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Abstract
In this paper we present four λ/2-wave plates made out of fused silica glass for operation in the terahertz frequency range. The design of the wave plates is based on form birefringence. They were fabricated by selective laser-induced etching resulting in a series of glass bars separated by air grooves. Wave plates operating at single, two and several frequencies were designed, fabricated and characterized.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In the last 20 years terahertz (THz) spectroscopy has significantly developed. It is widely used for basic research e.g. to study the carrier dynamics in semiconductors [1], or to monitor crystallization processes [2]. In addition, many practical applications in the field of non-destructive testing have been discussed [3–7]. Besides, short-range wireless communications is expected to become a mass market in a few years from now [8,9]. Driven by these applications and potential markets, THz technology has rapidly evolved in recent years; THz sources and THz detectors became more efficient.
Yet, a mature technology not only requires THz sources and detectors but also passive devices to guide or manipulate THz waves. This includes filters [10,11], reflectors [12], lenses [13,14], diffraction gratings [15,16], waveguides [17–19] and couplers [20,21], beam splitters [22,23], modulators [24,25], and last, but not least wave plates [26].
The most common way to fabricate a wave plate is to use materials with an intrinsic optical anisotropy. Examples are lanthanum aluminate [27], a liquid crystal polymer [28], or liquid crystals [29]. The latter even allows for the fabrication of switchable wave plates [29,30]. Stacking thin birefringent materials can lead to wave plates which do not only operate at one design frequency but turn the polarization of electromagnetic waves over a broad frequency range [31]. Furthermore, artificial structures can be used. On the one hand metamaterials can be designed to act as wave plates [30,32]. On the other hand an effect called form birefringence can be used [33–35] to turn the polarization of an electromagnetic wave.
Structures with form birefringence are known from the visible frequency range. They are fabricated by etching small grooves into a dielectric. This results in a periodic sequence of dielectric material and air grooves. In 2011 Scherger et al. demonstrated a very simple and cost-efficient λ/2-wave plate for THz waves made of paper [26], while in 2015 Zhang and Gong demonstrated an achromatic λ/4-wave plate at terahertz frequencies fabricated etching grooves into silicon [36].
A very simple method to produce inexpensive THz optics is 3D printing [21,37–39]. Yet, structures fabricated with a simple 3D printer show a considerable structural roughness. This limits the working frequency of many of the produced devices to the frequency range below 500 GHz. Therefore, a 3D printed tunable THz wave plate presented in 2014 by Busch el al. showed only a moderate performance [40]. Hence, methods which provide much smoother structures are desired.
Here, we demonstrate high-quality wave plates made of fused silica glass by selective laser-induced etching (SLE). SLE is a two-step process: In the first step ultra-short pulsed laser radiations is focused to micrometer-sized spots with NA > 0.2. The focal spot is positioned inside of a material that is transparent for the laser wavelength. At sufficient intensities in the order of 1012 W/cm2 and at pulse energies in the order of hundreds of nJ the threshold for non-linear absorption processes, such as multiphoton absorption or tunnel ionization, is surpassed and electrons can be excited into the conduction band. These free carriers can acquire more energy from the laser pulse by Bremsstrahlung absorption and ionize more atoms by impact ionization leading to avalanche-like increase of the number of free electrons [41]. The energy of the excited electron system is partially transferred to the atoms via electron-phonon coupling and, depending on the material and parameters of irradiation, leads to heating of the material up to temperature differences of several 1000 K [42]. Moving the focal spot through the material leads to rapid quenching of the material and thus a high temperature and high pressure state of the material is permanently frozen. By 3D movement of the focal spot through the material, a continuous line-shaped modification is formed. If the modified material has somewhere a contact to the outer side of the sample the second step of the process, wet etching, can follow. Putting the sample in a suitable wet etching agent results in the dissolving of the modified material at a higher rate than of the non-modified material. The ratio between the etching rates of modified and non-modified material is called selectivity and is equivalent to the possible maximum aspect ratio of machinable structures. SLE offers unique features for machining arbitrary hollow volumes within transparent materials like crystals or glasses with precisions in the order of 1 µm by stacking single line-shaped modifications to get the desired shape. The highest selectivity was found in sapphire [43], fused silica [44], Borofloat 33 and ULE [45]. The investigation of the SLE process for different materials is a matter of continuous, on-going development. The SLE process potentially works in any transparent and homogeneous material that can be polished to an optical surface quality, so even polymers are an interesting option for future developments.
In this study multiple rectangular slabs were precision-cut out of fused silica base material using the SLE technology with KOH as an etching agent [44] to produce THz wave plates based on form birefringence. Figure 1(a) shows exemplary a photo of wave plate 1 and a microscope image of the same wave plate [Fig. 1(b)]. The wave plate is made of a half a millimeter thick plate of fused silica glass with a design frequency around 1 THz. It consists of a series of 60 μm wide glass bars separated by 90 μm wide air grooves. These air grooves extend throughout the thickness of the glass plate, meaning that the thickness of the air grooves equals the glass bars’ thickness. This is the case for all wave plates presented here. The dimensions of the produced wave plates are listed in Table 1.
Fig. 1 a) Photo of wave plate 1 with an edge of a Euro coin for size comparison. b) Microscope image of the same wave plate. Bright and black stripes correspond to glass bars and air grooves, respectively. They are all of equal thickness, i.e. thickness of the wave plate. Note the difference in the width between glass bars and air grooves.
Table 1. Dimensions and design frequencies of the produced wave plates.
2. Characterization of the wave plates
To characterize the bare fused silica and the produced wave plates a fiber-coupled terahertz time-domain spectrometer was used (T-SPECTRALYZER, HÜBNER GmbH & Co. KG). The setup is shown in Fig. 2. Two linear polarizers were used to ensure clean polarization states for the generated and detected terahertz waves. Each wave plate was mounted on a rotational mount and placed into the focal plane between the two parallel polarizers. The frequency dependent transfer function of the wave plates was then measured at different azimuthal angles by rotating wave plates within the focal plane.
Fig. 2 Setup used for measuring the frequency- and angle-depended transfer function. A fiber-coupled terahertz time-domain spectrometer is used together with two polarizers (P). In the inset a drawing of a wave plate is shown. The THz waves propagate in the z-direction and α (azimuthal angle) denotes the angle of the polarization of the incident waves with respect to the y-axis. The p- and s- polarization correspond to the x- and y- component of the incident waves, respectively.
The complex relative permittivity of the bare fused silica was extracted using commercially available software based on the algorithm described in [46]. The parameters obtained from this initial material characterization were used for the design of the wave plates. They are shown in Fig. 3(a). The effective refractive indices for polarization parallel to the wave plate structure (p-polarization) and perpendicular to the structure (s-polarization) were calculated by using the second order effective medium theory as outlined by Scheller et al. [35]. Accordingly, the first order effective relative permittivity for p- and s-polarization ( and , respectively) can be written as:
where and are the complex relative permittivity of glass and air, respectively, and and are volume proportions of glass and air, respectively. The second order effective relative permittivity for p- and s-polarization ( and respectively) can be calculated as:where is the wavelength of radiation, is the sum of widths of a glass bar and an air groove. For this calculation the relative permittivity of air was taken to be one, while the permittivity of glass was measured [Fig. 3 (a)]. Using the following relation, the real part of the refractive index () and absorption coefficient () for p- and s- polarization can be calculated:where is the absolute value and is the real part of the complex relative permittivity.Fig. 3 a) Real () and imaginary () part of the relative permittivity of bare fused silica. b) Refractive index n and absorption coefficient α of wave plate 1 for p- and s-polarized waves in red and blue, respectively. Dots correspond to the measured values and dashed lines to the simulated values.
Due to the difference in the refractive index for p- and s-polarization, the wave plate can rotate the polarization of the incident THz waves. In addition, the transmission of the two components through the wave plate differs due to the difference in the absorption coefficient, which additionally affects the rotation of the incident wave. Finally, the transfer function of the rotated polarization through a linear polarizer can be simulated by using the Malus’ law [35].
The simulated and measured refractive index and absorption coefficient for p- and s-polarized THz waves are presented exemplary for wave plate 1 in Fig. 3(b). The measured refractive index and absorption coefficient were extracted using the commercially available software mentioned above. For p-polarized waves the refractive index is higher than for s-polarized waves. Although the refractive index slightly increases with frequency, the birefringence stays almost constant over the measured frequency range with a value of Δn = 0.3 at the design frequency of 0.95 THz for WP1. The absorption coefficient for p- polarization is higher than that for s-polarization. For both polarizations, the absorption coefficient also increases with frequency. The simulated refractive indices and absorption coefficients agree with the measured ones. Especially for lower frequencies, the simulation and the measurement are in good agreement.
3. Transfer function – frequency-dependence
The measured transfer function of all four wave plates are shown in Fig. 4. We observed clear dips at the design frequencies of 0.95 THz (WP1), 0.80 THz (WP2), 0.45 THz and 1.15 THz (WP3), and for periodic frequencies (WP4). At these frequencies the polarization of the THz radiation is rotated by 90° (or for 90° and an additional multiple of 180°, e.g. 270°, for higher design frequencies) and ideally no radiation can pass the second polarizer in front of the detector antenna. In reality however, no polarizer is perfect, yet, for most of the designed frequencies the noise level could be reached. Therefore, a pure polarization state was generated by the different wave plates. Some differences can be observed between the values of the simulated and the measured curves. The simulated transfer function should theoretically reach zero (minus infinity dB) at the design frequency. However, this is not observed, neither in the simulation nor in the experiment. The first reason is the finite frequency resolution in both cases. The resolution of the simulated transfer function is limited by the frequency resolution of the relative permittivity values of fused silica glass, which is limited by the frequency resolution of the spectrometer used. The frequency resolution of the spectrometer also limits the resolution of the measured transfer function. The second reason is that the measured values also fluctuate from one measurement to another especially once the noise level is reached. Therefore, the observed deviation in maximum attenuation between the theory and the experiment is expected.
Fig. 4 Transfer function as a function of the frequency for the different wave plates: a) wave plate 1, b) wave plate 2, c) wave plate 3, d) wave plate 4.
For thin wave plates with a thickness of 500 µm and 675 µm [Figs. 4(a) and 4(b), respectively] only a single dip in the transfer function at the design frequency was observed within the measured frequency range. For the thicker wave plate, two such dips were measured [Fig. 4(c)]. This led to the idea of building a periodic wave plate, for which several dips with a period of approximately 0.14 THz were expected. Its transfer function is presented in Fig. 4(d). In this case, the wave plate is nearly 7 mm thick therefore the absorption of the wave plate hampers its usability. For frequencies below 0.8 THz, the measured and simulated transfer function are still in agreement. For higher frequencies, however, the absorption is too substantial and therefore the wave plate does not work properly.
4. Transfer function – angle-dependence
After analyzing the design frequency for a polarization rotation of 90°, the angle-depended transfer function at the design frequency was measured. The measured and simulated transmission as a function of the azimuthal angle is shown in Fig. 5. For clearness, the different wave plates are presented in the four quadrants. This is possible, because the transfer function is periodic in 90°. As expected, for s- and p-polarized waves (0° and 90°, respectively), the transfer function is nearly 0 dB, therefore nearly all radiation is transmitted. Yet, there is a small difference between the different polarization states. This polarization dependent loss is responsible for a deviation of the wave plate angle required for a 90° polarization rotation from the 45° azimuthal angle. With increasing thickness of the wave plates an increase in the deviation from 45° is expected. The optimum wave plate angles for a minimal transfer function at the design frequency were simulated as: 46°, 46°, 47°, and 49° for the increasing thickness of the wave plates, respectively. These angles can be extracted from the measurements as well. However, the experimental angular resolution was only in the order of 2°. Within the error bar the experimental values agree to the simulated values given above.
Fig. 5 Measured (dots) and simulated (line) transfer function as a function of the azimuthal angle for the first design frequency of the four wave plates (0.95 THz, 0.80 THz, 0.49 THz and 0.44 THz for wave plates 1, 2, 3 and 4, respectively). For the definition of the azimuthal angle see Fig. 2.
5. Conclusions
In conclusion, we demonstrated high quality wave plates made with selective laser-induced etching out of fused silica glass for frequencies in the THz regime. By changing the width of the glass bars and air grooves, and wave plate’s thickness, the design frequency can be tuned. Furthermore, it is also possible to fabricate wave plates with periodic design frequencies.
With selective laser-induced etching precise structures forming a relatively low-cost material with tailorable birefringence can be produced. When used as a wave plate, we achieved operation at higher frequencies and with better overall performance compared to low-cost 3D printed wave plates [40] or a wave plate made from paper [26]. On one hand, optimizing the design can lead to a broadband wave plate operating in a frequency range of up to 0.4 THz [36]. On the other hand, broadband operation can be achieved by precisely stacking wave plates operating at a single frequency [31]. Using SLE actual stacking could be avoided by fabricating the complex structure from a single glass plate. Finally, the presented approach also allows fabrication of different kinds of devices based on birefringence.
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