1. Introduction

In modern communication systems, almost all of the devices are operating in the microwave band. The spectrum resource of microwave band is becoming increasingly scarce with the growing demands [1]. Increasing the utilization efficiency of spectrum resources by multi-band and broadband technologies is an effective way to solve the problem. However, the channel capacity is close to the Shannon limit [2]. Thus, the studies of higher frequency possess great potential application value for the future communication [3–5]. Terahertz (THz) region of the electromagnetic spectrum, which covers the range from 0.3 to 10 THz [6, 7], is categorized between the optical and the microwave band. In the past decades, it has become a hot topic in the fields of communication [8], imaging [9, 10] and detection due to its great deal of advantages [11–13]. Especially in the communication field, THz waves obtain inherent broader bandwidth compared to the conventional microwave wireless communication.

Antenna, regarded as one of the most critical components, plays an important role in communication system. There are many kinds of antennas, such as aperture antenna, reflector antenna, dielectric resonant antenna, microstrip antenna, etc. Among which, microstrip antenna has been attracting much attention from researchers owing to their distinct advantages such as light weight, low fabrication cost and easy to integrate. Nevertheless, the bandwidth of the classical microstrip antenna usually presents a narrow band at high operating frequency, which limits their practical application [14, 15]. To solve this problem, great efforts have been made in exploiting new approaches to increase the bandwidth of micrstrip antenna [16–18]. However, the present methods such as loading dielectric resonator [19], combining multiple structures [20] and adapting multiple layers [21] inevitably increase the complexity of the antenna, which is not benefit for practical application.

In this work, we demonstrate a complementary ring resonator based terahertz antenna. The complementary ring is etched in the ground plane to increase the bandwidth. From the simulated results, it is found that a new resonant peak appears in the range of 2.0 – 4.0 THz. As the new resonant peak is close enough to the inherent peak of the rectangle microstrip antenna, a broad bandwidth is realized.

2. Proposed structure

The structure of the proposed broadband terahertz antenna with complementary ring resonator is shown in Fig. 1. In the design of this prototype antenna, radiation element and ground plane are located on two sides of the quartz substrate which has a thickness of 10 μm and a relative permittivity of 3.75. The top layer of the antenna consists of a rectangle patch and a transmission line. In the design of rectangle patch, the parameters of the rectangle patch can be easily determined by the relationship between dimensions of the patch and resonant frequency. Here, the resonant frequency is set to 3 THz. Therefore, all parameters of the radiation element are determined: c = 26 μm, d = 2.5 μm, w = 30 μm, h = 20 μm. On the bottom layer of the antenna, a complementary ring resonator is located on the ground plane. The radius and width of the ring is 12.5 μm and 0.8 μm, respectively. It is obvious that the substrate and ground plane has the same size with width a of 50 μm and length b of 59 μm.

 

Fig. 1 Schematic diagrams of the proposed antenna. (a) Top-and-bottom views; (b) perspective view.

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Numerical predictions of the return loss for the proposed antenna were made using the commercial time-domain package CST Microwave Studio TM. The electromagnetic wave propagates along y direction, shown in Fig. 1(b). The boundary conditions of three directions are all open (add space). Figure 2(a) shows the simulated results of the terahertz antenna with and without the complementary ring. The −10 dB bandwidth of the antenna with and without the complementary ring are 0.57 THz (2.63 - 3.20 THz) and 0.28 THz (2.87 - 3.15 THz), respectively. Compared to the narrow bandwidth of the antenna without the complementary ring, the bandwidth of the antenna with complementary ring is broader because of the existence of a new resonant peak. And the increasing rate of the bandwidth can be over 100%. Moreover, the loading of the complementary ring resonator doesn’t increase the size of the antenna. It is worth noting that, for the two antennas, the center frequencies of the resonant peaks around 3 THz are almost the same. This phenomenon proves that loading of the complementary ring resonator can stimulate a new resonant peak without changing the inherent resonant peak. Combining the two resonant peak, a broad bandwidth of the proposed antenna is obtained.

 

Fig. 2 Simulated return loss of (a) the proposed antenna with and without complementary ring, (b) the proposed antenna with a series of t.

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The thickness t of the quartz substrate is an important factor to consider in the simulations. Figure 2(b) depicts the simulated return loss of the proposed antenna with a series of t. When the thickness t increases, the inherent resonant frequency shifts to low frequency band. And the energy transferred from the radiation patch decreases due to the increase of the dielectric loss. Therefore, the value of return loss at the new resonant frequency increases as the thickness of the quartz substrate increases. Considering the bandwidth efficiency, 10 μm is an appropriate value for the thickness t of the quartz substrate.

3. Performance and mechanism

To study the performance and generation mechanism of the broadband, the surface current distributions of the antenna at different resonant frequencies and phases are shown in Fig. 3. Figures 3(a) and 3(b) have a phase difference of 180 degrees at the resonant frequency of 2.8 THz. There are strong current distributions along the edges of the complementary ring. Moreover, the current of the two figures shows exactly the opposite direction at an interval of 180 degrees, which demonstrates that the complementary ring is acting as a resonator in the antenna. The current shocks back and forth in the complementary ring, generating a specific frequency of electromagnetic waves. Obviously, the frequency of the electromagnetic waves is related with the structure parameters of the complementary ring resonator. Thus, this resonator can provide a new desirable resonant frequency when the parameters of the complementary ring are in appropriate values.

 

Fig. 3 Surface current distribution of (a) the complementary ring at 2.8 THz with phase of 70 degrees, (b) the complementary ring at 2.8 THz with phase of 250 degrees, (c) the radiation patch with complementary ring at 3.1 THz, (d) the radiation patch without complementary ring at 3.1 THz.

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Figures 3(c) and 3(d) illustrate the surface current distribution of the radiation patch with and without complementary ring at 3.1 THz. It is clear that the current distributions in these two figures are almost the same. In this respect, the loading of the complementary ring can hardly affect the inherent resonant frequency of the radiation patch. This is in great agreement with the simulated return loss results that shown in Fig. 2. In addition, the circle center position of the complementary ring resonator is critical for the design of the proposed antenna. The new resonant peak can only be stimulated when the resonator is placed in the strong current concentrated location. Therefore, the circle center of the complementary ring resonator should coincide with the intersection point of rectangle patch and transmission line. It means that the position of the resonator is determined by the surface current distribution of the radiation patch at its inherent frequency. This is meaningful for loading of the complementary ring resonator in antenna design.

In order to figure out the specific relationship between the parameters of the complementary ring and the new resonant frequency, simulations of the proposed antenna are carried out. Figure 4(a) depicts the return loss of the proposed antenna with a series of R. As shown in this figure, the new resonant frequency increases from 2.59 THz to 2.94 THz as the radius R of the complementary ring decreases from 13.4 μm to 11.9 μm. When R is equal to 11.4, the solid curve of the return loss shows only one peak because that the distance between the new resonant peak and the inherent peak is too close. There is a lower limit for the radius R. When the value of R is lower than the lower limit, the new resonant peak will not exist on the right side of the inherent peak. The reason is that the energy in the complementary ring resonator comes from the radiation patch. Therefore, the stimulated frequency cannot exceed the inherent frequency. It is not difficult to find that the new resonant frequency is almost in equidistant distribution as R is in isometric distribution. By carefully observing the current distribution shown in Figs. 3(a) and 3(b), it is easy to find that the current shocked in the complementary ring acts as the same as being in cavity resonance. The bottom and top points of the complementary ring are the positions of the cavity walls. Thus, the length of the complementary ring resonator is πR. According to the cavity resonance theory, the condition for forming a standing wave is that the length of the resonator equals to an integer multiple of a half wavelength. Thus, the new resonant frequency can be expressed by [22]

 

Fig. 4 (a) Simulated return loss of the proposed antenna with a series of R. (b) Simulated and theoretical relationships between R and the new resonant frequency. (c) Simulated return loss of the proposed antenna with a series of e.

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For the complementary ring resonator, the y direction is limited. Thus, the radiation directions are along the directions of x and z axis. In the directions of x and z axis, there are silver and air, respectively. Therefore, the energy is mainly focused on the directions of z axis. And it is along two directions (z and -z) of z axis, behaving two-way symmetry. The radiation patterns of the proposed antenna at 2.8 THz shown in the Fig. 5(a) agree well with this prediction of symmetry. At this frequency, the gain of the proposed antenna can reach 5.39. Figures 5(b) and 5(c) show the comparisons of radiation patterns of the antenna with and without complementary ring at the inherent frequency of 3.1 THz. The gain, radiation patterns, E-plane and H-plane of this two kinds of antennas show no significant difference. In this respect, it can also prove that the complementary ring can hardly affect the performances of the antenna at the inherent frequency.

 

Fig. 5 (a) Radiation pattern of the proposed antenna at 2.8 THz and their E-plane and H-plane. (b) Radiation patterns of antenna with and without complementary ring at 3.1 THz. (c) comparisons of E-plane and H-plane of antenna with and without complementary ring at 3.1 THz.

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4. Conclusion

We proposed a complementary ring resonator based terahertz antenna. The complementary ring resonator can stimulate the generation of a new resonant peak. The coupling of the new resonant peak and the inherent resonant peak can help the proposed antenna to get the broadband property. According to the current distribution of the resonator, the cavity resonance theory can be used to explain the relationship between parameters of the resonator and the new resonant frequency. Moreover, the consistency between simulated and theoretical calculated values demonstrates the correctness of this explanation. The inherent resonant frequency of the antenna is not influenced by the complementary ring resonator according to the behaviors in the comparisons of surface current distribution and radiation pattern. It provides a way to design the broadband terahertz antenna.