Abstract

This paper investigates a new approach for tracking nematic uniaxial liquid crystal (LC) profile in partially ordered LC based sensors. This approach utilizes measuring critical angles for total internal reflection (TIR) at the interface of optically isotropic and partially ordered LC film. The proposed optical transduction requires measuring of the ordinary critical angle and two extraordinary critical angles in orthogonal directions to report the LC degree of ordering and the director axis orientation.

© 2009 Optical Society of America

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References

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  1. B. H. Clare and N. L. Abbott, "Orientations of nematic liquid crystals on surfaces presenting controlled densities of peptides: amplification of protein-peptide binding events," Langmuir 21, 6451-6461 (2005).
    [CrossRef] [PubMed]
  2. H. Zhang, P. Guo, P. Chen, S. Chang, and J. Yuan, "Liquid-crystal-filled photonic crystal for terahertz switch and filter," J. Opt. Soc. Am. B 26, 101-106 (2009).
    [CrossRef]
  3. T. Woliński, A. Czapla, S. Ertman, M. Tefelska, A. Domański, J. Wójcik, E. Kruszelnicki, and R. Dabrowski, "Photonic liquid crystal fibers for sensing applications," IEEE Trans. Instrum. Meas. 57, 1796-1802 (2008).
    [CrossRef]
  4. S. Sridharamurthy, K. Cadwell, N. Abbott, and H. Jiang, "A Liquid crystal based gas sensor using microfabricated pillar arrays as a support structure," Proc. IEEE Sensors Conference, 1044-1047 (2007).
  5. A. S. Abu-Abed and R. G. Lindquist, "Capacitive transduction for liquid crystal based sensors, part II: partially disordered systems," IEEE Sens. J. 8, 1557-15642008).
    [CrossRef]
  6. F. Yang and J. R. Sambles, "Critical angles for reflectivity at an isotropic-anisotropic boundary," J. Mod. Opt. 40, 1131-1142 (1993).
    [CrossRef]
  7. A. S. Abu-Abed, "Optical waves in partially ordered anisotropic media," Opt. Express 17, 1646-1651 (2009).
    [CrossRef] [PubMed]

2009 (2)

2008 (2)

T. Woliński, A. Czapla, S. Ertman, M. Tefelska, A. Domański, J. Wójcik, E. Kruszelnicki, and R. Dabrowski, "Photonic liquid crystal fibers for sensing applications," IEEE Trans. Instrum. Meas. 57, 1796-1802 (2008).
[CrossRef]

A. S. Abu-Abed and R. G. Lindquist, "Capacitive transduction for liquid crystal based sensors, part II: partially disordered systems," IEEE Sens. J. 8, 1557-15642008).
[CrossRef]

2005 (1)

B. H. Clare and N. L. Abbott, "Orientations of nematic liquid crystals on surfaces presenting controlled densities of peptides: amplification of protein-peptide binding events," Langmuir 21, 6451-6461 (2005).
[CrossRef] [PubMed]

1993 (1)

F. Yang and J. R. Sambles, "Critical angles for reflectivity at an isotropic-anisotropic boundary," J. Mod. Opt. 40, 1131-1142 (1993).
[CrossRef]

Abbott, N. L.

B. H. Clare and N. L. Abbott, "Orientations of nematic liquid crystals on surfaces presenting controlled densities of peptides: amplification of protein-peptide binding events," Langmuir 21, 6451-6461 (2005).
[CrossRef] [PubMed]

Abu-Abed, A. S.

A. S. Abu-Abed, "Optical waves in partially ordered anisotropic media," Opt. Express 17, 1646-1651 (2009).
[CrossRef] [PubMed]

A. S. Abu-Abed and R. G. Lindquist, "Capacitive transduction for liquid crystal based sensors, part II: partially disordered systems," IEEE Sens. J. 8, 1557-15642008).
[CrossRef]

Chang, S.

Chen, P.

Clare, B. H.

B. H. Clare and N. L. Abbott, "Orientations of nematic liquid crystals on surfaces presenting controlled densities of peptides: amplification of protein-peptide binding events," Langmuir 21, 6451-6461 (2005).
[CrossRef] [PubMed]

Czapla, A.

T. Woliński, A. Czapla, S. Ertman, M. Tefelska, A. Domański, J. Wójcik, E. Kruszelnicki, and R. Dabrowski, "Photonic liquid crystal fibers for sensing applications," IEEE Trans. Instrum. Meas. 57, 1796-1802 (2008).
[CrossRef]

Dabrowski, R.

T. Woliński, A. Czapla, S. Ertman, M. Tefelska, A. Domański, J. Wójcik, E. Kruszelnicki, and R. Dabrowski, "Photonic liquid crystal fibers for sensing applications," IEEE Trans. Instrum. Meas. 57, 1796-1802 (2008).
[CrossRef]

Domanski, A.

T. Woliński, A. Czapla, S. Ertman, M. Tefelska, A. Domański, J. Wójcik, E. Kruszelnicki, and R. Dabrowski, "Photonic liquid crystal fibers for sensing applications," IEEE Trans. Instrum. Meas. 57, 1796-1802 (2008).
[CrossRef]

Ertman, S.

T. Woliński, A. Czapla, S. Ertman, M. Tefelska, A. Domański, J. Wójcik, E. Kruszelnicki, and R. Dabrowski, "Photonic liquid crystal fibers for sensing applications," IEEE Trans. Instrum. Meas. 57, 1796-1802 (2008).
[CrossRef]

Guo, P.

Kruszelnicki, E.

T. Woliński, A. Czapla, S. Ertman, M. Tefelska, A. Domański, J. Wójcik, E. Kruszelnicki, and R. Dabrowski, "Photonic liquid crystal fibers for sensing applications," IEEE Trans. Instrum. Meas. 57, 1796-1802 (2008).
[CrossRef]

Lindquist, R. G.

A. S. Abu-Abed and R. G. Lindquist, "Capacitive transduction for liquid crystal based sensors, part II: partially disordered systems," IEEE Sens. J. 8, 1557-15642008).
[CrossRef]

Sambles, J. R.

F. Yang and J. R. Sambles, "Critical angles for reflectivity at an isotropic-anisotropic boundary," J. Mod. Opt. 40, 1131-1142 (1993).
[CrossRef]

Tefelska, M.

T. Woliński, A. Czapla, S. Ertman, M. Tefelska, A. Domański, J. Wójcik, E. Kruszelnicki, and R. Dabrowski, "Photonic liquid crystal fibers for sensing applications," IEEE Trans. Instrum. Meas. 57, 1796-1802 (2008).
[CrossRef]

Wójcik, J.

T. Woliński, A. Czapla, S. Ertman, M. Tefelska, A. Domański, J. Wójcik, E. Kruszelnicki, and R. Dabrowski, "Photonic liquid crystal fibers for sensing applications," IEEE Trans. Instrum. Meas. 57, 1796-1802 (2008).
[CrossRef]

Wolinski, T.

T. Woliński, A. Czapla, S. Ertman, M. Tefelska, A. Domański, J. Wójcik, E. Kruszelnicki, and R. Dabrowski, "Photonic liquid crystal fibers for sensing applications," IEEE Trans. Instrum. Meas. 57, 1796-1802 (2008).
[CrossRef]

Yang, F.

F. Yang and J. R. Sambles, "Critical angles for reflectivity at an isotropic-anisotropic boundary," J. Mod. Opt. 40, 1131-1142 (1993).
[CrossRef]

Yuan, J.

Zhang, H.

IEEE Sens. J. (1)

A. S. Abu-Abed and R. G. Lindquist, "Capacitive transduction for liquid crystal based sensors, part II: partially disordered systems," IEEE Sens. J. 8, 1557-15642008).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

T. Woliński, A. Czapla, S. Ertman, M. Tefelska, A. Domański, J. Wójcik, E. Kruszelnicki, and R. Dabrowski, "Photonic liquid crystal fibers for sensing applications," IEEE Trans. Instrum. Meas. 57, 1796-1802 (2008).
[CrossRef]

J. Mod. Opt. (1)

F. Yang and J. R. Sambles, "Critical angles for reflectivity at an isotropic-anisotropic boundary," J. Mod. Opt. 40, 1131-1142 (1993).
[CrossRef]

J. Opt. Soc. Am. B (1)

Langmuir (1)

B. H. Clare and N. L. Abbott, "Orientations of nematic liquid crystals on surfaces presenting controlled densities of peptides: amplification of protein-peptide binding events," Langmuir 21, 6451-6461 (2005).
[CrossRef] [PubMed]

Opt. Express (1)

Other (1)

S. Sridharamurthy, K. Cadwell, N. Abbott, and H. Jiang, "A Liquid crystal based gas sensor using microfabricated pillar arrays as a support structure," Proc. IEEE Sensors Conference, 1044-1047 (2007).

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Figures (4)

Fig. 1.
Fig. 1.

The director axis, n, and the propagation wave vector, k⃗, in the lab frame axes, xyz.

Fig. 2.
Fig. 2.

Schematic of the LC sensor experimental arrangement, (a) Side view (b) Top view

Fig. 3.
Fig. 3.

(a) The incident and extraordinary refracted wave vectors in orthogonal planes and (b) the transmitted power diagram, assuming θ ce1<θ ce2.

Fig. 4.
Fig. 4.

The extraordinary critical angles sensitivity versus ϕ when θ=π/2, at different ordering degrees, and Δθco and Δθce versus the prism refractive index, ni .

Equations (15)

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n = sin θ cos ϕ x ̂ + sin θ sin ϕ y ̂ + cos θ z ̂
n os = [ 2 n o 2 + n e 2 3 S 2 n ̄ Δ n 3 ] 1 2 , n es = [ 2 n o 2 + n e 2 3 + S 4 n ̄ Δ n 3 ] 1 2
k = k ( sin θ k cos ϕ k x ̂ + sin θ k sin ϕ k y ̂ + cos θ k z ̂ )
n es , eff = [ n os 2 n es 2 n os 2 + 2 S n ̄ Δ n ( k ̂ n ) 2 ] 1 2
n ̄ xx 2 = n is 2 + S 2 n ̄ Δ n ( sin 2 θ cos 2 ϕ 1 3 ) n ̄ xy 2 = n ̄ yx 2 = S 2 n ̄ Δ n sin 2 θ sin ϕ cos ϕ
n ̄ yy 2 = n is 2 + S 2 n ̄ Δ n ( sin 2 θ sin 2 ϕ 1 3 ) n ̄ yz 2 = n ̄ zy 2 = S 2 n ̄ Δ n sin θ cos θ sin ϕ
n ̄ zz 2 = n is 2 + S 2 n ̄ Δ n ( cos 2 θ 1 3 ) n ̄ xz 2 = n ̄ zx 2 = S 2 n ̄ Δ n sin θ cos θ cos ϕ
n i sin θ i = n os sin θ o
θ co = sin 1 [ 2 n o 2 + n e 2 S 2 n ̄ Δ n 3 n i 2 ] 1 2
S = 3 n is 2 3 n i 2 s in 2 θ co 2 n ̄ Δ n
n i sin θ i = n es , eff sin θ e
θ e = tan 1 [ n ̄ zz 2 Γ + csc 2 θ i n os 2 n es 2 n ̄ zz 2 n i 2 n ̄ zz 2 ( n ̄ xy 2 sin 2 ϕ k + n ̄ yy 2 sin 2 ϕ k + n ̄ xx 2 cos 2 ϕ k ) + Γ 2 ]
θ ce = sin 1 [ n os 2 n es 2 n ̄ zz 2 n i 2 [ n ̄ zz 2 ( n ̄ xy 2 sin 2 ϕ k + n ̄ yy 2 sin 2 ϕ k + n ̄ xx 2 cos 2 ϕ k ) m Γ 2 ] ] 1 2
θ e l , max ( ϕ k = π ) = tan 1 ( n ̄ zz 2 n ̄ xz 2 ) and θ e 2 , max ( ϕ k = 3 π 2 ) = tan 1 ( n ̄ zz 2 n ̄ yz 2 )
θ ce 1 = sin 1 n es n ̄ zz n i ( n ̄ zz 2 + n ̄ xx 2 n os 2 ) 1 2 and θ ce 2 = sin 1 n es n ̄ zz n i ( n ̄ zz 2 + n ̄ yy 2 n os 2 ) 1 2

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