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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 15 — Jul. 28, 2014
  • pp: 18044–18055
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Few-mode fiber with inverse-parabolic graded-index profile for transmission of OAM-carrying modes

B. Ung, P. Vaity, L. Wang, Y. Messaddeq, L. A. Rusch, and S. LaRochelle  »View Author Affiliations


Optics Express, Vol. 22, Issue 15, pp. 18044-18055 (2014)
http://dx.doi.org/10.1364/OE.22.018044


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Abstract

A novel type of few-mode fiber, characterized by an inverse-parabolic graded-index profile, is proposed for the robust transmission of cylindrical vector modes as well as modes carrying quantized orbital angular momentum (OAM). Large effective index separations between vector modes (>2.1 × 10−4) are numerically calculated and experimentally confirmed in this fiber over the whole C-band, enabling transmission of OAM(+/−1,1) modes for distances up to 1.1 km. Simple design rules are provided for the optimization of the fiber parameters.

© 2014 Optical Society of America

1. Introduction

2. Description of the IPGIF

Considering a cladding with a radius of 62.5 μm and a refractive index corresponding to that of undoped silica (n2 = 1.4440 at λ = 1550 nm), we performed numerical simulations based on the finite-element-method (FEM) with a commercial software (COMSOL). The IPGIF considered in Fig. 1 was found to support up to three mode groups (LP01, LP11 and LP21). The field profiles of the constitutive vector modes are shown in Fig. 2
Fig. 2 Transverse electric field, e, amplitude (grayscale) and direction (arrows) of the guided vector modes at λ = 1550 nm in the IPGIF with parameters a = 3 μm, N = −4, Δnmax = 0.05 and n2 = 1.4440. The graph shows the fields of the fundamental HE11 mode (LP01), the TE01, HE21, and TM01 modes (LP11 group), and the EH11 and HE31 modes (LP21 group) calculated with FEM.
.

3. Analysis of the effective index separation between vector modes

In this section we first develop an analytical understanding of the main physical factors that contribute towards large intermodal separations in optical fibers, and examine how these can be engineered in IPGIFs. We then provide numerical examples that validate our theoretical analysis.

3.1 Theoretical analysis of the modal separations in the IPGIF

3.2 Numerical analysis of the modal separations in the IPGIF

The effective index separation between vector modes was calculated using the FEM mode solver within the parameter space defined by (−4.75 ≤ N ≤ 0) and (0.02 ≤ Δnmax ≤ 0.07). For simplification purposes, the optimization solely focuses on maximizing the intermodal index separation (Δneff) between the modes of the LP11 group (TE01, HE21, and TM01). However, it is expected that higher-order modes sharing the same radial mode number, m = 1 (e.g. EH11 and HE31), will similarly achieve large intermodal separations.

Figure 3(a)
Fig. 3 (a) Minimum effective index separation inside the LP11 mode group as a function of IPGIF parameters N and Δnmax calculated by FEM. (b) Isolines along selected contrast values: Δnmax = [0.02, 0.05, 0.07]. Other simulation parameters were kept at a = 3 μm, n2 = 1.4440 and λ = 1550 nm.
plots the minimum effective index separation inside the LP11 mode group as a function of the profile curvature and maximum index contrast. The results show that Δneff indeed scales with |N| and Δnmax, thus indicating that the sharpest profiles with the highest refractive-index-contrasts are those that enable the largest effective index separation of vector modes. Moreover, the calculations in Fig. 3(a) suggest that very large effective index separations, Δneff >4.0 × 10−4, may theoretically be achieved with an IPGIF profile.

Closer inspection of the results [Fig. 3(b)] reveals that for a given index contrast value, Δnmax, the relationship between Δneff and -N takes a sigmoid behavior that grows towards a saturation value, Δneff,max. One could argue that an optimum profile curvature is close to N = −3 since more than 95% of the Δneff,max value is reached at this point.

4. Calculation of bend induced losses in IPGIFs

The effect of fiber bends on the attenuation properties of IPGIFs was simulated using a standard conformal mapping approach [17

17. M. Heiblum and J. H. Harris, “Analysis of Curved Optical Waveguides by Conformal Transformation,” IEEE J. Quantum Electron. 11(2), 75–83 (1975). [CrossRef]

] which has been shown to be fairly accurate in the case of singlemode fibers [18

18. D. Marcuse, “Influence of curvature on the losses of doubly clad fibers,” Appl. Opt. 21(23), 4208–4213 (1982). [CrossRef] [PubMed]

], FMFs [19

19. C. Schulze, A. Lorenz, D. Flamm, A. Hartung, S. Schröter, H. Bartelt, and M. Duparré, “Mode resolved bend loss in few-mode optical fibers,” Opt. Express 21(3), 3170–3181 (2013). [CrossRef] [PubMed]

] and even for strongly multimode fibers [20

20. J. M. Fini, “Bend-resistant design of conventional and microstructure fibers with very large mode area,” Opt. Express 14(1), 69–81 (2006). [CrossRef] [PubMed]

]. In this method, a coordinate transformation is performed on the original unperturbed fiber refractive index profile, nfiber, to obtain the equivalent index profile, neq, generated by a fiber bend, Rbend, applied along the transverse x-axis direction:
neq(x,y)=nfiber(x,y)(1+x1.40Rbend)
(6)
where the 1.40 factor was added in the denominator to account for the additional change in refractive index due to photoelastic effects created by the local strain in bent fused silica fibers, as derived in [19

19. C. Schulze, A. Lorenz, D. Flamm, A. Hartung, S. Schröter, H. Bartelt, and M. Duparré, “Mode resolved bend loss in few-mode optical fibers,” Opt. Express 21(3), 3170–3181 (2013). [CrossRef] [PubMed]

]. By implementing Eq. (6) in the FEM, bend-induced confinement losses of the fundamental HE11 mode were numerically computed for a tight bend of Rbend = 1 cm radius. The results are shown in Fig. 5
Fig. 5 Confinement losses of the HE11 mode induced by a Rbend = 1 cm fiber bend as a function of curvature (N) and for different refractive index contrasts (Δnmax). Other parameters are: a = 3 μm, n2 = 1.4440 and λ = 1550 nm.
as a function of the profile curvature and for different refractive index contrasts. We also note that bend-induced confinement losses of the higher-order modes within the LP11 group are approximately an order of magnitude larger compared to the fundamental HE11 mode.

5. Fabrication and characterization of the IPGIF

Based on the FEM calculations of Fig. 3 and Fig. 4(d) and the discussion therein, we selected the design parameters, N = −4, Δnmax = 0.05 and a = 3 μm, corresponding to the refractive index profile presented in Fig. 1. These IPGIF parameters theoretically enable large intermodal index separations of ΔneffLP11=2.37×104 and ΔneffLP21=1.55×104, while presenting a maximum refractive index contrast value (Δnmax = 0.05) that is still readily attainable in germania-doped silica glass preforms manufactured by the MCVD process.

By inspecting the data from Fig. 7(a) we determine that the minimum effective index separation is Δneff ≈2.1 × 10−4 inside the LP11 group (TE01, HE21, TM01) and Δneff ≈1.6 × 10−4 for the LP21 group (EH11, HE31) throughout the C-band. GVD values [Fig. 7(b)] for the fundamental HE11 and the LP11 mode group vary between 4 and 12 ps/(nm-km), while those of the LP21 mode group lies in the strongly normal dispersion regime (<-100 ps/(nm-km)) and exhibits a pronounced negative slope. The latter behavior may be explained by the relatively close proximity of the LP21 mode group to the cutoff (i.e. the index of undoped silica cladding) as shown in Fig. 7(a), hence resulting in greater group velocity dispersion.

The broader peaks identified as #1, #2 and #3 in Fig. 8, which correspond to the Bragg reflection of each mode group to itself [23

23. T. Erdogan, “Fiber Grating Spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997). [CrossRef]

], are centered at wavelengths λp = 1575.31, 1571.34, and 1554.01 nm respectively. The narrow peaks (λk-p) stem from the cross-coupling of a given mode “p” with another counter-propagating mode “k”. Values of the effective indices for each vector mode can be retrieved either through neff,p = λp/Λ (where λp is the wavelength at the self-reflection peak) or alternatively via neff,k = (2λk-p - λp)/Λ where λk-p is the cross-coupling peak of mode “k” with a lower-order mode “p” having a self-reflection peak at λp.

6. Transmission of OAM modes

Based on numerical simulations [Fig. 7], the fabricated IPGIF is expected to support up to 6 OAM±,m±states through coherent combinations of the even and odd hybrid modes: OAM±1,1±=HE21eiHE21o, OAM2,1±=EH11eiEH11o and OAM±2,1±=HE31eiHE31o, where the ± superscript indicates the circular polarization state of the OAM mode, the ± subscript its topological-charge and m denotes the radial mode number (i.e. the number of rings in the mode profile). Although strictly speaking the fundamental OAM0,1±=HE11± mode does not carry OAM, it still constitutes an important waveguide mode that can be harnessed for MDM.

We were also able to excite and recover the OAM+1,1 mode (excited by right( + ) circular polarized light) after a propagation distance of 1.1 km in the IPGIF, as shown on the right-hand side of Fig. 10. Due to the proximity of the LP21 mode group to the cutoff, the OAM ± 2,1 modes experienced higher losses that prevented us from reliably detecting their presence after >100 m distance. The propagation losses averaged over all mode groups, were measured by the cutback method and estimated at 8.6 dB/km. Finer measurements utilizing selective excitation of the fundamental HE11 mode indicate that this mode sustains lower losses, on the order of 6.5 dB/km. We are currently investigating the origin of these losses and whether they could be reduced by an optimization of the fiber fabrication process.

7. Conclusion

Acknowledgments

The authors thank PhD student Charles Brunet from the COPL (Université Laval) for helping in the theoretical understanding and description of OAM modes generation/propagation in optical fibers. The authors thank PhD student Cang Jin, also from the COPL, for his help in the measurement of fiber propagation losses. The authors are grateful to Pierre-André Bélanger from the department of physics at Université Laval for insightful discussions in the application of the inverse-parabolic graded-index profile, and Adrian Lorenz from the Leibniz Institute of Photonic Technology for valuable suggestions regarding fiber bend modeling. This work was supported by the Canada Research Chair in Advanced photonics technologies for emerging communication strategies (APTECS), by the Canada Excellence Research Chair in Enabling Photonic innovations for information and communications (CERCP), and by the Natural sciences and engineering research council of Canada (NSERC). B. Ung acknowledges the Fonds de recherche du Québec - Nature et technologies for a postdoctoral fellowship.

References and links

1.

R.-J. Essiambre and R. W. Tkach, “Capacity Trends and Limits of Optical Communication Networks,” Proc. IEEE 100(5), 1035–1055 (2012). [CrossRef]

2.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013). [CrossRef]

3.

P. M. Krummrich, “Spatial multiplexing for high capacity transport,” Opt. Fiber Technol. 17(5), 480–489 (2011). [CrossRef]

4.

P. J. Winzer, “Energy-Efficient Optical Transport Capacity Scaling Through Spatial Multiplexing,” IEEE Photon. Technol. Lett. 23(13), 851–853 (2011). [CrossRef]

5.

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photon. 3, 161–204 (2011).

6.

P. Z. Dashti, F. Alhassen, and H. P. Lee, “Observation of Orbital Angular Momentum Transfer between Acoustic and Optical Vortices in Optical Fiber,” Phys. Rev. Lett. 96(4), 043604 (2006). [CrossRef] [PubMed]

7.

S. Ramachandran, P. Kristensen, and M. F. Yan, “Generation and propagation of radially polarized beams in optical fibers,” Opt. Lett. 34(16), 2525–2527 (2009). [CrossRef] [PubMed]

8.

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(6140), 1545–1548 (2013). [CrossRef] [PubMed]

9.

P. Gregg, P. Kristensen, S. E. Golowich, J. Ø. Olsen, P. Steinvurzel, and S. Ramachandran, “Stable Transmission of 12 OAM States in Air-Core Fiber,” in Proc. of CLEO: 2012, CTu2K (2013). [CrossRef]

10.

C. Brunet, B. Ung, Y. Messaddeq, S. LaRochelle, E. Bernier, and L. A. Rusch, “Design of an Optical Fiber Supporting 16 OAM Modes,” in Proc. of OFC: 2014, Th2A.24 (2014). [CrossRef]

11.

Y. Yue, Y. Yan, N. Ahmed, J.-Y. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, S. Dolinar, M. Tur, and A. E. Willner, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4(2), 535–543 (2012). [CrossRef]

12.

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). [CrossRef] [PubMed]

13.

Y. Yue, L. Zhang, Y. Yan, N. Ahmed, J.-Y. Yang, H. Huang, Y. Ren, S. Dolinar, M. Tur, and A. E. Willner, “Octave-spanning supercontinuum generation of vortices in an As2S3 ring photonic crystal fiber,” Opt. Lett. 37(11), 1889–1891 (2012). [CrossRef] [PubMed]

14.

B. Ung, P. Vaity, L. Wang, Y. Messaddeq, L. A. Rusch, and S. LaRochelle, “Inverse-parabolic graded-index profile for transmission of cylindrical vector modes in optical fibers,” in Proc. of OFC: 2014, Tu3K.4 (2014). [CrossRef]

15.

R. L. Lachance and P.-A. Bélanger, “Modes in Divergent Parabolic Graded-Index Optical Fibers,” J. Lightwave Technol. 9(11), 1425–1430 (1991). [CrossRef]

16.

J. Bures, Guided Optics: Optical Fibers and All-Fiber Components (Wiley-VCH, 2009), Chap. 5.

17.

M. Heiblum and J. H. Harris, “Analysis of Curved Optical Waveguides by Conformal Transformation,” IEEE J. Quantum Electron. 11(2), 75–83 (1975). [CrossRef]

18.

D. Marcuse, “Influence of curvature on the losses of doubly clad fibers,” Appl. Opt. 21(23), 4208–4213 (1982). [CrossRef] [PubMed]

19.

C. Schulze, A. Lorenz, D. Flamm, A. Hartung, S. Schröter, H. Bartelt, and M. Duparré, “Mode resolved bend loss in few-mode optical fibers,” Opt. Express 21(3), 3170–3181 (2013). [CrossRef] [PubMed]

20.

J. M. Fini, “Bend-resistant design of conventional and microstructure fibers with very large mode area,” Opt. Express 14(1), 69–81 (2006). [CrossRef] [PubMed]

21.

M. E. Lines, W. A. Reed, D. J. DiGiovanni, and J. R. Hamblin, “Explanation of anomalous loss in high delta singlemode fibres,” Electron. Lett. 35(12), 1009–1010 (1999). [CrossRef]

22.

J. W. Fleming, “Dispersion in GeO2-SiO2 glasses,” Appl. Opt. 23(24), 4486–4493 (1984). [CrossRef] [PubMed]

23.

T. Erdogan, “Fiber Grating Spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997). [CrossRef]

24.

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(13), 15653–15661 (2014). [CrossRef] [PubMed]

OCIS Codes
(060.2280) Fiber optics and optical communications : Fiber design and fabrication
(060.2330) Fiber optics and optical communications : Fiber optics communications
(060.4230) Fiber optics and optical communications : Multiplexing
(050.4865) Diffraction and gratings : Optical vortices

ToC Category:
Fiber Optics

History
Original Manuscript: May 23, 2014
Revised Manuscript: July 2, 2014
Manuscript Accepted: July 6, 2014
Published: July 17, 2014

Citation
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)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-15-18044


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References

  1. R.-J. Essiambre and R. W. Tkach, “Capacity Trends and Limits of Optical Communication Networks,” Proc. IEEE100(5), 1035–1055 (2012). [CrossRef]
  2. D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics7(5), 354–362 (2013). [CrossRef]
  3. P. M. Krummrich, “Spatial multiplexing for high capacity transport,” Opt. Fiber Technol.17(5), 480–489 (2011). [CrossRef]
  4. P. J. Winzer, “Energy-Efficient Optical Transport Capacity Scaling Through Spatial Multiplexing,” IEEE Photon. Technol. Lett.23(13), 851–853 (2011). [CrossRef]
  5. A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photon.3, 161–204 (2011).
  6. P. Z. Dashti, F. Alhassen, and H. P. Lee, “Observation of Orbital Angular Momentum Transfer between Acoustic and Optical Vortices in Optical Fiber,” Phys. Rev. Lett.96(4), 043604 (2006). [CrossRef] [PubMed]
  7. S. Ramachandran, P. Kristensen, and M. F. Yan, “Generation and propagation of radially polarized beams in optical fibers,” Opt. Lett.34(16), 2525–2527 (2009). [CrossRef] [PubMed]
  8. 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,” Science340(6140), 1545–1548 (2013). [CrossRef] [PubMed]
  9. P. Gregg, P. Kristensen, S. E. Golowich, J. Ø. Olsen, P. Steinvurzel, and S. Ramachandran, “Stable Transmission of 12 OAM States in Air-Core Fiber,” in Proc. of CLEO: 2012, CTu2K (2013). [CrossRef]
  10. C. Brunet, B. Ung, Y. Messaddeq, S. LaRochelle, E. Bernier, and L. A. Rusch, “Design of an Optical Fiber Supporting 16 OAM Modes,” in Proc. of OFC: 2014, Th2A.24 (2014). [CrossRef]
  11. Y. Yue, Y. Yan, N. Ahmed, J.-Y. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, S. Dolinar, M. Tur, and A. E. Willner, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J.4(2), 535–543 (2012). [CrossRef]
  12. 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). [CrossRef] [PubMed]
  13. Y. Yue, L. Zhang, Y. Yan, N. Ahmed, J.-Y. Yang, H. Huang, Y. Ren, S. Dolinar, M. Tur, and A. E. Willner, “Octave-spanning supercontinuum generation of vortices in an As2S3 ring photonic crystal fiber,” Opt. Lett.37(11), 1889–1891 (2012). [CrossRef] [PubMed]
  14. B. Ung, P. Vaity, L. Wang, Y. Messaddeq, L. A. Rusch, and S. LaRochelle, “Inverse-parabolic graded-index profile for transmission of cylindrical vector modes in optical fibers,” in Proc. of OFC: 2014, Tu3K.4 (2014). [CrossRef]
  15. R. L. Lachance and P.-A. Bélanger, “Modes in Divergent Parabolic Graded-Index Optical Fibers,” J. Lightwave Technol.9(11), 1425–1430 (1991). [CrossRef]
  16. J. Bures, Guided Optics: Optical Fibers and All-Fiber Components (Wiley-VCH, 2009), Chap. 5.
  17. M. Heiblum and J. H. Harris, “Analysis of Curved Optical Waveguides by Conformal Transformation,” IEEE J. Quantum Electron.11(2), 75–83 (1975). [CrossRef]
  18. D. Marcuse, “Influence of curvature on the losses of doubly clad fibers,” Appl. Opt.21(23), 4208–4213 (1982). [CrossRef] [PubMed]
  19. C. Schulze, A. Lorenz, D. Flamm, A. Hartung, S. Schröter, H. Bartelt, and M. Duparré, “Mode resolved bend loss in few-mode optical fibers,” Opt. Express21(3), 3170–3181 (2013). [CrossRef] [PubMed]
  20. J. M. Fini, “Bend-resistant design of conventional and microstructure fibers with very large mode area,” Opt. Express14(1), 69–81 (2006). [CrossRef] [PubMed]
  21. M. E. Lines, W. A. Reed, D. J. DiGiovanni, and J. R. Hamblin, “Explanation of anomalous loss in high delta singlemode fibres,” Electron. Lett.35(12), 1009–1010 (1999). [CrossRef]
  22. J. W. Fleming, “Dispersion in GeO2-SiO2 glasses,” Appl. Opt.23(24), 4486–4493 (1984). [CrossRef] [PubMed]
  23. T. Erdogan, “Fiber Grating Spectra,” J. Lightwave Technol.15(8), 1277–1294 (1997). [CrossRef]
  24. L. Wang, P. Vaity, B. Ung, Y. Messaddeq, L. A. Rusch, and S. LaRochelle, “Characterization of OAM fibers using fiber Bragg gratings,” Opt. Express22(13), 15653–15661 (2014). [CrossRef] [PubMed]

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