Abstract

With the various forms of constitutive relations for chiral media integratedly considered, the modal theory is developed for chiral fibers where both the core and cladding are dielectrically chiral. The important role of the wave impedance in the analysis of chiral fibers is pointed out. Analytical and numerical results show that circularly polarized modes could be supported by a properly designed chiral fiber and the chirality in the core and cladding affect the waveguide dispersion in quite different ways.

© 2011 Optical Society of America

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Corrections

Yusheng Cao, Junqing Li, and Qiyao Su, "Guided modes in chiral fibers: erratum," J. Opt. Soc. Am. B 30, 1232-1233 (2013)
https://www.osapublishing.org/josab/abstract.cfm?uri=josab-30-5-1232

References

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    [CrossRef]
  2. R. Ulrich and A. Simon, “Polarization optics of twisted single-mode fibers,” Appl. Opt. 18, 2241–2251 (1979).
    [CrossRef] [PubMed]
  3. V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, and A. Z. Genack, “Chiral fiber gratings,” Science 305, 74–75 (2004).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. J. Li, L. Jin, L. Li, and C. Li, “Bandgap separation and optical switching in nonlinear chiral photonic crystal with layered structure,” IEEE Photonics Technol. Lett. 18, 1261–1263 (2006).
    [CrossRef]
  15. V. R. Tuz, “Polarization properties of symmetrical and asymmetrical nonreciprocal chiral photonic bandgap structure with defect,” J. Opt. Soc. Am. B 26, 1693–1701 (2009).
    [CrossRef]
  16. J. Li, Q. Su, and Y. Cao, “Circularly polarized guided modes in dielectrically chiral photonic crystal fiber,” Opt. Lett. 35, 2720–2722 (2010).
    [CrossRef] [PubMed]
  17. A. Lakhtakia, V. V. Varadan, and V. K. Varadan, “Field equations, Huygens’s principle, integral equations, and theorems for radiation and scattering of electromagnetic waves in isotropic chiral media,” J. Opt. Soc. Am. A 5, 175–184 (1988).
    [CrossRef]
  18. C. F. Bohren, “Light scattering by an optically active sphere,” Chem. Phys. Lett. 29, 458–462 (1974).
    [CrossRef]
  19. A. Lakhtakia, V. K. Varadan, and V. V. Varadan, “Bohren’s decomposition,” in Time-Harmonic Electromagnetic Fields in Chiral Media, Lecture Notes in Physics Series 335 (Springer-Verlag, 1989).
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    [CrossRef]
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    [CrossRef]

2010 (2)

2009 (2)

S. N. Volkov, K. Dolgaleva, R. W. Boyd, K. Jefimovs, J. Turunen, Y. Svirko, B. K. Canfield, and M. Kauranen, “Optical activity in diffraction from a planar array of achiral nanoparticles,” Phys. Rev. A 79, 043819 (2009).
[CrossRef]

V. R. Tuz, “Polarization properties of symmetrical and asymmetrical nonreciprocal chiral photonic bandgap structure with defect,” J. Opt. Soc. Am. B 26, 1693–1701 (2009).
[CrossRef]

2006 (1)

J. Li, L. Jin, L. Li, and C. Li, “Bandgap separation and optical switching in nonlinear chiral photonic crystal with layered structure,” IEEE Photonics Technol. Lett. 18, 1261–1263 (2006).
[CrossRef]

2004 (1)

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, and A. Z. Genack, “Chiral fiber gratings,” Science 305, 74–75 (2004).
[CrossRef] [PubMed]

2002 (1)

2001 (1)

1996 (1)

1994 (1)

1993 (1)

1989 (1)

1988 (2)

1986 (1)

A. Lakhtakia, V. V. Varadan, and V. K. Varadan, “A parametric study of microwave reflection characteristics of a planar achiral-chiral interface,” IEEE Trans. Electromagn. Compat. 28, 90–95 (1986).
[CrossRef]

1979 (2)

D. L. Jaggard, A. R. Mickelson, and C. H. Papas, “On electromagnetic waves in chiral media,” Appl. Phys. 18, 211–216 (1979).
[CrossRef]

R. Ulrich and A. Simon, “Polarization optics of twisted single-mode fibers,” Appl. Opt. 18, 2241–2251 (1979).
[CrossRef] [PubMed]

1974 (1)

C. F. Bohren, “Light scattering by an optically active sphere,” Chem. Phys. Lett. 29, 458–462 (1974).
[CrossRef]

1961 (1)

Bassiri, S.

Bohren, C. F.

C. F. Bohren, “Light scattering by an optically active sphere,” Chem. Phys. Lett. 29, 458–462 (1974).
[CrossRef]

Boyd, R. W.

S. N. Volkov, K. Dolgaleva, R. W. Boyd, K. Jefimovs, J. Turunen, Y. Svirko, B. K. Canfield, and M. Kauranen, “Optical activity in diffraction from a planar array of achiral nanoparticles,” Phys. Rev. A 79, 043819 (2009).
[CrossRef]

Canfield, B. K.

S. N. Volkov, K. Dolgaleva, R. W. Boyd, K. Jefimovs, J. Turunen, Y. Svirko, B. K. Canfield, and M. Kauranen, “Optical activity in diffraction from a planar array of achiral nanoparticles,” Phys. Rev. A 79, 043819 (2009).
[CrossRef]

Cao, Y.

Chao, N.

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, and A. Z. Genack, “Chiral fiber gratings,” Science 305, 74–75 (2004).
[CrossRef] [PubMed]

Churikov, V. M.

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, and A. Z. Genack, “Chiral fiber gratings,” Science 305, 74–75 (2004).
[CrossRef] [PubMed]

Ciric, I. R.

Cooray, M. F. R.

Dolgaleva, K.

S. N. Volkov, K. Dolgaleva, R. W. Boyd, K. Jefimovs, J. Turunen, Y. Svirko, B. K. Canfield, and M. Kauranen, “Optical activity in diffraction from a planar array of achiral nanoparticles,” Phys. Rev. A 79, 043819 (2009).
[CrossRef]

Engheta, N.

Fischer, H.

Flood, K. M.

Genack, A. Z.

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, and A. Z. Genack, “Chiral fiber gratings,” Science 305, 74–75 (2004).
[CrossRef] [PubMed]

Goldstein, D.

D. Goldstein, “The Stokes polarization parameters,” in Polarized Light (Dekker, 2003).
[CrossRef]

Herman, W. N.

Jaggard, D. L.

K. M. Flood and D. L. Jaggard, “Single-mode operation in symmetric planar waveguides using isotropic chiral media,” Opt. Lett. 21, 474–476 (1996).
[CrossRef] [PubMed]

D. L. Jaggard, A. R. Mickelson, and C. H. Papas, “On electromagnetic waves in chiral media,” Appl. Phys. 18, 211–216 (1979).
[CrossRef]

Janeiro, F. M.

Jefimovs, K.

S. N. Volkov, K. Dolgaleva, R. W. Boyd, K. Jefimovs, J. Turunen, Y. Svirko, B. K. Canfield, and M. Kauranen, “Optical activity in diffraction from a planar array of achiral nanoparticles,” Phys. Rev. A 79, 043819 (2009).
[CrossRef]

Jin, L.

J. Li, L. Jin, L. Li, and C. Li, “Bandgap separation and optical switching in nonlinear chiral photonic crystal with layered structure,” IEEE Photonics Technol. Lett. 18, 1261–1263 (2006).
[CrossRef]

Kauranen, M.

S. N. Volkov, K. Dolgaleva, R. W. Boyd, K. Jefimovs, J. Turunen, Y. Svirko, B. K. Canfield, and M. Kauranen, “Optical activity in diffraction from a planar array of achiral nanoparticles,” Phys. Rev. A 79, 043819 (2009).
[CrossRef]

Keiser, G.

G. Keiser, Optical Fiber Communications (McGraw-Hill, 2000).

Kopp, V. I.

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, and A. Z. Genack, “Chiral fiber gratings,” Science 305, 74–75 (2004).
[CrossRef] [PubMed]

Lakhtakia, A.

A. Lakhtakia, V. V. Varadan, and V. K. Varadan, “Field equations, Huygens’s principle, integral equations, and theorems for radiation and scattering of electromagnetic waves in isotropic chiral media,” J. Opt. Soc. Am. A 5, 175–184 (1988).
[CrossRef]

A. Lakhtakia, V. V. Varadan, and V. K. Varadan, “A parametric study of microwave reflection characteristics of a planar achiral-chiral interface,” IEEE Trans. Electromagn. Compat. 28, 90–95 (1986).
[CrossRef]

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, “Bohren’s decomposition,” in Time-Harmonic Electromagnetic Fields in Chiral Media, Lecture Notes in Physics Series 335 (Springer-Verlag, 1989).

Li, C.

J. Li, L. Jin, L. Li, and C. Li, “Bandgap separation and optical switching in nonlinear chiral photonic crystal with layered structure,” IEEE Photonics Technol. Lett. 18, 1261–1263 (2006).
[CrossRef]

Li, J.

J. Li, Q. Su, and Y. Cao, “Circularly polarized guided modes in dielectrically chiral photonic crystal fiber,” Opt. Lett. 35, 2720–2722 (2010).
[CrossRef] [PubMed]

J. Li, L. Jin, L. Li, and C. Li, “Bandgap separation and optical switching in nonlinear chiral photonic crystal with layered structure,” IEEE Photonics Technol. Lett. 18, 1261–1263 (2006).
[CrossRef]

Li, L.

J. Li, L. Jin, L. Li, and C. Li, “Bandgap separation and optical switching in nonlinear chiral photonic crystal with layered structure,” IEEE Photonics Technol. Lett. 18, 1261–1263 (2006).
[CrossRef]

Lu, I.-T.

Mickelson, A. R.

D. L. Jaggard, A. R. Mickelson, and C. H. Papas, “On electromagnetic waves in chiral media,” Appl. Phys. 18, 211–216 (1979).
[CrossRef]

Neugroschl, D.

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, and A. Z. Genack, “Chiral fiber gratings,” Science 305, 74–75 (2004).
[CrossRef] [PubMed]

Paiva, C. R.

Papas, C. H.

Pelet, P.

Qiu, R. C.

Simon, A.

Singer, J.

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, and A. Z. Genack, “Chiral fiber gratings,” Science 305, 74–75 (2004).
[CrossRef] [PubMed]

Snitzer, E.

Su, Q.

Svirko, Y.

S. N. Volkov, K. Dolgaleva, R. W. Boyd, K. Jefimovs, J. Turunen, Y. Svirko, B. K. Canfield, and M. Kauranen, “Optical activity in diffraction from a planar array of achiral nanoparticles,” Phys. Rev. A 79, 043819 (2009).
[CrossRef]

Thiel, M.

Topa, A. L.

Turunen, J.

S. N. Volkov, K. Dolgaleva, R. W. Boyd, K. Jefimovs, J. Turunen, Y. Svirko, B. K. Canfield, and M. Kauranen, “Optical activity in diffraction from a planar array of achiral nanoparticles,” Phys. Rev. A 79, 043819 (2009).
[CrossRef]

Tuz, V. R.

Ulrich, R.

Varadan, V. K.

A. Lakhtakia, V. V. Varadan, and V. K. Varadan, “Field equations, Huygens’s principle, integral equations, and theorems for radiation and scattering of electromagnetic waves in isotropic chiral media,” J. Opt. Soc. Am. A 5, 175–184 (1988).
[CrossRef]

A. Lakhtakia, V. V. Varadan, and V. K. Varadan, “A parametric study of microwave reflection characteristics of a planar achiral-chiral interface,” IEEE Trans. Electromagn. Compat. 28, 90–95 (1986).
[CrossRef]

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, “Bohren’s decomposition,” in Time-Harmonic Electromagnetic Fields in Chiral Media, Lecture Notes in Physics Series 335 (Springer-Verlag, 1989).

Varadan, V. V.

A. Lakhtakia, V. V. Varadan, and V. K. Varadan, “Field equations, Huygens’s principle, integral equations, and theorems for radiation and scattering of electromagnetic waves in isotropic chiral media,” J. Opt. Soc. Am. A 5, 175–184 (1988).
[CrossRef]

A. Lakhtakia, V. V. Varadan, and V. K. Varadan, “A parametric study of microwave reflection characteristics of a planar achiral-chiral interface,” IEEE Trans. Electromagn. Compat. 28, 90–95 (1986).
[CrossRef]

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, “Bohren’s decomposition,” in Time-Harmonic Electromagnetic Fields in Chiral Media, Lecture Notes in Physics Series 335 (Springer-Verlag, 1989).

Volkov, S. N.

S. N. Volkov, K. Dolgaleva, R. W. Boyd, K. Jefimovs, J. Turunen, Y. Svirko, B. K. Canfield, and M. Kauranen, “Optical activity in diffraction from a planar array of achiral nanoparticles,” Phys. Rev. A 79, 043819 (2009).
[CrossRef]

von Freymann, G.

Wegener, M.

Appl. Opt. (1)

Appl. Phys. (1)

D. L. Jaggard, A. R. Mickelson, and C. H. Papas, “On electromagnetic waves in chiral media,” Appl. Phys. 18, 211–216 (1979).
[CrossRef]

Chem. Phys. Lett. (1)

C. F. Bohren, “Light scattering by an optically active sphere,” Chem. Phys. Lett. 29, 458–462 (1974).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

J. Li, L. Jin, L. Li, and C. Li, “Bandgap separation and optical switching in nonlinear chiral photonic crystal with layered structure,” IEEE Photonics Technol. Lett. 18, 1261–1263 (2006).
[CrossRef]

IEEE Trans. Electromagn. Compat. (1)

A. Lakhtakia, V. V. Varadan, and V. K. Varadan, “A parametric study of microwave reflection characteristics of a planar achiral-chiral interface,” IEEE Trans. Electromagn. Compat. 28, 90–95 (1986).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (5)

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

Opt. Lett. (4)

Phys. Rev. A (1)

S. N. Volkov, K. Dolgaleva, R. W. Boyd, K. Jefimovs, J. Turunen, Y. Svirko, B. K. Canfield, and M. Kauranen, “Optical activity in diffraction from a planar array of achiral nanoparticles,” Phys. Rev. A 79, 043819 (2009).
[CrossRef]

Science (1)

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, and A. Z. Genack, “Chiral fiber gratings,” Science 305, 74–75 (2004).
[CrossRef] [PubMed]

Other (3)

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, “Bohren’s decomposition,” in Time-Harmonic Electromagnetic Fields in Chiral Media, Lecture Notes in Physics Series 335 (Springer-Verlag, 1989).

G. Keiser, Optical Fiber Communications (McGraw-Hill, 2000).

D. Goldstein, “The Stokes polarization parameters,” in Polarized Light (Dekker, 2003).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of a chiral fiber.

Fig. 2
Fig. 2

Dispersion curves for the first three pairs of guided modes of n = 1 and n = 1 in a fiber with a chiral core.

Fig. 3
Fig. 3

S 3 distribution (in the area r < 2 a ) of the modes M ± 11 , M ± 12 , and M ± 13 at k a = 60 .

Fig. 4
Fig. 4

S 3 distribution (in the area r < 4 a ) of the fundamental modes M ± 11 at k a = 10 .

Fig. 5
Fig. 5

Dispersion curves for the first three pairs of guided modes of n = 1 and n = 1 in a fiber with chiral cladding.

Tables (1)

Tables Icon

Table 1 Various Constitutive Relations and Corresponding Expressions of η, τ, and υ

Equations (28)

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

× E = τ E + υ ( i η H ) ,
× ( i η H ) = τ ( i η H ) + υ E ,
× F + = k + F + ,
× F = k F ,
F ± = f ± ( r ) e i n φ e i ( β ± z ω t ) ,
1 r d d r ( r d f ± z d r ) + ( k ± 2 β ± 2 n 2 r 2 ) f ± z = 0 ,
[ f ± r f ± φ ] = 1 k ± 2 β ± 2 [ ± k ± i β ± i β ± ± k ± ] [ i n f ± z / r d f ± z / d r ] .
f ± z = A ± J n ( p ± r ) ( r < a ) ,
f ± z = B ± K n ( q ± r ) ( r > a ) ,
f ± r = i A ± p ± [ ± n k ± 1 J n ( p ± r ) p ± r + β ± J n ( p ± r ) ] ( r < a ) ,
f ± r = i B ± q ± [ ± n k ± 2 K n ( q ± r ) q ± r + β ± K n ( q ± r ) ] ( r > a ) ,
f ± φ = A ± p ± [ n β ± J n ( p ± r ) p ± r ± k ± 1 J n ( p ± r ) ] ( r < a ) ,
f ± φ = B ± q ± [ n β ± K n ( q ± r ) q ± r ± k ± 2 K n ( q ± r ) ] ( r > a ) ,
E ± = ± i η H ± = F ± / 2 .
1 p ± [ n β ± p ± a ± k ± 1 J n ( p ± a ) J n ( p ± a ) ] + 1 q ± [ n β ± q ± a ± k ± 2 K n ( q ± a ) K n ( q ± a ) ] = 0 ,
E = ( F + + F ) / 2 , H = ( F + F ) / 2 i η .
κ P n ( a , p + , β , k + 1 ) + Q n ( a , q , β , k 2 ) P n ( a , p 1 , β , k 1 ) + Q n ( a , q , β , k 2 ) = P n ( a , p + , β , k + 1 ) + Q n ( a , q + , β , k + 2 ) P n ( a , p 1 , β , k 1 ) + Q n ( a , q + , β , k + 2 ) ,
P n ( ρ , σ 1 , σ 2 , σ 3 ) = 1 σ 1 [ n σ 2 σ 1 ρ + σ 3 J n ( σ 1 ρ ) J n ( σ 1 ρ ) ] ,
Q n ( ρ , σ 1 , σ 2 , σ 3 ) = 1 σ 1 [ n σ 2 σ 1 ρ + σ 3 K n ( σ 1 ρ ) K n ( σ 1 ρ ) ] .
2 k ± 1 k ± 2 p ± a J n ( p ± a ) J n ( p ± a ) + | n | ( k ± 1 2 + k ± 2 2 ) ( p ± a ) 2 k ± 2 2 | n | 1 = 0 ,
κ P n ( a , p + , k + 2 , k + 1 ) + Q n ( a , q , k + 2 , k 2 ) P n ( a , p , k + 2 , k 1 ) + Q n ( a , q , k + 2 , k 2 ) = P n ( a , p + , k + 2 , k + 1 ) + n 2 k + 2 a 1 2 k + 2 a n 1 P n ( a , p 1 , k + 2 , k 1 ) + n 2 k + 2 a 1 2 k + 2 a n 1 ( n > 1 ) ,
κ P n ( a , p + , k + 2 , k + 1 ) + Q n ( a , q , k + 2 , k 2 ) P n ( a , p , k + 2 , k 1 ) + Q n ( a , q , k + 2 , k 2 ) = 1 ( n < 1 ) ,
κ P n ( a , p , k 2 , k 1 ) + Q n ( a , q + , k 2 , k + 2 ) P n ( a , p + , k 2 , k + 1 ) + Q n ( a , q + , k 2 , k + 2 ) = 1 ( n > 1 ) ,
κ P n ( a , p , k 2 , k 1 ) + Q n ( a , q + , k 2 , k + 2 ) P n ( a , p + , k 2 , k + 1 ) + Q n ( a , q + , k 2 , k + 2 ) = P n ( a , p , k 2 , k 1 ) + n 2 k 2 a 1 2 k 2 a n + 1 P n ( a , p + , k 2 , k + 1 ) + n 2 k 2 a 1 2 k 2 a n + 1 ( n < 1 ) ,
( 1 κ ) k 2 2 n ± 1 + κ P n ( a , p ± , k ± 1 2 + k 2 2 , ± 2 k ± 1 k 2 ) P n ( a , p a , k 1 2 + k 2 2 , 2 k 1 k 2 ) = 0 ,
F ± = A ± [ β ± p ± J n 1 ( p ± r ) e i ( n 1 ) φ ( ± i x ^ y ^ ) + J n ( p ± r ) e i n φ z ^ ] e i ( β ± z ω t ) ( r < a ) ,
F ± = B ± [ β ± q ± K n 1 ( q ± r ) e i ( n 1 ) φ ( i x ^ y ^ ) + K n ( q ± r ) e i n φ z ^ ] e i ( β ± z ω t ) ( r > a ) ,
S 3 ( x , y ) = i ( E x E y * E x * E y ) / ( E x E x * + E y * E y ) | ( x , y ) .

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