Large Near-Field Enhancement in Terahertz Antennas by Using Hyperbolic Metamaterials with Hole Arrays

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The proposed approach can be used to further enhance the near fields of terahertz antennas, enabling stronger light–matter interactions and better device performance.

Abstract

Terahertz antennas can greatly enhance the near fields and enable strong light–matter interactions, and thus have been widely used in applications such as terahertz sensing and detection. Here we propose a novel approach to further enhance the near fields in terahertz antennas. We show that by sandwiching hyperbolic metamaterials that are composed of InSb and SiO${}_2$ multilayer and that are dressed with hole arrays, between a terahertz dipole antenna and the substrate, the near-field electric field intensities in the antenna can be further enhanced by more than three times. Simulations reveal that this enhancement originates from the doubly enhanced in-plane electric field component and the significantly enhanced out-of-plane electric field component. We expect this work will advance the design of terahertz antennas that are widely used in sensors and detectors.

1. Introduction

Terahertz (THz) wave refers to electromagnetic radiation with a frequency of 0.1–10 $\times {10}^{12}$ Hz (corresponding to wavelength of 3 mm–30 $\mathsf{\mu }$m). Because of its unique characteristics such as superior spatial resolution, perspective, and spectroscopic fingerprints, terahertz wave has been widely used in security or industrial inspection [1,2], material composition identification [3,4], and biosensing [5]. Since commercially available high-power terahertz sources are expensive, it is crucial to enhance the localized field intensity, thus enabling strong light–matter interactions in diverse exciting applications such as detection [6], sensing [7], absorption [8], spectral filtering [9], and emission [10], and significantly improving the performance of the corresponding devices. For example, by confining most electric energy to a small region filled with microfluid, the sensitivity of a terahertz sensor can be greatly improved [11].

By efficiently coupling and confining the free-space terahertz radiations to a small (usually subwavelength) region, a terahertz antenna can greatly enhance the localized near fields. Therefore, terahertz antennas have been widely used in a diverse range of applications including biosensing [11,12,13,14,15,16] and detection [17,18]. An important figure of merit for these terahertz antennas is the near-field enhancement, which is defined as the ratio of the near-field electric field intensity and the electric field intensity of the incidence [19]. In particular, for a dipolar type antenna, of which the strongly enhanced fields are mainly confined to the gap region of the dipole unit, the field enhancement usually refers to the enhancement of the near field in the gap. Since the field enhancement strongly depends on the antenna geometry, various antenna structures have been designed, including dipole antennas [20,21,22], log-periodic antennas [23,24] and spiral antennas [17,25]. To achieve large near-field enhancement, major efforts have been put on careful design and optimization of terahertz antennas.

In this work, we propose a novel approach to further improve the near-field enhancement of the terahertz dipole antenna. We show that by adding a hyperbolic metamaterial with hole arrays beneath the antenna, the near-field electric field intensity within the gap of the antenna can be further enhanced by more than three times. We will also analyze the underlying physics for this improvement and discuss the effects of the gap width and of the hyperbolic dispersion relationship of the metamaterials. We expect this proposed approach can be extended to other types of terahertz antennas.

2. Design and Theory

Figure 1 depicts the proposed terahertz dipole antenna, which is composed of two gold (Au) strips on top of a polyimide (PI) substrate, sandwiched by multiple alternating thin films of Indium Antimonide (InSb) and silica (SiO${}_2$) that are dressed with periodic hole arrays. The two gold strips are of thickness $t_{\mathrm{Au}}$, width w and length L, and are separated by an air gap of width g. The individual thicknesses of the InSb and SiO${}_2$ layers are $t_{\mathrm{m}}$ and $t_{\mathrm{d}}$, respectively. The hole arrays in the InSb-SiO${}_2$ multilayers, as illustrated in Figure 1a inset, have a radius of r for the holes and a period of p for the arrays. Compared with a conventional terahertz dipole antenna, which directly sits on the substrate, the sandwiched multilayers with hole arrays are novel.

Because the individual InSb and SiO${}_2$ layer dimensions satisfy the criteria of effective medium theory (EMT) [26], the effective dielectric tensor components of the anisotropic metamaterial composed of the InSb-SiO${}_2$ multilayers can be calculated using the EMT,

$$\begin{array}{c}\hfill \overline{\overline{\epsilon }}=\left(\begin{array}{ccc}{\epsilon }_{\perp }& 0& 0\\ 0& {\epsilon }_{\perp }& 0\\ 0& 0& {\epsilon }_{\Vert }\end{array}\right),\end{array}$$

(1)

where the subscripts ‖ and ⊥ indicate the components that are parallel and perpendicular to the x-y plane, respectively, and these components are given by [27],

$$\begin{array}{c}\hfill {\epsilon }_{\Vert }=\frac{t_{\mathrm{m}}{\epsilon }_{\mathrm{m}}+t_{\mathrm{d}}{\epsilon }_{\mathrm{d}}}{t_{\mathrm{m}}+t_{\mathrm{d}}},\end{array}$$

(2)

$$\begin{array}{c}\hfill {\epsilon }_{\perp }=\frac{{\epsilon }_{\mathrm{m}}{\epsilon }_{\mathrm{d}}(t_{\mathrm{m}}+t_{\mathrm{d}})}{t_{\mathrm{m}}{\epsilon }_{\mathrm{d}}+t_{\mathrm{d}}{\epsilon }_{\mathrm{m}}}.\end{array}$$

(3)

The unique properties of such metamaterials stem from the isofrequency surface of extraordinary (transverse magnetic polarized) waves, which is given by [28]

$$\begin{array}{c}\hfill \frac{k_x^2+k_y^2}{{\epsilon }_{\Vert }}+\frac{k_z^2}{{\epsilon }_{\perp }}={\left(\frac{\omega }{c}\right)}^2\end{array}$$

(4)

where $k_x$, $k_y$ and $k_z$ are wave vectors, $\omega$ is the wave frequency and c is the speed of light. By tuning the parameters of ${\epsilon }_{\mathrm{m}}$, ${\epsilon }_{\mathrm{d}}$, $t_{\mathrm{m}}$, and $t_{\mathrm{d}}$ such that ${\epsilon }_{\Vert }{\epsilon }_{\perp }<0$, one can attain the hyperbolic regime [28].

The frequency-dependent complex permittivities of semiconductor InSb at terahertz frequencies can be described by the Drude model [29]

$$\begin{array}{c}\hfill {\epsilon }_{\mathrm{m}}=\epsilon (\infty )-\frac{{\omega }_p^2}{{\omega }^2+i\omega \gamma },\end{array}$$

(5)

where $\epsilon (\infty )$ is the high-frequency permittivity, $\omega$ is the excitation frequency, ${\omega }_p^2=n{e}^2/\left(m^{\ast }{\epsilon }_0\right)$ is the plasma frequency with n the free electron density, and e and $m^{\ast }$ the electron’s charge and effective mass, respectively. $\gamma =1/\tau$ is the carrier momentum relaxation rate and $\tau$ is the average collision time of the charge carriers. For undoped InSb at 300 K, $\epsilon (\infty )=15.68$, $\gamma /\left(2\pi \right)=0.05$ THz, ${\omega }_p/\left(2\pi \right)\approx 2.8$ THz [29,30]. By using Equation (5), the real and imaginary parts of the permittivity of InSb are shown by Figure 1b, which are similar to those of metals in the visible and near-infrared.

We take the dielectric constant of SiO${}_2$ to be ${ϵ}_{\mathrm{d}}=3.8$, and the thicknesses of InSb and SiO${}_2$ layers to be $t_{\mathrm{m}}=t_{\mathrm{d}}=0.1\mathsf{\mu }$m. With Equations (2) and (3), the numerically obtained dielectric tensor components from the above equations are shown in Figure 1c. Results show that the InSb-SiO${}_2$ multilayers exhibit hyperbolic dispersion relationship for $f<1.65$ THz, as indicated by the purple region.

All the simulations in this work were performed with finite-difference-time-domain (FDTD) method based on MEEP codes. The structure under study is illuminated by terahertz plane wave polarized along the x direction, and the perfect matching layers were adopted as the boundary conditions for all the three directions. A uniform mesh size of 20 nm in the z direction and 100 nm in the x and y directions was used for the multilayer region with hole arrays. We take the substrate to be polyimide (PI) with a refractive index of $n_{\mathrm{sub}}=1.8$, take the normally incident terahertz wave to be of Gaussian profile with unitary electric field amplitude ($|E_0|=1$). The length and width of the gold dipole antenna are $L=50\mathsf{\mu }$m and $w=4\mathsf{\mu }$m, respectively, which has been optimized so as to be resonant at the frequency of 1.62 THz, at which the metamaterial composed of the InSb-SiO${}_2$ multilayers has hyperbolic dispersion relationship. The thickness of the gold antenna is $t_{\mathrm{Au}}=0.2\mathsf{\mu }$m and the gap width is $g=1\mathsf{\mu }$m. The radius and period of the hole arrays are $r=0.3\mathsf{\mu }$m and $p=0.9\mathsf{\mu }$m, respectively. The number of InSb and SiO${}_2$ layers is set to be $N=11$. Please note that here N is an odd number since we have InSb on the top and the bottom of the InSb-SiO${}_2$ multilayers.

3. Results and Discussion

Figure 2 shows the simulated near-field distributions in the $y=0$ or/and $z=1.2$$\mathsf{\mu }$m cross sections. It is clear that the terahertz electric field intensity in the antenna gap has been greatly enhanced, no matter the InSb-SiO${}_2$ multilayers with/without the hole array is sandwiched between the gold dipole antenna and the substrate or not. For the conventional terahertz antenna which directly sits on the PI substrate, the electric field intensity in the gap is enhanced to be $1.12\times {10}^4$ of the incidence intensity, as shown by Figure 2a,d,g. By sandwiched with the HMM composed of the InSb-SiO${}_2$ multilayers, Figure 2b,e,h shows that the enhancement is slightly increased to $1.85\times {10}^4$, corresponding to 50% improvement compared with the conventional terahertz dipole antenna. By further drilling periodic hole arrays in the HMM, as illustrated in Figure 1, Figure 2c,f,i shows that the enhancement can be further increased to $3.65\times {10}^4$, more than three times of that for the conventional antenna. Therefore, simulations reveal that by introducing the HMM with periodic hole arrays between the terahertz dipole antenna and the substrate, the near-field intensity localized in the antenna gap can be further enhanced by more than three times. Please note that quantitatively similar enhancement can also be achieved by using square-shaped periodic hole arrays.

To understand the origins of this near-field enhancement, we further plot the dominant in-plane and out-of-plane components of the electric field in Figure 3 and Figure 4. Results show that $E_y$ is negligible, $|E_x{|}^2$ in the gap of the conventional antenna is greatly enhanced to $1\times {10}^4$, whereas $|E_z{|}^2$ is very weak (only 12). In other words, $E_x$ dominates the near field, consistent with the literature [11]. However, for the proposed antenna structure, both the electric field components are greatly enhanced: $|E_x{|}^2=2.4\times {10}^4$, $|E_z{|}^2=1.5\times {10}^4$. Compared with the conventional antenna, $|E_x{|}^2$ is doubled, whereas $|E_z{|}^2$ is enhanced by three orders of magnitude such that it is now comparable to $|E_z{|}^2$. Figure 3a,b shows that the $|E_x{|}^2$ energy transmitted through the gap of the conventional dipole antenna is efficiently reflected back by the HMM with periodic hole arrays, resulting in double enhancement of the near-field intensity in the gap. A similar reflection effect also occurs for the $E_z$ component, as shown by Figure 3c,d.

Figure 5a shows that the gap width g plays a key role on the near-field enhancement. In above discussions, we take $g=1\mathsf{\mu }$m and obtain three times further enhancement compared with the conventional antenna. As g increases, the near-field enhancement factors for both the proposed and the conventional antennas decrease, consistent with the literature. Their ratios also decrease from 3.3 to 2.2, indicating smaller enhancement due to the introduction of the HMM with periodic hole arrays.

Figure 5b shows that the large near-field enhancement factor can be achieved only for $t_{\mathrm{m}}/t_{\mathrm{d}}$ = 1:1, and that the enhancement factors are small for both $t_{\mathrm{m}}/t_{\mathrm{d}}$ = 1:2 and $t_{\mathrm{m}}/t_{\mathrm{d}}$ = 2:1. Please note that for fair comparison, the individual layer thicknesses are properly chosen such that the InSb-SiO${}_2$ multilayers have exactly the same total thicknesses for these different values of $t_{\mathrm{m}}/t_{\mathrm{d}}$. To understand this interesting phenomenon, we turn to the effective relative permittivities expressed by Equations (2) and (3). As we have shown in Figure 1c, the InSb-SiO${}_2$ multilayers with $t_{\mathrm{m}}/t_{\mathrm{d}}$ = 1:1 have hyperbolic dispersion relationship since ${\epsilon }_{\Vert }{\epsilon }_{\perp }<0$ at $f=1.6$ THz. For both $t_{\mathrm{m}}/t_{\mathrm{d}}$ = 1:2 and $t_{\mathrm{m}}/t_{\mathrm{d}}$ = 2:1; however, Figure 5c,d shows that the InSb-SiO${}_2$ multilayers exhibit elliptical dispersion relationship because of the anisotropic uniaxial effective relative permittivities at $f=1.6$ THz, i.e., ${\epsilon }_{\Vert }{\epsilon }_{\perp }>0$ and meanwhile ${\epsilon }_{\Vert }\ne {\epsilon }_{\perp }$. Therefore, these results reveal that the hyperbolic regime of the HMM composed of the InSb-SiO${}_2$ multilayers is vital for achieving large field enhancement.

Please note that in this work we choose the InSb-SiO${}_2$ multilayers to form the hyperbolic metamaterial because they are typical hyperbolic metamaterial structures that are easy to fabricate through thin-layer deposition. In principle, we expect similar results can also be obtained by using other types of hyperbolic metamaterials.

4. Concluding Remarks

In conclusion, we have proposed a novel approach to further enhance the near-field intensity in the terahertz dipole antenna. It is achieved by introducing HMM with periodic hole arrays between the terahertz antenna and the substrate, where the HMM is composed of InSb-SiO${}_2$ multilayers. Fully vectoral simulation results have shown that by using this approach, the near-field intensity of a conventional dipole antenna can be further enhanced by more than three times. The greatly enhanced near-field intensity can improve the sensitivity of terahertz detectors or sensors. Simulations have also revealed that this enhancement originates from doubled $|E_x{|}^2$ and significantly enhanced $|E_z{|}^2$. We have showed that the smaller gap width, the larger the enhancement, and that the hyperbolic characteristic of the multilayers is vital for achieving large enhancement. Although we have focused on terahertz dipole antennas, we believe this approach should be applicable for other types of antennas. The proposed approach should also be applicable for other spectral regimes. For example, in the visible or near-infrared regime, one can shrink the size for such short waves according to the electromagnetic scaling law, which requires that the ratio of the geometric length to the wavelength is the same for different electromagnetic wave regimes. Furthermore, the semiconductor InSb used for the terahertz should also be replaced with noble metal gold for the visible. This is because InSb at THz frequencies and gold in the visible have similar permittivities [29]. A possible problem could be the structure size is so small that it may pose difficulties in fabrication. Therefore, we expect this work will advance the design of terahertz antennas, as well as antennas the visible and near-infrared regimes, which are widely used in biosensing and detecting applications.