Terahertz coherent receiver using a single resonant tunnelling diode

Towards exploring advanced applications of terahertz (THz) electromagnetic waves, great efforts are being applied to develop a compact and sensitive THz receiver. Here, we propose a simple coherent detection system using a single resonant tunnelling diode (RTD) oscillator through self-oscillating mixing with an RTD oscillator injection-locked by a carrier wave. Coherent detection is successfully demonstrated with an enhancement in the sensitivity of >20 dB compared to that of direct detection. As a proof of concept, we performed THz wireless communications using an RTD coherent receiver and transmitter. We achieved 30-Gbit/s real-time error-free transmission, which is the highest among all electronic systems without error correction to date. Our results show that the proposed system can reduce the size and power consumption of various THz systems including sensing, imaging and ranging, which would enable progress to be made in a wide range of fields in such as material science, medicine, chemistry, biology, physics, astronomy, security, robotics and motor vehicle.


Circuit Model
shows the circuit model of the resonant tunnelling diode (RTD) devices for the simulations S1 . An antenna, a coplanar stripline (CPS), a metal-insulator-metal (MIM) capacitor (CMIM), and a shunt resistor (Rsh) were modelled by lumped components to simplify the calculation. We used a circuit simulator, Keysight ADS. To simulate the injection-locking phenomenon, transient convolution was employed. Figure S2 shows the design of the RTD device. A bowtie antenna is used as a radiator. A CPS provides impedance matching between the antenna and the RTD. A CMIM provides a Figure S1 | Circuit model. We assumed that R A = 150 Ω, L res = 17 pH, C MIM = 120 fF, and R sh = 35 Ω, and the electrode area of the RTD = 1.4 µm 2 . short for a terahertz (THz) signal and an open circuit for a direct-current (DC) signal. A Rsh suppresses parasitic oscillation. We designed the oscillation frequency, which is determined by the capacitance of the RTD and the impedance of the resonator, using the circuit model S1 described in Supplementary Section 1. We fabricated four RTD devices of which parameters are shown in Table S1, for making various oscillation frequencies.

Layout of the Fabricated RTD Circuit Chip
The oscillation frequency can be slightly tuned by changing the bias voltage of RTD, as mentioned in Supplementary Section 3. Figure S3 shows the RTD layer structure S2 . The device No.4 has the thicker emitter spacer (20 nm) compared with other devices (No.1-3, 10 nm), which increases the operating voltage and current density, but the other layers are same among No.1-4. Mesa size of these devices are different due to process variation. Figure S3 shows the current-voltage (I-V) and oscillation frequency for each device and Table S2 summarized the operating voltage and oscillation frequency used in this study. It also includes estimated mesa size

Experimental Setup: Detection of Amplitude-Modulated Signals
A block diagram of the experimental setup is shown in Figure S5. A millimetre wave (36-40 GHz) from signal generator 1 was amplitude-modulated (AM) by an electrical mixer with a 1-GHz sine wave from signal generator 2 and amplified using a 29-dB driver amplifier. The signal was multiplied by nine times to generate THz signals at 324-360 GHz. A variable attenuator changed the Tx power. A circular horn antenna was used to generate THz signals in free space that were detected by an RTD Rx. The detected signals were amplified by a 30-dB electrical amplifier and measured using spectrum analyser 1.
We also measured the frequencies of the signals from the multiplier and RTD using a mixer system to observe the injection-locking phenomenon. The signals transmitted through the RTD were received by a circular horn antenna, which was connected to the mixer. An RTD oscillation signal radiating from the backside of the RTD module was also received by the horn antenna. These signals were down-converted to an intermediate frequency (IF) by the mixer using a LO for display on spectrum analyser 2, where the frequency and received power were measured.

Frequency Locking Range Measurement
The operation frequency range to induce the injection locking phenomenon of the RTD oscillator was measured in an experiment. Figure S6a shows a block diagram of the experimental setup. The locking phenomenon was observed by the RTD oscillation spectrum using a mixer system. The oscillation frequency of the Rx was set to 352.6 GHz.
The frequency of the multiplier Tx was changed from 338 GHz to 364 GHz. In theory, the  locking range can be expressed as where 0 is the oscillation frequency without locking, is the quality factor of the oscillator circuit, i is the injected power, and o is the oscillator output power S3 .
Equation S1 indicates that the locking range increases as the injected power increases. Fig.   S6b shows the locking range with various Tx output powers. As the Tx power increases, the locking range is increased over 10 GHz. The experimental results show good agreement with the theoretical curve for = 6 and o = -15 dBm, taking into account the propagation loss (20 dB) of the Tx power to calculate i .

Conversion Loss Estimation
Conversion loss ( C ) is generally defined as S4 where RF and IF are available RF input power and IF output power, respectively. C can be also calculated using the relationship between amplitude modulation(AM) signal and detected signal. When a mixer receives an AM signal and an LO signal which is coherent with the received RF carrier signal, both the upper sideband (USB) signal and the lower sideband (LSB) signal are down converted to the detected signal. Using equation (S2), C can be calculated by where USB is the power of the USB signal, LSB is the power of the LSB signal and Det is the detected power. When the modulation index ( ) is 1, the RF carrier signal power ( 0 ) is described as S5 0 = 2( USB + LSB ). (S4) Using equation (S3) and (S4), Therefore, if we can know 0 and Det , C can be calculated. 0 can be estimated by the relationship between square-law detection and homodyne detection.
When a diode receives an AM signal, the diode voltage is expressed as where 0 is the amplitude of the RF carrier signal, m is the modulation frequency and 0 is the RF carrier frequency. In the case of square-law detection, the detected current is expressed as where d ′ is the reciprocals of the second derivative of the diode's I-V curve S4 . Next, we consider homodyne detection with injection-locked self-oscillating mixer. When the RF signal (amplitude: r , frequency: r ) and LO signal (amplitude: l , frequency: l ) are combined in a diode mixer, the current in the mixer can be expressed as S4 d ′ 2 ( r cos r + l cos l ) 2 .
When the amplitude of free-running oscillation is OSC , the amplitude of oscillation injection-locked with the RF carrier signal is described as because the oscillation amplitude is limited by the negative conductance region. Using equation (S6), (S8) and (S9), the current in the mixer is expressed as The down-converted current is calculated as When 0 = OSC , equation (S11) is described as The conversion loss of the RTD device acting as a coherent detector is roughly estimated to be 10 dB.

Experimental Setup: Wireless Communications Using a Photonics-Based Tx
A schematic of the experimental setup is shown in Supplementary Figure S7. For the Tx, infrared-light signals from two wavelength-tuneable lasers were combined by a coupler, and the intensity was modulated by an electro-optic modulator (EOM). The resultant signal was then amplified by an Er-doped optical fibre amplifier (EDFA). The EOM was driven by a pseudo-random binary sequence (PRBS) from a pulse pattern generator (PPG) with a repetition length of 2 15 -1. The modulated optical signals were down-converted to a THz signal by using a uni-travelling-carrier photodiode (UTC-PD) module. The THz signals were radiated into free space through a circular horn antenna. The transmission distance was about 2 cm. On the Rx side, the THz signals were detected by the RTD device. The demodulated signals were amplified by a low-noise amplifier. The eye diagram and bit-error rate (BER) were measured using an oscilloscope and error detector, respectively. Two commercial equalisers enhanced the bandwidths of the baseband (BB) circuit.   the Tx and Rx. The BER reported here was directly measured in real time by a BER tester.

Experimental Setup: Wireless Communications Using an RTD Tx
Various modulation formats were employed, such as amplitude shift keying (ASK), phase shift keying (PSK), and quadrature amplitude modulation (QAM). The practical errorfree condition is a BER less than 10 -11 , which is sufficient for practical video transmission without interruption. For error-free transmission, the bit rate of the system proposed in this study is the highest among all systems based on all electronic devices without an error correction process to the best of our knowledge