Since its first proposal in 1991, optical coherence tomography (OCT) has become a research hotspot due to its advantages such as non-invasiveness, non-ionization, and non-destructiveness [1–3]. It has undergone three significant technological advancements: time-domain OCT (TD-OCT), Fourier-domain OCT (FD-OCT), and functional OCT [4–11]. Among these, swept-source OCT (SS-OCT), as a branch of FD-OCT, has been widely used in ophthalmic examination, intracoronary imaging, and industrial non-destruction, primarily due to its elimination of mechanical scanning inherent in TD-OCT [12]. The swept laser is the core component of SS-OCT. For fast and deep imaging, swept lasers are usually required to achieve fast sweeping rates and narrow instantaneous linewidths. Various types of swept lasers have been reported, including wavelength-swept amplified spontaneous emission sources, short cavity lasers, Fourier-domain mode-locked (FDML) lasers, swept vertical cavity surface-emitting lasers, and stretched ultrafast pulse lasers [13–22]. Among these, FDML lasers can achieve a sweeping rate of 1.68 MHz and an imaging depth of 3.8 mm with a 6 dB sensitivity roll-off [23]. Stretched ultrafast pulse lasers can achieve a sweeping rate of 2.5 MHz and an imaging depth of 111 mm with a 6 dB sensitivity roll-off [24]. However, in SS-OCT, these high-performance lasers cannot be fully utilized because the required acquisition bandwidth scales with the product of the laser speed and imaging depth range, and such high bandwidth is impractical. Additionally, in practical applications, the precise location of the detection target within the sample is not always clear. Maintaining high-resolution imaging while searching for the detection target greatly reduces efficiency and wastes valuable acquisition bandwidth.

To address these challenges, optical-domain subsampling OCT has been proposed [25–27]. This method replaces continuous wavelength-swept lasers with wavelength-stepped lasers (jumps discretely in fixed k-space increments) to actively reduce the spatial resolution to achieve greater imaging depth. However, research in this area is currently limited, with a focus primarily on improving laser performance. There is a lack of comprehensive investigation into the detailed operation mechanisms of lasers and the characterization of dynamic processes. In 2012, Siddiqui et al. introduced the concept of subsampling applied to FD-OCT fringe signals, outlining key methods and performance attributes of imaging [25]. They demonstrated this principle using a swept laser based on a polygon filter. Tozburun et al. proposed a dispersion-based wavelength-stepped swept laser utilizing a Fabry–Perot (FP) filter. However, to compensate for dispersion, the total cavity length exceeded 40 km, requiring multi-stage amplification within the cavity, thus increasing system complexity [26]. Subsequently, Khazaeinezhad et al. optimized the system using an 8.3-m chirped fiber Bragg grating [28]. Although laser performance was enhanced, there remains a lack of research into the dynamic processes of the laser.

In this article, we propose a novel k-space linear wavelength-stepped swept laser based on a dispersion-tuned swept fiber laser (DTSFL) using a Mach–Zehnder interferometer (MZI) as a comb filter. Subsequently, we conducted a detailed analysis of the dynamics of the laser in switching mode, static-sweeping mode, and sweeping mode using time-stretching dispersive Fourier transform. This analysis enabled real-time monitoring of wavelength variations and revealed the lag in wavelength during laser startup and change of sweeping direction. Modeling analysis has revealed for the first time that sub-cavity detuning, which is supposed to be detrimental to the stability of the laser, can play a key role in the stable operation of the laser in a synergistic manner. Furthermore, compared to DTSFL, the laser exhibits significantly narrowed linewidth, approximately 0.85 GHz, which remains relatively constant during the sweeping process. Finally, the laser was simulated using the Ginzburg–Landau equation, and the dynamic process of the laser was presented in both time and spectrum domains, showing consistency with experimental observations.

The laser setup is shown in Fig. 1. A 3-m erbium-doped fiber (EDF) is pumped by 980-nm laser diodes (LDs) via wavelength division multiplexers (WDMs). A ring fiber cavity was constructed by using an isolator (ISO), two polarization controllers (PCs), an MZI, two optical couplers (OCs) with a splitting ratio of 50:50, a 150-m dispersion compensated fiber (DCF), and an electro-optic modulator (EOM) driven by an arbitrary waveform generator (AWG). The total laser cavity length is ∼166m. The MZI contains an optical time delay line (OTDL) in one arm and a PC in the other, and the optical path difference is ∼20mm. The laser spectrum is measured by an optical spectrum analyzer (Yokogawa, AQ6370D) with resolution of 0.02 nm. To demonstrate the dynamic characteristics of the swept laser, the laser output is detected by a photodetector (CETC, GD45220R) with 18-GHz bandwidth, and then the electrical signal is measured by a high-speed real-time oscilloscope (Tektronix, DSA72004b) with a sampling rate of 25 GS/s.

For Nth-order active mode-locking, the modulation frequency (fm) needs to be N times the fundamental frequency of the laser. When there is significant intra-cavity dispersion, the fundamental frequency is not fixed but varies with the wavelength, so that the laser is capable of emitting narrowband lasers with different center wavelengths at different modulation frequencies [29,30]. The AWG was used to generate sinusoidal signal with a frequency range of 192.434–192.514 MHz, which was loaded onto the EOM. The center wavelength of the laser can be tuned by adjusting the fm. Figure 2(a) illustrates the typical laser spectra with center wavelengths of 1550.30 nm, 1552.85 nm, 1555.39 nm, 1557.94 nm, and 1560.50 nm when fm was fixed at 192.434 MHz, 192.454 MHz, 192.474 MHz, 192.494 MHz, and 192.514 MHz. Due to the comb filtering effect of the MZI, the laser can only work at the peaks of the comb. The optical signal-to-noise ratio of each wavelength in steady state is greater than 30 dB, and the 3-dB bandwidth is smaller than the resolution of the optical spectrum analyzer. It can be continuously swept without mode hopping between 1550.30 nm (λmin) and 1560.50 nm (λmax); partial output spectra are shown in Fig. 2(a). Figure 2(b) shows the average spectrum of the laser output when fm was switched between 192.434 MHz and 192.514 MHz with a period of 2 ms. Due to the limited measuring speed of the optical spectrum analyzer, we hardly obtain instantaneous spectra during the fast-switching process, and only obtain average spectra. Interestingly, the laser is no longer pure but generates many new wavelength components during the switching process; it is found that new wavelengths appear notably on both sides of λmin and λmax compared to Fig. 2(a). Figure 2(c) shows the spectra when the fm was cyclically swept between 192.434 MHz and 192.514 MHz with a sweeping period of 2 ms, exhibiting a series of comb spectra with a free spectral range (FSR) of 0.12 nm. The decrease in SNR compared to Fig. 2(a) is mainly because of the slower measuring speed of the optical spectrum analyzer. Finally, based on the aforementioned cyclic sweeping, the frequency is maintained stationary at 192.514 MHz for 2 ms. The average spectrum shown in Fig. 2(d) demonstrates no new wavelengths at λmin due to continuous sweeping, while distortion of the spectrum occurs at λmax due to stopping sweeping. To further investigate whether mode hopping occurs during wavelength sweeping, we refer to previous studies and utilize a high-speed oscilloscope to collect the time-domain signals of the laser under different operating modes. Due to the time-dependent variation of the wavelength, each pulse signal at a specific time corresponds to a different wavelength, thereby the laser allowing a mapping from the time-domain to the spectral domain, which can reveal the operational mechanism of the laser [29].

First, the intensity dynamics corresponding to Fig. 2(b) were measured, and the results of the time-intensity variation over round trips (RTs) are shown in Fig. 3(a). Under the modulation of the EOM, the pulse repetition rate remains consistent with the fm, resulting in 161 pulses emitted within one RT. However, the duration of a single RT is fixed at 841.68 ns, and the variation of fm over time causes the pulse curve to tilt in different directions. Figure 3(b) shows the integrated energy within each RT. It indicates that the laser undergoes relaxation oscillations (ROs) during fm switching, where the energy decays rapidly and then increases rapidly, and exhibits very smooth damped oscillations under the effect of intensity modulation of the EOM (stage 1, RTs≈534–984; stage 3, RTs≈2910–3360). Since the energy in the cavity at the beginning of the RO is much larger than in the steady state, the very high energy excites the nonlinear effect in the cavity, which is mainly shown by the spectral broadening caused by the four-wave mixing effect, and thus new wavelengths beyond λmin and λmax are generated in Fig. 2(b). Figure 3(c) provides a magnified view of the yellow dashed box in Fig. 3(a), clearly showing the pulse variations before and after fm switching. The resonance conditions of the laser change after the variation of fm, and due to the large change of fm all the photons in the cavity cannot resonate in the new condition leading to instantaneous annihilation after the switch of fm. Afterward, the laser begins to rebuild and exhibit RO. Therefore, in order to make the laser stable, fm needs to be continuously or quasi-continuously varied. After RO, the energy curve stabilizes, and the laser begins stable operation (stage 2, RTs≈984–2910; stage 4, RTs≈3360–5286). Figure 3(d) provides a close-up view of energy oscillations for RTs=1800–2800 and 4100–5100, demonstrating that the stability at λmin is better than at λmax during steady state. This is mainly due to the lower side mode suppression ratio (SMSR) at λmax compared to λmin [as shown in Fig. 2(a)]; therefore a high SMSR is beneficial for the stability of the laser.

Subsequently, the intensity dynamics corresponding to Fig. 2(d) were measured, and partial results are depicted in Fig. 4(a). Figure 4(b) shows the corresponding energy integration curve. Figures 4(c) and 4(d) represent magnified views of the yellow dashed box in Fig. 4(a), clearly showing the processes before and after the static state. During the transition from the sweep to static, the pulse curve gradually stabilizes from slight oscillations (stage 1, RTs≈981–3357) to a steady state. When transitioning from the static to sweep, the process is similar to the laser switching. As fm starts to vary from the static, the laser undergoes RO (stage 2, RTs≈3357–3837). However, due to the continuous variation of fm and the comb filtering effect of the MZI, the damping oscillation curve exhibits significantly reduced smoothness. In addition, the intensity of RO is weaker compared to Fig. 3 due to the small change in fm before and after RO. After the completion of RO, the laser begins stable sweeping (stage 3, RTs≈3837–8109), during which the energy exhibits irregular oscillations within a small range, attributed to the filtering effect of the MZI and uneven gain. In addition, the constant vanishing and rebuilding of the longitudinal mode during the sweeping introduces inevitable energy oscillations, which becomes more violent the faster the sweeping speed, explaining why the performance of the laser decreases at higher sweeping speed. However, under the constraint of pump power, the amplitude of the oscillation is limited, and as long as fm changes continuously without undergoing sudden changes, the laser can maintain stable sweeping indefinitely.

Figure 5(a) shows the intensity dynamics corresponding to Fig. 2(c) when the laser was continuously swept with a period of 2 ms. Figure 5(b) illustrates the corresponding energy integration curve, and Fig. 5(c) provides a magnified view of the yellow dashed box in Fig. 5(a), demonstrating the transition from negative sweep (NS) to positive sweep (PS). When the laser is stably swept, the laser sweeps to the next wavelength and the intensity of the previous wavelength rapidly decreases while the new wavelength is quickly generated. This process not only maintains stable energy within the cavity but also keeps the laser in a mode-hopping-free state. Additionally, at the points where the sweeping direction changes, the energy curve always exhibits a “gap”, which will be discussed in detail in Section 3. Due to fm not experiencing sudden changes, the laser can stably sweep without generating new wavelengths. Therefore, different fm almost linearly correspond to different center wavelengths in a small sweeping range. High-speed oscilloscopes can be used to dynamically monitor fast-sweeping lasers and identify the output state of the laser. By deriving one of the pulse curves in Fig. 5(a), the blue periodic curve depicted in Fig. 5(d) can be obtained, showing the variation of fm with RTs. The red line segments represent the center wavelengths of the laser at different RTs, achieving calibration of the laser output wavelength at any time. The inset shows a magnified view near RTs=620, demonstrating the change in center wavelength when the sweeping direction of the laser changes.

Adding a large dispersion element and an intensity modulator into the laser cavity enables the generation of narrowband lasers through Nth-order active mode-locking. Changing the fm allows for continuous sweeping of the central wavelength. The linear relationship between the Δλ and the Δfm after ignoring the higher-order dispersion is expressed as follows: Δλ=−n0LcDtotalf0Δfm,(1)where n0 is the refractive index at the center of the modulation frequency f0, L is the length of the laser cavity, and Dtotal denotes the total dispersion. According to this formula, it can be inferred that different wavelengths correspond to different fm, meaning that the laser will not operate in a detuned state. After adding the MZI into the laser cavity, the laser transforms from a single-ring cavity to a composite cavity. For the same fm, the output wavelength of the laser must satisfy the condition of resonance in both cavities simultaneously. Therefore, the laser must operate in a detuned state to output stable narrowband lasers [31,32]. For a certain fm, the shorter and longer cavity will give the output wavelength of λs and λl, respectively (λs<λl), as depicted by the blue and red curves in Fig. 6 [a(ii)]. Ideally, the laser wavelength λc should lie between λs and λl, when it is detuned, as shown by the cyan curve. The gray curve in Fig. 6(a) represents the transmission spectrum of the MZI. It is noteworthy that due to the comb filtering effect of the MZI, λc can only achieve maximum gain at the peak of the comb spectrum. This implies that, under the influence of gain competition, λc can only appear at a fixed wavelength, and the FSR must satisfy FSR=cΔL,(2)where ΔL represents the optical path difference of the MZI. It can be seen that the FSR is only related to ΔL and independent of fm. When ΔL is small, changing fm can be considered that λs and λl have swept in the same direction and within the same range. Stable λc is detuned for λs and λl; their detuning values are Δλs=λc−λs and Δλl=λl−λc respectively. As shown in Fig. 6(a), when the laser begins PS from its ideal steady state, both λs and λl sweep to the right. Under the influence of gain competition, Δλs gradually decreases and Δλl gradually increases even though λc remains stationary; at this time the laser shows better stability in the shorter cavity compared to the longer cavity. When Δλl exceeds its maximum detuning value (it is related to cavity length, ΔL, and fm), λc rapidly switches to the next peak of the comb spectrum and remains stationary. Subsequently, each time the sweeping distance of the λs (or λl) exceeds the FSR, λc continuously sweeps using FSR as a step. When changing the sweeping direction, Δλs gradually increases while Δλl decreases until Δλs exceeds its maximum value, then λc moves to the left, and the subsequent process is similar to the PS. Therefore, when the sweeping direction changes, λc will keep stationary for a long time. Even when λc precisely sweeps to the next wavelength and the sweeping direction changes, λc will not immediately return to the previous wavelength. Consequently, the laser shows asymmetry between PS and NS, meaning that for the same fm, the laser may output different wavelengths in PS and NS. The cyan, blue, and red curves in Fig. 6(b) represent the output spectra of the laser under normal operation, with the longer arm of the MZI disconnected, and with the shorter arm of the MZI disconnected, respectively. These spectra have central wavelengths of λc, λs, and λl, respectively, wherein Fig. 6[b(i)] shows the spectrum when λc just negatively sweeps to 1550 nm, with Δλs approximately 1.15 nm. Figure 6[b(ii)] depicts the spectrum when λc just positively sweeps to 1550.11 nm, with Δλl approximately 1.05 nm, slightly less than 1.15 nm. This is because the maximum detuning value is related to the fundamental frequency of the laser; the larger the fundamental frequency, the larger the maximum detuning value, and thus the maximum value of Δλs is slightly greater than Δλl. Subsequently, the laser continues PS until λc is exactly 1550.22 nm. The spectrum is shown in Fig. 6[b(iii)], where λc, λs, and λl all sweep 0.11 nm compared to Fig. 6[b(ii)], verifying that once the laser starts stable sweeping, the sweeping distance of the λs (or λl) exceeds the FSR each time; λc sweeps to the next wavelength with the FSR as a step.

Changing ΔL can adjust the FSR to enable wavelength sweeping at different steps. When ΔL is small, the sensitivity of the MZI to the environment increases, leading to a rapid decrease in the stability; a larger wavelength step is not conducive to applications. When ΔL is large, although the wavelength step and instantaneous linewidth decrease, the sweeping speed of λs and λl may differ significantly, causing deterioration in the linearity of λc over time. In extreme cases, mismatches in the sweeping speed of λs and λl may result in substantial steps in λc. As shown in Fig. 7(a), when ΔL exceeds 10 cm, despite the FSR being very small, the interval between adjacent λc as fm sweeps from 192.50 MHz to 192.51 MHz is not the FSR but 0.89 nm. The significant step of λc is due to the large ΔL caused, indicating the necessity of setting ΔL according to requirements in applications. Furthermore, as depicted in Fig. 6(b), it is evident that the 3-dB linewidth of the MZI-DTSFL is much narrower than that of DTSFL. This is because, for composite cavities, only the longitudinal mode at the peak of the MZI transmission spectrum can obtain maximum gain, while the intensity of other longitudinal modes rapidly attenuates due to the larger longitudinal mode spacing. Since the optical spectrum analyzer cannot measure the linewidth of the output spectrum of MZI-DTSFL, we utilized the heterodyne technique to measure the instantaneous laser linewidth [33,34]. The beatnote of the laser to be tested with the narrow-linewidth tunable fiber laser was analyzed, and the results are shown in Fig. 7(b). The Lorentz-fitted linewidth is approximately 0.85 GHz, which is significantly narrower than that of the DTSFL [29]. The laser can sweep over 30 nm under the aforementioned configuration. However, a larger sweeping range may lead to excessive curvature in the pulse curve shown in Fig. 5(a), which is not conducive to presentation in a single figure; segmentation can be used to solve this issue.

To verify the correctness of the above analysis, we constructed a simple laser model for simulation analysis. The model retains only the essential components of the laser, including a 3-m EDF, a 150-m DCF, an EOM, and an MZI. The propagation of light is described by the Ginzburg–Landau equation as follows: ∂A∂z−iβ22∂2A∂t2−iγ|A|2A=(g−α)A2+g2Ωg2∂2A∂t2+M(ωmt)2A2,(3)where A is the complex amplitude of the electrical field of the pulse, t and z represent the transmission time and distance, β2 and γ are the second-order dispersion and the cubic refractive nonlinearity, g and α are the saturation gain and attenuation, and M and ωm are the modulation depth and modulation angular frequency of the EOM. Ωg is the laser gain bandwidth; in passive fiber, g=0, and in EDF, g(z,t)=g(z)=g0(1+1Es∫0twin|A(z,t)|2dt)−1,(4)where g0 represents the small signal gain factor, Es is the gain saturation energy, and twin is the size of the simulation window. The transmittance function of MZI can be expressed as T=(1−cos(2πΔLλ))/2.(5)

In the simulation, we set the time window to 16 ns and the number of sampling points to 213 for the convenience of calculation; f0 is set to ∼200MHz. We fix ΔL and linear loss (including insertion loss, bending loss, etc.) at 2 cm and 1.5 dB, respectively. Due to the limitation of the time window, a maximum of three pulses can be observed within a single RT for f0. We add small perturbations to simulate noise caused by the sensitivity of the MZI to the environment while keeping the parameters of each component consistent with the experiment (as shown in Table 1). Weak noise is used as the initial signal input, and theoretical calculations are performed for both the switching mode and static-sweeping mode. For the switching mode, due to the filtering effect of the MZI, the spectrum remains comb-shaped initially. After ∼100 RTs, only a single-mode laser remains due to the combined effects of dispersion filtering and gain competition, with the intensity of other modes gradually decreasing. Eventually, a narrowband laser with an extinction ratio of ∼35dB, central wavelength of ∼1549nm, and 3-dB linewidth of ∼1GHz is formed, as shown in Fig. 8(a). At RT=300, increasing fm by ∼15kHz results in a rapid decrease in laser intensity, accompanied by spectral broadening. Subsequently, the spectrum concentrates near 1551 nm, and the intensity of other high-order modes decays continuously, eventually forming a narrowband laser. It is worth noting that although the evolution of the spectrum is similar for each change in fm, the intensities of different pulses show randomness due to the introduced small perturbations, as shown in Fig. 8(b). After the laser enters a steady state, the intensities of each pulse remain stable. However, after reconstruction of the laser, the intensities of the pulses still exhibit random distribution, unrelated to previous states, without any memory effect, consistent with the experimental results.Table 1.

Parameters Used in Simulation

We keep fm constant until the photons inside the cavity evolve from noise to a narrowband laser. Then, fm starts linear sweeping at RT=200 with a sweeping speed of −10Hz/RT, and at RT=1700, the sweeping speed changes to +10Hz/RT. The evolution of the spectrum is shown in Fig. 8(c). It can be observed that at the beginning of the sweeping, the laser shows slight RO, leading to a small broadening of the spectrum. However, the laser quickly returns to a stable state. Notably, despite the initiation of sweeping by fm, the wavelength remains stationary, until ∼220 RTs later when Δλs exceeds its maximum value, and the wavelength steps towards the shorter wavelength by ∼0.12nm. Consistent with the experimental results, when the sweeping direction changes, the wavelength does not immediately change but instead delays before stepping to the next wavelength. After the laser starts sweeping, the pulse intensity remains stable. Due to the small change in fm, it is difficult to discern changes in the pulse interval in Fig. 8(d) [and Fig. 8(b)]. Additionally, we found that this special stepped method keeps the wavelength stationary for most of the time, resulting in almost the same linewidths in both static and sweeping modes. This eliminates the problem of spectral broadening during the sweeping process in DTSFL.

On the basis of a dispersion-tuned swept laser, we added an MZI inside the laser cavity for comb filtering, controlling the laser output wavelength by changing the modulation frequency. During the sweeping process, the intensity of the laser does not show periodic changes over time. Instead, due to gain competition, the laser stabilizes at wavelengths that satisfy the resonance condition, changing from wavelength-swept to wavelength-stepped. Dynamic studies of the three operational modes revealed that in the case of discontinuous sweeping, the laser experienced nonlinear spectral broadening due to relaxation oscillations, which is disadvantageous for applications of the lasers. When the modulation frequency is continuously swept, relaxation oscillations disappear, and the narrowband laser is continuously output. For the two sub-cavities of the composite cavity, although they both operate in a detuned state, their synergistic effect enables the composite cavity to operate in a stable state. Compared to dispersion-tuned swept lasers, this not only effectively narrows the linewidth but also eliminates the problem of spectral broadening during the sweeping process. Since the laser needs to exceed the maximum detuning value of one sub-cavity to complete a wavelength step during the sweeping process, the wavelength remains stationary for a longer time at the start of sweeping and when the sweeping direction changes. This results in a delay in wavelength change relative to the modulation frequency change. Adjusting the optical path difference of the MZI can rapidly change the step of the wavelength according to different application requirements. The simulation results match the experimental results and clearly show the evolution of the spectrum during operation, providing a theoretical basis and guidance for the experiment.