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Abstract
A full C- and L-band covered second-order orbital-angular-momentum (OAM) mode generator has been proposed and experimentally demonstrated, which is realized by using a helical long-period fiber grating (HLPG) but inscribed in a thinned four-mode fiber. By optimizing the design of grating period and fiber diameter of the proposed HLPG, an ultra-broadband rejection filter with a depth of ∼23 dB, a bandwidth of ∼156 nm @-10 dB (ranging from 1522 nm to 1678 nm) and a bandwidth of ∼58 nm @-20 dB (ranging from 1574 nm to 1632 nm), has been successfully obtained as a typical sample. To the best of our knowledge, this is the first demonstration of such ultra-broadband second-order OAM mode generator by using only one fiber component, i.e., the thinned HLPG. In addition, the proposed generator is less polarization-dependent and less temperature-sensitive than those of the conventional HLPGs, which is believed to be considerably helpful to find potential applications of the device itself in wavelength division multiplexing (WDM) and OAM mode division multiplexing (MDM) optical fiber communication systems.
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1. Introduction
Mode division multiplexing (MDM) technology has recently attracted much attention in the fiber-based optical communication system, which in general refers to the technique utilizing the different spatial modes, e.g., the orbital angular momentum (OAM) modes, as the new carried channels to expand the transmission capacity in a fiber [1]. To date, various methods have been developed to generate the OAM modes, including the cylindrical lens, the q-plate, the integrated silicon device, and the fiber-based generators etc. [2]. Of all these methods, owing to the superior characteristics, such as the compact size, extremely low cost, low insertion-loss, high conversion-efficiency, and the inherent compatibility with other fiber devices, the fiber grating-based OAM generators have recently attracted a significant research interest [3–7]. However, among these fiber-based ones, some additional components are generally demanded, such as the polarization controller, which is especially used to induce a constant π/2 phase different between the even and odd linear polarization (LP) modes [3–7], which inevitably brings much more insertion and polarization-dependent losses. To address the above issue, the helical long-period fiber gratings (HLPGs) written in single-mode fibers (SMFs), few-mode fibers (FMFs), ring-core fibers (RCFs), and photonic-crystal fibers (PCFs), have been proposed and experimentally demonstrated, which have been used to produce the first- to sixth-order OAM modes, respectively, with few polarization-independent losses and without the need of any other additional components [7–15]. However, most of the HLPG-based OAM generators mentioned above are inherently the wavelength-dependent ones, which lacks the wideband performances. The ultra-broadband spectrum enabling to cover the full C- and L-band of fiber communication cannot be realized, which, however, are essential to the broadband OAM MDM system combined with the current wavelength division multiplexing (WDM) system.
To acquire a wideband HLPG, recently the dual-resonant peaks technique, i.e., periods of the utilized HLPGs are optimally selected so that the resonant couplings between two coupled modes occur at or near their dispersion-turning-points (DTPs) [3,8,9]. By using such method to a single-mode fiber (SMF)-based HLPG, Zhou et al. have experimentally demonstrated a band-tunable broadband OAM mode converter, where the rejection filters with a 10-dB bandwidth of ∼195 nm but centered at wavelengths of either 1700nm or 2000nm were successfully demonstrated [10]. However, both of the available bands obtained above are lied beyond the C- and L-band (ranging from 1530 nm to 1625 nm) and more importantly, the generated mode is limited to the first-order OAM one. To overcome the above issue, most recently, we have proposed a broadband second-order OAM converter, where a phase-modulated HLPG was particularly designed and assumed to be inscribed in a thinned four-mode fiber (4MF). As a result, a second-order OAM mode converter enabling to cover the full C- and L-band has been numerically demonstrated [15]. However, the proposed method requires precise control of each grating period, making it extremely difficult to be fabricated in practice. To date, the higher-order OAM mode generators with a broadband enabling to cover the full C- and L-band are strongly required but have rarely been practically demonstrated.
In this study, an ultra-broadband second-order OAM mode generator covering the full C- and L-band has been proposed and experimentally demonstrated, which is based on utilization of a HLPG operated near the dispersion turning point (DTP) and working at its second-order diffraction. As a typical result, an ultra-broadband rejection filter with a depth of ∼23 dB, a bandwidth of ∼156 nm @-10 dB (ranging from 1522 nm to 1678 nm) or a bandwidth of ∼58 nm @-20 dB (ranging from 1574 nm to 1632 nm), has been successfully achieved. To the best of our knowledge, this is the first experimental demonstration of such ultra-broadband second-order OAM mode generator by using only one fiber component. In addition, it has been experimentally demonstrated that the proposed HLPG features with less-sensitivity to the ambient temperature and much fewer polarization-dependence than those of the other fiber-based OAM generators.
2. Principle and design results
It is commonly believed that the refractive index modulation Δns induced in an HLPG is originated from either the eccentric core of the fiber or the resident strain produced during the periodical fiber-twisting procedure, which in general can be expressed as [11,16,17],
Furthermore, to realize an LPG/HLPG-based device with a wideband transmission spectrum, the modal dispersion of the coupled modes and its effects need to be considered [18]. In general, the 20-dB bandwidth Δλ of a uniform LPG/HLPG with length L that offers 30-dB maximal coupling can be approximated by [19],
where Δng represents the difference in group indices of the two coupled modes, which can be further expressed by the following equation based on the condition of Eq. (1),Equations (3) and (4) show that for a fixed length HLPG, the bandwidth of the resulting bandwidth is inversely proportional to the difference in group indices of Δng. Therefore, the broadband spectrum can be obtained as long as the HLPG is operated at a nominal wavelength λ0 where the condition Δng ≈ 0 (which can be equivalently expressed as dΛ/dλ ≈ 0) is satisfied [3,4,7,10]. As such, the wavelength λ0 is generally called the DTP wavelength. However, it has been demonstrated that in a commonly-used FMF, the DTP wavelengths for any two coupled in-core modes, e.g., the DTP one related to the modes LP01 and LP21, in general are lied beyond the C- and L-band [15], which makes the DTP method rarely used in FMF-based HLPGs to generate a broadband higher-order OAM mode.
In order to conquer the above obstacle, a thinned FMF instead of the conventional one was considered to realize the broadband HLPG in this study, which can be optimally obtained by adiabatically reducing the core/cladding diameter of the original four-mode fiber during the drawing process [10,20]. At beginning, a conventional four-mode fiber provided by YOFC Inc. was used, where the original core diameter, the original cladding diameter, and the difference in refractive indices between the core and cladding are 19.0 µm, 125.0 µm and 0.006, respectively. Based on Eq. (2), the required grating periods in terms of the different resonant wavelengths and the corresponding DTP wavelengths for both the conventional and the thinned HLPGs can be numerically obtained by using the finite element method [15]. The results are shown in Fig. 1(a), where original 4MF and four kinds of the thinned 4MFs, i.e., the fibers with cladding/core diameters of 125.0 µm/19 µm, 100.0 µm/15.2 µm, 97.5 µm/14.8 µm, 93.8 µm/14.3 µm, and 87.5 µm/13.3 µm, respectively, were particularly selected. Figure 1(a) shows that when the original 4MF is utilized, i.e., the cladding/core diameters are adopted as 125.0 µm/19.0 µm, the corresponding DTP wavelengths is larger than 1700nm, which is really beyond the C + L bands. For more clarity, the period slope spectra (i.e., the first derivative to those curves shown in Fig. 1(a)) are also depicted and shown in Fig. 1(b). Figure 1(b) shows that the DTP wavelengths decrease with a decrease in the cladding/core diameters. Specifically, as the cladding/core diameters change from 125.0 µm/19.0 µm to 100.0 µm/15.2 µm, 97.5 µm/14.8 µm, 93.8 µm/14.3 µm, and 87.5 µm/13.3 µm, respectively, the calculated DTP wavelengths change from larger than 1700nm to 1592 nm, 1567 nm, 1527 nm, and 1394 nm, respectively. Whereas the corresponding DTP periods shown in Fig. 1(b) change from less than 943.8 µm to 726.7 µm, 703.6 µm, 685.0 µm, and 635.9 µm, respectively. Especially, for case of 97.5 µm in the diameter of the cladding, the obtained DTP wavelength becomes 1567.0 nm (the corresponding period is 703.6 µm), which locates at almost the center of C + L bands as shown in Fig. 1(b).
Fig. 1. The calculated relationship between grating periods and resonant wavelengths of HLPGs with different cladding diameters. (a) Spectra of the required period and (b) spectra of the period slope.
By using transfer matrix method [17], we further calculated the transmission spectra of the HLPGs with five different cladding diameters of 125 µm, 100 µm, 97.5 µm, 93.8 µm, 87.5 µm, respectively. The operating wavelength is specially selected as 1580 nm as shown in the green dash line of the Fig. 1(a), which is near to the center of C + L bands. Then according to the results shown in Fig. 1(a), the required periods for the utilized five kinds of the fibers are adopted as 973.7 µm, 726.8 µm, 704.1 µm, 688.2 µm, and 700.8 µm, respectively. The transmission spectra of the five HLPGs are shown in Fig. 2, where all HLPGs are assumed to have rejection depth larger than 25 dB. Figure 2 shows that for the five different HLPGs, i.e., the HLPGs with cladding diameters of 125.0 µm, 100.0 µm, 97.5 µm, 93.8 µm, and 87.5 µm, respectively, the 10-dB bandwidth obtained are ∼65 nm, ∼126 nm, ∼168 nm, ∼226 nm, and ∼14 nm, respectively, and the 20-dB bandwidth obtained are ∼22 nm, ∼77 nm, ∼99 nm, ∼20 nm, and ∼5 nm, respectively. For the HLPG with a diameter of 100.0 µm, the flat-top spectrum can be obtained, however it cannot cover the full C + L bands. By using the HLPG with a diameter of 93.8 µm, although the widest 10-dB bandwidth (∼226 nm) can be obtained, the 20-dB bandwidth of itself is just ∼20 nm, which even cannot cover the individual L band. Of which, the HLPG with a diameter of 97.5 µm, has 10-dB and 20-dB bandwidths of ∼168 nm and ∼99 nm, respectively, which achieve a good balance between the wide bandwidth and the flat-top spectral characteristics. In view of the above results, the HLPG with the cladding diameter of 97.5 µm was further considered and used to demonstrate the wideband second-order OAM generator below.
Fig. 2. Transmission spectra of the five different HLPGs with cladding diameters and grating periods of (125.0 µm, 973.7 µm), (100.0 µm, 726.8 µm), (97.5 µm, 704.1 µm), (93.8 µm, 688.2 µm) and (87.5 µm, 700.8 µm), respectively.
To further characterize the wideband performance of the DTP method-based thinned HLPG selected in study (i.e., the HLPG with a diameter of 97.5 µm), transmission spectra of five thinned HLPGs with grating periods that are all very close to the DTP one (703.6 µm) had been calculated and compared each other. The calculated results are shown in Fig. 3, where the five different grating periods, i.e., 703.6 µm, 704.1 µm, 704.6 µm, 705.1 µm, and 705.6 µm, are particularly adopted. Figure 3 shows that when the grating period is precisely chosen as the value of 703.6 µm, a relative wide dip with a flat-top bandwidth of ∼44 nm@-26 dB can be obtained. As the grating period is further increased, the obtained bandwidths will gradually increase and at cost of the slight bandwidth enhancement, the resonant dip will be split into two, the spectral ripple larger than 7.5 dB can be observed when the grating period is changed from 703. 6 µm to 705.6 µm. The above results reveal that the HLPG with a specific period but very close to the DTP one may be expected to achieve a good balance between the wide bandwidth and the flat-top spectral characteristics. In concrete results, as the optimal designed results, the thinned HLPG with the period of 704.1 µm and the diameter of 97.5 µm was considered for fabrication, where a spectral dip with bandwidth of 168 nm @-10 dB (ranging from 1471 nm to 1639 nm) and a bandwidth 99 nm @-20 dB (ranging from 1515 nm to 1614 nm) then can be expected to be obtained in experiment.
Fig. 3. Transmission spectra of the thinned HLPGs (with a same magnitude of 97.5 µm for their cladding diameters) under the conditions of five different periods.
3. Fabrication and measurement results
In order to verify all the simulation results above, HLPGs operated at wavelengths near the DTP (THLPGNDs) were fabricated by using thinned 4MFs. All the parameters adopted for the designed grating are arranged to be the same as those optimally obtained in the simulation. The experimental setup is shown in Fig. 4, which mainly consists of a CO2 laser (Synrad, FSTI60SFH), three motorized translational stages (ThorLabs, LTS300/M), a motorized rotator (ThorLabs, DDR25/M), and a testing system for measuring the transmission spectra of the designed grating.
During the fabrication process, first, both ends of the utilized 4MF were fixed at a clamp (on stage 3) and center of the rotator (on stage 2), respectively, as shown in Fig. 4. Next, the utilized fiber was homogeneously heated to its fused status. By using a sapphire tube instead of a focused lens generally adopted in CO2 laser direct-writing techniques, part of the fiber located in the sapphire tube region can be homogeneously heated. As a result, the gratings with uniform diameter and extremely low insertion-loss can be obtained [20]. Subsequently, the utilized fiber was moved by driving the translation stages 2 and 3, and at the same time the heated fiber within the sapphire tube was twisted by driving the rotator on stage 2. The diameter and period of the designed grating were precisely controlled by adjusting the speeds of both the translational stages and the rotator simultaneously. Concretely, the diameter of the designed grating can be precisely controlled according to the following equation,
where Do and Dt represent the diameters of the original and thinned fiber, respectively. V2 and V3 represent the moving velocities of the stage 2 and the stage 3, respectively (in the unit of mm/s). In our experiment, the moving velocities for the stage 2 and stage 3 were set as 0.428 mm/s and 0.704 mm/s, respectively. Noted that since the speed of the stage 2 is smaller than that of the stage 3, an axial stress can be stably applied on the utilized fiber, which keeps the fiber straight all the time during the fabrication process and can precisely control the cladding diameter by lengthening the fiber itself. Meanwhile, the period of the designed grating can be precisely controlled according to the following relation, where Ω represents the rotation speed of the rotator (in the unit of rpm). In our experiment, the rotation speed of the rotator was set as 60 rpm. Based on the above settings, the really obtained diameter, period, and total length of the designed grating are 97.5 µm, 704 µm, and 35.2 mm (with 50 periods), respectively.For clarity, the microscopic images of the original 4MF (bottom figure) and the fabricated grating (top figure) are shown in Fig. 5. Figure 5 shows that the fabricated grating has a clear surface and a high-uniform diameter of approximately 97.5 µm through all length of the grating.
Fig. 5. Microscopic photos for part of the fabricated grating and the original four-mode fiber. (a) The fabricated grating and (b) the original four-mode fiber.
Figure 6 shows the transmission and polarization-dependent loss (PDL) spectra for one of the fabricated gratings, which were obtained by using an optical spectrum analyzer (OSA: Yokogawa, AQ6370), a wideband light source (YSL, SC-5), and a home-made polarization control system. From Fig. 6, it can be seen that a flat-top notch with a depth of ∼23 dB and a central wavelength around 1600 nm, 10-dB bandwidth of ∼156 nm (ranging from 1522 nm to 1678 nm), 20-dB bandwidth of ∼58 nm (ranging from 1574 nm to 1632 nm) has been successfully obtained. The obtained 10 dB and 20 dB bandwidths are slightly less than those of simulation results (as shown in Fig. 3) and the central wavelength of the obtained notch is slightly shifted to the long wavelength direction, which may be ascribed by the fact that there inevitably exist some fabrication deviations in both the grating period and the diameter of the utilized four-mode fiber. Except for the above discrepancy, the experimental results shown in Fig. 6 fairly agree with the simulation one, which, to the best of our knowledge, represents the first experimental demonstration such broad yet flat-top filter enabling to be operated at wavelengths covering the full C- and L-band. Moreover, the PDL spectrum of the fabricated grating was also measured. The result is shown in Fig. 6 also (the red solid line). All the PDLs measured at wavelengths ranging from 1300 nm to 1700nm are small ones less than 3 dB, which indicates that the grating proposed in this study is almost the polarization-independent, for the core mode HE11 with either the left circular polarization or the right circular polarization will be respectively coupled into the higher HE or the TE/TM modes which have similar effective refractive indices [21].
To further demonstrate that within the considered wavelength range (i.e., from 1530 nm to 1625 nm), the resonantly excited higher-order azimuthal modes in the fabricated grating are of second-order OAM modes, the experiments to measure both the intensity and the phase distributions of the beams emitted from the grating were introduced. Figure 7 shows the measuring setup, where a wavelength-tunable laser (ID Photonics, CBDX2-NC-NL-FA) emitted at wavelengths ranging from 1527.6 nm to 1611.7 nm was used as the light source. As shown in Fig. 7, the laser beam emitted from the tunable laser was split into two by a 3-dB fiber coupler. The beam in the upper arm was inputted into the fabricated grating. The output beam from the grating was collimated and combined with the reference beam by using an objective lens (40x) and non-polarization beam splitter (NPBS). Whereas the beam in the down-arm functions as a reference light (spherical Gaussian beam), which was specially used to produce the interference fringes (interferograms) with upper beam. Intensity distributions of the resulted OAM beams and the corresponding interferograms were recorded in-situ at imagining plane of the IR-CCD (Xenics Photonics, Bobcat 320). A polarization controller (PC) and an attenuator were especially inserted into the down-arm, which were used to adjust the visibility of the resulted interferogram.
Fig. 7. Intensity distributions and the interference patterns for the generated second-order OAM modes at five different wavelengths, respectively in (a) C band and (b) L band.
Figure 8 shows all the imaging patterns observed in the CCD display, where Figs. 8(a) and 8(b) represent the results measured at five different wavelengths which are lied in C- and L-band, respectively. Specifically, in Figs. 8(a) and 8(b), the intensity distributions of the tested beams are shown in the first raw of these two figures, which were directly obtained by blocking the reference beam. Whereas the interferograms, phase distributions of the tested beams are shown in the second raw of these two figures. From these figures, it can be obviously found that both the donut-like intensity distributions and the dual-pedal like interference patterns can be observed at the cases of ten different wavelengths, which in return means that a full C- and L-band covered second-order OAM generator has really been achieved in this study. The OAM modes with opposite topological charge can also be generated by using the THLPGND with opposite helicity [11].
Fig. 8. Intensity distributions and the interference patterns for the generated second-order OAM modes at five different wavelengths, respectively in (a) C band and (b) L band.
Next, the temperature effect on spectral characteristic of the fabricated grating was also investigated. In the experiment, the fabricated grating with room-temperature spectrum shown in Fig. 6 was used as the testing object, which was inserted into a temperature controller, where the temperature with resolution of ±0.5°C can be continuously changed. Figure 9 shows the measurement results for changes of the central wavelength and the bandwidth of the spectral band vs. the ambient temperature, where the temperature is changed from 30 °C to 60 °C with an interval of 5 °C. It can be seen that when the temperature is changed from 30 °C to 60 °C, the maximum fluctuation (ripple) on the central wavelength and bandwidth of the dip are less than 2 nm and 3.2 nm, respectively, showing that the fabricated grating is rarely affected by temperature changes, as the HPLG is written in a four-mode fiber and operated at its second-order diffraction [22].
Fig. 9. Changes of the central wavelength and bandwidth @20 dB of the spectral dip vs. the applied temperatures.
For comparison purpose, the performances of the main LPGs/HLPGs-based OAM generators demonstrated so far have been summarized in Table 1, where all the listed components are compared one another according to their characteristics including the 10-dB and 20-dB bandwidths (BWs), order of the generated OAM mode, with or without the need of additional component (AC), such as the polarization controller which may cause polarization-dependent characteristics, the useful band with or without covering the full C- and L-band. From this table, it can be seen that among all the listed OAM mode generators, besides the common features, such as the second-order OAM mode generation, without the need of addition component, the proposed device is the unique one enabling to provide a broadband fully covering the full C- and L-band. Moreover, the proposed device has the third widest 10-dB bandwidth and the widest 20-dB bandwidth. The 10-dB bandwidth of the proposed generator is merely less than that of the HLPG using the dual-resonant peaks technique (HLPGD) and the phase-shifted LPG, however they cannot generate second-order OAM modes. In addition, the better 20-dB bandwidth characteristics of the designed device (THLPGND) can help it generate higher purity second-order OAM modes. These excellent features make us believe that the proposed device may find potential applications in future WDM and OAM MDM systems.
Table 1. Performance comparisons for different LPGs/HLPGs-based OAM mode generators.
4. Conclusion
In this study, an ultra-wideband generator of second-order orbital-angular-momentum (OAM) modes based on a thinned helical long-period fiber grating is proposed and demonstrated. By optimally designing the diameter and period of the HLPG, the designed HLPG is operated near the dispersion turning point (DTP) and works at its second-order diffraction. As a result, the proposed generator can cover a bandwidth of 156 nm @-10 dB and 61 nm @-20 dB with a depth fluctuation of less than 0.1 dB @-23 dB. To the best of our knowledge, this is the first demonstration of a second-order OAM mode generator with a bandwidth enabling to cover the entire C- and L-band by using only one fiber component. Moreover, the proposed device is polarization-independent and the obtained bandwidth is less sensitive to the ambient temperature changes, which may find potential applications in OAM MDM combined with wideband WDM systems.
Funding
National Key Research and Development Program of China (2023YFB2804900); National Natural Science Foundation of China (62375134); Japan Society for the Promotion of Science (JP 22H01546); Amano Institute of Technology; Natural Science Research of Jiangsu Higher Education Institutions of China (22KJB510030); Graduate Research and Innovation Projects of Jiangsu Province (SJCX23_0575).
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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