Abstract

The optimization of the experimental parameters of two multiplexed holographic transmission gratings recorded in holographic polymer-dispersed liquid crystals is investigated. Two methods are used to record the holograms: simultaneous and sequential multiplexing. These two processes are optimized to produce two multiplexed Bragg gratings that have the same and the highest possible diffraction efficiencies in the first order. The two methods show similar results when suitable recording parameters are used. The parameters of the recorded gratings (mainly the refractive-index modulation) are retrieved by use of an extension of the rigorous coupled-wave theory to multiplexed gratings. Finally, the response of the holograms to an electric field is studied. We demonstrate few coupling effects between the behavior of both gratings, and we expect a possibility of switching from one grating to the other.

© 2005 Optical Society of America

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  1. A. K. Fontecchio, C. C. Bowley, S. M. Chmura, L. Li, S. Faris, G. P. Crawford, “Multiplexed holographic polymer dispersed liquid crystals,” J. Opt. Technol. 68, 652–656 (2001).
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    [CrossRef]
  4. H. Ren, S. Wu, “Inhomogeneous nanoscale polymer-dispersed liquid crystals with gradient refractive index,” Appl. Phys. Lett. 81, 3537–3539 (2002).
    [CrossRef]
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    [CrossRef]
  6. X. Han, G. Kim, R. T. Chen, “Accurate diffraction efficiency control for multiplexed volume holographic gratings,” Opt. Eng. 41, 2799–2802 (2002).
    [CrossRef]
  7. C. Carré, P. Saint-Georges, L. Bigué, F. Christnacher, “Advanced photopolymerizable material for creation of particular diffractive optical elements,” in Holography, Diffractive Optics, and Applications, D. Hsu, J. Chen, Y. Sheng, eds., Proc. SPIE4924, 322–333 (2002).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2004 (2)

2003 (1)

2002 (3)

R. L. Sutherland, V. P. Tondiglia, L. V. Natajaran, S. Chandra, D. Tomlin, T. J. Bunning, “Switchable orthorhombic F photonic crystals formed by holographic polymerisation-induced phase separation of liquid crystals,” Opt. Express 10, 1074–1082 (2002).
[CrossRef] [PubMed]

H. Ren, S. Wu, “Inhomogeneous nanoscale polymer-dispersed liquid crystals with gradient refractive index,” Appl. Phys. Lett. 81, 3537–3539 (2002).
[CrossRef]

X. Han, G. Kim, R. T. Chen, “Accurate diffraction efficiency control for multiplexed volume holographic gratings,” Opt. Eng. 41, 2799–2802 (2002).
[CrossRef]

2001 (1)

2000 (2)

C. C. Bowley, A. K. Fontecchio, G. P. Crawford, “Multiple gratings simultaneously formed in holographic polymer-dispersed liquid-crystal displays,” Appl. Phys. Lett. 76, 523–525 (2000).
[CrossRef]

T. J. Bunning, L. V. Natarajan, V. P. Tondiglia, R. L. Sutherland, “Holographic polymer-dispersed liquid crystals (H-PDLCs),” Annu. Rev. Mater. Sci. 30, 83–115 (2000).
[CrossRef]

1999 (2)

S. Piazzolla, B. K. Jenkins, “Dynamics during holographic exposure in photopolymers for single and multiplexed gratings,” J. Mod. Opt. 46, 2079–2110 (1999).
[CrossRef]

R. K. Kostuk, “Dynamic hologram recording in Dupont photopolymers,” Appl. Opt. 38, 1357–1363 (1999).
[CrossRef]

1996 (3)

1995 (1)

1994 (1)

G. Zhao, P. Mouroulis, “Diffusion model of hologram formation in dry photopolymerisable materials,” J. Mod. Opt. 41, 1929–1939 (1994).
[CrossRef]

1993 (1)

R. Bräuer, O. Bryngdahl, “Electromagnetic diffraction analysis of two-dimensional gratings,” Opt. Commun. 100, 1–5 (1993).
[CrossRef]

Bigué, L.

C. Carré, P. Saint-Georges, L. Bigué, F. Christnacher, “Advanced photopolymerizable material for creation of particular diffractive optical elements,” in Holography, Diffractive Optics, and Applications, D. Hsu, J. Chen, Y. Sheng, eds., Proc. SPIE4924, 322–333 (2002).
[CrossRef]

Bowley, C. C.

A. K. Fontecchio, C. C. Bowley, S. M. Chmura, L. Li, S. Faris, G. P. Crawford, “Multiplexed holographic polymer dispersed liquid crystals,” J. Opt. Technol. 68, 652–656 (2001).
[CrossRef]

C. C. Bowley, A. K. Fontecchio, G. P. Crawford, “Multiple gratings simultaneously formed in holographic polymer-dispersed liquid-crystal displays,” Appl. Phys. Lett. 76, 523–525 (2000).
[CrossRef]

Bräuer, R.

R. Bräuer, O. Bryngdahl, “Electromagnetic diffraction analysis of two-dimensional gratings,” Opt. Commun. 100, 1–5 (1993).
[CrossRef]

Bryngdahl, O.

R. Bräuer, O. Bryngdahl, “Electromagnetic diffraction analysis of two-dimensional gratings,” Opt. Commun. 100, 1–5 (1993).
[CrossRef]

Bunning, T. J.

Carré, C.

C. Carré, P. Saint-Georges, L. Bigué, F. Christnacher, “Advanced photopolymerizable material for creation of particular diffractive optical elements,” in Holography, Diffractive Optics, and Applications, D. Hsu, J. Chen, Y. Sheng, eds., Proc. SPIE4924, 322–333 (2002).
[CrossRef]

Chandra, S.

Chen, R. T.

X. Han, G. Kim, R. T. Chen, “Accurate diffraction efficiency control for multiplexed volume holographic gratings,” Opt. Eng. 41, 2799–2802 (2002).
[CrossRef]

Chevallier, R.

Chmura, S. M.

Christnacher, F.

C. Carré, P. Saint-Georges, L. Bigué, F. Christnacher, “Advanced photopolymerizable material for creation of particular diffractive optical elements,” in Holography, Diffractive Optics, and Applications, D. Hsu, J. Chen, Y. Sheng, eds., Proc. SPIE4924, 322–333 (2002).
[CrossRef]

Crawford, G. P.

de Bougrenet de la Tocnaye, J. L.

Escuti, M. J.

M. J. Escuti, J. Qi, G. P. Crawford, “Tunable face-centered-cubic photonic crystal formed in holographic polymer dispersed liquid crystals,” Opt. Lett. 28, 522–524 (2003).
[CrossRef] [PubMed]

M. E. Sousa, J. Qi, M. J. Escuti, G. P. Crawford, “Mesoscales lattices and temporal multiplexing in liquid crystal/polymer dispersions,” in Liquid Crystals VII, I.-C. Khoo, ed., Proc. SPIE5213, 130–138 (2003).
[CrossRef]

Faris, S.

Fontecchio, A. K.

A. K. Fontecchio, C. C. Bowley, S. M. Chmura, L. Li, S. Faris, G. P. Crawford, “Multiplexed holographic polymer dispersed liquid crystals,” J. Opt. Technol. 68, 652–656 (2001).
[CrossRef]

C. C. Bowley, A. K. Fontecchio, G. P. Crawford, “Multiple gratings simultaneously formed in holographic polymer-dispersed liquid-crystal displays,” Appl. Phys. Lett. 76, 523–525 (2000).
[CrossRef]

Gaylord, T. K.

Grann, E. B.

Han, X.

X. Han, G. Kim, R. T. Chen, “Accurate diffraction efficiency control for multiplexed volume holographic gratings,” Opt. Eng. 41, 2799–2802 (2002).
[CrossRef]

Jenkins, B. K.

S. Piazzolla, B. K. Jenkins, “Dynamics during holographic exposure in photopolymers for single and multiplexed gratings,” J. Mod. Opt. 46, 2079–2110 (1999).
[CrossRef]

Kaiser, J. L.

Kim, G.

X. Han, G. Kim, R. T. Chen, “Accurate diffraction efficiency control for multiplexed volume holographic gratings,” Opt. Eng. 41, 2799–2802 (2002).
[CrossRef]

Kostuk, R. K.

Lalanne, P.

Li, L.

Massenot, S.

Moharam, M. G.

Morris, G. M.

Mouroulis, P.

G. Zhao, P. Mouroulis, “Diffusion model of hologram formation in dry photopolymerisable materials,” J. Mod. Opt. 41, 1929–1939 (1994).
[CrossRef]

Natajaran, L. V.

Natarajan, L. V.

T. J. Bunning, L. V. Natarajan, V. P. Tondiglia, R. L. Sutherland, “Holographic polymer-dispersed liquid crystals (H-PDLCs),” Annu. Rev. Mater. Sci. 30, 83–115 (2000).
[CrossRef]

Nevière, M.

M. Nevière, E. Popov, Light Propagation in Periodic Media, Differential Theory and Design (Marcel Dekker, 2003).

Piazzolla, S.

S. Piazzolla, B. K. Jenkins, “Dynamics during holographic exposure in photopolymers for single and multiplexed gratings,” J. Mod. Opt. 46, 2079–2110 (1999).
[CrossRef]

Pommet, D. A.

Popov, E.

M. Nevière, E. Popov, Light Propagation in Periodic Media, Differential Theory and Design (Marcel Dekker, 2003).

Qi, J.

M. J. Escuti, J. Qi, G. P. Crawford, “Tunable face-centered-cubic photonic crystal formed in holographic polymer dispersed liquid crystals,” Opt. Lett. 28, 522–524 (2003).
[CrossRef] [PubMed]

M. E. Sousa, J. Qi, M. J. Escuti, G. P. Crawford, “Mesoscales lattices and temporal multiplexing in liquid crystal/polymer dispersions,” in Liquid Crystals VII, I.-C. Khoo, ed., Proc. SPIE5213, 130–138 (2003).
[CrossRef]

Ren, H.

H. Ren, S. Wu, “Inhomogeneous nanoscale polymer-dispersed liquid crystals with gradient refractive index,” Appl. Phys. Lett. 81, 3537–3539 (2002).
[CrossRef]

Renotte, Y.

Saint-Georges, P.

C. Carré, P. Saint-Georges, L. Bigué, F. Christnacher, “Advanced photopolymerizable material for creation of particular diffractive optical elements,” in Holography, Diffractive Optics, and Applications, D. Hsu, J. Chen, Y. Sheng, eds., Proc. SPIE4924, 322–333 (2002).
[CrossRef]

Sousa, M. E.

M. E. Sousa, J. Qi, M. J. Escuti, G. P. Crawford, “Mesoscales lattices and temporal multiplexing in liquid crystal/polymer dispersions,” in Liquid Crystals VII, I.-C. Khoo, ed., Proc. SPIE5213, 130–138 (2003).
[CrossRef]

Sutherland, R. L.

Tomlin, D.

Tondiglia, V. P.

Wu, S.

H. Ren, S. Wu, “Inhomogeneous nanoscale polymer-dispersed liquid crystals with gradient refractive index,” Appl. Phys. Lett. 81, 3537–3539 (2002).
[CrossRef]

Zhao, G.

G. Zhao, P. Mouroulis, “Diffusion model of hologram formation in dry photopolymerisable materials,” J. Mod. Opt. 41, 1929–1939 (1994).
[CrossRef]

Annu. Rev. Mater. Sci. (1)

T. J. Bunning, L. V. Natarajan, V. P. Tondiglia, R. L. Sutherland, “Holographic polymer-dispersed liquid crystals (H-PDLCs),” Annu. Rev. Mater. Sci. 30, 83–115 (2000).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (2)

C. C. Bowley, A. K. Fontecchio, G. P. Crawford, “Multiple gratings simultaneously formed in holographic polymer-dispersed liquid-crystal displays,” Appl. Phys. Lett. 76, 523–525 (2000).
[CrossRef]

H. Ren, S. Wu, “Inhomogeneous nanoscale polymer-dispersed liquid crystals with gradient refractive index,” Appl. Phys. Lett. 81, 3537–3539 (2002).
[CrossRef]

J. Mod. Opt. (2)

S. Piazzolla, B. K. Jenkins, “Dynamics during holographic exposure in photopolymers for single and multiplexed gratings,” J. Mod. Opt. 46, 2079–2110 (1999).
[CrossRef]

G. Zhao, P. Mouroulis, “Diffusion model of hologram formation in dry photopolymerisable materials,” J. Mod. Opt. 41, 1929–1939 (1994).
[CrossRef]

J. Opt. Soc. Am. A (4)

J. Opt. Technol. (1)

Opt. Commun. (1)

R. Bräuer, O. Bryngdahl, “Electromagnetic diffraction analysis of two-dimensional gratings,” Opt. Commun. 100, 1–5 (1993).
[CrossRef]

Opt. Eng. (1)

X. Han, G. Kim, R. T. Chen, “Accurate diffraction efficiency control for multiplexed volume holographic gratings,” Opt. Eng. 41, 2799–2802 (2002).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Other (3)

M. Nevière, E. Popov, Light Propagation in Periodic Media, Differential Theory and Design (Marcel Dekker, 2003).

C. Carré, P. Saint-Georges, L. Bigué, F. Christnacher, “Advanced photopolymerizable material for creation of particular diffractive optical elements,” in Holography, Diffractive Optics, and Applications, D. Hsu, J. Chen, Y. Sheng, eds., Proc. SPIE4924, 322–333 (2002).
[CrossRef]

M. E. Sousa, J. Qi, M. J. Escuti, G. P. Crawford, “Mesoscales lattices and temporal multiplexing in liquid crystal/polymer dispersions,” in Liquid Crystals VII, I.-C. Khoo, ed., Proc. SPIE5213, 130–138 (2003).
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

(Color online) H-PDLC structure after recording. ITO, indium tin oxide; LC, liquid crystal.

Fig. 2
Fig. 2

Multiplexing of two transmission Bragg gratings.

Fig. 3
Fig. 3

Comparison of the angular selectivities of holographic transmission of similar period diffraction gratings: (a) separate, (b) multiplexed.

Fig. 4
Fig. 4

Comparison of the angular selectivities of holographic transmission diffraction gratings with widely differing periods: (a) separate, (b) multiplexed.

Fig. 5
Fig. 5

(Color online) Experimental setup for recording.

Fig. 6
Fig. 6

Interference pattern for simultaneous multiplexing (which corresponds to beating between two sinusoidal patterns).

Fig. 7
Fig. 7

Evolution of the first diffracted orders for three exposure energies I0 for gratings of periods (a) 2.1 μm and (b) 0.73 μm.

Fig. 8
Fig. 8

Optimization of the recording parameters for simultaneous multiplexing. The variable parameter is the irradiance used for the 2.1 μm grating: (a) I0 = 17.1 mW/cm2, (b) I0 = 24.5 mW/cm2, (c) I0 = 25.7 mW/cm2, (d) I0 = 26.8 mW/cm2.

Fig. 9
Fig. 9

Balanced multiplexed gratings obtained with the simultaneous recording setup.

Fig. 10
Fig. 10

Angular characterization of two multiplexed gratings: comparison of experimental results (dotted curves) and theoretical prediction (continuous curves).

Fig. 11
Fig. 11

Time evolution of the first-order diffraction efficiency of two sequentially multiplexed transmission gratings with different exposure times for the first grating: (a) 3 s, (b) 4.3 s, (c) 4.5 s, (d) 5 s.

Fig. 12
Fig. 12

Normalized diffraction efficiency in the first order for the two gratings as a function of the applied electric field.

Fig. 13
Fig. 13

Diffraction efficiency in the first order for the two gratings as a function of the applied electric field when the angle of incidence is between the two Bragg angles.

Equations (1)

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ϕ ( x ,     t ) t = x [ D ( x ,     t ) ϕ ( x ,     t ) x ] - { F 0 ( 1 ) [ 1 + cos ( 2 π Λ 1 x ) ] 1 / 2 + F 0 ( 2 ) [ 1 + cos ( 2 π Λ 2 x ) ] 1 / 2 } ϕ ( x ,     t ) ,

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