the terahertz wave transmitted through the bamboo sample when the orientation angles are +45° and -45°. Comparison of theoretical and experimental results shows good agreement, indicating that the bamboo samples can be used to produce not only circularly polarized terahertz wave but also the terahertz wave with required ellipticity and handedness. The positive and negative values of ellipticity shows the left and right circularly polarized light at those frequencies. Moreover, the ellipticities close to ±1 indicate the bamboo sample can be used to generate purely circular polarized terahertz wave with the required handedness. For the reference, we plotted an electric field of left circularly polarized and right circularly polarized light at 405 GHz shown in Fig. 9(a) and 9(b). These visual representations also clearly indicate the purity of circularly polarized terahertz wave transmitted through the bamboo sample. In this section, we have investigated the potential of bamboo piece to function as a terahertz wave quarter wave plate. This result demonstrates that the terahertz wave transmitted through the bamboo sample can convert linearly polarized light into circularly polarized light. The ellipticity close to one indicates that the terahertz wave is purely circular polarized at the frequency of 405 GHz.

 figure: Fig. 9.

Fig. 9. Ellipticity of terahertz wave transmitted through the bamboo sample (a) The solids lines show the results obtained from the theoretical calculation and the squares show the results obtained from the experiment. Blue squares show the left circularly polarized terahertz wave whereas the orange squares show the right circularly polarized light (b) Electric field of left circularly polarized terahertz wave at 405 GHz and (c) Electric field of right circularly polarized terahertz wave at 405 GHz.

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5. Conclusion

This paper broadly deals with two main aspects of bamboo measurement. In the first half of this paper, we have reported the refractive index and absorption coefficient along with birefringence and linear dichroism properties of three bamboos using terahertz time domain spectroscopy in the frequency range of 200 GHz to 1 THz. The spectroscopic results presented here are of practical importance because the results allow us to understand how terahertz wave interacts with bamboo and its constituents such as microfiber, cellulose, hemicellulos, and lignin. For example, terahertz absorption information can be used to identify the inhomogeneity caused by the presence of foreign bodies and defect. Other bamboo properties that can be investigated are density mapping, thickness measurement and moisture content measurement. Since birefringence is mainly caused by the optical anisotropy of bamboo, it can be used to investigate the quality of bamboo. For example, rots in bamboo could be identified using birefringence imaging whereas other properties such as absorption may not produce enough contrast in the image. Similarly, birefringence and linear dichroism properties can be used to determine the optical axis of bamboo which may be helpful to investigate the strength and load bearing capacity of the bamboo.

In the second half of this paper, we have explored the possibility of using bamboo sample as a quarter wave plate in the sub-terahertz region as the birefringence of bamboo is sufficient to fabricate wave plate. We have evaluated the performance of quarter wave plate by computing the ellipticity of terahertz wave transmitted through the bamboo strip using Stokes polarization parameters. Ellipticity values close to +1 and -1 show that the linearly polarized terahertz wave can be converted to left and right circularly polarized terahertz wave respectively when an optic axis of the bamboo is placed in an appropriate angle with the electric field of terahertz wave. With this proof-of-principal demonstration, we have shown that the bamboo can be used as a low-cost and easily accessible optical element to convert linearly polarized terahertz wave into circularly polarized terahertz wave. This wave plate may find applications in terahertz sensing, imaging, and communication systems.

Funding

Japan Society for the Promotion of Science (21K04174).

Acknowledgement

The authors like to thank Kazuma Hashimoto and Kotaro Yamamura for their support in the experiment.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

1. E. Brundermann, H. W. Hubers, and M. F. Kimmitt, Terahertz Techniques (Springer, 2014).

2. P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - Modern techniques and applications,” Laser & Photon. Rev. 5(1), 124–166 (2011). [CrossRef]  

3. G.-H. Oh, H.-S. Kim, D.-W. Park, and H.-S. Kim, “In-situ monitoring of moisture diffusion process for wood with terahertz time-domain spectroscopy,” Opt. and Las. in Eng. 128, 106036 (2020). [CrossRef]  

4. J. F. Federici, “Review of moisture and liquid detection and mapping using terahertz imaging,” J. Infrared, Millimeter, Terahertz Waves 33(2), 97–126 (2012). [CrossRef]  

5. A. Ren, A. Zahid, D. Fan, X. Yang, M. A. Imran, A. Alomainy, and Q. H. Abbasi, “State-of-the-art in terahertz sensing for food and water security - A comprehensive review,” Trends Food Sci. Technol. 85, 241–251 (2019). [CrossRef]  

6. M. Kato, S. R. Tripathi, K. Murate, K. Imayama, and K. Kawase, “Non-destructive drug inspection in covering materials using a terahertz spectral imaging system with injection-seeded terahertz parametric generation and detection,” Opt. Express 24(6), 6425–6432 (2016). [CrossRef]  

7. A. G. Davies, A. D. Burnett, W. Fan, E. H. Linfield, and J. E. Cunningham, “Terahertz spectroscopy of explosives and drugs,” Mater. Today 11(3), 18–26 (2008). [CrossRef]  

8. M. R. Leahy-Hoppa, M. J. Fitch, X. Zheng, L. M. Hayden, and R. Osiander, “Wideband terahertz spectroscopy of explosives,” Chem. Phys. Lett. 434(4-6), 227–230 (2007). [CrossRef]  

9. K. Hashimoto and S. R. Tripathi, “Non-destructive identification of drugs in plastic packaging using attenuated total reflection terahertz time domain spectroscopy,” Optics 3(2), 99–106 (2022). [CrossRef]  

10. E. Berry, G. C. Walker, A. J. Fitzgerald, et al., “Do in vivo terahertz imaging systems comply with safety guidelines?” J. Laser Appl. 15(3), 192–198 (2003). [CrossRef]  

11. T. Nagatsuma, G. Ducournau, and C. C. Renaud, “Advances in terahertz communications accelerated by photonics,” Nat. Photonics 10(6), 371–379 (2016). [CrossRef]  

12. S. R. Tripathi, Y. Sugiyama, K. Murate, K. Imayama, and K. Kawase, “Terahertz wave three-dimensional computed tomography based on injection-seeded terahertz wave parametric emitter and detector,” Opt. Express 24(6), 6433–6440 (2016). [CrossRef]  

13. Y. H. Tao, A. J. Fitzgerald, and V. P. Wallace, “Non-contact, non-destructive testing in various industrial sectors with terahertz technology,” Sensors 20(3), 712 (2020). [CrossRef]  

14. S. R. Tripathi, E. Miyata, P. B. Ishai, and K. Kawase, “Morphology of human sweat ducts observed by optical coherence tomography and their frequency of resonance in the terahertz frequency region,” Sci. Rep. 5(1), 9071 (2015). [CrossRef]  

15. J. A. Zeitler, P. F. Taday, D. A. Newnham, M. Pepper, K. C. Gordon, and T. Rades, “Terahertz pulsed spectroscopy and imaging in the pharmaceutical setting - a review,” Journal of Pharmacy and Pharmacology 59(2), 209–223 (2010). [CrossRef]  

16. M. Naftaly, J. F. Molloy, G. V. Lanskii, K. A. Kokh, and Y. M. Andreev, “Terahertz time-domain spectroscopy for textile identification,” Appl. Opt. 52(19), 4433–4437 (2013). [CrossRef]  

17. C. Baker, T. Lo, W. R. Tribe, B. E. Cole, M. R. Hogbin, and M. C. Kemp, “Detection of concealed explosives at a distance using terahertz technology,” Proc. IEEE 95(8), 1559–1565 (2007). [CrossRef]  

18. T. Inagaki, B. Ahmed, I. D. Hartley, S. Tsuchikawa, and M. Reid, “Simultaneous prediction of density and moisture content of wood by terahertz time domain spectroscopy,” J. Infrared, Millimeter, Terahertz Waves 35(11), 949–961 (2014). [CrossRef]  

19. D. Banerjee, W. von Spiegel, M. D. Thomson, S. Schabel, and H. G. Roskos, “Diagnosing water content in paper by terahertz radiation,” Opt. Express 16(12), 9060–9066 (2008). [CrossRef]  

20. S. Wietzke, C. Jansen, M. Reuter, T. Jung, D. Kraft, S. Chatterjee, B.M. Fischer, and M. Koch, “Terahertz spectroscopy on polymers: a review of morphological studies,” J. Mol. Struct. 1006(1-3), 41–51 (2011). [CrossRef]  

21. A. Nakanishi and H. Takahashi, “Terahertz optical material based on wood-plastic composites,” Opt. Mater. Express 8(12), 3653–3658 (2018). [CrossRef]  

22. N. P. Yadav, A. Kumar, and G. Hu, “Terahertz parametric real-time imaging of jade stone by terasense,” Wireless Personal Communications 116(4), 2899–2911 (2021). [CrossRef]  

23. S. R. Tripathi, H. Inoue, T. Hasegawa, and K. Kawase, “Non-destructive inspection of chloride ion in concrete structures using attenuated total reflection of millimeter waves,” J. Infrared, Millimeter, Terahertz Waves 34(2), 181–186 (2013). [CrossRef]  

24. C. Jansen, R. Piesiewicz, D. Mittleman, T. Kurner, and M. Koch, “The impact of reflections from stratified building materials on the wave propagation in future indoor terahertz communication systems,” IEEE Trans. Antennas Propagat. 56(5), 1413–1419 (2008). [CrossRef]  

25. R. Piesiewicz, T. Kleine-Ostmann, N. Krumbholz, D. Mittleman, M. Koch, and T. Kurner, “Terahertz characterisation of building materials,” Electron. Lett. 41(18), 1002 (2005). [CrossRef]  

26. R. Piesiewicz, C. Jansen, S. Wietzke, D. Mittleman, M. Koch, and T. Kurner, “Properties of building and plastic materials in the THz range,” Int. J. Infrared Millimeter Waves 28(5), 363–371 (2007). [CrossRef]  

27. D. Han, K. Lee, J. Lim, S. S. Hong, Y. K. Kim, and J. Ahn, “Terahertz lens made out of natural stone,” Appl. Opt. 52(36), 8670–8675 (2013). [CrossRef]  

28. T. M. Todoruk, I. D. Hartley, and M. E. Reid, “Origin of birefringence in wood at terahertz frequencies,” IEEE Trans. Terahertz Sci. Technol. 2(1), 123–130 (2012). [CrossRef]  

29. C. Jordens, M. Scheller, M. Wichmann, M. Mikulics, K. Wiesauer, and M. Koch, “Terahertz birefringence for orientation analysis,” Appl. Opt. 48(11), 2037–2044 (2009). [CrossRef]  

30. M. Reid and R. Fedosejevs, “Terahertz birefringence and attenuation properties of wood and paper,” Appl. Opt. 45(12), 2766 (2006). [CrossRef]  

31. B. Scherger, M. Scheller, N. Vieweg, S. T. Cundiff, and M. Koch, “Paper terahertz wave plates,” Opt. Express 19(25), 24884 (2011). [CrossRef]  

32. J. M. O. Scurlock, D. C. Dayton, and B. Hames, “Bamboo: an overlooked biomass resource?” Biomass Bioenergy 19(4), 229–244 (2000). [CrossRef]  

33. L. Nayak and S. P. Mishra, “Prospect of bamboo as a renewable textile fiber, historical overview, labeling, controversies and regulation,” Fashion and Textiles 3(1), 2 (2016). [CrossRef]  

34. D. Liu, J. Song, D. P. Anderson, P. R. Chang, and Y. Hua, “Bamboo fiber and its reinforced composites: structure and properties,” Cellulose 19(5), 1449–1480 (2012). [CrossRef]  

35. S. Youssefian and N. Rahbar, “Molecular origin of strength and stiffness in bamboo fibrils,” Sci. Rep. 5(1), 11116 (2015). [CrossRef]  

36. S. Mannan, M. Zaffar, A. Pradhan, and S. Basu, “Measurement of microfibril angles in bamboo using Mueller matrix imaging,” Appl. Opt. 55(32), 8971 (2016). [CrossRef]  

37. S. Mannan, J. Paul Knox, and S. Basu, “Correlations between axial stiffness and microstructure of a species of bamboo,” R. Soc. open sci. 4(1), 160412 (2017). [CrossRef]  

38. X. Wang, S. Shan, S. Q. Shi, Y. Zhang, L. Cai, and L. M. Smith, “Optically transparent bamboo with high strength and low thermal conductivity,” ACS Appl. Mater. Interfaces 13(1), 1662–1669 (2021). [CrossRef]  

39. S. R. Tripathi, M. Aoki, M. Takeda, T. Asahi, I. Hosako, and N. Hiromoto, “Accurate complex refractive index with standard deviation of ZnTe measured by terahertz time domain spectroscopy,” Jpn. J. Appl. Phys. 52(4R), 042401 (2013). [CrossRef]  

40. P. U. Jepsen and B. M. Fischer, “Dynamic range in terahertz time-domain transmission and reflection spectroscopy,” Opt. Lett. 30(1), 29–31 (2005). [CrossRef]  

41. T. M. Todoruk, J. Schneider, I. D. Hartley, and M. Reid, “Birefringence in wood at terahertz frequencies,” Proc. SPIE 7099, 70992Q (2008). [CrossRef]  

42. E. Mavrona, Y. Hu, G. Siqueira, M. Rüggeberg, S. Popov, L. A. Berglund, E. Hack, G. Nyström, and P. Zolliker, “Efficiency assessment of wood and cellulose-based optical elements for terahertz waves,” Opt. Mater. Express 13(1), 92–103 (2023). [CrossRef]  

43. M. Tani, S. Matsuura, K. Sakai, and S. Nakashima, “Emission characteristics of photoconductive antennas based on low-temperature-grown GaAs and semi-insulating GaAs,” Appl. Opt. 36(30), 7853–7858 (1997). [CrossRef]  

44. S. Takagi, S. Takahashi, K. Takeya, and S. R. Tripathi, “Influence of delay stage positioning error on signal-to-noise ratio, dynamic range, and bandwidth of terahertz time-domain spectroscopy,” Appl. Opt. 59(3), 841–845 (2020). [CrossRef]  

45. S. Tanaka, K. Shiraga, Y. Ogawa, Y. Fujii, and S. Okumura, “Effect of pore conformation on dielectric anisotropy of oven-dry wood evaluated using terahertz time-domain spectroscopy and eigenvalue problems for two-dimensional photonic crystals,” J. Wood Sci. 60(3), 194–200 (2014). [CrossRef]  

46. P. Zolliker, M. Ruggeberg, L. Valzania, and E. Hack, “Extracting wood properties from structured THz spectra: birefringence and water content,” IEEE Trans. THz Sci. Technol. 7(6), 722–731 (2017). [CrossRef]  

47. K. Uetani, H. Koga, and M. Nogi, “Estimation of the intrinsic birefringence of cellulose using bacterial cellulose nanofiber films,” ACS Macro Lett. 8(3), 250–254 (2019). [CrossRef]  

48. Bahaa E. A. Saleh, Fundamentals of Photonics (Wiley, 2019).

49. H. Tomita, K. Hashimoto, K. Takeya, and S. R. Tripathi, “Development of a terahertz wave circular polarizer using a 2D array of metallic helix metamaterial,” Opt. Lett. 46(9), 2232–2235 (2021). [CrossRef]  

50. H. G. Berry, G. Gabrielse, and A. E. Livingston, “Measurement of the Stokes parameters of light,” Appl. Opt. 16(12), 3200–3205 (1977). [CrossRef]  

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (9)
Fig. 1.
Fig. 1. Schematic diagram of the test sample extracted from the bamboo culm. The angle between the terahertz electric field and the visible bamboo fiber is denoted by θ.

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Fig. 2.
Fig. 2. Photographs of the samples used in the terahertz time domain spectroscopic measurement. (a) Hachiku bamboo (Phyllostachys nigra) (b) Madake bamboo (Phyllostachys bambusoides) and (c) Moso bamboo (Phyllostachys edulis).

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Fig. 3.
Fig. 3. (a) Terahertz time domain spectroscopy in transmission mode. (b) Terahertz time domain pulse measured using THz-TDS and (c) its intensity spectrum.

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Fig. 4.
Fig. 4. Angular dependence of the terahertz wave transmitted through the 2 mm thick bamboo sample. (a) Time domain terahertz pulses for three angles (90°, 180° and 270°) of fiber orientation with respect to terahertz electric field polarization. These time domain signals are vertically offset for clarity. (b) Terahertz time domain pulses with varying angle of orientation from 0° to 360°.

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Fig. 5.
Fig. 5. Refractive index and absorption coefficient of three different samples of bamboo. (a) Hachiku bamboo (b) Madake bamboo (c) Moso bamboo. The refractive indexes for θ = 0° and θ = 90° are shown by the yellow circle and blue cross sign respectively. Similarly, the absorption coefficients of all samples for θ = 0° and θ = 90° are shown by green triangle and red plus sign respectively. Both refractive index and absorption coefficient for sample C is shown only up to 0.65 THz because of low signal-to-noise ratio data due to the strong terahertz absorption at higher frequencies.

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Fig. 6.
Fig. 6. Birefringence and linear dichroism (LD) of three bamboo samples (a) Hachiku bamboo (b) Madake bamboo and (c) Moso bamboo. In all these figures, birefringence is shown by red triangle whereas linear dichroism is shown by blue cross sign.

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Fig. 7.
Fig. 7. The relationship between frequency and phase difference for a dielectric slab. Here, birefringence (Δn) and thickness (d) of the sample are taken as 0.086 and 2.15 mm respectively.

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Fig. 8.
Fig. 8. Orthogonal components of terahertz time domain electric fields transmitted through the bamboo sample and their intensity and phase information. In this case the angle (θ) between terahertz electric field and bamboo fiber axis is -45°. (a) vertical and horizonal components of terahertz electric fields (b) their intensity spectra obtained from fast Fourier transformation and (c) the phase difference between vertical and horizontal component of terahertz electric field.

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Fig. 9.
Fig. 9. Ellipticity of terahertz wave transmitted through the bamboo sample (a) The solids lines show the results obtained from the theoretical calculation and the squares show the results obtained from the experiment. Blue squares show the left circularly polarized terahertz wave whereas the orange squares show the right circularly polarized light (b) Electric field of left circularly polarized terahertz wave at 405 GHz and (c) Electric field of right circularly polarized terahertz wave at 405 GHz.

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Equations (13)

Equations on this page are rendered with MathJax. Learn more.

T ( ω ) = | E sam ( ω ) | 2 | E ref ( ω ) | 2 = I sam ( ω ) I Ref ( ω )
Δ φ ( ω ) = φ sam ( ω ) − φ ref ( ω )
E ~ S ( ω ) E ~ R ( ω ) = T ( ω ) e x p [ i Δ φ ( ω ) ] , = t a s . t s a . exp ⁡ [ i ( n ~ ( ω ) − 1 ) d ω c ] .
n ( ω ) = 1 + c d ω Δ ∅ ( ω )
k ( ω ) = − c 2 d ω l n [ T ( ω ) { ( n ( ω ) + 1 ) 2 4 n ( ω ) } 2 ]
α ( ω ) = 2 ω k ( ω ) / c
Δ φ ( ω ) = 2 π f d Δ n ( ω ) c 0
S 0 ( ω ) = | E x ( ω ) | 2 + | E y ( ω ) | 2
S 1 ( ω ) = | E x ( ω ) | 2 − | E y ( ω ) | 2
S 2 ( ω ) = 2 | E x ( ω ) | | E y ( ω ) | cos ⁡ { Δ φ ( ω ) }
S 3 ( ω ) = 2 | E x ( ω ) | | E y ( ω ) | sin ⁡ { Δ φ ( ω ) }
χ ( ω ) = S 3 ( ω ) S 0 ( ω ) = 2 | E x ( ω ) | | E y ( ω ) | sin ⁡ { Δ φ ( ω ) } | E x ( ω ) | 2 + | E y ( ω ) | 2
χ ( ω ) = sin ⁡ { Δ φ ( ω ) } = s i n { 2 π f d Δ n c 0 } .
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