Fiber lasers with effective modal control to achieve specific high-order modes (HOMs) output have attracted much attention in the past few decades, thanks to their unique polarization, amplitude, and phase characteristics, which have been applied to mode division multiplexing^[1], industrial processing^[2], and so on. Moreover, further generation of cylindrical vector beams and vortex beams based on HOMs has also been verified^[3–9], which finds a tremendous range of applications, including plasmon excitation^[10], optical tweezers^[11], and electron acceleration^[12]. So far, several routines to achieve HOMs have been confirmed, such as specially designed fibers^[13,14], lateral offset splicing^[15], long-period fiber gratings (LPFGs)^[16–18], few-mode fiber Bragg gratings (FMFBGs)^[19–22], mode-selective couplers (MSCs)^[4,23–27], spatial light modulators^[28–32], active polarization control^[33,34], and acoustically induced fiber gratings (AIFGs)^[35–38].

Among those techniques above, fiber-based methods have shown great potential for power scaling of HOMs generation in all-fiberized systems, which are in demand in most practical applications. For example, Abedin et al. realized 100 W output of ${\mathrm{LP}}_{0,10}$ mode based on specially designed Yb:HOM fiber^[14]. Furthermore, Su et al. demonstrated a mode-switchable high-power all-fiber master oscillation power amplification (MOPA) system with the ${\mathrm{LP}}_{11}$ output power at the 500 W level by regulating the input polarization state of the seed laser at 1060 nm^[33]. Later in 2019, You et al. used similar methods and achieved $\sim 1.4\mathrm{kW}$ output at 1060 nm with ${\mathrm{LP}}_{11}$ modal purity of 78%, which is the highest power of ${\mathrm{LP}}_{11}$ mode in continuous-wave fiber lasers^[34]. Recently, Wu et al. utilized the AIFG to accomplish a hundred-watt mode switchable laser based on the Yb-doped MOPA scheme.

Nevertheless, one could find that most of the demonstrations above are based on rare-earth-doped fiber lasers, whose emission bands are highly restricted. In recent years, new applications have been continuously derived from lasers of HOMs, making precise wavelength manipulation of greater significance. For example, the combination of wavelength division multiplexing and mode division multiplexing can increase the transmission capacity of the communication system exponentially^[39]. To broaden the spectral window, the laser gain mechanism based on the stimulated Raman scattering (SRS) effect in purely passive fiber is expected to be a good solution, including Raman fiber laser (RFL)^[40] and random distributed feedback Raman fiber laser (RRFL)^[41]. In 2013, Jocher et al. demonstrated an RFL at 1115 nm, achieving azimuthally and radially polarized beams by controlling the polarization of a Gaussian pump beam^[42]. Compared with RFL, the RRFL has the advanced features of low coherence and simple structure, thanks to the random distributed feedback scheme provided by Rayleigh scattering. So far, RRFLs reported have predominantly utilized single-mode fibers (SMFs) with core pumping configuration, thus realizing single-transverse-mode output. Notwithstanding, RRFLs with different spatial modes have outstanding advantages in many practical applications, such as reducing laser speckle^[43], lowering turbulence-induced scintillation in free-space optical communication^[44], and a ghost-imaging technique that is not affected by meteorological conditions^[45]. The first exploration was reported by Du et al. in 2015^[15], realizing switchable output between the ${\mathrm{LP}}_{01}$ and ${\mathrm{LP}}_{11}$ modes in RRFL at 1070 nm by employing an offset splicing spot and two polarization controllers, while the power of ${\mathrm{LP}}_{11}$ mode was only 10 mW with a slope efficiency less than 1% due to the high loss introduced by the splicing spot. In order to improve efficiency, Lv et al. utilized a piece of annular doping Yb-doped fiber together with passive fiber to enhance the gain of ${\mathrm{LP}}_{11}$ mode in RRFL^[46]. The slope efficiency increased to 7.2% with a maximum output of 17 mW at 1055 nm, and the power level is still far from the practical requirement.

In this paper, we experimentally demonstrated a high-power all-fiberized RRFL with high-purity ${\mathrm{LP}}_{11}$ mode at 1134 nm. The mode conversion was achieved by employing an intracavity AIFG due to its wavelength tunability and fast conversion speed. The maximum signal light output power of the ${\mathrm{LP}}_{01}$ mode and ${\mathrm{LP}}_{11}$ mode is 96.6 W and 93.8 W, respectively. It is noticeable that the average purity of ${\mathrm{LP}}_{11}$ mode is as high as 82%, which is decomposed based on the stochastic parallel gradient descent (SPGD) algorithm. To the best of our knowledge, it is the highest power of high purity of ${\mathrm{LP}}_{11}$ mode generated from RRFL. For potential industry applications, the stability of the system was also verified with good results in 20 min.

The AIFG is the key component to generate ${\mathrm{LP}}_{11}$ mode in RRFL. As shown in Fig. 1(a), the basic structure of AIFG consists of a piezoceramic transducer (PZT) with a quartz horn and a piece of few-mode fiber (FMF) attached. The PZT is driven by a periodic electrical signal with high amplitude generated from the radio-frequency (RF) source, including an electrical signal generator and a voltage amplifier inside. When the periodic electrical signal loads, the PZT starts to vibrate, and the vibration is transmitted to FMF by the quartz horn. Then the acoustic wave caused by vibration further modulates the refractive index of FMF periodically, similar to the LPFG structure, whose grating period can be calculated by the following formula^[35,47]: $$\mathrm{\Lambda }=\sqrt{\pi R{C}_{\mathrm{ext}}/f},$$(1)where $R$ is the cladding radius of the FMF, $C_{\mathrm{ext}}=5760\mathrm{m}/\mathrm{s}$ is the propagation velocity of acoustic wave in the quartz fiber, and $f$ is the frequency of the loading signal and the acoustic wave.

According to the mode-coupling theory, the modes can be coupled when the following phase-matching condition is matched^[48]: $$\mathrm{\Lambda }=L_B=\lambda /(n_{01}-n_{11}),$$(2)where $\lambda$ is the wavelength of transmitted laser, and $n_{01}$ and $n_{11}$ represent the effective refractive indices of ${\mathrm{LP}}_{01}$ and ${\mathrm{LP}}_{11}$ mode propagating along the fiber, respectively. Hence, the input guided fundamental mode ${\mathrm{LP}}_{01}$ in FMF would be converted to higher-order mode ${\mathrm{LP}}_{11}$ at output.

Based on the principle of AIFG, in order to achieve efficient mode conversion, the loaded signal frequency of AIFG needs to be adjusted to satisfy mode-coupling conditions. To test the correspondence between the loaded signal frequency and the generated beam profile, the output beam profiles directly after the AIFG are measured first by injecting a laser signal at 1130 nm, as shown in Fig. 1(b). When the frequency increases from 780 kHz, the output beam profile gradually evolves from ${\mathrm{LP}}_{01}$ mode to ${\mathrm{LP}}_{11}$ mode until the appearance of the most obvious ${\mathrm{LP}}_{11}$ mode spot, corresponding to the eigenfrequency of 785 kHz. Then the frequency increases further, and the spot returns to ${\mathrm{LP}}_{01}$ mode. This means that the AIFG could not only switch the two modes, but also change their ratio by varying the frequency.

Furthermore, the ${\mathrm{LP}}_{01}$-mode transmission spectra of the AIFG are tested by a broadband light source, and some results are shown in Fig. 2(a). These discrete peaks do not imply that efficient mode conversion only occurred at these wavelengths. In fact, at any wavelength from 1050 to 1300 nm, we can always obtain an optimum frequency that makes the transmission curve of ${\mathrm{LP}}_{01}$ mode reach more than 15 dB, indicating a high mode conversion efficiency from ${\mathrm{LP}}_{01}$ mode to ${\mathrm{LP}}_{11}$ mode. As shown in Fig. 2(a), the modal conversion shifts to longer wavelengths when frequency increases, and their relationship is shown in Fig. 2(b). The fit curve satisfies the following linear expression: $$\lambda =1.238f+160.9,$$(3)where $\lambda$ is the wavelength (in nanometers) and $f$ is the loaded frequency (in kilohertz).

In order to generate controllable output beam profiles, the experimental setup of the RRFL is designed as shown in Fig. 3(a). An ytterbium-doped fiber laser (YDFL) operating at 1080 nm with a maximum output power of 120 W is utilized as the pump source. The half-open cavity of RRFL is formed by a high-reflection (HR) fiber Bragg grating (FBG), a piece of FMF, and a fiber end cap. The HR FBG is written in the FMF with a reflectance of more than 99.5% at 1134 nm. The end cap is antireflection-coated to evade unwanted end feedback. As shown in Fig. 3(b), the FMF is commercial graded-index (GRIN) fiber with a parabolic profile of the refractive index, providing both Raman gain and distributed feedback. The core diameter and numerical aperture (NA) of the FMF are 20 µm and 0.14 separately, with a length of 400 m that has been optimized thoroughly to achieve high efficiency. The HR FBG is written in the same GRIN FMF, which guarantees the mode field matching at the fusion splices in the laser. The AIFG described in the last section is located between the FMF and the fiber end cap to modify the generated mode. The fiber used in AIFG is step-index FMF with a core diameter and an NA of 16 µm and 0.11 separately, indicating four LP modes supported in the core at both 1080 and 1134 nm, as shown in Fig. 3(c).

Figure 4(a) exhibits the output signal power as a function of the pump power with the corresponding output beam spot inserted. By switching on/off the RF source operating at 787 kHz, which was precisely the eigenfrequency of 1134 nm, the mode conversion can be achieved. The red and the black lines refer to the ${\mathrm{LP}}_{01}$ mode and ${\mathrm{LP}}_{11}$ mode signal light being output individually. It can be observed that the output power of ${\mathrm{LP}}_{11}$ mode is always slightly lower than that of ${\mathrm{LP}}_{01}$ mode at the same pump power as a result of the loss in the mode conversion process. It is worth noting that the growth curve of output signal power is not straight. When the pump power exceeds the threshold of around 42 W, but is below 60 W, the signal power grows rapidly and the light-to-light conversion efficiency even exceeds 100%. This phenomenon has been explained by numerical calculation in detail in Ref. [41]. Indeed, in the RRFL with forward-pumped configuration, the highest power and efficiency are reached in a short fiber, despite the generation threshold being relatively high. Then, when the pump power exceeds 60 W, the power evolution curves of the ${\mathrm{LP}}_{01}$ and ${\mathrm{LP}}_{11}$ modes are approximately linear, with the slope efficiency of 93.8% and 90.3%. The maximum output power of ${\mathrm{LP}}_{01}$ mode and ${\mathrm{LP}}_{11}$ mode is 96.6 W and 93.8 W independently. Figure 4(b) illustrates the spectra at different output power levels for ${\mathrm{LP}}_{01}$ and ${\mathrm{LP}}_{11}$ modes. The central wavelength of the signal is 1134 nm, while the second-order Raman–Stokes wavelength is 1194 nm. At the maximum output power, the intensity of the second-order Stokes is 26 dB lower than that of the signal light, limiting further power scaling. Since the mode conversion is executed near the output end, there were not many differences in spectra in both working states.

The output modal content can be decomposed numerically by the method of MD based on the SPGD algorithm^[49,50]. The output beam profiles of the Raman laser at 1134 nm are captured at the focal plane by a CCD camera. Figure 5(a) shows the measured and reconstructed beam profiles at different power levels, respectively. The correlation coefficient $J$, defined as the similarity between actual and reconstructed beam profiles, remains above 0.99 in all results, indicating the high accuracy of MD. In addition, the purity of the ${\mathrm{LP}}_{11}$ remains around 80%, which means that the AIFG could achieve mode conversion effectively. Figure 5(b) shows the content of the ${\mathrm{LP}}_{01}$, ${\mathrm{LP}}_{11}$ modes and the other modes (${\mathrm{LP}}_{21}$ and ${\mathrm{LP}}_{02}$) at the highest power, from which we can see that in addition to the first two orders, the content of other modes is extremely low. For potential practical applications, the stability of output ${\mathrm{LP}}_{11}$ mode is also tested. Figure 5(c) exhibits the MD results, which are recorded every 2 min. The content of the ${\mathrm{LP}}_{01}$ mode and the ${\mathrm{LP}}_{11}$ mode remained comparatively stable within 20 min, with an average purity of ${\mathrm{LP}}_{11}$ mode of 82%. Furthermore, the system was stable with good repeatability, and none of the degradation of beam spots, spectrum, and power fluctuation was observed, even after the test time.

Thanks to the flexible mode control property of AIFG, the laser also possesses agile mode-switching capability. The switching time has been intensively studied. By placing a pinhole attached to a photon detector (PD), the detected intensity got changed once the spots changed, which means mode switching. The position of the pinhole should be adjusted carefully to make it close to the center of the beam profile, so that intensity changes can be detected when the mode changed. By capturing the rising edge of the temporal trace, the switching time from ${\mathrm{LP}}_{01}$ to ${\mathrm{LP}}_{11}$ mode is about 0.8 ms, as shown in Fig. 6(a). Likewise, the switching time from ${\mathrm{LP}}_{11}$ to ${\mathrm{LP}}_{01}$ mode can be obtained by capturing the falling edge of the temporal trace, which is still about 0.8 ms, as shown in Fig. 6(b). The switching time is mainly determined by the transit time of the acoustic flexural wave propagating through the acousto-optic coupling region of the AIFG, which could be further reduced if the acousto-optic coupling length was reduced.

In Table 1, a performance comparison of RRFLs aimed at generating HOMs is presented. In this table, we mainly take into account the method of achieving HOMs, maximum output power, and the slope efficiency in the references used in this paper. The comparison shows that the proposed RRFL in this paper has a relatively high slope efficiency and more than 2 orders of magnitude improvement in power level. The mode purity and switching time are not listed in Table 1, as most of other studies did not give the results.

In conclusion, we presented the experimental demonstration of swift and adaptive mode conversion between ${\mathrm{LP}}_{01}$ and ${\mathrm{LP}}_{11}$ modes in RRFL by applying an AIFG in the half-open cavity. The AIFG is a fast mode converter, and the switching time is as short as 0.8 ms. The maximum output power of the ${\mathrm{LP}}_{01}$ and ${\mathrm{LP}}_{11}$ modes is 96.6 and 93.8 W, respectively, with a high efficiency of over 90%. The MD technique based on SPGD algorithm is applied to calculate the mode purity, which is up to 82% for the ${\mathrm{LP}}_{11}$ mode. To our best knowledge, it is the first time that mode switching in RRFL using MD has been analyzed, and it is also the highest power of ${\mathrm{LP}}_{11}$ mode generated from RRFL. This experiment breaks through the power level that the AIFG can withstand directly rather than through the MOPA structure and also proves its superior performance at the hundred-watt level. The system has the advantages of small insertion loss, fast conversion speed, and good robustness, which gives it good potential in application. To achieve higher-order mode control and higher output power, further optimization of the laser system will be demonstrated. This work may lay a foundation for fiber lasers with special temporal and spatial characteristics for applications in the fields of mode division multiplexing, imaging, and laser material processing.