1. Introduction

Frequency-modulated continuous-wave (FMCW) laser source plays a key role in many fields such as light detection and ranging (Lidar) [1,2], optical frequency domain reflectometry (OFDR) [3], optical coherence tomography (OCT) [4] and so on. For FMCW coherent detection, the detection performance is determined by the quality of FMCW laser source. Specifically, the accuracy of the measurement is related to the chirp linearity of FMCW laser source [2], the maximum detection distance is associated with the linewidth [5], the acquisition of a real-time image with very-high frame rate is relevant to the sweep rate [6], and the spatial resolution is connected with the swept-frequency range [7]. Therefore, a FMCW laser source with high chirp linearity, narrow linewidth, fast sweep rate and large swept-frequency range is urgently required. However, in practice, it is very difficult to acquire a FMCW laser source with these features simultaneously. As a result, various methods have been proposed to improve the quality of FMCW laser source and can be divided into the following four main categories. First, direct current tuning is utilized to realize a large swept-frequency range. However, the linewidth is deteriorated, and the swept-frequency nonlinearity is introduced and needs to be calibrated by various linearization methods [2,8]. Second, intra-cavity modulation method based on an external-cavity laser (ECL) has been reported to obtain ultra-narrow linewidth [5,9], but the sweep rate and the swept-frequency range are sacrificed due to the intrinsic relaxation oscillation effect in laser together with other inherent side effects such as cavity mode selection and mode competition inside the cavity [6,10]. Third, coherent stitching technique such as stitching the swept spectra of separate laser sources [11,12] or the comb modes of a frequency-modulated (FM) comb [13], is applied to increase the swept-frequency range while keeping the linewidth and the sweep rate unchanged. However, this technique means complicated experimental scheme and signal processing process. The final one is the external modulation method, which guarantees high chirp linearity and fast sweep rate of FMCW laser source while the narrow linewidth can be maintained. Nevertheless, the disadvantage of this method is that the swept-frequency range is limited by the bandwidths of electronics and modulators. To broaden the swept-frequency range, numerous schemes have been proposed. For example, a broadband FMCW laser source is acquired by splicing FM segments with an optical recirculating frequency shifter loop [14]. However, it is really challenging to align all FM segments together to form a straight line in the time-frequency domain. High-order modulation-sideband injection-locking technique is used to obtain multiplied swept-frequency range [15], but the swept-frequency range is still limited by the operating bandwidths of electro-optic modulator and radio-frequency amplifier. In order to further break through the limitation, a cascaded four-wave-mixing (FWM) configuration is introduced to generate first-order idler with four-times broadened swept-frequency range [16], in which a signal with a fixed frequency and a FMCW signal are utilized as the original sources. However, the linewidth of the first-order idler is deteriorated because the optical phases of the two signals are incoherent. To ensure that the linewidth is not deteriorated, two sidebands generated by dual-sideband suppressed-carrier (DSB-SC) modulation are taken as the original sources in a single-stage FWM process [17]. Based on optical parametric wideband FM (OPWBFM) method, eleven-order idler with eleven-times broadened swept-frequency range is demonstrated [18]. However, the linewidth of the eleven-order idler is relatively large since the cascaded FWM process in OPWBFM method is driven by a complex conjugate pair of an optical FM signal generated by two independent laser sources combined with an intensity modulator. Very recently, via an optical frequency comb to generate an original conjugate pair with identical phase, a narrow-linewidth FMCW signal with a swept-frequency range of 140 GHz is successfully acquired through utilizing seven-order idler in the OPWBFM method [19], where the frequency gap between the original complex conjugate pair must be larger than the desired swept-frequency range (140 GHz) to avoid overlap between adjacent idlers.

In this work, based on DSB-SC modulation and two-stage cascaded FWM, a scheme of broadband dual-chirp FMCW laser source is proposed and experimentally demonstrated. First, a dual-sideband FMCW signal is generated by DSB-SC modulation. Next, the dual-sideband FMCW signal is sent to a 1 km dispersion compensation fiber for implementing first-stage FWM, and the first-order idlers with three-times broadened swept-frequency range are generated and extracted by a filter, which is taken as the pump for second-stage FWM. The second-stage FWM is implemented in a 200 m highly nonlinear fiber, and the first-order idlers with nine-times broadened swept-frequency range are generated and used as a dual-chirp FMCW signal. Compared with that in the OPWBFM method reported in [18,19], the required frequency gap between the original two sidebands is much smaller and only needs to be larger than the swept-frequency range of the original sideband. Moreover, since only the first-order idlers are utilized during two-stage FWM process in our proposed scheme, the power of generated FMCW signal is stronger compared with that based on high-order idlers. Finally, taking the generated FMCW signal as the emitted signal for ranging, the ranging error and resolution are analyzed.

2. Experimental setup and principle

Figure 1 displays the experimental setup of the proposed FMCW laser source based on DSB-SC modulation and two-stage cascaded FWM. An optical signal with a wavelength of 1550 nm (corresponding frequency $f_\mathrm {c}$ = 193.5483 THz) and a power of 10 dBm, output from a tunable semiconductor laser (TSL, Santec TSL-710, 100 kHz linewidth), is modulated by a saw-tooth FM signal via a Mach-Zehnder modulator (MZM, IXblue MXAN-LN-10, 10 GHz bandwidth) after passing through a polarization controller 1 ($\mathrm {PC_1}$). The saw-tooth FM signal with an amplitude of 300 mVpp is provided by an arbitrary waveform generator (AWG, Tektronix AWG70000, 1.5 KS/s-50 GS/s, 15 GHz bandwidth) and amplified by an electrical amplifier (AMP, Agilent 83006A, 23 dB gain). When the MZM is biased at its null point (about 12.1 V), a DSB-SC FMCW signal (point A) can be obtained at the output of the MZM. The frequencies for the $\pm 1$st-order sidebands are ${{f}_{-1}}={{f}_{\text {c}}}-{{f}_{0}}-(B/T)t$ and ${{f}_{+1}}={{f}_{\text {c}}}+{{f}_{0}}+(B/T)t$, respectively, where ${{f}_{0}}$ is the initial frequency of the saw-tooth FM signal, $B$ is the swept-frequency range, and $T$ is the swept-frequency period. The frequency-domain characteristics of the DSB-SC FMCW signal are analyzed by an optical spectrum analyzer (OSA, Aragon Photonics BOSA lite+C, 20 MHz resolution), and meanwhile the time-domain characteristics are observed by a photodetector ($\mathrm {PD_1}$, New Focus 1544B, 12 GHz bandwidth) combined with a digital storage oscilloscope (DSO, Agilent DSO-X91604A, 16 GHz bandwidth).

 

Fig. 1. Experimental setup of the proposed FMCW laser source. TSL: tunable semiconductor laser. PC: polarization controller. AWG: arbitrary waveform generator. AMP: electrical amplifier. MZM: Mach-Zehnder modulator. FC: fiber coupler. OSA: optical spectrum analyzer. PD: photodetector. DSO: digital storage oscilloscope. EDFA: erbium-doped fiber amplifier. DCF: dispersion compensation fiber. HNLF: highly nonlinear fiber. VA: variable attenuator. PM: optical power meter. OC: optical circulator. DFB: distributed-feedback semiconductor laser.

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The DSB-SC FMCW signal undergoes the first-stage FWM, which is implemented by a 1 km dispersion compensation fiber (DCF). In order to improve the FWM efficiency, an erbium-doped fiber amplifier 1 ($\mathrm {EDFA_1}$) is utilized to amplify the incident power, and another PC ($\mathrm {PC_2}$) is used to adjust the polarization of the incident light. As shown at point B in Fig. 1, first-order idlers denoted by $\mathrm {NFC_1'}$ and $\mathrm {NFC_1}$ are generated, and the corresponding frequencies are ${{f}_{\text {NF}{{\text {C1}}^{'}}}}=2{{f}_{-1}}-{{f}_{+1}}={{f}_{\text {c}}}-3{{f}_{0}}-3(B/T)t$ and ${{f}_{\text {NFC1}}}=2{{f}_{+1}}-{{f}_{-1}}={{f}_{\text {c}}}+3{{f}_{0}}+3(B/T)t$ respectively according to FWM principle. As a result, the swept-frequency ranges of the generated first-order idlers are three times of the original sidebands. Via a 1550 nm FBG filter with a fixed bandwidth of 35 GHz, the original two $\pm 1$st-order sidebands are filtered out, and the $\mathrm {NFC_1'}$ and $\mathrm {NFC_1}$ are reserved (point C). After passing through $\mathrm {PC_3}$ and $\mathrm {EDFA_2}$, the retained $\mathrm {NFC_1'}$ and $\mathrm {NFC_1}$ are sent to a 200 m highly nonlinear fiber (HNLF) for implementing the second-stage FWM. Similar to the first-stage FWM, first-order idlers denoted by $\mathrm {NFC_2'}$ and $\mathrm {NFC_2}$ are produced (point D). Based on the FWM principle, the swept-frequency ranges of the first-order idlers are broadened by nine times compared with that of the original $\pm 1$st-order sidebands. Moreover, due to the two original $\pm 1$st-order sidebands with identical phases, the linewidth does not deteriorate. It is worth noting that for our proposed scheme, the frequency gap between the original two $\pm 1$st-order sidebands is required to be larger than the swept-frequency range $B$.

3. Experimental results and discussion

Considering that the 3 dB-bandwidth of the FBG filter is 35 GHz, the frequency of the saw-tooth electrical signal is set to sweep from 6.0 to 10.0 GHz within a period $T$ of 20 $\mathrm{\mu}$s. Under this condition, the optical spectrum of the generated DSB-SC FMCW signal with the frequency offset to the central frequency of TSL is displayed in Fig. 2(a). It can be seen that the carrier suppression ratio is about 35 dB, and the swept-frequency range $B$ of the $\pm 1$st-order sidebands is 4.0 GHz, which corresponds to 0.2 GHz/$\mathrm{\mu}$s sweep rate. It should be noted that the optical powers of the $\pm 1$st-order sidebands fluctuate throughout the whole swept-frequency range due to the frequency response characteristic of the modulator. The time series of the DSB-SC FMCW signal captured by the DSO is shown in Fig. 2(b). Based on short-time Fourier transform (STFT) of the time series, the time-frequency analysis spectrogram is acquired, which is given in Fig. 2(c). The frequency linearly sweeps from 12.0 to 16.0 GHz, and the swept-frequency period is 20 $\mathrm{\mu}$s. Note that the frequency should sweep from 12.0 to 20.0 GHz within a period of 20 $\mathrm{\mu}$s due to the beating between the $\pm 1$st-order sidebands, and the part within 16.0-20.0 GHz can not be presented since the bandwidth of the DSO is only 16 GHz.

 

Fig. 2. (a) Optical spectrum of the DSB-SC FMCW signal with the frequency offset to the central frequency of TSL. RBW: 80 MHz. (b) Time series of the DSB-SC FMCW signal. (c) Time-frequency analysis spectrogram based on STFT of the time series.

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After experiencing the first-stage FWM, the optical spectrum of the signal is shown in Fig. 3(b). For comparison, the above DSB-SC FMCW signal is given in Fig. 3(a). As can be seen, first-order idlers ($\mathrm {NFC_1'}$ and $\mathrm {NFC_1}$) can be observed, and the frequency offset of the $\mathrm {NFC_1'}$ is from -30.0 to -18.0 GHz and the frequency offset of the $\mathrm {NFC_1}$ is from 18.0 to 30.0 GHz. Therefore, the swept-frequency ranges of the first-order idlers are broadened by three times compared to that of the $\pm 1$st-order sidebands, and the corresponding sweep rates are also increased by three times to 0.6 GHz/$\mathrm{\mu}$s. The optical powers of the first-order idlers are not flat within the whole swept-frequency ranges 3$B$ mainly due to the optical power fluctuations of the $\pm 1$st-order sidebands. After passing through the FBG filter, the optical spectrum of the signal is given in Fig. 3(c). Obviously, the $\pm 1$st-order sidebands are suppressed, and meanwhile the first-order idlers are successfully preserved to be used as the pump of second-stage FWM. After undergoing second-stage FWM, the optical spectrum of the signal is displayed in Fig. 3(d). It can be observed that two new first-order idlers ($\mathrm {NFC_2'}$ and $\mathrm {NFC_2}$) appear compared with Fig. 3(c). The frequency offset of the $\mathrm {NFC_2'}$ is from -90.0 to -54.0 GHz, and the frequency offset of the $\mathrm {NFC_2}$ is from 54.0 to 90.0 GHz. Thus, the swept-frequency ranges of the newly generated first-order idlers are broadened by nine times compared with that of the original $\pm 1$st-order sidebands. Accordingly, the sweep rates are also increased by nine times to 1.8 GHz/$\mathrm{\mu}$s. It should be noted that the nine-times broadened swept-frequency range of 36.0 GHz is limited by the bandwidths of the modulator and FBG filter utilized in the experiment. Through adopting a modulator with larger bandwidth combining with a matched filter, the swept-frequency range of generated FMCW signal can be further widened.

 

Fig. 3. Optical spectra (a) of DSB-SC FMCW signal, (b) after experiencing the first-stage FWM, (c) at the output of the FBG filter, and (d) after undergoing the second-stage FWM with the frequency offset to the central frequency of TSL, where RBW is 80 MHz for (a), (b) and (c), and 700 MHz for (d).

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In order to evaluate the quality of the first-order idlers shown in Fig. 3(d), a fiber under test (FUT) length measurement experiment is conducted, and the measured system is given in Fig. 4. The length of the FUT is 88.64 m, and the FMCW signals shown in Figs. 3(a), (c) and (d) are respectively utilized as the emitted signals for measuring the length of the FUT. The de-chirped signal extracted by a $\mathrm {PD_2}$ (u2t XPDV2120R, 50 GHz bandwidth) is sent to an electrical spectrum analyzer (ESA, R&S_FSW67, 67 GHz bandwidth) for acquiring the length information. The measured results are given in Fig. 5, where the $x$ axis has been demodulated into the fiber length and red, blue and green curves are measured results corresponding to the FMCW signals shown in Figs. 3(a) and (c) and the first-order idlers shown in Fig. 3(d), respectively. Both the measured values are 88.63 m, and the corresponding relative error is 0.011%. However, the ranging resolutions are significantly different. For the FMCW signal shown in Fig. 3(a), the ranging resolution expressed by the full-width at half-maximum (FWHM) [20] is 5.31 cm, which is close to the theoretical value (=$v/B$, $v$ is the speed of light in the optical fiber) of 5.01 cm. For the FMCW signal shown in Fig. 3(c), the ranging resolution is 2.04 cm, which is larger than the theoretical value of 1.67 cm (=$v/(3B)$). For the first-order idlers ($\mathrm {NFC_2'}$ and $\mathrm {NFC_2}$) shown in Fig. 3(d), the ranging resolution is 1.18 cm. Obviously, the ranging resolution is improved due to the first-order idlers with larger swept-frequency range. However, theoretically speaking, the ranging resolution should be improved to 0.56 cm determined by $v/(9B)$. The degraded ranging resolution may be resulted by the large optical power fluctuation within the whole swept-frequency range 9$B$.

 

Fig. 4. Experimental setup for fiber length measurement. ESA: electrical spectrum analyzer.

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Fig. 5. Measured results for a fiber with a length of 88.64 m, where red, blue and green curves are for the FMCW signals shown in Figs. 3(a), (c) and (d) taken as the FMCW laser source, respectively.

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In order to verify that the optical power fluctuation of FMCW laser source is a key factor for affecting the ranging resolution, we compare the measured results when two FMCW signals with different power fluctuations are taken as the laser sources. The signal shown in Fig. 3(c) is selected to be the FMCW laser source for measuring the fiber length, and the measured result is shown in the blue curve in Fig. 6(b). Based on the injection-locking technique [15,16,21–23], a FMCW signal with weak power fluctuation can be acquired. As shown in the bottom dotted box in Fig. 1, the signal shown in Fig. 3(c) is injected into a distributed-feedback (DFB) semiconductor laser which serves as the slave laser. The injection power ${{P}_{\text {inj}}}$ is monitored by an optical power meter (PM). The DFB laser can be stably injection locked under suitable operating condition [23], and the output of the DFB laser is injection-locked to the $\mathrm {NFC_1}$ when the injection power is 190.44 $\mathrm{\mu}$W and the frequency of the free-running DFB laser is 193.5749 THz (corresponding frequency offset of 26.6 GHz). The bias current and temperature of the DFB laser corresponding to this frequency are 38.00 mA and 22.2, respectively. The optical output of the injection-locked DFB laser is displayed in Fig. 6(a). It can be seen that the optical power fluctuation of the $\mathrm {NFC_1}$ is greatly suppressed compared with Fig. 3(c). Take the FMCW signal shown in Fig. 6(a) to measure the fiber length, and the measured result is given in Fig. 6(b) (red curve). The ranging resolution is improved to 1.77 cm from 2.04 cm, which is very close to the theoretical value of 1.67 cm.

 

Fig. 6. (a) Optical spectrum of the FMCW signal obtained after adopting injection-locking technique, where RBW is 80 MHz. (b) Measured results for a fiber with a length of 88.64 m, where the blue curve is for the signal shown in Fig. 3(c) as the FMCW laser source and the red curve is for the signal shown in Fig. 6(a) as the FMCW laser source.

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Similarly, the ranging resolution is hopeful to be improved by nine times when the optical powers within the 9$B$ swept-frequency ranges are equalized. Although injection-locking technique can greatly suppress the optical power fluctuation of the 3$B$ component as shown above, it is difficult to equalize the optical power of the 9$B$ component with injection-locking technique due to its large bandwidth. A possible scheme to solve the issue of optical power fluctuation is that by preprocessing the drive signal of the MZM to make the optical powers of $\pm 1$st-order sidebands increase over the $B$ swept-frequency ranges (the farther away from 0 frequency offset, the higher the power), the optical powers over the 9$B$ swept-frequency ranges may be equalized. We preliminarily confirm the feasibility of such a scheme by adopting an optimized saw-tooth FM signal whose amplitude increases linearly within a swept-frequency period, and the corresponding experimental results are shown in Fig. 7. For comparison, the results obtained under an ordinary saw-tooth FM signal with a constant amplitude are also given. As can be seen, after adopting the optimized saw-tooth FM signal, the optical powers of the $\pm 1$st-order sidebands generally increase over the $B$ swept-frequency ranges. Under this case, the optical power fluctuations of the 3$B$ components are reduced about 10 dB compared with those obtained under the ordinary saw-tooth FM signal. It can be predicted that by utilizing the improved 3$B$ components, the qualities of the 9$B$ components can be enhanced.

 

Fig. 7. Optical spectra of DSB-SC FMCW signal (a) and after experiencing the first-stage FWM (b) with the frequency offset to the central frequency of TSL, where RBW is 80 MHz. The blue and red curves represent the results obtained under ordinary and optimized saw-tooth FM signal, respectively.

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4. Conclusion

In this work, a scheme of broadband dual-chirp FMCW laser source based on DSB-SC modulation and two-stage cascaded FWM is proposed and experimentally demonstrated. First, an original DSB-SC FMCW signal with 4.0 GHz swept-frequency range and 0.2 GHz/$\mathrm{\mu}$s sweep rate is generated via a MZM biased at its null point. Then, the original DSB-SC FMCW signal is delivered to a 1 km dispersion compensation fiber to implement first-stage FWM, a dual-chirp FMCW signal with 12.0 GHz swept-frequency range and 0.6 GHz/$\mathrm{\mu}$s sweep rate is obtained and utilized as the pump for second-stage FWM. Finally, through the second-stage FWM in a 200 m highly nonlinear fiber, a dual-chirp FMCW signal with a swept-frequency range of 36.0 GHz and sweep rate of 1.8 GHz/$\mathrm{\mu}$s is generated. For the FMCW signal generated at different stages, the ranging resolution is evaluated through a fiber-based distance measurement, and the results demonstrate that the achieved ranging resolutions are 5.31 cm, 2.04 cm, and 1.18 cm, respectively. Additionally, via equalizing the optical power of generated FMCW signal over the swept-frequency range, the ranging resolution can be further improved. The proposed FMCW laser source has potential application in many fields such as Lidar, OFDR and OCT.