Enhancing directivity of terahertz photoconductive antennas using spoof surface plasmon structure

Terahertz photoconductive antenna (PCA) is an important device for generating ultrabroadband terahertz radiations, being applicable in various scenarios. However, the metallic electrodes in PCAs, a pair of coplanar strip lines (CSL), always produce horizontal electrode modes in a broad THz band, thus resulting in low directivity in the vertical direction. Here, we introduce spoof surface plasmon polariton (SSPP) structures to suppress horizontal electrode modes in a broad band. The suppression principles are accounted to both the forbidden band of the fundamental SSPP mode and the orthogonality between source and higher-order SSPP modes. In the SSPP-modified PCA, we achieve around 2 dBi higher directivity in the vertical direction compared to a typical CSL PCA. Unlike the narrow bands inheriting from conventional metamaterial resonators, the relative operational band of the SSPP-modified PCA is as broad as 48%. This planar SSPP structure is compatible with the well-developed micro fabrication technologies. Thus, our scheme can be combined with the semiconductor material engineering and plasmonic nanoscale structures for further increasing THz output power.


Introduction
Terahertz photoconductive antenna (PCA) [1,2] is an important device for generating ultrabroadband THz radiations, which show important applications in next-generation wireless communications [3,4], non-ionized imaging [5], non-destructive detections [6], and spectroscopic analysis [7,8]. The general principle of PCAs is that the picosecond carriers excited by femtosecond laser are driven by the biased voltages to generate THz radiations. Figure 1(a) is a typical PCA, whose horizontal and vertical directions are along x-and z-axis respectively. The vertical radiation of the PCA is usually harnessed for various applications. However, applications of THz PCAs are hindered by their low output efficiencies. The low-output issue originates from two reasons, including the low optical-to-THz conversion efficiency and low vertical directivity induced by horizontal electrode modes in PCAs.
Here, we propose a scheme to increase the directivity of PCAs in a broad band, by incorporating spoof surface plasmon polariton (SSPP) [33][34][35] structures in PCAs. The SSPP structure is a subwavelength metallic grating, which can host surface electromagnetic (EM) modes, analogous to surface plasmon polariton (SPP) in nano optics [36][37][38]. Different from the circuit-modeling scheme [39] improving output powers at specific frequencies, the SSPP-modified electrode can enhance directivity of the PCA antenna in a band of relative width 48%, and simultaneously achieve around 2 dBi higher directivity in the vertical direction than that of a typical CSL. This design allows for applying THz PCAs to sensing, imaging, and detections. Figure 1 shows the schematic diagrams of a typical CSL and a SSPP-modified PCAs. The typical PCA in figure 1(a) shows a CSL gold structure patterned on a gallium arsenide (GaAs) substrate. The terahertz radiation is generated at the center of the CSL structure, and collimated along the vertical (+z) direction by a silicon lens. However, partial THz waves could be guided along the CSL and form TL modes, which can travel horizontally, thus reducing the THz emission along the vertical (+z) direction. To address the issue of horizontal electrode modes, we propose a SSPP-modified electrode as shown in figure 1(b). The SSPP structure is composed of periodic metallic grooves, which has been intensively utilized to guide surface EM waves [33].

Results
To further quantify the advantages of the SSPP-modified electrode, we firstly compared the radiations from both CSL and SSPP-modified antennas without substrate. Both structures are illustrated in figure 2(a). They share the same parallel metallic CSL with a set of typical parameters, as length l = 2115 μm, width w = 10 μm, and separated by distance a = 90 μm. The parallel metallic strips in SSPP PCA are decorated by periodic metallic patches with period p = 105 μm, width b = 15 μm, and gap g = 15 μm. The thickness along the z-direction of the patches is 0.2 μm. We numerically explore the radiation performances by utilizing time-domain solver of CST Microwave Studio. In simulations, dipole sources in THz range are connected to the two metallic patches at the center of the CSL, to represent the photogenerated currents in PCAs. The boundary condition is open (add space). We employ directivity [40] D = max(P (θ,φ) )/P avg to characterize the performance of PCAs, where P (θ,φ) and P avg = π θ=0 2π φ=0 P(θ,φ) sin θ dθ dφ 4π represent the radiation power in unit solid angle and average radiation power respectively. Since the CSL are along the horizonal (x) directions (as shown in figure 2(a)), their traveling TL modes result in the horizontal leakage with power P +x . By simulation, we find that the SSPP-modified antenna shows lower P +x /P avg than that of the CSL one in 0.93-1.5 THz. The radiation patterns at 0.9 and 1.1 THz (shown in figure 2(c)) further verify that the SSPP electrode can suppress the horizontal leakage, which exist in CSL ones. Simultaneously, the vertical radiations have been increased at least 3 dBi (figure 2(d)). Since both antennas show z-mirror symmetry, the radiations along ±z directions are the same.
We then disclose that horizontal leakages are produced by the electrode modes. Here, we analyze the dispersion relations and eigenmode distributions by utilizing CST Microwave Studio. The backgrounds are 1600 μm along the y directions, and 200 μm along the z directions. The boundary conditions are periodic along the x direction, and perfect electric conductors along the y and z directions. We further show the simulated field patterns of the 3rd and 4th modes on the x-y (Figures S1(c) and (d) in SI) and y-z planes (Figure S1(g) and (h) in SI) (https://stacks.iop.org/NJP/24/073046/mmedia). Obviously, the dominated components (E z and E y ) are well confined around the SSPP structure. It indicates both the 3rd and 4th modes originate from the SSPP structure, instead of the waveguide modes induced by the boundaries of the background box. However, their dispersions, lying above the light line (shown in figure 3(a)), implies their leaky-wave natures. In figure 3(a), the dispersion of the CSL is a straight line without cutoffs, which supports broadband traveling or leaky TL modes. By integrating the SSPP structures, the modified electrode supports four SSPP modes (shown in figure 3(a)), instead of the leaky TL modes. Interestingly, none SSPP mode is excited by the y-polarized dipole in the broad band from 0.93 to 1.5 THz. This band is forbidden for the 1st eigenmode, whose cutoff frequency is 0.93 THz. Although 2nd, 3rd and 4th eigenmodes of SSPP all reside in between 0.93 and 1.5 THz, they cannot be efficiently excited by the dipole source located in the gap. We utilize the excitation efficiency [41] η i = E d * x, y, z · E ei x, y, z dx dy dz for explanation, where i represents the ith eigenmode, E d and E ei represent the normalized excitation field of the dipole and the ith normalized eigenmode field of the SSPP structure, respectively. Along the y direction, the 2nd eigenmode shown in figure 3(b) exhibits even parity, orthogonal to the mode of the dipole source with y-odd parity. Similarly, both excitation efficiencies of 3rd and 4th eigenmodes are vanished, since their odd parities along the x direction are incompatible with the x-even parity of the dipole source. Compared with the near-field patterns of CSL at 0.8 THz (as shown in figure 3(d)), the SSPP mode propagates along the x direction and the fields are confined along both the y and z directions (as shown in figure 3(c)). The excited near-field patterns at 1.2 THz (as shown in figures 3(e)-(f)) further demonstrate the results of suppressing SSPP electrode modes. From the symmetries of the excited SSPP mode shown in figure 3(e), we can tell that the mode pattern at 1.2 THz only belongs to 1st eigenmode, whose propagation is forbidden along the x direction. It is because that 1.2 THz falls into the band gap of 1st eigenmode. In contrast, the TL modes can propagate along the CSL (figure 3(f)), and induce horizontal leakages.
The theoretical analysis above can also be applied in the practical PCA integrated with substrates. We model the GaAs substrate as a 473.7 μm-thick slab with the relative permittivity ε GaAs = 12.94. A silicon lens (ε Si = 11.9) is also integrated for increasing the directivity of PCAs and modeled as a semi sphere with the radius of 1160 μm, whose focus is set at the location of dipole sources. Both metallic structures remain the same as above. Integrating with the substrate and lens, the SSPP-modified antenna still shows about 2 dBi higher directivity (in figure 4(a)) than that of the CSL. Due to the high permittivity of the substrate, the operational bandwidth is downshifted to the frequency range from 0.35 to 0.57 THz, which is consistent with the cutoff frequency of 1st eigenmode as depicted in the inset of figure 4(a). In contrast to the freestanding antennas, the radiation pattern (as shown in figure 4(b)) of substrate-integrated SSPP antenna does not show remarkable suppression of the horizontal leakages. The phenomenon of the similar horizontal leakages is because that the leaky TL modes in CSL are not allowed to radiate into ambient efficiently, rather than the disfunction of SSPP structures. The low outcoupling of TL modes is accounted to the impedance mismatching between the air and the high-permittivity substrate, which highly confines the THz waves. The substrate confinement is also verified with the drastic reduction of −z-direction radiation. The near-field patterns in figures 4(c) and (d) show that the substrate-integrated SSPP structures can still suppress the horizontal SSPP electrode modes, consistent with above freestanding case.
For further demonstrating the performance of SSPP-PCA, we replace the excitation of dipole source with the practical photo-generated current. The optical-to-THz conversion process consists of two steps, including photocurrent generation excited by a femtosecond optical pulse, and terahertz generation from the PCA. We numerically studied the two steps with COMSOL Multiphysics and CST respectively, where Maxwell's equations and drift-diffusion model are solved simultaneously. Regarding the first step, the optical pulse penetrating the GaAs, generates carriers, and then the electric field strength (E = 1.33 V μm −1 ) drives the carriers to drift along the y direction, thus forming the photocurrent. We numerically study this process with a two-dimensional model, whose simulation area is 10 μm × 25 μm on the y-z cross-section. The femtosecond optical pulse follows the Gaussian shape, whose temporal center and width are 2 ps and 133 fs respectively. The optical pulses also have a spatial Gaussian distribution along the y direction, whose half-power beam width is 2 μm. Taking the center wavelength λ = 800 nm of the pulse, we show its optical field spatial distribution on the GaAs substrate in figure 5(a). Driven by the electric field strength E = 1.33 V μm −1 , the photo-generated carriers form transient photocurrent I comsol (t) as depicted in figure 5(b), which quickly decays in several picoseconds. Taking the peak photocurrent at 2 ps, we show the electron spatial concentration in figure 5(c), which is consistent with the field distribution in figure 5(a). To numerically study the second step, we decompose the obtained transient current into Fourier components, whose coefficients are A f = I comsol (t)e −i2πft dt. The spectral response of the SSPP-PCA that is a 3D geometry is simulated in CST. The output radiation power P THz f is shown in figure 5(d), which is proportional to the input current I( f ). Compared with the typical PCA, the radiation power of the SSPP-modified PCA increases around 2 dB in the band 0.45-0.62 THz. We further obtain the total output radiation power with A( f )P THz f df . The optical-to-THz conversion efficiencies of the SSPP-modified PCAs are estimated to be 8.26 × 10 −5 .
The major parameters of optical and electrical properties in the simulation are shown in table 1 (the other details in SI section E).

Conclusion
In summary, we propose a SSPP-modified electrode for increasing the directivity of THz PCAs. The underlying principle is suppressing the horizontal SSPP electrode modes. Compared with the conventional CSL PCA, we numerically demonstrate that the directivity of SSPP-modified one is increased around 2 dBi. Since the SSPP-modified electrode is planar, it is compatible the well-developed micro fabrication technologies. Meanwhile, the microscale SSPP structure could be combined with the nanoscale metamaterial structures [9][10][11][12][13][14][15][16][17][18][19][20][21][22] which may increase photocarrier concentration for further increasing the THz output power. Our proposal could enable rich applications in high-performance terahertz sources.