1. Introduction

In the past decade, spectrally-encoding technology has been widely investigated for its potential capacity of fast line-scan spatial information acquisition by eliminating point-by-point raster-scanning [1,2]. The line-scan acquisition is accomplished by diffracting different wavelength components of a broadband laser onto distinct spatial locations of the object. This is actually analogous to the wavelength-division multiplexing (WDM) in the optical communication ― each point along one spatial line is encoded with a different wavelength. Afterwards, the spatial information encoded in the optical spectra can easily be decoded by spectral measurements such as heterodyne Fourier-transform spectroscopy [1], charge-coupled device (CCD) camera [3] and optical spectrum analyzer (OSA) [4]. Up to now, its superior performances have been well accepted in various optical imaging applications, e.g., confocal microscopy [1], minimized endoscopy [2,3] and flow cytometry [5,6]. While it provides a high imaging quality, the effective acquisition rate can be subsequently limited by the relatively slow detection elements. In addressing this issue, wavelength-swept laser sources have been introduced to enhance detection speed of the spectroscopic signal [7–9]. Since the wavelength of a swept source can be rapidly scanned across the whole bandwidth range, the time-domain signal representing the signal as a function of wavelength can be read out by a single-pixel high-speed photodiode.

Typically, wavelength sweeping can be actively obtained through either mechanical [8] or electrical tuning [10–13], typically operating at 10-100 kHz. However, for ultrafast studies, e.g., transient, dynamic and rapid changes of the observed samples, it requires a much higher wavelength-swept repetition rate up to MHz, particularly when the volumetric screening is desired, e.g., 3D in vivo optical coherence tomography (OCT) [14,15]. Although there are approaches, such as time-multiplexing with several buffering stages and microelectromechanical systems (MEMS) [14–17], to enable a MHz wavelength sweeping, they are complex and it is therefore difficult to further enhance their wavelength sweeping speed. All-optical time-stretch, as an inertia-free technology, is a passively wavelength-swept technology [18,19]. Time-stretch employs the group-velocity dispersion (GVD) from dispersive elements to introduce linear time delay for different wavelength components of a short laser pulse. Its wavelength-swept repetition rate is only limited by that of the pulse laser sources, typically ranging from 10’s MHz to several GHz. The superior high-speed capability of the time-stretch has been successfully demonstrated in analog-to-digital conversion [18], spectral measurement [19–22], soliton dynamics in mode-locked pulse lasers [23–28] and ultrafast optical imaging [29–31]. Unfortunately, such a superior technology is largely under-explored as high-speed wavelength-swept laser sources, particularly at the bio-favorable wavelength window (i.e., <1.0 μm) [32]. It is known that the duty cycle of the wavelength-swept pulse at a given repetition rate is determined by the GVD of the dispersive medium. Considering the interplay between duty cycle and the digitizer bandwidth, a full duty cycle is preferred in addition, otherwise a bandwidth of >10’s GHz is required as shown in prior works [33]. To achieve a higher sensitivity and real-time data processing through standard electrical devices, a few-MHz full-duty-cycle wavelength-swept laser is more preferred, which however equivalently requires a GVD larger than 1 ns/nm. Unfortunately, the standard dispersive medium at this wavelength window, typically a single-mode fiber (SMF, e.g., Nufern 1060-XP and Corning HI 1060), is lossy (~2 dB/km) and its dispersion coefficient is very small (~30 ps/nm/km). This can result in an insertion loss up to 66 dB for a GVD of 1 ns/nm, which is not feasible for time-stretch applications. Consequently, a new dispersive medium with better dispersion to loss ratio is yet to be designed especially for this shorter wavelength window.

On the other hand, the beam profiles of the wavelength-swept laser sources presented before or those commercially available [34], usually exhibit a Gaussian function. It is widely known that the Gaussian beam itself diffracts substantially beyond the Rayleigh range, which limits penetration depth particularly in the turbid environment. Thus, it is interested to equip the wavelength-swept source with a better penetrating capability. Airy beam as a diffraction-free and self-healing beam [35], shows the potential for enhancement of penetration depth [36]. In spite of such an advance, Airy beam laser has so far rarely been demonstrated [37,38]. Here, we demonstrate a 70-nm full-duty-cycle wavelength-swept fiber laser with an Airy-beam profile at the bio-favorable window. To perform efficient wavelength sweeping through all-optical time-stretch, a newly dispersive fiber at 1.0 μm is presented that can provide a GVD up to −1.7 ns/nm. By leveraging a double-pass scheme, the dispersion amount can be further scaled up to −3.5 ns/nm, which can largely reduce the electrical bandwidth requirement and enable the real-time data processing. The unique diffraction-free and self-healing properties of this high-speed wavelength-swept fiber laser are also demonstrated.

2. The experimental setup

The schematic diagram of the diffraction-free wavelength-swept fiber laser is illustrated in Fig. 1. It includes broadband short pulse generation, all-optical wavelength sweeping and beam profile modulation. For the broadband pulse generation, an all-fiber cavity was constructed by a single fiber-pigtailed unit, i.e., the optical integrated module (OIM), which can provide several functions such as pump coupling, signal extraction, unidirectional operation and polarization selection. The gain medium was a section of highly-doped ytterbium (Yb) fiber, 80 cm in length. It has a core-pump absorption up to 280 dB/m at 920 nm and a mode field diameter of 4.4 μm at 1060 nm. The gain fiber was pumped by a 600-mW single-mode laser diode (LD). To obtain a several-MHz repetition rate ($R=c/nL$, where c, n and L are the speed of light, refractive index and cavity length, respectively), the fiber cavity length was extended by a segment of SMF fiber to become ~23 m. The pulse was generated through nonlinear polarization rotation mode-locking [39], consisting of a polarization controller (PC) and the polarization-dependent loss provided by OIM. All the glass fibers exhibit a normal dispersion at a shorter wavelength (<1.3 μm), thus the present cavity shows an all-normal dispersion.

 

Fig. 1 The schematic diagram of the self-healing wavelength-swept fiber laser. SMF: single-mode fiber. OIM: optical integrated module. PC: polarization controller. Yb: ytterbium doped fiber. DCF: dispersion-compensating fiber. CPM: cubic-phase modulator.

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50% of the optical power was extracted from the tap port of the OIM, which was then launched into the wavelength sweeping unit, i.e., the bottom right inset of Fig. 1. The ultrashort pulse was chirped through a 7-km newly-designed dispersion-compensating fiber (DCF) at 1.0 μm, which was custom-made from OFS (model No., DCF solution for 800-1100 nm). As shown in Fig. 2, this new DCF can provide a GVD up to −1.7 ns/nm at a mere insertion loss of 15 dB. The dispersion to loss ratio of present DCF is almost 8 times better than that of the standard SMF, as well as its dispersion coefficient. It is noted that an ultrashort pulse (particularly fs pulse) can easily produce nonlinear effects and thus experience significant spectral broadening in the anomalous dispersion regime. Contrarily, current fiber cavity was constructed with all-normal dispersion fiber with a relatively long cavity length, resulting in a total intracavity dispersion up to −0.69 ps/nm. Thus, the extracted pulse is chirped, to be demonstrated later. Together with the highly chirping at the beginning of the DCF, the peak power of the short pulse can be rapidly decreased after propagating through the DCF. Thus the nonlinear effects were suppressed greatly even with 10’s of mW average power. It is noticed that the dispersion curve is not flat enough, e.g., changing from −1.5 ns/nm at 1020 nm to −1.9 ns/nm as shown in Fig. 2. It indeed influences the wavelength sweeping by a non-uniform mapping between wavelengths for a broadband optical pulse. Although it can be compensated by post data processing, it is required to optimize through fiber dispersion engineering for further improvements.

 

Fig. 2 The dispersion and loss characteristic of the new DCF at 1.0 μm. It should be pointed out that the measurement range of the GVD is limited by the tuning range of the signal source.

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The wavelength-swept pulse finally propagated through a custom-designed binary cubic phase modulator (CPM) to phase-modulate the Gaussian beam output from the single-mode DCF. A 2D Airy-beam profile with diffraction-free and self-healing properties was generated after the Fourier transformation through an optical lens at a focal length of 300 mm. The binary grating design of the CPM cannot only diffract a portion of the Gaussian beam into Airy beam, but also simultaneously residue a part of the Gaussian beam, i.e., zeroth order transmission. The CPM has a clear aperture of 2$\times$2 mm². To generate a clean and symmetrical 2D Airy beam, the beam size of the incident light should be field-matched with the clear aperture of the CPM. Thus, a telescope for beam-size control was employed, though not fully shown in Fig. 1.

3. Results and discussion

The mode-locking process of the fiber laser cavity was monitored in both time and frequency domains through a fiber optical coupler. In the time domain, a GHz sensitive balanced photodetector (Thorlabs, PDB480C-AC) and a real-time oscilloscope (OSC) worked together to continuously visualize the intensity information. In the meantime, a conventional OSA was employed for the spectral width optimization. These two approaches are complementary for the generation of stable mode-locked pulse with broad bandwidth. In the time domain, the real-time oscilloscope works in the continuous mode, and thus can timely present the real pulse intensity, which relates to the pulse stability. This is essential for optimizing the uniformity of the mode-locked pulse train. However, the temporal resolution of the real-time oscilloscope is typically in the order of 10’s ps. The actual transform-limited temporal width of the mode-locked pulse, usually 10’s of fs, cannot be obtained from the time-domain signal. Thus, the averaged OSA spectra can indirectly indicate the effective pulse width as well as the spectral shape, which is useful for the Fourier-transform-based applications, e.g., spectral-domain OCT where a Gaussian spectrum shape is preferred for the sidelobe suppression. In turn, although it may deliver a very broadband pulse train before stable mode-locking (e.g., what has been shown in Ref 25), the operation of the fiber cavity can be relatively unstable and not suitable for single-shot applications.

The operating condition of the fiber laser cavity was mainly controlled by the pump strength or the in-line PC. It evolved from a quasi-CW lasing to Q-switch-modulated mode-locking, and finally to continuously mode-locking as the pump power was increased from 0 to 550 mW. After careful manipulation, the fiber cavity can output a relatively smooth mode-locked spectrum, as shown in Fig. 3(a). It’s centered at around 1064 nm with a 3-dB spectral width of ~73 nm, yielding a theoretically transform-limited pulse width of 23 fs. The time-domain pulse train is illustrated in Fig. 3(b). The fundamental spacing between adjacent pluses is 115.4 ns, corresponding to a repetition rate of 8.7 MHz. The pulse width directly output from the fiber cavity was also measured by a second-harmonic-generation based autocorrelator, as shown in the inset of Fig. 3(b). It is clear that the output pulse is not transform-limited. This can be attributed to the frequency chirp induced by the intracavity dispersion. Normally, such a chirped pulse should be externally de-chirped through an opposite dispersion with respect to that of intracavity one [39] for those applications where a high peak power is desired, e.g., multiphoton imaging. However, rather than a high peak power, we pursued a wider pulse width at a given spectral width in this work. Thus, the intracavity dispersion is not the issue here. The average output optical power right before wavelength sweeping is 92 mW at a pump power of 600 mW.

 

Fig. 3 (a) The optical spectrum of the mode-locked ultrashort pulse. (b) The optical pulse train right before chirping by the new DCF. Inset shows the pulse width measured by an autocorrelator.

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Subsequently, the ultrashort pulse was wavelength-swept through the large GVD. To reveal the superior performance of the newly-design DCF at 1.0 μm, we performed wavelength sweeping with both standard SMF and this new DCF. As can be observed from Fig. 4(a), the pulse waveform has been chirped to a broader one, from ps shown in Fig. 3(b) to 11.1 ns, corresponding to a dispersion amount of −0.15 ns/nm. It is noted that the temporal spectrum shown in Fig. 4(a) is reversed with respect to that of Fig. 3(a). This is because that the dispersion of the silica-glass fiber exhibits a normal dispersion at 1.0 μm ― longer wavelength propagates faster. The duty cycle of the wavelength-swept pulse via the standard SMF is only 9.6%. To fully utilize the temporal spacing through the standard SMF, another 48 km SMF is required, which however can result in a huge insertion loss, up to ~100 dB in total. Apparently, it is not practical to generate full-duty-cycle wavelength-swept pulse operating in the range of 1-10 MHz through standard SMF at 1.0 μm. It is because the 10’s of km SMF is relatively bulky, and the huge insertion loss, on the other hand, greatly reduces the detection sensitivity of the optical system. Although external amplifications can be utilized to compensate the insertion loss, the broadband amplification is always an issue [29].

 

Fig. 4 (a) The wavelength-swept pulse train chirped by a standard SMF at 1.0 μm, i.e., 5-km Nufern 1060-XP in this case. (b) The wavelength-swept pulse train chirped by the new DCF. The arrow indicates an increasing loss from longer wavelengths to shorter ones, which is consistent with loss characteristic shown in Fig. 2, i.e., the blue curve.

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The wavelength sweeping performance of the newly-designed DCF is illustrated in Fig. 4(b). It is clear that the duty cycle of the wavelength-swept pulse is much larger than that of the standard SMF. Since the GVD is around −1.7 ns/nm, i.e., Fig. 2, the actual wavelength-swept pulse waveform should be ~124.1 ns at a spectral width of 73 nm. Thus, the successive wavelength-swept pulse waveforms shown in Fig. 4(b) are partially overlapped with each other. This can be further improved by extending the cavity length to enhance the original pulse spacing or relatively narrowing the spectral width, to be demonstrated later. The final output power of the wavelength-swept laser without any external optical amplifier was measured to be 2.8 mW. It should be pointed out that, the loss of the new DCF is not uniform over the whole wavelength range, i.e., wavelength-dependent as shown in Fig. 2, which can slightly change the optical power distribution over the spectral bandwidth. For example, the intensity of the shorter wavelength can be weakened by ~6 dB with respect to that of the longer wavelength. Given that the sensitivity of photodetectors and dynamic range of digitizers are typically < 100’s nW and > 20 dB, the intensity difference between shortest and longest wavelength over the wavelength-swept range would not affect the practical applications, and the whole 3-dB bandwidth of the wavelength-swept pulse can still be used, as shown in Fig. 4(b).

To further utilize the superior dispersion to loss ratio of the newly-designed DCF, we propose a modified configuration of the wavelength sweeping to achieve an even higher chirp rate as well as a much higher optical power, as shown in Fig. 5(a). In short, it is a double-pass scheme, resulting in a double GVD. Two fiber circulators at 1.0 μm were used to sandwich the new DCF, while second one was looped from port ③ to ① to guide the wavelength-swept pulse back to the DCF for the second stage of wavelength sweeping. To compensate the extra loss of the second pass in the DCF, a relay low-power amplifier (LPA) was inserted into the feedback optical path of the second fiber circulator, as shown in Fig. 5(a). The LPA was constructed by a single-cladding gain fiber, which could provide a saturated optical power of ~15 mW. The final output from port ③ of the first fiber circulator was fed into a high-power amplifier (HPA) at 1.0 μm. This HPA was constructed by two stages: one was a pre-amplifier with single-cladding core-pump scheme, and it could provide a saturated power of ~100 mW; the other one was a high power booster constructed by double-cladding cladding-pump scheme, and it has a saturated optical power up to 2 W. The short pulse laser source used for this demonstration is another mode-locked fiber laser similar to that of Fig. 1, however with a lower repetition rate at 5.9 MHz. It should be pointed out that the optical power of ultrashort pulse before chirping into nanosecond pulse was reduced to <10 mW for nonlinear effect suppression, i.e., mainly for the first-time propagation through the DCF. The pulse trains before and after the double-pass wavelength sweeping are shown in Fig. 5(b). The temporal spacing between successive pulses is 169.5 ns, consistent with the repetition rate of 5.9 MHz. The temporal width of the wavelength-swept waveform after the double-pass chirping is 25.2 ns, yielding a chirp rate of −3.5 ns/nm, which is twice of the single-pass GVD shown in Fig. 4(b). It is noted that there are weak narrow pulses presented beside the wavelength-swept pulse. It is introduced by the direct reflection of the first fiber circulator without going through the wavelength sweeping unit. By overlapping the optical spectrum measured by an OSA and the temporal wavelength-swept waveform measured by a real-time OSC, a good frequency-to-time mapping is obtained, as shown in Fig. 5(c). To further showcase the frequency-to-time mapping capability of this high-power highly-chirping laser, we launched it into an interferometer for spectral information encoding. The temporal interferogram train is shown in Fig. 6(a), which exhibits dense interfering fringes. By overlaying both OSA spectrum and single-shot temporal waveform together, a very well mapping between frequency and time domains is visualized, as shown in Fig. 6(b). Consequently, it is an efficient swept source for frequency-to-time mapping at such a high speed. Up to now, there are two significances in this work: 1) the high optical power can enable the applications involving high optical loss and wavelength shifting through nonlinear effects, e.g., four-wave mixing (FWM) and second harmonic generation (SHG); 2) it is the highest chirp rate which yet achieved through optical fiber at 1.0 μm, which is 23 times higher than previously demonstration [30]. This chirp rate makes it possible to leverage the off-the-shelf field-programmable gate array (FPGA) based platform to perform real-time data processing [40], particularly for those high-speed spectrally-encoded applications [1–7,9].

 

Fig. 5 (a) The schematic diagram of double-pass wavelength sweeping for GVD doubling. (b) The pulse trains before and after the double-pass wavelength sweeping. The weak narrow pulse is the direct reflection from port ① to ③ of the input fiber circulator, i.e., without chirping by the new DCF. (c) The mapping between frequency and time domains after double-pass wavelength sweeping.

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Fig. 6 (a) The temporal interferogram train after the interferometer. (b) The comparison between the OSA optical spectrum and single-shot OSC temporal waveform.

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The wavelength-swept laser in Fig. 4(b) was finally launched into the free-space through a fiber collimator for beam profile modulation. The beam size output from the fiber collimator needs to be optimized to match with the clear aperture of the CPM, which can be accomplished by an optical telescope. After the CPM, the Gaussian laser beam was imprinted with a cubic phase pattern. Subsequently, an optical lens was utilized to perform Fourier transformation for the diffraction beam from the CPM and generate a 2D Airy beam profile [41]. The Airy-beam profile was confirmed by using a near-infrared (NIR) camera. As shown in Fig. 7(a), the beam profile was recorded at different propagation distances away from the Fourier plane of the focal lens, i.e., at 0, 100 and 200 cm, respectively. It is evident that the 2D Airy beam profile is generated with symmetrical side lobes, and that the size of the individual sidelobe was not changed over the 2-m propagation. To verify the self-healing property, the central sidelobe was blocked at the Fourier plane, as indicated in the left panel of Fig. 7(b). It is clear that central sidelobe reappears gradually as it propagate, which confirms the self-healing nature of the generated 2D Airy beam.

 

Fig. 7 (a) The beam profiles at different propagation distance away from the Fourier plane of the focal lens, i.e., 0, 100 and 200 cm. (b) The self-healing performance of the wavelength-swept laser.

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4. Conclusion

In conclusion, we have demonstrated a compact MHz self-healing wavelength-swept fiber laser source at 1.0 μm with an unprecedented chirp rate up to −3.5 ns/nm ― 23 times higher than previous demonstrations. Such a high chirp rate enables the detection of the spectrally-encoded signal through sensitive off-the-shelf low-bandwidth photodiodes, which ensures the real-time high-speed spectroscopic applications. A wide spectrum width (>70 nm) would benefit those applications involving Fourier-domain signal processing, e.g., swept-source OCT and time-domain optical frequency domain reflectometry (OFDR). The high average output power (up to 2 W), on the other hand, can benefit other applications requiring a higher power budget such as wavelength conversion through FWM or frequency doubling to the visible wavelength window. The special beam profile with diffraction-free and self-healing properties, furthermore, can be a promising solution for a larger penetration depth in the turbid environment.