Abstract

In optical fiber telecommunications, there is much current work on the use of orbital angular momentum (OAM) modes for increasing channel capacity. Here we study the properties of a helically twisted photonic crystal fiber (PCF) that preserves the chirality of OAM modes of the same order, i.e., it inhibits scattering between an order +1 mode to an order 1 mode. This is achieved by thermally inducing a helical twist in a PCF with a novel three-bladed Y-shaped core. The effect is seen for twist periods of a few millimeters or less. We develop a novel scalar theory to analyze the properties of the twisted fiber, based on a helicoidal extension to Bloch wave theory. It yields results that are in excellent agreement with full finite element simulations. Since twisted PCFs with complex core structures can be produced in long lengths from a fiber drawing tower, they are of potential interest for increasing channel capacity in optical telecommunications, but the result is also of interest to the photonic crystal community, where a new kind of guided helical Bloch mode is sure to excite interest, and among the spin–orbit coupling community.

© 2014 Optical Society of America

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References

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N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, Science 340, 1545 (2013).
[Crossref]

C. N. Alexeyev, A. N. Alexeyev, B. P. Lapin, G. Milione, M. A. Yavorsky, Phys. Rev. A 88, 063814 (2013).
[Crossref]

X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, P. St.J. Russell, Phys. Rev. Lett. 110, 143903 (2013).
[Crossref]

T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, X. M. Xi, P. St.J. Russell, J. Opt. Soc. Am. B 30, 2921 (2013).
[Crossref]

S. Ramachandran, P. Kristensen, J. Nanophoton. 2, 455 (2013).

2012 (2)

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, P. St.J. Russell, Science 337, 446 (2012).
[Crossref]

N. Bozinovic, S. Golowich, P. Kristensen, S. Ramachandran, Opt. Lett. 37, 2451 (2012).
[Crossref]

2011 (3)

2009 (1)

W. Shin, Y. L. Lee, B. A. Yu, Y. C. Noh, K. Oh, Opt. Commun. 282, 3456 (2009).
[Crossref]

2008 (2)

2006 (2)

P. St.J. Russell, J. Lightwave Technol. 24, 4729 (2006).
[Crossref]

P. Z. Dashti, F. Alhassen, H. P. Lee, Phys. Rev. Lett. 96, 043604 (2006).
[Crossref]

2004 (3)

1998 (1)

1986 (1)

P. St.J. Russell, Appl. Phys. B 39, 231 (1986).
[Crossref]

Abdolvand, A.

Agha, Y. O.

A. Nicolet, F. Zolla, Y. O. Agha, S. Guenneau, COMPEL 27, 806 (2008).
[Crossref]

Ahmed, N.

Alexeyev, A. N.

C. N. Alexeyev, A. N. Alexeyev, B. P. Lapin, G. Milione, M. A. Yavorsky, Phys. Rev. A 88, 063814 (2013).
[Crossref]

Alexeyev, C. N.

C. N. Alexeyev, A. N. Alexeyev, B. P. Lapin, G. Milione, M. A. Yavorsky, Phys. Rev. A 88, 063814 (2013).
[Crossref]

Alhassen, F.

P. Z. Dashti, F. Alhassen, H. P. Lee, Phys. Rev. Lett. 96, 043604 (2006).
[Crossref]

Awaji, Y.

Y. Awaji, N. Wada, Y. Toda, T. Hayashi, in 37th European Conference and Exposition on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper We.10.P1.55.

Banzer, P.

Barnett, S. M.

Biancalana, F.

X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, P. St.J. Russell, Phys. Rev. Lett. 110, 143903 (2013).
[Crossref]

T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, X. M. Xi, P. St.J. Russell, J. Opt. Soc. Am. B 30, 2921 (2013).
[Crossref]

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, P. St.J. Russell, Science 337, 446 (2012).
[Crossref]

Birnbaum, K.

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, Science 340, 1545 (2013).
[Crossref]

N. Bozinovic, S. Golowich, P. Kristensen, S. Ramachandran, Opt. Lett. 37, 2451 (2012).
[Crossref]

Brenn, A.

Chang, G.

Chao, N.

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, A. Z. Genack, Science 305, 74 (2004).
[Crossref]

Chen, J. S. Y.

Chung, Y. J.

Churikov, V. M.

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, A. Z. Genack, Science 305, 74 (2004).
[Crossref]

Conti, C.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, P. St.J. Russell, Science 337, 446 (2012).
[Crossref]

Courtial, J.

Dashti, P. Z.

P. Z. Dashti, F. Alhassen, H. P. Lee, Phys. Rev. Lett. 96, 043604 (2006).
[Crossref]

Dolinar, S.

Elser, D.

Euser, T. G.

Fazal, I. M.

Förtsch, M.

Franke-Arnold, S.

Gabriel, C.

Galvanauskas, A.

Genack, A. Z.

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, A. Z. Genack, Science 305, 74 (2004).
[Crossref]

Gibson, G.

Golowich, S.

Guenneau, S.

A. Nicolet, F. Zolla, Y. O. Agha, S. Guenneau, COMPEL 27, 806 (2008).
[Crossref]

Hayashi, T.

Y. Awaji, N. Wada, Y. Toda, T. Hayashi, in 37th European Conference and Exposition on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper We.10.P1.55.

Huang, H.

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, Science 340, 1545 (2013).
[Crossref]

Joly, N. Y.

Kaminski, C. F.

Kang, M. S.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, P. St.J. Russell, Science 337, 446 (2012).
[Crossref]

Kopp, V. I.

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, A. Z. Genack, Science 305, 74 (2004).
[Crossref]

Kristensen, P.

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, Science 340, 1545 (2013).
[Crossref]

S. Ramachandran, P. Kristensen, J. Nanophoton. 2, 455 (2013).

N. Bozinovic, S. Golowich, P. Kristensen, S. Ramachandran, Opt. Lett. 37, 2451 (2012).
[Crossref]

Lapin, B. P.

C. N. Alexeyev, A. N. Alexeyev, B. P. Lapin, G. Milione, M. A. Yavorsky, Phys. Rev. A 88, 063814 (2013).
[Crossref]

Lee, H. P.

P. Z. Dashti, F. Alhassen, H. P. Lee, Phys. Rev. Lett. 96, 043604 (2006).
[Crossref]

Lee, H. W.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, P. St.J. Russell, Science 337, 446 (2012).
[Crossref]

Lee, K. R.

Lee, Y. L.

W. Shin, Y. L. Lee, B. A. Yu, Y. C. Noh, K. Oh, Opt. Commun. 282, 3456 (2009).
[Crossref]

Leuchs, G.

Liu, C.-H.

Ma, X.

Marquardt, C.

McGloin, D.

Milione, G.

C. N. Alexeyev, A. N. Alexeyev, B. P. Lapin, G. Milione, M. A. Yavorsky, Phys. Rev. A 88, 063814 (2013).
[Crossref]

Neugroschl, D.

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, A. Z. Genack, Science 305, 74 (2004).
[Crossref]

Nicolet, A.

A. Nicolet, F. Zolla, Y. O. Agha, S. Guenneau, COMPEL 27, 806 (2008).
[Crossref]

Noh, Y. C.

W. Shin, Y. L. Lee, B. A. Yu, Y. C. Noh, K. Oh, Opt. Commun. 282, 3456 (2009).
[Crossref]

Nold, J.

Oh, K.

W. Shin, Y. L. Lee, B. A. Yu, Y. C. Noh, K. Oh, Opt. Commun. 282, 3456 (2009).
[Crossref]

Oh, S. T.

Padgett, M. J.

Paek, U. C.

Pas’ko, V.

Ramachandran, S.

S. Ramachandran, P. Kristensen, J. Nanophoton. 2, 455 (2013).

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, Science 340, 1545 (2013).
[Crossref]

N. Bozinovic, S. Golowich, P. Kristensen, S. Ramachandran, Opt. Lett. 37, 2451 (2012).
[Crossref]

Ren, Y. X.

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, Science 340, 1545 (2013).
[Crossref]

Russell, P. St.J.

Scharrer, M.

Schmidt, M. A.

Shamee, B.

Shin, W.

W. Shin, Y. L. Lee, B. A. Yu, Y. C. Noh, K. Oh, Opt. Commun. 282, 3456 (2009).
[Crossref]

Simpson, N. B.

Singer, J.

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, A. Z. Genack, Science 305, 74 (2004).
[Crossref]

Toda, Y.

Y. Awaji, N. Wada, Y. Toda, T. Hayashi, in 37th European Conference and Exposition on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper We.10.P1.55.

Tur, M.

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, Science 340, 1545 (2013).
[Crossref]

Vasnetsov, M.

Wada, N.

Y. Awaji, N. Wada, Y. Toda, T. Hayashi, in 37th European Conference and Exposition on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper We.10.P1.55.

Wang, J.

Weiss, T.

T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, X. M. Xi, P. St.J. Russell, J. Opt. Soc. Am. B 30, 2921 (2013).
[Crossref]

X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, P. St.J. Russell, Phys. Rev. Lett. 110, 143903 (2013).
[Crossref]

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, P. St.J. Russell, Science 337, 446 (2012).
[Crossref]

Whyte, G.

Willner, A. E.

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, Science 340, 1545 (2013).
[Crossref]

Y. Yan, J. Wang, L. Zhang, J. Y. Yang, I. M. Fazal, N. Ahmed, B. Shamee, A. E. Willner, K. Birnbaum, S. Dolinar, Opt. Lett. 36, 4269 (2011).
[Crossref]

Wong, G. K. L.

T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, X. M. Xi, P. St.J. Russell, J. Opt. Soc. Am. B 30, 2921 (2013).
[Crossref]

X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, P. St.J. Russell, Phys. Rev. Lett. 110, 143903 (2013).
[Crossref]

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, P. St.J. Russell, Science 337, 446 (2012).
[Crossref]

Xi, X. M.

X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, P. St.J. Russell, Phys. Rev. Lett. 110, 143903 (2013).
[Crossref]

T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, X. M. Xi, P. St.J. Russell, J. Opt. Soc. Am. B 30, 2921 (2013).
[Crossref]

Yan, Y.

Yang, J. Y.

Yavorsky, M. A.

C. N. Alexeyev, A. N. Alexeyev, B. P. Lapin, G. Milione, M. A. Yavorsky, Phys. Rev. A 88, 063814 (2013).
[Crossref]

Yu, B. A.

W. Shin, Y. L. Lee, B. A. Yu, Y. C. Noh, K. Oh, Opt. Commun. 282, 3456 (2009).
[Crossref]

Yue, Y.

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, Science 340, 1545 (2013).
[Crossref]

Zang, L. Y.

Zhang, L.

Zolla, F.

A. Nicolet, F. Zolla, Y. O. Agha, S. Guenneau, COMPEL 27, 806 (2008).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (1)

P. St.J. Russell, Appl. Phys. B 39, 231 (1986).
[Crossref]

COMPEL (1)

A. Nicolet, F. Zolla, Y. O. Agha, S. Guenneau, COMPEL 27, 806 (2008).
[Crossref]

J. Lightwave Technol. (1)

J. Nanophoton. (1)

S. Ramachandran, P. Kristensen, J. Nanophoton. 2, 455 (2013).

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

W. Shin, Y. L. Lee, B. A. Yu, Y. C. Noh, K. Oh, Opt. Commun. 282, 3456 (2009).
[Crossref]

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. A (1)

C. N. Alexeyev, A. N. Alexeyev, B. P. Lapin, G. Milione, M. A. Yavorsky, Phys. Rev. A 88, 063814 (2013).
[Crossref]

Phys. Rev. Lett. (2)

X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, P. St.J. Russell, Phys. Rev. Lett. 110, 143903 (2013).
[Crossref]

P. Z. Dashti, F. Alhassen, H. P. Lee, Phys. Rev. Lett. 96, 043604 (2006).
[Crossref]

Science (3)

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, A. Z. Genack, Science 305, 74 (2004).
[Crossref]

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, Science 340, 1545 (2013).
[Crossref]

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, P. St.J. Russell, Science 337, 446 (2012).
[Crossref]

Other (1)

Y. Awaji, N. Wada, Y. Toda, T. Hayashi, in 37th European Conference and Exposition on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper We.10.P1.55.

Supplementary Material (1)

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Figures (4)

Fig. 1.
Fig. 1. (a) Schematic of the fiber core structure. (b) Scanning electron micrograph of the fiber used in the experiments. (c) Axial Poynting vector distribution of one of the ring modes at a wavelength of 800 nm and a twist rate of 1.26rad/mm, calculated by finite element modeling in a helicoidal reference frame. (d) Axial Poynting vector distribution of the lowest order mode of the same twisted structure, which does not carry OAM.
Fig. 2.
Fig. 2. (a) Illustrative wavevector diagram for an OBM, plotted over four Brillouin zones. It was obtained by solving Eq. (4) with β0ρ=27.3, αρ=0.0038, and κρ=0.1, including seven harmonics. Its shape is identical in each Brillouin zone (this ensures that every harmonic of the OBM shares the same group velocity—see text), and it is tilted at an average slope αρ (this ensures that the field pattern rotates with the helical structure). (b) Normalized strengths of each harmonic. The numbers correspond to the harmonic orders n of the backward-spinning (black) and forward-spinning (red) OBMs.
Fig. 3.
Fig. 3. (a) Comparison of FEM and analytical model. Left-hand axis: calculated refractive indices nOBM at 800 nm of the n=0 harmonic of the =+1 and 1 OBMs, plotted versus twist rate. The dots correspond to full vector finite element modeling and the solid lines are solutions of the analytical OBM model. The index of the nth Bloch harmonic is nOBM3nα/k. LC and RC polarized OBMs have refractive indices that differ by 3×106 [see (b)]. Right-hand axis: index splitting between =+1 and 1 OBMs, plotted versus twist rate. Within the narrow shaded region on the left, the (s,)=(1,+1) and (+1,1) modes are less than 97% circularly polarized (within the accuracy of the FEM, the other two OBMs are at least 99.9% circularly polarized at zero twist rate). (b) FEM calculations of the optical activity of each OBM, plotted against twist rate (see text).
Fig. 4.
Fig. 4. (a) Schematic of the experimental setup for generating and characterizing OAM states in the twisted PCF. LD, laser diode; BS, beam splitter. (b) Experimentally recorded (top) and calculated (bottom) interference patterns created when ring modes with different combinations of spin and OAM order interfere with an expanded Gaussian reference beam.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

ε(ϕ,r,z)=ε0+ε1cos[3(ϕαz)]exp[(rρ)2/w2],
EB(ϕ,z)=ei(β0+γ)znanexp(i(kBρ+3n)ϕi3nαz),
(1ρ22ϕ2+2z2+k2ε(ϕ,z))EB=0,
(2(γ3nα)+(kB+3n/ρ)2/β0)anκ(an1+an+1)=0,
(2(γ3nα)ρ+(+3n)2β0ρ)anκρ(an1+an+1)=0,
γ=γtw+(+s)α,

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