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Abstract
In this paper, we propose and demonstrate a novel spectrum stitching method for broadband linear frequency-modulated waveform (LFMW) generation. An optical frequency comb (OFC) is modulated by a narrowband LFMW whose bandwidth matches the free spectral range of the OFC. Optical injection locking is employed in extracting one broadband frequency sweeping component from the modulated OFC. In this way, seamless spectrum stitching is realized and a broadband LFMW with a multi-fold time-bandwidth product (TBWP) is obtained. Our scheme has a simple structure, which requires only a single OFC, a modulation module and a baseband waveform generator. An LFMW as broad as 20 GHz is generated from a baseband LFMW with 2GHz bandwidth experimentally. The TBWP is 100 times as large as that of the baseband LFMW. Moreover, the power fluctuation and the phase jumps are both eliminated, ensuring an excellent pulse compression performance. Benefiting from the injection locking technique, the linearity reaches 2.0 × 10−6. The central frequency tuning ability of our scheme is also demonstrated.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Broadband linear frequency-modulated waveforms (LFMWs) play an important role in modern ranging and sensing systems including radar imaging [1,2], 3D Lidar [3,4], and optical frequency-domain reflectometry [5]. It is not only due to that the pulse compression technique enables the LFMW with the capability of high-resolution and long-range detection [6], but also the unique de-chirp reception greatly lowers the bandwidth of signal acquisition and processing [2]. Conventionally, LFMWs are generated by electronic devices such as direct digital frequency synthesis and voltage-controlled oscillators, which usually suffer from limited bandwidth, poor linearity and serious timing jitter. Recently, microwave photonics based methods for broadband LFMW generation have aroused increasing research interest, trying to take advantage of large manipulation bandwidth and low transmission loss of optoelectronic devices [7,8].
Many schemes for LFMW generation have been proposed based on microwave photonic systems [9–13]. Compared with the general external modulation schemes [14], the photonics-assisted spectrum stitching technique has the potential to achieve greater bandwidth while maintaining good linearity [13,15–19]. The existing spectrum stitching schemes can be divided into three categories. The first one is based on dual coherent optical frequency combs (OFCs) and external modulation [13,15]. Multi-stage upconversion is realized by setting a slight difference between the free spectral ranges (FSRs) of the dual OFCs. In [15], the time delays of different up-converted components are implemented by optical fibers, which is hard to ensure the phase continuity at the stitching points. To address this problem, multiple baseband LFMWs with accurately controlled delays are employed to achieve the phase continuity [13]. However, multiple baseband generators and modulation modules greatly increase the complexity and cost of the system. The scale is thus hard to expand. The second class is based on recirculating frequency shifting technique, which can be classified into the optical frequency shifting loop [16,18] and the optoelectronic frequency shifting loop [17]. The former one can realize ultra-broadband linear frequency sweeping, but the phases between different recirculating loops are discontinuous. The latter can ensure phase continuity, but the synthesized bandwidth is only several GHz, which is limited by the frequency shift. Another noteworthy problem of the frequency shifting schemes is that the noise performance will gradually deteriorate with the increase of the recirculating times. The third category of the frequency shifting scheme is based on a single OFC and dispersion elements [19]. Each spectral line of the OFC is time-separated using a dispersion element such as a fiber Bragg grating and then phase-modulated by a periodic parabolic signal. As a result, the narrowband LFMW induced by the parabolic phase modulation is spliced and a broadband LFMW is then synthesized. However, the time duration of the synthesized LFMW is only several tens of nanoseconds limited by the amount of the dispersion. Besides, the phases at the stitching points are discontinuous owing to the phase differences between the different lines of the OFC.
In this paper, we propose a novel spectrum stitching method assisted by a single OFC and optical injection locking technique. A baseband LFMW is up-converted with multiple levels by modulating it onto an OFC. The spectrum is stitched seamlessly by matching the FSR of the OFC and the bandwidth of the baseband LFMW. As a result, a series of optical broadband frequency sweeping is generated. The optical injection locking technique is then used to select out one of the broadband linear frequency sweeping components. Compared with the previous schemes, our system features low complexity and easily expandable scale since only a single OFC and one baseband LFMW generator are needed. At the same time, phase continuity can be guaranteed. In the experiment, a 20-GHz LFMW is synthesized by stitching 10 segments of the 2-GHz baseband LFMWs. The corresponding time-bandwidth product (TBWP) is improved by 100 folds. The power unflatness and the phase discontinuity are eliminated by an amplitude shaper and adjusting the phase of the baseband LFMW, respectively. The pulse compression performance is also evaluated, which agrees well with the theoretical results. The excellent linearity, which benefits from the injection locking technique, is measured as ${2.0\times 10^{-6}}$. The frequency tuning ability is also demonstrated experimentally.
2. Principle
The principle of the proposed spectrum stitching scheme assisted by a single OFC and injection locking technique is sketched in Fig. 1. A periodically repeated baseband LFMW is modulated onto a single OFC with optical carrier-suppressed single-sideband (CS-SSB) modulation. The baseband LFMW and the optical field of the OFC can be expressed by
After CS-SSB modulation, the optical field is transformed to
The modulated OFC is then injected into a distributed-feedback (DFB) laser, which is driven by a ramp current. The drive current is pre-distorted in advance by taking the chirp rate of the LFMW component as the target [20]. The frequency sweeping error, which is induced by the temperature fluctuation and the relaxation effect of current modulation, can be suppressed to the MHz level. The detuning frequency between the target LFMW and the free-running frequency of the DFB laser can thus be optimized to several MHz by accurately tuning the wavelength of the optical carrier, which ensures the LFMW component within the locking range (usually as wide as hundreds of MHz or several GHz). As a result, injection locking is realized. The target component is extracted out while other components are suppressed [12,21]. The extracted LFMW component can be expressed as
3. Experiment and result
3.1 Spectrum stitching
A proof-of-concept experiment is conducted based on the setup presented in 2(a). A tunable laser source (TLS, Keysight 8164B) working around 1563 nm is split into two branches. One is reserved as a coherent optical carrier and the other branch is modulated by a 2-GHz single tone through a phase modulator to excite an OFC. A single tone is generated by an arbitrary waveform generator (AWG, Tektronix AWG 70002A) and then amplified by a microwave amplifier. The spectrum of the OFC is presented in Fig. 2(b). More than 39 lines are excited successfully. The OFC is then CS-SSB modulated by a narrow baseband LFMW in an integrated dual-parallel Mach-Zehnder modulator (DPMZM, Fujitsu FTM 7961EX). The bandwidth of the LFMW is exactly equal to the FSR of the OFC (2 GHz) and the frequency range is from 1 GHz to 3 GHz. The LFMW is generated from another channel of AWG and then divided into two parts with $90^{\circ }$ difference through a $90^{\circ }$ hybrid coupler. The two parts are injected into the two RF input ports of the DPMZM. The DPMZM consists of two sub Mach-Zehnder modulators (MZMs) and a main MZM. The detailed structure is shown in Fig. 2(c). To realize CS-SSB modulation, the sub MZMs are biased at the minimum transmission point and the main MZM is biased at the quadrature point. The suppression ratios of the carrier and other sidebands exceeds 30 dB. The modulated OFC is then amplified by an Erbium-doped fiber amplifier and injected into a DFB laser, which is driven by a ramp current. The slope of the current is carefully adjusted to make the free-running frequency close to the target broadband frequency sweeping component. A polarization controller is used to align the polarization of the injected light and the principal axis of the DFB laser. The injection-locked DFB laser passes by an amplitude shaper to compensate the optical power unflatness induced by the ramp current and then beats with the reserved optical carrier in a photodetector (PD, Finisar XPDV2120RA) to generate the broadband LFMW. A real-time oscilloscope with an acquisition bandwidth of 21 GHz (Keysight UXR0134) is used to capture the temporal waveforms.
Fig. 2. (a) Experimental setup, (b) spectrum of the OFC, (c) detailed structure of DPMZM. TLS: tunable laser source, OC: optical coupler, PM: phase modulator, AMP: microwave amplifier, AWG: arbitrary waveform generator, DPMZM: dual-parallel Mach-Zehnder modulator, EDFA: Erbium-doped fiber amplifier, AFG: arbitrary function generator, DFB: distributed-feedback laser, PD: photodetector.
Figure 3(a) presents the spectrogram of the baseband LFMW, which is obtained by the short-time Fourier transformation for the temporal waveforms. The time duration of each repetition period is 50 $\mathrm{\mu}$s and the corresponding TBWP is ${1\times 10^5}$. We also check the spectrogram of the beatings of the modulated OFC and the optical carrier to observe the time-frequency distribution of the modulated OFC. The spectrogram is shown in Fig. 3(b). As can be seen, there exist a series of broadband negative-chirped and positive-chirped LFMWs, which indicates that the OFC contains a set of frequency sweeping components with a frequency interval of 2 GHz. Assisted by the injection locking technique, the system output, which is the beating of the injection-locked DFB laser and the optical carrier, only contains a LFMW component. The spectrogram is presented in Fig. 3(c). The generated broadband LFMW is spliced from 10 segments of baseband LFMWs. The time duration and bandwidth of the output LFMW are 500 $\mathrm{\mu}$s and 20 GHz, respectively, which both are increased by 10 folds compared with the baseband LFMW. The corresponding TBWP is up to ${1\times 10^7}$, which is increased by 100 folds. The bandwidth of the generated LFMWs can be further improved by increasing the number of the stitched segments and the bandwidth of the input baseband LFMW. The bandwidth limit for this method is determined by the bandwidth of the PD and frequency-swept bandwidth of the DFB laser, which can be up to 100 GHz [22,23]. The powers of the target LFMW component and the harmonics are measured by separately integrating the corresponding power spectral density on the spectrogram. The suppression ratio for the spurs, which refers to the power ratio between the target LFMW component and the strongest harmonic, is measured as 21.2 dB. The suppression ratio can be further improved by injection locking the DFB laser from the rear facet [24].
Fig. 3. Spectrograms of (a) the baseband LFMW, (b) the beating of the modulated OFC and the optical carrier, and (c) the generated broadband LFMW.
A noteworthy issue is the intensity modulation of the DFB laser by the ramp drive current, which will lead to poor flatness of the generated broadband LFMW. In the experiment, the amplitude shaper is employed to compensate the optical power unflatness. The structure is presented in Fig. 4(a). The intensity of the DFB output is modulated by a feedback signal in an MZM. The optical power of the MZM output is monitored by a low-speed PD and the photocurrent is acquired by a data acquisition card. A simple iterative algorithm similar to those in [20,25] is employed to update the drive signal of the MZM. The update law is ${s_{n+1}(t)=pi_n(t)}$, where ${i_n(t)}$ denotes the acquired photocurrent of the ${n}$th iteration, ${s_{n+1}(t)}$ is the MZM drive signal of the ${(n+1)}$th iteration and ${p}$ is the iterative coefficient that decides the convergence speed. The optical powers with and without amplitude shaping are shown in Fig. 4(b). The power variation before shaping is up to 5.55 dB. While by contrast, the power variation is reduced to less than 0.4 dB after 44 iteration cycles. Figure 4(c) and (d) present the temporal waveform and the spectrum of the generated LFMW without amplitude shaping. The frequency range is from 1 GHz to 21 GHz. The unflatness of the spectrum is around 8.5 dB, which is caused by the amplitude modulation of the DFB laser. The temporal waveform and the spectrum after amplitude shaping are shown in Fig. 4(e) and (f), respectively. As can be seen, the unflatness is reduced to 2.5 dB. The residual unflatness is mainly attributed to the unflat response of the optoelectric and microwave devices. Note that the amplitude shaper will lead to the optical loss and thereby deteriorate the signal-to-noise ratio (SNR) of the generated LFMWs. The SNRs of the LFMWs with and without amplitude shaping are measured as 10.6 dB and 14.2 dB, respectively. Therefore, the amplitude shaper results in an SNR deterioration of 3.6 dB. This issue can be addressed by a more advanced amplitude shaping scheme such as gain-controlled semiconductor optical amplifiers [26].
Fig. 4. (a) Detailed structure of the amplitude shaper, (b) optical power of the DFB laser before and after amplitude shaping, (c) temporal waveform and (d) spectrum of the generated LFMW without amplitude shaping, (e) temporal waveform and (f) spectrum of the generated LFMW with amplitude shaping. AFG: arbitrary function generator, DAQ: data acquisition card, PD: photodetector, OC: optical coupler, MZM: Mach-Zehnder modulator.
3.2 Phase continuity and frequency tuning
The phase continuity near the stitching points is also investigated in our experiments. The phase is extracted by Hilbert transformation for the temporal waveform. The phase differences near the 9 stitching points are presented in Fig. 5(a). There exist great phase differences at the stitching points without compensation. Since the parameters of the baseband LFMW and the OFC satisfy Eq. (7), the phase discontinuities of the LFMW are totally induced by the phase differences of the OFC. Figure 5(b) presents the digitally down-converted waveform of the first stitching point. A phase jump can be observed at this point. By adjusting the phase of the baseband LFMW, the phase discontinuities are successfully compensated as shown in Fig. 5(a). The residual phase differences near the stitching points are within $\pm 10^{\circ }$. The digitally down-converted waveform near the first point with phase compensation is shown in Fig. 5(c), where the phase jump is eliminated. The pulse compression performances of the generated LFMWs are also investigated by calculating the cross correlation between the generated LFMWs and the ideal LFMW. The result without phase compensation is presented in Fig. 5(d). The pulse compression peak splits owing to the discontinuous phase. While after phase compensation, a sharp pulse compression peak is obtained as Fig. 5(e) and (f) show. Figure 5(e) and (f) compare the pulse compression results of the LFMWs without and with the power shaping. The full widths at half height of Fig. 5(e) and (f) are measured as 47 ps and 42 ps, respectively. The amplitude shaping brings a narrower pulse compression peak. It can be seen that the sidelobes in Fig. 5(e) and (f) are a bit asymmetrical. To explore the possible reason, the pulse compression result of the LFMW with the same phase discontinuity as the experiment result is simulated and also shown in Fig. 5(f). From the simulated result, the phase discontinuity level obtained in the experiments will not cause obviously asymmetric sidelobes. The asymmetrical sidelobes in the experiments may be attributed to the random jitter of the relative phase between the two separate fiber links, which can be addressed by a fiber phase-locked loop [12] or by integrating the system on a chip.
Fig. 5. (a) Phase differences near the 9 stitching points without and with phase compensation. Digitally down-converted waveforms (b) without and (c) with phase compensation. (d) Pulse compression result without phase compensation. (e) Pulse compression result with phase compensation but without amplitude shaping. (f) Pulse compression result with phase compensation and amplitude shaping.
Fig. 6. (a) Frequency error of the beatings of the optical carrier and the DFB laser under free-running (FR) and injection-locked (IL) states, red line: without phase compensation, blue line: with phase compensation. (b) Detailed version of the frequency errors without and with phase compensation.
To further demonstrate the benefits of the injection locking and the phase compensation, the linearity of the generated LFMW is measured with the method in [27]. Figure 6(a) presents the frequency errors compared with the ideal linear frequency sweeping. The black line corresponds to the beating of the optical carrier and the DFB laser under the free-running state. The standard deviation (STD) of the frequency error is up to 3.0 MHz and the linearity, which is defined as the ratio of the maximum frequency error and the bandwidth, is measured as ${5.4\times 10^{-3}}$. The blue line and the red line are the frequency errors of the beatings of the optical carrier and the injection-locked DFB laser without and with phase compensation. As can be seen, the frequency errors are greatly suppressed, which benefits from the injection locking and the excellent linearity of the baseband LFMW. The detailed versions of the frequency errors without and with phase compensation are shown in Fig. 6(b). The glitches on the red line are induced by the phase jumps at the stitching points. And all the glitches are eliminated after phase compensation. The frequency error STD with phase compensation is measured as 8.0 kHz and the linearity is optimized to $2.0\times 10^{-6}$, which is improved by 2700 folds compared with the free-running state.
The frequency tuning ability of the our scheme is also demonstrated experimentally. By accurately tuning the wavelength of the TLS, the DFB laser can be injection-locked with different LFMW component. As a result, the LFMWs with different initial frequencies are generated. The spectrums are presented in Fig. 7. All the bandwidths are 20 GHz, while the initial frequencies are tuned from 1 GHz to 21 GHz with a step of 2 GHz. It can be seen that the excellent flatness is still maintained when the frequency is tuned. To further improve the tuning resolution, another DPMZM working at CS-SSB modulation mode can be used to tune the frequency of the reserved optical carrier [28].
4. Conclusion
In summary, we have proposed and demonstrated a spectrum stitching scheme for broadband LFMW generation based on a single OFC and injection locking technique. An expanded TBWP by 100 folds is achieved experimentally by stitching 10 segments of 2-GHz baseband LFMWs. The bandwidth of the synthesized broadband LFMW is up to 20 GHz. The phase continuity and power flatness are guaranteed, which leads to a great pulse compression performance. The excellent linearity reaches ${2.0\times 10^{-6}}$. With the emerging thin-film lithium niobate [29] and hybrid integration technology [30], our scheme has the potential to achieve a on-chip broadband LFMW generator, promising to be applied to microwave photonics radar, joint radar-communication systems and spectrum sensing.
Funding
Wuhan National Laboratory for Optoelectronics (2018WNLOKF011); Major Scientific Project of Zhejiang Laboratory (2020LC0AD01); National Key Research and Development Program of China (2018YFA0701902).
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 can be obtained from the authors upon reasonable request.
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