Abstract

Microstructured fibres which consist of a circular step index core and a liquid crystal inclusion running parallel to this core are investigated. The attenuation and electro-optic effects of light coupled into the core are measured. Coupled mode theory is used to study the interaction of core modes with the liquid crystal inclusion. The experimental and theoretical results show that these fibres can exhibit attenuation below 0.16 dB cm−1 in off-resonant wavelength regions and still have significant electro-optic effects which can lead to a polarisation extinction of 6 dB cm−1.

© 2014 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. T. A. Birks, G. J. Pearce, D. M. Bird, “Approximate band structure calculation for photonic band gap fibres,” Opt. Express 14(20), 9483–9490 (2006).
    [CrossRef] [PubMed]
  5. D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. d’Alessandro, R. Beccherelli, “Guided-wave liquid-crystal photonics,” Lab Chip 12(19), 3598–3610 (2012).
    [CrossRef] [PubMed]
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  7. A. Lorenz, R. Schuhmann, H. S. Kitzerow, “Infiltrated photonic crystal fiber: experiments and liquid crystal scattering model,” Opt. Express 18(4), 3519–3530 (2010).
    [CrossRef] [PubMed]
  8. S. Ertman, T. R. Woliński, D. Pysz, R. Buczynski, E. Nowinowski-Kruszelnicki, R. Dabrowski, “Low-loss propagation and continuously tunable birefringence in high-index photonic crystal fibers filled with nematic liquid crystals,” Opt. Express 17(21), 19298–19310 (2009).
    [CrossRef] [PubMed]
  9. H.-S. Kitzerow, “Photonic micro-and nanostructures, metamaterials,” in Handbook of Liquid Crystals, J. W. Goodby, P. J. Collings, T. Kato, C. Tschierske, H. Gleeson, and P. Raynes, eds. (Wiley-VCH, 2014), Chap. 7.
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    [CrossRef]
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    [CrossRef]
  14. A. Hardy, W. Streifer, “Coupled mode solutions of multiwaveguide systems,” IEEE J. Quantum Electron. 22(4), 528–534 (1986).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  20. L. Scolari, T. Alkeskjold, J. Riishede, A. Bjarklev, D. Hermann, A. Anawati, M. Nielsen, P. Bassi, “Continuously tunable devices based on electrical control of dual-frequency liquid crystal filled photonic bandgap fibers,” Opt. Express 13(19), 7483–7496 (2005).
    [CrossRef] [PubMed]
  21. E. Jakeman, E. Raynes, “Electro-optic response times in liquid crystals,” Phys. Lett. A 39(1), 69–70 (1972).
    [CrossRef]
  22. S.-M. Kuo, Y.-W. Huang, S.-M. Yeh, W.-H. Cheng, C.-H. Lin, “Liquid crystal modified photonic crystal fiber (LC-PCF) fabricated with an un-cured SU-8 photoresist sealing technique for electrical flux measurement,” Opt. Express 19(19), 18372–18379 (2011).
    [CrossRef] [PubMed]

2012 (1)

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. d’Alessandro, R. Beccherelli, “Guided-wave liquid-crystal photonics,” Lab Chip 12(19), 3598–3610 (2012).
[CrossRef] [PubMed]

2011 (2)

2010 (2)

2009 (1)

2006 (2)

2005 (1)

2003 (1)

2002 (1)

O. Butov, K. Golant, A. Tomashuk, M. van Stralen, A. Breuls, “Refractive index dispersion of doped silica for fiber optics,” Opt. Commun. 213(4-6), 301–308 (2002).
[CrossRef]

2001 (1)

1987 (2)

S.-L. Chuang, “A coupled mode formulation by reciprocity and a variational principle,” J. Lightwave Technol. 5(1), 5–15 (1987).
[CrossRef]

S.-L. Chuang, “A coupled-mode theory for multiwaveguide systems satisfying the reciprocity theorem and power conservation,” J. Lightwave Technol. 5(1), 174–183 (1987).
[CrossRef]

1986 (2)

A. Hardy, W. Streifer, “Coupled modes of multiwaveguide systems and phased arrays,” J. Lightwave Technol. 4(1), 90–99 (1986).
[CrossRef]

A. Hardy, W. Streifer, “Coupled mode solutions of multiwaveguide systems,” IEEE J. Quantum Electron. 22(4), 528–534 (1986).
[CrossRef]

1974 (1)

1972 (1)

E. Jakeman, E. Raynes, “Electro-optic response times in liquid crystals,” Phys. Lett. A 39(1), 69–70 (1972).
[CrossRef]

1965 (1)

Alkeskjold, T.

Anawati, A.

Asquini, R.

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. d’Alessandro, R. Beccherelli, “Guided-wave liquid-crystal photonics,” Lab Chip 12(19), 3598–3610 (2012).
[CrossRef] [PubMed]

Bassi, P.

Beccherelli, R.

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. d’Alessandro, R. Beccherelli, “Guided-wave liquid-crystal photonics,” Lab Chip 12(19), 3598–3610 (2012).
[CrossRef] [PubMed]

Bird, D.

Bird, D. M.

Birks, T.

Birks, T. A.

Bjarklev, A.

Breuls, A.

O. Butov, K. Golant, A. Tomashuk, M. van Stralen, A. Breuls, “Refractive index dispersion of doped silica for fiber optics,” Opt. Commun. 213(4-6), 301–308 (2002).
[CrossRef]

Brown, T. G.

Buczynski, R.

Butov, O.

O. Butov, K. Golant, A. Tomashuk, M. van Stralen, A. Breuls, “Refractive index dispersion of doped silica for fiber optics,” Opt. Commun. 213(4-6), 301–308 (2002).
[CrossRef]

Cheng, W.-H.

Chuang, S.-L.

S.-L. Chuang, “A coupled-mode theory for multiwaveguide systems satisfying the reciprocity theorem and power conservation,” J. Lightwave Technol. 5(1), 174–183 (1987).
[CrossRef]

S.-L. Chuang, “A coupled mode formulation by reciprocity and a variational principle,” J. Lightwave Technol. 5(1), 5–15 (1987).
[CrossRef]

d’Alessandro, A.

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. d’Alessandro, R. Beccherelli, “Guided-wave liquid-crystal photonics,” Lab Chip 12(19), 3598–3610 (2012).
[CrossRef] [PubMed]

Dabrowski, R.

Ertman, S.

Golant, K.

O. Butov, K. Golant, A. Tomashuk, M. van Stralen, A. Breuls, “Refractive index dispersion of doped silica for fiber optics,” Opt. Commun. 213(4-6), 301–308 (2002).
[CrossRef]

Hardy, A.

A. Hardy, W. Streifer, “Coupled modes of multiwaveguide systems and phased arrays,” J. Lightwave Technol. 4(1), 90–99 (1986).
[CrossRef]

A. Hardy, W. Streifer, “Coupled mode solutions of multiwaveguide systems,” IEEE J. Quantum Electron. 22(4), 528–534 (1986).
[CrossRef]

Hedley, T.

Hermann, D.

Hu, C.

Huang, Y.-W.

Jakeman, E.

E. Jakeman, E. Raynes, “Electro-optic response times in liquid crystals,” Phys. Lett. A 39(1), 69–70 (1972).
[CrossRef]

Joly, N. Y.

Kitzerow, H. S.

Knight, J.

Kriezis, E. E.

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. d’Alessandro, R. Beccherelli, “Guided-wave liquid-crystal photonics,” Lab Chip 12(19), 3598–3610 (2012).
[CrossRef] [PubMed]

Kuo, S.-M.

Lee, H. W.

Lin, C.-H.

Lorenz, A.

Malitson, I. H.

Nielsen, M.

Nowinowski-Kruszelnicki, E.

Pearce, G. J.

Pottage, J.

Pysz, D.

Raynes, E.

E. Jakeman, E. Raynes, “Electro-optic response times in liquid crystals,” Phys. Lett. A 39(1), 69–70 (1972).
[CrossRef]

Riishede, J.

Roberts, P.

Russell, P.

Russell, P. S.

Russell, P. St. J.

Scharrer, M.

Schmidt, M. A.

Schuhmann, R.

Scolari, L.

Streifer, W.

A. Hardy, W. Streifer, “Coupled mode solutions of multiwaveguide systems,” IEEE J. Quantum Electron. 22(4), 528–534 (1986).
[CrossRef]

A. Hardy, W. Streifer, “Coupled modes of multiwaveguide systems and phased arrays,” J. Lightwave Technol. 4(1), 90–99 (1986).
[CrossRef]

Tomashuk, A.

O. Butov, K. Golant, A. Tomashuk, M. van Stralen, A. Breuls, “Refractive index dispersion of doped silica for fiber optics,” Opt. Commun. 213(4-6), 301–308 (2002).
[CrossRef]

Tyagi, H.

Uebel, P.

van Stralen, M.

O. Butov, K. Golant, A. Tomashuk, M. van Stralen, A. Breuls, “Refractive index dispersion of doped silica for fiber optics,” Opt. Commun. 213(4-6), 301–308 (2002).
[CrossRef]

Whinnery, J. R.

Wolinski, T. R.

Yeh, S.-M.

Zhu, Z.

Zografopoulos, D. C.

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. d’Alessandro, R. Beccherelli, “Guided-wave liquid-crystal photonics,” Lab Chip 12(19), 3598–3610 (2012).
[CrossRef] [PubMed]

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

A. Hardy, W. Streifer, “Coupled mode solutions of multiwaveguide systems,” IEEE J. Quantum Electron. 22(4), 528–534 (1986).
[CrossRef]

J. Lightwave Technol. (4)

S.-L. Chuang, “A coupled mode formulation by reciprocity and a variational principle,” J. Lightwave Technol. 5(1), 5–15 (1987).
[CrossRef]

S.-L. Chuang, “A coupled-mode theory for multiwaveguide systems satisfying the reciprocity theorem and power conservation,” J. Lightwave Technol. 5(1), 174–183 (1987).
[CrossRef]

A. Hardy, W. Streifer, “Coupled modes of multiwaveguide systems and phased arrays,” J. Lightwave Technol. 4(1), 90–99 (1986).
[CrossRef]

P. St. J. Russell, “Photonic-crystal fibers,” J. Lightwave Technol. 24(12), 4729–4749 (2006).
[CrossRef]

J. Opt. Soc. Am. (2)

Lab Chip (1)

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. d’Alessandro, R. Beccherelli, “Guided-wave liquid-crystal photonics,” Lab Chip 12(19), 3598–3610 (2012).
[CrossRef] [PubMed]

Opt. Commun. (1)

O. Butov, K. Golant, A. Tomashuk, M. van Stralen, A. Breuls, “Refractive index dispersion of doped silica for fiber optics,” Opt. Commun. 213(4-6), 301–308 (2002).
[CrossRef]

Opt. Express (8)

Z. Zhu, T. G. Brown, “Analysis of the space filling modes of photonic crystal fibers,” Opt. Express 8(10), 547–554 (2001).
[CrossRef] [PubMed]

J. Pottage, D. Bird, T. Hedley, J. Knight, T. Birks, P. Russell, P. Roberts, “Robust photonic band gaps for hollow core guidance in PCF made from high index glass,” Opt. Express 11(22), 2854–2861 (2003).
[CrossRef] [PubMed]

L. Scolari, T. Alkeskjold, J. Riishede, A. Bjarklev, D. Hermann, A. Anawati, M. Nielsen, P. Bassi, “Continuously tunable devices based on electrical control of dual-frequency liquid crystal filled photonic bandgap fibers,” Opt. Express 13(19), 7483–7496 (2005).
[CrossRef] [PubMed]

T. A. Birks, G. J. Pearce, D. M. Bird, “Approximate band structure calculation for photonic band gap fibres,” Opt. Express 14(20), 9483–9490 (2006).
[CrossRef] [PubMed]

S. Ertman, T. R. Woliński, D. Pysz, R. Buczynski, E. Nowinowski-Kruszelnicki, R. Dabrowski, “Low-loss propagation and continuously tunable birefringence in high-index photonic crystal fibers filled with nematic liquid crystals,” Opt. Express 17(21), 19298–19310 (2009).
[CrossRef] [PubMed]

A. Lorenz, R. Schuhmann, H. S. Kitzerow, “Infiltrated photonic crystal fiber: experiments and liquid crystal scattering model,” Opt. Express 18(4), 3519–3530 (2010).
[CrossRef] [PubMed]

H. W. Lee, M. A. Schmidt, P. Uebel, H. Tyagi, N. Y. Joly, M. Scharrer, P. S. Russell, “Optofluidic refractive-index sensor in step-index fiber with parallel hollow micro-channel,” Opt. Express 19(9), 8200–8207 (2011).
[CrossRef] [PubMed]

S.-M. Kuo, Y.-W. Huang, S.-M. Yeh, W.-H. Cheng, C.-H. Lin, “Liquid crystal modified photonic crystal fiber (LC-PCF) fabricated with an un-cured SU-8 photoresist sealing technique for electrical flux measurement,” Opt. Express 19(19), 18372–18379 (2011).
[CrossRef] [PubMed]

Phys. Lett. A (1)

E. Jakeman, E. Raynes, “Electro-optic response times in liquid crystals,” Phys. Lett. A 39(1), 69–70 (1972).
[CrossRef]

Other (3)

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon, 1993).

H.-S. Kitzerow, “Photonic micro-and nanostructures, metamaterials,” in Handbook of Liquid Crystals, J. W. Goodby, P. J. Collings, T. Kato, C. Tschierske, H. Gleeson, and P. Raynes, eds. (Wiley-VCH, 2014), Chap. 7.

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

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Figures (9)

Fig. 1
Fig. 1

Schematic cross sections of microstructured fibres: (a) Hollow core PCF, (b) solid core and (c) fibre design discussed in this paper. Λ denotes the pitch in (a) and (b) and the center-center-distance in (c). d incl denotes the inclusion diameter in (a)- (c) and d core the core diameter in (c). (d) Overview of the possible combinations of different types of PCFs and LCs and the resulting guiding principles.

Fig. 2
Fig. 2

(a) Schematics of the setup for measuring the attenuation and the electro-optic properties. (b) Image of the cell for electro-optic measurements. For further explanation see text.

Fig. 3
Fig. 3

(a) Experimentally determined attenuation spectrum (red solid line, □) and the predicted attenuation by CMT (black line, ∎) of fibre I filled with MLC2103. The blue lines correspond to the effective refractive indices of core (▼) and inclusion (▲) HE11 modes calculated with FEM. (b) The three patterns show the calculated square of the transverse electric fields of the normal modes labelled in (a) (marked with green dashed lines). The Ge-doped core is on the left and the liquid crystal inclusion on the right side in each image.

Fig. 4
Fig. 4

Plot of the relative power for fibre I filled with MLC2103 for the x- (blue line, □) and the y-polarisation (orange line, ○) with an applied voltage of 500 V at 1 kHz. The inset in the upper left corner shows a schematic of the electrooptic cell with labelled axes and the direction of the applied electric field E.

Fig. 5
Fig. 5

(a) The upper graph shows the effective refractive indices of the HE11 core mode (black) and the inclusion modes HE31 (magenta) and HE21 (green) for fibre I filled with BL036. The attenuation (solid) is plotted in the middle for the y-polarisation and at the bottom for the x-polarisation. The dashed curves in the latter two plots correspond to the attenuation determined by coupled mode theory. (b) The mode intensity patterns of the HE31 and HE21 modes at 500 nm, both are twofold degenerate. The arrows indicate the direction of the transversal electric field.

Fig. 6
Fig. 6

Plot of the relative power for fibre I filled with BL036 for the x- (green, ▲) and the y- polarisation (red, ▼) with an applied voltage of 500 V at 1 kHz. The blue curve (∎) shows the polarisation extinction at 500V.

Fig. 7
Fig. 7

Switching behaviour (left on, right off) at 590 nm with different applied voltages at 1 kHz: 200 V (black), 300 V (red), 400 V (green), 500 V (blue). Switching on/off occurs at t=0 . The experiment has been performed with x-polarized light.

Fig. 8
Fig. 8

Plot of the relative optical power per unit length (green, ▲: y- polarisation, red, ▼: x-polarisation) and the polarisation extinction (blue, ∎) for fibre II filled with E7 (left) and BL036 (right) with an applied voltage of 500 V.

Fig. 9
Fig. 9

Switching behaviour of fibre II filled with E7 (left on, right off) at 1310 nm with different applied voltages at 1 kHz: 200 V (black), 300 V (red), 400 V (green), 500 V (blue). Switching on/off occurs at τ = 0 . The experiment has been performed with y-polarized light.

Tables (2)

Tables Icon

Table 1 Specifications of fibres I to II: Diameters of core d core and inclusion d incl and center-to-center distance of core and inclusion Λ of the fibres investigated in this paper.

Tables Icon

Table 2 Coefficients for Cauchy fit of the refractive indices for the employed liquid crystals.

Equations (6)

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

n i = k B T 8Kλ n e 2 n o 2 n o 2 1 lg(e) ,
Imε=2 n r n i ,
Im β= 2π λ η n i ,
a=10lg( I 0   I s ) 1 s  ,
relative power= 10lg( P V=0V   P V ) 1 L  
extinction= 10lg( I x   I y ) 1 L  

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