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Abstract
Metallic deep-subwavelength features can aid in integration of microscopic components or strong light-matter interaction with a low-loss dielectric waveguide platform. A mode converter or coupler is required to integrate the devices. However, there is a vast difference in the physical scale and modal distribution between the deep-subwavelength structures and the dielectric waveguide platform. Here, we employ a tapered-slot mode converter to facilitate the electromagnetic wave transition from a gap width smaller than 1/100 of a wavelength (λ) to a larger-scale mode that is amenable to a terahertz (THz) silicon photonic-crystal waveguide. The mode converter is metallic, and fabricated on top of indium phosphide substrate, leading to incongruity with the modal field distribution of the silicon photonic-crystal waveguide. To mitigate this, a sandwiched structure is developed to match the symmetry of the mode of photonic-crystal waveguide, thereby facilitating efficient transfer of energy. For a proof of concept, we integrate a resonant tunneling diode (< 2 µm) as a THz detector in a photonic-crystal waveguide platform in the 0.3-THz band (λ ∼ 1 mm). The coupling efficiency is close to unity (∼90%) with broadband operation (∼50 GHz) in experiments. Thereafter, we employ the developed integrated device as a receiver in a THz communication experiment. In this manner, we successfully achieve real-time error-free data transmission at 32 Gbit/s, and demonstrate wireless transmission of uncompressed 4K high-definition video.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, there has been growing interest in the interaction of electromagnetic waves with structures much smaller than wavelength from terahertz (THz) to light waves [1,2]. Such deep-subwavelength structures can provide strong field confinement, interface with microscopic components, and achieve strong-light matter interaction. Various prospective applications have been developed such as integrated photonic circuits [3], bio-sensing [4] and quantum information technology [5]. Because deep-subwavelength structures are typically composed of metal, the high concentration of electromagnetic waves at the surface of the metal leads to severe Ohmic loss, which may suppress the expected benefits [6]. As such, it is desirable to seek a hybrid approach, which can achieve deep-subwavelength field confinement where required, but otherwise employs an efficient waveguiding structure. All-dielectric waveguides are a viable candidate for the latter, as they mitigate the possibility of Ohmic loss altogether. However, it is challenging to realize an interface between such structures due to the large difference in physical size and modal distribution. Therefore, an efficient mode converter is essential.
Recently, a highly efficient mode converter from a silicon (Si)-wire waveguide using Si-on-insulator substrate to a deep-subwavelength plasmonic waveguide has been demonstrated in the infrared range [7]. Here, we propose to employ a Si photonic-crystal waveguide instead of a Si-wire waveguide. Photonic-crystal waveguides are clad with physically-robust photonic-crystal, which renders the samples free-standing, and hence there is no need for a potentially-lossy substrate. The photonic-crystal waveguides also provide narrow field confinement in the in-plane dimension using a photonic band gap (PBG), and combined with total internal reflection for vertical confinement, this leads to highly efficient waveguiding [8]. Photonic-crystal waveguides with propagation loss less than < 0.1 dB/cm [9,10], which is two or three orders of magnitude smaller than that reported for metallic lines, have previously been demonstrated for THz wave [11,12]. Moreover, a variety of photonic-crystal passive devices have been developed for THz applications, including filters [13,14], absorbers [15], resonant cavities [16,17], diplexers [18], antennas [19–21], and near-field links [22].
Compact THz systems that are founded upon the photonic-crystal waveguide platform will depend on the incorporation of active devices. A resonant tunneling diode (RTD) is a promising candidate for this purpose, as they are highly compact, have low power-consumption, and can operate as both sources and detectors of THz waves at room temperature [23,24]. For THz-range operation, the size of the RTD mesa should be smaller than 2 µm, and hence it is a deep-subwavelength electronic device. Thus, in order to achieve efficient coupling between an RTD and a photonic-crystal waveguide, an efficient mode converter is required. Previously, we have integrated an RTD chip with a photonic-crystal waveguide in the 0.3-THz band [25]. To demonstrate the feasibility of applications using the developed devices, THz fiber communications have been demonstrated at 10 Gbit/s [26]. However, the achievable data rate in that work was limited by inefficient coupling, and hence bit rates over 30 Gbit/s have not yet been presented.
In this article, we design, fabricate and characterize a tapered-slot mode converter that interfaces between with a deep-subwavelength structure and a photonic-crystal waveguide in the 0.3-THz band. As a demonstration, we place an RTD in the deep-subwavelength structure, and operate it as a THz detector. In this way, we estimate the coupling efficiency, and show that this integrated device is viable for THz-range communication applications. The structure of the article is as follows. First, we present our theoretical design, and clarify how to achieve high coupling efficiency. Then, we characterize the fabricated device, and show that it supports high data rates. Finally, we demonstrate the wireless transmission and real-time reception of uncompressed 4K high-definition video via a free-space link.
2. Principle and design
An RTD was integrated into a sandwiched tapered-slot mode converter of a photonic-crystal waveguide, as shown in Fig. 1. The RTD chip was processed from indium phosphide (InP) substrate, while the photonic-crystal waveguide was based on a 200-µm-thick high resistivity (20 kΩ-cm) Si wafer designed specifically for this study. The relative dielectric constants of InP and Si were 12.6 and 11.6, respectively. The dielectric loss of the InP substrate can be neglected owing to the low tanδ (∼0.003) and the short length of the tapered-slot mode converter in the 0.3-THz band. For the 0.3-THz band operation, the lattice constant and air-hole radius of the photonic-crystal waveguide were set to 240 µm and 72 µm, respectively [9]. To bridge the disparities between the RTD and the photonic-crystal waveguide dimensions, a tapered-slot mode converter with an exponential-curve profile was used to provide an adiabatic-impedance (or effective-refractive-index) gradient from the former to the latter. The average impedance of RTD (∼ 50 Ω) was typically smaller than that of the photonic-crystal waveguide (∼300 Ω) in the 0.3-THz band. Therefore, the iterative impedance of such a tapered-slot mode converter behaves as an impedance transformer to achieve broadband characteristics [27–29]. The exponential taper profile y1(x) was determined by the width a, length l and curvature ρ, the exponential taper profile y2(x) was by the width a and length l, as shown in Fig. 1. The resulting exponential relation explains the taper section
Fig. 1. Schematic of RTD chip integrated with the photonic-crystal waveguide. A sandwiched tapered-slot-type RTD chip integrated into the groove of the photonic-crystal waveguide. To reduce radiation loss, a single-thickness InP substrate is capped onto the surface of the mode converter. The length of the top InP substrate is l + TL2. y1(x) and y2(x) are the exponential curves of the tapered-slot mode converter.
Fig. 2. Normalized electric-field intensity distribution of a sandwiched tapered-slot-type RTD chip integrated with the photonic-crystal waveguide. The relative dielectric constants of InP, Si, and SiO2 are 12.6, 11.6, and 3.4, respectively. The resistivity of Au and Si are 2.5 × 10−9 kΩ-cm and 20 kΩ-cm, respectively. The dielectric loss of the InP substrate can be neglected owing to the low tanδ (∼0.003) and the short length of the tapered-slot mode converter in the 0.3-THz band. The mode converter at the center plane of the photonic-crystal waveguide traps THz waves directly from the waveguide to enhance coupling efficiency. The dimensions of the RTD chip are l = 320 µm, TL1 = 55 µm, and TL2 = 0 µm; and the MIM size is 40 × 90 µm2 with a 0.6-µm-thick SiO2 layer. The gap g and width s of the coplanar stripline are 6 µm and 5 µm, respectively. The width of the RTD chip is 272 µm.
The detailed optimization process is as follows: we numerically investigated the coupling efficiencies between the tapered-slot mode converter and the photonic-crystal waveguide at 0.322 THz. We evaluated the coupling efficiency as a function of the InP substrate thickness d and taper length l, as shown in Fig. 1, using a three-dimensional (3D) finite-integral time-domain electromagnetic simulation (CST Studio Suite 2018). The terminal gap of the mode converter g was 6 µm. The width of the coplanar stripline and the RTD chip were 5 µm and 272 µm, respectively. Figure 3(a) shows the dependence of the coupling efficiency on d without top InP substrate. The result shows that d has a significant effect on the coupling efficiency. The intensity of THz waves of the photonic-crystal waveguide was the strongest in the center plane of the 200um-thick Si, and hence the optimum thickness was 100 µm, as it aligns the tapered-slot mode converter to the photonic crystal waveguide. Figure 3(b) shows the dependence of the coupling efficiency on l. By capping a second piece of InP substrate on top of the tapered-slot mode converter, the coupling efficiency was enhanced by approximately 15%. Consequently, the maximum coupling efficiency of ∼76% achieved was obtained at l = 320 µm. However, the taper length l was involved in a trade-off between the coupling efficiency and losses. The dielectric loss of the InP substrate can be neglected owing to the low tanδ (∼0.003) at the 0.3-THz band. Thus, the losses consisted of the metal loss, reflection loss, and radiation loss. Figure 3(c) shows the simulated loss as a function of l at 0.322 THz. The metal loss decreased with decreasing l. Meanwhile, the reflection and radiation losses increased dramatically, with values reaching 2.2 dB at l = 100 µm. The radiation and reflection losses exhibited small values, whereas the coupling efficiency achieved a maximum value for l = 320 µm. Figure 3(d) shows the dependence of coupling efficiency on curvature ρ of the exponential taper profile y1(x). The ρ was selected to be 0.8 for this design, which exhibited high coupling efficiency and broad bandwidth. Values of ρ under 0.8 produced a lower coupling efficiency above 0.365 THz, which was caused by standing waves occurring due to the interaction between the tapered-slot mode converter and photonic-crystal waveguide in the y direction as shown in the Fig. 2. A larger value of ρ over 0.8 produced lower coupling efficiency due to the impedance mismatch between the tapered-slot mode converter and the photonic-crystal waveguide. In addition, the simulation results indicate that the clearances between the tapered-slot mode converter and the photonic-crystal waveguide do not affect the coupling efficiency (see Appendix 1).
Fig. 3. Optimization of the tapered-slot mode converter. (a) Dependence of the simulated coupling efficiency for a structure without top InP on the thickness d. (b) Dependence of the simulated coupling efficiency on the taper length l. Red solid and blue dashed lines denote simulated coupling efficiency of a structure with and without top InP substrate, respectively. (c) Dependence of the simulated loss on the taper length l. (d) Dependence of the simulated coupling efficiency on the curvature ρ of the exponential taper profile y1(x). The yellow region indicates that the propagation band gap of the photonic-crystal is 0.298-0.385 THz.
We took into account the impedance of the RTD, which depends on the bias voltage, and coplanar stripline (CPS) as a circuit model [31] using a high-frequency circuit simulator (ADS 2018). The coupling efficiency can be changed by the lengths of CPS TL1 and CPS TL2. CPS TL1 acted as a sliding short for changing the coupling efficiency, while CPS TL2 served as an impedance transformer between the RTD and the tapered-slot mode converter. In the equivalent circuit shown in Fig. 4(a), the mode converter block represents the S-parameter results obtained by the 3D finite-integral time-domain method (CST Studio Suite 2018). Figure 4(b) and 4(c) show the dependence of coupling efficiencies on the lengths of CPS TL1 and CPS TL2 at 0.322 THz, respectively. Because the MIM operates as a THz wave reflector, phase cancellation occurs at the RTD when the phases of the received and reflected THz waves were different. Therefore, the coupling efficiency was decreased dramatically when the length of CPS TL1 was 0 µm and 185 µm. Because the characteristic impedance of the CPS was determined by its width and gap, CPS TL2 had a small effect of the coupling efficiency because the width and gap of CPS TL2 were the same as those of the ending of the tapered-slot mode converter. It was observed that the optimal lengths of CPS TL1 and CPS TL2 are 55 and 0 µm, respectively, resulting in a maximum coupling efficiency of ∼80% between the RTD and the photonic-crystal waveguide.
Fig. 4. Optimization of the sandwiched tapered-slot-type RTD chip. (a) Equivalent circuit of the RTD chip integrated with the photonic-crystal waveguide for coupling-efficiency calculation. (b) Dependence of the calculated coupling efficiency on the length of CPS TL1. (d) Dependence of the calculated coupling efficiency on the length of CPS TL2.
3. Coupling efficiency measurement
We employed a micro-electromechanical-systems (MEMS) fabrication foundry service to fabricate photonic-crystal waveguides in the THz-frequency range. The samples were fabricated by photolithography and plasma-etching based on the manufacturing process for a micromachine from a 200-µm-thick 4-inch (100) single crystalline Si substrate with resistivity over 10 kΩ-cm. The fabricated photonic-crystal waveguide is shown in Fig. 5(a). The groove of the photonic-crystal waveguide was used for hybridizing with an RTD chip.
Fig. 5. Fabricated photonic-crystal waveguide and tapered-slot-type RTD chip. (a) The fabricated photonic-crystal waveguide; (b) Cross-sectional view of the photonic-crystal waveguide, in which cross-sectional damage can be observed after the cutting; (c) Fabricated tapered-slot-type RTD chip.
The fabricated RTD chip is shown in Fig. 5(b). The RTD was situated at the end of the tapered-slot mode converter. The RTD has two electrodes for contact at the top and bottom sides of the epitaxial layer, which was similar to that shown in [31]. These electrodes with 150-nm-thick Au were formed through sputter deposition. Aside from the RTD region, the overall GaInAs epitaxial layer was removed from the semi-insulating InP wafer by wet-etching. Thereafter, a 600-nm-thick SiO2 insulating layer was covered all around, except on the contact, which was left open to facilitate electronical contact with the electrodes. The SiO2 layer of the electrodes was removed by photolithography and reactive ion-etching processes for the open contact. The tapered-slot mode converter was extended from the two contact electrodes of the RTD. The thickness of the Au formed by sputter deposition was 800 nm. Finally, the substrate thickness of the RTD chip was reduced to 100 µm. Hybrid integration of the RTD chip with the photonic-crystal waveguide was achieved by inserting the RTD chip into the groove of the photonic-crystal waveguide. In this way, propagating THz waves in the photonic-crystal waveguide were trapped into the sandwiched tapered-slot mode converter and guided to the RTD through the CPS.
To measure the coupling efficiency between the RTD and the photonic-crystal waveguide, we operated the RTD as a receiver by using the experimental setup shown in Fig. 6. The RTD and photonic-crystal waveguide devices were held on a polystyrene foam to measure the coupling efficiency. The polystyrene foam has a low refractive index (1.02), which is close to that of air in the 0.3-THz band [32]. The photonic-crystal waveguide was first fixed on the polystyrene foam using paper tape. Then, the RTD chip and top InP substrate were placed in the groove of the photonic-crystal waveguide using tweezers. In this experiment, the RTD input THz wave was generated by a 9× multiplier applied to a millimeter-wave signal, resulting in a generated THz frequency range of 0.30–0.39 THz. We integrated a Si tapered structure with the photonic-crystal waveguide to create efficient coupling to a WR3 hollow waveguide. The generated THz wave travelled through a 1-inch-long WR3 hollow waveguide into the zero-biased RTD for detection. The detection current produced by the RTD was measured through a coaxial cable by using a direct-current (DC) ammeter. The RTD was connected to the DC ammeter through electrode pads. The detected THz wave power with the RTD serving as receiver in this configuration can be calculated using the square law of detection. The responsivity of the RTD resulting from the current–voltage characteristics was considered in this measurement.
Fig. 6. Experimental block diagram of coupling efficiency measurement. To enhance the coupling efficiency, a 100-µm-thick InP substrate is capped onto the surface of the mode converter. A ground–signal–ground probe is connected to the pad of the RTD chip to provide DC supply and measure the detected signal. The dimensions of the tapered-slot-type RTD chip are l = 320 µm, TL1 = 30 µm, and TL2 = 110 µm.
Figure 7 shows a comparison of the theoretical and experimental coupling-efficiency results. It can be seen that the experimental results, shown by the dotted line, were in close agreement with the simulation results (solid line), which were calculated by using 3D finite-element frequency-domain method (CST Studio Suite 2018). The measured coupling efficiency was in very good agreement with the theoretical result. In this result, the measured maximum coupling efficiency was ∼90%, and the 3-dB bandwidth was ∼50 GHz. The results indicate the developed tapered-slot mode converter can trap the THz waves from the photonic-crystal waveguide efficiently as expected.
Fig. 7. Experimental and theoretical coupling efficiencies between the RTD and the photonic-crystal waveguide in the fabricated integrated device. The blue solid and red dotted lines indicate the theoretical and experimentally determined coupling efficiencies of the sandwiched tapered-slot-type RTD chip, respectively. The yellow region indicates that the propagation band gap of the photonic-crystal is 0.298-0.385 THz.
4. Terahertz communication experiment
We performed THz communication through a 1-inch-long WR3 waveguide, as shown in Fig. 8. Because the coupling loss between the Si tapered structure and the WR3 waveguide was less than 0.2 dB, it can be neglected [9]. The developed and fabricated RTD chip was integrated with the photonic-crystal waveguide as illustrated in Fig. 8(a). To make a module for THz communication experiments, we first spread a small quantity of glue on the surface of the baseband circuit. Then, we used a tweezer to place the RTD chip onto the baseband circuit. After the RTD chip was completely fixed, we implemented wire bonding to make interconnections between the RTD chip and coplanar waveguide of the baseband circuit. Finally, we integrated the photonic-crystal waveguide with the RTD chip on the baseband circuit using a tweezer and glue. The photonic-crystal waveguide length was ∼5 mm. On the transmitter side, a beating optical signal from two continuous-wave laser diodes was modulated using on–off keying by a pseudo-random bit stream. The optical signal modulated through the intensity modulator was amplified by an erbium-doped fiber amplifier, following which it was down-converted to THz frequencies via a uni-traveling-carrier photodiode (UTC-PD). The UTC-PD transmitter extracts the THz-range beat frequency via envelope detection, and it has a 3-dB bandwidth of over 50 GHz [33]. The UTC-PD transmitter was on–off modulated by using a pulse pattern generator through an optical intensity modulator, and a bias voltage was supplied through a bias tee. The carrier frequency was 0.35 THz in this experiment. The RTD receiver was located at the opposite side of the WR3 hollow waveguide. The detected signal was amplified using a 29-dB-gain pre-amplifier with a bandwidth of 38 GHz, following which it was waveform-sharpened by using a limiting amplifier. The RTD receiver was connected to the coplanar waveguide by using a coaxial connector with a 21-GHz bandwidth via wire-bonding. We also measured the responsivity of the RTD receiver depending on the bias voltage in another experiment. The result indicates that the RTD receiver has the highest responsivity (4 kV/W at 0.35 THz) in the nonlinearity region, as described in Appendix 2.
Fig. 8. (a) Photograph of a tapered-slot-type RTD integrated with a photonic-crystal waveguide device. (b) Block diagram showing the setup of the THz communication experiment.
Figure 9(a) shows the relationship between the THz transmission power and the bit error rate (BER) at 32 Gbit/s, which was measured using a BER detector. The UTC-PD transmitter’s output power for a carrier frequency of 0.35 THz was measured using a calibrated calorimeter-style power meter through a hollow metallic waveguide. The BER was decreased as the transmission power was increased. The power required to achieve the error-free condition (BER < 1 × 10−11) was 70 µW. Figure 9(b) shows a clearly opened eye diagram at 32 Gbit/s with a BER of 2.0×10−12. In Fig. 9(c), the BER increased with the data rate. The maximum error-free transmission data rate was obtained at 32 Gbit/s, and a forward error correction (FEC) data rate of 36 Gbit/s was achieved. THz communication was successfully demonstrated using the RTD integrated with the photonic-crystal waveguide operating as receiver. To the best of knowledge, this is the highest data rate reported thus far for real-time error-free THz transmission using an RTD integrated with a photonic-crystal waveguide [25,26,34–36].
Fig. 9. (a) Measured bit error rate as a function of transmission power. The carrier frequency and data rate are 0.35 THz and 32 Gbit/s, respectively. The error-free condition is defined as error being less than 1 × 10−11. (b) Measured eye diagram at 32 Gbit/s with a bit error rate of 2 × 10−12. (c) Dependence of the measured bit error rate on the data rate.
To demonstrate feasibility of the developed device in practical applications, we employed the RTD as THz receiver for the wireless transmission of uncompressed 4K high-definition video to a 4K video display in the background, as shown in Fig. 10. The transmission of 4K video requires a data rate higher than 6 Gbit/s with BER < 1 × 10−11. In this experiment, the Si tapered structure of the photonic-crystal waveguide can be operated as a dielectric rod antenna, which has an absolute gain greater than 10 dBi across the propagation band of the photonic-crystal waveguide (0.315–0.390 THz) [20]. Owing to the high coupling efficiency (∼90%) and high responsivity (∼4 kV/W) RTD receiver, THz wave wireless communication was successfully demonstrated with the designed and fabricated RTD receiver integrated with the photonic-crystal waveguide; the transmitted video is presented as Visualization 1.
Fig. 10. Wireless transmission of uncompressed 4K high-definition video using the UTC-PD transmitter and the tapered-slot-type RTD receiver integrated with the photonic-crystal waveguide (see Visualization 1). (a) Photograph of the 4K high-definition wireless transmission system. (b) Close-up view of the 4K high-definition wireless transmission system.
5. Conclusion
In this article, we developed a highly efficient mode converter in order to interface between a deep-subwavelength structure and a photonic-crystal waveguide platform in the 0.3-THz band. A general guideline for the design of an efficient mode converter for the photonic-crystal waveguide platform is as follows. Firstly, the thickness of the mode converter should be half that of the photonic-crystal waveguide, as the intensity of the electromagnetic wave of the photonic-crystal waveguide is the strongest in the center plane. Secondly, the taper shape of the mode converter must be optimized in view of the trade-off between Ohmic loss, radiation loss, and reflection loss. Finally, the sandwiched structure matches the symmetry of the photonic-crystal waveguide’s mode, and this is critical to reduce radiation loss. Following the mode-converter design, we described the successful integration of a RTD into the deep-subwavelength structure, and its subsequent operation as a receiver of THz waves via the photonic-crystal waveguide. We experimentally demonstrated high coupling efficiency (∼90%) and a large 3-dB bandwidth of ∼50 GHz. Simulation results showed close agreement with the measured results. In a THz communication experiment, we successfully demonstrated 32 Gbit/s error-free transmission as well as the wireless transmission of uncompressed 4K high-definition video. This validates the viability of this device in future compact systems for practical applications of THz waves.
The developed mode converter can be used in the efficient hybrid-integration of general two-terminal devices such as photodiodes, as well as CMOS integrated circuits, with a THz photonic-crystal waveguide. The developed mode converter renders a wide variety of THz passive photonic components accessible to such devices, including antennas, diplexers, filters, sensors, and connectors.
Appendix 1. Simulated coupling efficiency dependent on the clearances between the sandwiched tapered-slot mode converter and the photonic-crystal waveguide
The clearances between the sandwiched tapered-slot mode converter and the photonic-crystal waveguide in the x and y directions were investigated in the simulation, as shown in Fig. 11(a) and 11(b), respectively. The sandwiched tapered-slot mode converter was embedded in the groove of the photonic-crystal waveguide. We simulated the coupling efficiency dependent on the clearances w and h, by a three-dimensional finite-integral time-domain electromagnetic simulation (CST Studio Suite 2018). Figure 11(c) and 11(d) show the simulated coupling efficiencies at 0.322 THz dependent on the clearances w and h, respectively. Because the wavelength of the THz wave in free space is much larger than the clearance, the sandwiched tapered-slot mode converter can serve as an antenna in free space. We found that a clearance w less than 40 µm had a small impact on the coupling efficiency. When the clearance w was larger than 40 µm, the THz wave was radiated from the edge of the photonic-crystal waveguide and cannot be trapped efficiently by the mode converter. In contrast, while no clearances exist, the propagating THz wave confined in the photonic-crystal waveguide was directly trapped by the mode converter, and then, the THz wave was strongly confined in the gap of the mode converter as the electric-field intensity distribution shown in Fig. 2. Therefore, the coupling efficiency dependent on the clearance h of less than 30 µm was neglected. When the clearance h was larger than 30 µm, the coupling efficiency was decreased due to the leakage of the THz wave from the mode converter in the y direction where the THz wave was weakly confined by the photonic-crystal.
Fig. 11. Simulated coupling efficiency dependent on the clearances between the sandwiched tapered-slot coupling efficiency and the photonic-crystal waveguide. (a) Simulation model of the clearance influence in the x direction. (b) Simulation model of the clearance influence in the y direction. (c) Dependence of the simulated coupling efficiency on the clearance w. (d) Dependence of the simulated coupling efficiency on the clearance h.
Appendix 2. Measured responsivity of the fabricated RTD receiver
In order to measure the responsivity of the fabricated RTD receiver, we used the measurement system shown in Fig. 12(a). The RTD input THz wave was generated by a 9× multiplier applied to a millimeter-wave signal. The input THz wave signal at 0.35 THz with ∼1 µW output power was modulated at 30 kHz. The generated THz wave was input via the tapered structure at the edge of the photonic-crystal waveguide from the WR3 hollow waveguide. Then, the THz wave was detected by the RTD receiver, and the demodulated signal was transmitted to the coplanar strip line and coaxial connector, following which it was measured using a lock-in amplifier. A DC power was applied to the RTD receiver by using a bias tee, and the measured current–voltage characteristics are shown in Fig. 12(b). The RTD receiver had a parallel shunt resistance (∼35 Ω) and suppresses parasitic oscillations to stabilize the operation. The current–voltage characteristics of the RTD exhibited a negative differential conductance (NDC) region. The measured negative differential conductance region in bias voltage was 576–670 mV. Figure 12(c) shows the dependence of the measured responsivity on the bias voltage. The result indicates that the RTD receiver had the highest responsivity while biased at 576 mV, as expected. The measured maximum responsivity was 4 kV/W at 0.35 THz.
Fig. 12. Measured responsivity of the fabricated RTD receiver. (a) Block diagram of the measurement system. (b) Measured current–bias voltage characteristics. The gray region shows the negative differential conductance (NDC) region. (c) Dependence of the measured responsivity on the bias voltage at 0.35 THz.
Funding
The Core Research for Evolutional Science and Technology (CREST) program of Japan Science and Technology Agency (#JPMJCR1534); Grant-in-Aid for scientific research from the Ministry of Education, Culture, Sports, Science and Technology of Japan (#17H01764).
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