Introduction of THz technologies
Terahertz (THz) wave is located between the optical frequency region and microwave frequency region in the electromagnetic wave spectrum, covering the frequency range between 0.1 and 10 THz with the wavelength of 3 mm to 30 µm [Reference Lee1]. An overview of THz frequency region is illustrated in Fig. 1. Radiation of this frequency is nonionizing. Thus, it is identified as a much safer alternative to conventional ionizing radiation techniques used in medical diagnoses, such as CT scans and X-rays. The energy of a single photon in THz waves is significantly less than that of X-rays, approximately one millionth of the energy of X-ray photons [Reference Tabata2]. This gives a bright future to THz technology in the biomedical field, such as T-ray scanning used in pharmaceutical settings and skin cancer diagnoses [Reference Zeitler, Taday, Newnham, Pepper, Gordon and Rades3–Reference King, Buchanan and Korter6]. THz waves can penetrate various objects, including wood, plastic, fabric, leather, paper, and, most importantly, human skin [Reference Ho, Pepper and Taday7]. It provides great potentiality in novel sensing and imaging possibilities [Reference Tonouchi8–Reference Burford and El-Shenawee19].
Figure 1. The THz frequency band is positioned between the microwave region and the optical region of the electromagnetic spectrum.
However, despite the research on THz antennas, the current study on PCA is not yet mature. Although the theory of PCA is getting more exceptional, there appears to be a practical knowledge gap in efficiency and gain. There is a lack of joint research on efficiency and gain improvement in the prior literature of PCA enhancement, among which there is only the comparison of conventional substrates and research on various photoconductive materials, or only novel structures of substrates are mentioned. Current work studies and summarizes all the proven enhancement methods for efficiency and gain of PCA in the last decade, with detailed theoretical research and formula expressions. Relative research on silicon meta-lens [Reference Yu, Gu, Yang, Zhang, Li, Tian, Ouyang, Han, O’Hara and Zhang20, Reference Garufo, Sberna, Carluccio, Bueno, Freeman, Llombart, Linfield, Davies and Neto21], plasmonic nanostructures [Reference Catrysse, Veronis, Shin, Shen and Fan22–Reference Moradiannejad25], large area photoconductive nanoantenna arrays [Reference Dreyhaupt, Winnerl, Dekorsy and Helm26–Reference Yardimci and Jarrahi31], dielectric superstrate [Reference Berry, Hashemi and Jarrahi32–Reference Garufo, Carluccio, Freeman, Bacon, Llombart, Linfield, Davies and Neto35], and photonic crystal structures [Reference Rahmati and Ahmadi-Boroujeni36–Reference Alharbi, Alshamrani, Hussain, Alhamdan and Alfihed41] have been put forward in recent years. Also, this paper reviews several challenges and gives a brief overview of the PCA enhancement study, providing a concise direction of THz PCA technology for the next few years.
Theory of THz PCA
Physics
A PCA includes a photoconductive substrate and a set of antenna conductors, often consisting of a pair of DC-biased electrodes. The electrodes are usually metal dipoles with an antenna gap. The electrodes are patterned on the photoconductor, while the gap is positioned at the center of the substrate. The radiation performance of PCA is affected by three factors: the material composition of the photoconductive substrate, the geometry design of the antenna, and the femtosecond laser pulse. Current technology can produce a laser pulse of femtosecond levels, and the antenna geometry is continuing to innovate. In this paper, research on material and novel geometric structures is reviewed.
Regarding the study of photoconductive materials, substrate materials should possess shorter carrier lifetime, higher resistivity, and faster carrier mobility to meet the general requirements [Reference Xie and Lu42]. Thus, many researchers used GaAs, GaP, and ZnTe in various designs [Reference Cabello, De Los Reyes, Sarmiento, Ferrolino, Vistro, Vasquez, Bardolaza, Kitahara, Tani, Salvador and Somintac43, Reference Li, Shi, Huang, Chen, Chen, Chyi and Pan44]. When a PCA is excited, the laser pulses are focused on the center gap, with which the energy propagates into the photoconductor and is absorbed by the substrate; thus, transient photocurrent is produced by the accelerated photo carriers. In most studies, 800 and 1550 nm wavelength laser pulses are used to feed PCA in experiments [Reference Sartorius, Roehle, Kunzel, Bottcher, Schlak, Stanze, Venghaus and Schell45, Reference Ellrich, Weinland, Molter, Jonuscheit and Beigang46]. Figure 2(a) illustrates the process by which the transient photocurrent produced in the photoconductor drives the antenna and eventually leads to the emission of THz pulses. The PCA transient response is depicted in Figs. 2(b–e) [Reference Burford and El-Shenawee19]. When a light pulse is absorbed in a photoconductor, the generation of charge carriers is proportional to light. The photo carriers are accelerated along the DC field and produce a transient photocurrent whose rise time approaches the incident light rise time. The decay time following the peak of the photocurrent is determined by the properties of the photoconductive substrate instead of the temporal distribution of light. If the duration of the carriers of the photoconductor is short, the carriers produced by the optical pulse initiate the recombination process immediately following the absorption of the pulse.
Figure 2. (a) The excitation of PCA by laser; (b–e) generation of photocurrent in semiconductors (red trace) and photocurrent in the antenna gap for the photoconductive material for long carrier lifetime and short carrier lifetime, represented by gray and blue trace, respectively [Reference Burford and El-Shenawee19]; (f) Illustration of a PCA. Bias voltage is applied to both electrodes and surface current is generated on the substrate.
On the other hand, if the substrate material possesses a long carrier lifetime, the resulting carriers will continue to contribute photocurrent after the light pulse is completely absorbed. This causes an increase in the photocurrent pulse, leading to a corresponding enlargement in the output pulse and a decrease in the overall bandwidth of the THz frequency. To circumvent this problem, photoconductive materials with subpicosecond duration are typically utilized. The selection of materials will be discussed in the next section.
Key challenges in THz PCA
Although PCA is prospective due to its simple structure and tiny size, current research is not solving the problem of the low convention efficiency from laser to THz waves. Also, the free space path loss (FSPL) of THz waves is high. Thus, it can hardly cover a distance further than 10 m. The path loss can be computed by the Friis transmission equation [Reference Shaw47]:
\begin{equation}FSPL = 20\log \left( {\frac{{4\pi d}}{\lambda }} \right)\left[ {dB} \right]\end{equation}where d represents the distance and λ represents the wavelength. In accordance with the Friis equation, the THz band has a higher path loss due to its high frequency. This is because the molecule absorption loss leads to multiple degrees of high attenuations [Reference Tamminen, Makela, Ala-Laurinaho, Hakli, Koivisto, Rantakari, Saily, Luukanen and Raisanen48].
The efficiency of PCA comprises two factors—radiation efficiency and impedance matching efficiency, which are defined as [Reference Auston, Cheung and Smith49]
\begin{equation}{\eta _r} = \frac{{{P_r}}}{{{P_{in}}}},\,{\eta _m} = \frac{{{P_{in}}}}{{{P_s}}}\,\end{equation}These equations indicate that efficiency is defined by the ratio of the radiated power Pr to the input power Ps. The total efficiency of PCA is [Reference Auston, Cheung and Smith49]
\begin{equation}{\eta _t} = {\eta _m}{\eta _r} = {P_r}/{P_s}\end{equation}Thus, the optical-to-THz conversion efficiency of PCA is determined by the ratio of the laser power focusing on the PCA gap to the power of radiated THz signals. A study by Goldsmith [Reference Goldsmith50] approximated the laser-to-electrical efficiency as follows:
\begin{equation}{\eta _{LE}} = \frac{{{P_E}}}{{{P_L}}} \approx \frac{{eV_b^2\mu {\tau ^2}{\eta _L}{f_R}}}{{h{f_L}{l^2}}}\end{equation}In the above equation, e and µ correspond to the electron charge and mobility, Vb represents the applied bias voltage, τ signifies the decay time of the photocurrent, ηL denotes the illumination efficiency, fR and fL refer to the repetition rate and frequency of the laser, respectively, while l represents the length of the PCA gap.
Two challenging issues to be investigated in this area are laser-to-electrical efficiency and the gain enhancement due to a high loss of THz pulses. Different studies to improve efficiency and gain are studied in this paper, including the fields of geometric structures, substrate materials, and new technologies.
PCA efficiency and gain enhancement
The radiation of the PCA primarily depends on the following three factors: the material of the photoconductive substrate and antenna, the geometry structure of the antenna, and the femtosecond laser pulse. The current research in THz PCA designs has proved that it can be a promising technology for future use and can be applied in numerous fields of communication, such as medical imaging, spectroscopy, and security. However, because of the low optical-to-THz conversion efficiency and substantial material loss, a severe challenge is to improve efficiency and realized gain. Here, various studies are reviewed to summarize methods that improve PCA efficiency and gain.
Materials
Photoconductive materials of substrates and electrodes
In the past decades, the development in physics and material science has significantly been beneficial to the research in the antenna field. Several suitable photoconductive materials have been used in the design and fabrication of the THz PCA. To obtain high optical-to-THz conversion, a low-loss photoconductive-dielectric material is always required. Photoconductivity is an essential characteristic of THz signal generation; thus, the researchers choose III–V compound semiconductors like GaAs, SI-GaAs (Semi-insulting GaAs), and InGaAs (Indium Gallium Arsenide) in designs, among which the most widely obtained material is LT-GaAs (Low-Temperature Grown GaAs) [Reference Hou, Wen, Fengyue, Zhuo, Liu, Wang, Zhong, Pan and Zhao51]. According to research conducted by [Reference Karthikeyan, Johnston, Gayakwad, Mahapatra, Bodnar, Zhao, Joshi and Hudait52], in the absence of natural materials capable of transmitting THz waves with satisfactory efficiency, III–V compound semiconductors such as GaAs favored over other materials for THz wave generation due to their ability to optimize electrical and optical properties by manipulating their composition. GaAs, in particular, possess a bandgap of 1.424 eV at normal temperature [Reference Chuang53], which is compatible with commonly used titanium-doped sapphire (Ti3+:sapphire) femtosecond pulse sources used to stimulate PCAs [Reference Chia, Zhang, Li, Kusolthossakul, Sathukarn, Tantiwanichapan, Rattanawan, Jintamethasawat, Thamrongsiripak and Nuntawong54, Reference Chen and Yang55]. The use of LT-GaAs as a substrate for THz PCAs was first introduced in 1988 [Reference Smith, Le, Diadiuk, Hollis, Calawa, Gupta, Frankel, Dykaar, Mourou and Hsiang56]. LT-GaAs grown at 250°C via molecular beam epitaxy exhibits high crystallinity, resulting in increased carrier mobility, and excess As3+ within the crystal structure, leading to point defects [Reference Warren, Katzenellenbogen, Grischkowsky, Woodall, Melloch and Otsuka57]. LT-GaAs that grow at 200°C is proven to have a lifetime of around 0.4 ps [Reference Gupta, Frankel, Valdmanis, Whitaker, Mourou, Smith and Calawa58], while 250°C LT-GaAs is found to have 0.7 ps lifetime carrier [Reference Kono, Tani, Gu and Sakai59], indicating that the carrier lifetimes are higher once the temperature improves in LT scale. Table 1 shows the measured lifetimes of LT-GaAs by different research due to the growth temperature [Reference Nemec, Pashkin and Kuzel60].
Table 1. Carrier lifetimes of LT-GaAs at different growth temperatures, and the nature of three types of GaAs material
However, errors in the carrier lifetime measurement are unavoidable. During the last 30 years, the physical properties of GaAs have been studied and measured, and different measured results of the LT-GaAs carrier lifetime have been published. Taking 250°C as the example, in research of [Reference Nemec, Pashkin and Kuzel60], LT-GaAs grown at this temperature has a carrier lifetime of 0.66 ± 0.05 ps. It is also shown that GaAs carrier lifetimes with this temperature are 0.25 ps [Reference Bjamason, Chan, Lee, Brown, Driscoll, Hanson, Gossard and Muller62], 0.7 ps [Reference Kadow, Jackson, Gossard, Bowers, Matsuura and Blake61], 1 ps [Reference Liu, Tani, Nakajima and Hangyo63], and 1.4 ps [Reference Kadow, Jackson, Gossard, Bowers, Matsuura and Blake61]. The InGaAs is also used as photoconductive substrates; however, it has different mobility and resistivity. Table 2 shows the comparison of the properties of these three photoconductive compounds. Overall, LT-GaAs is regarded as the most favorable photoconductive material obtained in PCA studies due to its exceptional combination of characteristics.
Table 2. Comparison of the properties of LT-GaAs, SI-GaAs, and LT-InGaAs
In most antenna designs, copper, gold, and other extremely conductive metal materials are used for electrodes. In THz PCA design, Au (gold), Ti (titanium), and stacked Ti-Au structure are used more [Reference Gao, Chen, Yin, Ruffin, Brantley and Edwards70, Reference Shen, Upadhya, Beere, Linfield, Davies, Gregory, Baker, Tribe and Evans71]. Au has a conductivity of 45.2 × 106 S/m, and by 
$\delta = {\left( {\frac{1}{{\pi f\mu \sigma }}} \right)^{\frac{1}{2}}}$, the skin depth is 74.9 nm at 1 THz frequency [Reference Lee1]. In the Ti-Au structure, the stickiness of Au is improved by assimilating Ti sheets, so that the connection of electrodes and substrates is compact and stable [Reference Pozar72]. Also, no annealing is required after deposition in the Ti-Au fabrication process [Reference Vieweg, Mikulics, Scheller, Ezdi, Wilk, Hubers and Koch73]. Therefore, in the process of PCA design, simulation, and fabrication, the electrodes often consist of Au with tens of nanometers thickness and a 10–20 nm Ti layer.
Key challenges for lower bandgap materials include achieving carrier lifetimes, mobilities, breakdown thresholds, quantum efficiencies, and reproducibility levels comparable to or surpassing those of conventional photoconductive materials. In this case, GaAs and relevant III–V compound semiconductors continue to be the benchmark material for THz PCAs in the past, current, and future optoelectrical research.
Graphene-based PCA design
Graphene is another material that can potentially be the solution of PCA performance enhancement, with 1.5 Tpa Young’s modulus, 24 × 104 cm− 1 absorption coefficient, and 2 × 105 cm2 V− 1 s− 1 [Reference Tamagnone, Gomez-Diaz, Mosig and Perruisseau-Carrier74–Reference Heshmat, Pahlevaninezhad, Darcie and Papadopoulos76]. The intruding graphene layer can be adjusted by changing its Fermi energy level (Ef) through various significant means such as modifying gating voltage [Reference Fei, Rodin, Andreev, Bao, McLeod, Wagner, Zhang, Zhao, Thiemens, Dominguez, Fogler, Neto, Lau, Keilmann and Basov77], substrate effect [Reference Freitag, Low, Zhu, Yan, Xia and Avouris78], external doping [Reference Brar, Sherrott, Jang, Kim, Kim, Choi, Sweatlock and Atwater79], and optical doping [Reference Masyukov, Vozianova, Grebenchukov, Gubaidullina, Zaitsev and Khodzitsky80].
Graphene possesses a distinctive two-dimensional (2D) lattice structure comprising of a single layer of carbon atoms arranged in a hexagonal pattern [Reference Milovanovic, Peeters, Bonča and Kruchinin81], as depicted in Fig. 3. Due to its remarkable optical, electrical, and mechanical characteristics, graphene has become a subject of immense scientific and technological interest for manipulating its properties [Reference Liu, Xie, Du, Liu and Yang82]. To investigate the electromagnetic properties of graphene, initial efforts focus on utilizing Maxwell’s equations to model the electromagnetic waves propagating along the surface of graphene [Reference Wang, Zhang, Yin and Zhou83].
Figure 3. (a) A depiction of the hexagonal structure of graphene, with unit vectors a1 and a2 indicating the sublattice and two atoms per cell. The distance between every two closest atoms is represented by δ. The lattice vectors are shown as blue arrows. (b) b1 and b2 stand for the reciprocal lattice vectors at the Brillouin zone.
However, in some cases, Maxwell’s equations lack analytical methods, so that the use of numerical methods is crucial in comprehending the behavior of guided waves as well as scattering phenomena in graphene [Reference Shao, Yang and Huang84]. The most used methods to analyze this problem include the finite-different time domain (FDTD) method [Reference Wang, Yin and Chen85–Reference Wang, Zhao, Gu, Chen and Yin90], finite-element method [Reference Brar, Jang, Sherrott, Lopez and Atwater91, Reference Yang, Yang, Deng, Mao and Huang92], and method of moments [Reference Burghignoli, Araneo, Lovat and Hanson93, Reference Araneo, Burghignoli, Lovat and Hanson94]. The graphene model in theoretical electromagnetism study and antenna design can be simulated using various commercial simulation software, such as CST, COMSOL, HFSS, and FDTD solutions [Reference Shao, Yang and Huang84, Reference Fallahi, Low, Tamagnone and Perruisseau-Carrier95]. Besides, several published PCA designs and simulations based on graphene are exhibited in Fig. 4.
Figure 4. (a) A dipole PCA consists of two graphene strips placed on a substrate and integrated with a photo mixer at the antenna gap [Reference Zolfagharloo-Koohi and Neshat99]. (b) A graphene-based PCA with superstrate combined with LT-GaAs and SI-GaAs [Reference Emadi, Emadi, Emadi, Safian and Nezhad100]. (c) The schematic view of a graphene-based circular-patched Yagi-like THz MIMO antenna design [Reference Alharbi and Sorathiya101]. (d) The schematic representation of the unit cell of a graphene-based THz sensor, while the design is a THz metasurface composed of a plurality of groups of the unit, showing a high sensitivity to THz waves on a broadband (0.2–6 THz) [Reference Amlashi, Khalily, Singh, Xiao, Carey and Tafazolli102]. (e) A diagram illustrating a dipole PCA made of graphene with dimensions W × L, featuring a gap of length G and powered by a laser source. The electrodes may vary in structure, with different graphene-based stacks offering their unique benefits [Reference Abadal, Hosseininejad, Cabellos-Aparicio and Alarcon103].
The advantage of graphene-based PCA to generate THz waves lies in graphene’s excellent carrier dynamics. After being excited by the light field, due to the ultra-fast carrier relaxation and relatively slow electron-hole recombination, the number of graphene particles will be reversed near the Dirac point, resulting in the real part of the conductance oscillating in the THz range [Reference Ryzhii, Dobinov, Otsuji, Mitin and Shur96, Reference Vasko and Ryzhii97]. Based on this, Dubinov designed a graphene heterojunction THz emitter containing a Fabri–Perot resonator [Reference Dubinov, Aleshkin, Mitin, Otsuji and Ryzhii98]. In this design, graphene generates photoelectrons and holes under laser excitation. When a substantial quantity of electrons and holes are present in the conduction and valence bands, they generate THz radiation via the light-sound cascade phenomenon. The surface plasmons (SPs) have a comparatively low velocity, which results in a relatively high absorption coefficient, also known as SP gain. Consequently, it is significantly superior to conventional PCA with dielectric structures [Reference Dubinov, Aleshkin, Mitin, Otsuji and Ryzhii98].
G. Hanson researched and proposed a conductivity model for graphene at THz frequencies [Reference Hanson104]. Using the expression resulting from the Kubo formula [Reference Gusynin, Sharapov and Carbotte105], a conductivity equation is expressed as
\begin{equation}{\boldsymbol{\sigma }}\left( {\boldsymbol{\omega }} \right) = \frac{{2{{\boldsymbol{e}}^2}}}{{{\boldsymbol{\pi }}\hbar }}\frac{{{\boldsymbol{\,}}{{\boldsymbol{k}}_{\boldsymbol{B}}}{\boldsymbol{T}}}}{\hbar }\ln \left[ {2\cosh \left( {\frac{{{{\boldsymbol{E}}_{{{\boldsymbol{F}}^{\boldsymbol{\gamma }}}}}}}{{2{{\boldsymbol{k}}_{\boldsymbol{B}}}{\boldsymbol{T}}}}} \right)} \right]\frac{{\boldsymbol{i}}}{{{\boldsymbol{\omega }} + {\boldsymbol{i}}_{\boldsymbol{\tau }}^{ - 1}}}\end{equation} In this formula, three constants ћ, e, and kB represent the reduced Planck constant, the charge of one single electron, and the Boltzmann constant. Three variables T, EF, and τ represent temperature, the chemical potential, and the relaxation time of the graphene layer. It indicates better performance with higher chemical potential variation ∆EF. Meanwhile, high-quality graphene sheets display extended relaxation times, which increases their electrical conductivity and results in better antenna performance. From this, a THz metasurface sensor is proposed in [Reference Amlashi, Khalily, Singh, Xiao, Carey and Tafazolli102], and a THz dipole is designed and simulated by Abadal with a graphene radiating element [Reference Abadal, Hosseininejad, Cabellos-Aparicio and Alarcon103]. Figure 5(a) shows the high E-field distribution and surface current for the graphene element in Fig. 4(d). The results of [Reference Amlashi, Khalily, Singh, Xiao, Carey and Tafazolli102] are illustrated in Fig. 5(b) and (c), demonstrating that the graphene-based THz PCA in Fig. 4(e) has improved both efficiency and gain, especially the former. In Fig. 5(b), the growth of chemical potential enhances the PCA performance, as the efficiency and gain increase by 52% and 0.46 dB, respectively, for EF and τ are 0.8 eV and 1 ps. On the contrary, Fig. 5(c) demonstrates the resonant behavior being stronger as the relaxation time increases while the resonant frequency maintains. In this simulation, EF = 0.6 eV and τ is variable. The efficiency and gain increased by 32% and 2.34 dB at τ = 1 ps. In research of [Reference Wu, Zhang, Lian, Wang, Zheng, Ye and Wang106], a three-dimensional (3D) graphene-based photodetector exhibits a high specific detectivity of 1 × 1010 Jones and the response rate reaches 3.1 A/W under a excitation laser of 980 nm. Ref. [Reference Thomson, Ludwig, Holstein, Al-Mudhafar, Al-Daffaie and Roskos107] also uses graphene-based structure to significantly boost the coherent THz detection among nonbiased THz emitters under room temperature. Ref. [Reference Xiao, Degl’ Innocenti and Wang108] illustrates PCAs using nanometer scale plasmonic structures based on graphene is capable of remarkable increase in responsibility (several orders of magnitude). The design in [Reference Joint, Zhang, Poojali, Lewis, Pedowitz, Jordan, Prakash, Ali, Daniels, Myers-Ward, Murphy and Drew109] achieves a noise equivalent power of less than 
$300{\text{ pW}}/\sqrt {{\text{Hz}}} $.
Figure 5. (a) E-field distribution and surface current of a unit cell of the graphene-based metasurface used in THz sensing [Reference Amlashi, Khalily, Singh, Xiao, Carey and Tafazolli102]. (b) The resonance properties of the proposed graphene-based dipole PCA vary with the chemical potential EF [Reference Abadal, Hosseininejad, Cabellos-Aparicio and Alarcon103]. (c) Efficiency enhancement depending on the relaxation time τ [Reference Abadal, Hosseininejad, Cabellos-Aparicio and Alarcon103].
Given these, graphene is playing and will continue to play a fundamental role in the future research of THz PCA on account of its unique features exhibited in the THz band. Current methods used in graphene materials in industrial fields are the solid phase method, vapor phase method, and liquid phase method [Reference Zhou, Qiu and Huang110]. However, achieving high-quality graphene monolayers is a significant hurdle in the research of graphene-based THz PCA. Unless corresponding industrial technology in graphene production is improved, otherwise the cost will be the reduction of radiation effects.
Geometrical configurations
In current PCA designs, a convenient and cheap way to enhance the THz output efficiency and power is to apply silicon lens in PCA designs [Reference Yu, Gu, Yang, Zhang, Li, Tian, Ouyang, Han, O’Hara and Zhang20, Reference Garufo, Sberna, Carluccio, Bueno, Freeman, Llombart, Linfield, Davies and Neto21], and photonic crystals [Reference Rahmati and Ahmadi-Boroujeni36].
Silicon hyperhemispherical lens
During the optical-to-THz conversion process, the resulting THz waves experience significant diffraction at the interface between the substrate and the air. For most PCAs, GaAs is the material of substrates, which has a refractive index of n ∼ 3.4 at THz frequencies. To increase the intensity of emitted THz waves, a hemispherical lens with a similar refractive index to GaAs can be used. Thus, with n ∼ 3.42, silicon is the ideal material for the lens [Reference Afsar, Button and Button111]. With the refractive index, the boundary angle α at which total reflection occurs can be computed as approximately 17.1° using arcsin (n−1), and the solid angle Ω that describes the emitted THz waves is [112]
\begin{equation}{{\Omega }} = 4\pi {\sin ^2}\frac{\alpha }{2} = 2\pi \left( {1 - cos\alpha } \right) = 2\pi \left( {1 - \sqrt {\frac{{{n^2} - 1}}{{{n^2}}}} } \right)\end{equation} where α is the escape cone angle. The hyperhemispherical silicon lens helps increase the escape cone α due to its same refractive index [Reference Filipovic, Gearhart and Rebeiz113]. To reduce the divergence in the air, the lens is supposed to be hyperhemispherical, with a certain distance d between the lens tip and the emitter [Reference Zmuidzinas114]. As shown in Fig. 6(a), with the distance 
$d = R\left( {1 + \frac{1}{n}} \right)$, where n is considered as 3.4, it can be elicited as d = 1.29 R [112]. In these two equations, R represents the radius of the hemisphere.
Figure 6. (a) PCA based on a hyperhemispherical lens excited by a laser source and the geometric dimension of lens design. (b) The simulation results of E-field distribution of a point current dipole PCA in both y–z plane and x–z plane. The E-field distributions along the x-axis at 1 THz are emitting through the meta-lens in the y–z plane and the x–z plane. (c) The simulation of cross-section amplitude distribution in the x–y plane when z = 10, 15, and 20 mm. (d) 1D far-field radiation pattern of the meta-lens on both the y–z plane and the x–z plane [Reference Yu, Gu, Yang, Zhang, Li, Tian, Ouyang, Han, O’Hara and Zhang20].
Furthermore, in the research of [Reference Filipovic, Gearhart and Rebeiz113] and [Reference Gearhart and Rebeiz115], the theoretical analysis of a hyperhemispherical Si lens is proposed. Garufo et al. [Reference Garufo, Sberna, Carluccio, Bueno, Freeman, Llombart, Linfield, Davies and Neto21] proposed a PCA with silicon lens design in 2018 and the simulations show that the hyperhemispherical Si lens increased the radiation power by hundreds of µW within 0.1 and 1.5 THz. Zhu and Ziolkowski [Reference Zhu and Ziolkowski116] mentions several PCA designs, which discuss the performance with hyperhemispherical Si lens providing theoretical research and experimental results support, mentioning that the efficiency and gain of these PCAs have all been improved to over 80% and 13 dB. Research of [Reference Krysl, But, Ikamas, Holstein, Shevchik-Shekera, Roskos and Lisauskas117] indicates that such Si hyperhemispherical lens also provides optimized performance of THz photodetectors by increasing resonant frequency in THz range.
Hyperhemispherical Si lenses are currently one of the simplest ways that are used in THz PCA efficiency and gain enhancement. There is still more improvement in lens designs. The research of [Reference Yu, Gu, Yang, Zhang, Li, Tian, Ouyang, Han, O’Hara and Zhang20] demonstrates the radiation of a PCA with Si meta-lens, as depicted in Fig. 6(b–d), establishing that the PCA exhibits extremely high transmittance and almost parallel collimation THz radiation in the THz band. Such approaches are of significant prospect for THz PCA and even spectroscopy.
Plasmonic nanostructures
With the development of nanotechnology, it is possible to apply nanostructures to the design of antennas. Currently, typical nanostructures have been applied to the design of THz PCA and have proved to be effective means to improve the efficiency of THz signal generation such as plasmonic structures and optical nanocavities, which lead to a higher level of interaction between the photoconductive semiconductor and the optically pumped beam [Reference Yardimci and Jarrahi118].
To begin with, the plasmonic effect is the interaction of free electrons in metal nanoparticles with the incident electromagnetic field. This phenomenon is influenced by various factors such as the shape, size, spacing, and dielectric constant of the metal structure, as well as the material involved [Reference Jiang, Sun, Nowak, Kibrom, Zou, Ma, Fuchs, Li, Chi and Chen119]. The interaction of metal nanoparticles with electromagnetic fields results in surface plasmon resonance, which generates a stronger local electric field [Reference Berry and Jarrahi120]. The interaction between two plasmonic objects can squeeze the field and concentrate the local field when they are close enough to each other [Reference Berry, Wang, Hashemi, Unlu and Jarrahi33].
Notably, the metal plasmonic nano designs include concentrators at the gap, and contact electrodes, both to enhance the optical-to-THz conversion efficiency of THz PCA [Reference Lepeshov, Gorodetsky, Krasnok, Rafailov and Belov121]. The configuration of the plasmonic concentrators is intended to generate surface plasmon waves when illuminated by optical pumps. Surface plasmons refer to the coherent oscillations of electrons that arise at the interface of a metal and a dielectric medium. Upon coupling with an incident electromagnetic wave, the resultant surface plasmons have the ability to propagate along the dielectric interface [Reference Seniutinas, Gervinskas, Constable, Krotkus, Molis, Valusis, Lewis and Juodkazis122]. To enable the coupling of surface plasmons with electromagnetic waves, certain mechanisms need to be put in place. It is necessary to ensure that the parallel wave vectors of both match, which can be determined from both the metal and the dielectric permittivity values [Reference Dionne, Sweatlock, Atwater and Polman123]. By matching the electromagnetic waves and surface plasmon wave vectors of the metal surface, the graphic patterning of the metal surface can promote the excitation of the surface plasmon waves [Reference Heshmat, Pahlevaninezhad, Pang, Masnadi-Shirazi, Lewis, Tiedje, Gordon and Darcie124]. The capacity to stimulate surface plasmon waves offers a range of exceptional possibilities for directing and controlling electromagnetic waves [Reference Yardimci and Jarrahi118]. Such plasmonic nanostructures facilitate a high concentration of laser in the near field while opening the way to both THz transmitting PCA and receiving PCA with higher efficiency [Reference Ishi, Fujikata, Makita, Baba and Ohashi125–Reference Hashemi, Yang, Wang, Sepulveda and Jarrahi131].
According to the above study on the plasmonic concentrators, [Reference Pendry133–Reference Genet and Ebbesen137] have verified that such concentrators improve the optical-to-THz efficiency of THz PCA. The concentrators confine the stimulated surface plasmon waves very closely to the interface between the metal and the photoconductor, thus the laser absorption of the photoconductive substrate near the polymerized structure is significantly enhanced; therefore, the generation of photo carriers in the substrate region is enhanced. Ultimately, the radiation power level increases as the number of photo carriers reaching the antenna electrode increases.
The research of [Reference Park, Jin, Yi, Ye, Ahn and Jeong138, Reference Park, Choi, Oh and Jeong139] and [Reference Jooshesh, Smith, Masnadi-Shirazi, Bahrami-Yekta, Tiedje, Darcie and Gordon140] provides the comparison between conventional PCA and novel PCA with plasmonic nano concentrators, all based on semi-insulating (SI) GaAs substrate and excited by 800 nm wavelength optical pump, shown in Fig. 7. As a result, an approximately 100% increment over the 0.1–1.1 THz range is implemented to the radiation power in [Reference Park, Jin, Yi, Ye, Ahn and Jeong138]. The theoretical principle of the absorbed optical power P by the substrate in volume V can be explained by [Reference Lepeshov, Gorodetsky, Krasnok, Rafailov and Belov121]:
\begin{equation}P = \frac{1}{2}\mathop \int\nolimits^\sigma {\delta ^2}{\left| {{E_0}} \right|^2}dV\end{equation}
Figure 7. (a) Plasmonic concentrators (also known as quantum dots, or QD) that applied at the PCA gap [Reference Lepeshov, Gorodetsky, Krasnok, Toropov, Vartanyan, Belov, Alu and Rafailov132]. (b) The demonstration of a PCA with plasmonic concentrators design [Reference Yardimci and Jarrahi118]. (c) Comparison of measured THz emission power with conventional design and plasmonic concentrators design. (d) Comparison of radiation results of PCA with hexagonal nanostructure, plasmonic light concentrators, and conventional design. (e) SEM of the hexagonal plasmonic nanostructure [Reference Yardimci and Jarrahi31].
As 
$\delta = \frac{{\left| E \right|}}{{\left| {{E_0}} \right|}}$, σ is a medium conductivity, with E increased, there is also an increase on the concentration of nonequilibrium charge carriers near the electrodes. Therefore, the optical-to-THz efficiency is enhanced. In another study, a similar nanostructure was applied to PCA with SI-GaAs substrate. In contrast to the basic plasmonic concentrators, a hexagonal plasmonic structure is proposed [Reference Park, Choi, Oh and Jeong139, Reference Jooshesh, Smith, Masnadi-Shirazi, Bahrami-Yekta, Tiedje, Darcie and Gordon140], and including the conventional optical antenna, all three PCA designs are measured and compared. Hexagonal nanostructures were shown to provide stronger current density localization. The scanning electron microscope (SEM) images of all three PCAs are shown in Fig. 7(c–e). Consequently, the resulting THz field of the hexagonal plasmonic nanostructure is over three times enhanced compared to the PCA with normal plasmonic concentrators, and five times enhanced compared to the conventional PCA.
In more recent studies, another plasmonic nanostructure has been proposed, which applies a novel geometric design to the electrodes, also known as contact fingers [Reference Amlashi, Khalidy, Brown, Xiao and Tafazolli141–Reference Jarrahi143]. Similar to the plasmonic optical concentrator, the plasmonic contact electrode can excite the surface plasmon waves and tightly confine them to the metal–photoconductor interface, thereby increasing the laser absorption in the active region of the photoconductor near the contact electrodes. Another advantage of using such a method is that they are connected directly to the THz PCA, which shortens the transmission path of the photo carriers to the electrodes [Reference Khiabani, Huang, Garcia-Munoz, Shen and Rivera-Lavado144]. Thus, the utilization of plasmonic contact electrodes not only leads to an increase in the efficiency of converting optical energy to THz radiation but also significantly shortens the transport time of photo carriers transported to the PCA when compared to light concentrators. A logarithmic spiral PCA with plasmonic contact electrodes is depicted in Fig. 8(a), along with the optical transmission spectrum through the grating and its corresponding transmission performance, as shown in Fig. 8(b) [Reference Alharbi, Alshamrani, Hussain, Alhamdan and Alfihed41]. With such a structure, a 1.9 mW THz radiation power increase is obtained at the 0.1–2 THz range [Reference Berry, Hashemi, Preu, Lu, Gossard and Jarrahi145].
Figure 8. (a) and (b) A log-spiral PCA design with plasmonic contact electrodes and the figure of the optical transmission performance [Reference Alharbi, Alshamrani, Hussain, Alhamdan and Alfihed41]. (c) and (d) The demonstration and SEM of a 3D plasmonic gratings design for PCA contact electrodes and the measured radiation power comparison with different excite power of 1.4, 2.8, and 5.8 mW [Reference Yang and Jarrahi24]. (e) The implementation and SEM figure of an unincorporated plasmonic grating at the PCA gap. (f) The comparison of THz signal amplitude due to different structures, showing a more than 2 times increase with this structure [Reference Lepeshov, Gorodetsky, Krasnok, Rafailov and Belov121].
Moreover, Fig. 8(c) and (d) shows a 3D plasmonic gratings design for PCA contact electrodes [Reference Yang and Jarrahi24]. This research shows a record-high 7.5% conversion efficiency from optical power to THz radiation power. Another similar study proves a 40-fold stronger output photocurrent in response to an incident THz pulse compared with conventional design. All these PCAs are excited by an 800 nm laser [Reference Heshmat, Pahlevaninezhad, Pang, Masnadi-Shirazi, Lewis, Tiedje, Gordon and Darcie124]. Meanwhile [Reference Heshmat, Masnadi-Shirazi, Lewis, Zhang, Tiedje, Gordon and Darcie146] and [Reference Krotkus, Arlauskas and Adomavicius147] use unincorporated plasmonic grating to the PCA gap to enhance the generation of THz pulses. Such metal strips reduce the lifetime of electrons in semiconductors. The PCAs are based on GaAsBi semiconductor substrate, whose carrier lifetime is shorter than that of LT-GaAs substrate [Reference Krotkus, Arlauskas and Adomavicius147], and the amplitude of the THz signal can be increased by more than 2 times by using this structure, as shown in Figs. 8(e) and (f). However, compared with other methods, this design has a lower optical-to-THz conversion enhancement due to its large capacitance [Reference Heshmat, Masnadi-Shirazi, Lewis, Zhang, Tiedje, Gordon and Darcie146].
Figure 9 [Reference Berry and Jarrahi120] shows another implementation of plasmonic contact electrode design, and the comparison of THz emission power with different optical excite power is shown in Fig. 10(a). The end of the fingers is connected in this PCA, which significantly reduces the path of photo carriers. However, a disadvantage of this design is proved by [Reference Berry and Jarrahi120]: The efficiency of these structures is restricted to 50%, due to only half of the nonequilibrium electrons and holes being able to reach the internal electrodes within a picosecond timeframe.
Figure 9. An implementation of plasmonic contact electrode design and the SEM figure [Reference Berry and Jarrahi120].
Figure 10. (a) The THz power comparison with corresponding optical pump power [Reference Lepeshov, Gorodetsky, Krasnok, Rafailov and Belov121]. (b) A PCA featuring toothed plasmonic contact electrodes has been developed and is presented along with a photograph of the fabricated antenna under a microscope. A comparison between the proposed PCA and a conventional PCA is also included [Reference Zhang, Zhan, Wei, He and Ruan148].
Altogether, with the advancement of nanomanufacturing technology, the integration of plasmonic nanostructures is poised to enable substantial improvements in the performance of the forthcoming generation of high-performance, cost-effective PCAs.
Photonic crystals
It has been investigated that surface plasmon resonance can improve the local electrical field. In the design of THz PCA, there is another efficiency improvement method based on this theory. The photonic crystal structure can be used in the design of the substrate when the substrate is thick [Reference Rahmati and Ahmadi-Boroujeni36]. Based on this, a THz PCA design with a 2D hexagonal lattice of air holes drilled into the substrate is proposed and investigated in [Reference Rahmati and Ahmadi-Boroujeni36], shown in Fig. 11(a). This research proves that this structure can improve both efficiency and directivity. The hexagonal lattice of the proposed structure contains a defect core region that is comparable to the solid photonic crystal waveguide described in [Reference Birks, Knight and Russell149]. This region coincides with the excitation gap of the PCA. By incorporating this defect core region, the effective dielectric constant of the substrate is reduced, which results in a guiding mechanism along the defect axis. Consequently, the effective thickness of the substrate is also decreased, leading to reduced power leakage [Reference Rahmati and Ahmadi-Boroujeni36].
Figure 11. (a) The demonstration of a bowtie PCA with photonic crystal substrate structure. (b) The comparison of radiation efficiency and directivity respect to frequency [Reference Rahmati and Ahmadi-Boroujeni36]. (c) and (d) The radiation power magnitude of transverse electric and magnetic modal fields (|Ex|, |Ey|, |Hx|, and |Hy|) as well as longitudinal power flow (|Sz|) for the two modes of photonic crystal structure in xy-plane in the research of [Reference Rahmati and Ahmadi-Boroujeni36].
As shown in Fig. 11(c) and (d), with the appropriate photonic crystal substrate design, the radiation power is primarily positioned around the defect and directed along the axis of the defect. As a result, the radiation in transverse directions decreases. Therefore, the two major advantages of such designs are summarized as follows. Firstly, the radiated power is mainly oriented along the axis of the defect, so that the main lobe of the radiation pattern is oriented towards the Z-axis within the entire operating bandwidth. This will make the directivity significantly improved. Besides, the photonic crystal structure can reduce the capture power in the substrate, thus improving the radiation efficiency [Reference Garufo, Carluccio, Llombart and Neto34–Reference Rahmati and Ahmadi-Boroujeni36]. This structure provides an average radiation efficiency enhancement of 81%, and an average directivity enhancement of 10.9 dBi over 0.65–1.45 THz, shown in Fig. 11(b).
In a comparative study, a photonic crystal substrate is used in a PCA array design, which improves the radiation efficiency to 96% as that of the conventional contrast design is less than 55%, both in the 0.7–1.4 THz range. The directivity enhancement of this study is over 5 dBi [Reference Rahmati and Ahmadi-Boroujeni150].
Therefore, it is suggested that the THz conductivity and the radiation characteristics of PCA can be improved by using this structure in future research. The proposed substrate is an effective and low-cost method for obtaining high directivity and suitable radiation patterns of PCA arrays, as well as reducing the necessity of using hyperhemispherical silicon lens.
Future prospects
The advancement of photoconductive antennas (PCAs) has been driven by developments in materials, innovative geometries, and femtosecond laser applications. This review closely examines the first two factors, emphasizing the challenge of enhancing optical-to-THz conversion efficiency for future work. Achieving this improvement depends on multiple factors, particularly the choice of photoconductive materials and electrode configurations, which are analyzed in this study.
Although material research has progressed significantly, current fabrication techniques still fall short of fully realizing PCA capabilities. Further exploration into material physics promises potential breakthroughs, introducing advanced photoconductive materials to the field. While complex methods like photonic crystal and plasmonic nanostructures can improve THz radiation, they contradict the PCA’s core principle of design simplicity. Hence, a key research focus is developing novel, simplified structures that enhance THz radiation without compromising PCA’s intrinsic simplicity. The future material research will include the use of topological insulators such as bismuth selenide, and novel nanoparticles such as graphene quantum dots and molybdenum disulfide.
Recent years have seen notable progress in radiation enhancement techniques, such as metasurfaces, which are well-optimized and show potential for extending their operational range to THz frequencies—utilizing both PCA and metasurfaces in future THz communication applications is a promising research direction. Ultimately, advancing optical-to-THz conversion efficiency and THz wave generation could open new avenues for PCAs, offering transformative contributions to the field and reshaping future communication technologies.
Conclusion
This review examines various approaches to enhancing the efficiency of THz PCAs, focusing on material selection and structural design. For instance, advancements in photoconductive and 2D materials significantly improve optical-to-THz conversion efficiency. Additionally, innovative geometric designs in PCA gaps, electrode configurations, and substrates boost radiation output. All studies presented in this review are based on THz transmission PCAs, generating THz pulses excited by laser sources. In summary, THz antennas offer a landscape rich with opportunities and challenges, where even minor improvements in power generation and system design could unlock new directions for advancing future communication systems.
Data availability statement
No new data were created or analyzed in this study.
Acknowledgment
This work was funded by the UK EPSRC CHEDDAR Communications Hub ref: EP/X040518/1, EP/Y037421/1; and ARCOM EP/Z533609/1.
Author contributions
Ruobin Han, Abdoalbaset Abohmra, and Tomas Pires conducted the theoretical research and were the primary authors of the manuscript. Hasan Abbas, Farooq A. Tahir, and Joao Ponciano contributed to refining and optimizing the manuscript. Akram Alomainy, Muhammad Imran, and Qammer Abbasi provided the core research concept and secured funding support.
Competing interests
The authors report no conflict of interest.
Ruobin Han is a PhD candidate at the University of Glasgow, specializing in terahertz photoconductive antennas and nanophotonic device design. His work focuses on performance enhancement strategies in THz systems using novel materials and antenna geometries.
Dr. Abdoalbaset Abohmra is a researcher at the University of Glasgow. His research interests include microwave engineering, THz system integration, and antenna simulation techniques.
Tomas Pires is currently a PhD candidate at the University of Glasgow. His expertise lies in electromagnetic simulations, antenna design, and THz biomedical applications.
Prof. Joao Ponciano is a Senior Lecturer and Vice-Dean for the Glasgow College transnational partnership between University of Glasgow and University of Electronics Science and Technology of China. His research interests include networking systems and technologies, distributed systems and cybersecurity, relational database systems, data mining, simulation modelling and data analytics and software engineering design and development.
Dr. Hasan Abbas is a researcher at the University of Glasgow, focusing on RF systems and antenna design. His current work includes THz sensors and their applications in healthcare and security.
Prof. Akram Alomainy is a Professor of Antennas and Applied EM at Queen Mary University of London. He is internationally recognized for his work in body-centric wireless communications, antennas, and THz technologies.
Dr. Farooq A. Tahir is with the University of Glasgow and COMSATS University Islamabad. His research spans terahertz systems, 5G/6G wireless technologies, and reconfigurable antenna design.
Prof. Muhammad Imran is the Head of the Communications, Sensing and Imaging Group at the University of Glasgow. He has extensive experience in wireless systems, with contributions to 5G, IoT, and THz communication.
Prof. Qammer Abbasi is a Professor at the James Watt School of Engineering, University of Glasgow. His research focuses on antennas, body-centric communications, and THz technologies for healthcare, sensing, and communication applications.
Open access
