Abstract

In this paper, the phase effects of secondary reflections in reflective liquid-crystal cells are explored. The existence of such secondary reflections are analytically predicted and experimentally verified. The wavelength dependence of the phenomena is used to explore the magnitude of the effect. Changes of the net retardation due to these secondary reflections are measured to be +/- 3%. Numerical modeling verifies that the root cause of these changes is secondary reflections, and that as much as 10% change can be obtained for different liquid-crystal cell thicknesses and material compositions. The deleterious effects of these secondary reflections are explored from a device performance perspective, and found to be most harmful for incident light with a broad spectral bandwidth.

© 2003 Optical Society of America

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References

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    [CrossRef]
  2. G. D. Love, "Liquid crystal adaptive optics," pp. 4013-4023 in Adaptive Optics Engineering Handbook (New York: Marcel Dekker, 2000).
  3. S. Krueger, G.K. Wernicke, H. Gruber, N. Demoli, M. Duerr, and S. Teiwes, �??New challenges for spatial light modulators: laser beam splitting and beam shaping, and reconstruction of digital holograms,�?? Proc. SPIE 4291, 132-140 (2001).
    [CrossRef]
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    [CrossRef]
  6. J.A. Davis, P.Tsai, D.M. Cottrell, T. Sonehara, and J. Amako, �??Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,�?? Opt. Eng. 38, 1051-1057 (1999).
    [CrossRef]
  7. P. Yeh and C. Gu, Optics of Liquid Crystal Displays, (New York: John Wiley & Sons, 1999)
  8. See, for example, Y.A. Nastishin, R.D. Polak, S.V. Shiyanovshi, V.H. Bodnar, and O.D. Lavrentovich, �??Nematic polar anchoring strength measured by electric field techniques,�?? J. Appl. Phys. 86, 4199-4213 (1999), and references within.
    [CrossRef]
  9. See, for example, Chapter 4 of Reference 7, or Chapter 8 of Reference 10.
  10. E. Hecht, Optics, 3rd ed., (Reading, Massachusetts: Addison-Wesley, 1998).
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  12. X. M. Zhao and J.-C. Diels, �??Ultrashort Laser Sources,�?? pp. 14.1-14.29 in Handbook of Optics, vol. 1, 2nd ed., M. Bass, Ed. (New York: McGraw-Hill, 1995).

Appl. Opt.

J. Appl. Phys.

See, for example, Y.A. Nastishin, R.D. Polak, S.V. Shiyanovshi, V.H. Bodnar, and O.D. Lavrentovich, �??Nematic polar anchoring strength measured by electric field techniques,�?? J. Appl. Phys. 86, 4199-4213 (1999), and references within.
[CrossRef]

J. Lightwave Technol.

Opt. Eng.

J.A. Davis, P.Tsai, D.M. Cottrell, T. Sonehara, and J. Amako, �??Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,�?? Opt. Eng. 38, 1051-1057 (1999).
[CrossRef]

Other

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

See, for example, Chapter 4 of Reference 7, or Chapter 8 of Reference 10.

E. Hecht, Optics, 3rd ed., (Reading, Massachusetts: Addison-Wesley, 1998).

M.V. Klein and T. E. Furtak, Optics, 2nd ed, (New York: John Wiley & Sons, 1986) Chapter 5

X. M. Zhao and J.-C. Diels, �??Ultrashort Laser Sources,�?? pp. 14.1-14.29 in Handbook of Optics, vol. 1, 2nd ed., M. Bass, Ed. (New York: McGraw-Hill, 1995).

B.E.A. Saleh and M.C. Teich Fundamentals of Photonics, (New York: John Wiley & Sons, 1991) Chapter 18.
[CrossRef]

G. D. Love, "Liquid crystal adaptive optics," pp. 4013-4023 in Adaptive Optics Engineering Handbook (New York: Marcel Dekker, 2000).

S. Krueger, G.K. Wernicke, H. Gruber, N. Demoli, M. Duerr, and S. Teiwes, �??New challenges for spatial light modulators: laser beam splitting and beam shaping, and reconstruction of digital holograms,�?? Proc. SPIE 4291, 132-140 (2001).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

Depiction of various fields present in a medium (light blue) surrounded by weakly-reflecting interfaces (dark blue). The red arrows denote the various beams transmitting and reflecting through the structure.

Fig. 2.
Fig. 2.

(a) Material layers and interface reflection coefficients for liquid crystal cell used in experiments. (b) Experimental arrangement used for measuring properties of liquid-crystal cell

Fig. 3.
Fig. 3.

Extinction voltage as a function of incident wavelength for liquid-crystal cell in SLM geometry.

Fig. 4.
Fig. 4.

Normalized retardation residuals of liquid-crystal cell as a function of voltage for various wavelengths.

Fig. 5.
Fig. 5.

Calculated values of the normalized retardation residuals of liquid-crystal cell as a function of voltage for various wavelengths.

Fig. 6.
Fig. 6.

Actual vs. expected attenuation of liquid-crystal cell in SLM geometry calculated for various levels of normalized retardation residuals (NRR).

Equations (8)

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E R o = E 1 o + E 2 o = E 0 o t 1 2 r 2 exp ( i ϕ o ) [ 1 + r 1 r 2 exp ( i ϕ o ) ] ,
E R o = E 1 o [ 1 + 2 R 1 R 2 cos ( ϕ o + ϕ r ) + R 1 R 2 ] 1 2 exp ( i Δ ϕ o ) ,
Δ ϕ o = arctan [ R 1 R 2 sin ( ϕ o + ϕ r ) 1 + R 1 R 2 cos ( ϕ o + ϕ r ) ] .
Δ ϕ o = R 1 R 2 sin ( ϕ o + ϕ r ) .
ρ 2 = R 1 R 2 2 π [ sin ( ϕ ' o ) sin ( ϕ ' o + Δ ϕ ) ] ,
ρ 2 = 1 2 π T 1 R 1 R 2 [ sin ( ϕ o " ) sin ( ϕ o " + Δ ϕ ) ] ,
Δ ρ ¯ ( λ , V ) = ρ ( λ , V ) ρ ( λ , V ) λ ρ ( λ , V ) λ ,
P out = P in cos 2 ( ϕ 2 ) + ε 2 sin 2 ( ϕ 2 )

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