Photonic generation of terahertz dual-chirp waveforms ranging from 364 to 392&#x2005;GHz

Shiwei Wang; Lu Zhang; Zijie Lu; Hongqi Zhang; Mengyao Qiao; Nazar Idrees; Muhammad Saqlain; Shilie Zheng; Xiaofeng Jin; Xianmin Zhang; Xianbin Yu; Xianbin Yu

doi:10.1364/OE.422407

1. Introduction

Nowadays, modern radar systems have been widely used in military and our daily life [1]. Since a linear frequency modulated (LFM) signal can achieve high range resolution after pulse compression, it has been well-developed for radar systems. Typically, a LFM signal holds a knife-edge ambiguity function, which will induce an issue of the range-Doppler coupling when measuring the position of a moving object, resulting in a measurement error as a consequence. In order to eliminate the range-Doppler coupling effect, an LFM signal with complementarily chirp rates within its time duration, namely a dual-chirp signal, has been proposed [2–6]. A dual-chirp signal in turn features a thumb-tack-like ambiguity function, indicating that both high range resolution and high Doppler resolution can be obtained.

The range resolution of chirp signals is determined by the bandwidth, many efforts have been therefore made to increase the bandwidth of signals. However, the electronically-generated chirp signals have limited frequency bandwidth and range [7]. Alternatively, photonics-assisted techniques have exhibited the capability of breaking the electronic bandwidth bottleneck. In the past few years, lots of work based on photonic techniques has been proposed to generate broadband dual-chirp microwave signals for radars, such as optical modulation, frequency quadrupling, optical injection, etc. For example, a dual-chirp signal with a bandwidth of 10 GHz is generated by opto-electrically modulating a microwave carrier and a baseband single-chirp waveform [8,9], a S-band dual-chirp signal with a bandwidth of 1.2 GHz based on frequency quadrupling, as well as a dual-chirp signal with a bandwidth of 7.1 GHz at 20 GHz based on light injection have been also reported [10,11].

As we know, the THz band provides extremely large bandwidth, which can sufficiently enable an ultrahigh range resolution. Besides that, a THz radar exhibits the potentials of THz-waves, such as high penetration, anti-interference and anti-stealth, and hence are of great interest for future applications [12–17]. In this context, photonics-assisted schemes for generating large bandwidth single-chirp THz LFM signals have been also proposed and demonstrated [18,19], while the generation of a dual-chirp signal in the THz band has not so far been reported yet.

In this work, we propose a photonic scheme of generating a THz dual-chirp signal based on frequency doubling and photo-mixing. A proof-of-concept experiment is conducted to demonstrate the proposed system, and a dual-chirp signal ranging from 364 GHz to 392 GHz within a temporal period of 1 µs is successfully achieved. To be best of our knowledge, this is for the first time that a dual-chirp signal with large bandwidth and time duration aided by photonics is generated in the THz band above 300 GHz, which is expected to potentially applicable in multi-dimensional detection with high resolution.

2. Operation principle

The schematic diagram of generating a THz dual-chirp signal is shown in Fig. 1. A flat optical frequency comb (OFC) is used as optical source, and three optical comb lines of it are extracted by a filter before being sent into a Mach-Zehnder Modulator (MZM), can be expressed by

(1)$${E_i}(t) = E[\textrm{exp} (j{\omega _1}t) + \textrm{exp} (j{\omega _2}t) + \textrm{exp} (j{\omega _3}t)], $$

where E is the amplitude, ${\omega _1}$, ${\omega _2}$ and ${\omega _3}$ are the central angular frequency of the filtered optical signals, respectively, and t is time. Among them, the frequency spacing between ${\omega _1}$ and ${\omega _2}$ is relatively close, while ${\omega _3}$ is far from ${\omega _1}$ and ${\omega _2}$ in the range of terahertz frequency. Then a radio frequency (RF) LFM signal ${E_{LFM}}\textrm{ = }{V_{LFM}}\cos ({\omega _L}t + \pi k{t^2})$, with a central angular frequency of ${\omega _L}$ and a chirp rate of k, is applied to the MZM. When the MZM operates at its minimum transmission point, the output of the MZM can be given by

(2)$$\begin{array}{l} {E_{MZM}}(t) ={-} j{E_i}(t)\left\{ { - 2\sum\limits_{m = 1}^\infty {{{( - 1)}^m}} {J_{2m - 1}}(\beta )\cos [{(2m - 1)({\omega_L}t + \pi k{t^2})} ]} \right\}\\ \approx{-} jE{J_1}(\beta )\sum\limits_{n = 1}^3 {\{{\textrm{exp} j[{({\omega_n} + {\omega_L})t + \pi k{t^2}} ]+ \textrm{exp} j[{({\omega_n} - {\omega_L})t - \pi k{t^2}} ]} \}} \end{array}, $$

where ${J_m}(\beta )$ is the $m$-th-order Bessel function of the first kind and $\beta = \frac{{\pi {V_{LFM}}}}{{{V_\pi }}}$, ${V_{LFM}}$ is the amplitude of ${E_{LFM}}$, ${V_\pi }$ is the half-wave voltage of MZM. Subsequently, the second filter is used to select the components of $({\omega _1} + {\omega _L})t + \pi k{t^2}$, $({\omega _2} - {\omega _L})t - \pi k{t^2}$, $({\omega _3} - {\omega _L})t - \pi k{t^2}$ and $({\omega _3} + {\omega _L})t + \pi k{t^2}$. By illuminating the filtered optical signals into a photodetector (PD), the generated AC components in the electrical domain can be expressed as:

(3)$$i(t) = \eta {E_f}^2{J_1}^2({\beta _2})\left\{ \begin{array}{l} 2\cos (2{\omega_L}t + 2\pi k{t^2})\\ + 2\cos [({\omega_1} - {\omega_2})t + 2({\omega_L}t + \pi k{t^2})]\\ + 2\cos [({\omega_1} - {\omega_3})t] + 2\cos [({\omega_2} - {\omega_3})t]\\ + 2\cos [({\omega_1} - {\omega_3})t + 2({\omega_L}t + \pi k{t^2})]\\ + 2\cos [({\omega_2} - {\omega_3})t - 2({\omega_L}t + \pi k{t^2})] \end{array} \right\}, $$

where ${E_f}$ is the amplitude and $\eta$ is the responsivity of PD. Here, the low frequency components $\cos (2{\omega _L}t + 2\pi k{t^2})$ and $\cos [({\omega _1} - {\omega _2})t + 2({\omega _L}t + \pi k{t^2})]$ can be eliminated since they are typically outside the response bandwidth of PD. By appropriately setting a receiving local oscillator (LO), the down-converted frequency components $\cos [({\omega _1} - {\omega _3})t]$ and $\cos [({\omega _2} - {\omega _3})t]$ can be also filtered out by using another filter, and then the generated dual-chirp signal can be expressed as:

(4)$$i(t) = \eta {E_f}^2{J_1}^2({\beta _2})\left\{ \begin{array}{l} \cos [({\omega_1} - {\omega_3} + 2{\omega_L})t + 2\pi k{t^2}]\\ + \cos [({\omega_2} - {\omega_3} - 2{\omega_L})t - 2\pi k{t^2}] \end{array} \right\}, $$

Fig. 1. The schematic diagram of the proposed THz dual-chirp signal generation system. OFC: optical frequency comb, MZM: Mach-Zehnder Modulator, PD: photodetector, LO: local oscillator.

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From (4), we can notice that when setting ${\omega _L} = \frac{1}{4}({\omega _2} - {\omega _1})$, the generated up-chirp and down-chirp signals will have the same center frequency and bandwidth, which can be tuned by changing the chirp rate k.

3. Experimental setup

The experimental setup of our proposed system is shown as Fig. 2, which is composed of optical modulation part and THz dual-chirp waveform transceiver part. Part I shows the creation of an OFC and implementation of optical modulation. Part II presents the emission and reception of THz dual-chirp waveforms using a uni-travelling carrier photodiode (UTC-PD) as THz emitter [20] and a Schottky mixer as THz receiver.

Fig. 2. Schematic experimental configuration for photonic generation of THz dual-chirp signals. ECL: external cavity laser, PC: polarization controller, PM: phase modulator, RFS: radio frequency source, RFA: radio frequency amplifier, POF: programmable optical filter, EDFA: Erbium-doped fiber amplifier, MZM: Mach-Zehnder modulator, AWG: arbitrary waveform generator, VOA: variable optical attenuator, OC: optical coupler, UTC-PD: uni-traveling carrier photodiode, DSO: digital sampling oscilloscope, LO: local oscillator. The inset: optical spectrum at the output of PM.

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In the optical modulation part, an external cavity laser (ECL, <100 kHz linewidth) is used as optical continuous-wave source in C-band. After polarization aligned by a polarizer controller (PC), the optical source is injected into a phase modulator (PM) and modulated by a 28 GHz RF signal from a radio frequency source (RFS) for generating an OFC, as shown in the inset of Fig. 2. Here the RF signal is amplified by a RF amplifier (RFA1) with 22 dB gain. A programmable optical filter (POF) is used to selectively retain three optical comb lines from the OFC, with ${f_3} - {f_1} = 420\textrm{ GHz}$, ${f_3} - {f_2} = 336\textrm{ GHz}$, as shown in Fig. 3(a). These three lines are then amplified by an Erbium-doped fiber amplifier (EDFA1) and polarization controlled by PC2 before entering an MZM. An arbitrary waveform generator (AWG) generates a LFM signal ${f_L}$ with a period of 1 µs, and a bandwidth of 14 GHz centered at 21 GHz, which is amplified by a RF amplifier RFA2 for driving the MZM. By biasing the MZM at the minimum transmission point, the first-order sidebands are generated at the output. To minimize the clutter interference, the guard band is selected to ensure no overlap between the high-order sidebands and the first-order sidebands. After being amplified by EDFA2, the frequency components with center frequencies of ${f_1} + {f_L}$, ${f_2} - {f_L}$, ${f_3} - {f_L}$, ${f_3} + {f_L}$ are selectively remained by POF2, as shown in Fig. 3(b). Here the POF2 holds a bandwidth of 20 GHz and a spectral resolution of 10 GHz.

Fig. 3. The optical spectra after (a) POF1, (b) POF2.

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In the THz dual-chirp waveform transceiver part, the optical signals are first amplified by EDFA3, and then launched into a UTC-PD (NTT Electronics Corp. IOD-PMAM-13001, 200-1500 GHz) with polarization alignment by PC3 and a polarizer. Based on photomixing, RF components of $2{f_L}$, ${f_3} - {f_2} + 2{f_L}$, ${f_3} - {f_1}$, ${f_3} - {f_2}$, ${f_3} - {f_1} - 2{f_L}$, ${f_2} - {f_1} - 2{f_L}$ are consequently generated, where ${f_3} - {f_2} + 2{f_L}$ (364–392 GHz) and ${f_3} - {f_1} - 2{f_L}$ (364–392 GHz) are the desired components. Since the UTC-PD responses in the frequency band of 200–1500 GHz, two components $2{f_L}$ (28–56 GHz) and ${f_2} - {f_1} - 2{f_L}$ (28–56 GHz) are rejected. The output electrical spectrum from the UTC-PD is illustrated in Fig. 4, indicating a 28 GHz frequency gap between ${f_3} - {f_1}$ (420 GHz), ${f_3} - {f_2}$ (336 GHz) and the targeting signals. The signals within the UTC-PD bandwidth are then radiated into the air via a bow-tie antenna with estimated THz power of −24 dBm. In the free space link, we use a pair of THz lenses to collimate the THz beam to reduce the propagation loss.

Fig. 4. The frequency components at the output of UTC-PD.

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At the receiving side, a 12-order harmonics Schottky diode-based THz receiver (Virginia diode WR2.2, 325–500 GHz) is used, to down-convert the signals into the intermediate frequency (IF) domain by mixing with an electrical LO signal. When the 12-order multiplied LO signal is 407 GHz or 349 GHz, which serves 13 GHz away from the unmodulated components, and meanwhile 15 GHz away from the targeting component, avoiding signal aliasing during down-conversion. Then the down-converted signals are amplified by RFA3 with 26 dB gain, and sampled by using a broadband real-time digital storage oscilloscope (160 GSa/s, Keysight DSOZ594A, 59 GHz) for performance analysis in the digital domain.

4. Experimental results and discussions

Based on the approach described as above, a THz dual-chirp waveform with bandwidth of 28 GHz, located from 364 GHz to 392 GHz, is generated in the experiment. Figure 5(a) displays the received THz dual-chirp waveforms measured in the IF domain by supplying 12-order multiplied LO frequency of 407 GHz. By performing band-pass filtering and short-time Fourier transform on the signals, the time-varying instantaneous frequency of the signals is shown in Fig. 5(b). We can observe two LFM signals within a period of 1 µs, where the instantaneous frequency increases linearly from 15 GHz to 43 GHz for the first one, and decreases linearly from 43 GHz to 15 GHz for the second in the range of 364 GHz to 392 GHz. The bandwidth of both chirp signals is 28 GHz, which doubles the bandwidth of input LFM signal ${f_L}$, yielding a TBWP of 28000 and a chirp rate of 0.028 GHz/ns. It can be also observed that there is ignorable clutter interference. After being filtered out-of-band noise and equalized the envelope using the Hilbert transform, the waveform after compression is shown as Fig. 6. The compressed full width at half maximum (FWHM) is 45.9 ps, corresponding to a range resolution of 6.89 mm, and a pulse compression ratio (PCR) of 21787.

Fig. 5. (a)Temporal waveform of THz dual-chirp signal. (b) STFT analysis of the THz dual-chirp waveform. The multiplied local oscillator is at 407 GHz.

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Fig. 6. Autocorrelation of the dual-chirp waveform.

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To verify the potential of dual-chirp signals i eliminating the range-Doppler coupling effect, we simulate its ranging process of detecting moving targets. A THz dual-chirp signal centered at 378 GHz with 28 GHz bandwidth is used, and a time duration of 100 µs is alternatively used for principle illustration. Ideally, this signal can enable a frequency resolution of 10 kHz (=1÷100 µs) and a velocity resolution of 3.97 m/s (=10 kHz×3 × 10⁸m/s÷2÷378 GHz). Assuming a stationary object located at 100 m is used to obtain an echo signal as reference, which suffers from free space path loss of about 124 dB at 378 GHz according to the Friis equation [21]. When a target is 60 m away from the radar and is approaching at 71.43 km/h, a Doppler shift of 50 kHz will be generated. By performing autocorrelation on the up-chirp and down-chirp echo signals, the compressed signals are as shown in Fig. 7(a) and Fig. 7(b), respectively. We can see in this case the output peaks of two signals are individually located at time delays of −266.49 ns and −266.84 ns, corresponding to −39.97 m and −40.026 m from the reference object. This difference is due to the target movement. In principle, the up-chirp and down-chirp signals introduce same amount of measurement errors induced by the Doppler frequency shift, while in opposite directions. Therefore, by averaging the time delay of two peaks, we can obtain the actual time delay of −266.67 ns, which corresponds to a distance of −40 m away from the reference object. In this case, the estimated distance of target is 60 m from the radar, which agrees well with the actual scenario.

Fig. 7. Autocorrelation of (a) the up-chirp waveform, (b) the down-chirp waveform.

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On the other hand, the compressed up-chirp signal is +0.18 ns deviated from the actual delay, implying that the target is moving towards the radar and resulting in a positive Doppler frequency shift ${f_d}$ of +50.4 kHz (0.18 ns ${\times}$ 28GHz ${\div}$ 100µs). According to

(5)$$v = \frac{{\lambda {f_d}}}{2}, $$

where $\lambda$ is the center wavelength of the radar signal, the speed v of the target can be analyzed to approximately 72 km/h, which also agrees well with the actual moving speed.

5. Conclusion

In this work, we propose and experimentally demonstrate a proof-of-concept generation of dual-chirp THz signals assisted by photonics. By utilizing frequency doubling and photo-mixing techniques, a THz dual-chirp signal with 28 GHz bandwidth in the range of 364–392 GHz is successfully generated, which is beneficial in eliminating the distance-Doppler coupling effect and performing simultaneous target position and velocity measurement. The proposed system has a great potential for THz radar applications with high resolution.

Funding

National Key Research and Development Program of China ( 2020YFB1805700, 2018YFB1801500, 2018YFB2201700); National Natural Science Foundation of China (61771424); Natural Science Foundation of Zhejiang Province (LZ18F010001); Zhejiang Lab (2020LC0AD01).

Acknowledgments

The authors would like to thank Dr. B. Wei at the Training Platform of Information and Microelectronic Engineering at the Polytechnic Institute of Zhejiang University, for his support in the experiment.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Photonic generation of terahertz dual-chirp waveforms ranging from 364 to 392 GHz

Abstract

1. Introduction

2. Operation principle

3. Experimental setup

4. Experimental results and discussions

5. Conclusion

Funding

Acknowledgments

Disclosures

Data availability

References

Data availability

Cited By

Figures (7)

Equations (5)

Optics Express