Abstract

We study the applicability of geometrical optics to inhomogeneous dielectric nongyrotropic optically anisotropic media typically found in in-plane liquid-crystal configurations with refractive indices no=1.5 and ne=1.7. To this end, we compare the results of advanced ray- and wave-optics simulations of the propagation of an incident plane wave to a special anisotropic configuration. Based on the results, we conclude that for a good agreement between ray and wave optics, a maximum change in optical properties should occur over a distance of at least 20 wavelengths.

© 2010 Optical Society of America

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References

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  1. Y. A. Kravtsov and Y. I. Orlov, Geometrical Optics of Inhomogeneous Media (Springer-Verlag, 1990).
    [CrossRef]
  2. M. Kline and I. W. Kay, Electromagnetic Theory and Geometrical Optics (John Wiley & Sons, 1965).
  3. T. C. Kraan, T. van Bommel, and R. A. M. Hikmet, J. Opt. Soc. Am. A 24, 3467 (2007).
    [CrossRef]
  4. M. Sluijter, D. K. G. de Boer, and J. J. M. Braat, J. Opt. Soc. Am. A 25, 1260 (2008).
    [CrossRef]
  5. M. Xu, L. Sio, R. Caputo, C. P. Umeton, A. J. H. Wachters, D. K. G. de Boer, and H. P. Urbach, Opt. Express 16, 14532 (2008).
    [CrossRef] [PubMed]

2008 (2)

2007 (1)

Braat, J. J. M.

Caputo, R.

de Boer, D. K. G.

Hikmet, R. A. M.

Kay, I. W.

M. Kline and I. W. Kay, Electromagnetic Theory and Geometrical Optics (John Wiley & Sons, 1965).

Kline, M.

M. Kline and I. W. Kay, Electromagnetic Theory and Geometrical Optics (John Wiley & Sons, 1965).

Kraan, T. C.

Kravtsov, Y. A.

Y. A. Kravtsov and Y. I. Orlov, Geometrical Optics of Inhomogeneous Media (Springer-Verlag, 1990).
[CrossRef]

Orlov, Y. I.

Y. A. Kravtsov and Y. I. Orlov, Geometrical Optics of Inhomogeneous Media (Springer-Verlag, 1990).
[CrossRef]

Sio, L.

Sluijter, M.

Umeton, C. P.

Urbach, H. P.

van Bommel, T.

Wachters, A. J. H.

Xu, M.

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

Opt. Express (1)

Other (2)

Y. A. Kravtsov and Y. I. Orlov, Geometrical Optics of Inhomogeneous Media (Springer-Verlag, 1990).
[CrossRef]

M. Kline and I. W. Kay, Electromagnetic Theory and Geometrical Optics (John Wiley & Sons, 1965).

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Figures (6)

Fig. 1
Fig. 1

Rotation of the director by 90° over a distance L. Hence L is the distance over which a maximum change in optical properties occurs.

Fig. 2
Fig. 2

Periodic director profile (indicated by the bars) for x [ T , 2 T ] with the ray paths of extraordinary light rays indicated by the curved lines. The light rays are at normal incidence with the plane z = 0 .

Fig. 3
Fig. 3

Spatial intensity distributions according to the finite-element-method (FEM) simulations and the ray-tracing simulations (GOA) for T = 5 λ . This corresponds to a computational domain of 2.5 × 2.5 μ m , assuming λ = 500 nm .

Fig. 4
Fig. 4

Spatial intensity distributions for T = 20 λ . Then a period of the director profile corresponds to a computational domain of 10 × 10 μ m .

Fig. 5
Fig. 5

Spatial intensity distributions for T = 40 λ . Now the computational domain of the FEM is 20 × 20 μ m .

Fig. 6
Fig. 6

Spatial intensity distributions for T = 60 λ . The computational domain of the FEM has reached a maximum of 30 × 30 μ m owing to memory constraints.

Tables (1)

Tables Icon

Table 1 Values for T, L and Ratio λ L Used in the Simulations

Equations (5)

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d ̂ ( x , z ) = cos θ ( x , z ) x ̂ + sin θ ( x , z ) z ̂ ,
θ ( x , z ) = π 4 [ 1 cos ( 2 π x T ) ] sin ( π z D ) ,
ϵ ( x , z ) = ( n e 2 cos 2 θ ( x , z ) + n o 2 sin 2 θ ( x , z ) 0 Δ ϵ cos θ ( x , z ) sin θ ( x , z ) 0 n o 2 0 Δ ϵ cos θ ( x , z ) sin θ ( x , z ) 0 n e 2 sin 2 θ ( x , z ) + n o 2 cos 2 θ ( x , z ) ) ,
T e = S z t S z inc ,
I FEM ( x ) = S z t S z inc .

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