Band Broadening of Terahertz Photonic Crystals Circulator Using Two Symmetrical Hexagonal Aluminum Sheets

Abstract

Future 6G communication systems will require wideband nonreciprocal devices in the terahertz frequency domain. A novel ultra-wideband terahertz circulator is implemented by inserting a Ni_xZn_1−xFe₂O₄ ferrite sphere into the Al₂O₃ dielectric rod-array. The operating bandwidth of the circulator is broadened to 40 GHz via the external matching method through two hexagonal aluminum sheets. The three-dimensional numerical simulation suggests that the designed circulator also has an excellent insertion loss and isolation of 49.37 dB and 0.56 dB, respectively, via the finite element method. The low loss, high isolation and ultra-wideband show that the proposed scheme provides an effective path for realizing high-performance THz devices.

1. Introduction

Terahertz (THz) technology [1] has received extensive attention and been intensively studied due to its important applications in THz photonic crystal waveguides, fibers and absorbers [2,3,4], especially its potential value in future 6G communication systems [5]. With the development of high-speed communication systems, THz devices, such as isolators [6,7], detectors [8], sensors [9] and amplifiers [10], with higher operating frequencies require stricter performance parameters. Only devices with high integration and wide working bandwidth can meet the needs of future systems. Photonic crystals (PCs) have been considered as the core of integrated optical communication due to their unique ability to manipulate the motion of photons. This has been proven by flexibly using PCs to design communication devices, such as filters [11], mirrors [12,13], waveguides [14,15] and splitters [16]. This suggests that PCs have great potential in controlling the propagation of the THz waves that will be playing important roles in next-generation communication systems. When devices based on PCs transit from the one-dimensional (1D) designs [17] to two-dimensional (2D) [18], their performance makes a great leap. As a result, the fabrication of 2D PCs is more complicated than that of 1D PCs. There are two types of the 2D PC structures; as we know, one is the dielectric-rod array structure and another is the air-hole array structure. The 2D PCs based on hexagonally arranged nanocolumns have been fabricated via the porous alumina-assisted anodizing method [19]. A terahertz circulator based on a 2D magneto photonic crystal slab with triangularly arranged air holes has been developed [20].

Circulators are indispensable non-reciprocal devices in communication systems, such as high-speed data transmission, radio astronomy and high-resolution long-range radar, etc. With increasing communication frequency, the traditional circulator scheme has been unable to meet the requirements on miniaturization and high integration for future THz or optical communication systems [21,22]. The PC circulator can precisely overcome the problems of separating components and large volume of the existing scheme, so as to adapt to future needs [23,24]. Augmented with the optical local effect [25,26,27,28,29], PC devices have superior performances from THz to light wave frequency bands. In the sub-THz domain, a windmill-type PC circulator consists of a Si photonic crystal and has the highest isolation (65.2 dB) [25]. Based on square-lattice PCs, a cross-type circulator with an isolation of 30 dB is specially designed for THz systems [26]. However, the bandwidth of these two schemes is narrow (both relative bandwidths below 1%). In the optical frequency domain, a Y-type PC circulator consisting of a triangular lattice air-hole array achieves an isolation of 15 dB [27]. Similarly, based on air-hole PCs, the relative bandwidths of the other two schemes are only 0.052% (W-format) and 0.045% (windmill-format), respectively [28,29]. For the purpose of solving the problem of narrow bandwidth in the pre-existing schemes, the band-broadening method for PC circulators was tried in previous work [30], using two circular metal plates, according to the external matching broadening method (EMBM) of the traditional waveguide circulator [31,32]. The two symmetrically placed metal plates at the junction of the PC circulator work as a matcher to realize impedance matching. The bandwidth of the designed circulator is effectively stretched to 40 GHz, in which the isolator of the circulator is kept above 15 dB.

In order to further improve the performance of the PC circulator to meet the needs of the future terahertz communication systems, a novel ultra-wideband circulator is proposed here based on triangular lattice PCs and a spherical ferrite in the THz frequency domain. By employing the plane wave expansion method (PWEM), a lenient photonic band gap (PBG) from 0.11 to 0.17 THz is acquired though looking for the optimal structural parameters of the 2D Al₂O₃ PCs. Three-line defects are introduced into the PCs aiming to form a Y-typed PC waveguide, in which THz waves can transmit stably in the frequency range of the PBG. At the junction of the waveguide, two symmetrical hexagonal aluminum sheets are inserted above and below the central Ni-Zn ferrite sphere. The two sheets work as an impedance matching device to extend the bandwidth of the circulator. Not only is the impedance of the circulator coarsely tuned by changing the radius of the circumscribing circle of the two hexagonal sheets, but, also, it can be fine-tuned by rotating the angle of the hexagonal sheets. The external characteristics of the circulator simulated using the finite element method (FEM) suggest that the relative bandwidth is effectively broadened to 29.20%, covering from 0.117 to 0.157 THz. In this frequency range, the isolator in the designed circulator can be kept above 20 dB in this work, which is significantly higher than that in [30]. In addition, the insertion loss of the designed circulator is as low as 0.56 dB, while the isolation is up to 49.37 dB at 0.144 THz. It is also obvious that the other performance parameters of the circulator, including peak values of insertion loss and the isolation, are improved compared to previous results. Therefore, the proposed scheme with an ultra-wideband feature provides an effective path for realizing high-performance THz devices for future 6G communication systems.

2. Materials and Methods

2.1. Materials

The fabrication of photonic crystal materials is shown in Figure 1. Generally, three steps are required to make alumina powder with high purity of 99 percent into periodic photonic crystal structure, which are shown in Figure 1a, Figure 1b and Figure 1c, respectively. In our previous work, a four-port microwave photonic circulator was proposed and experimentally investigated based on a cross-type PC waveguide [33], which was formed by four tetragonal lattice Al₂O₃ dielectric rod arrays with a lattice constant of 12 mm, as shown in Figure 1c. The diameter Φ and height H of the Al₂O₃ dielectric rods are 2 mm and 10.16 mm, respectively. In addition, the Al₂O₃ dielectric rods also need a great surface finish, as shown in Figure 1b. The 2D magnetic–photonic crystal structure is established by inserting five ferrite posts into the junction of the cross-type PC waveguide [34]. Under an appropriate external dc magnetic field, the microwave photonic circulator obtains an excellent isolation of 30.2 dB at the X-band. In [19], the porous–alumina (PA)-assisted niobia nanostructured films of three types were fabricated through two-step anodizing. The morphology and optical properties in the UV-near-IR frequency range of the films were investigated with the aim of further possible formation of 2D PCs. The third type column-like film (CF) was obtained through the complete removal of PA. To test the applicability of the formed nanostructures as 2D PCs and to evaluate their efficiency, their optical characteristics were numerically simulated, through selecting such appropriate parameters that would make it possible to increase the efficiency of CF as a PC. Thus, as a result of simulating 2D PCs, the optimal parameters of their morphology were determined.

In this work, we still use the 99 percent Al₂O₃ powder to make triangular lattice photonic crystal structure, as shown in Figure 1a. The alumina powder with high purity above 99 percent comprises a little impurity and Al₂O₃ powder, wherein the average particle size of the Al₂O₃ powder is smaller than 50 nm. Technically, in order to make the powder in Figure 1a into the ceramic rods in Figure 1b, extrusion molding and injection molding technologies are essential. When the extrusion molding or injection molding step proceeds, binder and plasticizer need to be introduced into the powder. Generally, thermoplastic or resin organic binder with a weight ratio of 10 to 30 percent is mixed evenly with alumina powder at a temperature of 150 to 200 degrees Celsius in order to facilitate the molding operation. The size of ceramic rods for the PC structure reached the order of 100 microns due to the THz circulators working with higher operating frequency than that of microwave circulators. Thus, a higher-precision machining process is required to fabricate micron-scale photonic crystal structures for THz PC devices before the ceramic firing process.

2.2. Design of PC Circulator

In Figure 2a, the integral construction of the designed PC circulator is made up of a Y-type PC waveguide and the hexagonal matching sheets, dielectric sheaths and Ni-Zn ferrite sphere. The details of the matching sheets (purple) and ferrite sphere (green) are at the junction of the PC waveguide, as shown in Figure 2b. The ferrite sphere works as a spherical resonator, providing Faraday rotation under the external dc magnetic field. The two matching sheets can be considered as an impedance matcher, aiming to broaden the bandwidth of the circulator. Different from the circular metal plates in Figure 1 of [30], the two hexagonal matching sheets work as an impedance matcher with high matching efficiency due to the excellent electrical properties of the aluminum metal materials. It needs to be emphasized that the matcher can be fine-tuned by adjusting the size of the sheets and rotating the angle of the hexagon. In the simulation, the size of the sheets can be scaled by resizing the circumscribing circle’s radius of the hexagon.

The ferrite materials, magnetic ceramics, generally refer to composite oxides composed of iron group elements and one or more other appropriate metal elements, including soft magnetic, hard magnetic and gyro-magnetic ferrites. The spherical ferrite here chooses Ni_xZn_1−xFe₂O₄, in which a certain concentration of nickel and zinc atoms are doped in the ferric oxide. A fast fabrication method with low cost is usually used to blow ferrite balls in the process, called the compressed air blowing method [31].

Between the ferrite sphere and the two aluminous sheets, two dielectric sheaths (white) are used to fix the sphere, as shown in Figure 2c. The sheaths are made of resin materials, which has less effect on the performance of the designed circulator, owing to its low relative dielectric constant. The total height from the top hexagon sheet to the bottom hexagon sheet is expressed as h, which is exactly equal to the distance of the upper and lower boundary.

2.3. Ultra-Wideband PBG of the PCs

For easier identification of the parameters, the plane graph of the PC structure and the details of the circulator’s junction are shown in Figure 3. In Figure 3a, the three arms of the PC waveguide are expressed as Port 1, Port 2 and Port 3. The PC waveguide is formed by a triangular lattice Al₂O₃ rod array (blue) with three line defects, and the lattice constant of the PCs is marked as a with a value of 0.87 mm in Figure 3b. The value of the lattice constant of the PCs here is same as the previous design in Figure 2 of [30]. The radii of the two dielectric sheaths, the Al₂O₃ rods, the circumscribing circle of the two hexagonal sheets and the ferrite sphere are labeled as r₂, r₀, r₁ and R, respectively. In the simulation, the height of the Al₂O₃ rods is 0.83 mm, and they are fabricated by high-purity alumina with relative permittivity of 9.2, as shown in Figure 1a, mentioned above. The height and width of the line defects are 0.83 mm and 1.66 mm, which is the optimal size according to the standard size of the H-plane rectangular waveguide WR7.

Based on the structural parameters of the PCs, including r₁ = 0.79 mm and r₂ = 0.87 mm, the frequency regime of the PBG is simulated via PWEM with the Bandsolve module in Rsoftware, as shown in Figure 4, which is same as that in [30]. The fan-shaped area (red) in Figure 4a is the PBG, which has different bandwidth with increasing r₀. When r₀ reaches 0.19a, shown in Figure 4b, the broadest PBG with a gap ratio of about 43% is obtained. The corresponding lenient frequency domain covers from 0.11 to 0.17 THz, with a = 0.87 mm, as mentioned above. The numerical results suggest that the PBG of the PCs is significantly affected by the structural parameters of the PCs, and the width of the PBG is decided by the relationship between the radius r₀ of the rods and the lattice constant a. Thus, the center frequency of the transmission line can be flexibly adjusted by changing the ratio of r₀/a, in order to adapt to the requirement of the increasing frequency band for future communication systems. In theory, the signals with these frequencies within the PBG can be ideally transmitted from the sender to the receiver.

3. Numerical Results for the Designed THz PC Circulator

3.1. Theoretical Model of PC Circulator

The external characteristics of the PC circulator are numerically calculated using FEM according to the following wave equation with permeability tensor [μ_r]:

$${\epsilon }^{-1}·\nabla \times \left({\left[{\mu }_r\right]}^{-1}·\nabla \times \overrightarrow{E}\right)={\omega }^2/c^2·\overrightarrow{E}.$$

(1)

In THz frequency domain, the gyromagnetic characteristic of ferrite magnetized by the external DC magnetic field H₀, can be expressed as tensor permeability [μ_r], as in [6], in which a compact magneto-optical isolator based on the ferromagnetic resonance absorption effect was designed for 5G communication systems. For a spherical THz resonator, the permeability tensor [μ(r, θ, φ)] can be calculated through the matrix [T]:

$$\left[\mu \left(r,\theta ,\phi \right)\right]=\left[T\right]\left[{\mu }_r\right]{\left[T\right]}^{-1}$$

(2)

where

$$\left[T\right]=\left[\begin{array}{ccc}\mathit{sin} \theta \mathit{cos} \phi & \mathit{sin} \theta \mathit{sin} \phi & \mathit{cos} \theta \\ \mathit{cos} \theta \mathit{cos} \phi & \mathit{cos} \theta \mathit{sin} \phi & -\mathit{sin} \theta \\ -\mathit{sin} \phi & \mathit{cos} \phi & 0\end{array}\right]$$

(3)

For convenient simulation, the permeability tensor of the ferrite material is represented as an inverse matrix [μ(r, θ, φ)]⁻¹ without φ, as follows:

$${\left[\mu \left(r,\theta ,\phi \right)\right]}^{-1}=\frac{1}{{\mu }_0\left({\mu }^2-{\kappa }^2\right)}\left[\begin{array}{ccc}\mu {\mathit{sin}}^2 \theta +\left({\mu }^2-{\kappa }^2\right){\mathit{cos}}^2 \theta & \left({\kappa }^2-{\mu }^2+\mu \right)\mathit{sin} \theta \mathit{cos} \theta & -j\kappa \mathit{sin} \theta \\ \left({\kappa }^2-{\mu }^2+\mu \right)\mathit{sin} \theta \mathit{cos} \theta & \mu {\mathit{cos}}^2 \theta +\left({\mu }^2-{\kappa }^2\right){\mathit{sin}}^2 \theta & -j\kappa \mathit{cos} \theta \\ j\kappa \mathit{sin} \theta & j\kappa \mathit{cos} \theta & \mu \end{array}\right]$$

(4)

where μ and κ are the diagonal element of the permeability tensor [μ_r]. For the THz ferrite sphere PC circulator, the relationship between the resonant frequency of the spherical resonator and its size is given in [30]:

$$R=\frac{1.732c}{\left(\pi f\sqrt{{\epsilon }_r}\right)}$$

(5)

where R and ε_r are the radius and relative permittivity of the spherical ferrite, respectively. Depending on Equation (5) above, the radius of the spherical resonator can be calculated with a central frequency of 0.14 THz in the PBG, which is the atmospheric communication window with lower loss. It is important to develop photonic crystal devices at this frequency band, which will be the working frequency of the 6G communication systems in the future.

3.2. Numerical Simulations and Results

The transmission of the THz signals for the PC devices is usually researched via FEM in the frequency domain with the software Comsol Multiphysics. The height of 0.83 mm and radius r₀ of 0.16a for the Al₂O₃ rods are the same as those in Section 2.3. The power distributions in the operating circulator are simulated with the parameters of ε_r = 13.5, R = 0.23 mm, r₁ = 0.79 mm and r₂ = 0.87 mm, as shown in Figure 3. At the central frequency of 0.144 THz, the THz wave incident at Port 1 is deflected 120° through the ferrite region and output from Port 2, as shown in Figure 5a, while Port 3 is isolated.

Similar situations of signal incident at Port 2 or Port 3 will not be repeated here. Under the dc magnetic field H₀ of 4.9 × 10⁶ A/m, the THz wave takes place frequency splitting at the spherical ferrite area. When the composite wave moves away from the ferrite, there is a Faraday rotation of 120 degrees in the direction of propagation, as mentioned above in Figure 5. The simulation results clearly show the transmission path of the THz wave in the designed circulator. It is obvious that the impedance of the circulator can not only be coarse-tuned by changing the radius of the circumscribing circle of the two hexagonal sheets, as in [30], but can also be fine-tuned by rotating the angle of the hexagonal sheets.

4. Discussion

In order to broaden the bandwidth of the circulator, two metal plates are usually introduced into the junction of a waveguide circulator called EMBM [31]. In the previous work [31], two circular aluminum matching plates are introduced into the junction of the circulator to broaden the operating bandwidth. Here, we insert two hexagonal aluminum sheets sandwiching the ferrite sphere to modulate the impedance of our designed PC circulator. To secure the spherical ferrite exactly, two dielectric sheaths (resin material) are placed between the ferrite sphere and the hexagon sheets. It can be seen that the optimal placement and angle of the hexagonal matching sheets are shown in the central detail diagram in Figure 5b. By fine-tuning the angle of the hexagonal sheets, the circulator is working in the optimum state when one of the six sides of the hexagon is perpendicular to the direction of the transmission line. If two circular metal plates are used for impedance matching, as in reference [32], the external performances of the designed circulator cannot be optimized by fine-tuning the angle of the matching plates, like the hexagonal aluminum sheets in this work. A side view of the power distribution for the operating PC circulator is shown in Figure 5c. An interesting phenomenon is discovered, in that the power is evenly distributed in both hemispheres of the ferrite sphere (red dashed line), as shown in Figure 5d.

As we know, the S parameters are generally used to measure the external characteristics of the circulator. When the THz signal was incident at the input port, we checked the power of the other two output ports. For example, when Port 1 is the energy input port, the transmission, isolation and reflection characteristics of the PC circulator correspond to S21, S31 and S11, respectively, which are computed with the increasing frequency from 0.11 to 0.17 THz, as shown in Figure 6.

In Figure 6a, the curves of the parameters S21 and S31 change with the frequency. At a resonant frequency of 0.144 THz, the lowest insertion loss (S21) is 0.56 dB and the highest isolation (S31) is 49.37 dB, which is better than that in [32] by using two circular metal plates. It is obvious that our circulator’s bandwidth is assuredly extended to 40 GHz, which covers from 0.117 to 0.157 THz with isolation below −20 dB. The relative bandwidth reaches 29.20%, exceeding the ultra-wideband level of 25%.

The reflection (S11) of the PC circulator is also studied by analyzing the Smith chart, as shown in Figure 6b. Adjusting the radius of the circumscribing circle of the two hexagonal sheets makes the circulator match well. The impedance of the circulator can be further fine-tuned by changing the angle of the hexagon sheets to perfectly match at the interesting frequency. The numerical results show that the designed PC circulator achieves perfect matching with a central frequency of 0.144 THz, corresponding to a value of 1 in the center of the Smith’s circle diagram in Figure 6b. It means that the reflection efficiency of input Port 1 at the center frequency is essentially zero.

5. Conclusions

In conclusion, the International Telecommunication Union proposed the promotion of 6G wireless communication systems in the THz band as early as 2019. Non-reciprocal passive devices including a circulator are indispensable components in communication systems. In order to meet the increasing communication needs in the future, a novel three-port Y-type ferrite sphere PC circulator with ultra-wide operating bandwidth is implement based on a 2D triangular lattice A₂O₃ rod array in the THz band. The PCs consist of triangular lattice Al₂O₃ rods, with high purity of 99 percent. The Al₂O₃ PCs with an ultra-wideband PBG of 0.11 to 0.17 THz are analyzed via PWEM. A Y-type PC waveguide is formed by introducing three line defects in the PCs. Our circulator is designed by inserting a spherical ferrite in the junction of the waveguide. By using EMBM, the bandwidth of the circulator is assuredly extended to 40 GHz, owing to two hexagonal aluminum sheets. The numerical simulations suggest that the designed circulator also has an excellent insertion loss and isolation of 49.37 dB and 0.56 dB, respectively, at a resonant frequency of 0.144 THz through FEM. The low loss, high isolation and ultra-wide bandwidth show that the proposed scheme provides an effective path for realizing high-performance 6G or THz devices for easy integration.

As a result of the work, the following points emerged:

• In order to improve the bandwidth of the PC circulator to meet the needs of the future terahertz communication systems, a novel ultra-wideband circulator is proposed by using two hexagonal metal sheets. Not only is the impedance of the circulator coarse-tuned by changing the radius of the circumscribing circle in the two hexagonal sheets, but it also can be fine-tuned by rotating the angle of the hexagonal metal sheets in the junction.
• Through adjusting the proportional relationship between the radius of the dielectric rods and the lattice constant to be 0.19, the PBG is optimized to be 0.11 to 0.17 THz via PWEM for the Al₂O₃ PCs.
• The transmission of the THz signals for the PC circulator is simulated through FEM in the frequency domain of the PBG. At a central frequency of 0.144 THz, the transmission path of the THz wave is investigated in the designed circulator, and the power is evenly distributed in both hemispheres of the ferrite sphere.
• When one side of the hexagon is perpendicular to the direction of propagation of the signal, the bandwidth of the circulator is assuredly extended to 40 GHz by using EMBM, in which the peak values of the insertion loss and isolation are 0.56 dB and 49.37 dB, respectively.

In this work, we focus on broadening the operating bandwidth of the designed PC circulator by inserting two metal sheets in the junction of the Y-type waveguide, called the external matching broadening method. It needs to be emphasized that the impedance of the circulator can be fine-tuned by rotating the angle of the hexagonal sheets in order to achieve the perfect matching state. As for the designed circulator, it should also be noted that the manufacturing process of the ferrite balls has the characteristics of high convenience and low cost by using the press-and-blow method. Thus, the design scheme in this work using spherical ferrite will be a great potential alternative to the existing program for mass production.