Abstract

We present a polarization-maintaining PANDA ring-core fiber (PM-PRCF) characterized by the combination of a ring-core structure with two stress-applying rods. This special fiber design separates the adjacent modes and avoids the cutoff of the higher-order modes, which is a common problem in elliptical core polarization-maintaining few-mode fibers. Using a high-contrast index ring and stress-induced birefringence, the PM-PRCF features support for 10 vector modes, with effective refractive index separations from their adjacent modes >104. Broadband performance is investigated subsequently over a wide wavelength range from 1500 to 1630 nm. The proposed fiber is targeted at applications in space-division multiplexing while eliminating the complex multiple-input multiple-output signal processing.

© 2016 Chinese Laser Press

1. INTRODUCTION

The undamped exponential growth of cloud-based traffic, highly centralized data, and mobile services has been stimulating the exploration of expanding the capacity of networks. Miscellaneous multiplexing technologies, such as time-division multiplexing, wavelength-division multiplexing (WDM), and polarization-division multiplexing, have been widely applied to ease the capacity crunch. In view of the fact that existing multiplexing technologies have reached their scalability limits, space-division multiplexing (SDM) has emerged with great potential [1,2]. Few-mode fiber (FMF), as a promising candidate for SDM, has drawn close attention in the fiber-optical communication domain in the recent past [35].

Remarkably, six spatial and polarization modes have been successfully transmitted simultaneously, each carrying 40 Gbit/s quadrature-phase-shift-keyed channels over 96 km FMF [6]. An obstacle encountered with FMFs is mode coupling, and thus multiple-input multiple-output (MIMO) signal processing has to be used to withstand the induced cross talk, causing rises in the cost and the complexity of system [7]. One straightforward solution is to eliminate the degeneracy between adjacent eigenmodes by enlarging the effective refractive index differences to Δneff>104 [8]. From this point of view, a polarization-maintaining (PM)-FMF, having an elliptical core with a step-index profile, was suggested to realize MIMO-free systems [9], and the number of guided PM modes has been increased to eight by utilizing an elliptical ring-core fiber (RCF) [10]. However, in the elliptical core FMFs, the higher-order modes tend to cut off under high ellipticity. As reported in Ref. [11], even with a small ellipticity of 1.5, the odd mode of an LP11 mode group reaches cutoff at 1550 nm; in Ref. [10], this problem is alleviated by an FMF with an elliptical ring core, but the two fundamental modes remain degenerate with insufficient Δneff (105).

In recent years, a type of RCF containing a circularly symmetric ring core with a high-contrast refractive index was utilized for the transmission of orbital angular momentum (OAM) modes, which can split the effective refractive indices (neff) of transverse electric (TE), transverse magnetic (TM), hybrid (HE or EH) modes and greatly simplify the MIMO signal processing [12,13]. The ring-core structure combined with the multicore fiber technique has been proposed for ultrahigh-density SDM [14]. While the OAM modes in RCF are actually the linear combinations of two degenerate even and odd modes of the HE or EH mode groups [15], the ±L-order OAM modes inevitably couple to each other with anisotropic perturbations [16].

In this paper, we propose a PM PANDA RCF (PRCF) that features the combination of a ring core with two stress-applying rods. The ring-core structure, as in the OAM-mode-supported RCFs, is circularly symmetric with a high refractive index contrast between core and cladding, thus effectively preventing cutoffs of the higher-order modes and splitting the HE, TE, TM, and EH modes. The two stress-applying rods induce birefringence, separating the residual degenerate modes, i.e., the even and odd HE or EH modes [17,18]. The fiber structure parameters are selected to enable support of 10 polarization- and spatial-distribution-maintaining modes, with all the effective refractive index differences between the adjacent modes satisfying Δneff>104. Broadband characteristics over a wide wavelength range covering the whole C and L bands are also realizable, which indicates compatibility with the mature WDM technique.

2. FIBER PARAMETER SELECTION AND MODAL PROPERTIES

The schematic cross section and refractive index profile of the proposed PM-PRCF is shown in Fig. 1, where the cladding diameter is W and the gap between the ring core and stress-applying rods is a. The inner radius, outer radius of the ring core, and radius of the stress-applying rods are r1, r2, and r3, respectively. The cladding is made of silica with refractive index n1=1.444 at 1550 nm, while the ring core is GeO2-doped silica due its index n2=1.474, which corresponds to 0.202 molecular fraction doping of GeO2 in SiO2 [19]. The materials of the stress-applying rods, having index n3=1.436, are silica doped with 0.3 molecular fraction of B2O3, which has been reported and utilized in the practical fabrication of high-birefringence fibers [20]. The normalized frequency is defined as V=r2·2π(n22n12)/λ, where λ is the wavelength and the radius ratio is set to be ρ=r1/r2. The detailed elastic material parameters used for modeling are listed in Table 1. The elastic coefficients for the SiO2 cladding and the GeO2SiO2 ring core are obtained from Ref. [21], while the corresponding ones for the B2O3SiO2 stress-applying rods can be found in Refs. [17,22]. Numerical calculations are done by finite element analysis with the COMSOL software package.

 figure: Fig. 1.

Fig. 1. Schematic diagram of the PM-PRCF cross section.

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Tables Icon

Table 1. Elastic Parameters Used for Modeling

In order to determine the structure size of a PM-PRCF that supports 10 eigenmodes (two fundamental modes, four first higher-order modes, and four second higher-order modes) while meeting the requirement of effective refractive index differences Δneff>104 between adjacent modes, we fix W=125μm, a=1μm, and r3=20μm and sweep the two parameters V (from 4 to 6) and ρ (from 0.3 to 0.85) to calculate Δneff at 1550 nm. The selection of the two parameters a and r3 will be discussed later. Figure 2 shows a colormap of the minimum values of the effective refractive index differences between any two of the 10 supported modes as a function of ρ and V. The point V=4.51 and ρ=0.57 is chosen as the target fiber structure size, with neff and Δneff for all the modes listed in Table 2. As shown in Table 2 (as well as in Fig. 3), the superscripts of the mode names show the intensity patterns. The numbers in the subscripts refer to azimuthal and radial indices, while the x or y indicates the polarization direction of electrical field.

 figure: Fig. 2.

Fig. 2. Colormap of minimal Δneff between adjacent modes as a function of ρ and V at 1550 nm for W=125μm, a=1μm, r3=20μm.

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 figure: Fig. 3.

Fig. 3. Intensity distributions and electrical field orientations for the 10 eigenmodes (a) without the two stress-applying rods, (b) with the two stress-applying rods.

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Tables Icon

Table 2. Effective Refractive Index (neff), Effective Refractive Index Difference (Δneff) Between Adjacent Modes, and Chromatic Dispersion (D) at 1550 nm for a=1μm, r3=20μm, V=4.51, and ρ=0.57

Fiber eigenmode profiles are significantly affected by the fiber structure. Benefiting from the high-contrast index ring-core structure, high fields and field gradients exist in the ring core [23]. Figure 3(a) shows the vectorial mode intensity distributions at the ring core in the absence of the two stress-applying rods, along with arrows representing the polarization orientations of electrical fields. All the modes show circularly symmetric patterns and curved polarizations (except for HE11x and HE11y). With the introduction of the two stress-applying rods, the mode profiles distort from the ring shapes into corresponding linearly polarized (LP) mode intensity distributions, while the polarization directions become horizontal or vertical, as shown in Fig. 3(b).

Pursuant to the birefringence theory, stress anisotropy induced by the stress-applying rods increases the Δneff between the two adjacent modes oriented orthogonally in the same order [24], with the intensity of the stress birefringence depending on the gap a between the ring core and the stress-applying rods. As stress is applied to the ring core, the effective index separations occur among the mode pairs, accounting for the evolution from vectorial modes to corresponding LP modes. Along with the decrease in a, the stress exerted on the ring core is enhanced, resulting in an increase in all the Δneff values except for the one between LP11yodd and LP11yeven, shown in Fig. 4. Nevertheless, it is still above 104 for a>1μm. Although the separations between the neff values of the even and odd second higher-order modes (LP21yodd and LP21yeven, LP21xodd and LP21xeven) are influenced heavily by a, the other six modes (two fundamental modes and four first higher-order modes) continue to satisfy Δneff>104 within the range 1μm>a>5μm.

 figure: Fig. 4.

Fig. 4. Effective refractive index neff and effective refractive index difference Δneff as a function of a.

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The radius of the stress-applying rods is closely related to the difficulty of the manufacturing process and the performance of the PM-PRCF. In order to determine the value of r3 to simplify the fabrication process and achieve the target Δneff, we investigate the dependence of Δneff on r3. The Δneff values of the adjacent modes are barely affected by the changes in r3, with the exceptions of LP01x and LP01y, LP21yeven and LP21xodd, and LP11yeven and LP11xeven, as shown in Fig. 5. Though their Δneff values diminish when r3 decreases, the differences remain >104 within the region of r3>8μm. The designed PM-PRCF presents enhanced tolerance to the variations of r3, and hence it is appropriate to choose a small value for r3 such as 8 μm, for which the fabrication process is simpler.

 figure: Fig. 5.

Fig. 5. Effective index difference Δneff as a function of r3.

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By taking advantage of the high-contrast index ring core, the designed PM-PRCF gains large effective index separations between the modes with different polarization manifestations, namely, TE01/TM01 and HE21 for the first higher order, HE31 and EH11 for the second higher order. The introduction of the two stress-applying rods brings birefringence, splitting the remaining degenerate modes, i.e., the even and odd modes in the same order. Due to the unique capability of the PM-PRCF, the 10 modes are all separated from their adjacent modes at the selected fiber structure size in Fig. 2, with the maximum Δneff as large as 6.41×103 between the LP11yodd and LP21xeven modes; the minimum Δneff can still reach 1.29×104 between the LP21yeven and LP21yodd modes, as seen in Table 2.

3. BROADBAND CHARACTERISTICS

We evaluate the performance of the PM-PRCF over a wide wavelength range from 1500 to 1630 nm, covering the whole C and L bands. The refractive indices of SiO2, GeO2SiO2, and B2O3SiO2 at different wavelengths can be found in Refs. [19,20]. Results show the minimal Δneff for the 10 modes over such a wide range is 1.12×104. The chromatic dispersions (D) of all modes are compatible with the values of standard single-mode fiber, except that the maximum value of D, 104ps/nm/km for LP21yodd at 1630 nm, is a little large, as shown in Fig. 6. However, it can be compensated by the established dispersion-compensation techniques [25,26]. The values of D for 10 modes at 1550 nm are given in Table 2.

 figure: Fig. 6.

Fig. 6. Chromatic dispersions for the 10 modes.

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As for the fabrication of the designed PM-PRCF, we believe that it can been achieved using well-developed fiber manufacture technologies. The ring-core structures with high refractive index contrast (and more complex structures) have been realized through a modified/plasma chemical vapor deposition process and used for the transmission of OAM modes [27,28]. The stress-applying rods have been widely used in the PANDA fibers to maintain mode polarizations [2931]. The existing fiber manufacturing technologies provide a solid base for the fabrication of this PM-PRCF.

4. CONCLUSION

In conclusion, we have presented the design of a PM-PRCF supporting 10 polarization- and spatial-distribution-maintaining modes for SDM. The large effective refractive index differences of adjacent modes (>104) allow the maintenance of both the electrical field polarizations and intensity distributions. Broadband performance is demonstrated over a wide wavelength range covering the whole C and L bands with small chromatic dispersions. We are confident that the PM-PRCF will have broad application in MIMO-free SDM combined with WDM for improving optical communication capacity.

Funding

973 Program (2014CB340003); National Natural Science Foundation of China (NSFC) (61307081, 61321004, 61420106003).

REFERENCES

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. S. Yu, “Potentials and challenges of using orbital angular momentum communications in optical interconnects,” Opt. Express 23, 3075–3087 (2015). [CrossRef]  

3. F. Yaman, N. Bai, B. Zhu, T. Wang, and G. Li, “Long distance transmission in few-mode fibers,” Opt. Express 18, 13250–13257 (2010). [CrossRef]  

4. E. Ip, G. Milione, M. J. Li, N. Cvijetic, K. Kanonakis, J. Stone, G. Peng, X. Prieto, C. Montero, V. Moreno, and J. Liñares, “SDM transmission of real-time 10 GbE traffic using commercial SFP+ transceivers over 0.5km elliptical-core few-mode fiber,” Opt. Express 23, 17120–17126 (2015). [CrossRef]  

5. P. Sillard, M. Astruc, D. Boivin, H. Maerten, and L. Provost, “Few-mode fiber for uncoupled mode-division multiplexing transmissions,” in European Conference and Exposition on Optical Communications (Optical Society of America, 2011), paper Tu.5.LeCervin.7.

6. R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R. J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 × 6 MIMO processing,” J. Lightwave Technol. 30, 521–531 (2012). [CrossRef]  

7. S. O. Arik, D. Askarov, and J. M. Kahn, “Adaptive frequency-domain equalization in mode-division multiplexing systems,” J. Lightwave Technol. 32, 1841–1852 (2014). [CrossRef]  

8. S. Ramachandran, J. Fini, M. Mermelstein, J. Nicholson, S. Ghalmi, and M. Yan, “Ultra-large effective-area, higher-order mode fibers: a new strategy for high-power lasers,” Laser Photon. Rev. 2, 429–448 (2008). [CrossRef]  

9. N. Riesen, J. D. Love, and J. W. Arkwright, “Few-mode elliptical-core fiber data transmission,” IEEE Photon. Technol. Lett. 24, 344–346 (2012). [CrossRef]  

10. L. Wang and S. LaRochelle, “Design of eight-mode polarization maintaining few-mode fiber for multiple-input multiple-output-free spatial division multiplexing,” Opt. Lett. 40, 5846–5849 (2015). [CrossRef]  

11. Y. H. Kim and K. Y. Song, “Mapping of intermodal beat length distribution in an elliptical-core two-mode fiber based on Brillouin dynamic grating,” Opt. Express 22, 17292–17302 (2014). [CrossRef]  

12. 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]  

13. J. Wang, “Advances in communications using optical vortices,” Photon. Res. 4, B14–B28 (2016). [CrossRef]  

14. S. Li and J. Wang, “A compact trench-assisted multi-orbital-angular-momentum multi-ring fiber for ultrahigh-density space-division multiplexing (19 rings × 22 modes),” Sci. Rep. 4, 3853 (2014).

15. J. Liu, S. Li, J. Du, C. Klitis, C. Du, Q. Mo, M. Sorel, S. Yu, X. Cai, and J. Wang, “Performance evaluation of analog signal transmission in an integrated optical vortex emitter to 3.6-km few-mode fiber system,” Opt. Lett. 41, 1969–1972 (2016). [CrossRef]  

16. P. Gregg, P. Kristensen, and S. Ramachandran, “Conservation of orbital angular momentum in air-core optical fibers,” Optica 2, 267–270 (2015). [CrossRef]  

17. R. Guan, F. Zhu, Z. Gan, D. Huang, and S. Liu, “Stress birefringence analysis of polarization maintaining optical fibers,” Opt. Fiber Technol. 11, 240–254 (2005). [CrossRef]  

18. B. Yin, S. Feng, Z. Liu, Y. Bai, and S. Jian, “Tunable and switchable dual-wavelength single polarization narrow linewidth SLM erbium-doped fiber laser based on a PM-CMFBG filter,” Opt. Express 22, 22528–22533 (2014). [CrossRef]  

19. J. W. Fleming, “Dispersion in GeO2-SiO2 glasses,” Appl. Opt. 23, 4486–4493 (1984). [CrossRef]  

20. S. H. Wemple, D. A. Pinnow, T. C. Rich, R. E. Jaeger, and L. G. Van Uitert, “Binary SiO2-B2O3 glass system: refractive index behavior and energy gap considerations,” J. Appl. Phys. 44, 5432–5437 (1973). [CrossRef]  

21. W. Urbanczyk, T. Martynkien, and W. J. Bock, “Dispersion effects in elliptical-core highly birefringent fibers,” Appl. Opt. 40, 1911–1920 (2001). [CrossRef]  

22. N. Lagakos, J. A. Bucaro, and R. Hughes, “Acoustic sensitivity predictions of single-mode optical fibers using Brillouin scattering,” Appl. Opt. 19, 3668–3670 (1980). [CrossRef]  

23. 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]  

24. N. Imoto, N. Yoshizawa, J. Sakai, and H. Tsuchiya, “Birefringence in single-mode optical fiber due to elliptical core deformation and stress anisotropy,” IEEE J. Quantum Electron. 16, 1267–1271 (1980). [CrossRef]  

25. R. Noe, D. Sandel, M. Yoshida-Dierolf, S. Hinz, V. Mirvoda, A. Schopflin, C. Gungener, E. Gottwald, C. Scheerer, G. Fischer, T. Weyrauch, and W. Haase, “Polarization mode dispersion compensation at 10, 20, and 40 Gb/s with various optical equalizers,” J. Lightwave Technol. 17, 1602–1616 (1999). [CrossRef]  

26. C. D. Poole, J. M. Wiesenfeld, D. J. DiGiovanni, and A. M. Vengsarkar, “Optical fiber-based dispersion compensation using higher order modes near cutoff,” J. Lightwave Technol. 12, 1746–1758 (1994). [CrossRef]  

27. 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]  

28. H. Li, G. Ren, Y. Lian, B. Zhu, M. Tang, Y. Zhao, and S. Jian, “Broadband orbital angular momentum transmission using a hollow-core photonic bandgap fiber,” Opt. Lett. 41, 3591–3594 (2016). [CrossRef]  

29. Y. Zhang, Y. Wang, S. Cai, M. Lan, S. Yu, and W. Gu, “Mode converter based on dual-core all-solid photonic bandgap fiber,” Photon. Res. 3, 220–223 (2015). [CrossRef]  

30. J. Song, K. Sun, S. Li, and W. Cai, “Phase sensitivity to temperature of the guiding mode in polarization-maintaining photonic crystal fiber,” Appl. Opt. 54, 7330–7334 (2015). [CrossRef]  

31. Y. Dong, L. Teng, P. Tong, T. Jiang, H. Zhang, T. Zhu, L. Chen, X. Bao, and Z. Lu, “High-sensitivity distributed transverse load sensor with an elliptical-core fiber based on Brillouin dynamic gratings,” Opt. Lett. 40, 5003–5006 (2015). [CrossRef]  

References

  • View by:

  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. S. Yu, “Potentials and challenges of using orbital angular momentum communications in optical interconnects,” Opt. Express 23, 3075–3087 (2015).
    [Crossref]
  3. F. Yaman, N. Bai, B. Zhu, T. Wang, and G. Li, “Long distance transmission in few-mode fibers,” Opt. Express 18, 13250–13257 (2010).
    [Crossref]
  4. E. Ip, G. Milione, M. J. Li, N. Cvijetic, K. Kanonakis, J. Stone, G. Peng, X. Prieto, C. Montero, V. Moreno, and J. Liñares, “SDM transmission of real-time 10  GbE traffic using commercial SFP+ transceivers over 0.5km elliptical-core few-mode fiber,” Opt. Express 23, 17120–17126 (2015).
    [Crossref]
  5. P. Sillard, M. Astruc, D. Boivin, H. Maerten, and L. Provost, “Few-mode fiber for uncoupled mode-division multiplexing transmissions,” in European Conference and Exposition on Optical Communications (Optical Society of America, 2011), paper Tu.5.LeCervin.7.
  6. R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R. J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96  km of few-mode fiber using coherent 6 × 6 MIMO processing,” J. Lightwave Technol. 30, 521–531 (2012).
    [Crossref]
  7. S. O. Arik, D. Askarov, and J. M. Kahn, “Adaptive frequency-domain equalization in mode-division multiplexing systems,” J. Lightwave Technol. 32, 1841–1852 (2014).
    [Crossref]
  8. S. Ramachandran, J. Fini, M. Mermelstein, J. Nicholson, S. Ghalmi, and M. Yan, “Ultra-large effective-area, higher-order mode fibers: a new strategy for high-power lasers,” Laser Photon. Rev. 2, 429–448 (2008).
    [Crossref]
  9. N. Riesen, J. D. Love, and J. W. Arkwright, “Few-mode elliptical-core fiber data transmission,” IEEE Photon. Technol. Lett. 24, 344–346 (2012).
    [Crossref]
  10. L. Wang and S. LaRochelle, “Design of eight-mode polarization maintaining few-mode fiber for multiple-input multiple-output-free spatial division multiplexing,” Opt. Lett. 40, 5846–5849 (2015).
    [Crossref]
  11. Y. H. Kim and K. Y. Song, “Mapping of intermodal beat length distribution in an elliptical-core two-mode fiber based on Brillouin dynamic grating,” Opt. Express 22, 17292–17302 (2014).
    [Crossref]
  12. 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]
  13. J. Wang, “Advances in communications using optical vortices,” Photon. Res. 4, B14–B28 (2016).
    [Crossref]
  14. S. Li and J. Wang, “A compact trench-assisted multi-orbital-angular-momentum multi-ring fiber for ultrahigh-density space-division multiplexing (19 rings × 22 modes),” Sci. Rep. 4, 3853 (2014).
  15. J. Liu, S. Li, J. Du, C. Klitis, C. Du, Q. Mo, M. Sorel, S. Yu, X. Cai, and J. Wang, “Performance evaluation of analog signal transmission in an integrated optical vortex emitter to 3.6-km few-mode fiber system,” Opt. Lett. 41, 1969–1972 (2016).
    [Crossref]
  16. P. Gregg, P. Kristensen, and S. Ramachandran, “Conservation of orbital angular momentum in air-core optical fibers,” Optica 2, 267–270 (2015).
    [Crossref]
  17. R. Guan, F. Zhu, Z. Gan, D. Huang, and S. Liu, “Stress birefringence analysis of polarization maintaining optical fibers,” Opt. Fiber Technol. 11, 240–254 (2005).
    [Crossref]
  18. B. Yin, S. Feng, Z. Liu, Y. Bai, and S. Jian, “Tunable and switchable dual-wavelength single polarization narrow linewidth SLM erbium-doped fiber laser based on a PM-CMFBG filter,” Opt. Express 22, 22528–22533 (2014).
    [Crossref]
  19. J. W. Fleming, “Dispersion in GeO2-SiO2 glasses,” Appl. Opt. 23, 4486–4493 (1984).
    [Crossref]
  20. S. H. Wemple, D. A. Pinnow, T. C. Rich, R. E. Jaeger, and L. G. Van Uitert, “Binary SiO2-B2O3 glass system: refractive index behavior and energy gap considerations,” J. Appl. Phys. 44, 5432–5437 (1973).
    [Crossref]
  21. W. Urbanczyk, T. Martynkien, and W. J. Bock, “Dispersion effects in elliptical-core highly birefringent fibers,” Appl. Opt. 40, 1911–1920 (2001).
    [Crossref]
  22. N. Lagakos, J. A. Bucaro, and R. Hughes, “Acoustic sensitivity predictions of single-mode optical fibers using Brillouin scattering,” Appl. Opt. 19, 3668–3670 (1980).
    [Crossref]
  23. 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]
  24. N. Imoto, N. Yoshizawa, J. Sakai, and H. Tsuchiya, “Birefringence in single-mode optical fiber due to elliptical core deformation and stress anisotropy,” IEEE J. Quantum Electron. 16, 1267–1271 (1980).
    [Crossref]
  25. R. Noe, D. Sandel, M. Yoshida-Dierolf, S. Hinz, V. Mirvoda, A. Schopflin, C. Gungener, E. Gottwald, C. Scheerer, G. Fischer, T. Weyrauch, and W. Haase, “Polarization mode dispersion compensation at 10, 20, and 40  Gb/s with various optical equalizers,” J. Lightwave Technol. 17, 1602–1616 (1999).
    [Crossref]
  26. C. D. Poole, J. M. Wiesenfeld, D. J. DiGiovanni, and A. M. Vengsarkar, “Optical fiber-based dispersion compensation using higher order modes near cutoff,” J. Lightwave Technol. 12, 1746–1758 (1994).
    [Crossref]
  27. 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]
  28. H. Li, G. Ren, Y. Lian, B. Zhu, M. Tang, Y. Zhao, and S. Jian, “Broadband orbital angular momentum transmission using a hollow-core photonic bandgap fiber,” Opt. Lett. 41, 3591–3594 (2016).
    [Crossref]
  29. Y. Zhang, Y. Wang, S. Cai, M. Lan, S. Yu, and W. Gu, “Mode converter based on dual-core all-solid photonic bandgap fiber,” Photon. Res. 3, 220–223 (2015).
    [Crossref]
  30. J. Song, K. Sun, S. Li, and W. Cai, “Phase sensitivity to temperature of the guiding mode in polarization-maintaining photonic crystal fiber,” Appl. Opt. 54, 7330–7334 (2015).
    [Crossref]
  31. Y. Dong, L. Teng, P. Tong, T. Jiang, H. Zhang, T. Zhu, L. Chen, X. Bao, and Z. Lu, “High-sensitivity distributed transverse load sensor with an elliptical-core fiber based on Brillouin dynamic gratings,” Opt. Lett. 40, 5003–5006 (2015).
    [Crossref]

2016 (3)

2015 (7)

2014 (5)

2013 (2)

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]

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7, 354–362 (2013).
[Crossref]

2012 (2)

2010 (1)

2009 (1)

2008 (1)

S. Ramachandran, J. Fini, M. Mermelstein, J. Nicholson, S. Ghalmi, and M. Yan, “Ultra-large effective-area, higher-order mode fibers: a new strategy for high-power lasers,” Laser Photon. Rev. 2, 429–448 (2008).
[Crossref]

2005 (1)

R. Guan, F. Zhu, Z. Gan, D. Huang, and S. Liu, “Stress birefringence analysis of polarization maintaining optical fibers,” Opt. Fiber Technol. 11, 240–254 (2005).
[Crossref]

2001 (1)

1999 (1)

1994 (1)

C. D. Poole, J. M. Wiesenfeld, D. J. DiGiovanni, and A. M. Vengsarkar, “Optical fiber-based dispersion compensation using higher order modes near cutoff,” J. Lightwave Technol. 12, 1746–1758 (1994).
[Crossref]

1984 (1)

1980 (2)

N. Lagakos, J. A. Bucaro, and R. Hughes, “Acoustic sensitivity predictions of single-mode optical fibers using Brillouin scattering,” Appl. Opt. 19, 3668–3670 (1980).
[Crossref]

N. Imoto, N. Yoshizawa, J. Sakai, and H. Tsuchiya, “Birefringence in single-mode optical fiber due to elliptical core deformation and stress anisotropy,” IEEE J. Quantum Electron. 16, 1267–1271 (1980).
[Crossref]

1973 (1)

S. H. Wemple, D. A. Pinnow, T. C. Rich, R. E. Jaeger, and L. G. Van Uitert, “Binary SiO2-B2O3 glass system: refractive index behavior and energy gap considerations,” J. Appl. Phys. 44, 5432–5437 (1973).
[Crossref]

Arik, S. O.

Arkwright, J. W.

N. Riesen, J. D. Love, and J. W. Arkwright, “Few-mode elliptical-core fiber data transmission,” IEEE Photon. Technol. Lett. 24, 344–346 (2012).
[Crossref]

Askarov, D.

Astruc, M.

P. Sillard, M. Astruc, D. Boivin, H. Maerten, and L. Provost, “Few-mode fiber for uncoupled mode-division multiplexing transmissions,” in European Conference and Exposition on Optical Communications (Optical Society of America, 2011), paper Tu.5.LeCervin.7.

Bai, N.

Bai, Y.

Bao, X.

Bock, W. J.

Boivin, D.

P. Sillard, M. Astruc, D. Boivin, H. Maerten, and L. Provost, “Few-mode fiber for uncoupled mode-division multiplexing transmissions,” in European Conference and Exposition on Optical Communications (Optical Society of America, 2011), paper Tu.5.LeCervin.7.

Bolle, C.

Bozinovic, N.

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]

Brunet, C.

Bucaro, J. A.

Burrows, E. C.

Cai, S.

Cai, W.

Cai, X.

Chen, L.

Cvijetic, N.

DiGiovanni, D. J.

C. D. Poole, J. M. Wiesenfeld, D. J. DiGiovanni, and A. M. Vengsarkar, “Optical fiber-based dispersion compensation using higher order modes near cutoff,” J. Lightwave Technol. 12, 1746–1758 (1994).
[Crossref]

Dong, Y.

Du, C.

Du, J.

Esmaeelpour, M.

Essiambre, R. J.

Feng, S.

Fini, J.

S. Ramachandran, J. Fini, M. Mermelstein, J. Nicholson, S. Ghalmi, and M. Yan, “Ultra-large effective-area, higher-order mode fibers: a new strategy for high-power lasers,” Laser Photon. Rev. 2, 429–448 (2008).
[Crossref]

Fini, J. M.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7, 354–362 (2013).
[Crossref]

Fischer, G.

Fleming, J. W.

Gan, Z.

R. Guan, F. Zhu, Z. Gan, D. Huang, and S. Liu, “Stress birefringence analysis of polarization maintaining optical fibers,” Opt. Fiber Technol. 11, 240–254 (2005).
[Crossref]

Ghalmi, S.

S. Ramachandran, J. Fini, M. Mermelstein, J. Nicholson, S. Ghalmi, and M. Yan, “Ultra-large effective-area, higher-order mode fibers: a new strategy for high-power lasers,” Laser Photon. Rev. 2, 429–448 (2008).
[Crossref]

Gnauck, A. H.

Gottwald, E.

Gregg, P.

Gu, W.

Guan, R.

R. Guan, F. Zhu, Z. Gan, D. Huang, and S. Liu, “Stress birefringence analysis of polarization maintaining optical fibers,” Opt. Fiber Technol. 11, 240–254 (2005).
[Crossref]

Gungener, C.

Haase, W.

Hinz, S.

Huang, D.

R. Guan, F. Zhu, Z. Gan, D. Huang, and S. Liu, “Stress birefringence analysis of polarization maintaining optical fibers,” Opt. Fiber Technol. 11, 240–254 (2005).
[Crossref]

Huang, H.

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]

Hughes, R.

Imoto, N.

N. Imoto, N. Yoshizawa, J. Sakai, and H. Tsuchiya, “Birefringence in single-mode optical fiber due to elliptical core deformation and stress anisotropy,” IEEE J. Quantum Electron. 16, 1267–1271 (1980).
[Crossref]

Ip, E.

Jaeger, R. E.

S. H. Wemple, D. A. Pinnow, T. C. Rich, R. E. Jaeger, and L. G. Van Uitert, “Binary SiO2-B2O3 glass system: refractive index behavior and energy gap considerations,” J. Appl. Phys. 44, 5432–5437 (1973).
[Crossref]

Jian, S.

Jiang, T.

Kahn, J. M.

Kanonakis, K.

Kim, Y. H.

Klitis, C.

Kristensen, P.

Lagakos, N.

Lan, M.

LaRochelle, S.

Li, G.

Li, H.

Li, M. J.

Li, S.

Lian, Y.

Liñares, J.

Lingle, R.

Liu, J.

Liu, S.

R. Guan, F. Zhu, Z. Gan, D. Huang, and S. Liu, “Stress birefringence analysis of polarization maintaining optical fibers,” Opt. Fiber Technol. 11, 240–254 (2005).
[Crossref]

Liu, Z.

Love, J. D.

N. Riesen, J. D. Love, and J. W. Arkwright, “Few-mode elliptical-core fiber data transmission,” IEEE Photon. Technol. Lett. 24, 344–346 (2012).
[Crossref]

Lu, Z.

Maerten, H.

P. Sillard, M. Astruc, D. Boivin, H. Maerten, and L. Provost, “Few-mode fiber for uncoupled mode-division multiplexing transmissions,” in European Conference and Exposition on Optical Communications (Optical Society of America, 2011), paper Tu.5.LeCervin.7.

Martynkien, T.

McCurdy, A. H.

Mermelstein, M.

S. Ramachandran, J. Fini, M. Mermelstein, J. Nicholson, S. Ghalmi, and M. Yan, “Ultra-large effective-area, higher-order mode fibers: a new strategy for high-power lasers,” Laser Photon. Rev. 2, 429–448 (2008).
[Crossref]

Messaddeq, Y.

Milione, G.

Mirvoda, V.

Mo, Q.

Montero, C.

Moreno, V.

Mumtaz, S.

Nelson, L. E.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7, 354–362 (2013).
[Crossref]

Nicholson, J.

S. Ramachandran, J. Fini, M. Mermelstein, J. Nicholson, S. Ghalmi, and M. Yan, “Ultra-large effective-area, higher-order mode fibers: a new strategy for high-power lasers,” Laser Photon. Rev. 2, 429–448 (2008).
[Crossref]

Noe, R.

Peckham, D. W.

Peng, G.

Pinnow, D. A.

S. H. Wemple, D. A. Pinnow, T. C. Rich, R. E. Jaeger, and L. G. Van Uitert, “Binary SiO2-B2O3 glass system: refractive index behavior and energy gap considerations,” J. Appl. Phys. 44, 5432–5437 (1973).
[Crossref]

Poole, C. D.

C. D. Poole, J. M. Wiesenfeld, D. J. DiGiovanni, and A. M. Vengsarkar, “Optical fiber-based dispersion compensation using higher order modes near cutoff,” J. Lightwave Technol. 12, 1746–1758 (1994).
[Crossref]

Prieto, X.

Provost, L.

P. Sillard, M. Astruc, D. Boivin, H. Maerten, and L. Provost, “Few-mode fiber for uncoupled mode-division multiplexing transmissions,” in European Conference and Exposition on Optical Communications (Optical Society of America, 2011), paper Tu.5.LeCervin.7.

Ramachandran, S.

P. Gregg, P. Kristensen, and S. Ramachandran, “Conservation of orbital angular momentum in air-core optical fibers,” Optica 2, 267–270 (2015).
[Crossref]

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]

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]

S. Ramachandran, J. Fini, M. Mermelstein, J. Nicholson, S. Ghalmi, and M. Yan, “Ultra-large effective-area, higher-order mode fibers: a new strategy for high-power lasers,” Laser Photon. Rev. 2, 429–448 (2008).
[Crossref]

Randel, S.

Ren, G.

Ren, Y.

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]

Rich, T. C.

S. H. Wemple, D. A. Pinnow, T. C. Rich, R. E. Jaeger, and L. G. Van Uitert, “Binary SiO2-B2O3 glass system: refractive index behavior and energy gap considerations,” J. Appl. Phys. 44, 5432–5437 (1973).
[Crossref]

Richardson, D. J.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7, 354–362 (2013).
[Crossref]

Riesen, N.

N. Riesen, J. D. Love, and J. W. Arkwright, “Few-mode elliptical-core fiber data transmission,” IEEE Photon. Technol. Lett. 24, 344–346 (2012).
[Crossref]

Rusch, L. A.

Ryf, R.

Sakai, J.

N. Imoto, N. Yoshizawa, J. Sakai, and H. Tsuchiya, “Birefringence in single-mode optical fiber due to elliptical core deformation and stress anisotropy,” IEEE J. Quantum Electron. 16, 1267–1271 (1980).
[Crossref]

Sandel, D.

Scheerer, C.

Schopflin, A.

Sierra, A.

Sillard, P.

P. Sillard, M. Astruc, D. Boivin, H. Maerten, and L. Provost, “Few-mode fiber for uncoupled mode-division multiplexing transmissions,” in European Conference and Exposition on Optical Communications (Optical Society of America, 2011), paper Tu.5.LeCervin.7.

Song, J.

Song, K. Y.

Sorel, M.

Stone, J.

Sun, K.

Tang, M.

Teng, L.

Tong, P.

Tsuchiya, H.

N. Imoto, N. Yoshizawa, J. Sakai, and H. Tsuchiya, “Birefringence in single-mode optical fiber due to elliptical core deformation and stress anisotropy,” IEEE J. Quantum Electron. 16, 1267–1271 (1980).
[Crossref]

Tur, M.

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]

Urbanczyk, W.

Vaity, P.

Van Uitert, L. G.

S. H. Wemple, D. A. Pinnow, T. C. Rich, R. E. Jaeger, and L. G. Van Uitert, “Binary SiO2-B2O3 glass system: refractive index behavior and energy gap considerations,” J. Appl. Phys. 44, 5432–5437 (1973).
[Crossref]

Vengsarkar, A. M.

C. D. Poole, J. M. Wiesenfeld, D. J. DiGiovanni, and A. M. Vengsarkar, “Optical fiber-based dispersion compensation using higher order modes near cutoff,” J. Lightwave Technol. 12, 1746–1758 (1994).
[Crossref]

Wang, J.

Wang, L.

Wang, T.

Wang, Y.

Wemple, S. H.

S. H. Wemple, D. A. Pinnow, T. C. Rich, R. E. Jaeger, and L. G. Van Uitert, “Binary SiO2-B2O3 glass system: refractive index behavior and energy gap considerations,” J. Appl. Phys. 44, 5432–5437 (1973).
[Crossref]

Weyrauch, T.

Wiesenfeld, J. M.

C. D. Poole, J. M. Wiesenfeld, D. J. DiGiovanni, and A. M. Vengsarkar, “Optical fiber-based dispersion compensation using higher order modes near cutoff,” J. Lightwave Technol. 12, 1746–1758 (1994).
[Crossref]

Willner, A. E.

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]

Winzer, P. J.

Yaman, F.

Yan, M.

S. Ramachandran, J. Fini, M. Mermelstein, J. Nicholson, S. Ghalmi, and M. Yan, “Ultra-large effective-area, higher-order mode fibers: a new strategy for high-power lasers,” Laser Photon. Rev. 2, 429–448 (2008).
[Crossref]

Yan, M. F.

Yin, B.

Yoshida-Dierolf, M.

Yoshizawa, N.

N. Imoto, N. Yoshizawa, J. Sakai, and H. Tsuchiya, “Birefringence in single-mode optical fiber due to elliptical core deformation and stress anisotropy,” IEEE J. Quantum Electron. 16, 1267–1271 (1980).
[Crossref]

Yu, S.

Yue, Y.

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]

Zhang, H.

Zhang, Y.

Zhao, Y.

Zhu, B.

Zhu, F.

R. Guan, F. Zhu, Z. Gan, D. Huang, and S. Liu, “Stress birefringence analysis of polarization maintaining optical fibers,” Opt. Fiber Technol. 11, 240–254 (2005).
[Crossref]

Zhu, T.

Appl. Opt. (4)

IEEE J. Quantum Electron. (1)

N. Imoto, N. Yoshizawa, J. Sakai, and H. Tsuchiya, “Birefringence in single-mode optical fiber due to elliptical core deformation and stress anisotropy,” IEEE J. Quantum Electron. 16, 1267–1271 (1980).
[Crossref]

IEEE Photon. Technol. Lett. (1)

N. Riesen, J. D. Love, and J. W. Arkwright, “Few-mode elliptical-core fiber data transmission,” IEEE Photon. Technol. Lett. 24, 344–346 (2012).
[Crossref]

J. Appl. Phys. (1)

S. H. Wemple, D. A. Pinnow, T. C. Rich, R. E. Jaeger, and L. G. Van Uitert, “Binary SiO2-B2O3 glass system: refractive index behavior and energy gap considerations,” J. Appl. Phys. 44, 5432–5437 (1973).
[Crossref]

J. Lightwave Technol. (4)

Laser Photon. Rev. (1)

S. Ramachandran, J. Fini, M. Mermelstein, J. Nicholson, S. Ghalmi, and M. Yan, “Ultra-large effective-area, higher-order mode fibers: a new strategy for high-power lasers,” Laser Photon. Rev. 2, 429–448 (2008).
[Crossref]

Nat. Photonics (1)

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7, 354–362 (2013).
[Crossref]

Opt. Express (6)

Opt. Fiber Technol. (1)

R. Guan, F. Zhu, Z. Gan, D. Huang, and S. Liu, “Stress birefringence analysis of polarization maintaining optical fibers,” Opt. Fiber Technol. 11, 240–254 (2005).
[Crossref]

Opt. Lett. (5)

Optica (1)

Photon. Res. (2)

Sci. Rep. (1)

S. Li and J. Wang, “A compact trench-assisted multi-orbital-angular-momentum multi-ring fiber for ultrahigh-density space-division multiplexing (19 rings × 22 modes),” Sci. Rep. 4, 3853 (2014).

Science (1)

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]

Other (1)

P. Sillard, M. Astruc, D. Boivin, H. Maerten, and L. Provost, “Few-mode fiber for uncoupled mode-division multiplexing transmissions,” in European Conference and Exposition on Optical Communications (Optical Society of America, 2011), paper Tu.5.LeCervin.7.

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Figures (6)

Fig. 1.
Fig. 1. Schematic diagram of the PM-PRCF cross section.
Fig. 2.
Fig. 2. Colormap of minimal Δ n eff between adjacent modes as a function of ρ and V at 1550 nm for W = 125 μm , a = 1 μm , r 3 = 20 μm .
Fig. 3.
Fig. 3. Intensity distributions and electrical field orientations for the 10 eigenmodes (a) without the two stress-applying rods, (b) with the two stress-applying rods.
Fig. 4.
Fig. 4. Effective refractive index n eff and effective refractive index difference Δ n eff as a function of a .
Fig. 5.
Fig. 5. Effective index difference Δ n eff as a function of r 3 .
Fig. 6.
Fig. 6. Chromatic dispersions for the 10 modes.

Tables (2)

Tables Icon

Table 1. Elastic Parameters Used for Modeling

Tables Icon

Table 2. Effective Refractive Index ( n eff ), Effective Refractive Index Difference ( Δ n eff ) Between Adjacent Modes, and Chromatic Dispersion ( D ) at 1550 nm for a = 1 μm , r 3 = 20 μm , V = 4.51 , and ρ = 0.57

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