*Article* **Low-Frequency Terahertz Photonic Crystal Waveguide with a Lilac-Shaped Defect Based on Stereolithography 3D Printing**

**Jia Shi 1,\*, Yiyun Ding 1, Longhuang Tang 2, Xiuyan Li 1, Hua Bai 1, Xianguo Li 1, Wei Fan 1, Pingjuan Niu 1, Weiling Fu 3, Xiang Yang 3,\* and Jianquan Yao <sup>4</sup>**


**Abstract:** Terahertz (THz) photonic crystal (PC) waveguides show promise as an efficient and versatile waveguiding platform for communication, sensing, and imaging. However, low-frequency THz PC waveguides with a low-cost and easy fabrication remain challenging. To address this issue, a THz PC waveguide with a lilac-shaped defect has been designed and fabricated by 3D printing based on stereolithography (SLA). The reflection and transmission characteristics of the proposed waveguide have been analyzed using the finite difference frequency domain (FDFD) method. The waveguide spectral response is further optimized by changing the distance of the lilac-shaped resonant cavities. Consistent with the results of numerical modeling, the measured results show that the waveguide performs a resonant reflection in the region of 0.2 to 0.3 THz and low-pass transmission in the 6G mobile communication window. Furthermore, in order to characterize the performance of the proposed waveguide, parameters have been analyzed, including the Q factor, resonant frequency, and bandwidth. This work supplies a novel pathway for the design and fabrication of a lowfrequency THz PC waveguide with potential applications in communication, sensing, and imaging.

**Keywords:** terahertz; photonic crystal waveguide; 3D printing

## **1. Introduction**

Terahertz (THz) is electromagnetic radiation with a frequency in the range 0.1 to 10 THz, which lies in the gap between the microwave and infrared regions [1]. THz technology has been playing an increasingly important role in various fields, including wireless communication, security, biomedical applications, imaging, sensing, and spectroscopy [2–4]. Although THz waves have proven to be beneficial for many applications, most THz systems are based on free-space optics that are complex, delicate, and require frequent alignment [1]. To solve these issues, different types of THz waveguides have been proposed. Many of THz waveguides have been demonstrated for applications such as communication, sensing, and imaging. Notably, the THz band from 0.1 to 0.3 THz has been of significant research interest in recent years, as it is considered to be the main transmission band for 6G telecommunication; low-frequency THz waveguides working in the 6G mobile communication window are gaining immense demand [5]. Currently, the very limited design library of conventional waveguide structures substantially constraints their functionalities to mostly mere waveguiding. Researchers are still struggling to design and manufacture high-performance waveguides with a low-cost and easy fabrication [3].

A variety of waveguides have been explored, including metallic and dielectric waveguides [4,6–12]. Most metallic waveguides are only suitable for millimeter lengths [13], because of the strong trade-off between mode confinement and metallic loss [11,12]. Because

**Citation:** Shi, J.; Ding, Y.; Tang, L.; Li, X.; Bai, H.; Li, X.; Fan, W.; Niu, P.; Fu, W.; Yang, X.; et al. Low-Frequency Terahertz Photonic Crystal Waveguide with a Lilac-Shaped Defect Based on Stereolithography 3D Printing. *Appl. Sci.* **2022**, *12*, 8333. https://doi.org/10.3390/ app12168333

Academic Editor: Mira Naftaly

Received: 26 July 2022 Accepted: 16 August 2022 Published: 20 August 2022

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

**Copyright:** © 2022 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/).

of the existing surface plasmon polaritons (SPPs) [12], metallic PCs enable confinement of THz waves in the sub-millimeter scale. However, metallic PC waveguides are still inevitably accompanied by Ohmic losses, which limit the quality factors of resonance and compromise the efficiency of metallic-based devices [8]. In the past few years, a growing number of reports have shown that this problem could be solved by employing dielectric waveguides, which mostly rely on high-index and low-loss particles (such as silicon, SiO2, and TiO2) [7,9,10]. Consequently, interest in dielectric waveguides has increased with the application of dielectric antennas, resonators, polarizers, etc. [4,8–10,14]. Meanwhile, a number of researches have been focused on dielectric waveguides because of the wide variety of available materials and the greater flexibility of the waveguide design. Many dielectric waveguide structures, including planar [15], rectangular [16], circular [1], strip [17], and photonic crystal waveguides [10,18,19] have been investigated. Among them, photonic crystals can realize strong light confinement due to the nature of photonic band gaps, and show great potential in high-performance dielectric waveguides [10].

Currently, THz waveguides are mostly fabricated by photolithography, which requires multiple steps, including spin-coating, prebaking, the preparation of masks, exposure, etc. [20–22], leading to a long preparation cycle and a high cost [16,23]. In addition, most of these devices have a substrate, which significantly lowers the transmittance and causes internal interference. Therefore, it is of great significance that THz PC waveguides are fabricated in a simple, low-cost, and efficient way [16]. Furthermore, most of the related works are conducted at a microwave and millimeter wave; it remains challenging to obtain low-frequency THz PC waveguides with a low-cost and easy fabrication. Direct writing technology has been applied to create complex THz waveguides, such as microfluidic threedimensional photonic crystals [24]. High-accuracy 3D printing based on stereolithography (SLA) [13,23,25–27] as an emerging technology shows great potential in high-performance dielectric waveguides, but it has not been applied in THz PC waveguides.

In this work, a THz PC waveguide with a lilac-shaped defect is demonstrated. This proposed waveguide is fabricated with a high-density photosensitive resin by 3D printing based on SLA. The reflection and transmission properties of the waveguide in the 6G mobile communication window have been investigated. The waveguide spectral response is optimized by changing the distance of the lilac-shaped resonant cavities. The waveguide performance in the range of 0.1 THz to 0.5 THz has been analyzed, including the Q factors, resonant frequency (*fR*), full width half max (FWHM), −60 dB bandwidth, and loss.

## **2. Design and Simulations**

In this part, a low-frequency THz PC waveguide with a lilac-shaped defect is designed, as shown in Figure 1a,b. The symmetrical petal hollow core is induced in the waveguide structure to broaden the operation frequency bandwidth. For efficiently guiding the terahertz wave, the structural parameters are optimized to design a suitable structure. The lattice structure of the periodically arranged unit cells consists of air holes on the *o-xy* plane, which are described by the following [28,29]

$$\text{tr}(M, m) = \, aM \cos \left(\frac{2m\pi}{6M}\right) \tag{1}$$

$$y(M,m) = \
a M \sin\left(\frac{2m\pi}{6M}\right) \tag{2}$$

where *a* is the lattice constant, *M* is the number of the air hole rings, and *m* (1 ≤ *m* ≤ 6*M*) is the number of the air holes in the *Mth* ring. The lilac-shaped resonant cavities are formed by four larger symmetrical air holes at the center, with the first, second, and third rings of the periodically arranged unit holes removed. Each resonant cavity consists of an intersection of one circular air hole with a diameter of *D* and one square air hole with a length of *L*. The gap distance between four petals of the lilac-shaped resonant cavities is defined as *g*. Initial values of the structure parameters are *a* = 1000 μm, *d* = 0.8 *a* = 800 μm, *D* = 1500 μm, *L* = 750 μm, and *g* = 500 μm. Meanwhile, the depth of the air holes in the *z* direction is much larger than *a* (*h* >> *a*).

**Figure 1.** (**a**) The 2D structure of the THz PC waveguide. (**b**) The 3D structure of the THz PC waveguide. (**c**) The process of reflection and transmission characteristics of the THz PC waveguide. (**d**) The real and imaginary parts of the refractive index (RI) of the photosensitive resin.

In the simulation process, the optical characteristics of the THz PC waveguide were analyzed using COMSOL Multiphysics. The boundary condition was set to the scattering boundary condition to absorb energies. The physics-controlled mesh was applied to the model [29]. The process of the reflection and transmission characteristics of the proposed waveguide is shown in Figure 1c. The TE-polarized Gaussian form was injected into the waveguide from the left side and a monitor was set on the right side of the waveguide. Air holes were placed throughout the photosensitive resin background. In the simulation, the refractive index (RI) of the photosensitive resin used in the range of 0.1 to 0.5 THz were measured using the Terahertz Time-Domain Spectroscopy (THz-TDS) system (Menlo TeraSmart, Martinsried, Germany), which is shown in Figure 1d.

The gap distance (*g*) is an important parameter that can change the photonic bandgap of the photonic crystal; in particular, the guidance of the terahertz wave in the waveguide is caused by the photonic bandgap mechanism. Therefore, in order to explore the detailed functionality of the waveguide, the influence of the gap distance (*g*) has been simulated from 100 μm to 2000 μm in steps of 100 μm. The reflection map of the waveguide with different gap distances is shown in Figure 2a. As the gap distance increases from 100 μm to 2000 μm, the reflection loss performs a resonant dip in the frequency region of 0.2 to 0.3 THz. Correspondingly, as shown in Figure 2b, the transmission loss increases continually within 0.5 THz. For instance, when the gap distance is 1000 μm, the reflection loss (S11) and transmission coefficient (S21) are shown in Figure 2c. The band-stop behavior of the proposed waveguide is analyzed by the reflection loss. The resonant frequency of the band-stop is approximately at 0.23 THz with a transmission loss of about −44 dB. The transmission coefficient shows the low-pass behavior. To better understand the reflection and transmission effect, the simulated electric field patterns at different frequencies are analyzed in Figure 2d when *g* is 1000 μm. It is observed that the THz wave can smoothly pass through this waveguide within 0.2 THz and it is reflected mostly higher than 0.3 THz.

**Figure 2.** (**a**,**b**) The 2D contour maps of simulated reflection loss and transmission loss as a function of frequency with different gap distances (*g*), respectively. The black dashed line indicates *g* = 1000 μm. (**c**) The simulated S parameters of the THz PC waveguide with *g* = 1000 μm. These blue dashed lines indicate the frequency at 0.1 THz, 0.2 THz, 0.3 THz, and 0.5 THz, respectively. (**d**) Electric field distributions of the THz PC waveguide at *g* = 1000 μm with different frequencies (0.1 THz, 0.2 THz, 0.3 THz, 0.5 THz, respectively).

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

## *3.1. Fabrication of the Proposed Waveguides*

The exact reproduction of the designed structure requires tremendous efforts to optimize the parameters of the facility. Fortunately, 3D printing is a process of making prototype parts directly from computer models, which opens up almost unlimited possibilities for rapid prototyping [13]. In this study, waveguides with the gap distance (*g*) set as 500 μm, 1000 μm, and 2000 μm, respectively, were printed using the SLA 3D printing mechanism. Figure 3a shows an overview of the entire 3D printing methodology [25,26]. Figure 3b–e shows a cross-section of the optical electron microscopy (OEM) images of the waveguide (e.g., the gap distance *g* is 500 μm). The fabricated error of the waveguide structure was measured using a microscope camera to evaluate the accuracy of the dimensions [27]. The OEM results proved that the morphology of the 3D-printing was consistent with the design. According to the measurement result, as shown in Figure 3f, *d* = 800 ± 14.96 μm, *D* = 1500 ± 19 μm, *L* = 750 ± 18.74 μm, *g* = 500 ± 14.23 μm. It is noted that the difference between the measured and designed dimensions was within the allowable printer error (<50 μm). Therefore, the fabrication method of the proposed waveguide had the advantages of a low-cost and easy fabrication, and flexible design. These properties are desirable for applications of various terahertz devices [30].

## *3.2. 3D Printing Based on Stereolithography*

The desired waveguide devices were first drafted using commercial CAD drawing software and then translated into STL format, a suitable file for a 3D printer. The file was then sliced in a *Z* direction using the Photon Workshop software (Version 2.1.23.RC8). The sliced file was then sent to the 3D printer. This SLA printer (ANYCUBIC Photon Mono X) used an inverted lithography set-up with a 405 nm UV light irradiation and LCD screen selective voxel curing that resulted in the finished 3D structure [26]. The transverse

resolution was 47 μm and the longitudinal resolution was 1.25 μm (i.e., along the structure height) [23].

**Figure 3.** (**a**) Schematic of the SLA printing process and 3D printed object. Optical microscopy images of (**b**) the cross-section of the THz PC waveguide, (**c**) the periodically arranged unit cells of the THz PC waveguide, (**d**) the lilac-shaped resonant cavities of the THz PC waveguide, and (**e**) one petal of the lilac-shaped resonant cavities of the THz PC waveguide. (**f**) Statistical analysis of the size of four parameters after multiple measurements.
