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Abstract
We demonstrate a fiber-based optical vortex beam source operating in broadband or tunable mode in the spectral range of 1100–1400 nm. The vector vortices of the total angular momenta equal to +2, 0, and −2 are obtained by converting the respective linearly polarized (LP11) modes of the two-mode birefringent PANDA fiber with stress-applying elements by gradually twisting its output section. At the input end, the PANDA fiber is powered by broadband supercontinuum or tunable Raman solitons generated in the LP11 polarization modes of a birefringent microstructured fiber with a specially designed dispersion profile and coupled to the respective LP11 modes of the PANDA fiber. Two pulse lasers operating in different regimes (1 ns/1064 nm and 190 fs/1037 nm) were used as the pump to generate supercontinuum or tunable solitons directly in the LP11 modes of the microstructured fiber purely excited with a special Wollaston prism-based method. The high modal and polarization purities of the beams after successive transformations were experimentally confirmed. We also proved the vortex nature of the output beams using shearing interferometry.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical vortices (OVs) have attracted increasing attention in recent years owing to their unusual features, such as transferring orbital angular momentum (OAM) and better focusing capabilities than Gaussian beams [1]. OVs have already found numerous applications, such as optical tweezers [2], communication [3], microscopy [4], fiber lasers [5], and quantum optics [6]. Various techniques are used for the generation of vortex light beams in free space [7], but in-fiber methods are of particular interest owing to technological trends toward miniaturization. It is known that higher-order modes of cylindrical fibers carry different OAMs. However, such modes are difficult to access due to the demanding excitation methods and degeneracy, although it was recently shown that the degeneracy of first-order modes can be lifted in some specially designed fibers such as ring-core fibers [8,9] or helically twisted microstructured fibers [10,11]. Most methods for directly generating OVs in optical fibers are based on resonant coupling between fundamental and higher-order modes in long-period gratings [12–15], Bragg gratings [16], or selective couplers [17–19]; therefore, their spectral ranges are limited. OVs in a broader spectral range can be obtained using apodized long-period gratings [20], fibers with special dispersion profiles [21], fibers aligned with offset [22], or photonic lanterns [23]. However, these approaches often require high precision, complex manufacturing, or control of the phase shifts between the interacting modes, as in the case of photonic lanterns. Broadband generation of supercontinuum (SC) in higher order mode with OAM equal to 7 and 8 was recently demonstrated in [24] using a femtosecond pump laser. However, because of the ring-shaped fiber core, such an approach is difficult to apply to SC generation in modes with OAM equal to ±1.
The possibility of converting linearly polarized LP11 modes into OVs in a gradually twisted birefringent fiber was recently demonstrated in [25–27]. Owing to its topological nature, this method is spectrally broad and does not require complicated manufacturing. It was shown in [26] that different types of optical vortices, such as nearly circularly polarized HE21± modes with total angular momenta of ±2 and quasi-TE01/TM01 with a total angular momentum of 0, can be obtained by converting the respective LP11 modes of highly birefringent fiber excited at the non-twisted end. Excitation of first-order modes was realized in [26] using a liquid crystal spatial light modulator (SLM) and an external supercontinuum (SC) source. Recently, a simple method of pure excitation of LP11 polarization modes in a birefringent fiber was demonstrated using a Wollaston prism, half-wave plate, and linear polarizer [28]. Because this method utilizes standard optical components, it can be applied to high-power pulse lasers, in contrast to liquid-crystal SLMs. This opens up new possibilities for the generation of SC or tunable Raman solitons of high modal purity directly in the LP11 polarization modes of a birefringent fiber.
The broadband/tunable source of vortex beams, which we propose in this work, takes advantage of a recently described method for the transformation of LP11 modes into vortex modes by gradually twisting the highly birefringent PANDA fiber [26]. To ensure all fiber configuration as well as high power and broadband operation capabilities of such a source, we propose to generate SC or tunable Raman solitons directly in the LP11 polarization modes of a specially designed birefringent microstructure fiber, which is spliced to the non-twisted input end of the PANDA fiber. We show that the SC spectral and tunability ranges of the Raman solitons generated in this way in the respective LP11 modes spread from the pump wavelength (1064 and 1037 nm for the ns and fs lasers) to approximately 1500 nm. The useful spectral range of the vortex beams is slightly narrower and spreads up to 1400 nm because of increasing coupling to the cladding modes caused by the cut-off of the LP11 modes in the PANDA fiber arising at around 1650 nm. We experimentally proved the high polarization and modal purity of the spectra generated in the microstructured fiber and confirmed the vortex nature of the output beams using the shearing interferometry method presented in [29].
2. Vortex source concept
The proposed vortex beam source shown in Fig. 1 is composed of a specially designed microstructured fiber serving as a broadband source of the LP11 modes of high modal purity spliced with the PANDA fiber gradually twisted at its output end to transform the LP11 modes into vortex modes. The dispersion characteristic of the two-mode birefringent microstructured fiber is engineered in such a way that it allows for effective SC generation in any of the LP11 modes using a nanosecond Nd:YAG pulse laser as the pump. If powered by a femtosecond laser, the same fiber also allows the formation of tunable Raman solitons in any LP11 mode. The output end of the microstructured fiber was spliced with the non-twisted input end of the PANDA fiber with polarization axes aligned in parallel to allow for pure coupling between the corresponding LP11 polarization modes of the two fibers. The output end of the PANDA fiber was gradually twisted, thus enabling the transformation of the respective LP11 modes to vortex modes.
Fig. 1. Experimental setup for generation and characterization of broadband/tunable optical vortices. H1, H2 – half-wave plates; P1, P2, P3 – linear polarizers, Q – quarter-wave plate; WP1, WP2 – Wollaston prisms, IF – interference filter (1100–1500 nm), MO – microscope objectives. Polarization azimuth with respect to the y-axis is marked below each element.
To ensure the high purity of LP11 modes spectrally broadened by nonlinear processes in the microstructured fiber, which directly affects the purity of the generated vortices, we used the recently proposed Wollaston prism-based method for selective excitation of LP11 polarization modes by the pump laser [28]. As shown in Fig. 1, the initial azimuth of the linearly polarized laser beam was rotated by the half-wave plate (H1) to 45° with respect to the polarization axes of the Wollaston prism (WP1). The azimuths of the orthogonally polarized beams split by WP1 by 0.04° are then rotated by 45° by the half-wave plate H2, while polarizer P1 sets their polarizations vertically with opposite phases. When focused by the microscope objective on the fiber end face, the two light spots match well the modal field of the LP11xe mode, whereas the overlap with other LP11 or LP01 modes is practically equal to zero because of polarization orthogonality or different symmetries. By changing the azimuths of the respective polarization elements [28], it is possible to purely excite any of the polarization modes with a coupling efficiency of 26% for the LP11xe and LP11yo modes and 20% for the LP11xo and LP11ye modes, and the crosstalk to non-targeted modes is lower than −20 dB. The difference in coupling efficiency between the LP11xe/LP11yo and LP11xo/LP11ye mode groups is related to the different modal field distributions in the respective groups.
It is worth mentioning that the generation of SC and solitons in the LP11 modes has already been reported in the literature [30,31], however, using the excitation method with lateral offset which unavoidably leads to launching a combination of LP01 and LP11 modes. Consequently, the intermodal nonlinear effects can deteriorate the modal purity of the spectra generated in such a manner and exclude their use for conversion to vortex modes.
The light spectrally broadened by nonlinear processes in the LP11 polarization mode of the microstructured fiber is coupled to the respective LP11 polarization mode of the PANDA two-mode birefringent fiber with a cut-off wavelength of approximately 1650 nm. This fiber is gradually twisted over a 3 cm long output section indicated in Fig. 1 as TMC (twisted mode converter). As reported in [26], the length of the twisted section when the twist rate increases from 0 to 2 turns/mm is sufficient to convert the LP11 modes into the respective vortex modes. To avoid cross-coupling between the LP11 mode excited in the microstructured fiber and other modes in the PANDA fiber, the two fibers must be carefully azimuthally aligned prior to splicing.
The quality of the output vortex beams was characterized spectrally using an optical spectrum analyzer (OSA) and an InGaAs Hamamatsu C12741-03 camera with interference filters IF (FWHM of 10 nm) of central wavelengths changing in steps of 100 nm. The vortex-like nature of the output beams was confirmed experimentally using the Wollaston prism-based shearing interferometry method [29]. As the output vortex beams are circularly or elliptically polarized, they are split by WP2 into two beams with linear and orthogonal polarizations. After passing through polarizer P2 with a transmission azimuth of 45° with respect to the WP2 axes, the two vortex beams interfere, producing a characteristic pattern with fork-like interference fringes. Moreover, the output vortex beams were characterized in terms of polarization purity by measuring the polarization extinction ratio using a circular polarizer (Q, P3) and an OSA.
3. Microstructured fiber for supercontinuum and Raman soliton generation in LP11 polarization modes
For the nonlinear spectral broadening of ns/fs laser pulses selectively coupled to LP11 modes, a special microstructured fiber, as shown in Figs. 2(a),(b), was designed and fabricated. The fiber cladding of hexagonal symmetry is composed of 5 layers of air holes with a lattice pitch of 4 µm and a filling factor of 0.5 for grater holes and 0.36 for a pair of smaller holes located near the core to induce birefringence. The fiber supports two spatial modes up to 2500 nm. The effective mode areas at λ = 1064 nm for the LP11 modes determined by the simulations are in the range of 22–24 µm2, which results in an effective nonlinear coefficient γ = 7.3–6.6 W-1·km-1. The dispersion profiles for the fundamental polarization modes (LP01x, LP01y) and all first-order modes (LP11xe, LP11yo, LP11xo, LP11ye) measured in a meter long fiber are shown in Fig. 2(c). Measurements were conducted using a Mach-Zehnder interferometer with an adjustable reference arm, allowing for compensation of the optical path delay and zero-order interference fringe tracking versus the wavelength [32]. Thus, the chromatic dispersion was measured for each individually excited fundamental and first-order polarization mode with an external SC beam using the launching method outlined in the previous section.
Fig. 2. Cross-section of a specially designed microstructured fiber used to spectrally broaden pulses introduced to respective LP11 polarization modes (a),(b). Chromatic dispersion (c) and phase birefringence (d) measured for the fundamental and first order eigenmodes.
As shown in Fig. 2(c), the zero-dispersion wavelengths for the first-order modes are within the range of 964–989 nm; therefore, all these modes are pumped with both ns and fs lasers in the anomalous dispersion regime, which enables the effective generation of SC or tunable Raman solitons. To prevent coupling between the polarization modes, birefringence was induced in this fiber by a pair of small holes located symmetrically to the core in the first layer of the microstructured cladding. The phase birefringence measured for each pair of orthogonally polarized spatial modes using the spectral interference method combined with a point-force method [33] shows typical behavior for the microstructured fibers, that is, it increases monotonically with wavelength and takes the values of approximately 0.4×10−4 at 1000 nm up to 1.5×10−4 at 1500 nm for the first-order modes, as shown in Fig. 2(d). Birefringence in the fundamental mode shows a similar spectral dependency but is systematically lower by approximately 50%.
Using laser sources of 1 ns and 190 fs pulse durations, coupled to the respective LP11 polarization modes of 9.3 meters long microstructured birefringent fiber, we were able to obtain efficient spectral broadening/tuning in the excited LP11 mode without significant crosstalk to orthogonal polarization. In the nanosecond regime, for average input power 50 mW (measured before the coupling objective), a spectrally flat SC spread from the pump wavelength (1064 nm) to approximately 1550 nm was observed in each LP11 polarization mode. Due to the limited pulse peak power (3 kW) and higher dispersion slope compared to LP01 modes, we did not observe SC generation from the pump toward shorter wavelengths for any of the LP11 modes. Figure 3 shows the output SC spectra for LP11xe and LP11ye modes registered after passing through a linear polarizer set in transmission and extinction with respect to the mode polarization and the resulting polarization extinction ratio (PER). For both modes, the resulting PER was between −25 and −33 dB in the range from the pump wavelength to 1550 nm. Similar characteristics were obtained for the other modes, which proves the good polarization purity of the SC generated in each LP11 polarization mode. We also experimentally excluded the possibility of coupling between the different spatial modes. For this purpose, we used a reflective-type diffraction grating (300 lines/mm) to split the output SC beam in the horizontal direction. For any excited LP11 mode, the output end of the microstructured fiber was aligned such that the characteristic line of zero-intensity was set horizontally. As shown in Fig. 4, there is a clearly visible black line spreading throughout the diffracted SC spectrum (calibrated with the use of interference filters), which proves a lack of coupling between different spatial modes and therefore a high modal purity of the SC generated in each of the LP11 polarization modes.
Fig. 3. Supercontinuum spectra registered using optical spectrum analyzer after passing through a polarizer set in transmssion and extinction with respect to the excited mode of the microstructured fiber and the resulting PER for (a) LP11xe and (b) LP11ye modes shown in the insets.
Fig. 4. Supercontinuum generated in LP11xe mode of the birefringent microstructured fiber reflected by the diffraction grating (zero difraction order) (a) and spitted horizontally into first difraction order (b) registered by infrared camera. Blue arrows on each frame indicate calibration points determined with the use of interference filters.
Launching femtosecond pulses into LP11 polarization modes in an anomalous dispersion regime results in complex soliton dynamics [34]. For an average pump power greater than 0.2 mW, higher-order solitons are generated at the beginning of the fiber and break up into multiple fundamental solitons that shift toward longer wavelengths along with the propagation distance. The number of generated solitons and their Raman-induced long-wavelength shifts increase with pulse power. In Fig. 5(a), we show the registered output spectra for the LP11xo mode for increasing average pump power. Tuning the first ejected soliton to 1550 nm requires an average input power of 25–30 mW. At approximately 1400 nm, the solitons narrow spectrally, which is most probably caused by greater fiber loss related to glass contamination by OH− ions. In the insets, we show the output intensity distributions registered using the infrared camera and a series of interference filters with transmission bands matching the positions of the first soliton at different pump powers. These images confirm that the solitons are generated in first-order modes excited at the beginning of the fiber.
Fig. 5. Spectra registered at the output of the microstructured fiber for the LP11xo mode excited with different pump powers and pictures of the output mode taken by an infrared camera with the use of interference filters with transmission bands matching the positions of the first ejected soliton (a). Dependence of PER on the central wavelength of the first soliton (b) and change of the central wavelength of the first soliton upon input power (c) for the all LP11 modes.
The dependence of the central wavelength on the average input power (measured before the coupling objective) and the dependence of PER on the central wavelength of the first ejected solitons generated in the respective LP11 polarization modes are shown in Figs. 5(b) and 5(c). In the 1100–1400 nm spectral range, the PER varied from −22 to −32 dB depending on the mode type. For longer wavelengths and, therefore, greater pump powers, the PER for solitons excited in the LP11 polarization modes of the lower effective indices (LP11ye and LP11yo) increases above −20 dB. This effect is due to the nonlinear birefringence, which in part compensates for the intrinsic fiber birefringence and favors coupling between polarization modes. For x-polarized modes (LP11xe and LP11xo), the nonlinear birefringence sums up with the intrinsic fiber birefringence, and consequently, these modes show better polarization purity with PER approaching −30 dB in the long-wavelength range.
When the average input power increases above 6 mW, a continuous spectrum begins to build up between the soliton bands, which finally leads to the creation of the SC. Although the SC generated in the fs regime in the best case (for the LP11xo mode) has a PER of approximately −20 dB in the long-wavelength part of the spectrum, in the worst case (for the LP11yo mode), the PER increases above −10 dB, which proves that the intrinsic birefringence of the fiber is not sufficient to prevent significant nonlinear coupling between polarization modes. Therefore, because of the lack of modal purity, the SC generated in the femtosecond regime is not suitable in this case for conversion to vortex modes.
4. Transformation of LP11 modes into vortex modes
To transform the SC or solitons generated in the LP11 modes of the microstructured fiber into vortex modes, we used commercially available PANDA fiber (Nufern PM-1950) whose cross-section is shown in Fig. 6(a).
Fig. 6. Cross-section of the PANDA birefringent fiber (PM1950 Nufern) obtained in the scanning electron microscope showing slight ellipticity of the core (a). Increase in total twist angle φ vs. propagation distance and SAP captured in polarization microscope for twisted mode converter (b). Differences in effective indices of the first-order modes with respect to the mode of the highest index calculated versus wavelength in the non-twisted fiber (c). Evolution of averaged ellipticity of the first order modes in gradually twisted fiber calculated for λ = 1100 nm (d). Photograph of the splice (e).
The fiber core had a slightly elliptical shape with a major to minor axis ratio of approximately 1.1. The measured cut-off wavelengths are in the range of 1.6 to 1.7 µm for the first-order modes, numerical aperture of 0.19 and modal birefringence in the fundamental and first order modes are in the range of 3.47 to 3.62×10−4 at 1200 nm. As the birefringence in this fiber is induced by stress-applying parts (SAP), it has little dependency on the wavelength and mode order. To distinguish between the first-order modes of the microstructured fiber and the PANDA fiber, the modes of the latter are marked with the prime sign.
The simulated differences in refractive indices with wavelength for the LP11’ modes of the non-twisted PANDA fiber are shown in Fig. 6(c). Using the numerical approach employing finite element method and transformation optics formalism detailed in [25], we also modeled the evolution of the averaged ellipticity of the first-order modes in the gradually twisted PANDA fiber versus twist rate. According to the results presented in Figs. 6(c) and (d), the modes of the highest and lowest effective indices (LP11xo’ and LP11yo’) evolve in the gradually twisted fiber section toward the left- and right-handed circularly polarized HE21+ and HE21− of total angular momentum equal to ±2. However, the modes of the intermediate indices (LP11xe’ and LP11ye’) evolve to quasi-TE01/TM01 modes with a total angular momentum equal to 0. As discussed in [27], for sufficiently high initial differences in the effective indices of the LP11’ modes in the non-twisted fiber and a slow increase in the twist rate at the beginning of the TMC, it is possible to convert the LP11’ modes into the corresponding vortex modes without significant crosstalk.
The TMC used in our experiments was fabricated using Lightel Coupler Workstation CW-5000 with hydrogen flow = 140 ml/min, platform speed = 0.04 mm/s, torch height = 12.3 mm, and torch speed = 0.5 mm/s. The rotation speed of the fiber holders increased gradually from 0 to ±210°/s, which resulted in a counterclockwise twist with the period changing from infinity to 625 µm at the end of the TMC with a length of 27 mm. The dependence of the total twist angle φ on propagation distance z for the fabricated TMC converter is shown in Fig. 6(b).
A nonlinearly broadened spectrum in the LP11 mode of the microstructured fiber was coupled to the respective LP11’ mode of the PM-1950 fiber. The two fibers were spliced using Fujikura LZM-100 CO2 workstation without significant collapse of the microstructured cladding (Fig. 6(e)). Before splicing, the slow axis of the microstructured fiber was aligned parallel to the fast axis of the PANDA fiber so that the elliptical cores had the same orientation at the junction, which resulted in the excess loss of approximately –1.8 dB at 1064 nm. For such alignment, the LP11xo’ and LP11yo’ modes in the PANDA fiber are excited with the LP11yo and LP11xo modes of the microstructured fiber, respectively. Similarly, the LP11ye’ and LP11xe’modes of the PANDA fiber are excited respectively with the LP11xe and LP11ye modes of the microstructured fiber. Angular misalignment of the two fibers was estimated at 1–2° by comparing the PER at the output of the microstructured and PANDA fibers prior to splicing, Fig. 7. After correct alignment and splicing of the microstructured and PANDA fibers, the latter was twisted at the output end with a gradually decreasing twist period up to Λ = 625 µm, Fig. 6(b). In Fig. 7 we show the spectra of the SC generated with Nd:YAG laser in the LP11xo mode of the microstructured fiber registered successively at its output, at the output of the non-twisted PANDA fiber (LP11yo’), and after twisting the output end of the PANDA fiber (right-handed circularly polarized HE21− vortex beam). To determine the PER after each mode transformation, measurements were conducted using linear or circular polarizers set in transmitting and extinguishing configurations.
Fig. 7. SC generated in the LP11xo mode of the microstructured fiber registered at its output (a), at the output of the non-twisted PANDA fiber (b), and gradually twisted PANDA fiber (c) with the use of linear (a),(b) and circular (c) polarizers set in transmitting and extinguishing configuration. Blue lines show the calculated polarization extinction ratio (PER).
As Fig. 7 shows, the PER for the output vortex mode is approximately −20 dB in the range 1100–1500 nm, and the vortex is right-handed circularly polarized (RHCP), which corresponds to a spin angular momentum (SAM) of −1. When the LP11xo’ mode is excited in the gradually twisted PANDA fiber, it converts into the LHCP vortex mode with SAM = +1 and a similar PER of approximately −20 dB in the spectral range from 1100 to 1500 nm, Fig. 8(a). The other modes of the PANDA fiber (LP11xe’ and LP11ye’) evolve with increasing twist rate to vortex modes of more complex polarization structures with average ellipticity varying with the wavelength. At approximately 1200 nm, the polarization state of these modes is close to circular (LH for LP11xe’ and RH for LP11ye’ excitation), which is proven by the low PER (approximately −20 dB) obtained with circular polarizers (Figs. 8(b), (c)).
Fig. 8. Spectral and polarization characteristics of vortex modes measured at the output of gradually twisted PANDA fiber excited with the supercontinuum generated respectively in the LP11yo, LP11ye, and LP11xe modes of the microstructured fiber and coupled to LP11xo’ (a), LP11xe’ (b), and LP11ye’ (c) modes of the PANDA fiber. Black lines were obtained with the use of left (a),(b), and right (c) handed circular polarizers ensuring maximal transmission, red lines with circular polarizers of opposite handedness, blue lines show the calculated PER.
However, with increasing wavelength, the measured circular PER increases to approximately −10 dB, which corresponds to an average ellipticity angle of approximately 27° (averaged over the mode surface with local intensity as a weighting factor [26]). A circular PER equal to −10 dB suggests that, at least locally, the polarization state of these modes is closer to linear. This was confirmed by registering the intensity distribution in the respective vortex beams using a rotatable linear polarizer and IFs with transmission bands at 1200 nm and 1400 nm. All vortex beams have circular polarizations at 1200 nm because the rotation of the linear polarizer has practically no impact on their intensity distributions. As shown in Fig. 9, the structure of the converted beams differed at longer wavelengths. The vortices obtained by converting the LP11xo’ and LP11yo’ modes preserved the circular polarizations at 1400 nm. In contrast, there are clearly visible variations in intensity over the surface of the two other vortex beams generated by excitation of the LP11xe’ and LP11ye’ modes of the PANDA fiber, which confirm that their local polarization states significantly vary over the mode surface and approach linear polarization in certain areas.
Fig. 9. Intensity distributions registered for four vortex beams at the output of TMC at 1200 nm and 1400 nm after passing through a linear polarizer with the transsmission azimuth set at different angles.
The conversion of the LP11yo’ and LP11xo’ modes to the left- and right-handed circularly polarized vortex beams HE21± of total angular momentum ±2 is in agreement with the simulation results presented in Fig. 6(d). However, the experimentally observed conversion of LP11ye’ and LP11xe’ to the quasi-TE01/TM01 modes with a total angular momentum equal to 0 differs significantly from the simulation predictions shown in Fig. 6(d). Although the obtained output modes have the total angular momentum close to zero, similarly as TE01/TM01 modes, their polarization states are near circular in the spectral range of 1100–1300 nm (SAM = ±1, OAM = ∓1) which is far from the calculated elliptical polarization (|ϑavg| ≈ 20°) for the quasi-TE01/TM01 vortices. The origin of this discrepancy remains unclear. The possible reasons are the twist-induced frozen-in shear stress or radial stress induced in the core, which are not considered in the simulations, although they can potentially affect the evolution of the eigenmodes.
We also confirmed the vortex nature of the output beams by observing the characteristic fork-like splitting of the interference fringes in the shearing interference patterns obtained using the Wollaston prism [29], as shown in Fig. 10. To conduct such experiments, a Wollaston prism with a split angle of 0.6° was placed at the output of the TMC, as shown in Fig. 1. It splits the vortex beam into two tilted beams of linear and orthogonal polarizations, which interfere after passing through a linear polarizer of transmission azimuth set at ±45° with respect to the WP2 polarization axes, and creates two inversely oriented fork-like fringes. The orientation of the left fork “upwards” proves positive OAM, whereas the “downwards” orientation confirms negative OAM. Numerical simulations of the interference for the vortex mode with OAM = SAM = +1 are presented in Fig. 10(b). Therefore, for the circularly polarized left-handed and right-handed HE21+ and HE21− modes converted from the initially excited LP11xo’ and LP11yo’ modes, the orbital angular momenta (OAM) are +1 and − 1, respectively. Consequently, the total angular momenta for these modes were +2 and − 2, respectively. For the two other vortex modes converted from the LP11xe’and LP11ye’ modes of the non-twisted PANDA fibers, OAM and SAM have opposite signs; therefore, the total angular momenta for these beams are close to 0.
Fig. 10. Intensity distributions and shearing interference patterns with fork-like fringes registered for different wavelengths for all vortex modes generated in the gradually twisted PANDA fiber excited with respective LP11 modes (a). Numerical simulations of the shearing interference patter obtained with a Wollaston prism for the vortex beam with OAM = SAM = +1 (b).
As is clearly visible in Fig. 10(a), the interference patterns registered at 1400 and 1500 nm are progressively blurred with speckle noise. This effect is related to the increasing losses near the cut-off (arising for the LP11 modes in the range of 1600–1700nm). The helical structure of the twisted slightly elliptical core prompts couplings between the core and cladding modes [35], which in our case begins at approximately 1400 nm. Therefore, the speckle noise visible near the cut-off wavelength was produced by the interference of the parasitic cladding modes with the vortex modes generated in the fiber core, which limited the operation range of the proposed vortex beam source to approximately 1400 nm.
Similar conversion processes were demonstrated for solitons generated in the LP11 modes of the microstructured fiber using a femtosecond laser source. The soliton spectra at the output of the microstructured fiber, non-twisted PANDA fiber, and twisted PANDA fiber registered with the use of linear and circular polarizers set in transmitting and extinguishing configurations are shown in Fig. 11 for the LP11xo/LP11yo’ mode of the microstructured/PANDA fiber. In this figure, we also show photographs of the modes taken at the output of each fiber using interference filters with transmission bands matching the first ejected soliton tuned to 1100 and 1300 nm by changing the pump power. The dependence of PER on the wavelength for the first ejected soliton at different excited modes is shown in Fig. 12(a). Similar to the case of the SC, the best PER for solitons, lower than −20 dB in the full spectral range, was obtained for the LP11yo’ mode converted to HE21− vortex modes. This is related to the fact that the LP11yo’ mode in the PANDA fiber is powered by the LP11xo mode of the microstructured fiber, which also shows the best PER at its output. Moreover, as shown in [27] by numerical simulations, the crosstalk accompanying the conversion process is the lowest for LP11 modes, which have the greatest initial difference in effective indices with respect to other LP11 modes. In our case, these are the LP11xo/LP11yo modes that convert to HE21± vortex modes. The measured PER for HE21+ was lower than that for HE21− because the PER of LP11yo at the output of the microstructured fiber was also lower than that of the LP11xo mode.
Fig. 11. Sucessive steps of the modes conversion for the femtosecond pump: soliton spectra at the output of the microstructured fiber in the LP11xo mode (a),(d), non-twisted PANDA fiber in the LP11yo’ mode (b),(e) and gradually twisted PANDA fiber in the vortex mode HE21− (c),(f). Black/red lines indicate the spectra registered after passing through a linear (a), (b), (d), (e) or circular (c), (f) polarizer set in transmitting/extinguishing configurations. In the insets we show the photographs of modes at the outputs of respective fibers taken with the use of interference filters with transmission bands matching the first ejected solitons.
Fig. 12. Dependence of PER upon wavelength for the first ejected soliton in four excited modes of the PANDA fiber (a). Intensity distributions and shearing interference patterns with fork-shaped fringes registered for different wavelengths for all vortex modes generated in the gradually twisted PANDA fiber excited with respective LP11’ modes (b).
For the LP11xe’ and LP11ye’ modes initially excited in the PANDA fiber and converted to the quasi-TE01/TM01 modes at the output of the TMC, the PER was lower than −17 dB up to 1300 nm and increased above −15 dB for longer wavelengths despite the high PER of the input modes (−30 dB for the LP11xe at the output of the microstructured fiber at 1500 nm). This observation experimentally proves the simulation predictions reported in [27], which point to the fact that greater cross-talk accompanying conversion to quasi-TE01/TM01 modes is related to small differences in their effective indices.
The vortex nature of the generated solitons was confirmed using the Wollaston prism-based shearing interference method. The orientation of the fork-like fringes shown in Fig. 12(b) indicates the OAM of the respective modes, which is the same as that in the case of the SC generated in the nanosecond regime. Based on the SAM and OAM values, we experimentally proved the distinct types of output vortices that carry different total angular momenta equal to −2, 0, and +2.
5. Conclusions
We demonstrated the feasibility of a novel source of spectrally broad or tunable vortex beams of different types generated directly in optical fibers using nanosecond or femtosecond pump lasers. The proposed source concept is based on a combination of two types of two-mode birefringent fibers with specific characteristics. The first is a specially designed microstructured fiber used for the generation of the SC or tunable Raman solitons of high modal and polarization purity in the LP11 polarization modes. Second, the commercially available PANDA fiber gradually twisted at the output end, which transforms the LP11 modes into distinct vortex modes of different OAMs and SAMs. The operation range of the source extends over 300 nm from the pump wavelength to approximately 1400 nm and is limited by the speckle noise arising from the coupling of vortex modes to the cladding modes near the cut-off wavelength. The operation range of the proposed source can be extended by using a birefringent fiber with a greater cut-off wavelength and lower core ellipticity, which reduces the coupling to the cladding modes.
The conversion of the LP11yo’ and LP11xo’ modes to the left- and right-handed circularly polarized vortex beams HE21± of total angular momenta ±2 is in agreement with the simulation results, and these modes show the best quality in terms of PER. In particular, the PER for the HE21− mode obtained from the LP11yo’ mode with a polarization purity lower than −30 dB was lower than −20 dB in the full spectral range. This indirectly proves that for the HE21± modes, the crosstalk to other vortex modes introduced by the TMC is lower than −20 dB. The PER for the HE21+ mode was slightly worse (maximum value of −18 dB at 1300 nm for the fs pump), but this was caused by the lower polarization purity of the input LP11xo’ mode. The PER of the HE21± modes can be further improved by optimizing the twist gradient in the TMC to reduce crosstalk with the other vortex modes [27]. Moreover, the polarization purity of the input LP11 modes can be improved by increasing the birefringence of the microstructured fiber.
The experimentally observed conversion of LP11ye’ and LP11xe’ to the quasi-TE01/TM01 modes with a total angular momentum equal to 0 differs significantly from the simulation predictions shown in Fig. 6(d); however, the obtained output modes still have a total angular momentum close to zero, which is a characteristic feature of the TE01/TM01 modes.
In summary, the proposed broadband all-fiber source provides vortex beams with all possible combinations of OAM = ±1 and SAM = ±1 in the nanosecond and femtosecond regimes. The specific output vortex is selected by exciting the appropriate LP11 mode of the nonlinear microstructured fiber. A high polarization purity of approximately −20 dB was obtained for the HE21± vortex beams. The quality of all the output vortices can be further improved by optimizing the parameters of the constituent fibers. Because of its simplicity, broadband operation range, and possibility of easy switching between different vortex beams, the proposed source can potentially find applications in different fields of optics, including optical trapping, microscopy, fiber lasers, and quantum optics.
Funding
Narodowe Centrum Nauki (DEC-2016/22/A/ST7/00089, Maestro 8).
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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