Abstract

We investigate the properties of optical fibres made from chiral materials, in which a contrast in only optical rotation forms the waveguide, rather than a contrast in the refractive index; we refer to such structures as pure chiral fibres. We present a mathematical formulation for solving the modes of circularly symmetric examples of such fibres and examine the guidance and polarisation properties of pure chiral step-index, Bragg and photonic crystal fibre designs. Their behaviour is shown to differ for left-and right-hand circular polarisation, allowing circular polarisations to be isolated and/or guided by different mechanisms, as well as differing from equivalent non-chiral fibres. The strength of optical rotation required in each case is quantified.

© 2011 Optical Society of America

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References

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  1. D. B. Amabilino, Chirality at the nanoscale: Nanoparticles, surfaces, materials and more, (Wiley-VCH, Weinheim 2009).
  2. T. M. Lowry, Optical rotatory power, (Dover Publications, New York 1964).
  3. K. V. Varadan, V. V. Varadan, and A. Lakhtakia, Time-Harmonic Electromagnetic Fields in Chiral Media, (Springer-Verlag, 1989).
  4. J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. 4, 10711089 (1986).
    [CrossRef]
  5. I. Bassett, “Design principle for a circularly birefringent optical fiber,” Opt. Lett. 13, 844–846 (1988).
    [CrossRef] [PubMed]
  6. A. Argyros, J. Pla, F. Ladouceur, and L. Poladian, “Circular and elliptical birefringence in spun microstructured optical fibres,” Opt. Express 17, 15983–15990 (2009).
    [CrossRef] [PubMed]
  7. N. S. Pujari, M. R. Kulkarni, M. C. J. Large, I. M. Bassett, and S. Ponrathnam, “Transparent chiral polymers for optical applications,” J. Appl. Polym. Sci. 98, 58–65 (2005).
    [CrossRef]
  8. A. Argyros, M. Straton, A. Docherty, E. H. Min, Z. Ge, K. H. Wong, F. Ladouceur, and L. Poladian, “Consideration of chiral optical fibres,” Front. Optoelectron. China 3, 67–70 (2010).
    [CrossRef]
  9. A. K. Singh, K. S. Singh, P. Khastgir, S. P. Ojha, and O. N. Singh, “Modal cutoff condition of an optical chiral fiber with different chiralities in the core and the cladding,” J. Opt. Soc. Am. B 11, 1283–1287 (1994).
    [CrossRef]
  10. R. C. Qiu, and I. T. Lu, “Dispersion in chiral optical fibres,” IEE Proc., Optoelectron. 145, 155–158 (1998).
    [CrossRef]
  11. F. M. Janeiro, C. R. Paiva, and A. L. Topa, “Guidance and leakage properties of chiral optical fibers,” J. Opt. Soc. Am. B 19, 2558–2566 (2002).
    [CrossRef]
  12. P. K. Choudhury, and T. Yoshino, “Characterization of the optical power confinement in a simple chirofiber,” Optik (Stuttg.) 113, 89–95 (2002).
    [CrossRef]
  13. F. I. Fedorov, “Contribution to the theory of the optical activity of crystals. 1. The law of conservation of energy and tensors of optical activity,” Opt. I Spektrosk. 6, 85–93 (1959).
  14. A. W. Snyder, and J. D. Love, Optical Waveguide Theory, (Chapman and Hall, London 1983).
  15. The optical activity of a material is commonly quoted as the rotation α, in degrees per decimetre, at 589 nm, at a specified temperature and concentration. Note we use different units in this paper.
  16. A. Argyros, “Guided modes and loss in Bragg fibres,” Opt. Express 10, 1411–1417 (2002).
    [PubMed]
  17. H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, and S. Yamaguchi, “Absolutely single polarization photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 182184 (2004).
  18. I. Bassett, and A. Argyros, “Elimination of polarisation degeneracy in round waveguides,” Opt. Express 10, 1342–1346 (2002).
    [PubMed]
  19. A. Argyros, I. M. Bassett, M. A. van Eijkelenborg, and M. C. J. Large, “Microstructured optical fiber for singlepolarization air-guidance,” Opt. Lett. 29, 20–22 (2004).
    [CrossRef] [PubMed]
  20. P. St. J. Russell, “Photonic-cystal fibers,” J. Lightwave Technol. 24, 47294749 (2006).
    [CrossRef]
  21. A. Argyros, “Microstructured polymer optical fibers,” J. Lightwave Technol. 27, 1571–1579 (2009).
    [CrossRef]
  22. N. M. Litchinitser, A. K. Abeeluck, C. Headley, and B. J. Eggleton, “Antiresonant reflecting photonic crystal optical waveguides,” Opt. Lett. 27, 1592–1594 (2002).
    [CrossRef]

2010 (1)

A. Argyros, M. Straton, A. Docherty, E. H. Min, Z. Ge, K. H. Wong, F. Ladouceur, and L. Poladian, “Consideration of chiral optical fibres,” Front. Optoelectron. China 3, 67–70 (2010).
[CrossRef]

2009 (2)

2006 (1)

P. St. J. Russell, “Photonic-cystal fibers,” J. Lightwave Technol. 24, 47294749 (2006).
[CrossRef]

2005 (1)

N. S. Pujari, M. R. Kulkarni, M. C. J. Large, I. M. Bassett, and S. Ponrathnam, “Transparent chiral polymers for optical applications,” J. Appl. Polym. Sci. 98, 58–65 (2005).
[CrossRef]

2004 (2)

A. Argyros, I. M. Bassett, M. A. van Eijkelenborg, and M. C. J. Large, “Microstructured optical fiber for singlepolarization air-guidance,” Opt. Lett. 29, 20–22 (2004).
[CrossRef] [PubMed]

H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, and S. Yamaguchi, “Absolutely single polarization photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 182184 (2004).

2002 (5)

1998 (1)

R. C. Qiu, and I. T. Lu, “Dispersion in chiral optical fibres,” IEE Proc., Optoelectron. 145, 155–158 (1998).
[CrossRef]

1994 (1)

1988 (1)

1986 (1)

J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. 4, 10711089 (1986).
[CrossRef]

1959 (1)

F. I. Fedorov, “Contribution to the theory of the optical activity of crystals. 1. The law of conservation of energy and tensors of optical activity,” Opt. I Spektrosk. 6, 85–93 (1959).

Abeeluck, A. K.

Argyros, A.

Bassett, I.

Bassett, I. M.

N. S. Pujari, M. R. Kulkarni, M. C. J. Large, I. M. Bassett, and S. Ponrathnam, “Transparent chiral polymers for optical applications,” J. Appl. Polym. Sci. 98, 58–65 (2005).
[CrossRef]

A. Argyros, I. M. Bassett, M. A. van Eijkelenborg, and M. C. J. Large, “Microstructured optical fiber for singlepolarization air-guidance,” Opt. Lett. 29, 20–22 (2004).
[CrossRef] [PubMed]

Choudhury, P. K.

P. K. Choudhury, and T. Yoshino, “Characterization of the optical power confinement in a simple chirofiber,” Optik (Stuttg.) 113, 89–95 (2002).
[CrossRef]

Docherty, A.

A. Argyros, M. Straton, A. Docherty, E. H. Min, Z. Ge, K. H. Wong, F. Ladouceur, and L. Poladian, “Consideration of chiral optical fibres,” Front. Optoelectron. China 3, 67–70 (2010).
[CrossRef]

Eggleton, B. J.

Fedorov, F. I.

F. I. Fedorov, “Contribution to the theory of the optical activity of crystals. 1. The law of conservation of energy and tensors of optical activity,” Opt. I Spektrosk. 6, 85–93 (1959).

Ge, Z.

A. Argyros, M. Straton, A. Docherty, E. H. Min, Z. Ge, K. H. Wong, F. Ladouceur, and L. Poladian, “Consideration of chiral optical fibres,” Front. Optoelectron. China 3, 67–70 (2010).
[CrossRef]

Headley, C.

Janeiro, F. M.

Kawanishi, S.

H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, and S. Yamaguchi, “Absolutely single polarization photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 182184 (2004).

Khastgir, P.

Koyanagi, S.

H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, and S. Yamaguchi, “Absolutely single polarization photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 182184 (2004).

Kubota, H.

H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, and S. Yamaguchi, “Absolutely single polarization photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 182184 (2004).

Kulkarni, M. R.

N. S. Pujari, M. R. Kulkarni, M. C. J. Large, I. M. Bassett, and S. Ponrathnam, “Transparent chiral polymers for optical applications,” J. Appl. Polym. Sci. 98, 58–65 (2005).
[CrossRef]

Ladouceur, F.

A. Argyros, M. Straton, A. Docherty, E. H. Min, Z. Ge, K. H. Wong, F. Ladouceur, and L. Poladian, “Consideration of chiral optical fibres,” Front. Optoelectron. China 3, 67–70 (2010).
[CrossRef]

A. Argyros, J. Pla, F. Ladouceur, and L. Poladian, “Circular and elliptical birefringence in spun microstructured optical fibres,” Opt. Express 17, 15983–15990 (2009).
[CrossRef] [PubMed]

Large, M. C. J.

N. S. Pujari, M. R. Kulkarni, M. C. J. Large, I. M. Bassett, and S. Ponrathnam, “Transparent chiral polymers for optical applications,” J. Appl. Polym. Sci. 98, 58–65 (2005).
[CrossRef]

A. Argyros, I. M. Bassett, M. A. van Eijkelenborg, and M. C. J. Large, “Microstructured optical fiber for singlepolarization air-guidance,” Opt. Lett. 29, 20–22 (2004).
[CrossRef] [PubMed]

Litchinitser, N. M.

Lu, I. T.

R. C. Qiu, and I. T. Lu, “Dispersion in chiral optical fibres,” IEE Proc., Optoelectron. 145, 155–158 (1998).
[CrossRef]

Min, E. H.

A. Argyros, M. Straton, A. Docherty, E. H. Min, Z. Ge, K. H. Wong, F. Ladouceur, and L. Poladian, “Consideration of chiral optical fibres,” Front. Optoelectron. China 3, 67–70 (2010).
[CrossRef]

Noda, J.

J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. 4, 10711089 (1986).
[CrossRef]

Ojha, S. P.

Okamoto, K.

J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. 4, 10711089 (1986).
[CrossRef]

Paiva, C. R.

Pla, J.

Poladian, L.

A. Argyros, M. Straton, A. Docherty, E. H. Min, Z. Ge, K. H. Wong, F. Ladouceur, and L. Poladian, “Consideration of chiral optical fibres,” Front. Optoelectron. China 3, 67–70 (2010).
[CrossRef]

A. Argyros, J. Pla, F. Ladouceur, and L. Poladian, “Circular and elliptical birefringence in spun microstructured optical fibres,” Opt. Express 17, 15983–15990 (2009).
[CrossRef] [PubMed]

Ponrathnam, S.

N. S. Pujari, M. R. Kulkarni, M. C. J. Large, I. M. Bassett, and S. Ponrathnam, “Transparent chiral polymers for optical applications,” J. Appl. Polym. Sci. 98, 58–65 (2005).
[CrossRef]

Pujari, N. S.

N. S. Pujari, M. R. Kulkarni, M. C. J. Large, I. M. Bassett, and S. Ponrathnam, “Transparent chiral polymers for optical applications,” J. Appl. Polym. Sci. 98, 58–65 (2005).
[CrossRef]

Qiu, R. C.

R. C. Qiu, and I. T. Lu, “Dispersion in chiral optical fibres,” IEE Proc., Optoelectron. 145, 155–158 (1998).
[CrossRef]

Russell, P. St. J.

P. St. J. Russell, “Photonic-cystal fibers,” J. Lightwave Technol. 24, 47294749 (2006).
[CrossRef]

Sasaki, Y.

J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. 4, 10711089 (1986).
[CrossRef]

Singh, A. K.

Singh, K. S.

Singh, O. N.

Straton, M.

A. Argyros, M. Straton, A. Docherty, E. H. Min, Z. Ge, K. H. Wong, F. Ladouceur, and L. Poladian, “Consideration of chiral optical fibres,” Front. Optoelectron. China 3, 67–70 (2010).
[CrossRef]

Tanaka, M.

H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, and S. Yamaguchi, “Absolutely single polarization photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 182184 (2004).

Topa, A. L.

van Eijkelenborg, M. A.

Wong, K. H.

A. Argyros, M. Straton, A. Docherty, E. H. Min, Z. Ge, K. H. Wong, F. Ladouceur, and L. Poladian, “Consideration of chiral optical fibres,” Front. Optoelectron. China 3, 67–70 (2010).
[CrossRef]

Yamaguchi, S.

H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, and S. Yamaguchi, “Absolutely single polarization photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 182184 (2004).

Yoshino, T.

P. K. Choudhury, and T. Yoshino, “Characterization of the optical power confinement in a simple chirofiber,” Optik (Stuttg.) 113, 89–95 (2002).
[CrossRef]

Front. Optoelectron. China (1)

A. Argyros, M. Straton, A. Docherty, E. H. Min, Z. Ge, K. H. Wong, F. Ladouceur, and L. Poladian, “Consideration of chiral optical fibres,” Front. Optoelectron. China 3, 67–70 (2010).
[CrossRef]

IEE Proc., Optoelectron. (1)

R. C. Qiu, and I. T. Lu, “Dispersion in chiral optical fibres,” IEE Proc., Optoelectron. 145, 155–158 (1998).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, and S. Yamaguchi, “Absolutely single polarization photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 182184 (2004).

J. Appl. Polym. Sci. (1)

N. S. Pujari, M. R. Kulkarni, M. C. J. Large, I. M. Bassett, and S. Ponrathnam, “Transparent chiral polymers for optical applications,” J. Appl. Polym. Sci. 98, 58–65 (2005).
[CrossRef]

J. Lightwave Technol. (3)

J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. 4, 10711089 (1986).
[CrossRef]

P. St. J. Russell, “Photonic-cystal fibers,” J. Lightwave Technol. 24, 47294749 (2006).
[CrossRef]

A. Argyros, “Microstructured polymer optical fibers,” J. Lightwave Technol. 27, 1571–1579 (2009).
[CrossRef]

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

Opt. Express (3)

Opt. I Spektrosk. (1)

F. I. Fedorov, “Contribution to the theory of the optical activity of crystals. 1. The law of conservation of energy and tensors of optical activity,” Opt. I Spektrosk. 6, 85–93 (1959).

Opt. Lett. (3)

Optik (Stuttg.) (1)

P. K. Choudhury, and T. Yoshino, “Characterization of the optical power confinement in a simple chirofiber,” Optik (Stuttg.) 113, 89–95 (2002).
[CrossRef]

Other (5)

A. W. Snyder, and J. D. Love, Optical Waveguide Theory, (Chapman and Hall, London 1983).

The optical activity of a material is commonly quoted as the rotation α, in degrees per decimetre, at 589 nm, at a specified temperature and concentration. Note we use different units in this paper.

D. B. Amabilino, Chirality at the nanoscale: Nanoparticles, surfaces, materials and more, (Wiley-VCH, Weinheim 2009).

T. M. Lowry, Optical rotatory power, (Dover Publications, New York 1964).

K. V. Varadan, V. V. Varadan, and A. Lakhtakia, Time-Harmonic Electromagnetic Fields in Chiral Media, (Springer-Verlag, 1989).

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Figures (4)

Fig. 1
Fig. 1

Schematic of the pure chiral optical fibres considered in this work: (a) step-chiral-index, (b) pure chiral Bragg fibre and (c) pure chiral photonic crystal fibre. The refractive index profiles seen by the two circular polarisations are shown, as well as the modes that may be supported through the various mechanisms. Typical mode effective indices are indicated by the red dashed lines.

Fig. 2
Fig. 2

Comparing dispersion curves for step-chiral-index and conventional step-index fibres. The chiral modes are shown with solid curves and the conventional modes are shown with dashed curves. The colours correspond to different values of the azimuthal index: m = 0 (black), mp = 1 (red), mp = −1 (blue), mp = 2 (green),and mp = −2 (magenta). The chiral modes are all of the one circular polarisation that is guided, as the other will see a lower core index compared to the cladding and not be guided. The chiral modes are solutions of Eq. (32), and the conventional modes of Eq. (33 ).

Fig. 3
Fig. 3

Contours showing the V-parameter for a step-chiral-index fibre as a function of wavelength and optical rotation α; remaining parameters as in the text. The grey area corresponds to V < 1 where the fibre is deemed to not guide effectively. Contours corresponding to constant γ are indicated in red and labelled with the value of α they correspond to at 589 nm.

Fig. 4
Fig. 4

Dispersion curves for m = 1 and m = 0. Top and bottom graphs in each pair give the effective modal indices and the loss, respectively. Left and right graphs give the results for left- and right-circular polarisation respectively.

Equations (40)

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v LCP = c n ( 1 + δ ) , v RCP = c n ( 1 δ ) ,
B = n 1 δ n 1 + δ = 2 n δ 1 δ 2 ,
α = 1 2 k B k n δ .
D = ɛ ( E + γ × E ) ,
B = μ ( H + γ × H ) ,
δ = k n γ ,
( 1 δ 2 ) × E = i ω μ H + k n δ E ,
( 1 δ 2 ) × H = i ω ɛ E + k n δ H .
Q ± = E i Z H ,
× Q + = + k n 1 + δ Q + ,
× Q = k n 1 δ Q .
2 Q + + k 2 n 2 ( 1 + δ ) 2 Q + = 0 ,
2 Q + k 2 n 2 ( 1 δ ) 2 Q = 0 .
n p δ = n 1 + p δ
2 Q p + k 2 n p δ 2 Q p = 0 .
[ d 2 d r 2 + 1 r d d r + m 2 r 2 u p δ 2 ] Q z p ( r ) = 0 ,
u p δ = k n eff 2 n p δ 2 .
w p δ = k n p δ 2 n eff 2 .
Q ϕ p ( r ) = 1 u p δ 2 [ m k n eff r + p k n p δ d d r ] Q z p ( r ) = 1 u p δ 2 𝒟 Q z p ( r ) ,
( Q z p ( r ) Q ϕ p ( r ) ) = 𝒥 m , p ( u p δ , r ) ( A B ) = m , p ( u p δ , r ) ( C D ) = 𝒦 m , p ( w p δ , r ) ( E F ) ,
𝒥 m p ( u , r ) = ( J m ( u r ) Y m ( u r ) 1 u 2 𝒟 J m ( u r ) 1 u 2 𝒟 Y m ( u r ) )
m , p ( u , r ) = ( H m ( 1 ) ( u r ) H m ( 2 ) ( u r ) 1 u 2 𝒟 H m ( 1 ) ( u r ) 1 u 2 𝒟 H m ( 2 ) ( u r ) )
𝒦 m , p ( w , r ) = ( K m ( w r ) I m ( w r ) 1 w 2 𝒟 K m ( w r ) 1 w 2 𝒟 I m ( w r ) )
( Q z ( r n + 1 ) Q ϕ ( r n + 1 ) ) = 𝒯 m p ( u n , r n , r n + 1 ) ( Q z ( r n ) Q ϕ ( r n ) ) ,
𝒯 m , p ( u , r n , r n + 1 ) = m , p ( u , r n + 1 ) m , p ( u , r n ) 1 = 𝒥 m , p ( u , r n + 1 ) 𝒥 m p ( u , r n ) 1
( Q z ( r ) Q ϕ ( r ) ) = A 𝒥 m , p ( u c o , r ) ( 1 0 )
( Q z ( r ) Q ϕ ( r ) ) = C m , p ( u c l , r ) ( 1 0 )
( 0 1 ) m , p ( u c l , r ) 1 ( Q z ( r ) Q ϕ ( r ) ) = 0 .
( 0 1 ) m , p ( u c l , r N ) 1 [ i = 1 N 1 𝒯 m , p ( r i , r i + 1 , u i ) ] 𝒥 m , p ( u c o , r 1 ) ( 1 0 ) = 0 ,
( 0 1 ) 𝒦 m , p ( w c l , r N ) 1 [ i = 1 N 1 𝒯 m , p ( r i , r i + 1 , u i ) ] 𝒥 m , p ( u c o , r 1 ) ( 1 0 ) = 0 .
( 0 1 ) 𝒦 m , p ( w c l , a ) 1 𝒥 m , p ( u c o , a ) ( 1 0 ) = 0 .
u c o = k n co 2 n eff 2 , w c l = k n eff 2 n cl 2 .
n c o = n 1 | δ | > n 1 + | δ | = n c l
1 w c l 2 J m ( u c o r ) 𝒟 K m ( w c l r ) + 1 u c o 2 K m ( w c l r ) 𝒟 J m ( u c o r ) = 0
U = k a n co 2 n eff 2 , V = k a n co 2 n cl 2 , W = k a n eff 2 n cl 2
J m ( U ) U J m ( U ) + n cl n co K m ( W ) W K m ( W ) = m p n eff n co V 2 U 2 W 2 .
( J m ( U ) U J m ( U ) + K m ( W ) W K m ( W ) ) ( J m ( U ) U J m ( U ) + n cl 2 n co 2 K m ( W ) W K m ( W ) ) = m 2 n eff 2 n co 2 ( V 2 U 2 W 2 ) 2 .
N A = n c o 2 n c l 2 = 2 n δ 1 δ 2 2 n δ .
V = k a n c o 2 n c l 2 2 k a n δ .
α k n δ k n ( V 2 k a n ) 2 = V 2 4 k n a 2 .

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