Abstract

A concave diffraction grating with a tunable radius of curvature R is fabricated by embedding a nitinol wire within an elastomeric grating replica. Curvature of the grating is controlled via the shape memory effect, where strain in the wire is recovered due to martensite–austenite phase transformations induced by resistive heating. The generated force bends the grating into a variable curvature determined by applied current. The radius of curvature for the concave grating is variable from 170 to 44mm over a current range of 0 to 2.5A. Actuation of R redirects the grating normal, resulting in a scanning motion of the diffracted beam.

© 2010 Optical Society of America

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References

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    [CrossRef]
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2008 (1)

J. Jayender, R. V. Patel, S. Nikumb, and M. Ostojic, “Modeling and control of shape memory alloy actuators,” IEEE Trans. Contr. Syst. Technol. 16, 279–287 (2008).
[CrossRef]

2007 (2)

R. A. Guerrero, J. Barretto, J. Uy, I. Culaba, and B. Chan, “Effects of spontaneous surface buckling on the diffraction performance of an Au-coated elastomeric grating,” Opt. Commun. 270, 1–7 (2007).
[CrossRef]

E. H. Khoo, A. Q. Liu, T. H. Cheng, J. Li, and D. Pinjala, “Light focusing via Rowland concave surface of photonic crystal,” Appl. Phys. Lett. 91, 221105 (2007).
[CrossRef]

2006 (1)

2005 (1)

W. M. Huang and W. Xu, “Hysteresis in shape memory alloys. Is it always a constant?” J. Mater. Sci. 40, 2985–2986 (2005).
[CrossRef]

2004 (2)

H. S. Tzou, H. J. Lee, and S. M. Arnold, “Smart materials, precision sensors/actuators, smart structures, and structronic systems,” Mech. Adv. Mater. Struct. 11, 367–393 (2004).
[CrossRef]

Z. Shi, J. He, and S. He, “Analysis and design of a concave diffraction grating with total-internal-reflection facets by a hybrid diffraction method,” J. Opt. Soc. Am. A 21, 1198–1206(2004).
[CrossRef]

2003 (1)

2002 (2)

Y. Li, S. Jia, H. Wang, D. Chen, and K. Hane, “Pitch-variable transmission-type bulk gratings driven by shape memory alloy actuator,” Opt. Laser Technol. 34, 649–653 (2002).
[CrossRef]

M. Elahinia and H. Ashrafiuon, “Nonlinear control of a shape memory alloy actuated manipulator,” J. Vib. Acoust. 124, 566–575 (2002).
[CrossRef]

1998 (1)

B. J. de Blonk and D. C. Lagoudas, “Actuation of elastomeric rods with embedded two-way shape memory alloy actuators,” Smart Mater. Struct. 7, 771–783 (1998).
[CrossRef]

1996 (1)

1983 (1)

Arnold, S. M.

H. S. Tzou, H. J. Lee, and S. M. Arnold, “Smart materials, precision sensors/actuators, smart structures, and structronic systems,” Mech. Adv. Mater. Struct. 11, 367–393 (2004).
[CrossRef]

Aschwanden, M.

Ashrafiuon, H.

M. Elahinia and H. Ashrafiuon, “Nonlinear control of a shape memory alloy actuated manipulator,” J. Vib. Acoust. 124, 566–575 (2002).
[CrossRef]

Barbastathis, G.

Barretto, J.

R. A. Guerrero, J. Barretto, J. Uy, I. Culaba, and B. Chan, “Effects of spontaneous surface buckling on the diffraction performance of an Au-coated elastomeric grating,” Opt. Commun. 270, 1–7 (2007).
[CrossRef]

Chan, B.

R. A. Guerrero, J. Barretto, J. Uy, I. Culaba, and B. Chan, “Effects of spontaneous surface buckling on the diffraction performance of an Au-coated elastomeric grating,” Opt. Commun. 270, 1–7 (2007).
[CrossRef]

Chen, D.

Y. Li, S. Jia, H. Wang, D. Chen, and K. Hane, “Pitch-variable transmission-type bulk gratings driven by shape memory alloy actuator,” Opt. Laser Technol. 34, 649–653 (2002).
[CrossRef]

Cheng, T. H.

E. H. Khoo, A. Q. Liu, T. H. Cheng, J. Li, and D. Pinjala, “Light focusing via Rowland concave surface of photonic crystal,” Appl. Phys. Lett. 91, 221105 (2007).
[CrossRef]

Culaba, I.

R. A. Guerrero, J. Barretto, J. Uy, I. Culaba, and B. Chan, “Effects of spontaneous surface buckling on the diffraction performance of an Au-coated elastomeric grating,” Opt. Commun. 270, 1–7 (2007).
[CrossRef]

de Blonk, B. J.

B. J. de Blonk and D. C. Lagoudas, “Actuation of elastomeric rods with embedded two-way shape memory alloy actuators,” Smart Mater. Struct. 7, 771–783 (1998).
[CrossRef]

Elahinia, M.

M. Elahinia and H. Ashrafiuon, “Nonlinear control of a shape memory alloy actuated manipulator,” J. Vib. Acoust. 124, 566–575 (2002).
[CrossRef]

Fujii, Y.

Guerrero, R. A.

R. A. Guerrero, J. Barretto, J. Uy, I. Culaba, and B. Chan, “Effects of spontaneous surface buckling on the diffraction performance of an Au-coated elastomeric grating,” Opt. Commun. 270, 1–7 (2007).
[CrossRef]

Hane, K.

Y. Li, S. Jia, H. Wang, D. Chen, and K. Hane, “Pitch-variable transmission-type bulk gratings driven by shape memory alloy actuator,” Opt. Laser Technol. 34, 649–653 (2002).
[CrossRef]

He, J.

He, S.

Huang, W. M.

W. M. Huang and W. Xu, “Hysteresis in shape memory alloys. Is it always a constant?” J. Mater. Sci. 40, 2985–2986 (2005).
[CrossRef]

Jayender, J.

J. Jayender, R. V. Patel, S. Nikumb, and M. Ostojic, “Modeling and control of shape memory alloy actuators,” IEEE Trans. Contr. Syst. Technol. 16, 279–287 (2008).
[CrossRef]

Jeon, Y.

Jia, S.

Y. Li, S. Jia, H. Wang, D. Chen, and K. Hane, “Pitch-variable transmission-type bulk gratings driven by shape memory alloy actuator,” Opt. Laser Technol. 34, 649–653 (2002).
[CrossRef]

Khoo, E. H.

E. H. Khoo, A. Q. Liu, T. H. Cheng, J. Li, and D. Pinjala, “Light focusing via Rowland concave surface of photonic crystal,” Appl. Phys. Lett. 91, 221105 (2007).
[CrossRef]

Kim, S.

Lagoudas, D. C.

B. J. de Blonk and D. C. Lagoudas, “Actuation of elastomeric rods with embedded two-way shape memory alloy actuators,” Smart Mater. Struct. 7, 771–783 (1998).
[CrossRef]

Lee, H. J.

H. S. Tzou, H. J. Lee, and S. M. Arnold, “Smart materials, precision sensors/actuators, smart structures, and structronic systems,” Mech. Adv. Mater. Struct. 11, 367–393 (2004).
[CrossRef]

Li, J.

E. H. Khoo, A. Q. Liu, T. H. Cheng, J. Li, and D. Pinjala, “Light focusing via Rowland concave surface of photonic crystal,” Appl. Phys. Lett. 91, 221105 (2007).
[CrossRef]

Li, Y.

Y. Li, S. Jia, H. Wang, D. Chen, and K. Hane, “Pitch-variable transmission-type bulk gratings driven by shape memory alloy actuator,” Opt. Laser Technol. 34, 649–653 (2002).
[CrossRef]

Liu, A. Q.

E. H. Khoo, A. Q. Liu, T. H. Cheng, J. Li, and D. Pinjala, “Light focusing via Rowland concave surface of photonic crystal,” Appl. Phys. Lett. 91, 221105 (2007).
[CrossRef]

McGreer, K. A.

Minowa, J.

Nikumb, S.

J. Jayender, R. V. Patel, S. Nikumb, and M. Ostojic, “Modeling and control of shape memory alloy actuators,” IEEE Trans. Contr. Syst. Technol. 16, 279–287 (2008).
[CrossRef]

Ostojic, M.

J. Jayender, R. V. Patel, S. Nikumb, and M. Ostojic, “Modeling and control of shape memory alloy actuators,” IEEE Trans. Contr. Syst. Technol. 16, 279–287 (2008).
[CrossRef]

Patel, R. V.

J. Jayender, R. V. Patel, S. Nikumb, and M. Ostojic, “Modeling and control of shape memory alloy actuators,” IEEE Trans. Contr. Syst. Technol. 16, 279–287 (2008).
[CrossRef]

Pinjala, D.

E. H. Khoo, A. Q. Liu, T. H. Cheng, J. Li, and D. Pinjala, “Light focusing via Rowland concave surface of photonic crystal,” Appl. Phys. Lett. 91, 221105 (2007).
[CrossRef]

Shi, Z.

Stemmer, A.

Tzou, H. S.

H. S. Tzou, H. J. Lee, and S. M. Arnold, “Smart materials, precision sensors/actuators, smart structures, and structronic systems,” Mech. Adv. Mater. Struct. 11, 367–393 (2004).
[CrossRef]

Uy, J.

R. A. Guerrero, J. Barretto, J. Uy, I. Culaba, and B. Chan, “Effects of spontaneous surface buckling on the diffraction performance of an Au-coated elastomeric grating,” Opt. Commun. 270, 1–7 (2007).
[CrossRef]

Wang, H.

Y. Li, S. Jia, H. Wang, D. Chen, and K. Hane, “Pitch-variable transmission-type bulk gratings driven by shape memory alloy actuator,” Opt. Laser Technol. 34, 649–653 (2002).
[CrossRef]

Wong, C. W.

Xu, W.

W. M. Huang and W. Xu, “Hysteresis in shape memory alloys. Is it always a constant?” J. Mater. Sci. 40, 2985–2986 (2005).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

E. H. Khoo, A. Q. Liu, T. H. Cheng, J. Li, and D. Pinjala, “Light focusing via Rowland concave surface of photonic crystal,” Appl. Phys. Lett. 91, 221105 (2007).
[CrossRef]

IEEE Trans. Contr. Syst. Technol. (1)

J. Jayender, R. V. Patel, S. Nikumb, and M. Ostojic, “Modeling and control of shape memory alloy actuators,” IEEE Trans. Contr. Syst. Technol. 16, 279–287 (2008).
[CrossRef]

J. Mater. Sci. (1)

W. M. Huang and W. Xu, “Hysteresis in shape memory alloys. Is it always a constant?” J. Mater. Sci. 40, 2985–2986 (2005).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Vib. Acoust. (1)

M. Elahinia and H. Ashrafiuon, “Nonlinear control of a shape memory alloy actuated manipulator,” J. Vib. Acoust. 124, 566–575 (2002).
[CrossRef]

Mech. Adv. Mater. Struct. (1)

H. S. Tzou, H. J. Lee, and S. M. Arnold, “Smart materials, precision sensors/actuators, smart structures, and structronic systems,” Mech. Adv. Mater. Struct. 11, 367–393 (2004).
[CrossRef]

Opt. Commun. (1)

R. A. Guerrero, J. Barretto, J. Uy, I. Culaba, and B. Chan, “Effects of spontaneous surface buckling on the diffraction performance of an Au-coated elastomeric grating,” Opt. Commun. 270, 1–7 (2007).
[CrossRef]

Opt. Laser Technol. (1)

Y. Li, S. Jia, H. Wang, D. Chen, and K. Hane, “Pitch-variable transmission-type bulk gratings driven by shape memory alloy actuator,” Opt. Laser Technol. 34, 649–653 (2002).
[CrossRef]

Opt. Lett. (1)

Smart Mater. Struct. (1)

B. J. de Blonk and D. C. Lagoudas, “Actuation of elastomeric rods with embedded two-way shape memory alloy actuators,” Smart Mater. Struct. 7, 771–783 (1998).
[CrossRef]

Other (1)

K.Otsuka and C.M.Wayman, eds., Shape Memory Materials (Cambridge U. Press, 1998).

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Figures (6)

Fig. 1
Fig. 1

Training and actuation of an SMA wire: (a) the sample is shaped into a radius of curvature R o and annealed at T A f , (b) deformation into a new radius R d is possible at T < A f with the wire maintaining its new shape until (c) electrical heating above A s results in recovery of strain and an intermediate R < R d . R approaches R o as applied current increases. Grating curvature follows flexing of the wire.

Fig. 2
Fig. 2

Silicone replica of a planar diffraction grating is cylindrically bent to produce a concave variant. Curvature of the sample is due to partial strain recovery in the SMA wire during the elastomer curing process. Actual grating area is 25.4 mm × 12.7 mm .

Fig. 3
Fig. 3

Progression of steady-state grating curvature with increasing current: (a) initial R d is 170 mm at 0 A . Relatively low current values are needed for actuating the grating with (b) minor bending at 0.5 A and (c) a drastic change in radius at 1.0 A . Electrical heating induces phase transformations in the SMA until (d) full austenite recovery is achieved at 2.0 A with R R o .

Fig. 4
Fig. 4

Control of grating radius R with current. Rowland circle radius is tunable from 85 to 22 mm within the current range of 0 to 2.5 A . Fully actuated R at 25% of relaxed grating curvature is attained at 2.0 A . The theoretical curve assumes an exponential reduction in R toward a steady-state value.

Fig. 5
Fig. 5

Scanning of diffracted beam during grating actuation: (a) first-order diffraction is projected onto a screen at zero applied current. Electrical heating of the SMA modifies R and reorients the grating normal, resulting in (b) a translation of the diffracted beam. Steady-state Δ φ is 20.5 ° with respect to an arbitrary grating normal after 60 s at 2.0 A .

Fig. 6
Fig. 6

Dynamic response of the SMA-actuated grating in terms of Δ φ for different current levels. Time constants for the exponential fits vary with applied current.

Equations (5)

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sin α + sin φ = λ d ,
β = μ 1 + exp ( A s T T a + k σ ) ,
d T d t = c m [ p η ( T T o ) ] ,
R = R o [ 1 + exp ( I s I I a ) ] ,
Δ φ = Δ φ o [ 1 exp ( t τ ) ] ,

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