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

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2014

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]

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]

2013

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]

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[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(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

2012

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]

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

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]

2011

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

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

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

2009

2006

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]

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]

1999

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]

1997

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

1991

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

1984

1982

1975

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

Ahmed, N.

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]

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]

Alhassen, F.

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]

Bartelt, H.

Bélanger, P.-A.

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

Birnbaum, K. M.

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]

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

Dashti, P. Z.

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]

DiGiovanni, D. J.

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]

Dolinar, S.

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]

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]

Duparré, M.

Erdogan, T.

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

Erkmen, B. I.

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]

Essiambre, R.-J.

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

Fini, J. M.

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

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]

Flamm, D.

Fleming, J. W.

Hamblin, J. R.

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]

Harris, J. H.

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

Hartung, A.

Heiblum, M.

M. Heiblum and J. H. Harris, “Analysis of Curved Optical Waveguides by Conformal Transformation,” IEEE J. Quantum Electron. 11(2), 75–83 (1975).
[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(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

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]

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]

Kristensen, P.

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]

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]

Krummrich, P. M.

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

Lachance, R. L.

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

LaRochelle, S.

Lee, H. P.

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]

Li, S.

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]

Lines, M. E.

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]

Lorenz, A.

Marcuse, D.

Messaddeq, Y.

Nelson, L. E.

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

Padgett, M. J.

Ramachandran, S.

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]

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]

Reed, W. A.

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]

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

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]

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]

Richardson, D. J.

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

Rusch, L. A.

Schröter, S.

Schulze, C.

Tkach, R. W.

R.-J. Essiambre and R. W. Tkach, “Capacity Trends and Limits of Optical Communication Networks,” Proc. IEEE 100(5), 1035–1055 (2012).
[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(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

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]

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]

Ung, B.

Vaity, P.

Wang, J.

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]

Wang, L.

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

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]

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]

Winzer, P. J.

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

Yan, M. F.

Yan, Y.

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]

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]

Yang, J.-Y.

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]

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]

Yao, A. M.

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

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]

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]

Zhang, L.

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]

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]

Adv. Opt. Photon.

Appl. Opt.

Electron. Lett.

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]

IEEE J. Quantum Electron.

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

IEEE Photon. J.

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Figures (10)

Fig. 1
Fig. 1

IPGIF refractive index profile with parameters: a = 3 μm, N = −4, Δnmax = 0.05 and n2 = 1.4440.

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.

Fig. 3
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.

Fig. 4
Fig. 4

Minimum effective index separation for the LP11 group in an IPGIF (a = 3 μm, n2 = 1.4440 and λ = 1550 nm) as a function of (a) the relative permittivity contrast and for various profile curvatures, and (b) as a function of the profile curvature and for various relative permittivity contrasts. Modal separation in an IPGIF (N = −4, n2 = 1.4440 and λ = 1550 nm) as a function of the core radius size and for different values of the (c) relative permittivity contrast, and (d) maximum refractive index contrast.

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.

Fig. 6
Fig. 6

Fabricated IPGIF refractive index profile (solid black) and E-field intensity (dashed red) of the TE01 guided mode at λ = 1550 nm.

Fig. 7
Fig. 7

(a) Effective indices of the guided vector modes (neglecting polarization degenerate modes) of the fabricated IPGIF. (b) Corresponding group velocity dispersion in ps/(km-nm).

Fig. 8
Fig. 8

Reflectogram acquired by OFDR after vector modes interaction with the FBG inscribed in the IPGIF. The numbered mode groups (#1, #2 and #3) correspond respectively to the LP01, LP11 and LP21 mode groups.

Fig. 9
Fig. 9

Schematic of the experimental setup used to image the OAM carrying modes at the fiber output. Legend: M1, M2, M3: mirrors, SLM: spatial light modulator, QWP: quarter wave plate, SMF: singlemode fiber, BE: Beam expander, PBS: Polarizing Beam Splitter, PC: Polarization controller.

Fig. 10
Fig. 10

Output fiber modal intensity distributions (in top row) and corresponding interference patterns (bottom row) of the OAM(−1,1), OAM(−2,1) and OAM( + 2,1) modes excited by (-sign) circularly-polarized light, after 1 m propagation in the IPGIF. On the right-hand side: OAM( + 1,1) mode excited by ( + sign) circularly-polarized light after 1.1 km propagation in the IPGIF. We note that the corollary set of modes OAM( + 1,1), OAM( + 2,1) and OAM(−2,1) obtained with ( + sign) circular polarization were also recovered after 1 m distance and have similar field distributions as their counterparts shown above except that their helical phase rotates in the opposite direction.

Equations (6)

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n(r)={ n 1 12NΔ( r 2 / a 2 ) , 0ra n 2 , r>a
δ β 2 tot ( e )( e (ln n 2 ) )dA tot | e | 2 dA
e = 1 r [ (r e r ) r + ( e ϕ ) ϕ ]
(ln n 2 )= r ^ n 2 (r) d n 2 (r) dr
| (ln n IPGIF 2 ) | Δ| N | a
n eq (x,y)= n fiber (x,y)( 1+ x 1.40 R bend )

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