We demonstrate, by generating a THz electric field directly within the guiding structure, an active two-wire waveguide operating in the terahertz (THz) range of wavelengths. We compare the energy throughput of the active configuration with that of a radiatively coupled semi-large photoconductive antenna, in which the radiation is generated outside the waveguide, reporting a 60 times higher energy throughput for the same illumination power and applied voltage. This novel, active waveguide design allows to have efficient coupling of the THz radiation in a dispersion-less waveguide without the need of involved radiative coupling geometries.
© 2014 Optical Society of America
The development of waveguides with low dispersion propagation of broadband terahertz (THz) pulses is essential to realize interconnects for future THz communication networks, enhanced THz-time domain spectroscopy (TDS), and to develop new sensing technologies. To date, several THz waveguides have been reported based on dielectric and metallic structures. On the one hand, dielectric based waveguides such as sapphire fibers , plastic ribbon waveguides  and sub-wavelength fibers [3, 4] are not suitable for low dispersion propagation of THz pulses due to the inherent dispersive properties and losses at frequencies above 1 THz. Although hollow core dielectric fibers can boost low-loss and low-dispersion, they are limited in bandwidth due to resonances or bandgap effects . On the other hand, metallic waveguides such as single wire waveguides [6, 7], parallel plate waveguides  and two-wire waveguides [9–12] support the propagation of single cycle THz pulses with low dispersion due to their (almost) non-dispersive transverse electromagnetic mode (TEM). Single wire waveguides carrying radially polarized TEM modes are difficult to excite from commonly available linearly polarized THz sources – such as photoconductive (PC) antennas - due to mode mismatch, and hence it is necessary to make use of a radially polarized THz radiation source . Furthermore, single-wire waveguides are featured by high bending losses, which limit the flexibility of such a solution. Although the low dispersion modes of PPWGs can be conveniently excited by a commonly available PC antenna, such waveguides cannot be used for long propagation distances. This is due to the one dimensional THz confinement in these waveguides which leads to beam expansion in the unguided dimension, and hence subsequent loss due to diffraction. The linearly polarized TEM mode of a two-wire waveguide can be easily excited via a PC antenna and is featured by low bending losses - in contrast to single wire waveguides . In addition, a two-wire waveguide provides a tight two-dimensional confinement of the TEM mode and can thus be employed for guiding over longer distances.
Recently, a metal-dielectric air-core fiber with two embedded indium wires  and a two-wire waveguide structure supported by porous dielectric fibers  have been demonstrated experimentally and theoretically, respectively. The unique ability of the two-wire waveguide to carry a tightly confined linearly polarized TEM mode makes it very promising for future THz interconnects and opens up new prospects for short range ultra-broadband telecommunication networks. One issue that still needs to be addressed is how to efficiently couple THz pulses into the two-wire guiding structure. Both the TEM mode supported by a two-wire waveguide and the THz radiation generated by a PC antenna are linearly polarized. The combined system consisting of a PC antenna interconnected with a two-wire waveguide will therefore be a very effective solution for the efficient generation, coupling and routing of the THz signal. In earlier works [9, 16], the two-wire waveguide mode was excited by positioning a PC antenna close to the input of the waveguide. In this configuration, it can be assumed that the THz radiation is being coupled into the waveguide from free space, similar to the coupling demonstrated numerically in  by considering a single dipole source. However, a large fraction of this free space THz radiation, emitted by the PC antenna, is not coupled into the waveguide and the low, far-field mediated coupling efficiency of the system strongly limits its applicability. The main limiting factor is the difficulty of focusing the THz radiation at the input of the two-wire waveguide as the size of the gap between the wires is close to the diffraction limit.
In this work we address this issue by generating the THz radiation directly inside the waveguide (i.e. active wave-guiding). This is achieved by shining a short laser pulse on a thin piece of GaAs inserted between the wires under a given voltage, following the principle at the basis of a (semi-) large area photoconductive antenna [17–20]. We compare the energy throughput of the active waveguide configuration with that obtained by a semi-large area photoconductive antenna, driven by the same potential, illuminated by the same optical power and consisting of the same semiconductor sample. We also compare the active waveguide throughput with that obtained by placing the semi-large area PC antenna in close proximity to the 10 cm waveguide, so that radiative coupling can occur between the emitted and the guided mode. We note that these comparisons are only meant to provide an overview of the advantage of the active configuration proposed. No optimization of the radiative coupling between the semi-large PC antenna and the waveguide has been attempted.
2. Two-wire THz transmitter
The design of the fabricated active two-wire waveguide is based on the passive waveguide structure reported in , where the low-dispersion and broadband nature of this configuration was demonstrated for a wire separation of 300 µm. Figures 1(a) and 1(b) show photographs of the 10 cm long waveguide used to build the active waveguide and a detail of its input end, respectively. From here on, we shall refer to the resulting active waveguide as a two-wire THz transmitter (TWT). The TWT consists of a piece of GaAs highlighted in Fig.1(b), held between the wires of the waveguide, which is supported by an aluminum base plate acting as its backbone.
Two dielectric slabs are then attached to either ends of the base plate. The dielectric slabs have an 800 µm diameter hole drilled through their centres [Fig. 2(a)]. As shown in the figure, each of the two copper wires (diameter = 250 µm) pass through the centre of these holes on either side of the base plate. As the diameter of the hole is 800 µm, a space of 300 µm is left between the two wires. In order to maintain a uniform separation between the wires, they are kept under tension. Such tension is applied by wrapping the four free ends of the wires around a set of screws [Fig. 1(a)]. Finally, a thin rectangular piece of GaAs (300 µm × 300 µm × 5 mm) is inserted between the two wires to form the TWT as shown in Fig. 1(b). The electric field required for activating the integrated PC antenna is obtained by applying a voltage directly to the copper wires. Hence, to avoid a short circuit in the system, the screws were made of plastic. In order to increase the contact efficiency between the copper wires and the GaAs piece, silver paint was applied at the contact points.
The TWT supports a linearly polarized, tightly confined TEM mode at 1 THz. A theoretical study  has shown that with the increase in wire separation, the mode carried by the two-wire waveguide is no longer linearly polarized as it breaks down to two weakly coupled Sommerfeld modes (radially polarized modes). Hence in order for a two-wire waveguide to carry a linear polarization, the separation between the two wires needs to be very close to the wavelength of operation. In this work, we employed a wire separation of S = 300 µm so that the waveguide is suitable for carrying THz radiation with a central wavelength of λ = 300 µm (corresponds to 1 THz in frequency).
3. Results and discussions
3.1 Active and passive waveguide configurations
We compared the energy throughput for the passive configuration (THz semi-large area PC antenna; two-wire waveguide; detection) with the TWT (active two-wire waveguide; detection) at constant optical excitation power and applied potential. To this end we carried out three experiments employing an electro-optical sampling setup for THz detection. In the first experiment no waveguide was used. The purpose of the first measure was to record the THz pulse from a PC antenna, so that its THz pulse energy can be used as a reference to evaluate the coupling efficiency of the passive and active waveguide configuration. A scheme of this experiment is reported in Fig. 2(b). A thin rectangular piece of GaAs is held between two copper strips serving as electrodes [see Fig. 2(c)], so that when a bias voltage is applied, this configuration serves as a semi-large area PC antenna for THz generation. The emitted radiation is collimated by a parabolic mirror confocal to the emission point and, after properfiltering, is focused onto the detection crystal (Zinc Telluride - ZnTe) by a second parabolic mirror, collinearly with an 800 nm optical probe pulse. A balanced detection scheme allows to record the variation of the probe polarization induced by the THz field in the ZnTe crystal via the electro-optical effect as a function of the delay between the probe and the THz pulse, where the recorded signal is proportional to the THz electric field [21,22].
In a second experiment, we evaluated the coupling efficiency of the passive configuration. The same semi-large area PC antenna, external to the guiding structure, was coupled to the 10 cm length two-wire waveguide [passive configuration; Fig. 2(d)]. The THz pulse was measured after propagation through the waveguide, with the output of the waveguide focused on the first parabolic mirror of the detection scheme. We note that this configuration does not guarantee optimal coupling of the radiation emitted by the semi-large photoconductive antenna into the waveguide. To that end specific optimization strategies should be investigated, which elude the scope of this paper.
Finally, in the third experiment, the mode coupling of the THz pulse from the 10 cm long two-wire transmitter in the active configuration [Fig. 2(e)] was recorded. The waveguides used for the second and the third had the same dimensions (for the sake of comparison). Note that we employed the same GaAs piece in all three experiments.
In order to pump the THz Kit we used a Ti:Sapphire mode locked laser (Mai-Tai, Spectra-Physics) with 125 fs pulse duration and 80 MHz repetition rate. Electro-optical sampling has been performed in a  ZnTe crystal of 2 mm thickness, in order to characterize the THz signal. The copper wires are connected to a modulator, consisting of a bipolar high voltage source able to supply 110 V at 11 kHz.
3.2 Comparison of energy throughputs
Figure 3(a) shows the reference THz waveform as emitted by the semi-large PC antenna [Fig. 2(c)], normalized to its peak. We note that here reflections occur both in the detection and in the generation side of our experiment, an issue that we are currently addressing. The measured power spectra of the semi-large PC antenna (blue curve) and of the signals obtained from both waveguide configurations, namely passive two-wire waveguide (green shaded) and TWT (red for a 10 cm long WG and black for a 20 cm long WG) are presented in Fig. 3(b).
The energy of the output pulses, normalized to the energy of the PC antenna was extracted by integrating the square of their measured temporal field profile. We found that the pulse energy for the 10 cm long waveguide and TWT were nearly 0.6% and 40% of the pulse energy of the PC antenna, respectively, showing that the TWT couples a THz signal 60 times stronger than that achieved by approaching the semi-large area PC antenna to the waveguide.
In order to estimate the propagation losses of our TWTs, we compared the normalized output energy of the 10 cm long TWT with a 20 cm long equivalent structure, and found that the additional 10 cm of waveguide added ~11 dB of loss. Figure 3(c) shows the output waveforms for the 20 cm long TWT (normalized to its peak). We note that the 20 cm waveguide has not been optimized in all its parameters, for instance in terms of uniformity of the separation between the copper wires. Yet at this stage we only wish to demonstrate that single cycle pulses can be generated and transported by the proposed configuration and that the spectrum is not significantly different with respect to the 10 cm long case.
We numerically investigated the 20 cm active waveguide case and we show in Fig. 3(d) the comparison between the spectrum of the simulated pulse (orange) and that of the experimentally recorded electric field (black). In the inset of Fig. 3(c) we present the simulated time dependent electric field. The comparison shows a quite good agreement between our numerical simulation and the experimental results. For the numerical evaluation of the 20 cm long TWT’s signal, a commercial package (CST Microwave Studio) has been employed and perfectly matched layer boundary conditions have been used with “open-add space” boundary conditions applied in all directions. The simulation environment mimics the experimental configuration with a photoexcitation signal of 120 fs duration, which determines the rise time of the photocurrent in GaAs. Subsequently, free carriers are generated in the substrate and hence the decay time depends on the carrier lifetime of the photoconductive material. The GaAs wafer is considered to be lossless and dispersionless and the copper wires are completely homogenous. The discrepancy between the experimental results and simulated data can be ascribed to inhomogeneity in the wires along the waveguide and accompanying losses and scattering.
In conclusion, we have addressed the issue of coupling THz radiation efficiently in a passive two-wire waveguide by introducing a novel active waveguide design (named as a two-wire THz transmitter, TWT), in which the generation of the THz signal occurs directly inside the guiding structure. This was realized by inserting a small piece of GaAs in between the two wires of the waveguide, serving as a semi-large photoconductive antenna. The wires of the waveguide act as the electrodes of the device, connected to a modulator, consisting of a bipolar high voltage source able to supply 110 V at 11 kHz. We found that the pulse energy collected by our detection system for the 10 cm long passive waveguide is 40% of the pulse energy of the semi-large area photoconductive antenna when employing as emitter the same piece of semiconductor (for a given potential and illumination power). These results may be of interest for the development of future ultra-broad band short-range telecommunication networks.
As an example of application of the proposed two-wire waveguide, and in order to show the potential for a modular approach, we demonstrated “active” frequency filtering by inserting a polymer Bragg grating between the two wires. Bragg gratings are a key component of fiber optics based communication systems. They have been employed for dispersion compensation , the realization of band rejection filters , wavelength selective devices [25, 26], sensing , structural health monitoring  and other applications. Similarly, Bragg gratings can also be used to achieve THz frequency filtering [29, 30] which can find several applications in THz communication and spectroscopy.
For this work, we fabricated a Bragg grating from a low-cost polymer mesh made of extruded polypropylene. In the original polymer mesh shown in Fig. 4(a), horizontal and vertical sets of polymer rods are woven together. To obtain a one-dimensional structure for the grating, we removed the horizontal set of polymer rods from the mesh and used the vertical rods as the Bragg grating (Fig. 4(b)). The average diameter of these rods - as measured under an optical microscope - is 110 ± 10 µm and the average air spacing in between the rods is 137 ± 20 µm. As a result the period of the grating is approximately 247 ± 30 µm. For the proposed experiment, 16 periods of the grating were employed, approximately resulting in a 4 mm long sample.
The measured temporal signals are shown in Fig. 5(a). As it can be clearly seen, the peak amplitude of the signal is delayed due to the insertion of the grating, which increases theeffective optical path length of the THz pulse propagating in the waveguide. The transmission spectrum of the grating is shown in Fig. 5(b). We can observe from the spectrum that the insertion loss for the grating varies from 1 dB to 7 dB between 0.3 and 1 THz. A fine notch of about 23 dB was observed at 0.58 ± 0.01 THz with a line width of ~16 GHz.
As the grating consists of non-uniform polymer rods and the spacing between the rods is not equal to its diameter, it is difficult to determine the effective refractive index (neff) and directly apply the Bragg condition λBragg =2neffɅ (where λBragg is the reflected wavelength and Ʌ is the period of the grating). Hence, a commercial-grade simulator based on a finite difference time domain (FDTD) method  (where the grating structure can be properly modelled) was used to predict the dip in the transmission spectrum. For the simulation of the grating, the rods were assumed to be regular, featured by a 110 µm diameter and uniformly spaced by 137 µm.
Figure 6(a) displays a snapshot of the FDTD simulation layout. The simulation involved a PML boundary that encloses the simulation area comprising the waveguide, the Bragg grating and the THz single dipole source. A PML provides an index-matching boundary for the simulation region, which thereby prevents the Fresnel reflection of the electromagnetic radiation leaving the simulation region, while avoiding any alteration of the FDTD simulation results from the reflected radiation. For the FDTD simulation the real part of the refractive index of polypropylene was taken to be equal to 1.51 in the range from 0.2 THz to 2.5 THz . The metallic wires were assumed as perfect electric conductors (PECs). The power spectrum from the FDTD simulation predicted the dip in the grating’s response to be at ~0.59 THz (Fig. 6(b)) which is in good agreement with the experimental results. However, the dip in case of simulation is ~8 dB as compared to the experimentally observed value of 23 dB. This mismatch in the depth of the dip is most probably due to the simplistic model of our FDTD simulations where the metal wires are assumed as PECs and the loss coefficient of polypropylene is not taken into account.
The authors would like to gratefully acknowledge NSERC (the National Science and Engineering Research Council) in Canada and the MESRST (the Ministère de l'Enseignement supérieur, de la Recherche et de la Science et la Technologie) in Quebec. M.C. acknowledges support from the People Program (Marie Curie Actions) of the European Union's Seventh Framework Program (FP7/2007-2013) under the REA grant agreement n° . M.P. acknowledges the support from the FP7 Marie Curie Actions of the European Commission, via the Career-Integration Grant contract-Nº . C.R. acknowledges support from a Vanier Canada Graduate Scholarship. M.F. acknowledges support from the People Program (Marie Curie Actions) International Outgoing Fellowship (ATOMIC) under REA grant agreement n° .
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