Open Access
Add to BibSonomyAbstract
We propose a family of ring-core fibers, designed for the transmission of OAM modes, that can be fabricated by drawing five different fibers from a single preform. This novel technique allows us to experimentally sweep design parameters and speed up the fiber design optimization process. Such a family of fibers could be used to examine system performance, but also facilitate understanding of parameter impact in the transition from design to fabrication. We present design parameters characterizing our fiber, and enumerate criteria to be satisfied. We determine targeted fiber dimensions and explain our strategy for examining a design family rather than a single fiber design. We simulate modal properties of the designed fibers, and compare the results with measurements performed on fabricated fibers.
© 2015 Optical Society of America
1. Introduction
Spatial division multiplexing (SDM) is a promising technique for increasing fiber capacity [1, 2]. SDM can be supported by multimode (or few-mode) fibers, multicore fibers, or both. In most cases, this new multiplexing scheme is incompatible with standard monomode or multimode fibers, and requires the design of new types of fibers.
We concentrate on mode-division multiplexing using the orbital angular momentum (OAM) of light in multimode fibers, as it has the potential to provide an additional degree of freedom for data multiplexing, without the need for heavy MIMO processing [3]. These modes are characterized by an annular field intensity. Each OAM mode is composed from a single vector mode, as opposed to LP modes that are combinations of multiple vector modes in a mode group. To support OAM modes, the fiber must exhibit 1) large effective index separation between vector modes to minimize intermodal coupling between OAM modes and to avoid degeneracy into LP modes, and 2) a fiber profile that is compatible with the donut shaped OAM fields. Those two characteristics lead to the choice of a fiber design with an annular profile, or a ring-core fiber (RCF), with a high index contrast [4].
For ease of both analysis and fabrication, we examine a simple step-index, ring-core profile. While more complex profiles, e.g., with graded index [5], with hollow core [6], or with a trench of lower index in the cladding [7], could potentially improve fiber performance, their design cannot be tackled as easily analytically. Our interest is twofold – first system performance, but also greater understanding of parameter impact on performance in the transition from design to fabrication. We have a theoretical basis to relate step-index parameters to fiber characteristics such as number of supported modes and their relative effective index separation. By concentrating on step-index RCF we can relate measured fiber characteristics to design parameters in a straightforward manner.
In section 2, we discuss the design parameters of our fiber. We enumerate criteria to be satisfied and we determine the targeted fiber dimensions. Finally, we explain our motivation for examining a design family rather than a single fiber design. In section 3, we simulate modal properties of the designed fibers, and compare the results with the criteria we set. In section 4, we give some measurements performed on fabricated fibers, and we compare those measurements with simulated values. Finally, in section 5, we discuss our results.
2. Choice of fiber parameters
In the design of an optical fiber, many parameters need to be determined. Some parameter values are imposed by physical constraints, e.g., the use of a silica cladding, or a given fiber fabrication process. Other parameter values are determined by the characteristics we want to achieve. We must also take into account the potential impact of fiber imperfections induced by the fabrication process.
Because fiber preform produced by the modified chemical vapor deposition (MCVD) process is the costliest part of fiber fabrication, we adopt a novel technique to sweep parameters of a family of OAM fibers at comparable cost to a single fiber fabrication. The family of fibers could be created by drawing five different fibers from a single preform. By changing the drawing speed at several points in the fiber drawing, we will create fibers with different diameters. As no couplers or definite diameters currently exist for OAM-transmitting fibers, this incurs no greater experimental difficulty – a free space coupling system must be used in any case.
The ratio between the inner and outer radius of the core will remain constant, but each fiber will have different modal characteristics. In theory, one fiber will be superior to the other (the true design target), however variations during the fabrication of the fiber could favor a neighboring target value. More importantly, we will produce many closely related fiber specimens, facilitating experimental comparisons and inferences for our design process. In the next section we focus on the development of this model.
2.1. Design constraints and refractive index modeling
The first design goal to be set is the number of modes we want our fiber to support. The fundamental mode (HE1,1 or LP0,1) is always present and can be used for multiplexing, however, it is not really an OAM mode as it cannot carry angular momentum (topological charge is zero). The first OAM modes are OAM±1,1, based on the HE2,1 vector mode. The second set of OAM modes is OAM±2,1 composed of HE3,1 or EH1,1 modes. We elected to target three fibers supporting OAM±1,1 modes and two fibers supporting both OAM±1,1 and OAM±2,1 modes.
The information bearing capacity of the fiber is determined by the combination of modal and polarization multiplexing. The fundamental mode (HE1,1) can support two polarizations. With OAM fiber modes, we must use left and right circular polarizations for multiplexing. The first OAM modes (OAM±1,1) can carry only one circular polarization each. The OAM±2,1 modes (and all higher order OAM modes) can carry both left and right circular polarization, thus four channels for multiplexing. The family of fibers we design will then have three fibers supporting four information channels, and two fibers supporting eight information channels.
A step-index profile of a ring-core fiber is illustrated in Fig. 1. We target a specific ratio ρ = a/b constant across fibers, a value used for the production of the preform. The external cladding diameter Φclad must be between 80 μm and 200 μm, otherwise the fiber would be too fragile. The value of n2 is determined by the refractive index of the silica cladding. The refractive index of the core can be varied by adjusting the composition of the glass.
Finally, to favor the transmission of OAM modes, we will target a refractive index separation Δneff only slightly above a 1 × 10−4 threshold. This was demonstrated to reliably support OAM modes [6, 8]. All these criteria are summarized in Table 1.
Table 1. List of design criteria
A high refractive index contrast favors the separation of the effective indices of the modes [5, 6, 7]. However, material constraints must be considered, as too high GeO2 doping causes the glass to break. We therefore fix n1 to the highest possible value we can reach without compromising the integrity of the preform. This value will be Δn = n1 n2 = 0.03 at λ =1550nm. This corresponds to a 19% molar fraction of GeO2 in SiO2. We −neglect the presence of any other materials, such as phosphorus, that might be present in the doped silica. Another way to express this contrast is to use the ratio , as this parameter is used in cutoff equations of RCF [9]. For our n1 choice, this yields .
To model the wavelength dependency of the silica refractive index, we use the well-known Sellmeier equation [10]. Refractive index of the GeO2 doped region is calculated using the Claussius-Mossotti interpolation scheme, given in [11]. This formula provides a well-behaved functional relationship, and is in agreement with many measured glass compositions. Therefore, it is more robust than a simple linear interpolation [12], where the accuracy of the interpolation depends on a single data set. The fiber refractive index parameters used in our simulations are summarized in Table 2.
Table 2. Fiber index parameters.
2.2. Choice of core dimensions
Having fixed refractive indices n1 and n2, the choice of inner and outer radii a and b remains, as it will determine the number of guided modes supported by the fiber, and the minimal distance Δneff between the effective indices of the supported modes.
We recently [9] developed simplified cutoff equations for RCF, allowing production of a modal map that plots cutoff limits of different modes as a function of fiber parameters. A modal map specifies the number of guided modes for given fiber parameters. In Fig. 2, we plot a modal map using the fiber parameters determined so far. Regions delimited by cutoff curves give us the number of guided modes supported by a given fiber design. On the same figure, we also plot the minimum Δneff as function of fiber parameters, as a colormap. The minimization is taken over the pair-wise index difference of all modes supported in that parameter region.
Fig. 2 Modal map (solid black lines), along with minimal Δneff (colormap), as function of core radius ratio ρ and normalized frequency V0 [see (2)]. Horizontal dashed line is the chosen ρ parameter, while dots indicate chosen fiber parameters.
Consider the four regions delimited by the cutoff curves. The white region (labeled I) is where parameters lead to a monomode fiber. This region is separated from the next region by the cutoffs for TE0,1, TM0,1, and HE2,1 modes (curves are superimposed). In the next region (II), fiber supports OAM±1,1 mode, and Δneff is the minimal separation between TE0,1, TM0,1, and HE2,1 modes. Then we have the cutoffs of EH1,1 and HE3,1 modes (curves tightly spaced). The third region (III) corresponds to fibers supporting both OAM±1,1 and OAM±2,1 modes. In that region Δneff refers to the minimum mode separation within both families. Finally, at bottom right we have the cutoff of HE1,2 mode; the region under that line (IV) also includes all other modes and HE1,2. We want to avoid that region, because modes with higher radial order (i.e. with m ≥ 2) are more difficult to multiplex and demultiplex. The m = 1 solution with a single intensity ring have been the focus of data transmission demonstrations as they are easier to manipulate, given the paucity of components available today for OAM. There is the added complication of finding a design that avoids crosstalk between modes of different radial order, since modes with m > 1 have effective indices with a different slope, resulting in effective index curves that cross at some wavelengths, thereby causing Δneff to become very small.
The goal is to choose a fixed value of ρ (the ordinant) along which five values of V0 (the abscissa), so as to obtain five targeted fibers with large Δneff, preferably above our threshold of 1 × 10−4, i.e., as red as possible in the colormap and avoiding dark blue. We also want to avoid modes with m parameter greater than one, otherwise the fiber would support modes having concentric rings of intensity in their fields. Finally, it is desirable to have fiber parameters that are significantly away from cutoff, as modes near cutoff are less tolerant to fiber imperfections. The set of five fibers, once fabricated, will allow us to compare the simulated characteristics with measured fiber properties. The first three should support the LP1,1 mode group (OAM1,1) and the two last ones should also support the LP2,1 mode group (OAM2,1). Taking the goals as described, we chose a design illustrated in Fig. 2 by a horizontal dotted line at the selected value of ρ = 0.35. Five dots for the V0 values selected correspond to the five values of a and b indicated in Table 3. Fiber 1 has the smallest cladding diameter, while fiber 5 has the thickest.
Table 3. Geometry of the designed fibers (rounded to the second decimal).
3. Description of modal properties
Effective indices of the different modes are numerically calculated using the transfer-matrix method [13]. Results are summarized in Table 4. We also plot, in Fig. 3, normalized propagation constant
as a function of normalized frequency for all the guided modes. In Fig. 3, vertical dashed lines indicate V0 for the different fibers when λ = 1550nm. For the transmission of OAM modes, we are interested in the separation between the effective indices within a mode group (Δneff). We target this separation to be as large as possible, and at least 1 × 10−4 (criteria #4). The calculated effective index separations are given in Table 5. As we can see, our design criteria is respected for three fiber designs, but not for fiber 1 and fiber 5. This will allow us to test the stability of OAM modes vis-a-vis our threshold of 1 × 10−4.Table 4. Effective indices of the modes (at 1550 nm).
Table 5. Effective index separation within mode groups (at 1550 nm).
4. Fiber fabrication and tests
4.1. Fiber fabrication
The optical fibers were fabricated in-house with modified chemical vapor deposition (MCVD) and fiber drawing facilities. Two steps were used in order to produce the correct preform geometry. First, adequate concentrations of SiO2 and GeO2 were deposited to produce the ring core layer, followed by a deposit of SiO2 to match the index profile cladding. Finally, the tube was collapsed to produce the glass preform. The ring-core diameter was controlled during the fiber drawing process to achieve the desired geometry of the fiber.
The fiber refractive index profile (RIP) was measured using an EXFO NR-9200 operating at 657.6 nm. On Fig. 4, we plotted the designed rectangular profile (transposed to this wavelength) along with the x-scan and y-scan (light traces), for two fiber samples. The bolder, rounded trace represents an average over the four measurements with symmetry imposed. As we can see, the fabricated fiber is a relatively good match to the designed profile. However, the 0.4 μm spatial resolution of the RIP profiler cause the measured profile to appear smoother that it really is.
Fig. 4 Designed (red) and measured (blue: averaged, others: x- and y-scan on both directions) profile (at λ = 657.6nm), for samples of fiber 2 and fiber 4. Profile of other fibers are similar.
We successfully transmitted OAM modes through the fabricated fibers, generating OAM modes in free-space using a spatial light modulator (SLM), and coupling the OAM beam into the fiber. The ring intensity profile was measured, as well as an interference pattern confirming the characteristic OAM spiral form. Representative measurements for fiber 2, after transmission through 2 m, are presented in Fig. 5. The intensity profile is not as perfectly ring-shaped for all fiber samples, especially when transmitting over a longer distance, because of the coupling between modes. However, in all cases, including transmissions between 1 and 1.5 km, we could visualize the spiral interference pattern, confirming the presence of the launched OAM modes. Coupling into RCF4 and RCF5 was particularly challenging due to the size of fiber (poor match with available bare fiber adapters) and, in the case of RCF5, its brittleness.
Fig. 5 Output intensity profiles after 2 m transmission in fiber 2 for the (a) OAM−1,1 and (b) OAM+1,1 modes, at 1550 nm. Corresponding output interference patterns with a Gaussian beam for the (c) OAM−1,1 and (d) OAM+1,1 modes.
4.2. Effective index measurement
To verify calculated values for effective index, we wrote a weak FBG on the fibers, then we analyzed the reflectogram, using the method described in [14]. The designed grating length is 40 mm with a tanh shape apodization (coefficient s = 4), and the mask period is ΛPM = 1070nm. For each fiber design, we measured the Bragg reflection on three different samples, and we averaged the wavelength positions of the reflection peaks. A sample reflectogram is given on Fig. 6. Figure 7 was generated by taking reflectograms for all five fibers (including that shown in Fig. 6), scaling each reflectogram so that the peak values appear similar, and plotting them along a common x-axis. The y-axis remains roughly in dB and relative heights within a reflectogram are noteworthy, however absolute heights from reflectogram to reflectogram convey no information.
Fig. 7 Superimposed FBG reflectogram for all fibers. This allows comparison of reflection wavelengths for the different fibers. All reflectogram were vertically aligned and scaled to fit the graph, hence absolute heights from reflectogram to reflectogram convey no information.
On fibers 1 and 3, we measured four different peaks on the second mode group, instead of the three expected peaks. We suspect the two central peaks to be the result of birefringence, caused by fiber imperfections. Therefore, we considered the average between the wavelengths of those two peaks as the reflection wavelength of the HE2,1 mode.
We cannot rely on the absolute measured neff values, as many parameters can shift this value, e.g., fiber stress during FBG writing and temperature when performing the measurement. However, since we expect the effective indices of all modes to shift together, we can compare the measured effective index separation within mode groups (Δneff) with the predicted values. Results are summarized in Table 6. The relative difference is given by the absolute error divided by the measured Δneff. As we can see, there is some variation between measured and simulated values. However, this variation always is at the fifth or the sixth decimal of the effective index. We compare very small values, and the difference can be attributed to both non-ideal fabricated fiber — e.g., longitudinal variation of the index profile along the fiber, core ellipticity (i.e. form birefringence), any bends of the fiber, and environmental variations (moving air, temperature, etc) — and measurement errors.
Table 6. Δneff measured values (using FBG), compared to calculated values.
5. Discussion
Our simulations show that as expected the lower is the number of supported modes, the easier it is to design a fiber with a large effective index separation within mode groups. We can see this in Fig. 2, where the red area (corresponding to Δneff ≥1×104) is more extensive for the region supporting only the first OAM mode, than it is for the region supporting more OAM modes.
We fabricated one fiber preform which we used to engineer the family of five different fibers in a single drawing run. The measured RIP shows a relatively good agreement between targeted and realized profiles. The fact that all fibers but fiber 2 have unusual cladding diameters led to unexpected challenges. While free-space coupling is used for advanced experimentation, simple characterization of power, etc. would be greatly facilitated if we could exploit telecom equipment and measurement systems made for 125 μm fibers. Furthermore, it could be possible to draw fibers with different core dimensions, but with the same cladding diameter, by etching the preform as needed, before fiber drawing. Were we to again fabricate a family of fibers from a single preform, this is the approach we would prefer.
Experimental manipulations also highlighted the impact of the core dimensions on OAM coupling from free-space to fiber. Several lenses were tested via trial and error to achieve good coupling of the free-space OAM beam with the RCF. The inner / outer core radius ratio ρ also is important. In free-space OAM beams, this ratio is a function of topological charge; it is lower for lower order OAM modes [7]. Therefore, the ideal coupling setup on a given fiber is different for each mode, and a trade off is needed when simultaneously coupling all OAM modes. A commercial OAM system will use multiplexers whose efficiency may ultimately also vary with ρ, however these technologies are still under research [15, 16, 17].
Measurements on effective index performed using FBG confirmed that the fabricated fibers support the expected number of modes. We also observed high birefringence on fibers 1 and 3, probably caused by imperfections induced to the fibers during the fabrication process. As the measurement of effective index difference Δneff requires very precise values, our conclusions are limited to confirming that the effective index separation within mode groups is higher that 1 × 10−4 for most of the modes, as expected.
6. Conclusion
We proposed the design of a family of five ring-core fibers, using the modal map developed in [9]. We proposed a novel way of producing those five different fibers from a single preform, to reduce production costs. We took advantage of the similarities and the differences among those five fibers to better understand how the dimensions of a ring-core with a fixed ρ parameter influence the modal characteristics of the fiber. Experimental manipulations of the fabricated fibers allowed us to confirm that the modal behavior of the fabricated fibers is similar to what was predicted by simulation, and therefore increased our degree of confidence in simulation results. It also revealed some challenges that were not obvious from simulations, giving us new design constraints to consider when fabricating RCF. We confirmed that our design targets were reached, and we have a good knowledge of the modal characteristics of each fabricated fiber.
Acknowledgments
The authors would like to thank Dr. Pravin Vaity for validating transmission of OAM modes in each fiber and providing measurements in Fig. 5.
References and links
1. D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7, 354–362 (2013). [CrossRef]
2. G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photon. 6, 413–487 (2014). [CrossRef]
3. N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013). [CrossRef] [PubMed]
4. S. Ramachandran, P. Gregg, P. Kristensen, and S. E. Golowich, “On the scalability of ring fiber designs for oam multiplexing,” Opt. Express 23, 3721–3730 (2015). [CrossRef] [PubMed]
5. B. Ung, P. Vaity, L. Wang, Y. Messaddeq, L. A. Rusch, and S. LaRochelle, “Few-mode fiber with inverse-parabolic graded-index profile for transmission of oam-carrying modes,” Opt. Express 22, 18044–18055 (2014). [CrossRef] [PubMed]
6. P. Gregg, P. Kristensen, S. Golowich, J. Olsen, P. Steinvurzel, and S. Ramachandran, “Stable transmission of 12 oam states in air-core fiber,” in “CLEO: 2013,” (Optical Society of America, 2013), p. CTu2K.2.
7. C. Brunet, P. Vaity, Y. Messaddeq, S. LaRochelle, and L. A. Rusch, “Design, fabrication and validation of an oam fiber supporting 36 states,” Opt. Express 22, 26117–26127 (2014). [CrossRef] [PubMed]
8. S. Ramachandran, P. Kristensen, and M. F. Yan, “Generation and propagation of radially polarized beams in optical fibers,” Opt. Lett. 34, 2525–2527 (2009). [CrossRef] [PubMed]
9. C. Brunet, B. Ung, P.-A. Belanger, Y. Messaddeq, S. LaRochelle, and L. Rusch, “Vector mode analysis of ring-core fibers: Design tools for spatial division multiplexing,” J. Lightwave Technol. 32, 4046–4057 (2014). [CrossRef]
10. I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55, 1205–1208 (1965). [CrossRef]
11. H. Sunak and S. Bastien, “Refractive index and material dispersion interpolation of doped silica in the 0.6–1.8μm wavelength region,”, IEEE Photonics Technol. Lett. 1, 142–145 (1989).
12. J. W. Fleming, “Dispersion in GeO2–SiO2 glasses,” Appl. Opt. 23, 4486–4493 (1984). [CrossRef]
13. P. Yeh, A. Yariv, and E. Marom, “Theory of bragg fiber,” J. Opt. Soc. Am. 68, 1196–1201 (1978). [CrossRef]
14. L. Wang, P. Vaity, B. Ung, Y. Messaddeq, L. A. Rusch, and S. LaRochelle, “Characterization of oam fibers using fiber bragg gratings,” Opt. Express 22, 15653–15661 (2014). [CrossRef] [PubMed]
15. N. K. Fontaine, C. R. Doerr, and L. Buhl, “Efficient multiplexing and demultiplexing of free-space orbital angular momentum using photonic integrated circuits,” in “Optical Fiber Communication Conference,” (Optical Society of America, 2012), p. OTu1I.2.
16. R. Scott, B. Guan, C. Qin, N. Fontaine, T. Su, C. Ferrari, M. Cappuzzo, F. Klemens, B. Keller, M. Earnshaw, and S. Yoo, “Free-space coherent optical communication demonstration using a 3d photonic integrated circuit device for orbital angular momentum multiplexing/demultiplexing,” in “Optical Communication (ECOC 2013), 39th European Conference and Exhibition on,” (2013), pp. 1–3.
17. G. Labroille, B. Denolle, P. Jian, P. Genevaux, N. Treps, and J.-F. Morizur, “Efficient and mode selective spatial mode multiplexer based on multi-plane light conversion,” Opt. Express 22, 15599–15607 (2014). [CrossRef] [PubMed]
