Optimized 3D printing of THz waveguides with cyclic olefin copolymer

: There is a need for low-cost and easily accessible optical devices for THz applications. THz devices can be manufactured rapidly with 3D printing while using THz transparent materials. In this work, we optimized the parameters for high-resolution 3D printing of a THz transparent filament, cyclic olefin copolymer (TOPAS), in order to 3D print high quality pipe THz waveguides. We used nozzles with diameters between 0.15 mm and 0.80 mm in a wide range of temperatures and speeds. We show that for high quality TOPAS 3D printing, the most important parameters are the bed and the printing temperature. The optimized 3D printing parameters for the nozzle diameter 0.15 mm were used for THz pipe waveguides with diameters in the range of 5-9 mm and cladding thickness of 0.3-0.8 mm. Transmission measurements corroborated the results predicted by simulations for core mode frequencies in the range of 250-900 GHz.


Introduction
Terahertz (THz) science and technology has been growing in the past 30 years [1].The wide range of applications from THz imaging [2] to 6G communication [3] have brought THz in the center of scientific interest.Also, 3D printing has been widely used for a broad range of applications from biological [4][5][6] to mechanical engineering [7,8].The low cost and the fast process of 3D printing have made it popular from UV up to microwaves [9].In the THz regime, 3D printing has been widely used for THz devices, especially diffractive lenses [10], hollow-core fibers [11] and rectangular waveguides [12].The majority of the commercially available materials, such as Acrylonitrile Butadiene Styrene (ABS) and Polylactic Acid (PLA), have shown high absorption in the THz regime, especially at frequencies higher than 1.5 THz [13,14].Recently, a more transparent material, high impact polystyrene (HIPS), has been used for 3D printing of THz waveguides due to the low THz absorption, α<10 cm −1 demonstrating very high quality [15].Van Puttern et al. presented the 3D printing of THz waveguides with dimensions as low as 0.6 mm using polystyrene [16].A popular material is also the cyclic olefin copolymer (TOPAS), and it has already been the filament for the 3D printing of THz lenses and diffraction gratings [17].In comparison with other 3D printing materials, TOPAS shows very low absorption and a constant refractive index (n = 1.53), from UV up to 10 THz [18,19].TOPAS has been used for the fabrication of THz waveguides with broadband transmission [20], and for THz broadband antennas for quantum cascade lasers (QCLs) [21].Moreover, it has been used for the fabrication of microfluidic devices [22] and biosensors for bacteria RNA detection and retrieval [23].The THz properties of TOPAS make it an important candidate for the further development of 3D printing in the THz regime.However, to develop state-of-the-art 3D printed THz devices such as waveguides, the 3D printing parameters must be thoroughly studied.Even though there are suggested 3D printing parameters from the filament producers, the task-specific parameters can always be affected by using, e.g., nozzles with different diameters.In addition, small nozzle diameters are required for the 3D printing of samples with fine structures.3D printing with a smaller nozzle can lead to high-quality 3D printing of low dimension THz devices, which is crucial in microfluidics.Also, pipe waveguides have a thin cladding so for 3D printing of THz pipe waveguides a smaller nozzle can be essential.A THz pipe waveguide can exhibit excellent THz mode confinement, high coupling efficiency while the THz waves can be guided even using a THz transparent material as TOPAS for the cladding [24].
In this work, we present the optimization of the 3D printing parameters using TOPAS.We 3D printed rectangular bulk samples using various nozzles with a diameter range from 0.15 up to 0.80 mm, printing temperatures, bed temperatures, printing speed, chamber temperature, and we also study the effect of polishing on the 3D printed bulk samples.Moreover, we measured the complex refractive index of the optimized 3D printed bulk samples and used it for the simulations of a THz waveguide with fundamental core mode f = 350 GHz.We believe the optimized 3D printing parameters of TOPAS can be used for high-quality and low-cost THz devices and, eventually, 3D printed spectrometers in combination with other THz materials [25].

Sample preparation and characterization
For this work, a 3D printer Kühling & Kühling RepRap Industrial and cyclic olefin copolymer (TOPAS) filament with diameter 2.85 mm from Creamelt were used.For better understanding the influence of the 3D printing parameters on the quality of the sample, firstly cuboid samples with 20 mm × 20 mm × 10 mm were 3D printed with various settings of printing speed, printing strategy, bed and chamber temperature, as well as nozzle diameter.After the 3D printing, the samples were characterized with a commercial THz-TDS system (TOPTICA-TeraFlash).For the calculation of the THz transmission of the samples, a measurement of the sample (E sample (t)) and a reference measurement (E ref (t)) are required.The Fourier transforms of the THz electric field of the reference and the sample are used for the calculation of the experimental value of the THz transmission T exp (ω)= E sample (ω) (ω) .The calculation of the THz transmission is used for waveguides characterization and also for the extraction algorithm of the complex refractive index (ñ = n + ικ) of the cuboid TOPAS samples.In the case of the refractive index extraction, the experimental value of the THz transmission (T exp (ω)) is fitted with a theoretical transmission based on the propagation and Fresnel formulas.For the fitting, a numerical method, Newton Raphson, is used and the only unknown parameter is the complex refractive index which is finally calculated using this fitting [26][27][28].The absorption is given by: α = 4πκ/λ, where λ is the wavelength.The refractive indices and the absorptions of the samples with optimized parameters were compared with those of a TOPAS substrate from the company TOPAS Advanced Polymers GmbH.
For the optimization of the 3D printing quality, firstly printing infill was optimized (Fig. 1(a)).Then, the bed temperature, the nozzle diameter, the printing temperature, the speed were optimized and finally the chamber temperature (Fig. 1(b)).However, some parameters depend on others (e.g., nozzle diameter and printing temperature) as it is described below.
The following optimized parameter set was used for further samples in this study: nozzle diameter d n = 0.3 mm, bed temperature T bed = 90 • C, printing speed v print = 2000 mm/min and printing temperature T print = 230 • C. We also present the effect of the mechanical polishing of the samples since all the bulk samples were mechanically polished after the 3D printing.For the 3D printing of THz pipe waveguides, the nozzle diameter was changed to d n = 0.150 mm for more detailed printing while the rest of the printing parameters remained the same.

Solid cuboids
The main 3D printer components are the extruder, where the filament is melting, the nozzle and the bed which is the surface where the sample is being printed (Fig. 1(b)).For this study, the best printing strategy was investigated first, which includes the infill pattern and the layer configuration (Fig. 1(a)).The broad transparency of TOPAS to both visible light and THz radiation made the samples' validation more straightforward.In the THz regime (Fig. 1(c)), we compared the TOPAS substrate's refractive index and absorption with a 3D printed sample using the optimized parameters and wiggle rectilinear settings with another sample using honeycomb rectilinear.The wiggle rectilinear infill offers better infill of TOPAS and the air presence inside the 3D printed samples is minimized, demonstrating less air scattering in optical and THz regime and higher quality 3D printing.In Fig. 1(a) a schematic representation of the wiggle rectilinear infill is illustrated.As we can see, the refractive index and the absorption of the optimized sample are very similar to the TOPAS substrate's values, but in the sample before the optimization, the absorption exceeded 5 cm −1 .For the TOPAS substrate we obtained n TOPAS = 1.53 and α TOPAS = 0.20 cm −1 at 1 THz, while for the 3D printed optimized sample n 3D = 1.52 and α 3D = 0.30 cm −1 at 1 THz.A comparison of the transparency before and after the optimization in the optical regime is shown in Fig. 1(d) with the optimized sample being more transparent than the sample before the optimization.Programming the nozzle to wiggle while doing the rectilinear infill ensures high transparency and hinders the formation of air bubbles in the final print.If not explicitly stated, all the samples were 3D printed with the rectilinear wiggle strategy.As expected, the density of the sample is affected while optimizing the 3D printing parameters.Before the optimization the density was ρ = 0.95 g cm −1 and after ρ = 1.00 g cm −1 , which is very close to the density of the substrate ( ρ = 1.02 g cm −1 ).
The bed temperature is one of the parameters that can highly affect the 3D printing quality.Three samples were 3D printed with temperatures 80 °C, 85 °C and 90 °C.The bed temperature contributes to the quality of the 3D printing since a higher bed temperature improves the shape accuracy of the printed structure (Fig. 1(a)).As shown in Fig. 2(a), the influence of the bed temperature on the 3D printed samples is obvious.The absorption is lower for higher bed temperature, despite that the refractive indices' values are not affected.T bed = 90 • C is the highest bed temperature that can be used for TOPAS.Exceeding this value, the printed samples started deforming.The refractive indices with different bed temperatures varied from n = 1.51 to n = 1.52 (T bed = 90 • C) and the absorption from α = 0.35 cm −1 (T bed = 90 • C) to α = 0.89 cm −1 at 1 THz.The printing speed does not notably contribute to the 3D printing quality, as shown in Fig. 2(b).Despite that, slower printing grants a more transparent final print, especially when the nozzle diameter is smaller than 0.3 mm and faster printing guarantees lower absorption in the THz regime (Fig. 2(b)).Besides that, faster printing with printing speed v print = 2000 mm/min is more time-efficient.The average absorption values in samples with various printing speeds were α = 0.41 cm −1 and refractive index n = 1.52 at 1 THz.
Regarding the printing temperature, a lower temperature is necessary for precise printing.However, higher printing temperature resulted in higher transparency in the optical regime (T print >260 • C).For this part of the study, we printed samples with printing temperatures 220 °C, 260 °C and 300 °C and nozzle diameter d n = 0.30 mm.In the THz regime, for higher printing temperature (T print = 260 • C) the printed samples had higher absorption with α 260 • C = 0.7 cm −1 and lower refractive index n 260 • C = 1.52 (Fig. 2(c)) at 1 THz.Another crucial parameter is the chamber temperature because it is related with how the sample forms after the 3D printing.As Fig. 2(d) shows, the absorption is lower at T chamber = 30 • C and T chamber = 40 • C in comparison with T chamber = 50 • C. For further work, T chamber = 40 • C was used in order to ensure that the filament will be perfectly attached during the 3D printing.
With nozzle sizes, the printing temperature had to be increased, otherwise the filament cannot melt enough to go through the nozzle.For this study we used six nozzles with diameters d n = 0.15, 0.30, 0.40, 0.50, 0.60, 0.80 mm.For the nozzle with d n = 0.15 mm, we used printing temperature T print = 260 • C and for the rest of the samples T print = 220 • C. The samples' refractive index is affected considerably by the nozzle's diameter, as shown in Fig. 3(a).For nozzle diameters d n = 0.60 mm and d n = 0.80 mm, the refractive index value was closer to the refractive index of the TOPAS substrate (n sub = 1.53), and for smaller diameter nozzles the refractive indices were as low as n = 1.51.These low refractive indexes can be due to the lower filling with filament in the 3D printed sample, allowing more air inside the printed structures.Bigger diameter nozzles allow better infill during the 3D printing.Similarly, the absorption was slightly higher in the samples that were printed with nozzles diameters d n = 0.60 mm and d n = 0.80 mm (Fig. 3(b)).Despite that, smaller nozzles are capable of creating more detailed and precise structures that are important for THz applications.During this work, 3D printing with diameter nozzle d n = 0.10 mm was also attempted, however, the printing was not possible with our current system because of the thickness (2.85 mm) of the filament.We polished the samples using a DAP-V from Struers and various polishing papers for an average time of 10 minutes to achieve higher transparency in the optical regime.For this reason, we measured the THz refractive index and absorptions of samples printed with three different nozzle diameters, namely, d n = 0.15 mm, d n = 0.30 mm, and d n = 0.80 mm.As the Figs.3((a),  (b), (c) and (d)) show, the refractive index is not considerably affected by the polishing.However, the absorption decreases a lot after the polishing for the printed sample with d n = 0.15 mm, which can be due to the sample's surface roughness before polishing that introduces scattering.No effect in the absorption with the mechanical polishing was observed, if the samples were printed with larger nozzle diameters.
The 3D printing resolution is essential for high-quality THz devices.For achieving high resolution, we focused on 3D printing using the smaller nozzle with d n = 0.15 mm.One interesting finding using the nozzle d n = 0.15 mm was, that the optimal printing temperature was T print = 260 • C.However, for lower printing temperatures, the samples cannot be printed because of the difficulty of the filament to go through the nozzle, and for higher temperatures, the sample's absorption is increasing.

Waveguides
The optimized parameters for 3D printing with nozzle diameter d n = 0.15 mm were used for the 3D printing of THz pipe waveguides.We used the optical parameters extracted from the cuboid sample printed with d n = 0.15 mm and TOPAS refractive index n TOPAS = 1.53 to simulate such a pipe waveguide using COMSOL Multiphysics and the radio frequency (RF) module.For mode analysis a simulation based on a 2-dimensional model was done in the frequency range 0.2-3.0THz [29].For example, using a waveguide model with core diameter D = 5.0 mm and a cladding thickness τ = 0.5 mm (Fig. 4(a)) leads to a fundamental mode at 350 GHz (Fig. 4

(bi)).
No relevant electrical field is found for 400 GHz (Fig. 4(bii)) and a higher mode develops at 450 GHz (Fig. 4(biii)).Thus we expect large variation of the transmission with frequency in that range.In Fig. 4(bi), the simulated intensity distribution inside the waveguide is shown when the THz electric field can be successfully guided in the central air core.
The waveguides were 3D printed in three different lengths L = 70 mm, L = 100 mm, and L = 120 mm, to investigate how the waveguide's length affects the guiding of the THz waves.Also, the waveguides were 3D printed with two different printing speeds v print = 50 mm/min and v print = 2000 mm/min to study whether the waveguides' quality is affected by the different printing speeds while the other process parameters were fixed at the values found above.Figure 4(c) shows the 3D printed waveguides with various lengths and two different printing speeds.The quality with lower speed is more precise than in faster printing visibly, but the waveguide dimensions are affected, especially the cladding thickness.In Table 1 the sample dimensions namely, the waveguides length (L), inner diameter (D) and cladding thickness (τ) for the simulated, printed with v print = 2000 mm/min and v print = 50 mm/min are presented.Interestingly, the cladding thickness of the sample printed with lower speed v print = 50 mm/min was much higher (τ print = 0.75 mm) for the waveguide with L = 70 mm.The higher cladding thickness can be due to the longer heating of the filament while printing.The THz transmission through the waveguides was measured using the TOPTICA-TeraFlash, a THz-TDS system.The transmission calculated using the E ref (t) and E wave (t) (Fig. 4(e)), E ref (ω) and E wave (ω) (Fig. 4(f)) and described before in the section 2. For the measurements, a holder was designed and fabricated, and planar mirrors were used for increasing the transmission of the THz waves inside the waveguide (Fig. 4(d)).The holder allows the THz waves to propagate only through the waveguide for accurate measurements of the transmission.Also, for each of the samples, first a reference measurement was taken only of the holder, and then the waveguide was inserted and measured.
As shown in Fig. 5(a and d), the waveguide length does not affect the fundamental core mode as it was suggested by Lai et al. [24].However, the transmission is reduced due to TOPAS dielectric properties and the THz transmission is higher for the shortest waveguide.In the Fig. 5    All the experimental data and the results of the simulations that are presented in the figures are available in [30].

Conclusion
We optimized the 3D printing parameters with TOPAS, and we focused mainly on the 3D printing with 0.15 mm diameter nozzles.The parameters that were optimized are bed temperature, printing speed, printing temperature, chamber temperature and nozzle diameter.Interestingly, the most crucial parameter for achieving the best THz transparency and low absorption is the bed temperature.We also studied how polishing can affect the THz transparency and concluded that the polishing does not contribute dramatically to 3D printing quality in the THz regime in contrast to the visual appearance.For bulk samples using a 0.15 mm diameter nozzle, the low printing speed can significantly contribute.However, this is not the case for the printing of fine structures such as waveguides.In addition, the 3D printing optimized parameters with nozzle diameter d n = 0.15 mm were used for the 3D printing of THz pipe waveguides with fundamental core mode f = 350 GHz.The printed waveguides in various lengths L = 70 mm, L = 100 mm, and L = 120 mm, show fundamental core mode at f = 350 GHz results that are in agreement with COMSOL simulations.The optimized 3D printing parameters can be used for the further fabrication of THz transparent devices such as THz lenses, waveguides, and microfluidic.

Fig. 1 .
Fig. 1.(a) Schematic representation of the wiggle rectilinear infill in the nozzle direction and how the printed structure forms while 3D printing.(b) Illustration of the extruder, nozzle, bed and sample while 3D printing.(c) Refractive index (blue lines) and absorption (red lines) of 3D printed samples before (honeycomb rectilinear) and after the optimization (wiggle rectilinear) of the 3D printing parameters and a TOPAS substrate between 0.3 and 2 THz.(d) Illustration of the sample before (right) and after (left) the 3D printing optimization.

Fig. 2 .
Fig. 2. (a) Refractive index and absorption of 3D printed samples with various bed temperatures between 0.3 and 2 THz.(b) Refractive index and absorption of 3D printed samples with different printing speed.(c) Refractive index and absorption of 3D printed samples with various printing temperatures.(d) Refractive index and absorption of 3D printed samples which changing the chamber temperature.

Fig. 3 .
Fig. 3. (a) Refractive indices of various samples printed using nozzles with diameters between 0.15 mm and 0.80 mm in the THz frequency range from 0.3 to 2 THz.(b) THz absorption of the same samples.(c) Refractive index of 3D printed samples with various nozzles (d n = 0.15 mm, d n = 0.30 mm and d n = 0.80 mm) before and after the polishing between 0.3 and 2 THz (d) Absorption of the same samples.
(b), the transmission of two waveguides is shown with printing speeds v print = 2000 mm/min and v print = 50 mm/min, respectively.All the waveguides with v print = 2000 mm/min demonstrated fundamental core mode close to the nominal value f = 350 GHz even though the diameter

Fig. 4 .
Fig. 4. (a) Schematic representation of the cross section of the waveguide (b) Simulations of the normalized intensity distribution of the THz electric field in the waveguide for frequency i. f = 350 GHz ii.f = 400 GHz and iii.f = 450 GHz (c) 3D printed waveguides in various lengths (L = 70 mm, L = 100 mm, and L = 120 mm) and printing speeds v print = 2000 mm/min (left, red color) and v print = 50 mm/min (right, green color).(d) Schematic representation of the THz-TDS system with the holder used for the waveguide measurements.(e) THz electric field measurement of the empty holder and a waveguide with THz-TDS.(f) The calculated THz spectra.

Fig. 5 .
Fig. 5. Experimental results: (a) Transmission comparison of the 3D printed waveguides with lengths L = 70 mm, L = 100 mm and L = 120 mm.(b) The transmission of the waveguide printed with speed v print = 50 mm/min and with v print = 2000 mm/min.(c) The transmission of a waveguide with fundamental core mode f = 350 GHz, a waveguide with f = 330 GHz, and of a waveguide with f = 550 GHz.(d) Transmission comparison of the 3D printed waveguides with lengths L = 70 mm, L = 100 mm and L = 120 mm of a waveguide with modes at f = 230 GHz, f = 470 GHz and f = 830 GHz.