Abstract

Reflection at an interface between two materials can be modulated by means of varying the optical properties at the interface. We have studied this modulation of the reflected light with an aim to develop a flashing retroreflector for roadside conspicuity applications. Reflectance modulation has previously been studied under the conditions of total internal reflection (TIR), where a light-absorbing material placed in the associated evanescent wave region can be used to attenuate the intensity of the reflected light. If instead the light rays strike the interface at an angle that is slightly smaller than the critical angle required for TIR, they instead undergo a substantial, but partial, reflection. We have demonstrated that an analogous attenuation effect to the TIR situation is observed, even though there is no evanescent wave present under these circumstances. We have studied this behavior and have developed a model to describe the motion of the absorbing material and the related interference effects that occur.

© 2006 Optical Society of America

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References

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  1. P. Lorrain, D. Corson, and F. Lorrain, Electromagnetic Fields and Waves (Freeman, 1987), pp. 583-584.
  2. E. Hecht, Optics, 3rd ed. (Addison-Wesley-Longman, 1998), p. 126.
  3. L. A. Whitehead, M. A. Mossman, and A. Kotlicki, "Visual applications of total internal reflection in prismatic microstructures," Phys. Can. 57, 329-335 (2001).
  4. M. A. Mossman and L. A. Whitehead, "Controlled frustration of total internal reflection by electrophoresis of pigment particles," Appl. Opt. 44, 1601-1609 (2005).
    [CrossRef] [PubMed]
  5. M. A. Mossman, V. H. Kwong, and L. A. Whitehead, "A novel reflective image display using TIR," J. Disp. 25, 215-222 (2004).
    [CrossRef]
  6. R. J. N. Coope, L. A. Whitehead, and A. Kotlicki, "Modulation of retroreflection by controlled frustration of total internal reflection," Appl. Opt. 41, 5357-5361 (2002).
    [CrossRef] [PubMed]
  7. Diamond Grade Reflective Sheeting, manufactured by 3M Company, St. Paul, Minn., 55144-1000.
  8. Ref. 1, pp. 584-585.
  9. I. N. Court and F. K. Willisen, "Frustrated total internal reflection and application of its principle to laser cavity design," Appl. Opt. 3, 719-726 (1964).
    [CrossRef]
  10. M. A. Mossman, D. S. Arney, R. W. Biernath, R. N. J. Coope, A. Kotlicki, M. J. Pellerite, J. E. Potts, S. P. Rao, and L. A. Whitehead, "New reflective display technique based on total internal reflection in prismatic microstructures," in Society for Information Display Symposium Proceedings (Society for Information Display, 2000), pp. 311-314.
  11. TAOS TSL 250 light-to-voltage optical sensor, manufactured by Texas Advanced Optoelectronic Solutions, Inc., 800 Jupiter Road, Suite 205, Plano, Texas, 75074.
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    [CrossRef]
  13. H. A. MacLeod, "Thin film optical coating design," in Thin Films for Optical Systems, F. R. Flory, ed. (Marcel Dekker, 1995).
  14. Ref. , p. 420.

2005

2004

M. A. Mossman, V. H. Kwong, and L. A. Whitehead, "A novel reflective image display using TIR," J. Disp. 25, 215-222 (2004).
[CrossRef]

2002

2001

L. A. Whitehead, M. A. Mossman, and A. Kotlicki, "Visual applications of total internal reflection in prismatic microstructures," Phys. Can. 57, 329-335 (2001).

2000

1964

Arney, D. S.

M. A. Mossman, D. S. Arney, R. W. Biernath, R. N. J. Coope, A. Kotlicki, M. J. Pellerite, J. E. Potts, S. P. Rao, and L. A. Whitehead, "New reflective display technique based on total internal reflection in prismatic microstructures," in Society for Information Display Symposium Proceedings (Society for Information Display, 2000), pp. 311-314.

Biernath, R. W.

M. A. Mossman, D. S. Arney, R. W. Biernath, R. N. J. Coope, A. Kotlicki, M. J. Pellerite, J. E. Potts, S. P. Rao, and L. A. Whitehead, "New reflective display technique based on total internal reflection in prismatic microstructures," in Society for Information Display Symposium Proceedings (Society for Information Display, 2000), pp. 311-314.

Coope, R. J. N.

Coope, R. N. J.

M. A. Mossman, D. S. Arney, R. W. Biernath, R. N. J. Coope, A. Kotlicki, M. J. Pellerite, J. E. Potts, S. P. Rao, and L. A. Whitehead, "New reflective display technique based on total internal reflection in prismatic microstructures," in Society for Information Display Symposium Proceedings (Society for Information Display, 2000), pp. 311-314.

Corson, D.

P. Lorrain, D. Corson, and F. Lorrain, Electromagnetic Fields and Waves (Freeman, 1987), pp. 583-584.

Court, I. N.

Garcia-Valenzuela, A.

Hecht, E.

E. Hecht, Optics, 3rd ed. (Addison-Wesley-Longman, 1998), p. 126.

Kotlicki, A.

R. J. N. Coope, L. A. Whitehead, and A. Kotlicki, "Modulation of retroreflection by controlled frustration of total internal reflection," Appl. Opt. 41, 5357-5361 (2002).
[CrossRef] [PubMed]

L. A. Whitehead, M. A. Mossman, and A. Kotlicki, "Visual applications of total internal reflection in prismatic microstructures," Phys. Can. 57, 329-335 (2001).

M. A. Mossman, D. S. Arney, R. W. Biernath, R. N. J. Coope, A. Kotlicki, M. J. Pellerite, J. E. Potts, S. P. Rao, and L. A. Whitehead, "New reflective display technique based on total internal reflection in prismatic microstructures," in Society for Information Display Symposium Proceedings (Society for Information Display, 2000), pp. 311-314.

Kwong, V. H.

M. A. Mossman, V. H. Kwong, and L. A. Whitehead, "A novel reflective image display using TIR," J. Disp. 25, 215-222 (2004).
[CrossRef]

Lorrain, F.

P. Lorrain, D. Corson, and F. Lorrain, Electromagnetic Fields and Waves (Freeman, 1987), pp. 583-584.

Lorrain, P.

P. Lorrain, D. Corson, and F. Lorrain, Electromagnetic Fields and Waves (Freeman, 1987), pp. 583-584.

MacLeod, H. A.

H. A. MacLeod, "Thin film optical coating design," in Thin Films for Optical Systems, F. R. Flory, ed. (Marcel Dekker, 1995).

Mossman, M. A.

M. A. Mossman and L. A. Whitehead, "Controlled frustration of total internal reflection by electrophoresis of pigment particles," Appl. Opt. 44, 1601-1609 (2005).
[CrossRef] [PubMed]

M. A. Mossman, V. H. Kwong, and L. A. Whitehead, "A novel reflective image display using TIR," J. Disp. 25, 215-222 (2004).
[CrossRef]

L. A. Whitehead, M. A. Mossman, and A. Kotlicki, "Visual applications of total internal reflection in prismatic microstructures," Phys. Can. 57, 329-335 (2001).

M. A. Mossman, D. S. Arney, R. W. Biernath, R. N. J. Coope, A. Kotlicki, M. J. Pellerite, J. E. Potts, S. P. Rao, and L. A. Whitehead, "New reflective display technique based on total internal reflection in prismatic microstructures," in Society for Information Display Symposium Proceedings (Society for Information Display, 2000), pp. 311-314.

Pellerite, M. J.

M. A. Mossman, D. S. Arney, R. W. Biernath, R. N. J. Coope, A. Kotlicki, M. J. Pellerite, J. E. Potts, S. P. Rao, and L. A. Whitehead, "New reflective display technique based on total internal reflection in prismatic microstructures," in Society for Information Display Symposium Proceedings (Society for Information Display, 2000), pp. 311-314.

Pena-Gomer, M. C.

Potts, J. E.

M. A. Mossman, D. S. Arney, R. W. Biernath, R. N. J. Coope, A. Kotlicki, M. J. Pellerite, J. E. Potts, S. P. Rao, and L. A. Whitehead, "New reflective display technique based on total internal reflection in prismatic microstructures," in Society for Information Display Symposium Proceedings (Society for Information Display, 2000), pp. 311-314.

Rao, S. P.

M. A. Mossman, D. S. Arney, R. W. Biernath, R. N. J. Coope, A. Kotlicki, M. J. Pellerite, J. E. Potts, S. P. Rao, and L. A. Whitehead, "New reflective display technique based on total internal reflection in prismatic microstructures," in Society for Information Display Symposium Proceedings (Society for Information Display, 2000), pp. 311-314.

Whitehead, L. A.

M. A. Mossman and L. A. Whitehead, "Controlled frustration of total internal reflection by electrophoresis of pigment particles," Appl. Opt. 44, 1601-1609 (2005).
[CrossRef] [PubMed]

M. A. Mossman, V. H. Kwong, and L. A. Whitehead, "A novel reflective image display using TIR," J. Disp. 25, 215-222 (2004).
[CrossRef]

R. J. N. Coope, L. A. Whitehead, and A. Kotlicki, "Modulation of retroreflection by controlled frustration of total internal reflection," Appl. Opt. 41, 5357-5361 (2002).
[CrossRef] [PubMed]

L. A. Whitehead, M. A. Mossman, and A. Kotlicki, "Visual applications of total internal reflection in prismatic microstructures," Phys. Can. 57, 329-335 (2001).

M. A. Mossman, D. S. Arney, R. W. Biernath, R. N. J. Coope, A. Kotlicki, M. J. Pellerite, J. E. Potts, S. P. Rao, and L. A. Whitehead, "New reflective display technique based on total internal reflection in prismatic microstructures," in Society for Information Display Symposium Proceedings (Society for Information Display, 2000), pp. 311-314.

Willisen, F. K.

Appl. Opt.

J. Disp.

M. A. Mossman, V. H. Kwong, and L. A. Whitehead, "A novel reflective image display using TIR," J. Disp. 25, 215-222 (2004).
[CrossRef]

Phys. Can.

L. A. Whitehead, M. A. Mossman, and A. Kotlicki, "Visual applications of total internal reflection in prismatic microstructures," Phys. Can. 57, 329-335 (2001).

Other

H. A. MacLeod, "Thin film optical coating design," in Thin Films for Optical Systems, F. R. Flory, ed. (Marcel Dekker, 1995).

Ref. , p. 420.

P. Lorrain, D. Corson, and F. Lorrain, Electromagnetic Fields and Waves (Freeman, 1987), pp. 583-584.

E. Hecht, Optics, 3rd ed. (Addison-Wesley-Longman, 1998), p. 126.

M. A. Mossman, D. S. Arney, R. W. Biernath, R. N. J. Coope, A. Kotlicki, M. J. Pellerite, J. E. Potts, S. P. Rao, and L. A. Whitehead, "New reflective display technique based on total internal reflection in prismatic microstructures," in Society for Information Display Symposium Proceedings (Society for Information Display, 2000), pp. 311-314.

TAOS TSL 250 light-to-voltage optical sensor, manufactured by Texas Advanced Optoelectronic Solutions, Inc., 800 Jupiter Road, Suite 205, Plano, Texas, 75074.

Diamond Grade Reflective Sheeting, manufactured by 3M Company, St. Paul, Minn., 55144-1000.

Ref. 1, pp. 584-585.

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Figures (11)

Fig. 1
Fig. 1

Light retroreflecting from a corner-cube structure.

Fig. 2
Fig. 2

Light undergoing TIR on two of the three corner-cube facets.

Fig. 3
Fig. 3

Intensity of reflected light as a function of incident angle at a glass–air interface.

Fig. 4
Fig. 4

Electrophoretically active pigment particles control the intensity of the reflected light.

Fig. 5
Fig. 5

Experimental setup used to measure the intensity of the reflected light. A∕D, analog to digital.

Fig. 6
Fig. 6

Reflectance versus time as one period of a square-wave voltage is applied.

Fig. 7
Fig. 7

Motion of the pigment particles under the influence of applied voltage: (a) under one field direction, pigment particles are pressed into contact with the top electrode; (b) polarity of the field is reversed and particles move toward the rear electrode; (c) the pigment collective begins to pull away from the top surface, creating a thin, well-defined fluid layer that causes interference; (d) interference is no longer observed since the fluid layer is no longer well defined; (e) polarity of the field is again reversed and particles near the top electrode quickly migrate toward it.

Fig. 8
Fig. 8

Light entering a thin film of index n 1 .

Fig. 9
Fig. 9

(a) A simple three-layer model of PIR modulation; (b) scatter and absorption caused as nonuniformity at the fluid–particle interface increases with time.

Fig. 10
Fig. 10

Model compared with experiment for θ i = (a) θ c + 0.8 ° , (b) θ c , (c) θ c - 0.7 ° , (d) θ c - 1.5 ° .

Fig. 11
Fig. 11

Flashing retroreflective chevron by use of modulation of TIR and PIR: (a) highly reflective on state, (b) highly absorptive off state.

Equations (6)

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

θ c = arcsin ( n 2 n 1 ) ,
r = n 1 cos θ 1 - n 2 cos θ 2 n 1 cos θ 1 + n 2 cos θ 2 ,
r = n 2 cos θ 1 - n 1 cos θ 2 n 2 cos θ 1 + n 1 cos θ 2 ,
R = 1 2 ( | r | 2 + | r | 2 ) .
d 1 d 2 = λ 1 λ 2 ,
r = Y 0 m 11 + Y 0 Y 2 m 12 - m 21 - Y 2 m 22 Y 0 m 11 + Y 0 Y 2 m 12 + m 21 + Y 2 m 22 ,

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