Abstract

We present a general approach for optimizing the diffraction efficiency of a phase-type spatial light modulator (SLM). While the SLM displays a one-dimensional phase grating, the phase shift of one pixel in the grating is varied and the first-order diffraction efficiency is measured. This is repeated pixel-by-pixel to find the optimum phase encoding for the device that maximizes the diffraction efficiency. This method compensates for nonlinearity of the modulator phase response and is especially useful for optimizing modulators with less than 2π phase shift.

© 2013 Optical Society of America

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References

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2011 (3)

M. Padgett and R. Di Leonardo, Lab Chip 11, 1196 (2011).
[CrossRef]

K. Dholakia and T. Cizmar, Nat. Photonics 5, 335 (2011).
[CrossRef]

R. Bowman, V. D’Ambrosio, E. Rubino, O. Jedrkiewicz, P. Di Trapani, and M. J. Padgett, Eur. J. Phys. 199, 149 (2011).
[CrossRef]

2009 (1)

N. Savage, Nat. Photonics 3, 170 (2009).
[CrossRef]

2008 (2)

2006 (1)

2004 (1)

2003 (1)

D. G. Grier, Nature 424, 810 (2003).
[CrossRef]

1970 (1)

H. Dammann, Optik 31, 95 (1970).

Bowman, R.

R. Bowman, V. D’Ambrosio, E. Rubino, O. Jedrkiewicz, P. Di Trapani, and M. J. Padgett, Eur. J. Phys. 199, 149 (2011).
[CrossRef]

Campos, J.

Cizmar, T.

K. Dholakia and T. Cizmar, Nat. Photonics 5, 335 (2011).
[CrossRef]

Cooper, J.

Courtial, J.

D’Ambrosio, V.

R. Bowman, V. D’Ambrosio, E. Rubino, O. Jedrkiewicz, P. Di Trapani, and M. J. Padgett, Eur. J. Phys. 199, 149 (2011).
[CrossRef]

Dammann, H.

H. Dammann, Optik 31, 95 (1970).

Dholakia, K.

K. Dholakia and T. Cizmar, Nat. Photonics 5, 335 (2011).
[CrossRef]

Di Leonardo, R.

M. Padgett and R. Di Leonardo, Lab Chip 11, 1196 (2011).
[CrossRef]

Di Trapani, P.

R. Bowman, V. D’Ambrosio, E. Rubino, O. Jedrkiewicz, P. Di Trapani, and M. J. Padgett, Eur. J. Phys. 199, 149 (2011).
[CrossRef]

Fernández, E.

Gibson, G.

Grier, D. G.

D. G. Grier, Nature 424, 810 (2003).
[CrossRef]

Hahn, J.

Iemmi, C.

Jedrkiewicz, O.

R. Bowman, V. D’Ambrosio, E. Rubino, O. Jedrkiewicz, P. Di Trapani, and M. J. Padgett, Eur. J. Phys. 199, 149 (2011).
[CrossRef]

Jordan, P.

Karunwi, K.

Kim, H.

Laczik, Z. J.

Leach, J.

Lee, B.

Lizana, A.

Márquez, A.

Moreno, I.

Padgett, M.

Padgett, M. J.

R. Bowman, V. D’Ambrosio, E. Rubino, O. Jedrkiewicz, P. Di Trapani, and M. J. Padgett, Eur. J. Phys. 199, 149 (2011).
[CrossRef]

Rubino, E.

R. Bowman, V. D’Ambrosio, E. Rubino, O. Jedrkiewicz, P. Di Trapani, and M. J. Padgett, Eur. J. Phys. 199, 149 (2011).
[CrossRef]

Savage, N.

N. Savage, Nat. Photonics 3, 170 (2009).
[CrossRef]

Sinclair, G.

Thomson, L.

Wulff, K.

Yzuel, M. J.

Appl. Opt. (3)

Eur. J. Phys. (1)

R. Bowman, V. D’Ambrosio, E. Rubino, O. Jedrkiewicz, P. Di Trapani, and M. J. Padgett, Eur. J. Phys. 199, 149 (2011).
[CrossRef]

Lab Chip (1)

M. Padgett and R. Di Leonardo, Lab Chip 11, 1196 (2011).
[CrossRef]

Nat. Photonics (2)

K. Dholakia and T. Cizmar, Nat. Photonics 5, 335 (2011).
[CrossRef]

N. Savage, Nat. Photonics 3, 170 (2009).
[CrossRef]

Nature (1)

D. G. Grier, Nature 424, 810 (2003).
[CrossRef]

Opt. Express (1)

Optik (1)

H. Dammann, Optik 31, 95 (1970).

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Figures (6)

Fig. 1.
Fig. 1.

One unit cell of the quantized phase of a SLM, showing the ideal linear phase (dashed) and the phase error (shaded).

Fig. 2.
Fig. 2.

Schematic of SLM optimization algorithm. (a) Simulated nonlinear SLM response with reduced phase shift. (b) Initial identity LUT showing three example gray values that are varied (red dotted; green dashed; and blue dotted–dashed). (c) Resultant diffraction efficiency curves and (d) optimized LUT.

Fig. 3.
Fig. 3.

One unit cell of the linearized, phase saturated output of the SLM after employing the optimized LUT. The inset shows the phase obtained with the identity LUT. In both cases, the phase error is shown as shaded.

Fig. 4.
Fig. 4.

Experiment to measure first-order diffracted power.

Fig. 5.
Fig. 5.

Measured diffracted power (normalized) as a function of output gray level for three choices of input gray level. The parabolic fit for each data set is also shown.

Fig. 6.
Fig. 6.

Optimized SLM gray level LUT for 1064 nm showing nonlinearity and saturated phase encoding. The inset shows the optimized LUT for 532 nm where the phase shift is greater than 2π.

Equations (5)

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a1=k2π02π/keikx+iΔϕ(x)eikxdx=k2π02π/keiΔϕ(x)dx.
a1k2π02π/k[1+iΔϕ(x)12Δϕ2(x)]dx1+ik2π02π/kΔϕ(x)dx12k2π02π/kΔϕ2(x)dx1+iΔϕ(x)12Δϕ2(x),
η1=|a1|21+Δϕ(x)2Δϕ2(x)1σΔϕ2.
η1=[sin(π/Z)π/Z]21π23Z2.
η11i=1NΔϕi2/N

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