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Abstract
We demonstrate ultralinear and ultrawideband frequency-modulated continuous-wave (FMCW) signal generation using an optical parametric wideband frequency modulation (OPWBFM) method. The OPWBFM method optically expands the bandwidths of FMCW signals beyond the electrical bandwidths of optical modulators via a cascaded four-wave mixing (FWM) process. Compared to the conventional direct modulation approach, the OPWBFM method simultaneously achieves high linearity and a short measurement time of the frequency sweep. On the other hand, it is also known that the OPWBFM method expands the phase noise of idlers as well as their bandwidths if an input conjugate pair has different phase noise. To avoid this phase noise expansion, it is crucial to synchronize the phase of an input complex conjugate pair of an FMCW signal using an optical frequency comb. For demonstration, we successfully generated an ultralinear 140-GHz FMCW signal by using the OPWBFM method. Moreover, we employ a frequency comb in the conjugate pair generation process, leading to the mitigation of phase noise expansion. By using a 140-GHz FMCW signal, we achieve a range resolution of ∼1 mm through fiber-based distance measurement. The results show the feasibility of an ultralinear and ultrawideband FMCW system with a sufficiently short measurement time.
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1. Introduction
Nonlinear optics is a central research field that has been extensively investigated for a long time [1,2]. Among various types of nonlinear phenomena, four-wave mixing (FWM) plays a particularly important role since it enables many applications, including signal amplification [3–6], wavelength conversion [7–9], phase conjugation [10–12], and frequency comb generation [13–19]. Recently, we proposed a novel FWM-based concept that enables the generation of wideband optical frequency-modulated (FM) signals [20]. By using this scheme, via a cascaded FWM process driven by an input complex conjugate pair of an optical FM signal, we can generate optical FM signals with odd multiples of the original conjugate pair bandwidth. Therefore, it becomes possible to optically expand the bandwidth of an FM signal beyond the electrical bandwidths of optical modulators. We refer to this FWM-based method of generating wideband FM signals as the optical parametric wideband FM (OPWBFM) method. Generation of such a wideband optical FM signal is important, especially for frequency-modulated continuous-wave (FMCW) laser-based light detection and ranging (LiDAR) systems. This is because the range resolution of FMCW systems is determined by the bandwidth of an FM signal; i.e., an FM signal with a wider bandwidth is able to resolve smaller differences in distance. The range resolution $\Delta d$ is inversely proportional to the FM bandwidth as
where $c$ is the speed of light and $B$ is the FMCW bandwidth. In particular, LiDAR systems can benefit from this FMCW’s feature, as they have abundant spectral resources compared to the micro/millimeter-wave region. In fact, there have been numerous reports on GHz-class FMCW experiments that exploit the bountiful spectral resources in the optical domain [21–26]. In [20], we also demonstrated the optical generation of FMCW signals up to 55 GHz using the OPWBFM method. On the other hand, FMCW signal generation of > 100 GHz was also reported using direct modulation of a laser [26]. However, the direct modulation approach usually suffers from inherently poor sweep linearity and a slow sweep rate. These disadvantages result in the necessity of pre/postprocessing of sample data for linearization and long measurement times. In contrast to this approach, the OPWBFM method purely reflects the linearity of the original signal in idlers. In addition, the frequency sweep time of the idlers becomes the same as that of the original signal. Therefore, good linearity and short frequency sweep time can easily be accomplished at the same time as long as the original signal has both of them. Such an original signal can also be easily generated since its bandwidth can be narrow enough to be directly manipulated in the electrical domain.The mitigation of laser phase noise is also crucial as well as bandwidth expansion for FMCW systems. In contrast to the time-of-flight (ToF) method, where reflected light is received via simple direct detection, an FMCW signal is received via heterodyne (or homodyne) detection; thus, a beat note from an optical receiver becomes sensitive to laser phase noise. Although reflected light interferes with the delayed version of itself, the occurrence of phase noise is inevitable since reflected light after a round trip between a transmitter and an object has different phase noise [27]. In particular, phase noise has more impact when the path difference exceeds the coherence length of a laser source. In this case, the spectral shape of a beat note becomes the Lorentzian shape, and this shape severely degrades the range resolution. Thus, the phase noise of FMCW signals should be as small as possible. However, as we have discussed in [20], the OPWBFM method expands the phase noise of FM signals as well as their bandwidths when the initial conjugate pair has different phase noise. This is especially the case when the conjugate pair is generated from independent laser sources. The use of a frequency comb offers a potential solution, i.e., the conjugate pair can have the same phase noise when generated from coherently synchronized two-tone components of a frequency comb. In this case, the expansion of phase noise can potentially be mitigated.
In this paper, we demonstrate 140-GHz FMCW signal generation using the OPWBFM method and fiber-based distance measurement with a 140-GHz signal. The generated FMCW signal has excellent linearity and thus eliminates the need for pre/postprocessing. In addition, unlike our previous demonstration, an input conjugate pair is generated using a frequency comb. This results in the mitigation of phase noise expansion as discussed above and thus enables ranging with a sufficiently small range resolution. According to Eq. (1), the achievable range resolution of this experiment is $\sim$1 mm. Thus, we validate it through a fiber-based distance measurement experiment and actually achieve a range resolution of $\sim$1 mm. These results show the feasibility of an ultralinear and ultrawideband FMCW-based LiDAR system with a sufficiently short measurement time.
2. Concept of the OPWBFM method and system architecture for FMCW systems
In this section, we briefly introduce the concept of the OPWBFM method and how it accomplishes the bandwidth expansion of FMCW signals [20]. Although the concept covers all angle modulation formats, including phase modulation (PM), we limit the discussion here to FM. We first prepare an optical FM signal as
It is worth noting that these idlers have threefold modulation indices compared to the original conjugate pair. This indicates that the frequency excursions of the idlers also become threefold. By repeating this FWM process, idlers with wider frequency excursions are successively produced. As a result, we can generate FMCW signals with much wider bandwidths, as shown in Fig. 1. Since this method purely reflects the linearity of the original signal in all idlers, we can accomplish wideband signal generation and high linearity at the same time.
Fig. 1. Illustration of the optical spectrum in the OPWBFM method for generating wideband FMCW signals.
In the above discussion, we have assumed the absence of phase noise. However, it can easily be understood from Eqs. (4) and (5) that phase noise also increases with the modulation indices if the conjugate pair has different phase noise, as discussed in [20]. However, it can also be found that if the pair has the same phase noise, all idlers also have the same phase noise. Therefore, it is important to synchronize the phase of the initial conjugate pair using a frequency comb.
Figure 2 shows a sample architecture of an FMCW system with the OPWBFM method. A coherently synchronized two-tone signal is first generated, and its two wavelength components are separated using a wavelength-division multiplexing (WDM) filter. Then, one of them is modulated using an in-phase/quadrature modulator (IQM) driven by an FMCW signal, while the other is modulated by another IQM driven by the complex conjugate of the FMCW signal. Note that this conjugate pair generation can also be accomplished using a single intensity modulator and WDM filters, as demonstrated in the following experiment. After being amplified using an erbium-doped fiber amplifier (EDFA), they are injected into a nonlinear medium. Such nonlinear mediums can include silica (i.e., optical fiber), silicon, or silicon nitride. Although optical fiber is the most popular nonlinear platform, it requires a relatively long transmission distance to induce large nonlinearity and thus leads to an increase in equipment size. On the other hand, integrated nonlinear waveguides based on silicon and silicon nitride platforms have also been reported; thus, we can reduce equipment size using these platforms. After the nonlinear stage, one of the idlers with wider bandwidths is selected using an optical bandpass filter (OBPF) and is emitted into the environment. It bounces off an object and is received using a heterodyne receiver after being mixed with the delayed version of itself, as in the case of normal FMCW LiDAR systems.
3. Experiments
3.1 Setup
Figure 3 shows the experimental setup. First, an optical signal was generated from a laser source, the linewidth of which was <0.1 kHz. Its wavelength was set at 1555.8 nm. Then, it was injected into a frequency comb generation part consisting of two sections: an electro-optic (EO) comb section and a parametric comb section. In the EO comb section, the optical signal was first modulated by a phase modulator driven by a 40-GHz sinusoidal signal. It was subsequently input to an intensity modulator driven by another sinusoidal signal split from the same RF oscillator. The phase difference between the two sinusoidal signals was adjusted using an optical delay line inserted between the modulators and optimized so that the sidebands of the frequency comb became maximum. Unfortunately, since the number of sidebands was limited due to the relatively low output power of the RF oscillator, we input the signal to the second parametric comb section to generate more sidebands. Specifically, the signal was amplified using an EDFA and injected into a dispersion-shifted fiber (DSF). As a result, FWM occurring in the DSF grew the sidebands more, as shown in Fig. 4(a). Among the generated sidebands, two components with a frequency gap of 160 GHz were extracted using a wavelength selective switch (WSS), as shown in Fig. 4(b). Note that this frequency gap must be larger than the bandwidths of FMCW signals to avoid overlap among them. Therefore, the frequency gap was chosen to be greater than 140 GHz since it was our target bandwidth in this experiment.
Fig. 4. Optical spectra. (a), (b), (c), (d), and (e) show those observed at points labeled (i), (ii), (iii), (iv), and (v) in Fig. 3, respectively.
Subsequently, the two-tone signal was injected into another intensity modulator. It was driven by an electrical FMCW signal outputted from an arbitrary waveform generator (AWG) operating at 120 GS/s. The FMCW signal had a triangle shape in the time-frequency map and was generated using offline digital signal processing (DSP). Its bandwidth and start frequency were set at 20 GHz and 15 GHz, respectively. Therefore, the total bandwidth occupied 35 GHz. Note that the start frequency of 15 GHz was determined based on the filter performance of the WSS. If the start frequency is too large, it consumes the electrical bandwidth, while if it is too small, the WSS cannot suppress the carrier components sufficiently. Therefore, 15 GHz was found to be an optimal value considering these factors. The sweep time was set to 1 $\mu$s. Figure 4(c) shows the optical spectrum after the intensity modulator. As shown in the figure, both tones had 20-GHz upper and lower sidebands, and their frequency gaps from the center carriers were 15 GHz. Then, the outermost sidebands were extracted using another WSS after amplification, as shown in Fig. 4(d). These were complex conjugates of each other. Note that the innermost sidebands were also complex conjugates of each other. However, since the frequency interval between them was less than 140 GHz, the outermost sidebands were extracted. We should also note that such a conjugate pair can also be generated using the architecture shown in Fig. 2
The conjugate pair was input to a DSF to induce FWM, and as discussed above, multiple idlers with wider bandwidths were observed, as shown in Fig. 4(e). The asymmetric spectrum may be attributed to the asymmetric dispersion profile of the DSF. Since the widest bandwidth was 140 GHz among the idlers having sufficient signal-to-noise ratios (SNRs), we extracted the $E_{7}$ component at approximately 1550 nm using an OBPF and conducted a fiber-based distance measurement experiment using it as follows: the signal was first split, and one of them was input to an optical circulator. The output from the circulator was subsequently input to a free space-type optical delay line to change the path length, and the output was reflected at the end facet of an optical fiber. The return light from the circulator was mixed with the original signal and detected using a single photodiode (PD) with a 50-GHz bandwidth. Finally, the electrical output from the PD was captured using a digital oscilloscope running at 40 GS/s.
3.2 Results and discussion
We first confirmed the linearity of the 140-GHz signal using homodyne detection. Since its bandwidth was too wide to directly observe using a single receiver, we separately detected it by changing the frequency of a local oscillator (LO). Figure 5 shows the separately captured spectrograms. The LO frequency was changed at 30-GHz intervals. It can be seen in the figure that the total bandwidth was indeed 140 GHz. In addition, excellent linearity was also observed over the 140-GHz bandwidth.
Fig. 5. Separately captured spectrograms of the 140-GHz FMCW signal by changing the LO frequency at 30-GHz intervals.
To quantitatively confirm the linearity, we performed a peak frequency search of beat notes by changing the path length of the optical delay line from 0 to 10 cm with a 1-cm interval. In addition, we calculated peak frequency values theoretically predicted from the path lengths using the following equation for comparison:
where $R$ is the distance from the object and $T_{s}$ is the measurement time. Then, we compared these peak frequency values to those obtained experimentally, as shown in Fig. 6. Figure 6 indicates the relationship between the theoretical frequency values (the $y$-axis) and those obtained experimentally (the $x$-axis). The corresponding path lengths to the theoretical values are also shown on the right-hand side of the $y$-axis. A linear relationship can be found as shown there. To quantitatively evaluate the linearity, we first plot a linear fitting line based on the measurement data, as shown in the dashed line of Fig. 6. Then, its slope was calculated to be 1.00, which clearly indicates its linear relationship. In addition, we calculated the standard deviation of the measurement data from the fitting line, and it was found to be $\sim$0.32 MHz. Note that since we manually adjusted the path lengths of the delay line, $R$, the measured frequency peaks should have errors due to the inaccurate manual adjustment. However, even taking this into account, the standard deviation was still much smaller than that reported in [26].Next, we confirmed the range resolution using the 140-GHz FMCW signal. According to Eq. (1), the corresponding range resolution is $\sim$1 mm. Therefore, we first obtained a reference beat note and then separately obtained another beat note by setting the path difference to 1 mm. Figure 7 shows the range FFT plot. This FFT plot was obtained using 4000 data points which correspond to a time length of 1$\mu$s. The blue plot shows the reference case, while the red plot shows the case when the path difference was 1 mm. As shown in the figure, two peaks can be separately observed. The peak frequency of the former case was found at 4.608 GHz, while that of the latter case was found at 4.609 GHz. Since the FFT resolution was 1 MHz (this value was derived from the measurement time of 1 $\mu$s), the difference between the two frequency peaks was indeed the same as the resolution. This means that we achieved a minimum range resolution in this system. We should note that this was also thanks to the use of an optical frequency comb. Although we used a fiber laser with a sufficiently narrow linewidth in this experiment, the typical linewidths of semiconductor lasers such as distributed feedback (DFB) lasers and external cavity lasers (ECLs) are > 100 kHz. If we use them as initial conjugate inputs, the linewidth of $E_{7}$ ($E_{-7}$) is expanded to 2.5 MHz, according to [28] even if the initial linewidths are 100 kHz. The expanded linewidth already exceeds the FFT resolution and obviously prevents accurate ranging. On the other hand, typical semiconductor lasers are applicable since the linewidth can be preserved when using our comb-based approach.
Fig. 7. Range-FFT plot. The blue plot shows the reference case, while the red plot shows the case when the path difference was 1 mm.
Thus far, we have demonstrated the OPWBFM method using bulky components. However, they could potentially be integrated into a single chip except for laser and EDFA sections. For example, the comb generation part can be replaced with a single microring resonator-based comb generator. In addition, other components, such as IQMs and OBPFs, can also be integrated using mature silicon-photonic platforms. The nonlinear section with a relatively long waveguide for the OPWBFM method can also be implemented on either a silicon or silicon nitride platform [29–31]. Therefore, the experimental setup presented in this paper is expected to be replaced with a compact integrated chip. In addition, while the fiber-based FWM process usually suffers from instability due to environmental fluctuations such as temperature change, it is relatively easy to stabilize integrated chips. Therefore, integrated chips offer system stability as well as device miniaturization.
4. Conclusion
We have demonstrated ultralinear and ultrawideband FMCW signal generation with the OPWBFM method and fiber-based distance measurement using the signal. Although such a wideband FMCW signal can be generated using direct modulation of a laser, the OPWBFM method has two significant advantages: its linearity and short measurement time. Regarding the linearity issue, while the direct modulation approach usually suffers from linearity, the OPWBFM method purely reflects the linearity of the original signal in all idlers. Therefore, the linearity of idlers can be guaranteed since the bandwidth of the original signal is narrow enough to be directly handled in the electrical domain. In addition, the sweep rates of the direct modulation approach tend to be limited to the order of kHz. In the OPWBFM method, on the other hand, the sweep rates of idlers become the same as that of the original signal; thus, it can be freely chosen by designing the sweep rate of the original signal.
For demonstration, we generated a 140-GHz FMCW signal by using the OPWBFM method. Moreover, we employed a frequency comb in the conjugate pair generation process. This leads to the mitigation of phase noise expansion and thus enables ranging with a sufficiently high range resolution. We successfully generated a 140-GHz FMCW signal with sufficiently high linearity and confirmed a range resolution of $\sim$1 mm through fiber-based distance measurement. The results show the feasibility of an ultralinear and ultrawideband FMCW-based LiDAR system with a sufficiently short measurement time.
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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