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Abstract
An ultra-thin single band metamaterial (MTM) based perfect absorber with suppressed higher order absorption modes is presented in this paper. The unit cell structure is comprised of square shaped resonant patch whose sides are attached to interdigitally coupled fingers providing strong cell to cell electromagnetic coupling, which is found to have a significant impact in reducing the effect of higher order absorption modes. The structure is designed to operate in terahertz (THz) regime with a perfect absorption band centered at 1.61 THz. The absorption behavior is computationally studied and thoroughly analyzed using full wave simulations as well as circuit model approximation. The proposed structure exhibited remarkable characteristics such as polarization insensitivity, high absorption level over wide range of incident angles for both TE and TM polarizations and very weak excited higher order bands for TM polarized wave. In addition to that, it is capable to detect thin layers analyte overlays with sensitivity of 550 GHz/RIU. The absorber is very compact, where the overall thickness is about 1.67% of the wavelength at resonance. Furthermore, it could be viewed as continuous medium since the achieved cell size is around 0.1 times the operating wavelength. The absorber has the potential to be utilized in removing the unwanted peaks in thermal emission and detection as well as in rejecting unwanted modes in resonant structures such as accelerating cavities. It also might be applied to other classes of resonant structures.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metamaterial structures are composites of sub-wavelength resonant elements arranged in periodic fashion that are mutually interacting with the applied electromagnetic (EM) fields [1,2]. In General, these sub-wavelength size features are much smaller than the wavelength of incident wave. Therefore, MTM structures behave as a homogeneous medium such that their properties can be described by their effective constitutive parameters [3,4]. Due to the easiness and flexibility of manipulating the properties of the resonant elements, such as material type, dimensions, and arrangement …etc., exotic phenomena and unique material characteristics could be created, which are far superior over the existed ordinary conventional materials. This includes negative index of refraction (NIR), backward propagation and reversal of Snell’s law. Thus, MTMs have been intensively engaged in widespread electromagnetic components, such as; antennas [5], filters [6], sensors [7,8], light detectors [9], invisibility cloaks [10] and many other devices. They can be engineered to operate at any wanted frequency regime depending on the desired applications, whether in industrial, medical or military fields. MTM inspired absorbing structures have been gaining a great attention amongst the research community. Such structures are designed to possess single band [11], multi-band [12,13] or wide band [14,15] absorption over GHz [16], THz [17] or optical [18] frequency regimes. In contrast to most MTM based components, absorbers are high loss resonant structures such that the applied EM energy is totally trapped and transformed into heat [19]. Several efforts have been reported in demonstrating the absorption mechanism using circuit theory [20,21], interference theory [22] and effective medium theory [23]. In THz frequencies, absorbers have interesting applications in imaging, sensing biological [24], chemical materials [25] and drugs as well as THz spectroscopy [26]. Narrow band type absorbers are intensively employed in sensors to sense analyte materials based on their refractive index. Also they are exploited in the detection of substances that have unique spectral signature such as explosives. Typically, MTM absorbers possess higher-order resonances [3] due to the inherited nature of the resonant elements. These resonances are usually uncontrollable and occur at multiples of the fundamental frequency. However, they are advantageous in designing wideband [27] and multi band [28] absorbing structures. In addition to that, higher order modes are excited when the impinging wave is obliquely incident at the absorber surface [29,30]. These higher order frequencies are observed in some particular applications such as thermal emitters [31]. Large unwanted peaks are exhibited in the emissivity wavelength range. The peaks in the spectra are undesirable and must be mitigated. The proposed absorber can be exploited to remove the unwanted peaks and produce selective thermal emission.
Recently, MTM based absorbers have been integrated to remove unwanted modes in resonant structures such as accelerating cavities [32]. They are used as damping elements [33] for the undesired different modes in microwave cavities. The problem of beam instabilities or power losses may rise if the higher order modes exist in the resonant cavities. Therefore, the mitigation of spurious resonance effects is essential to accomplish high quality particle beams. This promising technology opens the door to extend the investigation at higher frequencies up to the sub-mm wave and THz regions. Because of the fact that terahertz radiation has short wavelength, there is insufficient available technology to use terahertz radiation to enhance particle energies in accelerators. Cavities in a terahertz accelerator are considerably compact in size, which is capable to produce particle pulses a thousand times shorter than conventional copper structures [34]. Yet, researchers are now developing both electron beam and laser based terahertz generation to deliver the high powers needed in the next-generation X-ray lasers and electron microscopes. These beams could be projected for cancer treatment. As a result, to achieve higher particles beam stability and energy boosting, higher order modes must be avoided. In this work, absorption bands caused from higher order modes are significantly reduced by means of incorporating strong cell to cell magnetic coupling. The strong interaction is accomplished by using interdigitally coupled resonators linking between the adjacent neighboring cells. The organization of this paper is as follows: section two reviews the design of a common MTM absorber based on square shaped patches and presents the geometry of the proposed design. Section three conducts a profound discussion and analysis of the main results in great details. Finally, the major findings are concluded in section four.
2. Absorber structure geometry
2.1. Square shaped patch absorber
It is commonly known that metamaterial inspired absorbers are basically a 3-layred structures; conductor-dielectric-conductor, where a dielectric spacer is sandwiched between two conductive layers; a bottom ground plane and a top array of conductive periodic pattern. Pattern’s shape, size and arrangement are all playing a key role in determining the absorption characteristics. One simple shape that is widely utilized in building metamaterial absorbers is the square shaped patch resonator. It is easily optimized and scaled to operate at different frequency regimes. To highlight the importance of the work presented in this paper, the performance of a square shaped patch absorber design is firstly studied. This structure has been broadly inspected in literature and exploited to operate at various frequency bands, especially at THz regime. Fig. 1(a) depicts the structure’s top view of a square shaped patch array. The width of each patch is $W = 42\; $µm and thickness of ${t_g} = 0.4\;$µm. The gap between the adjacent patches is $g = 3\; $µm. The unit cell period is $p = 45\; $µm and the dielectric spacer thickness is $d = 2.3$ µm.
These optimized dimensions produce the absorption spectrum shown in Fig. 1(b). The first absorption band appears at frequency of 1.66 THz and the higher order bands appear at odd multiples of the first band (5 THz, 8.3 THz, 11.6 THz and 14.8 THz). All resonance frequencies can be calculated using the formula ${f_{ij}} \approx {{c\sqrt {{i^2} + {j^2}} } / {(2\sqrt {{\varepsilon _r}} W)}}$. Where c represents the speed of light, $W$ is the width of the square patch, $i,j = 0,1,2,\;\ldots $ are integers [35]. In fact, the higher order modes occur at THz frequencies due to the patch size is larger than a multiple of a half-wavelength of the modes [28,35,36]. The inherited nature of these resonances restricts the applications of this design, where higher order absorption bands are unwanted. Therefore, the objective of this work is to modify the structure in order to suppress the unwanted higher order absorption bands simultaneously with keeping the main absorption band unaffected. The next section proposes the design of the modified structure along with its comprehensive investigation.
2.2. Proposed design of the compact size absorber
In order to suppress the undesirable resonances, the nature of coupling between the adjacent cells must be modified. All absorption bands observed in Fig. 1(b) are due to the interaction between the top square patches and the ground film [30,36]. The energy is trapped and converted in to heat as ohmic loss within the conductor part. By introducing new cell-to-cell coupling mechanism, it could be possible to decrease the resonance strength of all high order resonances using interdigitated coupled lines. The proposed structure is constructed as follows. A continuous conductive layer of thickness 0.4 µm is placed in the bottom. It is typically larger than the skin depth at the operating frequency to ensure zero transmission. A middle layer of dielectric insulator is modeled by Silicon Nitride (S3N4) of thickness $d = 2.3$ µm, and relative permittivity of εr = 4.4. It is broadly used in THz and optical applications because of its low surface roughness that limits the scattering losses. The top layer is composed of conductive periodic array of thickness ${t_g} = 0.4$ µm.
The two dimensional array’s top view of the proposed absorber structure is depicted in Fig. 2(a). The array consists of square shaped conductive patches. Each side is terminated with long rectangular fingers that overlap with the adjacent fingers from the neighboring cells. The single unit cell of size p is shown in Fig. 2(b). The square shaped patch at each corner of the unit cell has a width wx such that the actual width of the patch in Fig. 2(a) is 2wx. The number of rectangular fingers attached to each side of the patch is N i.e. 2N interdigitally coupled fingers. Each finger has a length L, and a width w. The gap between the interdigitated fingers is G. The simulation process is carried out with the aid of full wave microwave studio computer simulation tool (MWS CST) [37]. This numerical simulation package has the capability to model planar periodic arrays with build in solver, which is based on finite element method. Particularly, frequency domain solver is utilized to obtain all responses.
Unit cell boundary conditions are chosen to mimic infinite periodicity in the horizontal plane. Open Floquet ports are set up to excite the incident wave at the input port and to collect the wave at the output port. The excited source wave is propagating along z-direction. The electric field component is in the y-direction (Ey) and the magnetic field component is in the x-direction (Hx). The conducting material in the simulation is chosen to be gold. It has the conductivity of $1.6 \times {10^7}$ S/m in THz regime. The normalized absorption can be found using Eq. (1).
where $A(\omega )$ is the normalized absorbed power; $R(\omega )= {|{{\textrm{S}_{11}}(\mathrm{\omega } )} |^2}$ is the reflected power. The transmitted power $T(\omega ) = |{S_{21}}(\omega ){|^2}$ is not considered in Eq. (1) since the ground screen prevents the wave from propagating through the structure towards the receiving port.The simulated transmission, reflection and absorption curves are shown in Fig. 3. The optimized dimensions are listed in Table 1. As can be deduced from Fig. 3, the reflection dip is observed at frequency, f1 = 1.61 THz. As expected, the wave transmitted through the absorber is zero, which can be seen from the transmission curve. Therefore, perfect absorption peak occurs at this frequency. Very weak higher order absorption peaks are observed at f2 = 4.38 THz and f3 = 7.72 THz. The structure profile is very small, where the absorber thickness is much smaller than the fundamental operating wavelength, i.e. $d = 0.012 \times {\lambda _1}$. Also, the cell size to operating wavelength ratio is small ${{p / \lambda }_1} = 0.11$.$\; $
Fig. 3. Simulated response for the dimensions listed in Table 1, reflection (red line), transmission (blue line) and absorption (black line).
Table 1. Optimized Dimensions to Obtain the Results of Fig. 3
2.3. Equivalent circuit model
Theoretical approximations based on circuit and transmission line theories can be incorporated to extract the equivalent circuit model for various types of absorbing structures [38,39]. Due to the strong interaction of the incident wave with the resonant elements, induced electric charges and currents are generated in the conductors. This interaction can be demonstrated by equivalent R, L, and C lumped components. Circuit theory approximation is very advantageous in optimization, tuning and estimation of the resonance frequencies. Moreover, the behavior of the repeated physical resonators in the periodic structure can be simplified by equivalent discrete elements to provide more insights into the absorber response. According to circuit theory, the absorber structure based on square shaped patch unit cell shown in Fig. 1 can be approximated by the circuit model “A” depicted in Fig. 4(a). The cell to cell electric and magnetic coupling is realized by the shunt RLC branch. Where L1 is the inductance produced by the surface current flowing over the square shaped patch. C1 is the capacitance formed between each two adjacent cells, and R1 represents the conductor resistance. The capacitance between the top square patch and the ground plane is realized by Cp. The approximate values of C1, Cp and L1 can be calculated from the geometry’s dimensions W, g and d using Eq. (2) [40,41].
Fig. 4. (a) Equivalent circuit model “A” for square shaped patch absorber, (b) circuit model “B” for the proposed absorber, and (c) the corresponding absorption spectra.
The dielectric layer backed by a ground plane is characterized as a short circuited transmission line of Zo1 characteristic impedance. The free space characteristic impedance is Zo, which is equal to 377 Ω. The reflection coefficient $\Gamma $, is calculated using Eq. (3).
where ${Z_{in}}$ is the equivalent input impedance. The absorption ($A$) is found using the formula $A = 1 - {|\mathrm{\Gamma } |^2}$. The introduced inter-coupled fingers between the adjacent cells shown in Fig. 2 can be modeled as an extra RLC circuit connected in series with the existing resonance circuit. The modified circuit model “B” is illustrated in Fig. 4(b), where, R2, L2 and C2 are the introduced components to resemble the effect of the interdigitally coupled fingers. The magnetic coupling between the fingers produces an inductance L2 and the electric field coupling forms the capacitance C2. The ohmic loss within the metallic fingers is modeled by the resistance R2.The empirical design equations [20] for the interdigital capacitor can be utilized to predict the circuit elements. The approximate values of L2, C2 are evaluated from the geometry dimensions $w$, $d$, ${t_g}$ and $L$ using the following equations
Equations (2) and (4) may be used only as guideline and a starting guess for design. All elements values are then tuned using Advanced Design System (ADS) circuit design and simulation software [42] to obtain the complete fitted values of the components for both circuit models. The optimized values are listed in Table 2. The absorption response for each circuit model is plotted in Fig. 4(c). The black curve is the absorption response due to circuit model “A”, which is very similar to the response of the simulated square shaped patch structure depicted in Fig. 1(b). It is seen that the circuit model “A” predicts all absorption bands due to the higher frequency modes. On the other hand, these higher modes are suppressed as can be seen from the red lined response plotted in Fig. 4(c), which resembles the response for circuit model “B”. Similarly, the response of circuit model “B” is following the response of the proposed modified structure illustrated in Fig. 3.
Table 2. Optimized Components’ Values for the Circuit Models “A” and “B”
3. Simulation results and discussion
3.1. Field maps analysis
With the purpose to comprehend the mechanism behind each absorption band, electric, magnetic and current density field maps are inspected at each resonance. The excitation plane wave has $y$-electric field component (Ey) and $x$- magnetic field component (Hx). It should be noted that all field illustrations in Fig. 5 are showing only 8 intercoupled fingers out of 16 fingers. They represent the left hand side of the xz cut plane. The remaining 8 fingers of the unit cell are not shown, since the right hand side of the cut plane is a mirror image along the x–axis, where the field symmetry is about the z–axis.
Because of the incident wave has an electric field vector oscillating linearly along the y-direction, an induced dipole moment is established due to the interaction with the surface charge on the upper conductor. Charges build up on both patch’s endings such that positive charges appear on the side aligned with the field direction, while negative charges appear on the other side. On the other hand, opposite polarities are induced on the bottom ground conductor. The field enhancement confined between the intercoupled fingers is an evidence for the induced dipole moment. This can be seen from Fig. 5(a), which shows the electric field vector map at the first resonance f1. All fingers associated with the positive charge are labeled with a positive sign and fingers from the adjacent cell are labeled with negative sign. Furthermore, the coupled magnetic field is circulating around the top conductor and mainly confined in the dielectric region as indicated by the big black arrow shown in Fig. 5(d). Consequently, anti-parallel currents are induced on the top and bottom conductors as depicted in Fig. 6(a), which shows the xy cut plane field map for the current density for both top layer (left) and the bottom layer (right). The arrows indicate the direction of the induced currents. As a result, the incident energy at this resonance is dissipated as ohmic loss.
Fig. 6. Current density field maps of the top and bottom conductors at frequencies (a) f1 = 1.61 THz, (b) f2 = 4.38 THz and (c) f3 = 7.72 THz.
The weak absorption band located at f2 represents a higher order resonant mode, which is almost three times the first absorption band center frequency f1. It can be observed from the E-field map in Fig. 5(b) that the field splits into three regions and reverses its phase twice as seen from fingers polarities associated with the same patch. Similarly, the third absorption peak at f3 occurs at five times the first frequency f1. The E-field map at this frequency is shown in Fig. 5(c). The field is concentrated in five regions and phase reversal is observed in each region as denoted by the plus and minus signs. The weak absorption strength at these two higher modes are caused by the circulating antiparallel currents at the top and bottom conductors as can be seen for the current density maps depicted in Fig. 6(b) and Fig. 6(c) at frequencies f2 and f3 respectively. These induced currents indicated by the big black arrows are driven by the circulating magnetic fields shown in Fig. 5(e) and Fig. 5(f) for frequencies f2 and f3 respectively.
3.2. Structure parametric study
The optimized structure’s dimensions are obtained after studying the effect of each parameter on the absorption characteristics. Several parameters are swept within specific range in order to understand the influence of each parameter on the absorber performance. Since the structure consists of overlapped fingers N, the effect of increasing number of fingers in each side of the unit cell is depicted in Fig. 7. It is observed that by increasing the number of fingers from N=2 to N=8, the strength of higher order sidebands weakens, especially, frequencies beyond 7 THz. This can be observed from the response for N=8, where the absorption curve is almost flat for the frequencies off the main absorption band.
The absorption peak can be shifted up or down in frequency by adjusting finger’s length L. Fig. 8(a) shows the 2D map for absorption strength by varying L from 0.5 µm to 4 µm. It is seen that the main absorption peak shifts down in frequency when the finger’s length increases. It is also observed that a higher order band appears at around 11 THz and is shifted down for longer lengths. But it disappears when L goes beyond 2.5 µm. This is because the increasing coupling between the interdigitated fingers when they start to overlap from each adjacent cells. Similar behavior is noticed when increasing the finger’s width w, as shown in Fig. 8(b). The width w is swept in the range from 0.1 µm to 0.6 µm. The main absorption peak is shifted down in frequency for larger values of w. Again, higher order absorption bands are vanished when the interdigitated fingers overlap. It must be kept in mind that the patch width wx is a function of both finger width w and spacing gap G between the fingers. Therefore, a smaller value of w or G gives a smaller patch width wx taking into consideration the values L, G and p are maintained unchanged. This would make the fingers from the adjacent cells not long enough to overlap.
The variation of the gap width G is shown in Fig. 9(a), where G is varied from 0.1 µm to 0.4 µm. The response shows only a single absorption band when G exceeds 0.2 µm width. The higher absorption bands that are seen for G less than 0.2 µm are resulted when the fingers are not overlapping. As mentioned earlier, the width wx is depending on the gap width G. Finally, the variation of dielectric spacer thickness d is depicted in Fig. 9(b). It is observed that a slight shift down in frequency occurs as the thickness increases from 1 µm to 8 µm range, as well as, the absorption strength drops considerably when d goes beyond 5 µm. This is because the resonance is mainly due to the surface coupling between the adjacent cells, rather than the resonance due to the interaction between the patch and the ground film.
Fig. 9. Absorption response due to the varying of (a) gap width G, and (b) dielectric spacer thickness d.
3.3. Propagation angle effect
It is usually preferable to have high absorption strength for wide range of incident angles. Moreover, it is desirable to possess polarization independence behavior. Therefore, the performance of this absorber is investigated in terms of changing the direction of the incident wave hitting the surface of the structure at both wave polarizations; transvers electric (TE) and transvers magnetic (TM) polarizations. The direction of the incident wave is identified by the two angles θ and Φ. The inclination angle θ is the angle between the propagating wave vector and the normal vector (z-axis) to the structure surface. The azimuthal or the rotational angle Φ is specified by the angle formed between the x-axis and the projection of the wave vector on the structure surface (xy-plane). These angles are illustrated in the inset of Fig. 10(a). The effect of the angle θ variation for TE polarization case is shown in Fig. 10(a). It is seen from the 2D absorption strength map that strong absorption is maintained for wide range of angles. However, rapid reduction in the strength is observed when θ goes beyond 70°. It is attributed to the reduction of the tangential component of incident magnetic field that sustains the induced antiparallel currents and hence, weakening the magnetic resonance.
Fig. 10. 2D absorption strength maps versus incident wave elevation angle, θ, for (a) TE polarization, (b) TM polarization, and azimuthal angle, Φ, for (c) TE polarization and (d) TM polarization.
In contrast, the magnetic field component in TM polarization is always strong enough to maintain high absorption strength for wide range of θ as can be observed in Fig. 10(b). The absorption strength starts to decay slightly when θ goes beyond 70°. Also, it is observed that new weaker higher order absorption bands have emerged beyond 70° due to the strengthening of the normal electric field component. Usually, the higher modes start to show up with significant strength at small angles [3,30]. The strong magnetic interaction between the cells diminishes the strength of the higher modes. On the other hand, the absorption response subjected to the variation of the rotational angle Φ for both TE and TM polarizations are depicted in Fig. 10(c) and Fig. 10(d) respectively. Owing to the symmetry of the geometry, the absorption strength is apparently independent of the angle Φ variation.
3.4. Effective constitutive parameters
Further investigation has been conducted by extracting the effective constitutive parameters from the complex scattering coefficients; electric relative permittivity ε, magnetic relative permeability µ and impedance Z. The process is carried out by exploiting the retrieval method demonstrated by Smith et al. [43]. The curves plotted in Fig. 11(a) are the real and the imaginary parts of the permittivity as function of frequency. The resonance f1 = 1.61 THz indicates the frequency at which the permittivity’s real part approaches to zero. The permittivity is $\varepsilon ={-} 15.3 + j55.2$ at resonance. Same principle applies to the permeability’s real and imaginary parts. The permeability is equal to $\mu \; ={-} 4.9 + j67$ at resonance as deduced from Fig. 11(b). It is observed that larger values of the imaginary parts represent the high loss in the material. Since the incident wave exhibits minimum reflection at resonance, the impedance of the structure matches the free space characteristic impedance as can be seen from Fig. 11(c). The normalized impedance is $Z = 1.07 - j0.1\; \mathrm{\Omega }$, which is very close to unity. Therefore, most of the incident wave is converted to a surface wave when it hits the absorber surface. This surface wave decays quickly and dissipated in the conductor as heat [19].
Fig. 11. Retrieved effective constitutive parameters, (a) permittivity, (b) permeability and (c) normalized impedance.
3.5. Absorber as a sensing device
An alternate application for MTM based perfect absorbing structures is to be employed in sensing thin dielectric overlays and surrounding refractive index, such as sensing slight amounts of chemicals and biochemical materials [44]. This is could be done by observing the change in frequency shift of the reflection minima. As seen earlier, the proposed absorber has a strong resonance frequency at f1 = 1.61 THz. Sensor sensitivity is defined as the ratio of the change in the resonance frequency to the change in refractive index unit (RIU) (Δf/Δn), which has the unit of, GHz/RIU. Sensors with high sensitivity show substantial shift in the reflection dip for small change in the surrounding medium’s refractive index. The sensitivity curve in Fig. 12(a) is showing the effect of the analyte thickness over the sensor surface as it changes from 1 to 14 µm. It is seen that the sensitivity shows very slight increment for thicker layers of analyte material. It reaches a steady value of around 550 GHz/RIU when the thickness goes more than 3 µm. This means that a very little amount of analyte material is enough to be detected with this sensor.
Fig. 12. (a) Sensitivity response versus analyte thickness, and (b) frequency shift in the reflection minima as a function of analyte refractive index.
The proposed structure possesses a linear frequency shift in the resonance frequency with respect to the change in the surrounding medium refractive index as depicted in Fig. 12(b). The analyte thickness is fixed at 3 µm and the refractive index is varied from 1 to 1.8. The black line represents the data from the simulated structure while the red line represents the fitted data. It is clearly observed that the response has a linear behavior, which can be described by the relation $y = 550x - 541.6$. The slope denotes the value of the sensitivity at this analyte thickness. In order to highlight the main features of this proposed absorber, Table 3 summarizes some of the previously reported results in THz regime compared to the results obtained in this work. The proposed absorber design has the smallest structure profile and cell size with relatively high sensitivity value. Moreover, it possesses very good overall characteristics.
Table 3. Comparison of the proposed design performance with some previously reported work
Unfortunately, due to unavailability of fabrication and testing facilities, it is worth mentioning that this proposed absorber can be easily fabricated using Electron Beam Lithography (EBL). This technique uses a mechanical embossing process to produce nano-scale structures. It is seen as a manufacturable and scalable solution for large area metamaterials. EBL involves several steps; wafer cleaning, deposition of Si3N4 spacer, spin coating of electron resist material, e-beam exposure, development, Au metal deposition process, and finally the lift- off process. This fabrication process facilitates the absorber structure to be experimentally verified in future. We believe that the presented work in this paper will develop the existing cutting edge technology of MTM based absorbers.
5. Conclusions
In this paper, a new design of MTM inspired absorber is proposed. The absorption bands due to inherited higher order modes have been rejected using strong cell to cell magnetic coupling by introducing interdigitally coupled fingers between the adjacent cells. The strong magnetic coupling is achieved by increasing the number of fingers. Several parametric variations have been conducted to investigate the effect on the absorption performance. The response of the suggested equivalent circuit model complies with the behavior of the proposed structure. Because of the highly symmetrical structure, the absorption response is polarization independent for both TE and TM polarizations. Furthermore, a very good oblique incidence performance was attained; where the absorption strength remained greater than 70% and 90% up to 70° of incident angle for both TE and TM polarizations respectively. The extracted normalized input impedance has shown well free space impedance matching. Moreover, the high values of the imaginary parts for effective permittivity and permeability reveal the high loss in the material. This design could be utilized in sensing applications since it has a sensitivity of 550 GHz/RIU for thin layer of analyte material. Finally, the promising findings in the proposed structure might pave the road to the development of the existing and future applications in the THz frequency band.
Disclosures
The author declares no conflicts of interest.
Data availability
No data were generated or analyzed in the presented research.
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