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Abstract
Narrow linewidth and fast-chirped frequency are essential in frequency-modulated continuous-wave lasers. We introduce a laser that meets these requirements by coupling a distributed feedback laser with an external high-Q microring resonator, where a bulky stacked piezoelectric chip is attached to the resonator for fast tuning. The laser demonstrates an ultranarrow intrinsic linewidth of 22 Hz in the self-injection-locked state. Actuated by the bulky piezoelectric chip, the maximum triangular actuation bandwidth can reach 100 kHz. The driving voltage is filtered to avoid a resonant mechanical mode, obtaining the minimum residual linearity error at 10 kHz with a 4.2 GHz tuning range. A light detection and ranging system was set up for a proof-of-concept experiment, demonstrating a high detection precision with standard deviations of 2.7 and 4.0 cm for targets at 15 and 30 m, respectively.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Research on frequency-modulated continuous-wave (FMCW) light detection and ranging (LiDAR) has become widespread in the industry and academy [1–3]. In automated vehicles, compared with time-of-flight LiDAR, FMCW LiDAR can provide additional data about the velocity distribution, supporting perception fusion algorithms for rebuilding the surrounding environment [4–6]. For an FMCW LiDAR source, the linewidth (or phase noise), modulated frequency range, and chirped linearity are the most critical intrinsic parameters that determine the detection resolution, maximum detection distance, and point density [7,8]. Currently, low-noise lasers are typically obtained by coupling a semiconductor laser or gain chip with a high-Q microresonator [9]. The $\textrm{S}{\textrm{i}_3}{\textrm{N}_4}$ waveguide platform is suitable for setting up a microresonator owing to its low waveguide loss [10,11]. However, the modulated bandwidth of low-noise lasers is limited because the thermal transfer delay is in the order of microseconds [12]. For faster frequency tuning, lithium niobate ($\textrm{LiNb}{\textrm{O}_3}$) has been applied with frequency modulation by the electro-optic effect [13]. High-speed modulated external cavities using $\textrm{LiNb}{\textrm{O}_3}$ thin films have been applied in self-injection-locked (SIL) lasers, enabling a tuning rate above 1 MHz [14]. Nevertheless, the 3 kHz intrinsic linewidth should be further reduced to support long-distance detection.
We propose a laser that achieves ultranarrow linewidth and fast frequency tuning. For ultralow noise output, we couple a $\textrm{S}{\textrm{i}_3}{\textrm{N}_4}$ high-Q microring resonator (MRR) with a distributed feedback (DFB) laser diode. In the SIL state, the intrinsic linewidth of the laser is reduced by three orders of magnitude to 22 Hz. For fast tuning, a bulky piezoelectric chip is attached to the MRR, achieving an actuation frequency up to 100 kHz. Unlike monolithic integrated actuators, the bulky piezoelectric actuator is fixed to the fabricated external cavity using rigid glue, without requiring wafer bonding or chemical vapor deposition. Thus, the laser retains the high Q-value of the external cavity, securing the ultranarrow linewidth. In addition, the mechanical resonance mode is filtered from the actuating voltage. The minimum residual error is obtained at 10 kHz with a 4.2 GHz tuning range, and a proof-of-concept LiDAR experiment was performed at this frequency chirp. Measurements for targets at 15 and 30 m show less than 0.2% detection error and a signal-to-noise ratio above 10 dB. The proposed fast-chirped narrow-linewidth FMCW laser can improve the detection resolution and range, being promising for high-performance LiDAR applications.
2. Principle and design
The proposed hybrid integrated FMCW laser induces the SIL effect via an external high-Q MRR. In [15], we investigated thermal tuning of the laser, obtaining a limited modulated bandwidth of 1 kHz. In this study, we used a bulky piezoelectric chip to improve the modulated frequency.
2.1 SIL state
The hybrid integrated FMCW laser consists of a DFB laser diode, external cavity, and bulky piezoelectric chip (Fig. 1(a)). The DFB laser diode is butt-coupled to a high-Q MRR through a spot-size converter [16]. The MRR is designed based on a low-loss $\textrm{S}{\textrm{i}_3}{\textrm{N}_4}$ waveguide platform to obtain a high Q-value with a strong self-reflected injection. Details of the MRR and waveguide structure can be found in [15,17]. A concise schematic diagram of the waveguide structure is shown in Fig. 1(b). The size of the $\textrm{S}{\textrm{i}_3}{\textrm{N}_4}$ rectangular waveguide is $2.7\mathrm{\;\ \mu m} \times 100\textrm{nm}$, on which a $\textrm{Si}{\textrm{O}_2}$ cladding layer with a thickness of 8 $\mathrm{\mu m}$ is deposited. The preparation of the external cavity does not include a piezoelectric chip, but it is attached to the silicon photonic chip with glue. Commercial PZT is tightly pressed over the waveguide and wrapped with glue around it.
Fig. 1. (a) Structure of hybrid integrated FMCW laser. (b) Schematic diagram of the cross section of the waveguide
The regimes of the theory of semiconductor laser feedback characterize the linewidth and optical spectrum properties based on the strength of the optical feedback [18]. With strong optical feedback, the laser enters a stable external cavity mode of operation, demonstrating a highly stable linewidth reduction and high side-mode suppression ratio [19]. In this state, the hybrid laser frequency can be tuned by varying the MRR frequency [20]. The FMCW output can be achieved if the resonant frequency is linearly modulated. The Lang–Kobayashi model expresses the linewidth reduction and locked frequency range, as follows [21,22]:
2.2 Bulky piezoelectric chip actuator
We use the photoelastic effect for MRR fast tuning [23]. By applying stress on the top surface of the silicon photonic chip, the refractive index of the waveguide varies depending on the strength, which in turn tunes the resonant frequency. As shown in Fig. 1, a bulky piezoelectric chip is used to actuate the waveguide. The chip consists of multiple stacked piezoelectric ceramic layers and has a size of $1.5 \times 1.5 \times 1\; \textrm{m}{\textrm{m}^3}$, which is sufficient to cover the MRR.
Currently, ultrasonic actuation involves the deposition of piezoelectric materials above the cladding layer to actuate integrated waveguides [23–25]. Although this process has many benefits, we used a bulky piezoelectric chip for the following reasons. 1) Bulky piezoelectric chip actuation is a more general approach that avoids chemical deposition or microelectromechanical system fabrication [26]. The chip can be attached to an existing photonic chip without redesigning. Therefore, the MRR can use our existing structure, which has a high Q-value and low loss. 2) The bulky piezoelectric chip is a multilayer stacked piezoelectric ceramic structure that can deliver a stronger force to the waveguide [27]. Because our $\textrm{S}{\textrm{i}_3}{\textrm{N}_4}$ waveguide has a thick $\textrm{Si}{\textrm{O}_2}$ cladding layer ($8\; \mathrm{\mu m}$), more force should be delivered on the top surface of the chip. In contrast, a deposited thin piezoelectric material (in the order of a few microns) cannot provide sufficient stress to actuate an MRR beyond 1 GHz [28]. 3) Commercial bulky piezoelectric chips are available with sizes in the order of millimeters, matching the size of the MRR. There are various options of piezoelectric chips, and the most suitable one can be selected based on the following model analysis.
The change in the refractive index of the material induced by the photoelastic effect is given by [29,30]
Fig. 2. (a), (b) $yz$ and $xy$ cross-sections of the model structure. Stress distribution with actuated voltage of 80 V on (c) $yz$ and (d) $xy$ cross-sections. The white line represents the location of the ring waveguide.
The bulky photoelastic effect on the fabricated silicon photonic chip was simulated by finite element analysis, obtaining the results shown in Fig. 2. The top cube represents the piezoelectric chip, whose piezoelectric parameters (i.e., elasticity matrix and coupling matrix) were calculated using material THP-51 from Thorlabs. The lower cuboid in Fig. 2 shows the silicon photonic chip. Without loss of accuracy, we use $\textrm{Si}$ for the entire chip, ignoring micron-scale structures ($\textrm{S}{\textrm{i}_2}\textrm{O}$ cladding and $\textrm{S}{\textrm{i}_3}{\textrm{N}_4}$ waveguide). The white lines in Fig. 2 represent the locations of the $\textrm{S}{\textrm{i}_3}{\textrm{N}_4}$ waveguides. Figure 2(c) shows the results for the $yz$ cross-section at the middle of the MRR, with calculated ${\sigma _{zz}}$ of 40 MPa at the waveguide area for an actuation voltage of 80 V. The $xy$ cross-section at the waveguide layer ($8\; \mathrm{\mu m}$ below the surface) shows the stress distribution on the entire ring. The effective index change, $\mathrm{\Delta }{n_{eff}}$, of the waveguide ($2.7 \times 0.1\; \mathrm{\mu }{\textrm{m}^2}$) has the highest value, with $\mathrm{\Delta }{n_{eff}} > {10^{ - 6}}$ [24].
3. Laser characteristics
In this section, we provide details of the developed packaged hybrid laser. We measured wavelength and phase noise in the SIL state. Then, a digital filter for the actuation voltage that suppresses mechanical resonance was designed to improve the chirp linearity. Finally, we obtained FMCW waveforms at different modulated frequencies.
3.1 Ultranarrow linewidth
Since the structure of the MRR is the same as Ref. [15], the measured results of the transmission/reflection spectrum are not repeated here. The hybrid laser was operated at a pumped current of 200 mA. By tuning the thermoelectric cooler controller, the laser went through free-running, multimode, chaotic, and finally entered the SIL state. The optical spectrum and frequency noise were measured in a static SIL state, obtaining the results shown in Figs. 3(a) and 3(b). The optical spectrum showed a single longitudinal mode at 1553.93 nm, side-mode suppression ratio of more than 60 dB, and output power of 9.5 dBm. The static frequency noise was measured by a 20 m short-delay heterodyne [31], obtaining the results shown in Fig. 3(b). The white noise floors of the free-running and SIL states were 2072$\textrm{H}{\textrm{z}^2}/\textrm{Hz}$ and 7 $\textrm{H}{\textrm{z}^2}/\textrm{Hz}$, with intrinsic linewidths calculated as $2072 \times \mathrm{\pi } = 6.5\textrm{kHz}$ and $7 \times \mathrm{\pi } = 22\textrm{Hz}$, respectively [32]. If low-frequency noise is considered, the calculated integral linewidth is 43 and 4.5 kHz for the free-running and SIL states, respectively [33]. The reduction efficiency is demonstrated to be $6500/22 = 295$. According to our previous measurements, the Q value of the designed MRR is $6.2 \times {10^5}$ and $y \approx 10\%$ (estimated by MRR reflection spectrum while considering the coupling loss). Substituting reasonable numbers in Eq. (1) for $\alpha = 5$ and ${Q_{LD}} = 3000$, we obtain the $\mathrm{\delta }{\mathrm{\omega }_0}/\mathrm{\delta \omega } \approx 100$, which is close to the experimental value. As for the locking range $\mathrm{\Delta }{\omega _{lock}}$, the calculated result from Eq. (2) is $\Delta {\omega _{lock}} \approx 30\; \textrm{GHz}$. In Ref. [15], by the phase-compensated MRR tuning, the continuous frequency tuning can be achieved within the locked range. Here, the actual tuning range is related to the applied stress. The current supply circuit and thermoelectric cooler controller circuit were designed such that the laser can be portable to operate in various environments. The entire packaged laser is shown in the inset of Fig. 3(a).
Fig. 3. (a) Optical spectrum of SIL state. The inset shows the packaged FMCW laser. (b) Frequency noise spectrum at free-running and SIL states.
For range detection, when the phase noise is the only limitation, the 3 dB bandwidth of the beat note frequency spectrum is broadened, mainly owing to low-frequency noise. The coherence length of the laser can be regarded as the maximum detection length, which is in the order of kilometers for this laser [7]. However, the nonlinearity of the chirped frequency appears as random frequency fluctuations in the beat-note spectrum, which can also be considered as frequency noise.
3.2 Fast linear frequency modulation
Optical phase-locked loop (OPLL) feedback is often used to suppress low-frequency noise in real time [34–36]. We used iterative learning to update the modulated predistortion voltage for linear modulation [37]. The mechanical resonance of the piezoelectric actuator was challenging to mitigate in high-speed modulation, hindering iteration convergence [38]. First, the frequency response of the hybrid laser was measured. The measured range was set to $1-{-}500\textrm{kHz}$, and the driving voltage was given as a sample function with repetition rate of 1 kHz, as shown in Fig. 4(b). The chirped output was generated by a short-delay self-heterodyne Mach–Zehnder interferometer [39]. The chirped instantaneous frequency could then be calculated using Hilbert transform, as shown in Fig. 4(c). The fast Fourier transform (FFT) of the chirped frequency is the optomechanical transmission response of the laser, which represents the frequency range that a unit voltage can drive. The results after normalization are shown in decibels in Fig. 4(a). The first resonant and anti-resonant frequencies were 300 kHz, whereas the no-load resonant and anti-resonant frequencies were 920 kHz for the piezoelectric actuator. The resonant frequency of the loaded system shifted to a low frequency mainly owing to the hardness of the silicon photonic chip and glue. Reshaping the silicon chip to break the mechanical resonance mode can increase the resonant frequency close to that of the piezoelectric actuator. The resonance can also be filtered from the actuating voltage at the expense of a frequency response [40]. Therefore, we designed a lowpass Butterworth filter with a 3 dB bandwidth at 50 kHz to suppress the unwanted high-order resonant frequency, as illustrated in Fig. 4(a).
Fig. 4. (a) Optomechanical response actuated by bulky piezoelectric chip (red line) and designed digital filter (purple line). (b) Input excitation signal. (c) Demodulated chirped frequency.
Linear FMCW outputs at different modulation frequencies can be obtained. Figure 5 shows the results at actuating frequencies of 10 and 100 kHz. The actuating voltage is given as 80 V peak-to-peak of 10 kHz and 40 V peak-to-peak of 100 kHz. The reduction of actuating voltage is mainly due to the power consumption and thermal stabiltity of high frequency operation. The output parameters at 20, 30, and 60 kHz are listed in Table 1, where the highest linearity and maximum frequency range were obtained at 10 kHz, which was used for the LiDAR experiment reported in Section 4. Figure 5(a) shows the modulated linearity according to the number of iterations at 10 kHz. We use the linear regression coefficient r to define the linearity [41]:
Fig. 5. Linear frequency modulation with chirped frequencies of (a)–(c) 10 and (d)–(f) 100 kHz. (a), (d) Linearity of up- and down-ramps according to number of iterations. (b), (e) Heterodyne time–frequency spectrum of FMCW laser with reference laser. (c), (f) Laser frequency sweep and its residual frequency error.
Table 1. Parameters of generated FMCW signal
4. LiDAR experiment
To evaluate the performance of the proposed laser, a proof-of-concept experiment was conducted, as illustrated in Fig. 6(a). The laser output power of 90% was amplified to 60 mW by an erbium-doped fiber amplifier and connected to an optical circulator. The output port (port 2 of the circulator) was connected to a collimator such that the beam diameter could be expanded to 7 mm. A double-axis galvanometric scanning system was used for beam steering. The reflected light was received by the same collimator and then output from port 3 of the circulator. The reflected and local beam beats in the 50:50 optical coupler were then detected using a balanced photodetector. As shown in Figs. 6(b) and 6(c), a box was placed at two distances for measurement. At 15 m, it was placed in front of a whiteboard, and in front of a door at 30 m. The red dashed line in Fig. 6(b) and white dashed line in Fig. 6(c) show the scanning area. The experimental devices are shown in Fig. 6(d), including the collimator and galvanometric scanning mirror.
Fig. 6. Experimental setup and results. (a) Experimental setup diagram. The laser output was divided into 90:10, with 90% of the output amplified by an erbium-doped fiber amplifier (EDFA). Port 2 of the optical circulator was connected to a collimator. The reflected light beat with the local beam at the balanced photodetector (BPD). A double-axis galvanometric mirror was used for scanning the beam at (b) 15 and (c) 30 m, with the scanning area marked by the red and white boxes. (d) Experiment equipment. (e), (k) 3D point cloud of detected object in (b) and (c), respectively, and (f), (l) Point clouds distributed on $xz$ plane, respectively. FFT spectrum of detected waveform of (g) front box and (m) rear board at 15 and 30 m. (h)–(j), (n)–(p) Histograms of distance distribution, with the red line being the Gaussian distribution fit. (DAQ, data acquisition device; LUT, laser under test; PC, polarization controller)
The experiment was conducted at a modulated frequency of 10 kHz. The mirror rotation frequencies of the x and y axes were set to 60 and 2 Hz, respectively. The scanning waveform was a 50% duty-cycle triangle wave, resulting in the 15 horizontal lines shown in Figs. 6(e) and 6(k). Collection lasted for 1 s to acquire ${10^4}$ datapoints scattered in the point map. Figures 6(e)–6(j) show the measured results for the box at 15 m, and Figs. 6(k)–6(p) show the results for 30 m. In Figs. 6(e) and 6(f), the blue and yellow dots represent the front box and rear board, respectively. The projection of the points onto the $xz$ plane is shown in Fig. 6(f). The corresponding histograms are shown in Figs. 6(h)–6(j). The histograms of the front box and rear board are shown in Figs. 6(i) and 6(j), respectively. The calculated mean distances were ${d_{1,f}} = 13.61\; \textrm{m}$ for the box and ${d_{1,r}} = 15.05\; \textrm{m}$ for the board. The standard deviations were ${\sigma _{1,f}} = 2.81\; \textrm{cm}$ for the box and ${\sigma _{1,r}} = 2.71\; \textrm{cm}$ for the board. The red curves in Figs. 6(h)–6(j) show the results of Gaussian distribution fitting for the distance. Considering the full width at half maximum of the Gaussian curve to represent the distance resolution, it should be $\mathrm{\Delta }{d_1} = 2.355 \times \sigma < 7\textrm{cm}$. The results of the 30 m measurements are shown in Fig. 6(n)–6(p), where the mean distance is 27.99 and 31.64 m for the front box and rear board, respectively. Compared with the results of the 15 m measurements, ${\sigma _{2,f}}$ and ${\sigma _{2,r}}$ increase to 4.66 and 4.04 cm, and the distance resolution is $\mathrm{\Delta }{d_1} < 11\textrm{cm}$.
Figures 6(g) and 6(m) show the FFT spectra of a randomly selected point at the front box and rear board. In each spectrum, the blue and purple curves represent the up- and down-ramps over a period, respectively. The Blackman–Harris window was used for each ramp, and we used the root-mean-square envelope of the frequency spectrum to smooth the curve, obtaining a signal-to-noise ratio peak above 10 dB. The green and red lines in Figs. 6(g) and 6(m) are enveloped curves, and their peaks are considered as the measured distances. Here, the peak width broadening is mainly limited by the modulation linearity. A concise estimation of the effect due to modulated linearity can illustrate it [42]:
where $\mathrm{\Delta }d$ is the distance resolution, c is the light speed, ${\tau _t}$ is the time of flight. When $2\pi {\tau _t}{\nu _{rms}} \ll 1$, the modulation linearity can be ignored and Eq. (6) reduces to $\mathrm{\Delta }d = c/({2B} )$. While our modulation linearity let $2\pi {\tau _t}{\nu _{rms}} \approx 6 \gg 1$, the modulation linearity dominates the distance resolution. In Section 3.2, we gave a method for breaking the mechanical resonance to improve the linearity, but for the ultra-low linewidth laser, further linearity improvements are required to achieve higher resolution. The OPLL system is a potential method of dynamically correcting the modulation linearity. It can achieve a high linearity frequency modulated signal by phase locking the delayed beat note to a pure reference RF source. The overall phase noise whether the linewidth or modulation linearity can be suppressed. The ultra-narrow linewidth FMCW laser with OPLL correction may be a direction to achieve the ideal linearity of the FMCW LiDAR source [34].5. Conclusion
We propose an ultranarrow linewidth fast-tuning FMCW laser. By coupling a high-Q MRR with a DFB laser diode, the hybrid laser has an intrinsic linewidth as low as 22 Hz in the SIL state. For fast tuning, a bulky piezoelectric chip is glued to the MRR, and the actuation bandwidth is improved to 100 kHz. A proof-of-concept LiDAR experiment was performed for 15 m and 30 m measurements, confirming high detection precision and high signal-to-noise ratio.
Funding
National Key Research and Development Program of China (2021YFB2800802); National Natural Science Foundation of China (61771285).
Disclosures
The authors declare no conflicts of interest.
Data availability
The 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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