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Abstract
Polarized THz time domain spectroscopy was used to study the anisotropic properties of wood-based materials for potential optical elements in the THz range, such as half-wave and quarter-wave plates. Wood samples of different species and sample thickness were studied experimentally showing high birefringence but rather high absorption. We elaborate on two approaches to optimize the optical properties for use as wave plates and assess them based on a figure of merit describing their efficiency as a function of birefringence and absorption. The first approach is to dry the wood samples, which significantly improves the efficiency of wave plates. The second approach is the use of artificially produced cellulose samples using 3D printing and freeze drying techniques, which also show birefringence caused by their similar macroscopic cellulose fibre structure. These materials have the potential as cost effective THz elements that are easy to tailor and produce for use at specific frequencies.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Wood is a highly anisotropic and inhomogeneous biological material. It shows anisotropic optical properties in the THz frequency range [1,2], in particular birefringence and diattenuation (also known as linear dichroism), which are mainly caused by preferential orientation of cellulose microfibrils in the wood cell walls [3–5]. In recent years, artificial materials made out of organic components, in particular cellulose fibres, have gained attention since they are from renewable resources and show interesting functionalities. They are produced by different methods such as 3D printing [6], freeze casting [7], oxidation from cotton [8] or by delignifying wood [9]. In order to design compounds with new properties, wood plastic composites [10] were used or various functional additives, e.g. carbon particles, metallic fibres of nanoparticles were embedded [11].
Despite the rapid growth of the THz science and technology over the last 20 years, there is still a lack of devices in particular suitable wave plates for the THz range. The basic principles for quarter-wave plates for the sub-millimetre wavelengths were already discussed forty years ago [12]. Their availability is still limited in particular for cost effective elements easily tunable to a specific frequency. The potential of wood for use as cost effective optical elements was reported in the literature [13] but not systematically investigated up to now. THz wave plates fabricated using ordinary paper [14] are also based on birefringent properties of structured cellulose. Recently, 3D printing technology has been adopted for the development of cost effective THz wave plates and polarizers [15–18]. However, these wave plates are usually efficient only for frequencies below 400 GHz. Many approaches on THz wave plates were reported all with advantages and disadvantages. Wave plates made from birefringent materials are mainly suitable for single wavelength use, because the retardation is strongly wavelength dependent [19]. Such wave plates made from crystal quartz are available commercially, however they are expensive and have to be ordered for a specific working wavelength. THz wave plates were reported to be produced for specific frequencies from fused silica glass [20] or by anisotropically etching low-loss dielectric silicon [21]. In order to overcome single wavelength use, concepts for tunable [22,23], switchable [24] or achromatic [25] wave plates have been suggested. However, these types of optical elements are in general not easily available.
Here we introduce a new efficiency measure for phase retardation elements such as half-wave plates (HWP) and quarter-wave plates (QWP), appropriate for anisotropically absorbing systems. For this, we develop the formalism to derive wave plate properties from the anisotropic refractive index and extinction coefficient. This efficiency measure is used to assess different wood and cellulose based materials for their use as wave plates. We investigate the potential for improvement using dry wood and demonstrate that cellulose based materials are suitable for THz polarization optical elements in the frequency range around 0.5 THz, because the efficiency of the investigated wood samples is highest here. We propose cellulose 3D printing as well as freeze casting to overcome humidity challenges inherent to native wood, and to introduce silver nanowires to offer a tunable way to optimize the efficiency of wave plates in the low THz frequency range.
2. Modelling of wave plate efficiency
2.1 Jones formalism
In this work, the Jones Matrix formalism is used to describe the properties of a birefringent optical element in view of its use as QWP and HWP. The complex refractive index $\tilde {n} = n - i \kappa$ of the material is known either from theory or determined by an experiment. If we assume that the magnetic permeability of the material is $\mu _r =1$, the refractive index relates to the permittivity according to $n^2 = \epsilon _r$. We will look at an arrangement of optical elements and make use of the following optical elements:
The Jones matrix of a birefringent, absorbing material and refractive indices $\tilde {n}_1(\nu )$ and $\tilde {n}_2(\nu )$ with principal axes oriented along the x- and y-axis can be described as
With a rotation matrix for angle $\alpha$
In the next two subsections we will derive key optical properties, i.e. working frequency, working angle and efficiency for QWPs and HWPs.
2.2 Quarter-wave plate (QWP)
The property of a birefringent optical element acting as a QWP, i.e. converting a linear polarized light into a circular polarized light, can be analysed with the following configuration:
Inserting Eq. (4) into Eq. (5) and (6) yields the intensity $I_R$ of the right circular component and the intensity $I_L$ of the left circular component.
The condition for a QWP for a left circular polarization is that $I_R = 0$. This is the case if the following two conditions for frequency $\nu$ and rotation angle $\alpha$ are satisfied:
Note, that for an optical element without absorption ($\kappa _1 = \kappa _2 = 0$) the efficiency is $\epsilon _\mathrm {Q} = 1$ and the working angle $\alpha _\mathrm {Q}$ is $45^\mathrm {o}$. A similar condition is obtained for right-circular polarization.
2.3 Half-wave plate (HWP)
Properties of a HWP can be analysed using the following configuration:
Inserting Eq. (4) into Eq. (12) and (13) yields the intensity of the x- and y-linear polarized components
The condition for a HWP to rotate linearly polarized light by $90^\circ$ is $I_x = 0$. This is the case, if the following two conditions for frequency $\nu$ and rotation angle $\alpha$ are satisfied:
Note, that for $\kappa _1 = \kappa _2 = 0$ the efficiency is $\epsilon _\mathrm {H} = 1$ and the working angle $\alpha _\mathrm {H}$ is $45^\mathrm {o}$.
2.4 Illustration based on a birefringent wood sample
As an illustration, we apply the method described above to a birefringent spruce sample with 2 mm thickness. Its complex refractive indices $\tilde {n}_1$ and $\tilde {n}_2$ for the two main axes were determined with THz time domain spectroscopy with the method described in section 4.1. In Fig. 1 we show the relative intensity magnitudes $I_R/I_{in}$, $I_L/I_{in}$, $I_X/I_{in}$ and $I_Y/I_{in}$ as a function of frequency $\nu$ and sample rotation angle $\alpha$. The frequency conditions for a QWP and a HWP are shown in the figures as vertical black lines. The angular condition is frequency dependent and is shown as a black horizontal curve. The working condition for a wave plate is at the position where two curves intersect. At this frequency and angular position one polarization is zero whereas the corresponding orthogonal polarization has a non-zero value, which is defined as the efficiency of the wave plate.
Fig. 1. Relative intensity magnitudes $I(\alpha,\nu )/I_{in}(\nu )$ of a spruce sample (SE-amb in Table 1) as a function of frequency and sample rotation angle for a linear polarized incoming THz pulse shown in $\log _{10}$-scale. Left-polarized (a), right-polarized (c), x-linear polarized (b) and y-linear polarized (d) components of the outgoing wave. ($\log _{10}$-scale). Vertical black lines show angular condition of a QWP (z=1,2) and HWP (z=1). Horizontal black curves show angular condition.
Table 1. Key properties of samples
3. Experimental
3.1 Samples
The main properties of the samples are summarized in Table 1. Refractive indices, birefringence, extinction coefficients and diattenuation are listed for 0.5 THz. Densities were determined from the weight and volumes of the samples.
3.1.1 Wood samples
Wood samples of three different species, spruce, beech and birch were tested. All wood samples were cut in the LT direction, where L is the longitudinal direction along the fibres and T is the tangential direction to the annual rings, which is perpendicular to the longitudinal direction (for definition see also Fig. 1 in [26]). Spruce and beech samples were the same as samples #4, #19 and #20 used in Zolliker et al. [26] and we also used those measurements to extract the optical properties. Two spruce samples were prepared from the latewood (LW) or the earlywood (EW) part of the annual rings, respectively. The beech and spruce samples were measured in two humidity conditions, one by oven drying samples for 24 hours at 103 °C, and putting them into a desiccator for intermediate storage and the other after storing the samples for several days in ambient humidity conditions resulting in a moisture content in the range of 5-8 wt$\%$. Furthermore, birch wood samples of thickness 1.5 mm, 3.1 mm and 5.0 mm were used to investigate the tunability of the wave plate properties with thickness.
3.1.2 3D printed cellulose samples
Aqueous-based cellulose nanocrystal (CNC) inks were prepared by dispersing 20 wt$\%$ of freeze-dried CNC in deionized water [6]. Next, the materials were homogenized using a planetary centrifugal speed mixer at 800, 1500, and 2250 rpm for 5 min. Prior to printing tests, the inks were loaded into 40 mL syringes and centrifuged at 3000 rpm for 3 min to remove air bubbles. The syringe containing 20 wt$\%$ water-based CNC ink was mounted in a Direct Ink Writing printer (3D-Bioplotter "Manufacturer Series", EnvisionTEC, Germany) and the ink was driven pneumatically through a micro-nozzle of ${410}\;\mathrm {\mu }\textrm {m}$. The CNC-ink was printed on-to a hydrophobized glass slide, and extruded under pressures of 1.5-2.5 bar at a speed of 10-20 mm/s. Cubic shaped samples with a size of typically 8 mm in each direction were printed with different structuring of the layers: CP3 unidirectional (0$^{\circ }$/0$^{\circ }$), CP2 grid (0$^{\circ }$/90$^{\circ }$), CP1 twisted (+15$^{\circ }$ each layer), see also Fig. 2(a,b,c). All samples were prepared with filling density of ${100}\%$ and air dried at ambient conditions. The sample CP1 was cut to obtain thinner slices to investigate the tunability of wave plate properties with thickness.
Fig. 2. Schematic of 3D printed cellulose sample structure: (a) unidirectional, (b) grid, (c) twisted. (d) Preparation and structure of cellulose-Ag aerogels.
3.1.3 Cellulose nanofibres with silver nanowires
Cellulose samples were prepared in three steps:
1. Cellulose nanofibre (CNF) dispersion: In a typical synthesis process, 0.1 mM TEMPO and 1.0 mM NaBr per gram of cellulose pulp were mixed with 2 wt$\%$ cellulose fibre (elemental chlorine-free fibres extracted from bleached softwood pulp fibres, Mercer Stendal Company, Berlin, Germany) aqueous suspension. After adjusting pH to 10 by using NaOH solution, 10 mM NaClO per gram of cellulose pulp was added for the cellulose oxidation. Afterwards, the TEMPO-oxidized cellulose fibres were washed until the conductivity was similar to that of distilled water. Finally, the oxidized and purified cellulose fibres aqueous suspensions were ground by a Supermass Collider (MKZA10-20J CE Masuko Sangyo, Japan) to obtain a stable CNF dispersion with a concentration of $\sim$1.4 wt$\%$.
2. Silver nanowires (AgNWs) dispersion: Before the AgNWs preparation, 0.01 M NaCl and 0.005 M NaBr dissolved in ethylene glycol (EG) were prepared in advance. During the fabrication process, 0.2 g of polyvinylpyrrolidone (PVP) was dissolved in 6 mL of EG under stirring. Afterwards, 200 µL of NaCl solution, 500 µL of NaBr solution, and 0.2 g of AgNO$_3$ were added into the solution and well mixed. The mixture was then heated to 175 °C by oil bath for around 20 min with low-speed magnetic stirring. After reaction, the mixture was washed with ethanol by centrifugation at 4500 rpm for 5 min. The centrifugation processes were repeated several times until the supernatant became colourless The collected silver nanowires were redispersed in water for further use.
3. Preparation of Cellulose-Ag aerogels: The AgNWs embedded CNF aerogels were manufactured by directionally freezing the mixture of AgNWs dispersion and CNF dispersion. The mixture was cast in a mold with stainless steel as a cold-finger, and liquid nitrogen was used to provide a temperature gradient. The frozen samples were then freeze-dried (−80 °C, 5 Pa) to obtain the CNF-Ag aerogels. The solid contents of the dispersion mixture were controlled at 0.4 wt$\%$, and the corresponding densities of the resultant aerogels were around 6 mg/cm$^{3}$. The freeze drying process and the layered structure of the resulting samples is shown in Fig. 2(d). For this study, three aerogel samples were produced by tuning the weight ratios of CNF/AgNWs, CNF-Ag10 (CNF/AgNWs = 9), CNF-Ag20 (CNF/ AgNWs = 4), and CNF-Ag50 (CNF/ AgNWs = 1).
3.2 THz time domain spectroscopy (THz-TDS)
THz-TDS is a very suitable tool to extract frequency dependent optical properties of materials from pulsed THz data. The samples were investigated with a time-domain spectrometer (Tera-FlashTF-1503, Version 4 December 2015, Toptica Photonics AG, Gräfelfing, Germany) covering the frequency range of 0.1-7 THz. The time delay between the pump and the probe pulse was set so, that the maximum of the reference peak falls within the first 5-10 ps of the acquisition interval. The experimental setup is illustrated in Fig. 3. The samples are placed in the focused beam with a spot size of approximately 2 mm. Two polarizers P1 and P2 (wire grid polarizers G30X10-S from SEMIC RF) allowed to set the polarization direction before the sample and to analyse the linear polarization after the sample, respectively. The polarization direction with respect to the sample was set either by rotating the sample or setting the rotation angle of the polarizer.
Fig. 3. Schematic representation of the THz-TDS set up for measurements of the optical properties of samples.
4. Results
4.1 Optical properties
The refractive index $n$ and the extinction coefficient $\kappa$ are determined as described in Zolliker et al. [26] using the thick sample approximation ($d >> \lambda$) [27]. The optical properties of typical samples used in this study are shown in Fig. 4(a) (refractive index) and in Fig. 4(b) (extinction coefficient). All samples show high birefringence combined with diattenuation. Above 0.3 THz the refractive index is basically frequency independent, whereas the extinction coefficients show a minimum in the range of 0.3-0.6 THz. Wood generally shows a high birefringence in the LT and LR plane. In this study we used the LT-samples. The refractive index of wood is in the range of $n=1.2-1.5$ with a birefringence of typically $\Delta n=0.1$. Both values roughly linearly increase with density. The 3D printed cellulose cubic samples show a refractive index in the range of $n=1.1$ with a birefringence of typically $\Delta n = 0.03$ in two directions which can be attributed to the stacking of printed cellulose layers. In the third direction, perpendicular to the planar structure, no or only marginal birefringence is present. For the further analysis for wave plate properties we selected the direction with the highest birefringence. The aerogel from cellulose nanofibres with silver nanowires has very low density in the order of 0.005 g cm−3. Their refractive index, birefringence and extinction all scale with silver content.
Fig. 4. Refractive index (a) and extinction coefficient (b) of selected samples determined by time domain spectroscopy
4.2 Wave plate efficiencies
With the knowledge of $n_1(\nu )$, $n_2(\nu )$, $\kappa _1 (\nu )$ and $\kappa _2 (\nu )$, we can determine the optical properties relevant for a wave plate. The operating frequencies can be extracted from Eqs. (9) and (16) for a sample acting as a QWP or a HWP, respectively. In the following we will set $z=1$ which is generally the best mode for operating a wave plate. Equations (10) and (17) give the respective working angle and Eqs. (11) and (18) present the wave plate efficiencies. Efficiency as a function of frequencies are shown in Fig. 5. Markers show the efficiencies for every sample in Table 1 with the specific thickness. Using Eqs. (11) and (18) the efficiencies can be extrapolated to any frequency, as shown by the lines. The corresponding sample thickness for that frequency can be determined solving Eqs. (9) and (16) for $d$. In Fig. 6, the efficiencies as a function of thickness are shown, markers for the measured samples with extrapolations are shown as lines. Samples of different thicknesses were measured for birch wood (1.5 mm, 3.1 mm and 5.0 mm) and one of the printed cellulose samples (CP-1, 3.6 mm, 5.5 mm and 7.8 mm). The extrapolation of efficiencies using the thickest sample (Bi-50 and CP-1-78, respectively) shows good agreement with the two thinner samples, confirming the validity of our extrapolation method. Table 2 lists the maximum reachable efficiencies for use as QWPs and HWPs, the corresponding thickness for QWPs and their operating frequencies. The efficiency of a HWP is approximately the square of that of the corresponding QWP. Note, that the operating frequencies are almost equal for QWPs and HWPs and the thickness of a HWP is twice that of a QWP with the same operating frequency.
Table 2. Maximum efficiencies, operating frequencies and wave plate thickness for wood and cellulose based samples.
5. Discussion
The limiting factor for the wave plate efficiency is the ratio of birefringence $\Delta n$ to the extinction coefficient $\kappa$. The fact that $\kappa$ has a minimum in the frequency range of 0.3-0.6 THz for all investigated samples implies, that efficient use of such materials as QWP or HWP are restricted to that frequency range. The main contributions to wood absorption are from water and the cell wall material. At 0.5 THz liquid water has an extinction coefficient of about $\kappa = 0.7$, an order of magnitude higher than that of dry wood ($\kappa = 0.03-0.04$). Already a water content of 5-8 wt$\%$ typical for in wood stored at ambient humidity condition lowers the efficiency considerably. For dried samples the efficiency could be improved by $50-100\%$ due to a decrease in $\kappa$. For both, beech and spruce early wood, the efficiency exceeds ${50}\%$ for a QWP. However, the fact, that such an element works only in dry condition and that the operating frequency is shifted with water content (see measured efficiencies for dry and ambient SE and SL samples in Fig. 5), artificially made materials with similar structure can yield more stable devices, and their optical properties can be easier optimized.
One approach is to 3D print cellulose in a layered structure with layer thicknesses comparable to the typical pore structure in wood. All three investigated samples (CP-1, CP-2, CP-3) show efficiency-frequency behaviour very similar to that of beech wood at ambient conditions. Due to their lower cellulose density the efficiency-thickness relation is shifted to higher thicknesses. The three different stacking of the layers, parallel, perpendicular or twisted neighbouring layers, seem not to have an influence, indicating that the birefringent properties are governed by layering geometry. Another approach is to embed conducting nanoparticles into a cellulose structure. THz optical properties of such materials were recently described by Zeng et al. [11]. The samples doped with silver nanowires show promising properties. The CNF-Ag20 shows a high efficiency, matching the properties of the best wood samples in our study.
6. Conclusion
It is tempting to make use of the anisotropic optical properties of wood for cost effective optical elements in the THz regime (QWP, HWP). However, its rather low efficiency and the dependency on humidity calls for optimization. We showed that artificially produced cellulose structures have potential for further developing such optical elements. An especially promising material is cellulose nanofibres with embedded conducting nanowires. The systems of combining cellulose nanofibres with silver nanowires allow optimization in two directions: the sample thickness and the silver content. Its potential is not yet fully explored, in particular with other conducting nanomaterials. The very low density of the cellulose may allow to design a low absorption material for further increasing the efficiency of wave plates. This opens a pathway toward a cost efficient and simple method to produce THz optical elements which currently have very limited availability commercially.
Funding
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (200021-179061/1); China Scholarship Council.
Acknowledgement
The authors would like to thank Sofie Gnannt for the cellulose density measurements.
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.
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