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Abstract
This study presents, what we believe to be, a novel approach to enhance the spectrum of extraordinary terahertz transmission utilizing surface plasmon polaritons (SPPs) mode coupling in metal-dielectric compound annular hole array metamaterial. The transmitting properties of the structure are thoroughly assessed through a combination of theoretical analysis and numerical simulation, with a particular focus on understanding the surface plasmon mode coupling. Our investigation revealed the presence of propagating surface plasmon polaritons (PSPP), localized surface plasmon resonance (LSPR) and Fabry-Perot (FP) resonances within the compound layer. We find that the coupling of PSPP and LSPR modes plays a crucial role in determining the broadband nature of the structure. Interference theory is utilized to mitigate the FP resonance, while further optimization of the transmission bands is attained by implementing the impedance matching hypothesis. By adjusting the structure parameters, the effective coupling of the SPPs modes and numerous reflections in the dielectric cavity produced a remarkably smooth and transparent character, leading to a significant enhancement of transmission spectrum and a reduction in the incident loss of terahertz wave.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Terahertz (THz) high-transmission metamaterials have attracted much significant attention in recent decades, owing to their potential applications in diverse fields such as semiconductors, biology, medicine, communications, defense, and security [1–8]. These versatile metamaterials play a crucial role in advancing the development of highly sensitive sensors and photodetectors [9–11], enabling breakthroughs in fields such as biomedical imaging and wireless communications. To further improve the capabilities of terahertz metamaterial devices for filtering, sensing, and detection applications, it is crucial to achieve higher transmittance and broader transmission bandwidth simultaneously. However, balancing between wideband operation and high transmission poses a significant challenge in the practical design of these devices. Consequently, extensive research has been dedicated to exploring multiple approaches and optimizations to broaden the bandpass of Frequency Selective Surfaces (FSS), opening up possibilities for even more versatile and efficient THz metamaterial-based devices [12–14]. Das introduced a ring-shaped FSS device and improved its performance by optimizing the equivalent capacitance and inductance values [15]. Abad developed a third-order bandpass FSS with a multi-layer complementary pattern stacking approach, leveraging an analysis of an equivalent circuit model [16]. Ferraro proposed a cyclic FSS array featuring cross-shaped holes and optimized its bandwidth by adjusting the diffraction order using the guided mode resonance (GMR) theory [17]. Cai proposes a terahertz FSS based on low-loss flexible materials, which shows that low-loss materials can help widen the passband [18].
In addition to the mentioned methods, manipulating the coupling between surface plasmon polaritons (SPPs) modes of metamaterials offers a promising avenue to achieve higher transmittance and broader transmission bandwidth in the terahertz band. Initially, a surface-wave metamaterial based on metal hole arrays was reported in [19], in which THz transmission relied on the propagating surface plasmon polaritons (PSPP). Subsequent efforts to enhance transmittance included modifying the hole configuration, the refractive index of the surrounding medium, and the incident angle of the incident wave [20–23], which were limited to a certain frequency range, had a narrow bandwidth, low peaks, and wave troughs. Studies in infrared provided an effective reference to broaden the bandwidth of terahertz transmission [24–26]. Combining periodic hole and column arrays enabled the coupling of PSPP and localized surface plasmon resonance (LSPR), which dramatically improved the transmission amplitude [27–30]. The metal-dielectric multilayer configuration overcame the narrow-band limitation of standard single-layer hole structures and improved the transmission bandwidth further [31–39]. Qi introduced a metal-dielectric-metal (MDM) terahertz metamaterial that exhibited an improved transmission bandwidth by leveraging multiple resonances between two ring apertures [40]. Xiao proposed a bandpass multilayer frequency selective surface (FSS) and analyzed the Fabry-Perot (FP) resonance from the perspective of multipath interference, demonstrating the impact of destructive interference on the passband [41]. However, effectively couplin PSPP, LSPR and other resonances remains a challenging task.
In this study, we propose a novel approach to enhance the spectrum of extraordinary terahertz transmission by exploiting the coupling of SPPs in a metamaterial consisting of a compound annular hole array in metals and dielectrics. To achieve this, we utilize the multiple interference theory (MIT) to suppress the Fabry-Perot (FP) resonance peak and widen the transmission band by adding a matching layer based on the impedance matching theory. Through optimization, the structure was able to achieve a transmittance of above 80% across a wide frequency range from 1.04 to 2.26 THz. The effectiveness and versatility of our methodology in optimizing various etched pattern structures have also been validated through a comprehensive examination of its key parameters and characteristics. This approach is useful in applications such as wide spectral band detectors. Moreover, the broad spectrum and high transmission characteristics in the THz band make it a promising technology for a variety of applications, including biological detection, radar, and wireless communication systems.
2. Modeling
The structural diagram of the MDM compound metamaterial is shown in Fig. 1, in which annular holes are etched symmetrically and periodically on both the top and bottom metal layers. The periodic ring hole arrays in the bilayer metal film excite the PSPP, while LSPR is triggered around the metal pillars. The radius of the external ring and inner ring is denoted as R and r. The thickness of the metal film and the dielectric are represented by D and d, respectively. The simulation area size is set to 3D layout, and the x and y-directions are set to periodic boundary conditions. The lattice period of the array is denoted as p. The z-direction is set to perfect matching layer (PML) boundary condition. Silver (Ag) is considered the metal material, and its permittivity in the THz range is described using the Drude model:
Fig. 1. (a) Schematic diagram of the proposed metamaterial array structure. (b) Schematic diagram of cell configuration : d = 25 µm, D = 1 µm, r = 19 µm, R = 40 µm, and p = 84 µm.
The transmittance, electromagnetic field distribution, and current density of the metamaterial are calculated using the finite-difference time-domain (FDTD) method. To guarantee the accuracy and convergence of the simulation, the structure is discretized into a mesh with a size of 0.5µm*0.5µm*0.1µm. The TE polarized incident wave, with a frequency range of 0.5-2.5 THz, propagates along the negative z-direction with the electric field polarization in the x-direction. The practical design and optimization based on the subwavelength array structure will be illustrated below.
3. Analysis and discussion
3.1 Spectral response
The transmission spectrum of terahertz wave at vertical incidence is shown in Fig. 2. The spectrum exhibits two distinct bandwidths, with widths of 0.24 THz and 0.14 THz, respectively, and average transmissivity over 80% centered around f1 = 1.18 THz and f2 = 1.82 THz. The peak transmittance in both bandwidths exceeds 90%, while the transmittance trough between f1 and f2 is over 60%. It is noticed that a narrow band peak at f3 = 2.06 THz produces a sharp drop in the spectrum, which is not favorable for broadband transmission.
To refine the THz transmission spectrum further, we clarify the resonance mechanism of this structure by employing numerical simulations at three frequencies: f1 = 1.18 THz, f2 = 1.82 THz, and f3 = 2.06 THz, which correspond to the observed transmission peaks in the spectrum. Song has demonstrated all the resonant modes of these peaks from the perspective of dispersion [43]. In this paper, our analysis revolves around the dominant resonance mode observed at the transmission peak, with a specific focus on studying its characteristics through field distribution. The electric and magnetic fields that were normalized and visualized using logarithm log (|E/E0|2) and log(|H/H0|2), the energy flow density P, and the current density log(J) were illustrated in Fig. 3.
Fig. 3. TE calculated field distribution (a1-c1) log(|E/E0|2), (a2-c2) log(|H/H0|2), (a3-c3) energy flow density P, and (a4-c4) current density log(J) at 1.18 THz (first column), 1.82 THz (middle column), and 2.06 THz (last column).
At f1 = 1.18 THz (first column) as depicted in Fig. 3(a1), a prominent concentration of the electric field is observed in the air etching region between the metal column and the metal spacer interface. This phenomenon arises due to the interaction between the incident THz wave and the free electrons in the structure. When the transverse wave vector on the surface of the MDM structure aligns with the THz wave vector, it leads to the propagation of charge density waves known as PSPP on the surface [44]. The strong electric field presence is a direct consequence of the PSPP phenomenon. In Fig. 3(a2), the distribution of the magnetic field on the surface of the upper and lower metal layers is evident. It is noteworthy that the overall strength of the magnetic field appears to be relatively weak. The energy flow density depicted in Fig. 3 (a3) is predominantly distributed between the surface of the metal layer, aligning with the interface propagation characteristics of PSPP.
At a frequency of f2 = 1.82 THz, the electric field exhibits a concentration of intensity specifically at the edge of the metal column, as depicted in the middle column of Fig. 3(b1). Strong electric field coupling is observed between the upper and lower metal columns. Such behavior can be attributed to the presence of LSPR within the metal column. When the metal column is much smaller than the incident wavelength, it acts like an isolated metal particle. At this point, LSPR occurs when the incident wave frequency matches the particle natural frequency of oscillation [44]. In particular, when two isolated metal particles are in proximity, and their LSPR frequencies match, they interact and trigger resonant coupling. In Fig. 3(b2-b3), the local magnetic field and energy flow density between the metal columns are observed significantly coupled and enhanced, indicating the presence of LSPR at the upper and lower surfaces. This resonance further amplifies the interaction between the metal columns, contributing to the observed strong field coupling at f2.
When f3= 2.06 THz (last column), compared with Fig. 3(b2-b3), the electric field at the surface etch and the magnetic field between the upper and lower metal columns weaken, as shown in Fig. 3(c1-c2). At the same time, the electric field energy is evenly distributed in the medium cavity inside the structure, which is consistent with the distribution characteristics of FP cavity resonance, as shown in Fig. 3(c3). The current distribution in Fig. 3(a4-c4) can also show the characteristics of SPPs at different frequencies. Compared with the resonant characteristics of PSPP and LSPR, the current intensity between metal layers is significant when FP resonance occurs in the structure, indicating that considerable charge is collected in the medium cavity during FP resonance.
3.2 FP resonance suppression using multiple interference theory
As mentioned in the previous section, the FP resonance resulted in the formation of a detached transmission band, which narrowed the transmission curve. To attenuate these adverse effects, we suppress the FP resonance using MIT [45]. The basic principle of MIT is shown in Fig. 4(a1), which is to calculate total transmittance by direct reflection (transmission) of terahertz waves in a structure and multiple internal reflections. In the theoretical calculation, we consider terahertz waves entering the dielectric layer through a monolayer metal interface from the air, and then entering the air through a monolayer metal layer from the dielectric layer interface, as illustrated in Fig. 4(a2-a3).
Fig. 4. (a1) MIT transmission schematic diagram based on MDM structure. (a2-a3) Decomposed structure transmission optical path schematic. (b-c) The transmissivity and phase of transmission obtained by MIT calculation and simulation.
In this section, we focus on the contributing factors of the third transmittance peak f3 by analyzing the phase delay in the cavity. To do so, the reflection coefficient r and transmission coefficient t of the MDM structure was described by the following semi-analytic Eqs. (2) and (3).
The phase delay curve of the wave after multiple reflections in the cavity is described in Fig. 5(a). FP resonance phenomenon is highly dependent on the cavity phase, which represents the phase delay experienced by the wave inside the FP cavity. At the frequency f3, the phase delay of the resonator is approximately 2π, and generated a constructive interference FP resonance that forms a transmission peak. As the cavity phase is directly related to the propagation distance of the wave inside the cavity, it is possible to control FP resonance by adjusting the Pi thickness, which corresponds to the propagation distance of the wave between the two mirrors of the FP cavity. To suppress FP resonance in the multilayer structure, we have scanned the thickness of the medium layer, as shown in Fig. 5(b). It is seen that when the thickness of the medium layer d is set to 19 µm, the phase delay around f3 deviates from integer multiples of 2π, effectively inhibiting the emergence of FP resonance, as demonstrated in Fig. 5(c). To clarify the following optimization procedure, we define the original design before MIT optimization as step 1, and the MIT optimization as step 2. Notably, this change has a negligible effect on the position of the f1 and f2 transmission peaks, which remain dominated by PSPP and LSPR, respectively. Moreover, this approach extends the operating bandwidth of the structure without compromising its spectral selectivity.
Fig. 5. (a) Phase delay curve of the optical wave reflected through the cavity multiple times. (b) Parameter scanning of dielectric layer thickness. (c) Transmission spectrum of the MDM structure before and after the suppression of FP resonance.
3.3 Spectrum optimization by impedance matching
While the transmission band generated by FP resonance was suppressed by MIT, there still exists a transmission trough between the f1 and f2 transmission peaks in the spectrum. To improve the transmittance of transmission trough, the reflection of the incident wave should be minimized further. According to impedance matching theory [47], achieving this requires matching the structural effective impedance to the free-space impedance. The impedance matching optimization is defined as step 3. The detailed analysis process is provided below.
According to Smith's research [48,49], the effective impedance of the structure is expressed in terms of the scattering parameters:
where S21, S12, S11, and S22 are the scattering parameters. S21 and S12 denote the forward and backward transmission coefficients, while S11 and S22 are the forward and backward reflection coefficients, respectively. The reflectance and transmittance of the structure can be expressed by the effective structure impedance in Eq. (5).Fig. 6. (a) The structure diagram of step 2. (b1-b2) Effective parameters before effective impedance optimization. (c) The structure diagram of step 3. (d1-d2) Effective parameters after effective impedance optimization.
Based on the above ideas, we attempted to make the real part of the Zeff and neff of the metamaterial converge to 1 by loading two dielectric layers (thickness denoted by L) on the upper and lower metal surfaces, as shown in Fig. 6(c). Additional dielectric layers can improve the impedance matching between the MDM structure and free space, as well as reduce the reflection of the structure into free space [50]. This results in higher transmission in the passband. Considering the dielectric loss, the material used for the additional dielectric layer was defined to be identical to the inner dielectric layer. By comparing Zeff diagrams of the two structures shown in Fig. 6(b1, d1) and taking the vicinity of 1.6 THz as an example, it can be observed that the peak value of the real part of Zeff increases from 0.45 to 0.65 as the thickness L reaches 25 µm, bringing it closer to 1. Meanwhile, the real part of neff around the trough also gradually approaches 1, while the imaginary part remains close to 0 (see Fig. 6(b2, d2)). Through scanning the thickness of the additional dielectric layers, it is seen that L = 25 µm did achieve a great impedance match between the structure and free space. This resulted in a flattened and broadened transmission spectrum, as demonstrated in Fig. 7.
Fig. 7. (a) Parameter scanning for additional dielectric layer thickness L. (b) Transmission spectrum before and after effective impedance matching optimization.
3.4 Structural parameters analysis
The effects of various configuration parameters, such as period, the radius of the inner and external ring, and the thickness of the Pi layer, were examined in the following discussion, as shown in Fig. 8. The optimized transmission spectrum parameters are indicated by dotted lines. To clearly illustrate the transmission properties observed in Fig. 8, we have designated three distinct transmission peaks at 1.1 THz, 2 THz, and 2.4 THz as the “PSPP peak,” “LSPR peak,” and “FP peak,” respectively, based on the predominant resonance modes associated with each peak.
Fig. 8. The transmission spectrum is based on the variation of structural geometric parameters (a) Period, (b) Externa radius, (c) Inner radius, and (d) Pi Thickness.
The transmission spectrum for various lattice period p is depicted in Fig. 8(a). With the increasing of p, the spacing between cells increases, which affects the transmission of PSPP and causes a blueshift of the PSPP peak. Once p deviates from the optimized value, the FP peak emerges since the FP resonance condition is reached again. The decline of external radius R of the air ring hole causes a redshift of the PSPP peak since a reduction of R is accompanied by an indirect increase in the lattice period. Meanwhile, the amplitude of the trough increased, as shown in Fig. 8(b). Compared to Fig. 8(a), the change of R and p exerts the reverse effect on the PSPP peak while having a trivial effect on the LSPR peak. The LSPR is vulnerable to the size of the metal pillar, as displayed in Fig. 8(c). The decrease in r results in a remarkable redshift and damping of the LSPR peak. According to the interference theory, the change of the metal pillar radius would alter the cavity resonance space, and impact the indirect transmission value. Consequently, the FP resonance is also sensitive to r. As depicted in Fig. 8(c), it is evident that variations in the radius r lead to the generation of a transmission peak corresponding to the FP resonance mode. Similarly, the thickness of the intermediate dielectric layer d dominates the cavity resonance and would be prone to trigger FP resonance, as illustrated in Fig. 8(d). With the increase of the d, the coupling between the top and bottom metal columns weakens, and the transmission peak generated by LSPR is redshifted and weakened.
3.5 Polarization and incidence angle dependence
To assess the metamaterial's performance, we also consider the polarization angle and incident angle dependencies of the structures, as illustrated in Fig. 9. Owing to the periodic and symmetric performance of the metamaterial arrays, the polarization interval of [0, 90] would denote the influence related to the overall arbitrary polarization. Scanning the polarization angle of the incident wave reveals that the transmission spectrum remains almost unchanged, indicating the polarization stability of the array (Fig. 9(a)). While the incident angle of the wave exerts a prominent effect on the transmission spectrum. As the incidence angle increases, there is a trivial blueshift on the first transmission band, while the second transmission band is split into many narrow transmitting bands, as shown in Fig. 9(b). This behavior arises due to the susceptibility of the metamaterial, with a lattice period size close to the wavelength size, to diffraction. According to the diffraction theorem, an increase in the incidence angle promotes higher-order diffraction [51]. Consequently, the near-vertical incidence of the wave yields the best performance for the structure.
Fig. 9. Transmission spectrum of the structure at (a) different polarization angles, and (b) different incidence angles.
3.6 Application of optimization method
This approach also has a good potential for improving the spectrum of metamaterial-based devices with different etching patterns, as long as they have the same type of resonant coupling. We implemented this technique on metamaterials with square and hexagon etching patterns, as illustrated in Fig. 10(a1-a2). When maintaining a constant metal thickness and period, the optimized thickness of the upper and lower dielectric layers for the square loop array composite structure is 23 µm, and the thickness of the dielectric medium layer is 27 µm. Similarly, the optimized thickness of the upper and lower dielectric layers for the hexagonal loop array composite structure is 30 µm, with a middle dielectric layer thickness of 26 µm. The simulation results demonstrated that the spectrum of extraordinary terahertz transmission of the metal-dielectric multilayer compound square loop array and hexagon loop array structures are significantly improved, see Fig. 10(b1-b2). Specifically, the transmittance within the frequency band of 0.92-2.04 THz for the square loop array exceeds 80%, with a maximum transmittance of 95%. Similarly, the optimized bandwidth of the hexagon loop array exceeds 80% within the frequency band of 1.22-2.00 THz, with a maximum transmittance of 90%.
Fig. 10. (a1) Diagram of square loop structure, and (a2) Diagram of the hexagonal loop structure. (b1) The simulation result of square pattern after optimization, and (b2) The simulation result of hexagonal pattern after optimization.
While this study presents a promising approach to enhancing the performance of passband frequency selective surfaces, there are still some limitations including the manufacturing challenges and constraints related to the physical properties of the materials. The realization of complex micro-nano scale structures, such as multi-layer annular hole terahertz arrays requires more precise processing conditions. Ensuring the alignment of the upper and lower layers, as well as accurately controlling layer spacing, often requires specialized equipment and expertise. Furthermore, the transmission loss of terahertz waves in thick dielectric materials, such as absorption and scattering, and high-order diffraction under high-angle oblique incidence, can introduce additional challenges and affect the overall performance of the metamaterial.
Based on the findings of this study, we are motivated to pursue further research by exploring the integration of the proposed metamaterial with other functional components or hybrid structures, with a specific focus on incorporating phase change materials. Phase change materials, like vanadium dioxide (VO2), exhibit the remarkable ability to dynamically control their optical properties through reversible phase transitions. By integrating these materials with the proposed metamaterial structure, we can develop multifunctional tunable broadband terahertz devices, granting us dynamic control over terahertz transmission characteristics, including the capability to tune the transmission frequency or adjust the bandwidth [52–56]. This dynamic control opens up new possibilities for applications in terahertz communications, spectroscopy, imaging, and sensing, where adaptability and tunability are highly desirable
4. Conclusion
We proposed a novel method that utilizes SPPs to enhance the spectral characteristics of extraordinary terahertz transmission in a metamaterial consisting of metal-dielectric compound annular holes array. Through the combination of theoretical analysis and numerical simulation, the presence of PSPP, LSPR and FP resonances in the composite structure was revealed, and the coupling between LSPR and PSPP plays a critical role in determining the broadband characteristics of the structure. Interference theory is applied to alleviate the impact of FP resonance, while the impedance matching hypothesis can further enhance the transmission band. The combination of these techniques significantly improves the quality and efficiency of wave transmission. This approach is verified in square and hexagon etched surface patterns, which have demonstrated the effectiveness of these techniques in optimizing wave transmission. These findings hold great promise for practical applications, particularly in fields such as bio-detection, radar technology, and wireless communication systems.
Funding
National Natural Science Foundation of China (No.62101476).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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