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Abstract
In this paper, we propose and demonstrate a novel photonics-enabled frequency multiplication system with an ultrahigh multiplication factor (MF) for broadband linear frequency modulated (LFM) microwave generation. A pair of distributed feedback (DFB) lasers are injection-locked to two optical sidebands with different orders, which are excited by a narrow-band LFM waveform with a frequency range of 2∼3 GHz. Frequency-multiplied LFM waveforms are generated by beating the two DFB outputs. Thanks to the injection locking, the frequency-multiplied signals have excellent spurious suppression and linearity. The measured spurious suppression ratio exceeds 21.4 dB and the linearity is better than 1 × 10−5. The MF reconfigurability and the central frequency tunability are also demonstrated. A series of 20-fold frequency-multiplied LFM waveforms with different central frequencies and a 30-fold frequency-multiplied signal with a frequency range from 16 GHz to 46 GHz are generated. Moreover, a feedback setup is employed to stabilize the waveform phase against environmental interferences. The measured standard deviation of the remaining phase jitter is around 5.5$^{\circ}$.
© 2021 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Linear frequency-modulated waveforms (LFMW) have been widely applied in microwave continuous-wave radar systems to achieve high-resolution and long-range detection simultaneously due to their pulse compression capacity [1]. Compared with other continuous-wave radars, LFMW radar requires a much lower sampling rate of the analog-to-digital converter in the receiver owing to the unique dechirp receiving scheme [2,3]. With the ever extending application scenarios, radar systems are expected to achieve a higher imaging resolution, which corresponds to a broader transmitting bandwidth. For example, detection for obstacles and foreign-object debris on the airport runways usually requires an imaging resolution of millimeter level and a radar bandwidth of tens of GHz [4,5]. However, traditional electronic techniques, when generating such broadband LFMWs, suffer severe performance degradation, such as serious time jitters, spurious interference, strong electromagnetic interference, etc.
In recent years, photonics-enabled LFMW generation has attracted extensive research interest as an effective alternative scheme, owing to the ability to achieve wide bandwidth, low jitters, resistance to electromagnetic interference, etc. One of the most promising techniques is optical frequency multiplication, which generally beats two different optical sidebands excited by a narrow-band LFMW [4,6–10]. Compared with other photonics-based schemes [11–15], optical frequency multiplication can realize broadband LFMW generation with a long duration while keeping an excellent linearity. It has thus been widely applied to numerous systems, such as radio-over-fiber links [16], microwave photonic radar [17] and wireless access [18]. The key point of optical frequency multiplication is to generate high-order optical sidebands utilizing the nonlinearity effect in the microwave and optoelectric devices, such as modulation nonlinearity in modulators [8], four-wave mixing in fibers [19]. Unfortunately, these nonlinearity effects will not only generate the target sidebands but also a series of unwanted sidebands, giving rise to two main drawbacks for the conventional optical frequency multiplication schemes. On one hand, quite weak power is allocated to the high-order sidebands in general owing to the simultaneous power occupation of unwanted sidebands and the limited nonlinearity. It leads to a limited frequency multiplication factor (MF) and poor noise characteristics in frequency-multiplied signals. The MFs of the state-of-art LFMW frequency multiplication systems are usually less than 10, for example, dupling in [7], quadrupling in [6,10,17], sextupling in [8]. On the other hand, unwanted sidebands will also beat with each other, resulting in a series of spurious components, which are essentially frequency multiplication components of other MFs. These spurs will introduce serious interference to the electronic systems, e.g., dynamic range deterioration for LFMW radars [20]. Especially when generating broadband LFMWs, spurs may overlap with the target frequency-multiplied signal in the frequency domain, which cannot be separated by a conventional filter.
Optical sideband injection locking is an effective method to boost the power of the target optical sideband and suppress other unwanted sidebands [21,22], which has been introduced into the frequency multiplication system. In [23], a radiofrequency signal up to 100 GHz is generated by injection locking the 25th order sideband. The output phase noise of this system is very close to that of the ideal frequency-multiplied signal. However, the slave DFB laser worked at a single wavelength mode and the system output was a single-tone radiofrequency signal. The application of sideband injection locking in the LFMW frequency multiplication systems has not been reported yet.
In this paper, we introduce the sideband injection locking technique into the LFMW frequency multiplication system to improve the MF and suppress the spurious components. Two optical sidebands injection-locking to two DFB lasers are reserved and boosted, while other sidebands are suppressed deeply. Then the two laser outputs beat with each other to generate the frequency-multiplied LFMW with an ultrahigh MF. In the experiment, a cascaded modulator configuration is employed to generate a series of high-order sidebands. By injection locking different pairs of optical sidebands, the multiplication factor can be reconfigured easily. The spurious suppression ratio exceeds 21.4 dB. The central frequency tuning ability is also investigated and demonstrated. A series of 20-fold LFMWs with different central frequencies and a 30-fold LFMW are generated. To our best knowledge, this is the highest MF achieved by optical LFMW frequency multiplication systems. A feedback stabilization structure is also proposed to suppress the phase jitters attributed to fiber disturbances and the standard deviation of the phase jitters is measured as 5.5$^{\circ}$ with this structure.
2. Principle
Conventional photonics-based microwave frequency multiplication systems are achieved by beating two high-order optical sidebands, which are usually generated by modulating a narrowband LFMW into a master laser. The optical field of the ${n}$th order sideband can be expressed as
where ${\Omega _0}$ denotes the angular frequency of the master laser, ${f_0}$ and ${k}$ are the initial frequency and the chirp rate of the input LFMW, ${E_n}$ is the amplitude of the ${n}$th optical sideband. Thus, the frequency of the ${n}$th optical sideband sweeps from ${\frac {\Omega _0}{2\pi }+nf_0}$ to ${\frac {\Omega _0}{2\pi }+nf_0+nkT}$, where ${T}$ is the duration of the input LFMW. As presented in Fig. 1(a), the optical sidebands with different orders may overlap in the frequency domain. For example, when the sideband order and the parameters of the input LFMW satisfy or the ${n}$th order optical sideband will overlap with the ${(n-1)}$th or ${(n+1)}$th order sidebands, respectively. Correspondingly, the generated frequency-multiplied signal has massive in-band spurious components, which cannot be removed using a conventional filter as shown in Fig. 1 (a). Equation (2) and Eq. (3) can be simplified as It can be seen that higher-order sidebands are more likely to overlap. Noted that ${nkT}$ also denotes the bandwidth of the ${n}$th order optical sideband and overlap is thus almost inevitable when generating broadband LFMWs.To address this issue, we propose a novel LFMW frequency multiplication system based on optical sideband injection locking technique. As presented in Fig. 1(b), the generated optical sidebands are splitted into two branches. The first branch is frequency-shifted in a frequency shift module driven by a single-tone local oscillator (LO). Then the two branches are both injected into two slave lasers. The two lasers are driven by two ramp currents with a positive slope and a negative slope to injection lock to a positive sideband and a negative sideband, respectively. The frequency and phase of the slave laser track well with the target sideband when the injection locking occurs. The slave laser can thus be regarded as the amplified replica of target sideband, leading to an improved noise characteristic in high-MF frequency-multiplied signals, which are generated by beating the two injection-locked slave lasers. Meanwhile, the other sidebands and the corresponding spurious components in frequency-multiplied signals are suppressed deeply. Ignoring the unwanted sidebands, the two injection-locked laser outputs can be expressed as
Fig. 1. Principle of the conventional frequency multiplication (a) and the frequency multiplication based on optical sideband injection locking (b). LO: local oscillator, OSIL: optical sideband injection locking, FS: frequency shift.
3. Experiment and results
3.1 MF-reconfigurable LFMW generation
Figure 2(a) shows the experimental setup of the proposed LFMW frequency multiplication system. A single-wavelength light emitted from a tunable laser source (TLS, Keysight 8164B) passes through an optical comb generator. Here, we refer to the optical comb generation scheme based on cascaded modulators to excite a series of high-order sidebands [24]. The detailed configuration of the comb generator is presented in Fig. 2(b). A narrow-band LFMW with a frequency range of 2${\sim }$3 GHz is generated by an arbitrary waveform generator (Tektronix AWG 700002A) and used as the microwave input of the comb generator. The duration and repetition period of the LFMW are 500 $\mathrm{\mu}$s and 1 ms, respectively. As shown in Fig. 2(b), the baseband LFMW input is amplified and then splitted with a ratio of 9:1. 90${\%}$ is modulated by a Mach-Zehnder modulator (MZM). And the rest 10${\%}$ is amplified again and then modulated by a phase modulator (PM). The delay between the two parts of baseband signals is tuned by a phase shifter (PS). The output spectrum of the comb generator is shown in Fig. 2(c). For a clear display, the baseband input is replaced by a 3-GHz single tone when acquiring the spectrum. A 30-line comb is generated within a power fluctuation of 10 dB as Fig. 2(c) shows. In other words, at least ${\pm }$15th order sidebands are excited.
Then a waveshaper (Finisar waveshaper 4000s) is employed to roughly filter a positive sideband and a negative sideband from the excited sidebands, which is outputted from two ports respectively. One is then carrier-suppressed-double-sideband (CS-DSB) modulated by a single-tone LO signal in an MZM, which is served as a frequency shift module. One sideband in the CS-DSB modulated spectrum can be regarded as a frequency-shifted replica of the target sideband. Then the two branches of lights are amplified and injected into two DFB lasers. Two polarization controllers (PC) are employed to optimize the injection ratios. The injection ratios are around 30 dB and the locking ranges of the two DFB lasers are 800 MHz and 760 MHz, respectively. The DFB lasers are driven by a positive-slope drive current and a negative-slope drive current, respectively. The repetition rate and the duty cycle of the two currents are 1 kHz and 50%, respectively, which correspond to those of the input narrow-band LFMW. The two ramp signals are generated by a two-channel arbitrary function generator (AFG, Tekronic AFG31000) and converted to drive currents in two laser diode controllers (Newport LDC-3726). The drive currents are predistorted using the method introduced in [25] to make the free-running frequency sweep as linear as possible and the slope as close to that of the target sideband as possible. At the same time, the AFG outputs a trigger signal into the AWG to ensure the narrow-band LFM signal synchronized with the two drive currents. Then the TLS wavelength and work temperatures of the two DFB lasers are adjusted carefully. When the frequency difference between the free-running DFB laser and the target sideband is less than the locking range, the two DFB lasers will be injection-locked. Finally, the injection-locked DFB lasers beat with each other in a broadband photodetector (Finisar XPDV2120RA) and a broadband LFMW is generated. Note that the waveshaper here is used to avoid the overlap between the two sidebands of the MZM served as the frequency shift module. It can be replaced by an optical coupler if carrier-suppressed-single-sideband modulation is employed in the frequency shift module.
Fig. 2. (a) Setup of the frequency multiplication system. (b) Schematic diagram of the comb generator. (c) Output optical spectrum of the comb generator when the input is a 3-GHz single tone. TLS: tunable laser source, AWG: arbitrary waveform generator, MZM: Mach-Zehnder modulator, LO: local oscillator, EDFA: erbium-doped fiber amplifier, PC: polarization controller, PD: photodetector, PS: phase shifter, AMP: microwave amplifier, PM: phase modulator, MC: microwave coupler, AFG: arbitrary function generator, LDC: laser diode controller.
The MF of this system can be reconfigured by injection locking different pairs of optical sidebands. Limited by the bandwidth of the available oscilloscope in our lab (OSC, Keysight UXR0134A, 20GHz), we first demonstrated the reconfigurable MFs from 2 to 6 by injection locking the +1st and -1st, +1st and -2nd, +2nd and -2nd, +2nd and -3rd, +3rd and -3rd order sidebands, respectively. The frequency shift module is not employed in these cases. The temporal waveforms and spectrums are acquired by the oscilloscope and a spectrum analyzer (SA, ROHDE & SCHWARZ FSWP50). The spectrums are shown in Fig. 3(a), whose frequency ranges are 4$\sim$6GHz, 6GHz${\sim }$9GHz, 8GHz$\sim$12GHz, 10$\sim$15GHz, and 12$\sim$18GHz, respectively. The spectrograms are calculated by the short-time Fourier transformation for the temporal waveforms and presented in Fig. 3(b). It can be seen from the spectrograms that these frequency-multiplied waveforms keep excellent linearity. Frequency spurs can also be observed which come from the beatings between the residual unwanted sidebands. We then integrated the power density of each spurious component in these waveforms to accurately evaluate the performance of spurious suppression. The normalized power of spurs with different orders, as well as the target frequency-multiplied component, under MFs from 2 to 6 are shown in Fig. 4(a). The spurious suppression ratio of each waveform, which is defined as the power ratio between the target frequency-multiplied signal and the spurious component with the maximum power, is 22.9 dB, 27.3 dB, 25.8 dB, 23.9 dB, and 24.0 dB, respectively. The cross correlation peaks with the ideal LFMWs are presented in Fig. 3(c) (in red), which agree well with the autocorrelation peaks of ideal LFMWs (in black). And the full width at half maximum (FWHM) of each pulse compression peak is presented in Fig. 4(b), which is very close to the ideal result.
Fig. 3. Experimental results of MF-reconfigurable (MF=2, 3, 4, 5, 6) LFMW generation. (a) Spectrum. (b) Spectrogram. (c) Cross correlation with ideal LFMWs.
Fig. 4. (a) Normalized power of each spurious component under different MFs. (b) FWHMs of the cross correlation peaks.
For comparison, the waveforms are also acquired when the two DFB lasers are under free-running states. In this case, the frequency sweep slopes of the two DFB lasers are close to those of ${\pm 3}$rd order sidebands. Figure 5(a) (blue line) presents the cross correlation result with the ideal LFMW (frequency range: 12GHz${\sim }$18GHz). Owing to the residual frequency sweep nonlinearity and strong frequency noise, a correlation peak cannot be obtained through the cross-correlation process. In contrast, the cross-correlation result of the generated 6-fold frequency-multiplied LFMW presents a sharp peak (red line), which is attributed to the fact that the sideband injection locking technique suppresses the sweep nonlinearity and frequency noise effectively. The frequency error compared with the ideal linear sweep under free-running and injection-locking states are also measured using the method in [26]. The results are presented in Fig. 5(b). The maximum frequency offset under the free-running state exceeds 20 MHz. The corresponding linearity, which is defined as the ratio of the maximum frequency offset and frequency sweep range, is measured as ${3.8\times 10^{-3}}$. By contrast, the red line presents the frequency error of injection locking state, which is compressed to several tens kHz. The corresponding linearity is improved to ${9.3\times 10^{-6}}$.
Fig. 5. Cross correlation with the ideal LFMW (a) and frequency error (b) under free-running (FR) and injection-locked (IL) states, respectively.
3.2 Central frequency tuning and LFMW generation with an ultrahigh MF
Then we demonstrate the central frequency tunability of the proposed system. In the experiments, a series of 20-fold frequency-multiplied LFMWs are generated by injection locking ${\pm 10}$th order sidebands. The LO frequency is set as 40 GHz, 30 GHz, and 20 GHz in turn. The corresponding frequency range under different frequency shifts are 0${\sim }$20 GHz, 10${\sim }$30GHz, and 20${\sim }$40 GHz, respectively. Their spectrums are shown in Fig. 6(a). The LFMW with the frequency range of 0${\sim }$20 GHz is acquired by the OSC and its spectrogram is presented in Fig. 6(b). It can be seen that the waveform still keeps excellent spurious suppression. Figure 6(c) presents the calculated spurious power of each order. Compared with the 20-fold frequency-multiplied component, the suppression ratios for 19-fold and 21-fold components are 21.5 dB and 21.4 dB, respectively. Other components have much higher suppression ratios. The cross correlation peak with the ideal waveform, as well as the autocorrelation of the ideal LFMW, is shown in Fig. 6(d). The FHWM of the cross correlation peak is measured as 43 ps, which agrees with the ideal result. The slightly deteriorated noise floor may be attributed to the attenuation of frequency shift module. A higher-efficient frequency shift can address this issue.
Next, the LO frequency is set as 44 GHz and the two DFB lasers are injection-locked to ${\pm }$15th order sidebands by resetting the drive currents. The slopes of the two drive currents are around -137 mA/ms and 159 mA/ms. We demonstrated the generation of a 30-fold frequency-multiplied LFMW with a frequency range of 16${\sim }$36 GHz. The corresponding time-bandwidth product is up to ${1.5\times 10^{-7}}$. Its spectrum is shown in Fig. 7(a). As far as we know, this is the highest MF ever reported for photonics-based LFMW frequency multiplication systems. Such broadband LFMWs cannot be acquired using the OSC in our lab. We thus calculated the linearity of the LFMW by measuring the frequency error of the two injection-locked DFB lasers [26]. The two DFB lasers pass by two unbalanced Mach-Zehnder interferometers (MZI). By Hilbert transformation for the photocurrents outputted by the followed PDs, the optical instantaneous frequency can be extracted. The frequency errors of the two DFB lasers compared with ideal linear frequency sweep are presented in Fig. 7(b). Owing to the frequency drift of the master laser, the two DFB lasers have an frequency error up to MHz level. By beating the two DFB outputs, the effects of the frequency drift are eliminated and the calculated frequency error of the 30-fold frequency-multiplied LFMW is below 230 kHz as shown in Fig. 7(b). The corresponding linearity is ${7.7\times 10^{-6}}$. The slopes observed at the top of the spectrums shown in Fig. 6(a) and Fig. 7 (a) is mainly caused by the fluctuation of the frequency response of photodetector and microwave devices including amplifiers and coaxial cables.
Fig. 6. (a) Spectrums of 20-fold frequency-multiplied LFMWs when the LO frequency is 40 GHz (red line), 30 GHz (pink line), and 20 GHz (blue line), respectively. Spectrogram (b), spurious component power (c), cross correlation peak (d) of the 20-fold frequency multiplied LFMW with a frequency range from 0 GHz to 20 GHz.
Fig. 7. (a) Spectrum of the 30-fold frequency-multiplied LFMW. (b) Frequency errors of the two DFB lasers that are injection-locked to the +15th order sideband (positive) and -15th order sideband (negative), as well as the calculated frequency error of the beat note of the two DFB lasers.
3.3 Phase stabilization
Owing to the relative phase jitter between the two DFB laser outputs which are attributed to acoustic noise coupling from the environment into fibers [23], the coherence of frequency-multiplied LFMWs between different periods is seriously deteriorated. To address this issue, a feedback stabilization configuration is introduced into our frequency multiplication system to suppress the phase jitters. The configuration is shown in Fig. 8(a). Another TSL (TSL2, Santec TSL-550), whose wavelength is far away from those of the two DFB lasers, is served as a seed light. The seed light is splitted into two branches together with the optical sidebands and then injected into the two DFB lasers, respectively. After reflected by the two DFB lasers, the two branches of seed lights are coupled together. The phase jitter between the two branches is converted into the power fluctuation of the seed light. An optical bandpass filter is employed to remove the DFB outputs and reserve the seed light only. Another PD is used to detect the power of the seed light and then a feedback signal is generated by amplifying and integrating the photocurrent using a high-speed servo controller (Newport LB1005). The signal is amplified by a fiber stretcher driver and then drives a piezoelectric lead zirconate titanate (PZT) fiber stretcher. By controlling the length of the PZT fiber stretcher dynamically, the phase jitters between the two branches are well compensated. It is worth noting that the fiber stretcher will lead to longer transmission delay and polarization variation in that branch. The transmission delay difference between the two branches will convert the frequency noise of the master laser to the phase noise of the beat signal. Meanwhile, the polarization variation induced by the fiber stretcher may cause the power reductions of the generated frequency-multiplied signals. In the experiments, the delay difference is compensated accurately by adding an extra fiber in the other branch. The polarization of the two branches is also adjusted carefully by two polarization controllers to align the polarization of the two branches at the photodetector. Figure 8(b) presents the zoom-in 6-fold frequency-multiplied waveforms of 200 different periods without feedback stabilization. As can be seen, the waveforms between different periods are incoherent and have a serious phase jitter, which limits their application scenarios such as coherent radar imaging. By contrast, the 200 feedback-stabilized waveforms measured repeatedly in half an hour have relatively stable phases as shown in Fig. 8(c). By fitting with the ideal waveforms, the phases of the waveforms with feedback stabilization are extracted and presented in Fig. 8(d). The standard deviation of the the remaining phase jitter is measured as 5.5°.
Fig. 8. (a) Frequency multiplication system with feedback stabilization. Zoom-in waveforms of 200 different periods without feedback stabilization (b) and with feedback stabilization (c). (d) Extracted phases of the 200 waveforms with feedback stabilization. PZT: piezoelectric lead zirconate titanate fiber stretcher, OBPF: optical bandpass filter.
3.4 Discussion
It should be noted that the current sweep will also cause laser power variation. We measured the power changes of the two DFB lasers when generating 20-fold LFMWs and 30-fold LFWMs. The results are presented in Fig. 9(a) and (b). For 20-fold LFMWs, the output power of the two lasers sweeps from 10 dBm to 6.7 dBm and from 7.7 dBm to 10.5 dBm, respectively. For 30-fold LFMWs, the power of the two DFB lasers sweeps from 10.9 dBm to 6.8 dBm and from 7.2 dBm to 10.7 dBm, respectively. Thanks to the opposite sweep slope, the power fluctuation of the generated LFMWs is suppressed effectively. As shown in Figs. 9(a) and (b), the estimated power fluctuation induced by the amplitude modulation of DFB lasers for 20-fold and 30-fold frequency-multiplied LFMWs is only 0.2 dB and 0.6 dB, respectively. Therefore, the impact of laser power variation is actually negligible. The spectral variation of the generated wideband microwave signals in our experiments is mainly attributed to the frequency responses of the photodetector, amplifier and coaxial cables. Flatter spectrum can be obtained by using devices with broader bandwidth.
Fig. 9. Power of the two DFB lasers and the estimated power of the 20-fold LFMWs (b) and 30-fold LFMWs (b), respectively.
Compared with the frequency multiplication system for single-tone signals in [23], our scheme has four significant improvements. (a) Optical comb generation based on cascaded modulators is introduced into the system to enhance the order of excitable optical sidebands. (b) A pair of DFB lasers are injection-locked to a negative sideband and a positive sideband, respectively, doubling the maximum achievable MF. (c) Our system can achieve arbitrarily tunable central frequency. (d) An extra feedback stabilization structure is introduced to suppress the phase jitters caused by fiber disturbances and improve the coherence between different periods. Restricted to the SA acquisition range and PD bandwidth, we demonstrated the generation of frequency-multiplied waveforms only below 50 GHz in our experiments. In fact, for a DFB laser, the frequency sweep range attributing to the current modulation can reach 100 GHz. Using a wider-band PD [27] and a relatively boarder baseband LFMW, our system has the potential to generate broadband LFMWs with a bandwidth over 100GHz.
4. Conclusion
In this paper, we have proposed and demonstrated a frequency multiplication system for broadband LFMW generation based on optical sideband injection locking technique. The MF is reconfigurable by injection locking different orders of optical sidebands. The achieved maximum MF is up to 30 and a 30-GHz-bandwidth LFMW is generated using a baseband signal with a narrow bandwidth of only 1 GHz. Benefiting from injection locking, the frequency-multiplied LFMWs have excellent spurious suppression and linearity. The arbitrary tunability for the central frequency is also well demonstrated. A feedback stabilization structure are further proposed and deeply suppress the phase jitters that are attributed to environmental interferences. Combined with integrated schemes for optical comb generation [28] and injection locking [29,30], our system has the promising potential to be integrated on chips and applied in broadband radar and spectrum sensing systems.
Funding
National Key Research and Development Program of China (2018YFA0701902); National Natural Science Foundation of China (61690192); Major Scientific Project of Zhejiang Laboratory (2020LC0AD01); Open Project Program of Wuhan National Laboratory for Optoelectronics (2018WNLOKF011).
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analyzed in the presented research.
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