As a classically structured light beam, the orbital angular momentum (OAM) beam has gained growing attention in a variety of applications, such as optical communication^[1–5], particle manipulation^[6,7], beam shaping^[8,9], and optical tweezers^[10,11]. Generally, the OAM beam has a hollow ring structure in intensity distribution and a helical phase structure, which is described by exp(ilφ), where φ is the azimuthal angle and l corresponds to the topological charge (TC) of the corresponding OAM^[12–14]. Owing to these unique physical properties, the OAM beam holds promising prospects both in photonic technologies and physical study^[15,16]. Accordingly, the technique of generating the OAM beam has inspired researchers to develop it intensively^[14,17–21]. For instance, the OAM beam can be generated effectively by utilizing specially designed optical devices, such as spatial light modulators (SLMs)^[22–24], metasurfaces^[25,26], and Dammann gratings^[27]. As an attractive method, this technique can transform a single OAM beam into an OAM beam array as well. Similarly, the nematic cholesteric liquid crystals exhibit advanced properties for customizing the OAM beams with multiple OAM modes^[28]. In addition, the interference of multiple plane waves can also generate exotic light beams, which can carry an OAM network^[29–31]. Despite the advantages of these methods, the power scaling and OAM mode-switching capacity are limited^[14,32], which are urgently demanded in many fields. On the one hand, the high-power OAM beam is required in materials processing^[33] and laser ablation^[34]. On the other hand, fast OAM mode switching is very important to optical communications^[35], which may determine communication capacity and speed. Therefore, it is necessary and urgent to generate high-power and mode-tunable OAM beams.

To address these challenges, the optical phased array (OPA) based on a coherent fiber laser array can provide a promising solution for both power scaling and fast OAM mode switching^[36,37]. For one thing, the output power can be scaled while maintaining excellent beam quality by the coherent beam combining (CBC) of the OPA^[38–40]. Recently, the output power has been scaled to be over 10 kW^[41]. For another thing, the OPA could be performed as a digital laser source^[36]. The fast OAM mode switching can be realized with the electric phase modulators^[37], and the response frequency is over several gigahertz. The technique of generating the OAM beam with an OPA via the CBC technique has been significantly investigated^{[36,37,42–45]}. Both a single OAM beam and the OAM beam array could be generated effectively with the OPA^[46]. Especially, researchers have presented the high-power OAM generation with 61 femtosecond fiber amplifiers^[36]. The OAM modes could be switched from −1 to −3. However, when the output power reached hundreds of watts, the intensity distributions of the OAM beam would severely degrade due to thermal effects^[36]. Despite recent advancements, the output power of generated OAM beams remains much less than 1 kW. Additionally, the bulky size of existing high-power CBC systems limits their practical applications. Therefore, we are motivated to further generate the OAM beam with higher output power.

In this paper, a high-power OPA is presented via an internal phase-sensing technique, which could directly emit the high-power mode-programmable OAM beam with flexible phase control. Additionally, the system’s compact design enables it to function as a packageable OAM beam emitter. In the experiment, when the dynamic phase noise is compensated based on the stochastic parallel gradient descent (SPGD) algorithm^[47,48], the programmable liquid crystals (LCs) are applied for synchronously shifting the piston phase of the OPA^[45,49]. As a result, we present (to our best knowledge) the first effective generation of over 1.5 kW mode-programmable OAM beam in a continuous-wave domain. The TC values of the corresponding OAM can be switched from −1, +1 to −2 in real time. More importantly, the OAM beam copier is exhibited, and the generated single OAM beam can be easily modulated to be an OAM beam array by changing the fill factor of the OPA, which could yield promising prospects in optical communication^[3–5] and beam shaping in nonlinear fields^[8,9]. Meanwhile, further power scaling, and mode-switching speed are fully discussed as well. Owing to the advantages of both having high power and mode switching in real time, the generated OAM beam can be beneficial to a variety of applications. This work could pave the way for generating high-power structured light beams and advancing their applications.

Generally, an OPA refers to a system that uses the laser array as the carrier to flexibly control the individual phase of optical elements^[50,51], which could manipulate the combined beam pattern in the far field. The OPA has attracted growing attention and is widely applied in a range of applications, such as lidar^[50,52], beam steering^[51,53], and optical communications^[54,55]. Different from the on-chip OPA^[50–54], the OPA that is based on a coherent fiber laser array has a promising prospect for forming the high-power OAM beam emitter^[36,43–45]. In practice, to generate the OAM beam with an OPA, the piston phase of each element in the source plane is modulated to fit a whole helical phase structure^[36,43–45]. When the array beams propagate to the far field, which is larger than the Rayleigh distance, the initially separated input beams would completely overlap and become perfectly coherent to form the OAM beam with a vortex phase structure^[43]. However, real-time phase control is difficult in a practical high-power CBC system. Moreover, the current methods detect the phase based on the external phase-sensing technique. However, the system is bulky due to using large-aperture optical devices. Additionally, thermal effects can significantly impact phase control, which limits their practical applications^[49]. Owing to the advantages of the internal phase-sensing technique, which can effectively suppress dynamic phase noise and enable the programmable LCs to form desired phase structures^[45,49], the high-power OAM beam can be easily generated through effective thermal management. Meanwhile, the compactness of the internal phase-sensing system allows for constructing a packageable OAM beam emitter. The geometric construction of the emitted OPA for OAM beam generation in the source plane is shown in Fig. 1 (the elements are arranged in a clockwise direction). The color presents the piston phase. We assume that there are M elements in the laser array. Thus, we can obtain the combined optical fields in the far field in cylindrical coordinates according to Ref. [44], as shown in Eq. (1), Uarray(ρ,θ)=kMA0w022fexp(−ρ2k2w024f2)∑T=−∞∞il−TM−1Jl−TM(ρkRf)⁢exp[i(l−TM)θ],(1)where A0, ω0, k, f, Jl(x), and R account for the amplitude, waist width, wave vector, the focus length of the lens, the modified Bessel function, and the radius of the laser array, respectively. We find that the combined optical field is a complex Bessel vortex optical field, which can be formed by the coherent superposition of the vortex optical field carrying OAM of l−TM, where T is an integer and presents the OAM order.

To present the OAM beam generation, an experiment with a six-channel coherent fiber laser array was carried out. The setup is shown in Fig. 2. The seed laser (SL) is a single-clad ytterbium-doped polarization-maintained fiber laser with a central wavelength of 1064 nm, while the linewidth is ∼10GHz. The laser from the SL is coupled into a pre-amplifier (PA), and the power is scaled to 400 mW, and then is split into six channels by a fiber splitter (FS). Following that, each channel laser is coupled with a LiNbO3 phase modulator (PM) and an electric variable delay line (VDL). The response frequency of the PM is about 150 MHz, which can be used for locking the dynamic phase noise at a fast speed. The VDL is applied for compensating for the optical path difference (OPD) among the elements of the OPA, which could compensate for the OPD with a precision of 30 µm. Then, each laser channel is scaled to be about 250 W by a polarization-maintained cascaded fiber amplifier (CFA). After that, the high-power laser from the CFA is collimated by the collimator (CO). The diameter of each collimated element is about 10 mm, while the distance between the adjacent collimated elements is 40 mm.

To form a high-power OPA with a high fill factor, all the collimated elements are divided into two parts by a small splitter (SP) array; the reflectivity of the SP is 99.9%. Then, the reflected part is expanded by a beam expander (BE) array. The diameter of each expanded element is about 38 mm. The expanded elements array is arranged by the BEs to form a regular hexagonal OPA, which can emit the high-power OAM beam. The distance between the adjacent elements is 40 mm. Thus, the fill factor is calculated to be 95% based on a ratio of 38 mm/40 mm^[56].

As for the phase control, to avoid the large optical devices and make the system compact and packageable, the transmitted part is formed from the sampled elements array. The sampled elements array transmits through the programmable LCs and is focused by a lens (L1). Finally, the focused laser is truncated by a pinhole with a diameter of 100 µm and detected by a photodetector (PD) for phase-error detection. The signal from the PD is used as the power in the bucket (PIB) metric. One part of the signal is sent into the field programmable gate array (FPGA) controller for extracting the phase-error information, which could be used for driving the PMs to actively lock the phase noise. Another part is detected by the oscilloscope for observing the phase control performance. The experiment was carried out in four steps. First, the VDL is driven to compensate for the OPD among the elements of the emitted OPA according to Ref. [57]. As a result, the intensity signal detected by the PD would fluctuate to the maximum after optimizing each VDL’s position. Second, the dynamic phase noise was detected and locked by the PMs based on the signal of the PD. Third, based on interference measurements^[49], the LC driver drove LCs to compensate for the phase differences among the emitted elements array; fourth, the LCs were dynamically driven in real time to shift piston phases of the emitted elements array to generate OAM beams^[45].

The process of dynamic phase noise compensation could be presented with the value of the PIB, as shown in Fig. 3, which was detected by the PD. When the FPGA controller was turned off, the PIB changed randomly due to the thermal and environmental noise. The normalized average value was around 0.20, as shown in Fig. 3(a). In comparison, when the FPGA controller was turned on and performed the SPGD algorithm, the PIB was stably locked to be nearly at the maximum, as shown in Fig. 3(b). The normalized average value was 0.93, which was 4.65 times that when the FPGA controller was turned off. As a result, the dynamic phase noise was locked effectively. The corresponding root mean square (RMS) of residual phase error was calculated to be λ/22. In addition, the power spectral density in the open loop (the FPGA controller was turned off) and closed loop (the FPGA controller was turned on) was calculated, as shown in Fig. 3(c). We can find that the phase noise of below 900 Hz had been compensated for efficiently.

To observe the OAM emitting, a high reflectivity mirror (HRM) is set in the emitting path to sample the high-power emitted OAM beam, as shown in Fig. 4. The reflectivity of the HRM is 99.9%. The reflected part is directly emitted to free space for power collecting, and the total power was measured to be 1523 W. The transmitted part is focused by another lens (L2) to form a far field, which has a large aperture with a focal length of 2 m. A camera (CCD) is set in the focus plane for observing the OAM beam generation.

We first drive the LCs to compensate for the phase differences among the emitted OPA based on interference measurements^[49], and then shift the emitted OPA phase with the same value, as shown in Fig. 5(a), which is equivalent to the case of l=0. Because the OPA elements have the same phase structures in the source plane, it is similar to the conventional CBC system. As we can see, the intensity profiles had a prominent central main lobe in Fig. 5(c). The PIB was calculated to be ∼42.6%, which was 44.9% in an ideal CBC system. Thus, the CBC efficiency was about 94.9%. Figure 5(b) shows the intensity profiles of the emitted OPA when the FGPA controller was turned off; the intensity profiles were dark. We can find that the brightness had been improved effectively after locking the dynamic phase noise.

We then drove the LCs to shift the emitted OPA phase with different values, which is equivalent to the case of l=−1 and +1, respectively. In detail, the phases of the emitted elements were shifted with π/3,2π/3,…,6π/3 in a clockwise direction when the l was −1, while those were 6π/3,5π/3,…,π/3 in a clockwise direction when the l was +1. The phase structures of the OPA in the source plane are shown in Figs. 6(a1) and 6(b1), respectively. As one can see, the high-power OAM beams were generated effectively, which had the doughnut intensity structures, as shown in Figs. 6(a2) and 6(b2). The intensity distribution was the same as the other when l was −1 and +1. The theoretical results are shown in Figs. 6(a3) and 6(b3), while the phase distributions are shown in Figs. 6(a4) and 6(b4). One can find that the experimental results were in a high degree matched with the theoretical results, which indicated that the phase control was efficient, and our system had the advantage of emitting the high-power OAM beam.

To tune the OAM beams with higher-order OAM states, the LCs were further driven to shift the emitted OPA phase with the larger phase step, which was equivalent to the case of l=−2,−3, respectively. In detail, the phases of the emitted elements were shifted with 2π/3,4π/3,…,12π/3 in a clockwise direction when l=−2, while those were 3π/3,6π/3,…,18π/3 in a clockwise direction when l=−3. The phase structures of the OPA in the source plane are shown in Figs. 7(a1) and 7(b1), respectively. As one can see that the generated OAM beams did not have the doughnut intensity structures, the intensity distributions were like the flower petal, as shown in Figs. 7(a2) and 7(b2). Owing to the large phase steps among the elements of the OPA, the intensity distribution would split. In addition, we also noted that when the TC was −3, there was no phase singularity in the generated OAM beam, as shown in Fig. 7(b4). According to Ref. [42], by generating the OAM beam with a TC of l, the element number in an OPA should be not less than 3l. Therefore, we should note that only six-element beams were applied for experimental presentation, which could not generate the OAM beam with a TC value larger than 2. To further expand the OAM modes, the element number should be increased.

Owing to the advantages of the internal phase-sensing technique, the OPA emitting system is detached from the phase detection system. The emitted OPA could be easily modulated in both the phase and element arrangement. Here, the fill factor of the OPA in the source plane was changed by using a diaphragm to adjust the element aperture. The fill factor was adjusted to 75%. Because the equivalent lateral displacement of the OPA in the source plane was increased, it resulted in the spread of the OAM spectrum^[46,58]. As a result, the generated OAM beam could be transformed into an OAM beam array^[45,46]. As an example, we shifted the phase of the OPA with a TC of −1. The phase structures of the OPA in the source plane are shown in Fig. 8(a), while the generated OAM beam array is shown in Fig. 8(b). The phase structure of the generated OAM beam array in the far field is shown in Fig. 8(d). One can find that there were multiple OAM beams with several phase singularities arranged in a hexagonal pattern. Because the newly generated OAM beams had the same phase singularities and OAM modes, they could be called the OAM beam copier^[46,59]. Compared to a single OAM beam with an isolated phase singularity, the generated OAM beam array had an OAM network with several phase singularities, which has a promising application in various fields, such as optical tweezers^[10,11] and quantum information processing^[59].

Based on the internal phase-sensing technique, the first (to our best knowledge) effective generation of over 1.5 kW mode-programmable OAM beam in a continuous-wave domain was presented. In addition, the generated OAM beam could be modulated with multiple dimensions. First, the output power was scaled to 1.5 kW based on the CBC technique. Second, the OAM modes could be tuned in real time with the programmable LCs. Here, the OAM modes were switched to −1, +1, and −2 for an experimental presentation. It should be noted that only six-element beams were applied in our experiment, which limited the tunable TC values. The TC expansion could be easily achieved by increasing the applied element number^[42]. Third, an interesting and significant result was presented. The OAM beam emitter could be performed as an OAM beam copier, and the generated OAM beam could be easily transformed into an OAM beam array, which could inspire promising applications in optical tweezers^[10,11] and optical manipulation^[6,7]. Additionally, the generated OAM beam array could form the optical vortex lattice (OVL), which can promote the development of photonic technologies, such as one-to-many OAM multicasting links^[60]. Owing to the advantages of the compact internal phase-sensing system, the OPA could be packaged as a compact OAM emitter for emitting high-power mode-programmable OAM beams. Furthermore, further power scaling and mode-switching speed should be discussed and analyzed. For further power scaling, on the one hand, the output power of each element of the OPA could be further improved. In the experiment, phase detection was enabled by several separated beam splitters, which could avoid the thermal effects. Thus, the possible thermal effects were not observed in our experiment, which meant that the output power could be further scaled by applying the higher-power CFAs. In recent years, the output power of a single polarization-maintained fiber laser has been scaled to 5 kW^[61], which may be used in our system. On the other hand, the element number of the OPA could be increased for power scaling, and the higher-order OAM beam could be generated as well^[42]. However, there are two challenges to face. First, the laser array would have a large cross section, raising practical difficulties for phase detection. Second, the phase control bandwidth would decrease as the element number increases, thus decreasing the CBC efficiency. To address the two challenges, the whole laser array can be divided into several subarrays, and the cascaded internal phase-sensing technique could be applied to improve the phase control bandwidth, and the compact system could easily be applied for phase detection^[62,63]. As for the mode-switching speed, in the experiment, the phase locking of the dynamic phase noise was enabled by the PMs with a response frequency of over 100 MHz, which has a promising prospect for phase control. However, the real-time piston phase shifting of the OPA for emitting the OAM beam was enabled with the programmable LC, which has a high damage threshold for power scaling. However, the modulation frequency was about 200 Hz, which may limit the switching speed. To switch the OAM modes with a higher speed, the LCs could be replaced with some optical devices, such as electro-optic (EO) polymers^[64]. Here, we should also note that the elements of OPA had the same polarization direction. As an important dimension of the beam, the polarization direction of the elements could be modulated for generating more complex optical fields as well, such as forming a radially polarized OPA or an azimuthally polarized OPA for emitting the vector vortex beams^[65,66]. Related research is being carried out.

In summary, a high-power mode-programmable OAM beam emitter was presented with an internally sensed OPA. In the experiment, when the dynamic phase noise was compensated for based on the SPGD algorithm, the programmable LCs were applied for synchronously shifting the piston phase of the OPA to generate the OAM beam. As a result, the first effective generation of over 1.5 kW mode-programmable OAM beam in a continuous-wave domain was presented. The TC values of the corresponding OAM could be switched from −1 or +1 to −2 in real time. Especially, the OAM beam copier could be performed. The generated single OAM beam could be easily modulated to be an OAM beam array by changing the fill factor of the OPA, which could find promising prospects in optical communication^[1–5], beam shaping^[8,9], and so on. Additionally, further power scaling, mode-switching speed, and constructing the more complex optical fields were fully discussed. Owing to the advantages of both having high power and mode switching in real time, the generated OAM beam can be beneficial in a variety of applications that refer to the OAM beams. This work could open a path for generating high-power structured light beams and advancing their applications.