*Article* **Study of 3D-Printed Dielectric Barrier Windows for Microwave Applications**

**Mikhail D. Proyavin , Dmitry I. Sobolev, Vladimir V. Parshin, Vladimir I. Belousov, Sergey V. Mishakin and Mikhail Y. Glyavin \***

> Institute of Applied Physics of the Russian Academy of Sciences, 603950 Nizhny Novgorod, Russia; pmd@ipfran.ru (M.D.P.); sobolev@ipfran.ru (D.I.S.); parsh@ipfran.ru (V.V.P.); vbelousov@ipfran.ru (V.I.B.); mishakin@ipfran.ru (S.V.M.)

**\*** Correspondence: glyavin@ipfran.ru

**Abstract:** 3D printing technologies offer significant advantages over conventional manufacturing technologies for objects with complicated shapes. This technology provides the potential to easily manufacture barrier windows with a low reflection in a wide frequency band. Several 3D printing methods were examined for this purpose, and the dielectric properties of the various types of materials used for 3D printing were experimentally studied in the frequency range 26–190 GHz. These measurements show that the styrene-butadiene-styrene and polyamide plastics are suitable for broadband low-reflection windows for low-to-medium-power microwave applications. Two barrier windows with optimized surface shapes were printed and tested. Results demonstrate that the studied technique can fabricate windows with a reflection level below −18 dB in the frequency band up to 160 GHz. Studied windows can be used for spectroscopic tasks and other wideband microwave applications.

**Keywords:** dielectric properties; low-reflection barrier windows; broadband window; microwaves; terahertz radiation

## **1. Introduction**

Additive manufacturing technologies have great potential for industry, science, and technology. There are a number of tasks that are difficult or almost impossible to implement with traditional fabrication methods. In particular, 3D printing from dielectric materials is a highly convenient and cheap tool for prototyping and manufacturing radiofrequency components. It creates a method of readily obtaining components with a sophisticated surface shape. For low-reflection microwave windows, a subwavelength grating with a specially designed shape at both sides of the window disk could significantly reduce the reflection coefficient of incident radiation in a wide frequency band [1]. This paper explores the possibility of using 3D printing to make millimeter-wave barrier windows that can operate in a wide frequency range.

Currently, there are several areas in which windows with the broadband transmission of low-power microwave radiation are used. These areas include molecular gas spectroscopy and DNP/NMR spectroscopy [2,3], measurements of fine positronium structure [4], which require both broadband-tunable microwave radiation sources such as backward-wave oscillators, gyrotrons, orotrons, and input windows in the working chamber of the spectrometer. Other examples are the radiometers and geophysical instruments used for atmospheric transparency studies, which require windows with a low reflection coefficient at different frequencies, corresponding to atmospheric transparency windows, with a bandwidth up to 20 GHz [5]. The cryogenic resonator complex requires an even wider frequency band [6], which needs a low reflection from the input and output windows in the entire operating frequency band (50–500 GHz). Reflections from windows lead to spurious interference, which ultimately reduces the sensitivity of the spectrometer. Such

**Citation:** Proyavin, M.D.; Sobolev, D.I.; Parshin, V.V.; Belousov, V.I.; Mishakin, S.V.; Glyavin, M.Y. Study of 3D-Printed Dielectric Barrier Windows for Microwave Applications. *Electronics* **2021**, *10*, 2225. https://doi.org/10.3390/ electronics10182225

Academic Editor: Anna B. Piotrowska

Received: 30 June 2021 Accepted: 9 September 2021 Published: 10 September 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

devices are currently equipped with lenses with concentric triangle-shaped grooves, which are noticeably worse in terms of reflections compared to the alternative surfaces considered in this paper [7]. At the same time, it is well known that reflections dramatically affect the gyrotron operation regime [8]. For all the mentioned applications, the radiation power does not exceed a few watts, which allows one to use windows made of polymers without the risk of overheating.

There are different methods to obtain the broadband transmission of microwave radiation through the windows. The almost reflectionless transmission of a linearly polarized wave can be achieved for the Brewster-angle disk; however, this output suffers from an inefficient use of space, which may be especially important for divergent wave beams and some distortion of the transverse field structure [9]. Polymers can be mixed with nanoparticles to produce a multilayer dielectric coating [10]. Metamaterial devices and gradient index photonic structures are also used to reduce reflection [11]. Another known method considered in this paper is the use of windows with a surface grating of a specially optimized shape, providing a significant reduction in reflection [12]. For the manufacture of such a surface, it is highly convenient to use 3D printing. Besides low cost and time consumption, 3D printing has no restrictions on the curvature of the surface compared to Computerized Numerical Control (CNC) machining. Furthermore, it has advantages in creating thin elements from relatively soft and brittle materials.

There are several different 3D printing technologies, each of which has its characteristics and uses its own types of polymers. Fused deposition modeling (FDM) technology [13] is readily available, easy to operate, and allows the use of a wide range of materials, including polyethylene, which has excellent properties in transmitting high-frequency radiation. However, this type of 3D printing is characterized by a low accuracy (up to 100 microns) and sufficiently pronounced layering, limiting the frequency range of applications. In addition, the print resolution in the transverse plane is limited by the diameter of the nozzle and the quality of the alignment. Selective laser sintering (SLS) technology [14], due to a similar process of plastic melting, also has a wide selection of materials. However, compared to FDM, it has higher accuracy and better resolution; a layer thickness of several tens of microns, a resolution in the transverse plane approximately equal to the size of the pellets of the plastic used. Finally, Photopolymer 3D printing (stereolithography, SLA) provides excellent print quality but currently proposes a limited choice of printing materials. In this paper, the SLS method was used for printing the studied window samples.

Currently, many different materials for 3D printing are presented on the market, and their number is constantly growing. Unfortunately, manufacturers usually do not provide information on the dielectric properties of materials, especially in the microwave, millimeter, and terahertz regions. In order to design the microwave components, the dielectric properties are of great importance, so the characterization of the materials used for additive manufacturing is needed.

This paper is organized as follows. In Section 2, the results of measurements of the dielectric properties of the commercially available plastics are described. In Section 3, the measurements of the transmission and reflection coefficients for 3D-printed windows with several surface shape profiles are presented, and the results are compared with conventionally manufactured windows. Section 4 discusses the transmitted power restrictions for the printed windows due to thermal properties. Finally, the results of the study are discussed and concluded in Section 5.

#### **2. Characterization of Dielectric Properties of Plastics Materials for 3D Printing**

To study the loss tangent and dielectric constant of the plastics, two independent methods were used to increase the reliability of the results. In the first method, a rod made of the investigated plastic was inserted into a rectangular waveguide. The reflection and transmission coefficients were measured, and the dielectric properties were calculated from the experimentally obtained frequency dependences. Formulas for reflection and transmission of the dielectric waveguide plug can be found in [15]. The scheme of the measurement is shown in Figure 1a. The measurements were made in the entire Ka frequency band (26–40 GHz), and the measured reflection and transmission curves were matched by analytic curves calculated using the constant dielectric permittivity approximation. It can be seen in Figure 1b that the constant dielectric permittivity approximation fits the measured data well.

**Figure 1.** (**a**) The scheme of measurement of the reflection and transmission coefficients with the test sample in the form of the waveguide insert 7.2 mm × 3.4 mm × 100 mm (**a**); (**b**) comparison of the measurement results and simulation data for SBS plastic in the frequency range 26–40 GHz.

During the experiments, polymer samples printed using various technologies were studied. Results of dielectric permittivity and loss tangent measurements of various plastics printed using different 3D printing technologies at 100% infill are presented in Table 1. The dispersion of dielectric permittivity is relatively small within the Ka-band. Analysis of experimental data shows that styrene-butadiene-styrene (SBS) and polyethylene terephthalate glycol (PETG) are the most suitable materials for windows due to low losses and moderate dielectric permittivity. Different samples of PETG and SBS were printed using filaments from different manufacturers and showed minor differences. However, we note that these types of plastics were only suitable for FDM technology printers, which provided fair accuracy and thus were not applicable at sub-terahertz frequencies but sufficient for frequencies of several tens of GHz. This method and this plastic were used earlier, in particular, to print a two-dimensional Bragg resonator operating in the frequency range 55–65 GHz, and the measurement results were in good agreement with the theory [16]. Since the windows for spectroscopic and atmospheric measurements are also required at higher frequencies, the study of the applicability of FDM printing for these purposes is of interest.

**Table 1.** Dielectric properties of the 3D-printed samples in Ka-band.


The second method for measuring the properties of dielectrics was to place samples in the form of flat disks between the mirrors of a high-quality open two-mirror Fabry-Perot

resonator. By measuring the quality factor of an empty cavity and a cavity with a dielectric insert, it is possible to measure the properties of the test sample with high accuracy [17]. These measurements were made for selected materials and frequencies up to 185 GHz. The real part of the dielectric permittivity is the same as in the Ka-band measurements. The scheme of the measurement setup is shown in Figure 2a. The loss tangent data for plastic used for FDM printing (SBS) and plastic used for SLS printing (polyamide) is shown in Figure 2b.

**Figure 2.** (**a**) The scheme of measurement of dielectric properties with the test sample in the form of the disk in the quasioptical resonator; (**b**) loss tangent of the SBS and polyamide.

The polyamide plastic for SLS printers has a somewhat higher absorption than SBS and PETG. Therefore, it could be an optimal solution for some applications as a trade-off between the higher losses and better printing quality of the SLS method.

The photopolymer materials have significantly larger losses than polyamide (tangent delta higher than 0.03). However, we consider these materials a good solution for highfrequency applications with a 1 milliwatt or lower level of microwave power, since SLA printing allows much better print accuracy and surface quality.

#### **3. Reflection Measurements for 3D-Printed Prototype Barrier Windows**

For the experimental study of the broadband windows prototypes, we chose SLS printing from polyamide due to low losses and high manufacturing accuracy, which allow the creation of small-scale structures suitable for devices operating at frequencies of several hundred GHz. The sizes of the subwavelength antireflection structures were chosen to produce fine details by the selected printing method adequately. These structures should perform well when half of the wavelength is bigger than the period of the structure because there could be no ±1st order diffraction scattering in these conditions. However, the performance at higher frequencies might degrade faster or slower depending on the shape of the elements. This paper considers the two variants of known antireflection subwavelength gratings at window disks for additive manufacturing. The first variant of the surface shape is a periodic array of pyramids with a base size smaller than the wavelength [18]. The shape of the pyramidal grating is shown in Figure 3a. The advantages of such a surface are a weak dependence of the reflection coefficient on the frequency and polarization of the incident radiation. The base side of the pyramids was chosen to be 1 mm, and the height was 2 mm. Simulations show that this corrugation applied to both surfaces of the polyamide window disk and provided reflections of less than −20 dB in the frequency band wider than one octave. For comparison, the flat polyamide disk had reflections of up to −9 dB in this band. The second option is a one-dimensional periodic corrugation of a special shape, proposed in [19]. This profile is optimized to minimize the reflection of the polarization with the direction of the electric field orthogonal to the groove direction at the frequency range of 60–160 GHz. The shape of the grooves is shown in Figure 3b. The period and depth of one-dimensional corrugation are 2 mm and 2.5 mm,

respectively. The corrugation profile was optimized for one linear polarization only, and the reflection coefficient was less than −20 dB for frequencies below 105 GHz.

**Figure 3.** 3D-printed windows with (**a**) pyramids; (**b**) one-dimensional grating of special shape.

Three discs were printed: the first one had a flat surface on both sides, the other two had gratings of the tested shape on both sides. The reflection coefficients were obtained by two measurement setups by a vector network analyzer with a step of 30 MHz in the bands of 75–110 GHz and 130–160 GHz, where the disks with optimized surface shapes calculated reflection minima. The window disks were attached to the output of the corrugated tapers providing the gaussian wave beam flat phase front (Figure 4a). The 0-dB level of the setup was set using the flat mirror closing the end of the taper, and the minimum sensitivity limit was set as the reflection from the open end of the taper.

**Figure 4.** Schematics of the setups used to measure the dielectric disks parameters: (**a**) reflection measurements; (**b**) transmission measurements.

Reflection measurement results are shown in Figures 5–7 for the flat-surface disk, disk with pyramids, and disk with one-dimensional corrugation, correspondingly. The disk with a one-dimensional corrugation of the surface was measured for both orthogonal linear polarizations. However, the results for the second polarization are significantly worse than for the optimal polarization. The measured reflection coefficient is below −18 dB for both corrugated disks in the frequency ranges of 75–110 GHz and 130–160 GHz. In contrast, the flat disk has a much narrower band with low reflections (10 GHz at the level of −20 dB). Note that the option with pyramids is more advantageous if radiation of arbitrary polarization is required, while the option with one-dimensional corrugation is better for specific linear polarization. The one-dimensional corrugation works better for lower frequencies but (due to its larger period) is worse for higher frequencies. Due to the high sensitivity of this shape to manufacturing tolerances, the measured reflection of

one-dimensional corrugation significantly deviates from the calculated one, which is also noted in [19].

**Figure 5.** Reflection from the 3D-printed disk with a flat surface on both sides. The black line corresponds to the numerical simulation in CST Studio. The blue line is the measured reflection coefficient, and the red line is the lower sensitivity limit of the measurement setup.

**Figure 6.** Reflection from the 3D-printed disk with pyramids on both sides. The black line corresponds to the numerical simulation in CST Studio. The blue line is the measured reflection coefficient, and the red line is the lower sensitivity limit of the measurement setup.

To measure wideband transmission, we used a quasioptical setup consisting of a vector network analyzer (VNA), a pair of tapers with PTFE lenses on adaptors, and an air gap between them (Figure 4b). Disks were placed in the center of the air gap, which is also the position of the Gaussian beam waist. The transmission through the two thinner disks is presented in Figure 8. The flat disk has a thickness of 3.15 mm, and the average thickness of the disk with pyramids is 3.33 mm. The low-reflection disk has a significantly better transmission and is very close to the maximum transmission predicted using the measured loss tangent of the polyamide. The disk with one-dimensional corrugation is not shown because it has high dielectric losses in this frequency band due to its bigger average thickness of 7.5 mm. The oscillations of the flat-sided disk transmission are caused by Fabry–Perot resonances inside the disk (period approximately 30 GHz) and resonances between the disk and one of the lenses (approximately 4 GHz). The reflection from the tapers causes fast oscillations (approximately 1 GHz).

**Figure 7.** Reflection from the 3D-printed disk with special one-dimensional corrugation on both sides. The black line corresponds to the numerical simulation in CST Studio. The blue line is the measured reflection coefficient, and the red line is the lower sensitivity limit of the measurement setup.

**Figure 8.** Transmission through the disks. The red line corresponds to the disk with pyramids on both sides, and the blue line corresponds to the flat-surface disk. The black line shows dielectric losses calculated in the 3.33 mm thick polyamide disk with zero reflections.

It is interesting and instructive to compare the results obtained for 3D-printed windows with the earlier results for windows with the same shape profiles but manufactured by traditional mechanical methods. Thus, the disk made from raflon (radiation-modified PTFE) by CNC machining had reflections lower than −20 dB in the frequency range of 50–200 GHz [19], which is very similar to the results presented in this paper. Therefore, we conclude that the current additive technologies are competitive with traditional manufacturing methods for dielectric microwave components at the 1 mm and longer waves.

## **4. Estimation of the Applicability of the Considered Materials**

Based on the obtained values of the real and imaginary parts of the dielectric permittivity, as well as the mechanical and thermal parameters of the tested materials given in [20], it is possible to determine the losses and temperature conditions of a window that can withstand atmospheric pressure, depending on its diameter and the supplied microwave power. When considering the heat problem, the transverse dependence of the microwave radiation intensity on the radius was taken as a Gaussian wave beam with a width of 0.64 of the window radius. Numerical modeling was performed with the following parameters to represent many plastics with similar properties: *n* = 1.5, emissivity ε = 0.9, and the thermal conductivity of plastic <sup>κ</sup> = 0.4 W·m−1K−<sup>1</sup> . The dielectric loss tangent was taken as slightly larger than the best-tested plastic δ = 0.002. The temperature of the cooled edge of the window (ambient temperature) was T<sup>0</sup> = 20 ◦C, with a convection coefficient of h = 10 W·m−<sup>2</sup> ·K−<sup>1</sup> . Several window diameters were considered between 1 cm and 10 cm with different thicknesses from 1 mm to 10 mm, and the wavelength was set as *λ*<sup>0</sup> = 3 mm, which corresponded to the 100 GHz base frequency. Dielectric losses are proportional to the frequency; therefore, the maximum power for any other frequency can be calculated by multiplying the ratio of the base frequency to the target frequency. Numerical modeling of the dielectric disk heating by a Gaussian beam was performed in COMSOL Multiphysics. The reflections of the beam on disk surfaces were neglected, assuming the antireflection surfaces. We simulated maximum beam power, which can be transmitted through the disk, given that the maximum stationary temperature is 120 ◦C. The decimal logarithm of the maximum transmitted continuous wave (CW) power value in Watts is presented in Figure 9, e.g., a disk with diameter 100 mm and thickness 10 mm can withstand approximately 150 W of CW transmitted power at a frequency of 100 GHz without convective cooling.

**Figure 9.** Simulation results for maximum 100 GHz CW transmitted power through the polymer windows without overheating. (**a**) the decimal logarithm of the maximum power value in watts without convective cooling (vacuum at both sides); (**b**) decimal logarithm of the maximum power value in watts with convective air cooling on one side.

## **5. Conclusions**

Current 3D printing technologies allow easy-to-manufacture dielectric microwave components, such as broadband barrier windows with low reflections. In this paper, the dielectric properties of the materials used in various 3D printing methods were measured. The most suitable materials were found to be useful in microwave systems with a frequency of up to several hundred gigahertz and a power of up to several tens of watts. The analytical calculations and numerical simulations verify the use of the studied materials for microwave devices with a power of about 100–200 watts.

Barrier windows with surface shapes specially optimized for low reflection in a wide frequency band were printed and examined at low power. The printed windows provided a reflection coefficient below −18 dB at frequencies of up to 160 GHz, making it possible to use in microwave devices that require the reception/transmission of a signal in a wide frequency range. We conclude that the current additive technologies are competitive with traditional manufacturing methods for dielectric microwave components at 1 mm and for longer waves.

**Author Contributions:** Conceptualization, M.Y.G., M.D.P. and D.I.S.; methodology, M.D.P. and D.I.S.; investigation, M.D.P., D.I.S., V.V.P., V.I.B. and S.V.M.; writing—original draft preparation, M.D.P.; writing—review and editing, D.I.S.; project administration, M.Y.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Russian Science Foundation, grant number 21-19-00877.

**Data Availability Statement:** Data available on request from the authors.

**Conflicts of Interest:** The authors declare no conflict of interest.

## **References**


## *Article* **Over-Size Pill-Box Window for Sub-Terahertz Vacuum Electronic Devices**

**Tongbin Yang <sup>1</sup> , Xiaotong Guan 2,3 , Wenjie Fu 1,3,\* , Dun Lu <sup>1</sup> , Chaoyang Zhang <sup>1</sup> , Jie Xie <sup>1</sup> , Xuesong Yuan 1,3 and Yang Yan 1,3**

	- University of Electronic Science and Technology of China, Chengdu 610054, China

**Abstract:** The pill-box window is one of the important components of microwave vacuum electronic devices (VEDs), and research into it is of great significance. As the operating frequency increases, the problems associated with the reduction in the structure size include the reduction of the brazing plane and the reduction in the tolerance of the pill-box window. These problems will cause traditional pill-box windows to be unsuitable in high-frequency bands, especially in terahertz and sub-terahertz regions. The most influential factor is the length of the circular waveguide in the box window. The welding plane of the over-size pill-box window is the annular bottom surface on both sides of the dielectric sheet, which is larger than the circular waveguide, and the operating frequency does not directly affect the area of the brazing surface. Choosing a suitable diameter for the dielectric sheet can effectively increase the tolerance to the length of the pill-box window circular waveguide. Therefore, an over-size pill-box window would be a practicable approach to improve the performance compared to the traditional pillow-box in high-frequency bands. This paper describes, in detail, the theoretical design, simulation optimization and experimental process of this improved pill-box window. An over-size pill-box window suitable for G band VEDs was successfully developed. The experimental result in the 215–225 GHz band is that the maximum transmission loss is −1 dB, and the overall transmission loss is close to −0.5 dB. The overall reflection is less than −11 dB.

**Keywords:** pillbox window; 220 GHz; low loss; sub-terahertz

## **1. Introduction**

In Recent decades, with the rapid development of terahertz science and technology, the lack of terahertz radiation sources has become, have limiting the research into and applications of the terahertz wave. Vacuum electronic devices (VEDs) (e.g., TWT, klystron, BWO, Gyrotron), which could transfer energies from electrons to electromagnetic waves in vacuum tubes, are the most powerful radiation sources in the low-frequency terahertz region and sub-terahertz region. The IAP-RAS (Institute of Applied Electronics-RAS) reported 10 kW, 1 THz gyrotron, CAEP (China Academy of Engineering Physics) reported 3.1 W, 336.96 GHz TWT, and CPI (Communications & Power Industries) reported 10 W, 264 GHz EIO/EIK (Extended Interaction Klystrons/Oscillatiors). The vacuum window is an important component of the vacuum electronic device [1–3]. It is used to maintain the high-vacuum condition while in the tubes, while inputting or outputting electromagnetic waves from or into the tubes.

The pill-box window is a widely used configuration in VEDs design [4–7], with the advantages of bandwidth, easy brazing, and high power capacity. Figure 1a shows the

**Citation:** Yang, T.; Guan, X.; Fu, W.; Lu, D.; Zhang, C.; Xie, J.; Yuan, X.; Yan, Y. Over-Size Pill-Box Window for Sub-Terahertz Vacuum Electronic Devices. *Electronics* **2021**, *10*, 653. https://doi.org/10.3390/ electronics10060653

Academic Editor: Mikhail Glyavin

Received: 8 February 2021 Accepted: 9 March 2021 Published: 11 March 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

standard structure of a traditional pill-box window. It consists of a standard waveguide with input and output ports, a circular waveguide with a diameter equal to the diagonal of the standard waveguide, and a dielectric sheet brazed into the circular waveguide. The traditional pill-box window has a wide range of applications. However, the size of the traditional pill-box window is directly proportional to the operating wavelength. As the working frequency increases, the overall size of the pill-box window is reduced, and some problems arise in the realization of the traditional pill-box windows a result. The brazing surface of the traditional pill-box window is the cylindrical side surface of the dielectric sheet. The reduction in the size of the pill-box window will cause the reduction in the brazing surface, decreasing the air tightness and experimental tolerances. The higher the working frequency band of the pill-box window, the more difficult it is to process. The parameter that is most prone to experimental errors, and has the greatest impact on the experimental results, is the length of the circular waveguide of the pill-box window (*L*1) [5,6]. In the W-band, an asymmetric structure is used, and the influence of processing errors on the test results of the box window can be reduced through multiple transmission tests [6]. However, in the G-band, the asymmetric structure cannot solve the problem of a too-small welding surface, and the air tightness of the pill-box window cannot be guaranteed. The improved over-sized pill-box window shown in Figure 1b can effectively solve the above problems. The brazing surface of the improved pill-box window is the annular bottom surface of the dielectric sheet, which is larger than the circular waveguide. The brazing area will not change with the increase in working frequency. During the design process, we found that the tolerances in dielectric sheets with different diameters to pill-box windows are different. Choosing a suitable diameter for the dielectric sheet can effectively increase the tolerance of the pill-box window, thereby reducing the difficulty of achieving high-frequency pill-box windows.

**Figure 1.** Structure of the (**a**) traditional pillbox window and (**b**) improved pillbox window.

In this paper, an over-size pill-box window for sub-terahertz VEDs at G band (215–225 GHz) is investigated, as outlined in the above structure. In the second part of this article, the theoretical design and simulation optimization of the improved box window are described in detail. The third part realized the G-band pill-box window according to the design and processing. The fourth part summarizes this article.

#### **2. Model Design and Simulation**

The pill-box window design begins with choosing the right material as the medium window sheet. Materials such as quartz, ceramics, diamond and sapphire are often used for the dielectric sheets of pill-box windows. Compared with other dielectric materials, sapphire has the advantages of high mechanical strength, low loss tangent, and mature metallization technology. Sapphire is an anisotropic material, but the perturbation of its dielectric constant does not affect the transmission of the transverse electric (TE) mode in

the over-size pill-box window [7]. Therefore, the dielectric material selected in this design is sapphire, and its dielectric constant is 9.4.

There are many published theoretical calculation methods, such as the impedancematching approach [3,5], the method of moments [8], and the equivalent circuit method [4–9]. In this paper, the equivalent circuit method, with a relatively simple calculation, is selected. In the equivalent circuit theory, the connection point between the waveguides and the waveguide of the pill-box window are equivalent to a two-port circuit element. The transmission modes of the rectangular waveguide and the circular waveguide in the pill-box window are TE<sup>10</sup> mode and TE<sup>11</sup> mode, and the equivalent circuit is shown in Figure 2.

**Figure 2.** Equivalent circuit diagram of pill-box window.

In Figure 2, *L* is the length of the rectangular waveguide; *β* is the propagation constant of the rectangular waveguide; *Z* is the characteristic impedance of the rectangular waveguide; *Bc* is the equivalent susceptance of the connecting part of the rectangular waveguide and the circular waveguide; *L*<sup>1</sup> is the length of the cylindrical waveguide; *β*<sup>1</sup> is the propagation constant of the cylindrical waveguide; *Z*<sup>1</sup> is the characteristic impedance of the cylindrical waveguide; *L*<sup>0</sup> is the length of the sapphire cylinder; *β*<sup>0</sup> is the propagation constant of sapphire dielectric waveguide; *Z*<sup>0</sup> is the characteristic impedance of sapphire dielectric waveguide; a *M* is the transfer matrix of the connection part and each waveguide.

The multiplication of the transmission matrix of each the transition part and each waveguide of the pill-box window is equal to the overall transmission matrix of the pill-box window. This can be written as

$$M = M\_1 \bullet M\_2 \bullet M\_3 \bullet M\_4 \bullet M\_5 \bullet M\_4^s \bullet M\_3 \bullet M\_2 \bullet M\_1 \tag{1}$$

where the '•' in the formula means multiply, the '\*' in the formula represents the inverse matrix. The specific expression formula of each transfer matrix can be found in the literature [7]. Through the simplification of the transfer matrix and the relationship between the scattering matrix and the transfer matrix, the scattering matrix of the equivalent circuit can be obtained. The specific derivation process can be obtained from the literature [6,7]. By substituting the ideal transmission conditions: *S*<sup>12</sup> = *S*21, *S*<sup>11</sup> = *S*<sup>22</sup> = 0 into the scattering matrix the equations for the structural parameters of the box window can be obtained as

$$\begin{cases} \tan\beta\_1 L\_1 = A/B \pm \sqrt{\left(A/B\right)^2 - \mathcal{C}/B} \\ \left(A/B\right)^2 - \mathcal{C}/B \ge 0 \end{cases}$$

$$\begin{cases} A = \left(-\frac{Z}{Z\_1} + \frac{Z\_0}{Z}B\_c^2 + \frac{Z}{Z\_1}\right)\cos\beta\_0 L\_0 + \left(\frac{Z\_0}{Z\_0}B\_c^2 + \frac{Z\_0}{Z\_1}B\_c\right)\sin\beta\_0 L\_0 \\ B = -2B\_c\cos\beta\_0 L\_0 + \left(\frac{Z\_1^2}{ZZ\_0}B\_c^2 - \frac{ZZ\_0}{Z\_1^2} + \frac{Z\_1^2}{ZZ\_0}\right)\sin\beta\_0 L\_0 \\ \mathcal{C} = 2B\_c\cos\beta\_0 L\_0 + \left(\frac{Z}{Z\_0} - \frac{Z\_0}{Z}B\_c^2 - \frac{Z\_0}{Z}\right)\sin\beta\_0 L\_0 \end{cases} \tag{2}$$

According to the test conditions of the vector network analyzer (VNA) in our laboratory and the operating frequency of the pill-box window, the rectangular waveguide selected in this design is WR-5 (waveguide name of EIA standard). Equation (2) is an equation about *f*, *L*1, *L*0, *R*1, *R*0. When the frequency is determined to be 220 GHz, these four parameters have countless solutions. In order to obtain the ideal over-size pill-box window structure parameters, it is necessary to limit the values of the parameters before solving. The increase in the thickness of the sapphire sheet will increase the mechanical strength and

power capacity of the pill-box window. However, the increase in thickness will reduce the matching degree of the pill-box window, that is, the bandwidth will become smaller. Therefore, the thickness of the sapphire sheet can be limited one-quarter waveguide wavelength to half the waveguide wavelength (0.11 mm < *L*<sup>0</sup> < 0.22 mm). If the radius of the circular waveguide is too large, it is easy to produce higher-order modes. However, when the diameter of the circular waveguide is the diagonal length of the rectangular waveguide, the bandwidth of the box window is narrow. Therefore, the radius of the circular waveguide can be selected as <sup>√</sup> *a* <sup>2</sup> + *b* <sup>2</sup>/2 < *R*<sup>1</sup> < 1 mm. To simplify the theoretical calculation, the radius of the dielectric sheet is temporarily set as *R*<sup>0</sup> = *R*<sup>1</sup> + 1. When the length of the circular waveguide is less than the length of the dielectric sheet, the matching degree of the box window will be reduced, and the bandwidth will be reduced. In order to reduce the calculation time, the length of the circular waveguide should be controlled within one waveguide wavelength. The length of the circular waveguide is between the length of the dielectric sheet and a waveguide wavelength (*L*<sup>0</sup> < *L*<sup>1</sup> < 0.44 mm). Substituting the solutions in Equation (2) that meet the value ranges of the four parameters into the scattering matrix of the window system, take the solutions with the largest bandwidth with a reflection less than −15 dB as the theoretical design parameters of the pill-box window, as shown in Table 1.

**Table 1.** Structural size parameters of the pill-box windows.


The equivalent circuit theory is not an accurate theoretical calculation, and the designed structural parameters can only be used as an initial value. The specific size of the over-size pill-box window should be optimized by 3D electromagnetic simulation software (HFSS). In the simulation, the dielectric constant of sapphire is 9.4, and the dielectric loss tangent is 0.006. In the high-frequency pill-box window experiment process, the error capacity of the circular waveguide length (*L*1) is the biggest factor affecting the pill-box window test results. The optimized condition is to ensure that the transmission bandwidth of the pill-box window is 215–225 GHz, which maximizes the tolerance of *L*1. The specific optimization process is that the thickness of the sapphire and the radius of the circular waveguide remain unchanged, the radius of the different dielectric sheets are taken, and the transmission and reflection of different *L*<sup>1</sup> values (*L*<sup>0</sup> < *L*<sup>1</sup> < 0.44 mm) at 220 GHz are scanned. This paper selected five different *R*<sup>0</sup> values, and recorded the transmission loss and reflection corresponding to different *L*<sup>1</sup> values at 220 GHz, under the condition that the maximum reflection in the 215–225 GHz band is less than −15 dB. The results are shown in the Figure 3. In the theoretical calculation of the traditional pill-box window, the size of the rectangular waveguide, and the radius of the circular waveguide and the dielectric sheet are determined by the operating frequency. Equation (2) is an equation about the length of the circular waveguide and the thickness of the dielectric sheet. The same theoretical calculation and simulation optimization are carried out in the traditional medicine box window. The results of the same simulation optimization of the traditional pill-box window are shown in Figure 3.

**Figure 3.** (**a**) The transmission loss and (**b**) reflection simulation results of pill-box windows values with different *L*<sup>1</sup> .

From Figure 3a, the radii of the sapphire sheets of the over-size pill-box window are 1.75, 2, 2.5 and 3 mm, the change in the value of *L*<sup>1</sup> has less influence on the transmission loss, and it is also less than the influence of traditional pill-box windows. When the radius of the dielectric sheets of the over-size pill-box window is larger (*R*<sup>0</sup> = 3.75 mm), the change in the value of *L*<sup>1</sup> has a greater impact on the transmission loss. In Figure 3b, it can be seen that the tolerance of *L*<sup>1</sup> is different for sapphire sheets with different radii. Under the condition that the reflection of the pill-box window at 220 GHz is less than −30 dB and the maximum reflection in the 215–225 GHz frequency band is less than −15 dB, when the radius of the sapphire sheet of the over-size pill-box window is 1.75, 2, and 2.5 mm, the value change range of *L*<sup>1</sup> is 0.08 mm. The range of *L*<sup>1</sup> value of the traditional pill-box window under the same reflection condition is 0.03 mm. It can be seen that the radius of the sapphire sheet of the over-size pill-box window is set to an appropriate value, which can increase the tolerance of the structural parameters of the window system. The final radius of the sapphire in this paper is selected to be 2 mm because of the brazing and miniaturization of the pill-box window. The final structural parameters of the box window are shown in Table 1.

In a simulation template with PEC (Perfect Electric Conductor) as the background material, a pill-box window model, as shown in Figure 4, is established, and the rectangular waveguide openings at the upper and lower ends are set as the excitation source. The simulation result and theoretical calculation results of the transmission characteristics of the pill-box window are shown in Figure 5. It can be seen that the over-size pill-box window calculated by the equivalent circuit theory has a reflection of −42.5 dB at 220 GHz, but its bandwidth is relatively narrow. The optimized over-size pill-box window structure has good transmission performance in the simulation. The reflection in the 210–230 GHz frequency band is less than −30 dB, and the maximum transmission loss is −0.2 dB in the frequency band.

In order to provide the corresponding error and accuracy of the experimental assembly and processing, it is necessary to perform error analysis on the structural parameters of the over-size pill-box window. It can be concluded from Figure 3 that the structural parameters *L*<sup>1</sup> and *R*<sup>0</sup> of the over-size pill-box window have a large tolerance. The error analysis is mainly on the radius of the circular waveguide (*R*1) and the thickness of the dielectric sheet (*L*0). By keeping the other structural dimensions of the pill-box window unchanged, the change in the value of *R*1, and the transmission loss and reflection of the pill-box window are shown in Figure 6. When the radius of the circular waveguide (*R*1) changes within 0.96–0.98 mm, the reflection of the pill-box window in the frequency band 215–225 GHz is less than −20 dB, and its transmission loss changes little. The same simulation error analysis is performed on the thickness of the dielectric sheet (*L*0), and the result is shown in Figure 7. When the variation range of *L*<sup>0</sup> is 0.194–0.206 mm, the reflection parameters of the pill-box window are less than −20 dB in the 215–225 GHz band, and the transmission loss is less than −0.15 dB. It can be seen from the above that the tolerance difference in the two parameters *R*<sup>1</sup> and *L*<sup>0</sup> is ±0.01 mm and ±0.006 mm.

**Figure 4.** The simulation structure of over-size pill-box window.

**Figure 5.** Theoretical and simulated transmission characteristics.

**Figure 6.** (**a**) The transmission loss and (**b**) reflection of pill-box windows values with different *R*<sup>1</sup> .

**Figure 7.** (**a**) The transmission loss and (**b**) reflection of pill-box windows values with different *L*<sup>0</sup> .

#### **3. Experiment Results**

In the preliminary test of the over-size pill-box window, we found that the test size of the individual components was within the tolerance of the error analysis, but the test results after assembly and welding were not ideal. Because the over-size pill-box window being tested is composed of many parts, the final test result is determined by the errors of all components. In order to increase the utilization rate of over-size pill-box window components and the yield of over-size pill-box windows, this paper optimizes the testing process, as shown in Figure 8. The components of the over-size pill-box window are cleaned and dimensioned, and components with qualified dimensions are selected for assembly, and then the first test is performed on the vector network analyzer (CEYAER AV3672C (Shandong, China)). The sapphire sheet of the over-size pill-box window that passes the test is selected for metallization, and the second transmission test is performed after assembly with the original components. The over-size pill-box window that passes the second transmission test is selected to complete the final assembly and brazing. Finally, the third transmission test is performed. In this test scheme, the first two transmission tests can eliminate unqualified assembly components during the test process, minimize the waste of the pill-box window components, and ensure the qualification of the over-size pill-box window components for the final transmission test to increase the yield of over-size pill-box windows.

It is worth mentioning that, when formulating a pill-box window soldering plan, the solder should be isolated from the cavity waveguide in the pill-box window, that is, the solder slot in the soldering plan should be a closed space, as shown in Figure 9a. The deformation of the solder in the high-temperature furnace under the high pressure of the fixture should be controlled. This can reduce the influence of transmission characteristics of the over-size pill-box window by solder deformation. According to the structural parameters optimized by the simulation, the components of the over-size pill-box window are processed; the overall pill-box window after brazing is shown in Figure 9b. The experimental system of the over-size pill-box window is shown in Figure 8.

**Figure 8.** The test flow chart for the over-size pillbox window.

**Figure 9.** (**a**) The b razing diagram of the window system (**b**) The pillbox windows after brazing assembly.

From the experimental process of the pill-box window, it can be seen that each successful window needs three tests on the VNA. In the first test, the non-metalized dielectric window sheet and other components were assembled into a pill-box window system with screws and pins. The test results on VNA are shown in Figure 10. It can be seen from the figure that there is a large reflection at 214.3 GHz, the transmission loss reaches −2 dB, and the spurious modes are produced at the frequency of 221.9 GHz. The reason for this phenomenon may be that the annular air grooves on both sides of the tested pill-box window dielectric sheet affect the transmission characteristics of the window system. This can be verified by a simulation calculation. The ring-shaped hollow groove with a ring width of 0.5 mm and a ring height of 0.2 mm on both sides of the dielectric sheet are added to the simulation calculation, and the result is shown in Figure 11. There is a larger reflection point at 213.5 GHz in the simulation result, which is 0.9 GHz different from the frequency of the reflection point in the test result. The two results are quite similar. It can be determined that this reflection point is the influence of the ring-shaped groove on the transmission of the pill-box window. The test results have good overall transmission

characteristics after removing the spurious mode points in the 215–225 GHz frequency band, and are highly similar to the simulation results. This shows that the processing error of the tested pill-box window parts is small, and the next test can be carried out.

**Figure 10.** Experimental testing of the pill-box windows.

**Figure 11.** Results of the non-metallization and non-brazed pill-box windows.

After the first test of the pill-box window, the dielectric window sheet is metalized and then assembled and tested. In this case, the ring-shaped solder grooves on both sides of the dielectric sheet are blocked by the metalized film, and the transmission effect on the pill-box window is negligible. With the support of mature metallization and brazing technology, the results of the last two tests are basically the same. The final test results are shown in Figure 12. It can be seen from the figure that there is a large gap between the tested pill-box window transmission coefficient and the simulated value, but the numerical trend is very similar. In the design frequency band 215–225 GHz, the over-size pill-box window has good transmission characteristics, its maximum transmission loss is −1 dB, the overall transmission loss is close to −0.5 dB, and the overall reflection is less than −11 dB. Its characteristics fully meet the parameter requirements as an input window.

**Figure 12.** Results of the metallization and brazed pill-box windows.

### **4. Conclusions**

This paper introduces the design, production and testing of a pill-box window developed for G band VEDs. The tolerance of the circular waveguide length (*L*1) of the pill-box window in the different radius mediums of the improved pill-box window is discussed, which effectively provides a higher tolerance of the box-shaped window to the length of the circular waveguide. This provides a new idea for the selection of the radius of the dielectric sheet of this type window. After the theoretical calculation and simulation optimization, the reflection of the box window in the 210–230 GHz frequency band was less than −30 dB, and the maximum transmission loss was −0.2 dB. The problems of the experiment process and optimized the test process are summarized. The test results of pill-box windows without metallization and brazing are shown. The simulation analysis on test results was performed to determine the eligibility of pill-box window components. The pill-box window was within the design frequency band of 215–225 GHz, the overall transmission loss was close to −0.5 dB, and the overall reflection was −11 dB. The test results show that this over-size pill-box window is a design that can be applied to the vacuum window of a sub-THz VEDs, and has development potential at higher terahertz region frequencies.

**Author Contributions:** T.Y. and W.F. contributed to the overall study design, analysis, computer simulation, and writing of the manuscript. X.G., D.L., J.X., C.Z., X.Y., and Y.Y. provided technical support and revised the manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported in part by National Key Research and Development Program of China under 2019YFA0210202, in part by the National Natural Science Foundation of China under Grant 61971097 and 6201101342, and in part by the Terahertz Science and Technology Key Laboratory of Sichuan Province Foundation under Grant THZSC201801.

**Acknowledgments:** The authors gratefully acknowledge Yin Huang and Weirong Deng for their kind assistance on engineering design and assembling.

**Conflicts of Interest:** The authors declare no conflict of interest.

## **References**

