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Abstract
We report an experimental study on transmission of orbital angular momentum mode in antiresonant fibers generated with a dedicated all-fiber optical vortex phase mask. The vortex generator can convert Gaussian beam into vortex beams with topological charge l = 1. Generated vortex beam is directly butt-coupled into the antiresonant fiber and propagates over distance of 150 cm. The stability and sensitivity of the transmitted vortex beam on the external perturbations including bending, axial stress, and twisting is investigated. We demonstrate distortion-free vortex propagation for the axial stress force below 0.677 N, a bend radius greater than 10 cm.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical vortex (OV) beams feature wavefront rotating azimuthally around its optical axis and forming a helical structure in three-dimensional space [1]. The OV beam has phase singularity at its center; consequently, its transverse intensity exhibits a doughnut-like distribution. OV beam with its phase characterized by the term exp(ilα) caries an orbital angular momentum (OAM) of lh/2π per photon (where l is the topological charge of the beam, α defines the azimuthal angle and h is Planck’s constant) [2]. The introduction of the OAM-carrying beams gave rise to the new active field of singular optics and concept of structured light [2,3] which advanced the basic knowledge of its fundamental properties and generated numerous novel applications [3,4]. The latter include e.g. Stimulated emission depletion (STED) microscopy [5,6]; optical trapping and manipulation [7–10]; laser micromachining [11]; and optical vortex coronagraph in astronomy [12,13]. Equally, the OAM-carrying beams also have significantly contributed to optical communication [14,15], particularly, using OAM for data signal transmission allows increasing the capacity of the communication links.
There is a need for efficient generation and stable transmission of OV beams to further develop those practical applications. For that purpose, many studies have been conducted using both free-space bulk-optics such as q-plates [16], spatial light modulators [17], spiral phase mirrors [18] and spiral phase plates (SPP) [19]. These approaches use bulk components well suited for applications where reconfiguration of vortex beam or imaging system are required and compact integration is not a main issue [5–10]. The fiber optics-based platform requires compact all-fiber votex beam generators easy to integrate in stable all-solid system resistant to vibration and other environmental perturbations [20]. Recently a few methods of OV beam generation in fiber system has been proposed using few mode fibers and microbend grating [21], long-period fiber gratings (LPFGs) [22,23] and fiber mode selective coupler (FMSC) [24,25]. A micro-bend grating and polarization controller was used to excite LP11 modes in a 20 m long sample of custom made few mode fiber [21]. A tilted LPFG inscribed in a two-mode fiber allows to generate linearly polarized OV modes [22]. OV mode generation in the all-fiber system composed of several polarization controllers, mode stripper and a pair of LPFGs inscribed in four mode fiber was demonstrated [23]. A successful implantation of OV beam generation based on development of mode selective couplers with fusion splicer composed of tapered input single mode fiber and dedicated few mode fiber was also demonstrated [24,25]. Control of tapering and length of fused area allow engineering of mode coupling. All above fiber systems based on LPFG and FMSC technique are relatively complex, well suited only to narrow wavelength bandwidth and often require active control of their performance.
Optical fibers are an important transmission medium of light, but the standard step-index optical fiber cannot maintain the propagation of OV beams. Instead, specific fiber designs have been studied theoretically and experimentally to generate and transfer vortices [26,27]. One of the most efficient approaches is based on the fibers designed with a high-index annular core, so-called ring-core fibers (RCF). So far, several variations of RCFs have been developed. The first version of RCF reported in 2009 was shown to generate and propagate OV beams over a distance greater than 20 m [28]. A few years later, researchers reported a significant increase of propagation distance reaching to a km-long fiber [29] as well as on the number of OAM states supported (up to 36 OAM states) [30]. In addition, inverse-parabolic graded-index fibers were designed to make the refractive-index transition inside its ring-like profile smoother [31]. Although this fiber provides an easier coupling with free-space OV beams than other RCFs, it is limited in the number of supported OAM modes. It should be noted that these works usually adopt small-size high-contrast-index RCFs, which will result in a small mode effective area and, consequently, an undesired large nonlinear coefficient. Moreover, a small-size high-contrast-index structure is also not conducive to fiber fabrication and mode excitation.
Recently, the development of microstructured fibers (MFs) and photonic crystal fibers (PCFs) has offered additional flexibilities in designing fiber structures for OV transmission purposes. An annular-core PCF (AC-PCF) design often has a big center air-hole surrounded by the glass ring and a cladding consisting of several surrounding air-hole rings, allowing OAM modes to propagate [32,33]. Stable propagation of OAM beams along AC-PCF has been experimentally demonstrated over a wavelength range from 805 to 845 nm [34]. However, most studies reported on OAM fibers are numerical, and rarely designed fibers have been fabricated.
Very recently, hollow-core, antiresonant (AR) fibers has gained substantial attention as a mean for low attenuation, broad bandwidth light guiding [35]. The light guiding in an AR fiber is based on inhibited coupling between the core and cladding modes, not on the photonic bandgap mechanism. As a result, single mode operation can be maintained for relatively large core diameters (50 µm and more) without periodic photonic crystal structure in the cladding. Subsequently, very broadband transmission widows can be obtained over visible and infrared ranges, even in the spectral regions where typical material for fiber fabrication has high losses. Large-core silica-based AR fibers are considered for application in telecommunication, optofluidic systems, gas sensing, and ultrashort pulses delivery [35–37]. Until now, however, AR fibers have not been used for OAM beam delivery. Only very recently polymer AR fibers were considered for OAM generation and transmission in THz range using fiber twisting [38].
In this paper, we report on direct excitation and propagation of OAM mode in AR fiber. The fiber-based vortex generator composed of two nanostructured gradient index micro-optical components for beam shaping and collimating/focusing that were designed and developed in-house. This compact device can generate an OV beam with a very low divergent angle allowing efficient coupling into AR fibers. The possibility of stable transmission of optical vortex beam in the straight air core AR fibers is demonstrated experimentally. However, it is well known that the light transmission in the optical fiber can be affected by external factors such as lateral force or/and bend inducing birefringence, mode coupling and losses [39–42]. Such factors could be particularly detrimental to stability of complex modal structures such as vortices. Therefore, in this work the effect of external stimuli, namely, lateral force, bending and twist of the AR fiber on structural stability of the transmitted vortex beam is investigated.
2. Description of the butt-coupling all-fiber system
The all-fiber system used for generation and transmission of OV beams is schematically presented in Fig. 1. It is composed of two main parts: a compact all-fiber vortex generator butt-coupled with AR fiber.
Fig. 1. Schematic of the OAM mode excitation in ARF butt-coupled with all-fiber system for generation of OV beams.
The first part of the system converts a standard Gaussian beam into a vortex beam. It consists of a standard single mode fiber (SMF), a coreless fiber, a nanostructured gradient index vortex phase mask (nVPM) and a nanostructured gradient index nGRIN microlens as depicted in Fig. 2(a). The active alignment technique was applied to maintain axial symmetry of the whole system, which was reported in detail in [42]. The microoptical components were integrated manually on the SMF tip under the microscope using UV cured optical adhesive (Optical Adhesive 61, Norland). The flat surfaces of the components allow robust integration of the components with the fiber. As a result, fully integrated fiber-based vortex beam converter easy for manipulation is obtained, as we recently reported in [44].
Fig. 2. The optimized fiber-based vortex generator composed of a spacer, an nVPM, an nGRIN lens integrated on a SMF tip (a). Magnified SEM images of the fabricated nVPM (b) and nGRIN lens (c).
Among the integrated components, nVPM is the most important one used for generating OV beam by imposing the azimuthal phase shift on wavefronts of the incident beam. Such spatial phase modulation is achieved by the azimuthal variation of the refractive index distribution inside the nVPM, not by the profile of its surfaces. A detailed description of the concept and design of nVPMs is given in earlier works [43,45–47]. In short, the component was fabricated using a modified stack-and-draw method which is commonly employed for the fabrication of photonic crystal fibers [45,48]. The nVPM has an internal structure composed of 7651 nanorods made of two borosilicate in-house made glasses with high and low refractive indices (Fig. 2(b)). Their refractive index values are nh = 1.5414 and nl = 1.5167 measured at a wavelength of 980 nm. The arrangement of these rods was determined using effective medium theory [49] and simulated annealing algorithm [50] so that the obtained effective refractive index distribution of the nVPM would mimic the ideal continuous index gradient distribution. The fabricated nVPM used in this work has an outer diameter of 125 µm. Its center hexagonal vortex structure has a 20 µm long diagonal, which contains 101 nanorods. Figure 2(b) presents a scanning electron microscopy (SEM) image of this mask cross-section. The thickness of the used vortex component is 40 µm which is necessary to achieve the total angular phase shift of the beam equal to 2π (generation of OV beams with charge l = 1) at the wavelength of 980 nm.
The flat surfaces nGRIN microlens at the end of the fiber-based vortex generator allows controlling the beam divergence for coupling into the AR fiber. It should be noticed that the AR fiber has a very low numerical aperture (∼0.038 as discussed below) which is much lower than in standard fibers. Therefore, for efficient coupling, the generated OV beams should match numerical aperture of NA ≤ 0.038. This is possible to obtain controlling the length of the nGRIN lens. The nGRIN lens was fabricated using the same modified stack-and-draw technique. It contains 5419 nanorods made of Ge-doped silica glass and fused silica glass with the refractive index of nh = 1.45495 and nl = 1.45109 measured at 980 nm, respectively. The final nanostructure provides an effective continuous parabolic refractive index profile with the maximum on the optical axis and the minimum on the edge of the lens structure. In this work, the nGRIN microlens structure has a diameter of 56 µm (Fig. 2(c)), while the total outer diameter of the lens component with a cladding area surrounding its lens structure is 200 µm. The thickness of the used nGRIN lens is 600 µm.
We used a single-mode fiber (SM600, Thorlabs) with a core diameter of 4.3 µm for light delivery. The diameter of the fundamental mode guided SMF is much smaller than the aperture of the nVPM (20 µm), so we used an 85 µm long coreless-fiber segment as a spacer to expand the beam to fully illuminate the nVPM’s aperture. The spacer was made of borosilicate glass, like the one used for nVPM fabrication. The outer diameter of the spacer is 125 µm to match the diameter of the SMF.
We used the fiber-based vortex beam generator to excite OAM mode in 150 cm long section of developed in-house silica based AR fiber [51]. The fiber structure has a typical geometry of 6 circular, non-touching capillaries fixed into a jacket tube. These capillaries have an external diameter of 23 µm and a wall thickness of 1.3 µm. According to literature [52], the choice of six capillaries in AR-fiber cladding ensures the low confinement loss. The outer diameter of our ARF is 125 µm to match fiber commercial standards. The geometrical and optical parameters of the AR fiber used in the experiments are listed in Table 1. The scanning electron microscopy (SEM) image of its cross-section is sown in Fig. 3(a).
Fig. 3. (a) SEM image of the cross-section of the developed AR fiber; (b) transmission spectrum measured over full aperture of the antiresonant hollow-core fiber used in this work.
Table 1. Geometrical and optical parameters of the silica AR fiber
The numerical aperture of the ARF was measured at the wavelength of 980 nm. A lens (A110, Thorlabs) with NA = 0.40, f = 6.24 mm was used at the AR fiber input. The intensity distribution of the output beam at the far field was scanned using a photodetector (2 mm slit diameter) mounted on a motorized angular stage. When the fundamental mode was excited, the half-angle of emission cone was measured (θ = 1.56°), and then the NA was calculated (NA = 0.027). For high-order mode excitation, the half-angle of emission beam equals θ = 2.18° (NA = 0.038). The ARF offers high transmission in the near infrared window range 940 -1180 nm, as measured for a fiber length of 150 cm (Fig. 3(b)). Fiber attenuation was measured for a 5.5-m-long AR fiber sample using the cutback technique. For this measurement, we used a supercontinuum source (Leukos SM-30-HE-450, spectral coverage 450–2400 nm) and two spectrometers needed for two wavelength ranges: Ocean Optics Red Tide (350-1000 nm) and Avantes AvaSpec NIR 256 (1000-1700nm). The fiber has an attenuation around 0.5 dB/m at the wavelength of 980 nm.
3. Excitation of OAM in AR fiber with the vortex generator
To study the excitation and guidance of OAM modes in the test AR fiber, we used four experimental setups which share a common excitation method. The principle of the system operation is as follows: the incident light beam propagating in the SMF is expanded in spacer element to fully illuminate the aperture of the nVPM that generates the OV beam with topological charge l = 1. The vortex then passes through the nGRIN lens to be focused with a divergent angle not exceeding the critical angle of the AR fiber (θC = 2.18°), which allows easy and direct coupling into the AR fiber. In the setup, the end of the fiber-based vortex generator and one end of the AR fiber were clamped on the fiber clamper attached with two separate 3D nanomax stages for the alignment adjustment. Those two ends should be well aligned to ensure the generated OV beam being normally incident to the AR fiber for the coupling. The beam propagates in the AR fiber over the distance of 150 cm. The output from the AR fiber is subsequently recorded by an external imaging system consisting of a microscope objective lens (magnification ×20, NA = 0.35) and a CMOS camera (1280 × 1024 pixels, DCC1240C, Thorlabs). The distance between the output facet of the AR fiber and the imaging system is fixed during experiments to image the output facade on the camera chip.
In all measurements, we used a pigtailed single mode diode laser operating at 980 nm wavelength (CLD1015, Thorlabs) as a light source which was directly fusion spliced to the fiber-based vortex generator. The other end of the vortex generator was placed on a 3-axis stage (Nanomax, Thorlabs) and manually butt-coupled into the AR fiber.
Figure 4(a) presents the experimental setup for the analysis of the intensity distribution and vorticity of the vortex beam emerging from the AR fiber. Diagnostic of the topological charge was conducted using astigmatic transformation of the vortex. To this end, a cylindrical lens (f = 15 cm) was placed in front of the camera so the imaging plane was located at the focal plane of the lens. As a result, the collimated cylindrically symmetric OV beam is converted into an astigmatic pattern of bright elongated regions clearly separated by one or several dark stripes which correspond to the value of the topological charge of the vortex beam [53,54]. For example, for the OV beam with topological charge l = 1, its astigmatic transformation will display only one dark stripe. Moreover, the dark stripes are tilted in the opposite directions for vortices with the same topological charge values but opposite signs.
Fig. 4. Schematic of measurement setups for the optical performance of the butt-coupling all-fiber system for generation and transmission of vortex beams (a). Setups for study on the influence of stress force (b), the fiber bends (c), and the fiber twist (d) on the OV transmission through the AR fiber.
The schematic of a setup for investigating the influence of stress on the maintenance of the OAM mode is shown in Fig. 4(b). In this case, a lateral point force was applied to the AR fiber. The various lateral stress forces were applied at the same point of the AR fiber and then the process was repeated for different positions along the fiber. At the same time both the intensity of the outgoing OAM mode and its astigmatic transformation pattern were recorded by the camera.
Figure 4(c) shows the schematic of a setup for measurements of bending sensitivity of the AR fiber with excited OAM mode. For that purpose, the AR fiber was bent with different radius ranging between 15 and 5 cm. As previously, we recorded both the mode intensity profile and its astigmatic transformation pattern for vortex analysis.
Figure 4(d) shows the schematic of a setup for studying sensitivity of the transmitted vortex beam to the twist of the fiber. In this experiment the AR fiber was carefully twisted with different rate ranging from zero to tens of radians/meter.
4. Results and discussions
Figure 5 shows the light intensity distribution before (input beam) and after (output beam) propagation through the AR-fiber. At first, the conversion of the Gaussian beam into an OV beam was confirmed using an imaging system, which was done before building the butt-coupled all-fiber system. It can be seen from Figs. 5(a)-(c) that the beam generated using the optimized fiber-based vortex generator exhibits a uniform doughnut-like intensity distribution with a dark center region indicating the on-axis phase singularity. Moreover, the astigmatic transform pattern with a single dark stripe indicates the single topological charge of the phase structure (l = 1). We also experimentally observed that the OV beam focused at a distance of 370 µm from the end surface of the generator. After the focal plane, the vortex beam is slowly expanding with a divergence angle of θ = 2.18°. In the waist this vortex beam has a diameter of 47 µm which fits the core diameter of the selected AR fiber (46.5 µm). Therefore a high-quality optical vortex beam with topological charge l = 1 is used as an appropriate input for excitation in the AR fiber sample. After determining the parameters of the vortex beam generated by the fiber-based vortex generator, we assembled the optical system, as depicted in Fig. 4(a). Graphs shown in Figs. 5(d)-(f) present images recorded at the output of AR fiber in the measurement setup with schematic in Fig. 4(a). Notice that the contrast of the vortex [Fig. 5(e)] is slightly decreased after propagation through the fiber. This is caused by the excitation of other fiber modes which results in decreasing mode purity of the vortex beam. However, as the singular phase structure is very well preserved this effect will not be detrimental in practical application of the AR fiber to transfer singular beams.
Fig. 5. Experimental results for intensity distribution of OV beams before (input) and after (output) propagating through the AR fiber and their corresponding astigmatic transformation patterns.
Figure 5 illustrates the transmission of the input charge one vortex beam (top) through a straight, 150 cm long AR fiber. The output intensity and phase structures are shown in the bottom graphs. Clearly the fiber transmits an optical vortex beam without affecting its fundamental properties. However, in real application the fiber will never be straight. In fact, it will be subject to deformations caused by bending, twist and application of point-wise force, which may affect the quality of the transmitted vortex beam. Therefore, in the following we will determine experimentally the role of these of external perturbations on the quality of the OAM mode. The measurements were performed using the experimental setups shown in Figs. 4(b)-(d). Figure 6 presents the recorded output beam transmitted through the AR fiber subject to external lateral point force. By varying the magnitude of this force from 0 N to 1N with the step of 0.1 N, we found that the vortex beam survives if the force is less than 0.677 N. However, for larger force the perturbation to the transmission characteristic of the AR fiber is strong enough to destroy subtle phase structure of the initial vortex beam. In the end, the singularity disappears, and the beam loses its donut shape. The astigmatic transformation pattern now contains only a single bright elongated region, typical for a beam without singularities. This is more clearly visible for the case of F = 0.875 N as shown in Figs. 6(g),(h). For smaller external pressure, we still obtained OV beams with topological charge 1 as confirmed by the astigmatic transformation measurements (Fig. 6(d)). However, the stress force increases the light localization in one form of the bright spot on the doughnut-shape beam pattern (Fig. 6(c)). The reason for this behavior is the stress induced birefringence in the fiber [32] which perturbs the phase structure of the vortex leading, ultimately, to its destruction.
Fig. 6. Intensity distribution (top row) and astigmatic transformation patterns (bottom row) of output beams transmitted through the AR fiber when different stress forces were applied at the same position on the fiber. The OVB is maintained at output of the AR fiber for the force below 0.677 N.
Next, we investigated the effect of fiber bending on the propagation of OV beam. It is well known that the bending introduces birefringence into the fiber and is often used to control polarization of guided light [39,40]. However, bend-induced birefringence will inevitably perturb the topological phase structure of the vortex causing its instability. For this studying purpose, we bend a part of 150 cm long AR fiber with an initial bending radius of 20 cm and then reduced the bend radius regularly with the step of 0.5 cm. The results presented in Fig. 7 confirm this behavior. The vortex phase and intensity structure are preserved over the 150 cm long AR fiber as long as the bend radius is greater than 10 cm. We clearly observe the doughnut-like intensity profile at the output and typical astigmatic transformation pattern for OV beam with charge 1 (Figs. 7(c)-(d)). Interestingly, while for the bend radius of 10 cm the intensity distribution still exhibits characteristic donut shape (Fig. 7(e)), the helical phase structure is already perturbed as evident in corresponding astigmatic transformation (Fig. 7(f). For tighter bend (6.5 cm), the output beam loses its dark center and acquires form of a bright spot (Fig. 7(g)). Corresponding astigmatic transformation pattern (Fig. 7(h)) is now a single bright line as expected from the singularity-free beam.
Fig. 7. Intensity distribution (top row) and astigmatic transformation patterns (bottom row) of output beams transmitted through the AR fiber when the AR fiber was bent with different levels. The OVB is maintained at the output of the AR fiber for the bends with a circle radius diameter above 10 cm.
In the last part of this section, we will discuss the effect of fiber twisting on the propagation of OV beam. It has been recently shown that twist of the photonic crystal fiber introduces small amount of angular momentum to the propagating light beam [55,38]. In fact, this effect has been employed to generate THz vortices in hollow core fibers [38]. In case of vortex propagation the extra contribution to the angular momentum could perturb the helical phase structure of the vortex beam causing its transformation in propagation. Indeed, the experiments confirmed that the structure of the vortex beam at the exit of the 60-cm fiber varies with the rate of the fiber twist (T [rad/m]). The AR fiber was twisted gradually by rotating its one end with the rate from 0 rad (straight AR fiber) with the step of π/4 rad. However, unlike the case of lateral force and bend, the dynamics of vortex transformation is more complex and requires more thorough further studies. Here we provide few results of the preliminary experiments in which a charge one vortex beam was launched into a straight piece of ARF which was gradually twisted. Figure 8 depicts the output intensity distribution (1st and 3rd rows) and their astigmatic transformation pattern (2nd and 4th rows), respectively. The twist was carried out for both directions: anti-clockwise and clockwise. In the former case, for small twist rate (Figs. 8(a)-(c)) the vortex’s intensity and phase structures are generally well preserved. We do observe nonuniformity development for higher twist rate. Interestingly, for even higher twist (Figs. 8(d),(e)) we observe vortex’s revival when the original donut shape and phase singularity is restored. Furthermore, for the same input topological charge, we observe certain asymmetry in vortex transformation pattern between clockwise and counterclockwise twists (Figs. 8(g)-(m)). All the phenomena observed previously for the anti-clockwise twist, were also observed now, but they took place at different twist rate. This could be caused by interplay of vortex’s own original angular momentum (as following the sign of topological charge) and that provided by the fiber twist whose sign depends on the direction of the twist.
Fig. 8. Intensity distribution (1st and 3rd rows) and corresponding astigmatic transformation patterns (2nd and 4th rows) of output beams transmitted through the twisted AR fiber as a function of the rate of the twist. The twist was done for both anti-clockwise and clockwise direction.
The presented here propagation of vortex beam is a result of specific properties of AR fibres. AR fibres are multimode fibers but their propagation properties are very different from well-known all-solid silica glass multimode fibers [35]. AR fibers can support propagation of multiple modes unperturbed because coupling between modes is very limited since they propagate mostly in air and there is no mechanism for intra-mode coupling in air. As we have shown for the first time experimentally it is also a case for OAM modes if these modes are individually excited with nVPM component. Due to unique limited intra-mode coupling properties AR fibres can maintain polarization modes although, they have multiple-fold symmetry of their internal structure (higher than 2) [56]. An introduction of external perturbation as directional stress, twist or bending causes deformation of the fibre and increase overlap of propagation mode with glass. Therefore, intra-mode coupling can occur and purity of excited OAM mode is reduced, since other modes are excited.
5. Conclusions
We have demonstrated the feasibility of efficient all-fiber generation and transmission of optical vortices in antiresonant optical fibers. The compact fiber-based vortex generator was composed of two flat-surface nanostructured gradient index components (a 40-µm-long nVPM and a 600-µm-long nGRIN microlens). In contrast to previously proposed all-fiber systems based on LPFG and FMSC for OV, presented here beam generator it is very compact and does not require any active control.
Experimental results confirmed that this fiber-based vortex generator allows converting a Gaussian beam into a high-quality OV beam with topological charge l = 1 at the wavelength of 980 nm. This generated OV beam with divergence angle of θ = 2.18° and waist of 47 µm at the working distance of 370 µm perfectly matched the core diameter of 46.5 µm and numerical aperture (NA = 0.038) of the test AR fiber and, consequently, allowed an efficient direct butt-coupling. We experimentally demonstrated an excitation of OAM mode that corresponds to OV beams with topological charge l = 1 in 150-cm long sample of AR fibers.
Furthermore, we have verified experimentally the stability of guidance of OAM mode in AF fibers. Usually, OV beam is supposed to be very sensitive for external perturbation in free space, therefore this type of beam is not considered as a guided mode in anti-resonant hollow-core fibers. The influence of fiber bending, lateral stress and fiber twist on the OAM transmission in AR fiber was investigated. The results show that OV beams can be maintained, when it propagates along the 150 cm long AR fiber with the maximum lateral stress force of F = 0.677 N and the minimum bending radius 10 cm. In the case of fiber’s twist, the vortex maintains its structure for small twist (here 5.9 rad/m) but experiences strong transformation for larger twist. Moreover, the asymmetry between clockwise and counterclockwise twist as well as vortex’s revival for relatively large twist is also observed. These aspects of the vortex evolution in twisted fiber merits further systematic studies.
In general, our experiments demonstrate that vortex beam guided by AR hollow core fiber propagates stably for the modest external perturbations to the fiber, including lateral force, bend and twist making these fibers attractive for transmission of singular beams.
It should be noted that for OAM generation, we used an optical fiber without use of any bulk free-standing optical components. The proposed all-fiber system for OAM mode excitation in AR fibers offers high flexibility to adjust its performance for specific requirements. A charge of OV beam can be easily increased by changing the length of the nVPM. The divergence angle of the generated OV beams can also be adapted by modifying the length of nGRIN lens. In addition, while the reported fiber-based vortex generator performs at the wavelength of 980 nm, it can easily be modified to generate OV beam with the same topological charge at other wavelengths. This can be done by replacing the used nVPM with the similar component with suitable thickness to work at new wavelengths. (e.g. 25 µm long nVPM for the wavelength of 633 nm). We admit that full integration of fiber-based vortex generator and AR fiber with fusion splicing is still an unsolved issue that limits the proposed system practical application. However, recently we have demonstrated that efficient fusion splicing of AR fibers with standard single mode fiber is feasible [57]. Future development of nVPM component with silica glass would allow the development of all components from the same type of silica glasses and allow full integration of all components with modern fusion splicer.
Funding
Fundacja na rzecz Nauki Polskiej (POIR.04.04.00-00-1C74/16); Qatar National Research Fund (NPRP12S-0205-190047); Narodowe Centrum Nauki (UMO-2021/41/N/ST7/01517, UMO-2016/21/M/ST2/00261).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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