Abstract

We propose the application of a thermally tunable grating as a spatial light modulator. The grooves of a square-well grating are filled with a liquid whose refractive index depends on temperature. The variation of optical characteristics of such a grating with respect to temperature is investigated theoretically and also by simulation and experiment. A thin-film heater is then used as a heat source. The relation between intensity of the first order of diffraction versus power consumption of the thin-film heater is investigated. Finally, a thin-film heater with a desired pattern is placed at the surface of the grating to fabricate spatial light modulator. By applying electrical current to different elements of the thin-film heater, the fabricated device can project a desired pattern on a screen using a 4f imaging system. The restrictions of such a device are discussed and another structure is proposed and discussed by numerical calculations to increase the ability of the device.

© 2009 Optical Society of America

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References

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  4. R. Eriksen, V. Daria, and J. Glückstad, “Fully dynamic multiple-beam optical tweezers,” Opt. Express 10, 597-602(2002).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2008

2006

2005

2004

J. I. Trisnadi, C. B. Carlisle, and R. Monteverde, “Overview and applications of grating-light-valve-based optical write engines for high-speed digital imaging,” Proc. SPIE 5348, 52-64 (2004).
[CrossRef]

2003

2002

R. Eriksen, V. Daria, and J. Glückstad, “Fully dynamic multiple-beam optical tweezers,” Opt. Express 10, 597-602(2002).
[PubMed]

L. Xu,L. Li, N. Nakagawa, R. Morita, and M. Yamashita, “Application of a spatial light modulator for programmable optical pulse compression to the sub-6-fs regime,” IEEE Photonics Technol. Lett. 121540-1542(2002).

2000

1999

A. D. Cohen, M. C. Parker, and R. J. Mears, “100 GHz resolution dynamic holographic channel management for WDM,” IEEE Photonics Technol. Lett. 11, 851-853 (1999).
[CrossRef]

1995

J. Chen, P. J. Bos, H. Vithana, and D. L. Johnson, “An electrooptically controlled liquid crystal diffraction grating,” Appl. Phys. Lett. 67, 2588-2590 (1995).
[CrossRef]

1983

W. E. Ross, K. M. Snapp, and R. H. Anderson, “Fundamental characteristics of the Litton iron garnet magneto-optic spatial light modulator,” Proc. SPIE 388, 55-64 (1983).

1982

A. I. Nagaev, V. N. Parygin, and S. Yu. Pashin, “Image processing by a spatial light modulator utilizing the Pockels effect,” J. Quantum Electron. 12, 1178-1181 (1982).
[CrossRef]

Anderson, R. H.

W. E. Ross, K. M. Snapp, and R. H. Anderson, “Fundamental characteristics of the Litton iron garnet magneto-optic spatial light modulator,” Proc. SPIE 388, 55-64 (1983).

Barbastathis, G.

Bernet, S.

Bos, P. J.

J. Chen, P. J. Bos, H. Vithana, and D. L. Johnson, “An electrooptically controlled liquid crystal diffraction grating,” Appl. Phys. Lett. 67, 2588-2590 (1995).
[CrossRef]

Carlisle, C. B.

J. I. Trisnadi, C. B. Carlisle, and R. Monteverde, “Overview and applications of grating-light-valve-based optical write engines for high-speed digital imaging,” Proc. SPIE 5348, 52-64 (2004).
[CrossRef]

Chen, J.

J. Chen, P. J. Bos, H. Vithana, and D. L. Johnson, “An electrooptically controlled liquid crystal diffraction grating,” Appl. Phys. Lett. 67, 2588-2590 (1995).
[CrossRef]

Cohen, A. D.

A. D. Cohen, M. C. Parker, and R. J. Mears, “100 GHz resolution dynamic holographic channel management for WDM,” IEEE Photonics Technol. Lett. 11, 851-853 (1999).
[CrossRef]

Cohn, R. W.

Daria, V.

Duelli, M.

Efron, Uzi

Uzi Efron, Spatial Light Modulator Technology (CRC, 1994).

Eriksen, R.

Fürhapter, S.

Ge, L.

Glückstad, J.

Jeon, Y.

Jesacher, A.

Johnson, D. L.

J. Chen, P. J. Bos, H. Vithana, and D. L. Johnson, “An electrooptically controlled liquid crystal diffraction grating,” Appl. Phys. Lett. 67, 2588-2590 (1995).
[CrossRef]

Joseph, J.

Kim, S. G.

Latifi, H.

Li, L.

L. Xu,L. Li, N. Nakagawa, R. Morita, and M. Yamashita, “Application of a spatial light modulator for programmable optical pulse compression to the sub-6-fs regime,” IEEE Photonics Technol. Lett. 121540-1542(2002).

Mears, R. J.

A. D. Cohen, M. C. Parker, and R. J. Mears, “100 GHz resolution dynamic holographic channel management for WDM,” IEEE Photonics Technol. Lett. 11, 851-853 (1999).
[CrossRef]

Moghimislam, G.

Monteverde, R.

J. I. Trisnadi, C. B. Carlisle, and R. Monteverde, “Overview and applications of grating-light-valve-based optical write engines for high-speed digital imaging,” Proc. SPIE 5348, 52-64 (2004).
[CrossRef]

Morita, R.

L. Xu,L. Li, N. Nakagawa, R. Morita, and M. Yamashita, “Application of a spatial light modulator for programmable optical pulse compression to the sub-6-fs regime,” IEEE Photonics Technol. Lett. 121540-1542(2002).

Nagaev, A. I.

A. I. Nagaev, V. N. Parygin, and S. Yu. Pashin, “Image processing by a spatial light modulator utilizing the Pockels effect,” J. Quantum Electron. 12, 1178-1181 (1982).
[CrossRef]

Nakagawa, N.

L. Xu,L. Li, N. Nakagawa, R. Morita, and M. Yamashita, “Application of a spatial light modulator for programmable optical pulse compression to the sub-6-fs regime,” IEEE Photonics Technol. Lett. 121540-1542(2002).

Parker, M. C.

A. D. Cohen, M. C. Parker, and R. J. Mears, “100 GHz resolution dynamic holographic channel management for WDM,” IEEE Photonics Technol. Lett. 11, 851-853 (1999).
[CrossRef]

Parygin, V. N.

A. I. Nagaev, V. N. Parygin, and S. Yu. Pashin, “Image processing by a spatial light modulator utilizing the Pockels effect,” J. Quantum Electron. 12, 1178-1181 (1982).
[CrossRef]

Pashin, S. Yu.

A. I. Nagaev, V. N. Parygin, and S. Yu. Pashin, “Image processing by a spatial light modulator utilizing the Pockels effect,” J. Quantum Electron. 12, 1178-1181 (1982).
[CrossRef]

Riahi, M.

Ritsch-Merte, M.

Ross, W. E.

W. E. Ross, K. M. Snapp, and R. H. Anderson, “Fundamental characteristics of the Litton iron garnet magneto-optic spatial light modulator,” Proc. SPIE 388, 55-64 (1983).

Snapp, K. M.

W. E. Ross, K. M. Snapp, and R. H. Anderson, “Fundamental characteristics of the Litton iron garnet magneto-optic spatial light modulator,” Proc. SPIE 388, 55-64 (1983).

Trisnadi, J. I.

J. I. Trisnadi, C. B. Carlisle, and R. Monteverde, “Overview and applications of grating-light-valve-based optical write engines for high-speed digital imaging,” Proc. SPIE 5348, 52-64 (2004).
[CrossRef]

Vithana, H.

J. Chen, P. J. Bos, H. Vithana, and D. L. Johnson, “An electrooptically controlled liquid crystal diffraction grating,” Appl. Phys. Lett. 67, 2588-2590 (1995).
[CrossRef]

Waldman, D. A.

Weber, M. J.

M. J. Weber, Handbook of Optical Materials (CRC, 2003).

Wong, C. W.

Xu, L.

L. Xu,L. Li, N. Nakagawa, R. Morita, and M. Yamashita, “Application of a spatial light modulator for programmable optical pulse compression to the sub-6-fs regime,” IEEE Photonics Technol. Lett. 121540-1542(2002).

Yamashita, M.

L. Xu,L. Li, N. Nakagawa, R. Morita, and M. Yamashita, “Application of a spatial light modulator for programmable optical pulse compression to the sub-6-fs regime,” IEEE Photonics Technol. Lett. 121540-1542(2002).

Appl. Opt.

Appl. Phys. Lett.

J. Chen, P. J. Bos, H. Vithana, and D. L. Johnson, “An electrooptically controlled liquid crystal diffraction grating,” Appl. Phys. Lett. 67, 2588-2590 (1995).
[CrossRef]

IEEE Photonics Technol. Lett.

L. Xu,L. Li, N. Nakagawa, R. Morita, and M. Yamashita, “Application of a spatial light modulator for programmable optical pulse compression to the sub-6-fs regime,” IEEE Photonics Technol. Lett. 121540-1542(2002).

A. D. Cohen, M. C. Parker, and R. J. Mears, “100 GHz resolution dynamic holographic channel management for WDM,” IEEE Photonics Technol. Lett. 11, 851-853 (1999).
[CrossRef]

J. Quantum Electron.

A. I. Nagaev, V. N. Parygin, and S. Yu. Pashin, “Image processing by a spatial light modulator utilizing the Pockels effect,” J. Quantum Electron. 12, 1178-1181 (1982).
[CrossRef]

Opt. Express

Proc. SPIE

W. E. Ross, K. M. Snapp, and R. H. Anderson, “Fundamental characteristics of the Litton iron garnet magneto-optic spatial light modulator,” Proc. SPIE 388, 55-64 (1983).

J. I. Trisnadi, C. B. Carlisle, and R. Monteverde, “Overview and applications of grating-light-valve-based optical write engines for high-speed digital imaging,” Proc. SPIE 5348, 52-64 (2004).
[CrossRef]

Other

M. J. Weber, Handbook of Optical Materials (CRC, 2003).

Uzi Efron, Spatial Light Modulator Technology (CRC, 1994).

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Figures (9)

Fig. 1
Fig. 1

(a) Square-well grating with n 1 and n 2 for the refractive indices of the surface and the groove. (b) Wavefront of laser immediately after the grating. (c) Efficiency of grating for different a and different Δ φ . (d), (e), and (f) Simulation results of the diffraction from grating with a = 4 for phase differences equal to 0, π / 2 , and π, respectively. In vertical axes, the maximum intensity has been normalized to unity. (g) Sensitivity γ for different diffraction orders and for different fill factors for a constant phase difference.

Fig. 2
Fig. 2

(a) Setup for investigating the relation between temperature and the intensity of the first order of diffraction. (b) Intensity of the first order of the diffraction versus temperature.

Fig. 3
Fig. 3

(a) Fabricated thin-film heater. (b) Fabrication of a TTG utilizing the thin-film heater. (c) Intensity of the first order of diffraction versus electrical current of the heater.

Fig. 4
Fig. 4

9a) Fabricated seven-segment heater. (b) The whole SLM system.

Fig. 5
Fig. 5

(a) Schematic setup of projecting the pattern of the SLM on a screen. Here, the screen has been replaced by a CCD camera. (b) The captured image before applying heat. (c) Producing number 3 by applying heat to appropriate segments.

Fig. 6
Fig. 6

Computer simulation results of the thermal distribution in the thermally actuated SLM, after applying current to one segment.

Fig. 7
Fig. 7

Proposed reflective grating with fast response time. (a) Coating of polycarbonate on top of copper substrate. (b) Patterning the polycarbonate by hot embossing. (c) Coating a thin film of aluminum as a reflective surface. (d) Filling the grooves of the grating with polycarbonate. (e) Coating by ITO thin-film heater.

Fig. 8
Fig. 8

(a) and (b) Distribution of temperature in a 20 μm thick grating for t = 100 , t = 2500 μs , respectively. c) Temperature of a point 10 μm below the surface of the grating. (d) Response time of gratings in different thicknesses.

Fig. 9
Fig. 9

Proposed setup for a projection system. (a) 1D array of TTG and (b) projection system.

Equations (23)

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Δ φ = φ 1 φ 2 = 2 π ( n 1 n 2 ) λ d ,
φ 1 = 2 π ( n 1 ) λ d ,
φ 2 = 2 π ( n 2 ) λ d .
f ( x ) = A 0 + m = 1 A m cos ( m K x ) + m = 1 B m sin ( m K x ) ,
A 0 = 2 Λ 0 Λ f ( x ) d x ,
A m = 2 Λ 0 Λ f ( x ) cos ( m K x ) d x ,
B m = 2 Λ 0 Λ f ( x ) sin ( m K x ) d x .
E ( x ) = { E 0 for     0 < x < Λ a E 0 e i Δ φ for     Λ a < x < ( Λ Λ a ) E 0 for     ( Λ Λ a ) < x < Λ .
B m = 0.
A 0 = 2 E 0 [ ( 2 a ) + ( 1 2 a ) e i Δ φ ] ,
A m = 2 E 0 m π [ sin ( 2 m π a ) + e i Δ φ ( sin ( 2 m π a ) ) ] .
I 0 , order = I 0 , max [ 1 + 2 ( 4 a 8 a 2 ) ( cos 2 ( Δ φ 2 ) 1 ) ] ,
I m = 4 I 0 , max m 2 π 2 sin 2 ( 2 m π a ) sin 2 ( Δ φ 2 ) ,
I 0 , order = I 0 , max cos 2 ( Δ φ 2 ) ,
I m , odd = 4 I 0 , max m 2 π 2 sin 2 ( Δ φ 2 ) .
I m , even = 0
I 0 , max = I l .
EFF = 2 ( 4 a 8 a 2 ) ( 1 cos 2 ( Δ φ 2 ) ) .
γ m = d I m d n 2 .
γ m = 4 d I l λ m 2 π sin 2 ( 2 m π a ) sin ( Δ φ 2 ) cos ( Δ φ 2 ) .
Δ ( Δ φ ) = 2 π ( n 2 n 1 T 1 ) λ ( d ) 2 π ( n 2 n 1 T 2 ) λ ( d ) = 2 π Δ n λ ( d ) ,
Δ φ = φ 1 φ 2 = 2 π ( n 1 n 2 ) λ ( 2 d ) .
Δ ( Δ φ ) = 2 π Δ n λ ( 2 d ) must be π .

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