Dielectric rod nanoantenna fed by a planar plasmonic waveguide

This paper presents a tapered dielectric rod antenna excited by a folded dipole coplanar waveguide operating at terahertz frequencies. The effective refractive index of the plasmonic transmission line is obtained by two numerical methods, the Finite Element Method and the Finite-Difference Time-Domain, and it is used to obtain the dimensions of the gap connected to the line. We examine the antenna using two lengths of the rod. For 10 and 5 μm tapered rods, impedance bandwidths of 43.47% and 32.55%, maximum gains of 12.58 and 9.84 dB, and radiation efficiencies of more than 72.09%, and 72.15% are achieved, respectively. The dielectric rod nanoantenna operates at all the optical communication band frequencies: original (O), extended (E), short (S), conventional (C), long (L), and ultra-long (U). The structure of the antenna consists of three layers. The substrate is made of silicon oxide. This paper discusses the effect of using a layer of silicon oxide to prevent direct contact between the silicon rod and the hollow T-shaped silver feedline.


Introduction
Nanotechnology is advancing at an astounding pace and is anticipated to address the escalating need for high-capacity wireless communications. The antennas operating at these frequencies must have a broad bandwidth to maintain a high data rate, high gain, and low dissipation to compensate for the free space path loss, which increases quadratically with frequency. According to Shannon's theorem, shifting to higher frequencies delivers more bandwidth and increases channel capacity. Waves with THz frequency have the advantages of millimetre waves and light waves. Compared to millimetre waves, the usable frequency band is wider; the beam direction is more robust; the confidentiality and anti-interference performance is better. A THz wave is more efficient and penetrates further than light waves. The design ideas of THz antennas are primarily generated as follows. Researchers adopt the method of frequency ratio scaling, which is based on traditional microwave antennas. Optimization of the dielectric layer is another approach as the design of THz antennas could be based on high-gain planar antennas. Also, the high-precision antennas are designed based on new materials Huang et al. 2019;Zhang et al. Aug. 2018). New materials, such as a carbon nanotube dipole antenna (Hao and Hanson 2006) or graphene (Jornet and Akyildiz 2010) are replacing metallic parts in recent designs. Graphene exhibits excellent dynamic continuous control characteristics, producing surface plasmons by adjusting bias voltage. There are surface plasmons in the presence of negative dielectric substrates (such as precious metals and graphene) and positive dielectric substrates (such as silicon and silicon oxide). There are many free electrons or plasmas in conductors like precious metals and graphene. At high THz frequencies, graphene has complex conductivity, meaning slow propagation is associated with the plasma mode, thus demonstrating its feasibility as a THz replacement material (Jornet and Akyildiz December 2013). Due to their capability to optimally connect propagating and spatially confined optical fields, nano antennas for visible and infrared radiation will significantly improve the interaction of light with nanoscale matter. This feature offers a vast array of possibilities regarding the applications of optical devices. In the continually expanding area of nano photonics, optical antennas and resonant devices that optimally capture free-space light and concentrate it into a nano-meter scale volume are essential (He et al. 2020;Siegel 2002Siegel , 2003Biagioni et al. 2012). In general, efficient radiation could be attained by utilizing a single tapered rod dielectric. This antenna forms a wide functional aperture by progressively radiating a guided mode in a specific area (Schuller and Brongersma 2009;Withayachumnankul et al. 2018;Kobayashi et al. 1982). In previous studies, rod antennas and their potential applications have been investigated by researchers. In ), a photonic crystal waveguide was used to excite the DRA, which resulted in an end-fire radiation pattern in the antenna. A nanoscale optical dielectric rod antenna for on-chip interconnecting networks is proposed. The designed rod is placed between the top silicon (Si) layer and a bottom buried oxide (BOX) layer (Zhou et al. 2011). Dielectric rod fed with photonic crystal waveguide has also been used to realize an array with multi-beam properties. An end-fire radiation pattern has also been obtained in this structure (Headland et al. 2018).
This work proposes a Dielectric Rod Nanoantenna fed by the Folded Dipole Coplanar Waveguide. The FDCP waveguide, which consists of a noble silver metal 'Ag', excites the entire antenna. The DRNA functions in the majority of the telecom wavelength bands, such as original (O), extended (E), short (S), conventional (C), long (L), and ultralong (U) bands (Batagelj et al. 2012). RF and microwave antenna theories and design principles can be applied to the burgeoning field of optical antennas (Balanis 2005;Sethi et al. 2015aSethi et al. , 2016Zou et al. 2013;Zhao and Alu 2013;Pierce and Spicer 1972;Krishna et al. 2017;Jung et al. 2009;Malheiros-Silveira and Hernandez-Figueroa 2015). The designed nano antenna is predicted to provide a high gain over its 100 THz bandwidth. The nanorod is tapered to substantially reduce reflection while maintaining a high directivity of over 10 dB. Numerical investigations have been developed for two tapered rods with different lengths, and the results are discussed. A comparison has been made between the gains of a tapered and a non-tapered rod with the same rod length. The antenna is explored using two different numerical methods, i.e., time-domain finite integration technique (FIT) and finite element method (FEM).
The paper is organized as follows: In Sect. 2, the antenna's geometry is explained. A parametric study is performed in Sect. 3. The final simulation data for the reflection coefficient, gain, and radiation patterns are discussed in the fourth section. Finally, the article's conclusion is presented. Figure 1 shows the geometry of the proposed dielectric rod nanoantenna (DRNA). The antenna consists of a multi-layer design. The substrate is made of silicon oxide with a thickness of h sub = 0.2 µm; the length of the square-shaped substrate equals L sub = 3 µm. The rod is made from silicon and coupled to a folded dipole coplanar waveguide (FDCPW). In the optical frequency band, silicon has a relatively constant permittivity in the entire band. The permittivity of silicon is r = 12.1 at the wavelength of 1.55 µm (Pierce and Spicer 1972). For the tapered dielectric rod, R bottom and R top are equal to 0.165 µm and 0.09 µm, respectively. The Coplanar Waveguide (CPW) is made of silver with a thickness of h silver = 0.02 µm and is filled with silicon oxide dielectric material. The top view of the antenna is depicted in Fig. 1c, and its optimized parameters are as follows: S = W = 0.08 µm, W d1 = 0.13, L d1 = 0.29 µm, W d2 = 0.055 µm and L d2 = 0.24 µm. A silicon oxide cover layer with a thickness of h cover = 0.02 µm is placed above the CPW feedline to avoid direct contact between the rod and the CPW feed line.
The optimization method is as follows: first, the initial dimensions for all parameters have been obtained by parametric study, then the structure is optimized around these values using the optimization tool of CST software.
The dispersive properties of silver parts of the feedline were calculated by the Drude model as demonstrated below (Johnson and Christy 1972): where 0 = 8.85 × 10 −12 Fm −1 is the permittivity of the vacuum,ε ∞ = 5 is the offset of the real part of the dielectric constant, p = 2 * 2175 Rad S −1 is the plasma frequency, is the collision frequency, and it is the inverse of the relaxation time τ, is the operating frequency, and ε Ag is the permittivity of silver. The metal dispersion is more critical in photonic devices than those operating at microwave frequencies.
3 Results and discussion Figure 2A, b show the electric field distribution in the cross-sectional view of the CPW line obtained by two different numerical methods, FDTD and FEM. It is apparent that surface plasmon CPW even mode is supported by this structure. Note that both the even and odd fundamental modes are supported within the structure (Krishna et al. 2017;Jung et al. 2009). The effective refractive index of the surface plasmon even and odd modes are calculated to be n eff = 2.16 − j0.016 , n eff = 1.63 − j0.13 for the CPW dimensions of W = S = 0.08 m , h sub = 0.2 m , h cover = h silver = 0.02 m , which are presented with respect of Fig. 1. Figure 2c shows the electric field profile in the x-axis direction. The electric field profile of this waveguide reveals that the field is primarily confined inside the gaps. Figure 3 shows the mode characteristics of the surface plasmon coplanar waveguide for different values of the gap width, W . Observe that by increasing the gap width W , the real parts of n eff decrease, as shown in Fig. 3a. Also, the propagation length and normalized mode area are shown in Fig. 3b, c, respectively. The propagation length and effective mode area are defined as follows (Jung et al. 2009): where (r) is the permittivity of the various materials used in the waveguide, and E(r) and H(r) are the electric and magnetic fields, respectively. A value of 0.08 μm for W is (d) Fig. 2 Electric field distribution in the transverse plane a FEM method, even mode b FDTD method, even mode, c FEM method, odd mode, d FDTD method, odd mode, and e normalized electric field profile in x-axis direction for the proposed design, even and odd modes. The parameters are as follows: S = W = 0.08 µm, W d1 = 0.13, L d1 = 0.29 µm, W d2 = 0.055 µm, L d2 = 0.24 µm, and h silver = 0.02 µm. The odd mode is excited in the final antenna design. FDTD results are obtained using Lumerical software and FEM results are obtained using COMSOL software selected to make a tradeoff between the high propagation length and high energy confinement. Propagation length is the distance that surface plasmon polariton (SPP) must travel to reduce its electric field intensity to (1/e) of its initial value. Figure 4 shows the effective refractive index, propagation length, and normalized mode area of the surface plasmon coplanar waveguide for different values of the width of the middle Ag piece, S . It is observed in Fig. 4a that with increasing S, the real part of n eff of even mode decreases, but the imaginary part shows different behavior so that it decreases up to S = 0.07 μm and then increases. Figure 4b shows that the maximum propagation length is obtained for S = 0.07 μm . It can also be seen that for S in the range of 0.06 to 0.08 μm, the diffusion length is approximately close to the value obtained for S = 0.07 μm . Figure 4c shows the normalized mode area versus S. The odd mode is excited in the transmission line to feed the antenna. Note that the SPP mode can be excited in the transmission line by illuminating periodic surface structures consisting of rectangular grooves and steps with focused beams (Cruz et al. 2012).
The proposed structure is optimized by using a parametric study in the simulation, and the results of the optimal structure are presented below. Figure 5a illustrates the simulated results of the reflection coefficient of DRNA, which shows an impedance bandwidth of 43.47% from 180 to 280 THz. The best reflection coefficient was obtained at 217 THz.  Figure 5b shows the simulated gain of the proposed nanoantenna. The antenna gain varies from 7 to 12.5 dB over the entire bandwidth. The radiation efficiency of the DRNA is illustrated in Fig. 5c. The calculated radiation efficiency in most of the band is above 65%. It reaches 46% at the end of the band, which is a high radiation efficiency for the antenna in the optical band. Figure 5d displays the simulated directivity of the tapered dielectric rod nanoantenna. Observe that the maximum directivity is 14.3 dB, obtained at the frequency of 234 THz. Also, it is higher than 10 dB over the whole band of operation. The simulated electric field distribution inside the antenna at 193 THz is shown in Fig. 6, which confirms that a traveling wave has formed inside the long dielectric rod.
The tapered rod provides a more significant gain and better return loss values than a non-tapered rod in the shape of a cylinder, as depicted in Fig. 7a, b, respectively. The propagating mode inside the rod fed by the CPW feedline suffered from considerable lateral leakage. Therefore, we designed a different structure. The new structure of the rod changed from a cylinder to a cone. After this improvement, the coupling efficiency was enhanced. As a result, the gain of the antenna improved as illustrated in Fig. 7b. It can be seen in Fig. 7c that for most frequencies, better radiation efficiency is delivered by the tapered rod with a greater length. Note that for L = 10 µm, better radiation efficiency, gain and return loss are achieved. It should be noted that metals are highly lossy at optical frequencies that occur due to the penetration of waves into the metal. Therefore, the radiation efficiency of about 60 to 70% is acceptable for the antenna. The comparison between radiation patterns of tapered and non-tapered antennas is demonstrated in Fig. 8. The tapered rod performs better than the non-tapered rod in radiation patterns at different frequencies.
To prevent direct contact between the rod with the CPW feed line, a silicon oxide layer is placed between the rod and the CPW line. Figure 9 shows that this SiO 2 layer significantly affects the antenna responses. Figure 9a shows that placing the silicon oxide cover improves the antenna impedance matching. The application of this layer also improves the gain and radiation efficiency of the antenna, as shown in Fig. 9b, c. Figure 10 shows the changes in the antenna performance with the variation of the cover thickness, h cover . It can be seen in Fig. 10a that changes in the thickness of the cover cause significant changes in Fig. 5 The simulated results of the proposed nanoantenna with the length of 10 μm, a reflection coefficient, b gain, c radiation efficiency, and d directivity. The parameters are as follows: S = W = 0.08 µm, W d1 = 0.13, L d1 = 0.29 µm, W d2 = 0.055 µm, L d2 = 0.24 µm, and h silver = 0.02 µm. The results of this part have been obtained by using CST software the reflection coefficient of the antenna. Also, Fig. 10b, c show that with increasing the thickness of the cover from 0.01 to 0.03 μm, the gain decreases at the beginning of the band but increases at the end of the band. Therefore, the value of 0.02 μm for the cover thickness results in the best performance of the antenna in the entire band. Figures 11 and 12 indicate the 2D radiation patterns of the DRNA at 195, 225, 255 and, 275 THz for φ = 90° and φ = 0°, respectively. Observe that a broadside radiation pattern is achieved in both planes. Also, a good agreement between the results of both solvers is attained. Table 1 depicts the comparison of the proposed antenna with previous works that operate at similar frequencies. Wider impedance bandwidth and better radiation efficiency are among the superiorities of this antenna.

Comparison
One of the common features of most antennas is reciprocity. The reciprocity of the antenna leads to the similarity of characteristics such as impedance, gain, radiation pattern, bandwidth and resonance frequencies for the antenna in the sending and receiving mode of operations (Balanis 2015;Stutzman and Thiele 2012;Elliot 1981).
Antenna reciprocity has been examined by simulating two plasmonic antennas facing each other. Figure 13 shows the distribution of the electric field in two antennas for two situations where port 1 is excited, and port 2 is excited. It can be seen that the electric field distribution in the transmitter of cases 1 and 2 and the receiver of cases 1 and 2 are similar. Comparison between the results of tapered (with two different lengths of 5 and 10 μm) and nontapered dielectric rod antennas a Reflection Coefficient, b Gain, and c Radiation Efficiency. The values of the antenna parameters are as follows: S = W = 0.08 µm, W d1 = 0.13, L d1 = 0.29 µm, W d2 = 0.055 µm, L d2 = 0.24 µm, and h silver = 0.02 µm. The results of this part have been obtained by using CST software Also, parameters s12 and s21, which indicate the amount of signal received from the transmitter antenna in the receiver and vice versa, are also shown in Fig. 14. In the whole frequency band, these two parameters are exactly the same.

Conclusion
A planar feeding network is proposed for a dielectric rod antenna in the optical band. This planar feeding system consists of a CPW transmission line connected to a slot placed at the bottom of the dielectric rod. This method makes it possible to integrate the antenna with the optical circuits. The antenna achieves an impedance bandwidth of 43.47% (180-280 THz), the best gain of 12.58 dB at 234 THz and 12.47 dB at 193 THz, and the radiation efficiency above 45.84% over the entire bandwidth. To attain these results, metal dispersion and dielectric losses were taken into account in this numerical analysis. Fig. 8 The normalized simulated radiation patterns of tapered and non-tapered dielectric rod nanoantennas at 195 THz, a in YoZ plane (φ = 90°) and, b in XoZ plane (φ = 0°). The values of the antenna parameters are as follows: S = W = 0.08 µm, W d1 = 0.13, L d1 = 0.29 µm, W d2 = 0.055 µm, L d2 = 0.24 µm, and h silver = 0.02 µm. The results of this part have been obtained by using CST software Fig. 9 The Comparison between the results of the structures with and without SiO 2 cover a reflection coefficient, b gain, and c radiation efficiency. The values of the antenna parameters are as follows: S = W = 0.08 µm, W d1 = 0.13, L d1 = 0.29 µm, W d2 = 0.055 µm, L d2 = 0.24 µm, and h silver = 0.02 µm. The results of this part have been obtained by using CST software   Fig. 13 Electric field distribution for two identical antennas placed at a distance of 5 μm from each other. It is simulated twice: first, port 1 is excited and port 2 is in receive mode, and then port 2 is excited and port 1 is in receive mode. The values of the antenna parameters are as follows: S = W = 0.08 µm, W d1 = 0.13, L d1 = 0.29 µm, W d2 = 0.055 µm, L d2 = 0.24 µm, L = 5 µm and h silver = 0.02 µm Fig. 14 Simulated S parameter for two identical antennas placed at a distance of 10 μm from each other. It is simulated twice: first, port 1 is excited and port 2 is in receive mode, and then port 2 is excited and port 1 is in receive mode. The values of the antenna parameters are as follows: S = W = 0.08 µm, W d1 = 0.13, L d1 = 0.29 µm, W d2 = 0.055 µm, L d2 = 0.24 µm, L = 5 µm and h silver = 0.02 µm