Abstract

This paper investigates light wave propagation in partially ordered birefringent optical media, with focusing on the influence of the degree of molecular ordering on the propagating modes. The double refraction at isotropic/partially ordered interface is also studied, where the impact of the order parameter on the ordinary and extraordinary refracted waves is discussed. This paper also demonstrates the importance of involving the order parameter in studying the total internal reflection (TIR).

©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. C-Y Liu and L-W Chen, “Tunable photonic-crystal waveguide MachZehnder interferometer achieved by nematic liquid-crystal phase modulation,” Optics Express 122616–2624 (2004).
    [Crossref] [PubMed]
  3. S. A. Alboon and R. G. Lindquist, “Flat top liquid crystal tunable filter using coupled Fabry-Perot cavities,” Optics Express 16231–236 (2008).
    [Crossref] [PubMed]
  4. A. Yariv and P. Yeh, Optical Waves in Crystals, Propagation and Control of Laser Radiation (Wiley and Sons, New York, 2003).
  5. P. Yeh and C. Gu, Optics of Liquid Crystal Displays, (Wiley and Sons, New York, 1999).
  6. I.-C. Khoo, Liquid Crystals (Wiley and Sons, New York, 2007).
  7. V. N. Tsvetkov, Acta Physicochim. USSR 16, 132 (1942)
  8. A. S. Abu-Abed and R. G. Lindquist, “Capacitive transduction for liquid crystal based sensors, part II: partially disordered systems,” IEEE Sens. J. 81557–1564, Sep. (2008).
    [Crossref]

2008 (2)

S. A. Alboon and R. G. Lindquist, “Flat top liquid crystal tunable filter using coupled Fabry-Perot cavities,” Optics Express 16231–236 (2008).
[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. 81557–1564, Sep. (2008).
[Crossref]

2007 (1)

I.-C. Khoo, Liquid Crystals (Wiley and Sons, New York, 2007).

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]

2004 (1)

C-Y Liu and L-W Chen, “Tunable photonic-crystal waveguide MachZehnder interferometer achieved by nematic liquid-crystal phase modulation,” Optics Express 122616–2624 (2004).
[Crossref] [PubMed]

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 and R. G. Lindquist, “Capacitive transduction for liquid crystal based sensors, part II: partially disordered systems,” IEEE Sens. J. 81557–1564, Sep. (2008).
[Crossref]

Alboon, S. A.

S. A. Alboon and R. G. Lindquist, “Flat top liquid crystal tunable filter using coupled Fabry-Perot cavities,” Optics Express 16231–236 (2008).
[Crossref] [PubMed]

Chen, L-W

C-Y Liu and L-W Chen, “Tunable photonic-crystal waveguide MachZehnder interferometer achieved by nematic liquid-crystal phase modulation,” Optics Express 122616–2624 (2004).
[Crossref] [PubMed]

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]

Gu, C.

P. Yeh and C. Gu, Optics of Liquid Crystal Displays, (Wiley and Sons, New York, 1999).

Khoo, I.-C.

I.-C. Khoo, Liquid Crystals (Wiley and Sons, New York, 2007).

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. 81557–1564, Sep. (2008).
[Crossref]

S. A. Alboon and R. G. Lindquist, “Flat top liquid crystal tunable filter using coupled Fabry-Perot cavities,” Optics Express 16231–236 (2008).
[Crossref] [PubMed]

Liu, C-Y

C-Y Liu and L-W Chen, “Tunable photonic-crystal waveguide MachZehnder interferometer achieved by nematic liquid-crystal phase modulation,” Optics Express 122616–2624 (2004).
[Crossref] [PubMed]

Tsvetkov, V. N.

V. N. Tsvetkov, Acta Physicochim. USSR 16, 132 (1942)

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals, Propagation and Control of Laser Radiation (Wiley and Sons, New York, 2003).

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals, Propagation and Control of Laser Radiation (Wiley and Sons, New York, 2003).

P. Yeh and C. Gu, Optics of Liquid Crystal Displays, (Wiley and Sons, New York, 1999).

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. 81557–1564, Sep. (2008).
[Crossref]

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]

Optics Express (2)

C-Y Liu and L-W Chen, “Tunable photonic-crystal waveguide MachZehnder interferometer achieved by nematic liquid-crystal phase modulation,” Optics Express 122616–2624 (2004).
[Crossref] [PubMed]

S. A. Alboon and R. G. Lindquist, “Flat top liquid crystal tunable filter using coupled Fabry-Perot cavities,” Optics Express 16231–236 (2008).
[Crossref] [PubMed]

Other (4)

A. Yariv and P. Yeh, Optical Waves in Crystals, Propagation and Control of Laser Radiation (Wiley and Sons, New York, 2003).

P. Yeh and C. Gu, Optics of Liquid Crystal Displays, (Wiley and Sons, New York, 1999).

I.-C. Khoo, Liquid Crystals (Wiley and Sons, New York, 2007).

V. N. Tsvetkov, Acta Physicochim. USSR 16, 132 (1942)

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Figures (3)

Fig. 1.
Fig. 1. The director axis, n, and the propagation wave vector, k⃗, in the lab frame axes, xyz.
Fig. 2.
Fig. 2. Index ellipsoid for a positive uniaxial partially ordered material at different ordering degrees. â1, â2, and â3 are the director principal axes. Ellipsoids intersect with â3 at ne , nes and nis represent cases for well ordered (S = 1), partially ordered, (0 < S < 1), and disordered (S = 0) phases, respectively
Fig. 3.
Fig. 3. Schematic of the experimental arrangement

Equations (13)

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[ ε 0 0 0 ε 0 0 0 ε ] = [ n o 2 0 0 0 n o 2 0 0 0 n e 2 ]
n = sin θ cos ϕ x ̂ + sin θ sin ϕ y ̂ + cos θ z ̂
S = 0.5 < 3 ( m · n ) 2 1 >
ε ̄ = [ ε ̄ xx ε ̄ xy ε ̄ xz ε ̄ yx ε ̄ yy ε ̄ yz ε ̄ zx ε ̄ zy ε ̄ zz ] = 2 ε + ε 3 I + Δ ε Q
Q = S [ sin 2 cos 2 ϕ 1 3 sin 2 θ sin ϕ cos ϕ sin θ cos θ cos ϕ sin 2 θ sin ϕ cos ϕ sin 2 θ sin 2 ϕ 1 3 sin θ cos θ sin ϕ sin θ cos θ cos ϕ sin θ cos θ sin ϕ cos 2 θ 1 3 ]
k × ( k × E ) + ω 2 μ o ε o ε E = 0
k = k ( sin θ k cos θ k x ̂ + sin θ k sin θ k y ̂ + cos θ k z ̂ )
[ ε ̄ xx n 2 ( 1 sin θ k 2 cos ϕ k 2 ) ε ̄ xy + n 2 sin θ k 2 cos ϕ k sin ϕ k ε ̄ xz + n 2 sin θ k cos θ k sin ϕ k ε ̄ xy + n 2 sin θ k 2 cos ϕ k sin ϕ k ε ̄ yy n 2 ( 1 sin 2 θ k sin 2 ϕ k ) ε ̄ yz + n 2 cos θ k sin θ k sin ϕ k ε ̄ xz + n 2 sin θ k cos θ k cos ϕ k ε ̄ yz + n 2 cos θ k sin θ k sin ϕ k ε ̄ zz n 2 sin 2 θ k ] [ E x E y E z ] = 0
n 1 = [ 2 n o 2 + n e 2 3 S 2 n ̄ Δ n 3 ] 1 / 2 , and n 2 = n os n es [ n os 2 + 2 S n ̄ Δ n ( k ̂ · n ) 2 ] 1 / 2
k ̂ · n = cos θ cos θ k + sin θ sin θ k cos ( ϕ ϕ k )
ν es , eff = ν es 2 + ( ν os 2 ν es 2 ) ( k ̂ es · n ) 2
θ co = sin 1 [ 2 n o 2 + n e 2 S 2 n ̄ Δ n 3 n i 2 ] 1 / 2
θ ce = sin 1 [ ε ε ε ̄ zz ε i ( ε ̄ zz sin 2 ϕ k + ε ̄ yy sin 2 ϕ k + ε ̄ xx cos 2 ϕ k ) ( S n ̄ Δ n sin 2 θ cos ( ϕ ϕ k ) ) 2 ] 1 / 2

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