Generation of off-axis phased Gaussian optical array along arbitrary curvilinear arrangement

Vortex beams, which possess orbital angular momentum (OAM), are gaining significant interest because of their potential applications in optical communication  [1], [2], [3], imaging [4], and processing applications  [5], [6]. Moreover, due to the property of OAM, optical tweezers  [7], [8] and the trapping [9], [10], [11], [12], [13] and guiding of cold atoms  [14] are also being investigated widely. Recently, in contrast to classical vortex beams (which contain a single-phase singularity), optical vortex arrays (OVAs) with complexly structured light fields have garnered attention because they contain multiple singularities, which can facilitate more flexible and intricate applications [15], [16], [17]. In previous studies, researchers investigated many multi-singularity modes, such as Airy modes [18], [19], Laguerre–Gaussian modes  [20], [21], Ince–Gaussian modes  [22], [23], and Hermite–Gaussian modes [24], for which traditional vortex beams were selected as component beams to manipulate the vortices. In our previous work, we proposed a composite optical vortex array with multi-singularity properties, which was based on the coaxial interference of Bessel–Gaussian (BG) beams [25].

However, in OVAs, the radius of the bright ring obtained using traditional methods is proportional to the topological charge (TC)  [26], [27]. As a result, it is inconvenient to overlap two or more traditional vortex beams to create complicated optical fields. Based on the superposition of two concentric perfect optical vortices, Ma et al. presented a novel optical vortex array known as the circular optical vortex array [28]. Li et al. proposed a method to generate vortex arrays along arbitrary curvilinear arrangements, such as circles, squares, and pentagrams, based on the coaxial interference of two width-controllable component curves [29]. In addition, optical vortex lattices containing multiple independent vortex beams have attracted considerable interest because they provide additional information and modulated dimensions  [30], [31], [32], [33].

These advantages have resulted in the widespread use of vortex beams in several fields. However, owing to the intrinsic beam expansion and power loss that occur during propagation, which cannot be ignored, the power of experimentally generated vortex beams has remained relatively low and cannot satisfy the requirements of practical applications [34]. Coherent beam combination (CBC) has been proposed to generate higher-power OAM beams, which can surpass the physical limits of single-channel laser beams  [35], [36]. By utilizing the coherent combination of a laser array technique and helical phase approximation via a piston phase array, researchers have proposed systems for generating high-power beams possessing controllable OAM, which can overcome the power limitations of conventional vortex phase modulators and single beams  [37], [38], [39], [40], [41]. Furthermore, on the basis of CBC technology, a method to generate a BG beam using a Gaussian beam array has also been reported  [42], [43], [44]. Moreover, through the reversal of Huygens Fresnel diffraction and using the greedy algorithm, a novel approach to generate a spatially distributed OAM beam array has been presented [45], in which the arrangement of the multiple fundamental Gaussian beams at the initial plane can be determined.

However, most of the high-power beams studied at present can only be arranged along circular curves. Therefore, in this study, we generated a phased Gaussian optical array (PGOA) that can be arranged along arbitrary curves, and we systemically analyzed the generation conditions and modulation properties of this beam. In the proposed approach, two concentric QPVBs are superimposed to construct a complex vortex optical field exhibiting multi-singularity, in which the width, shape, TCs, and phase difference are all adjustable. This field is referred to as a quasi-perfect optical vortex array (QPOVA). Furthermore, the energy flow distribution and transmission characteristics of the POVA are studied. The proposed POVA is expected to inspire the way for new applications, such as multi-target optical manipulation and large-capacity space optical communication.

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