Tunable lasers, which have the ability to dynamically adjust their emission wavelength, have found widespread applications in a variety of industrial and scientific fields. For example, as shown in Fig. 1(a), in biomedical imaging, optical coherence tomography (OCT) [1–3] employs a widely tunable laser that provides a noninvasive and noncontact imaging modality for high-resolution, two-dimensional cross-sectional and three-dimensional volumetric imaging of tissue structures. In optical communication systems, optical frequency-domain reflectometry (OFDR) [4,5] uses tunable lasers for broadband loss and dispersion characterization. In laser spectroscopy, tunable diode laser absorption spectroscopy (TDLAS) [6–8] allows compound analysis of gases, as well as their conditions such as concentration, pressure, temperature, and velocity. For light detection and ranging (LiDAR), frequency-modulated continuous-wave (FMCW) LiDAR [9–14] uses a tunable laser to measure the distance (based on the time of flight) and speed (based on the Doppler effect) of a moving object.

In all of these applications, as well as others, the laser chirp range determines the measurement resolution and spectral bandwidth. However, due to the nonlinearity of laser gain and dynamics, tunable lasers typically exhibit chirping nonlinearity that is particularly deteriorated for a wide chirp range, as illustrated in Fig. 1(b). As a result, the laser chirp rate deviates from the set value, which compromises the frequency resolution, precision, and accuracy in applications. Therefore, widely tunable lasers require careful characterization and linearization for demanding applications.

To track the laser chirp rate, a fiber unbalanced Mach–Zehnder interferometer (UMZI) is commonly used to calibrate the instantaneous laser frequency, e.g., in data processing [15–17], active linearization [9], and laser drive signal optimization [18]. However, for a wide chirp range, the fiber dispersion seriously reduces the calibration precision of fiber UMZIs and causes phase-instability issues, leading to insufficient accuracy for linearization. In comparison, fully stabilized optical frequency combs (OFCs) with equidistant grids of frequency lines can essentially resolve these issues [10,19–22].

Here we demonstrate an approach to characterize the chirp dynamics of widely tunable lasers. We apply this method on 12 lasers from Toptica, Santec, New Focus, EXFO, and NKT that are commonly used in fiber optics and integrated photonics. Using an OFC and digital band-pass filters, the instantaneous laser frequency is tracked with 1 MHz intervals over terahertz bandwidth. This allows the linearization of laser frequency with pre-calibrated chirp rate, particularly useful for coherent LiDAR.

To measure the laser chirp rate, we use a commercial, fully stabilized, fiber-based OFC (Quantum CTek) as a frequency “ruler” [23–25] to trace the instantaneous laser frequency during chirping. In our case, the comb repetition rate $f_{\mathrm{rep}}=200\mathrm{MHz}$ and its carrier envelope offset frequency $f_{\mathrm{ceo}}$ are actively locked to a rubidium atomic clock; thus the OFC is fully stabilized. Consequently, in the frequency domain, the $n$th comb line’s frequency is unambiguously determined as $f_n=f_{\mathrm{ceo}}+n·f_{\mathrm{rep}}(n\in \mathbb{N})$.

When the laser chirps, it beats against tens of thousands of comb lines with precisely known frequency values, as shown in Fig. 2(a). Beat signals of frequencies $|f_n-f_l(t)|$ are generated, where $f_l(t)$ is the instantaneous frequency of the tunable laser at time $t$. As the frequency comb is fully stabilized, for a mode-hop-free tunable laser, the dynamics and linearity of $f_l(t)$ are projected onto the beat signals. The simplest beat signals to analyze are the two generated by the tunable laser with its two neighboring comb lines, i.e., $|f_n-f_l(t)|<f_{\mathrm{rep}}=200\mathrm{MHz}$. Experimentally, the two beat signals are recorded by an oscilloscope after passing through a low-pass filter (LPF, Mini-Circuits, $\mathrm{BLP}–150+$), whose 3-dB cutoff frequency is 155 MHz in our case. We denote the frequencies of the two beat signals as ${\beta }_1$ and ${\beta }_2$ (${\beta }_1+{\beta }_2=f_{\mathrm{rep}}=200\mathrm{MHz}$ and ${\beta }_1<{\beta }_2$). As shown in Fig. 2(b), for a continuous linear chirp, when the laser frequency passes through the comb lines sequentially, ${\beta }_1$ and ${\beta }_2$ vary in a sawtooth waveform. The time-domain waveform near ${\beta }_1=0$ is shown in the leftmost panel of Fig. 2(d), corresponding to the situation when the laser chirps across a comb line.

Here, we concentrate on the analysis of ${\beta }_1$, since ${\beta }_1+{\beta }_2=200\mathrm{MHz}$. The dynamics and linearity of ${\beta }_1(t)$ as a function of time are identical to those of the laser frequency $f_l(t)$. We process the ${\beta }_1(t)$ signal and extract the instantaneous frequency value as illustrated in Fig. 2(d). A finite impulse response (FIR) band-pass filter with a specific pass-band center frequency $f_{\mathrm{FIR}}$ is applied to the recorded ${\beta }_1(t)$ signal. The FIR filter only transmits the temporal segments when ${\beta }_1(t)$ is around $f_{\mathrm{FIR}}$, as illustrated in the left middle panel of Fig. 2(d). Then Hilbert transform [26] is applied to obtain the pulse’s envelope. Via peak searching, the exact time of the pulses’ centers is extracted and recorded when ${\beta }_1(t)=f_{\mathrm{FIR}}$. Experimentally, we repeatedly apply FIR filters whose $f_{\mathrm{FIR}}$ values are digitally set from 3 to 97 MHz with an interval of $\mathrm{\Delta }{f}_{\mathrm{FIR}}=1\mathrm{MHz}$, as shown in Fig. 2(e). In this way, during continuous laser chirp over a wide bandwidth, the ${\beta }_1(t)$ time trace is frequency-calibrated and recorded with 1 MHz intervals.

Next, we unwrap the sawtooth-like ${\beta }_1(t)$ trace. Pulses corresponding to $f_{\mathrm{FIR}}=3\mathrm{MHz}$ are selected as markers. As shown in the bottom panel of Fig. 2(e), when the laser chirps over a pair of comb lines (dashed lines), i.e., $f_{\mathrm{rep}}$ distance, two markers are created by the $f_{\mathrm{FIR}}=3\mathrm{MHz}$ filters. With the known comb spacing $f_{\mathrm{rep}}=200\mathrm{MHz}$, ${\beta }_1(t)$ can then be unwrapped to an increasing function of time $t$, which is $\mathrm{\Delta }f(t)=f_l(t)-f_l(t_0)$, where $f_l(t_0)$ is the starting laser frequency at time $t_0$. As shown in Fig. 2(c), the instantaneous chirp rate—estimated as the average rate within $\mathrm{\Delta }{f}_{\mathrm{FIR}}=1\mathrm{MHz}$ calibration interval—is calculated as $\alpha (t)=\mathrm{d}\mathrm{\Delta }f(t)/\mathrm{d}t$, and is later used for chirp linearization.

Now we use this frequency-comb-calibrated method to characterize a total of 10 widely tunable, mode-hop-free, external-cavity diode lasers (ECDLs), including three Toptica CTL lasers, four Santec lasers, two New Focus lasers, and one EXFO laser. These lasers are all operated in the telecommunication band around 1550 nm, and are extensively used in fiber optics and integrated photonics. For example, Toptica CTL and New Focus lasers are widely used in the generation of microresonator-based dissipative Kerr soliton frequency combs [27–35]. Santec and EXFO lasers are widely used in the wideband characterization of waveguide dispersion [6,22,33,36,37]. In addition, two NKT fiber lasers are characterized, although their frequency tuning ranges are significantly narrower.

An ECDL typically has two tuning modes, i.e., the wide and fine tuning modes. In the wide tuning mode, the external cavity length that determines the laser frequency is controlled by a stepper motor, enabling a frequency tuning range exceeding 10 THz. In the fine tuning mode, the external cavity length is controlled by a piezo under an external voltage that determines the laser frequency. In this mode, the laser can only be tuned by tens of gigahertz. Triangular and sinusoidal voltage signals are often used to drive the piezo, and to determine the laser chirp range $B$ and modulation frequency $f_{\mathrm{mod}}$. The average chirp rate is $\overline{{\alpha }_{\mathrm{set}}}=2B{f}_{\mathrm{mod}}$.

First, we characterize these lasers in the wide tuning mode. We take one Toptica CTL laser as the first example. Experimentally, the laser is configured to a single run that chirps from 1550 to 1560 nm. On the laser panel, we manually set the chirp rate ${\alpha }_{\mathrm{set}}$ to 1, 2, 5, and 10 nm/s. Experimentally, we characterize the Toptica laser’s output power variation, which is below 1% over 10 MHz spectral width. Since the FIR filter’s 3-dB pass bandwidth is smaller than 10 MHz, this laser power variation is too small to change the SNR of the beatnote.

The oscilloscope’s sampling resolution is set to 155 Hz for different ${\alpha }_{\mathrm{set}}$. The instantaneous chirp rate $\alpha (t)$ within 1 MHz intervals is tracked, allowing retrieval of the instantaneous laser frequency $f_l(t)$ as well as the wavelength $\lambda (t)$. In this manner, $\alpha (t)$ can be converted to $\alpha (\lambda )$ for a better comparison among cases of different ${\alpha }_{\mathrm{set}}$ in the same scale.

Figure 3 shows representative $\alpha (\lambda )$ traces with different ${\alpha }_{\mathrm{set}}$ within a 0.2 nm wavelength range (1555–1555.2 nm) during chirping. To facilitate comparison, we normalize the measured $\alpha (\lambda )$ to the set value ${\alpha }_{\mathrm{set}}$ on the laser panel; i.e., the normalized chirp rate is $\alpha (\lambda )/{\alpha }_{\mathrm{set}}$. Here $\alpha (\lambda )/{\alpha }_{\mathrm{set}}=1$ corresponds to a perfectly linear chirp at a constant rate. Figure 3(a) shows that the experimentally measured $\alpha (\lambda )/{\alpha }_{\mathrm{set}}$ fluctuates and exhibits nonlinearity. Particularly, when ${\alpha }_{\mathrm{set}}=1$ and 5 nm/s, prominent frequency oscillation is observed; whereas for ${\alpha }_{\mathrm{set}}=2$ and 10 nm/s, this oscillation is inhibited. The oscillation pattern of $\alpha (\lambda )/{\alpha }_{\mathrm{set}}$ is repeated every 1.6 pm, probably due to the laser’s intrinsic configuration or regulation. Besides, mechanical modes of the external laser cavity might also cause chirp rate jitter. Figure 3(b) shows $\alpha (t)/{\alpha }_{\mathrm{set}}$ spectra in the frequency domain. The amplitude of the spectra presents the chirp rate jitter strength. A component at 3.84 kHz Fourier offset frequency—independent of ${\alpha }_{\mathrm{set}}$—is revealed, likely linking to the eigen-frequency of the cavity’s fundamental mechanical mode. Higher-order mechanical modes can also be observed in Fig. 3(b) at 28.22 kHz and 56.43 kHz frequencies when the laser chirps more slowly.

Since Fig. 3(a) shows the optimal laser chirping performance at ${\alpha }_{\mathrm{set}}=2$ and 10 nm/s, we further investigate $\alpha (\lambda )/{\alpha }_{\mathrm{set}}$ over the entire 10 nm bandwidth. Figure 3(c) shows the laser’s chirp rate drift with ${\alpha }_{\mathrm{set}}=2$ and 10 nm/s. Limited by the oscilloscope’s memory depth (400 Mpts) and sampling rate (400 MSa/s), we can only acquire data in 1 s. We set the laser to repeatedly chirp from 1550 to 1560 nm, and characterize one segment of the chirp trace each time. Multiple segments displayed with different colors are stitched to form a complete trace covering the full 10 nm range. It becomes apparent that, although Fig. 3(c) bottom shows weak chirp rate jitter with ${\alpha }_{\mathrm{set}}=10\mathrm{nm}/\mathrm{s}$, the overall chirp rate drifts considerably. With ${\alpha }_{\mathrm{set}}=2\mathrm{nm}/\mathrm{s}$, the laser completes its acceleration at 1550.5 nm and reaches stability at 1552.0 nm, until it begins to decelerate at 1559.5 nm. The laser maintains good linearity in the center 7.5 nm range. We therefore conclude that, in the wide tuning mode, the optimal chirp rate of Toptica CTL is ${\alpha }_{\mathrm{set}}=2\mathrm{nm}/\mathrm{s}$.

We further characterized another two Toptica CTL lasers, four Santec lasers, two New Focus lasers, and one EXFO laser in their wide tuning modes. The laser chirping performance is investigated within 1550–1560 nm bandwidth, and ${\alpha }_{\mathrm{set}}$ is set from 1 to 200 nm/s. Table 1 presents a summary of different lasers’ chirp dynamics with their respective optimal ${\alpha }_{\mathrm{set}}$. We refer the readers to Appendix A for detailed characterization results of each laser, which can be useful for readers currently using these lasers. Overall, in the wide tuning mode, the Santec and EXFO lasers work best with ${\alpha }_{\mathrm{set}}=100\mathrm{nm}/\mathrm{s}$, and the Toptica CTL and New Focus lasers work best with ${\alpha }_{\mathrm{set}}=2\mathrm{nm}/\mathrm{s}$.Table 1.

Comparison of Laser Chirp Dynamics of Different Lasers with Different Conditions

To show the deviation of laser chirp rate from $\alpha (t)/{\alpha }_{\mathrm{set}}=1$, we calculate the root mean square error (RMSE) as $$\mathrm{RMSE}=\sqrt{\frac{\sum _{i=1}^T{({\alpha }_i/{\alpha }_{\mathrm{set}}-1)}^2}{T}},$$(1)where ${\alpha }_i$ is the sample of the chirp rate and $T$ is the sample number. Besides, the wavelength linearity can be estimated by nonlinearity error [38] ${\delta }_L=\mathrm{\Delta }{\lambda }_{\max }/{\lambda }_{\mathrm{f}\text{.s}\text{.}}$, where $\mathrm{\Delta }{\lambda }_{\max }$ is the maximum deviation of the measured wavelength from its linearly fitted value, and ${\lambda }_{\mathrm{f}\text{.s}\text{.}}$ is the full-scale wavelength range. This indicator mainly considers whether the laser chirp is linear, but not whether the average chirp rate $\overline{{\alpha }_{\mathrm{set}}}$ matches the set value ${\alpha }_{\mathrm{set}}$. Particularly, Table 1 shows that the EXFO laser features the smallest RMSE and ${\delta }_L$ with ${\alpha }_{\mathrm{set}}=100\mathrm{nm}/\mathrm{s}$.

Next, we characterized 11 lasers in the fine tuning modes, including three Toptica CTL lasers, four Santec lasers, two New Focus lasers, and two NKT lasers. We note that the EXFO laser does not feature the fine tuning mode. These lasers are frequency-modulated at 193.3 THz optical frequency and with an excursion range of 10 GHz (except 8 GHz for the NKT lasers). The drive voltage signal to the piezo is either triangular or sinusoidal. We set the modulation frequency $f_{\mathrm{mod}}$ to 2, 10, 50, and 100 Hz. For normalization, the set chirp rate ${\alpha }_{\mathrm{set}}(t)$ is calculated according to the drive signal. The optimal $f_{\mathrm{mod}}$ for different lasers with different drive manners is listed in Table 1 (see Appendix B for detailed characterization results of each laser). For the cases with sinusoidal drive, ${\alpha }_{\mathrm{set}}$ represents the average set chirp rate $\overline{{\alpha }_{\mathrm{set}}}$. For the Toptica CTL and New Focus lasers, different drives have different effects, as the triangular drive may cause resonance in the piezo at certain frequencies (see Appendix B). Therefore, these lasers behave better with a sinusoidal drive.

Based on our frequency-comb-calibrated laser chirp dynamics, we further demonstrate a linearization method for widely tunable lasers for FMCW LiDAR. LiDAR can quickly and accurately map the environment, provide insights into the structure and composition, and allow operators to make informed decisions on the protection of natural resources [39,40] and environment [41,42] or manage agriculture [43]. For autonomous vehicles, LiDAR enables safe and reliable navigation by providing high-resolution, real-time 3D mapping of the environment [44–47]. The technology has also revolutionized archaeology, allowing nondestructive imaging of hidden features and artifacts [48–50].

The principle of LiDAR is to project an optical signal onto a moving object. The reflected or scattered signal is received and processed to determine the object’s distance from the laser [13,51]. The light received by the photodetector experiences a time delay $\tau$ from its emission time. Thus the object’s distance is calculated as $d=c\tau /2$, where $c$ is the speed of light. For FMCW LiDAR, the time delay $\tau$ is obtained in a coherent way [9,10,14]. The frequency-modulated laser is split into two paths as shown in the LiDAR panel of Fig. 1(a). In one path, the laser passes through a collimator, enters free space, and is reflected by the object. The reflected laser is then combined with the reference path, and the beat signal between the two paths is recorded by a photodetector. If the laser frequency is modulated linearly at a constant chirp rate $\alpha$, the time delay $\tau$ creates a beat signal of frequency $\mathrm{\Delta }f=\alpha \tau$. Thus, the photodetected beat signal is $$\begin{gathered} V(t)\propto \cos (2\pi \mathrm{\Delta }ft) \\ =\cos \left(2\pi \alpha \frac{2d}{c}t\right). \end{gathered}$$(2)Equation (2) indicates that the distance $d$ can be obtained with fast Fourier transformation on $t$.

The ranging resolution [15] $\delta d$ of FMCW LiDAR is limited by the chirp range $B$, as $\delta d=c/2B$. High resolution, i.e., small $\delta d$, requires a large $B$ of the tunable laser. However, chirp nonlinearity causes a varying $\alpha$ over time. Consequently, the beat frequency $\mathrm{\Delta }f$ varies as shown in Fig. 1(b). To extract the precise value of $d$ from $V(t)$, an accurate trace of $\alpha (t)$ is mandatory, necessitating the calibration of the instantaneous laser frequency during chirping. The chirp linearization is performed by rescaling the beat signal’s time axis by $t^{\prime }=\alpha (t)t$ to $$V(t^{\prime })=\cos \left(2\pi \frac{2d}{c}{t}^{\prime }\right).$$(3)

Here, using our frequency-comb-calibration method, the characterized laser chirp rate $\alpha (t)$ in return allows chirp rate linearization. The chirp rate can be pre-linearized when the laser is tuned by a piezo, i.e., when the laser is working in the fine tuning mode. Again we use the Toptica CTL laser as the example. The laser has optimal performance of chirp linearity when driven by a 50 Hz sinusoidal wave. The chirp range is set to 35 GHz in the fine tuning mode, and $\alpha (t)$ is characterized (see Appendix C). The same characterization of $\alpha (t)$ is performed three times, and the averaged result is used as the pre-linearized chirp rate ${\alpha }_c(t)$. By rescaling the time axis in Eq. (2) by $t^{\prime }={\alpha }_c(t)t$, the laser is pre-linearized and the range profile can be extracted from Eq. (3). The photodetected signal is rescaled with $t^{\prime }$. Zero-padding [52] is also implemented to reduce resolution ambiguities. We note that the pre-linearization does not function well for the stepper motor-based wide tuning mode.

Finally, we proceed with a LiDAR experiment without any linearization unit (see Appendix D). Experimentally, a stainless steel cylinder with an engraved text of 2.8 mm depth on its surface is imaged using our LiDAR setup. The stainless steel cylinder is placed on a 2D translation stage 4 m away from the collimator. As the translation stage moves, the distance between the cylinder surface and the collimator is continuously measured to produce a 2D ranging map.

To highlight the effect of linearization, we measure the surface profile using two methods, i.e., with pre-linearization and without any linearization. We emphasize that the former case only requires a characterized ${\alpha }_c(t)$ as prior knowledge for signal processing; neither OFC nor real-time frequency calibration is used in the ranging experiment. To retrieve the ranging profile, for pre-linearization, the beat signal $V(t^{\prime })$ of Eq. (3) is rewritten as $V(l^{\prime })=\cos (2\pi d{l}^{\prime })$, where $l^{\prime }=2t^{\prime }/c$. By fast Fourier transform on $l^{\prime }$, the space spectrum is obtained, as shown in the top panel of Fig. 4(b). The peak corresponds to the distance $d=4\mathrm{m}$ of the surface to the laser. For the case without linearization, the beat signal $V(t)$ of Eq. (2) is rewritten as $V(l)=\cos (2\pi dl)$, where $l=2{\alpha }_{\mathrm{set}}t/c$ and ${\alpha }_{\mathrm{set}}$ is the set chirp rate. The space spectrum obtained by fast Fourier transform on $l$ is shown in the bottom panel of Fig. 4(b). Without linearization, the peak is broadened due to ranging imprecision, leading to ambiguous determination of distance. Figure 4(a) shows the measured relative distance map with pre-linearization (left) and without any linearization (right). The long-term stability of pre-linearization is verified by a precision test (see Appendix D).

In conclusion, we have demonstrated an approach to characterize chirp dynamics of widely tunable lasers based on an OFC. Compared to the frequency calibration method using a UMZI, our method is more accurate and precise (see Appendix E for details). Using this method we have characterized 12 lasers including three Toptica CTL lasers, four Santec lasers, two New Focus lasers, two NKT fiber lasers, and one EXFO laser. By comparing the laser’s chirp linearity with different settings, the optimal operation condition of each laser is found. For example, the optimal chirp rates of Toptica CTL, New Focus, Santec, and EXFO lasers are ${\alpha }_{\mathrm{set}}=2$, 2, 100, and 100 nm/s, respectively. Operating the laser with its optimal setting and pre-linearizing laser chirp, we successfully apply the laser for coherent LiDAR without any extra linearization unit. Field-programmable gate arrays (FPGAs) to implement multiple FIR filters can be further added to increase data processing speed and reduce the amount of data to be stored by real-time data processing. Our method of characterizing and pre-linearizing laser chirp dynamics has been proven to be a critical diagnostic method for applications such as OCT, OFDR, and TDLAS.

Acknowledgment. We thank EXFO for lending us one laser for characterization. J. Liu acknowledges support from the NSFC, Shenzhen-Hong Kong Cooperation Zone for Technology and Innovation, and Guangdong Provincial Key Laboratory. Y.-H L. acknowledges support from the China Postdoctoral Science Foundation.

B. S., W. S., Y.-H. L., and J. Long built the experimental setup, with assistance from X. B. and A. W. B. S. performed the laser characterization. B. S. and Y. H., and Y.-H. L. performed the LiDAR experiments. B. S., W. S., Y.-H. L., and J. Liu analyzed the data and prepared the manuscript with input from others. J. Liu supervised the project.