2 Principle of mode control with the PL

The PL is an all-fiber passive optical device that connects a bundle of single-mode fibers (SMFs) and a multi-mode fiber (MMF)^[ Reference Lu, Chen, Liu, Jiang, Yang, Zhou, Zhang, Chai and Jiang ^{25 ]}. The structure of the 5×1 PL is shown in Figure 1. As the number of PL input ports increases, the complexity of fabrication correspondingly escalates. In order to optimize the mode evolution process of the PL, it is necessary to strictly control two structural parameters. The first is the lateral dimension, in which the cladding of SMFs is required to corrode from 10/125 to 10/90 μm, and the inner diameter of the low-index capillary tube is reduced to 30 μm with the double tapering process. The second is the longitudinal dimension, in which the long taper region (20 mm) of the 5×1 PL facilitates highly efficient mode evolution.

Figure 1 Structure of the 5×1 photonic lantern using the double tapering method.

The unique structure of PLs enables a mode-selective operation. The PL can be effectively approximated as an optical linear converter that facilitates the transition between the FM and HOMs. This conversion process can be mathematically represented using a transmission matrix. The relationship between the input and output ports of the PL is expressed as follows: $Av=u$ , where ${v}^T=\left[{v}_1{e}^{j{\theta}_1},{v}_2{e}^{j\theta 2},\cdots, {v}_i{e}^{j\theta i}\right]$ is the column vector describing the optical field of the SMFs ( ${v}_i$ , ${\theta}_i$ represent the amplitude and phase of the ith input ports, respectively), ${u}^T=\left[{u}_1{e}^{j{\theta}_1},{u}_2{e}^{j{\theta}_2},\cdots, {u}_n{e}^{j\theta n}\right]$ is the column vector describing the optical field of the MMF ( ${u}_n$ , ${\theta}_n$ represent the amplitude and phase of the LP _nm mode, respectively) and A is the transmission matrix of the PL:

$$\begin{align*}A=\left[\begin{array}{@{}c@{\ \,}c@{\ \,}c@{\ \,}c@{\ \,\kern1pt}c@{}}0.4{e}^{i\cdot \left(0\pi \right)}& 0.4{e}^{i\cdot \left(0\pi \right)}& 0.4{e}^{i\cdot \left(0\pi \right)}& 0.4{e}^{i\cdot \left(0\pi \right)}& 0.4{e}^{i\cdot \left(0\pi \right)}\\ {}0.6{e}^{i\cdot \left(-0.3\pi \right)}& 0.2{e}^{i\cdot \left(-0.3\pi \right)}& 0.2{e}^{i\cdot \left(-0.3\pi \right)}& 0.5{e}^{i\cdot \left(0.7\pi \right)}& 0.5{e}^{i\cdot \left(0.7\pi \right)}\\ {}0& 0.5{e}^{i\cdot \left(-0.3\pi \right)}& 0.5{e}^{i\cdot \left(0.7\pi \right)}& 0.3{e}^{i\cdot \left(-0.3\pi \right)}& 0.3{e}^{i\cdot \left(0.7\pi \right)}\\ {}0.25{e}^{i\cdot \left(-0.2\pi \right)}& 0.2{e}^{i\cdot \left(0.8\pi \right)}& 0.2{e}^{i\cdot \left(0.8\pi \right)}& 0.1{e}^{i\cdot \left(-0.2\pi \right)}& 0.1{e}^{i\cdot \left(-0.2\pi \right)}\\ {}0& 0.3{e}^{i\cdot \left(-0.2\pi \right)}& 0.3{e}^{i\cdot \left(0.8\pi \right)}& 0.5{e}^{i\cdot \left(0.8\pi \right)}& 0.5{e}^{i\cdot \left(-0.2\pi \right)}\end{array}\right]\end{align*}$$

The specific modes (LP₀₁, LP_11e, LP_11o, LP_21e and LP_21o modes) can be selectively generated by adjusting specific amplitudes and phases of the input ports. For example, when input ports are setting the same amplitudes and phases, ${v}^T=\left[0.4{e}^{i\cdot \left(0\pi \right)},0.4{e}^{i\cdot \left(0\pi \right)},0.4{e}^{i\cdot \left(0\pi \right)},0.4{e}^{i\cdot \left(0\pi \right)},0.4{ie}^{i\cdot \left(0\pi \right)}\right]$ . The highly pure LP₀₁ mode is obtained in the output port. When the input port information with specific amplitude and phase is applied respectively, ${v}^T=\left[0.6{e}^{i\cdot \left(-0.3\pi \right)},0.2{e}^{i\cdot \left(-0.3\pi \right)},0.2{e}^{i\cdot \left(-0.3\pi \right)},0.5{e}^{i\cdot \left(0.7\pi \right)},0.5{e}^{i\cdot \left(0.7\pi \right)}\right]$ . Those beams with the same phase will undergo a specific coupling process to enhance the LP₁₁ mode^[ Reference Lu, Jiang, Chen, Jiang, Yang, Zhou, Zhang, Zhang, Chai, Yang and Liu ^{26 ,} Reference Lu, Jiang, Xiao, Chen, Jiang, Chai, Yang, Ding, Zhang, Zhang, Zhou and Liu ^{27 ]}.

The evolution process of the beam in the PL is numerically simulated based on the beam propagation method (BPM) algorithm. Figure 2 shows that different input port energy coupling occurs along the direction of propagation in different cross-sections (A–E). After entering the waist region, the light evolves into a corresponding supermode, and then it is transferred into the output port. As an example, we monitor the content of the LP₀₁ and LP₁₁ modes through the 5×1 PL structure. Figure 3(a) shows that the content of the LP₀₁ mode of SMFs gradually decreases along the long taper region, and is steadily maintained at 92% in the MMF. When the LP₁₁ mode is regarded as the control target, as shown in Figure 3(b), the content change of the LP₀₁ mode presents a similar situation in the taper region. Finally, the content of the LP₁₁ mode is stable at about 88%.

Figure 2 The mode evolution of the 5×1 photonic lantern varies with the taper ratio.

Figure 3 The modal content evolution process in the 5×1 photonic lantern varies with the length of the taper region. (a) Targeting the LP₀₁ mode output. (b) Targeting the LP₁₁ mode output.

3 Experimental setup

The experimental setup of the mode-adaptive control system is shown in Figure 4. The seed is a single-frequency laser operating at a wavelength of 1064 nm. The white noise source (WNS), driven by the radio frequency high-voltage amplifier, applies electrical signals to a LiNbO₃ electro-optic modulator (EOM), thereby achieving spectrum broadening to enhance the SBS threshold. The splitter can divide light into five equal parts. The phases of input SMFs are controlled by the phase modulators (PMs). The delay lines (DLs) are used to match the optical path difference (OPD) of each input port. The isolators (ISOs) are fusion spliced with band-pass filters (BPFs), and this setup simultaneously filters out background spectral noise and isolates the reverse power.

Figure 4 The mode-adaptive control system based on a 5×1 photonic lantern.

The amplification system adopts two-stage amplification technology. In the preamplifier systems, the output beam of the PL serves as the seed for the amplifier. The 976 nm laser diodes (LDs) are combined to pump 30/250 μm gain fiber (NA ~ 0.066) via a (6 + 1) × 1 pump and signal combiner, and achieve a total output power of 40 W. The 915 and 981 nm semiconductor lasers are used to precisely control the pump absorption coefficient. The absorption coefficient of the gain fiber for pump light can be adjusted by combining 915 and 981 nm pumping, which allows the thermal load per meter of the gain fiber to be controlled within a suitable range. Therefore, the fiber length is also controlled within a suitable range, which allows for simultaneous suppression of the transverse mode instability (TMI) and SBS effects at kW-level output power^[ Reference Wen, Wang, Yang, Zhang, Xi, Wang and Xu ^{28 ]}. The main amplifier consists of a 42/250 μm Yb-doped fiber (NA ~ 0.069) and a (6 + 1) × 1 signal-pump combiner. Finally, a quartz block holder (QBH) embedded with cladding power strippers (CPSs) is fused for simultaneously filtering excess pump light and outputting the beam.

The beam is received by an M ² analyzer and a charge-coupled device (CCD) for the purpose of beam quality evaluation. The power-in-the-bucket (PIB) detected by a photonic detector (PD) is used as the evaluation function of the stochastic parallel gradient descent (SPGD) algorithm. By measuring the corresponding change in intensity at the source, an approximate gradient with respect to the phase of each element can be calculated. The controller has an execution speed of more than 500,000 times per second. Thus, the phase-locked loop convergence can be completed within less than 100 iterations^[ Reference Ze, Liu, Zhang, Hu, Ding, Yan, Zhang, Zhou and Liu ^{29 ]}.

When the laser system operates at high power, the LMA active fiber inevitably excited excessively more HOMs. For gain fiber with a core diameter of 42 μm, over 20 modes can be supported. We employed the method of bending the fiber to reduce the number of modes in the LMA fibers^[ Reference Wang, Chen, Zhu, Li, Yin, Wu, Li, Cai, Fu, Qin and Wei ^{30 ]}. The FM and HOM losses with respect to the bending radius are illustrated in Figure 5. As the bending radius decreases, the bend loss of both the FM and HOM increases nonlinearly. Notably, the HOM shows a stronger sensitivity to the physical deformation of fiber bending, and its bending loss demonstrates a more pronounced increasing trend compared to lower-order modes. Controlling the bending radius of LMA fibers serves dual objectives. Firstly, the bend losses of LP₀₁, LP_11e, LP_11o, LP_21e and LP_21o modes maintain a low level, thereby enabling highly efficient and high-purity signal transmission. Secondly, other HOM losses are large enough to have more efficient mode control of the PLs. As depicted in Figure 5, when the bending radius is 7 cm, the bending loss for the LP₂₁ mode amounts to 0.02 dB/m, while that of the LP₀₂ mode reaches 1.36 dB/m. In the experiment, we choose the bending radius of 7 cm, ensuring that only LP₀₁, LP_11e, LP_11o, LP_21e and LP_21o modes can be transmitted in the gain fiber. This approach of employing fiber bending to reduce the number of modes not only reduces mode crosstalk but also enables more precise controlling of the target mode.

Figure 5 Bend loss of different modes versus bend radius.

For the high-power mode-adaptive control system, the requirements of a high SBS threshold and high coherence of the input ports must be met simultaneously. In order to improve the coherence of each input port, it is essential to utilize a seed laser with narrower spectrum width. However, the reduction in the spectrum linewidth leads to decrease of the SBS threshold, which consequently limits the ability to amplify the output power. Figure 6 shows the SBS threshold of the fiber amplifier within mode control adaptive systems measured at various spectral widths. When the output power exceeds the SBS threshold, a pronounced Stokes peak emerges in the spectrum, as shown in Figure 6(a). The SBS threshold conversion with the spectral width is shown in Figure 6(b). As the spectral width increases, the SBS threshold exhibits a nonlinear increase until the SBS threshold exceeds 1 kW with the spectral width of 18 GHz.

Figure 6 Comparison of the SBS threshold of different 3 dB linewidths. (a) The spectrum of the SBS effect occurring with the different spectral widths. (b) The SBS threshold versus the spectral width.

However, the corresponding coherence lengths of each input port are only 16 mm with the spectrum width of 18 GHz. To ensure the optical lengths of each input port are precisely confined within the coherence length, it is necessary to employ a high-precision optical metrology technique to measure the fiber length. We utilized a picosecond pulsed laser source (repetition frequency of 9 MHz, pulse width of 1 ns) to measure the OPD of each input port, as shown in Figure 7(a). By analyzing the pulse time delays on the oscilloscope, the differences in the fiber length between the input ports can be measured. Before compensation, Figure 7(b) shows that the minimum OPD is 259 ps, corresponding to the fiber length difference of 5.38 cm. Based on the results, we trimmed the fiber length of each input port, ultimately controlling the OPD within 20 ps, corresponding to the fiber length difference of 4.3 mm, as shown in Figure 7(c). This value falls within the adjustable range of the DLs, ensuring precise phase matching and optimal system performance.

Figure 7 The results of measuring and compensating the OPD. (a) Experimental setup for measuring the OPD of the photonic lantern. OPD among five input ports fiber of the photonic lantern (b) before compensation and (c) after compensation.

Through the implementation of fiber bending, spectral linewidth optimization and OPD adjustment, we demonstrate a mode-adaptive control system based on a 5×1 PL, which enables effective mode control and power scaling in 42-μm LMA fiber lasers with a minimized number of control ports.

4 Results and discussion

When the FM is designated as the control target mode, the output characteristics of the fiber amplifier based on the PL are investigated first. The output power conversion with the pump power is shown in Figure 8(a). As the pump power increases, the output power exhibits a linear and stable increase. Finally, more than 1 kW output power is achieved with an optical conversion efficiency of 73%. For conventional fiber lasers, further power amplification may be limited by SBS and TMI. However, in a PL-based fiber laser, the SBS threshold in the amplifier can be well suppressed by tuning the seed linewidth and the optical path of the input ports. Meanwhile, the high-frequency disturbance in the PL will set up a fast refreshed multi-mode interference optical field to disrupt the thermally induced refractive index in the gain fiber. So, the PL-based fiber laser will suppress the TMI well in LMA fiber. In Figure 8(b), a pure output spectrum without nonlinear characteristic peaks is presented with different output powers. Meanwhile, the detailed spectra of the signal laser at different pump powers are also measured and are shown in Figure 8(c).

Figure 8 Output properties of the fiber amplifier based on the 5×1 photonic lantern. (a) Output power and efficiency versus pump power. (b) Spectra at different output powers. (c) Detailed spectra at different output powers.

The SPGD algorithm adaptively controls the phase of the input port fiber by utilizing the maximum PIB as the evaluation function. At the maximum output power, the on-axis signal of the PD changing over time is as shown in Figure 9(a). Before the control is turned on, the output field is generally a superposition of the FM and the HOMs, and the voltage signal exhibits significant fluctuations. After the control is turned on, a stable high-level signal is received by the PD. Figure 9(b) shows the beam quality and the content of LP₀₁ mode of the output laser versus the output power. The M ² factor of the seed laser is 1.28; after passing through the pre-amplification it is reduced to 1.47. Then at the highest output power of 1007 W, the M ² factor is 1.97. As the pump power increases, the modal content of the LP₀₁ mode attenuates from 96% to 86%. The complete mode decomposition effect is evaluated by the numerical method^[ Reference Shapira, Abouraddy, Joannopoulos and Fink ^{31 ]}. The mode decomposition results are shown in Figure 9(c). The modal content of the LP₀₁ mode is 86.46% with the output power of 1 kW. The correlation coefficient between the measured spot and the reconstructed spot is 0.9906. Furthermore, the system demonstrates the capability to generate HOMs. When the target mode is set to the LP₁₁ mode, the output characteristics of the fiber amplifier are as shown in Figure 9(d). The LP₁₁ mode output was achieved at the output power of 219 W with a high optical conversion efficiency of 75%. However, this system creates more intense mode competition after the amplifier, and then the LP₁₁ modal content caused a drop from 90% to 75%.

Figure 9 Beam profiles of the 5×1 photonic lantern amplifier. (a) PD signal over time when the SPGD was turned off and on. (b) Beam quality and mode content versus the LP₀₁ output power. (c) Mode decomposition of the obtained beam. (d) Output power and mode content of the LP₁₁ mode versus the pump power (insets: beam profiles).

There has always been an extreme challenge in achieving high-power HOM output in LMA fiber lasers. As shown in Table 1, the previous work of other groups has been focused on mode-selective operation in the fiber laser with core diameters below 25 μm. The previous work of our group only achieved near-FM output at the kilowatt level, but was not capable of controlling high-order modes^[ Reference Ze, Liu, Zhang, Hu, Ding, Yan, Zhang, Zhou and Liu ^{24 ]}. Lu et al. ^[ Reference Lu, Jiang, Chen, Jiang, Yang, Zhou, Zhang, Zhang, Chai, Yang and Liu ^{26 ]} only achieved a 50-W HOM output. In this paper, for the first time, we have simultaneously realized a kilowatt-level FM and a hundred-watt-level HOM in a 42-μm LMA fiber laser.

Table 1 Output performances of mode-selective operation in a fiber laser with different methods.

We observe that, despite the PL exhibiting good mode control ability for the LMA fiber amplifier, the beam quality of the LP₀₁ mode and the purity of the LP₁₁ mode appeared to undergo a certain degradation phenomenon with the increase of pump power. The decrease of beam quality and mode purity is primarily attributed to the transverse spatial-hole burning effect and the spatial mode competition in the LMA fiber amplifiers. In the next step, the implementation of specialty fibers, such as tapered fibers, could be strategically employed to mitigate the transverse spatial-hole burning effect and consequently enhance the mode purity^[ Reference Napartovich and Vysotsky ^{37 ,} Reference Jiang and Marciante ^{38 ]}.