Abstract

We report a method to maximize the broadband modulation diffraction efficiency of liquid-crystal spatial light modulators for polychromatic applications requiring a wide range of wavelengths. An optimized encoding pattern based on the minimum Euclidean projection principle is applied in order to increase the diffraction efficiency at large wavelengths that exhibit phase modulation depth lower than 2π. We demonstrate modulation efficiencies over 80% on a wavelength range from 454 to 633 nm, which can reach up to 98% when the range is reduced to 60 nm. Experimental results are shown to confirm the calculations.

© 2012 Optical Society of America

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2009 (1)

L. Martínez-León, P. Clemente, E. Tajahuerce, G. Mínguez-Vega, O. Mendoza-Yero, M. Fernández-Alonso, J. Lancis, V. Climent, and P. Andrés, Appl. Phys. Lett. 94, 011104 (2009).
[CrossRef]

2008 (1)

A. Lizana, A. Marquez, I. Moreno, C. Iemmi, J. Campos, and M. J. Yzuel, J. Eur. Opt. Soc. Rapid Publ. 3, 08012(2008).
[CrossRef]

2007 (2)

2006 (1)

2004 (3)

2001 (2)

1995 (2)

I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, Jpn. J. Appl. Phys. 34, 6423 (1995).
[CrossRef]

M. Kuittinen and H. P. Herzig, Opt. Lett. 20, 2156 (1995).
[CrossRef]

1992 (1)

Andrés, P.

L. Martínez-León, P. Clemente, E. Tajahuerce, G. Mínguez-Vega, O. Mendoza-Yero, M. Fernández-Alonso, J. Lancis, V. Climent, and P. Andrés, Appl. Phys. Lett. 94, 011104 (2009).
[CrossRef]

Bartels, R. A.

Boer, G.

Brooker, G.

Buralli, D. A.

Campos, J.

A. Lizana, A. Marquez, I. Moreno, C. Iemmi, J. Campos, and M. J. Yzuel, J. Eur. Opt. Soc. Rapid Publ. 3, 08012(2008).
[CrossRef]

A. Márquez, C. Iemmi, J. Campos, and M. J. Yzuel, Opt. Lett. 31, 392 (2006).
[CrossRef]

I. Moreno, C. Iemmi, A. Márquez, J. Campos, and M. J. Yzuel, Appl. Opt. 43, 6278 (2004).
[CrossRef]

I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, Jpn. J. Appl. Phys. 34, 6423 (1995).
[CrossRef]

Clemente, P.

L. Martínez-León, P. Clemente, E. Tajahuerce, G. Mínguez-Vega, O. Mendoza-Yero, M. Fernández-Alonso, J. Lancis, V. Climent, and P. Andrés, Appl. Phys. Lett. 94, 011104 (2009).
[CrossRef]

Climent, V.

L. Martínez-León, P. Clemente, E. Tajahuerce, G. Mínguez-Vega, O. Mendoza-Yero, M. Fernández-Alonso, J. Lancis, V. Climent, and P. Andrés, Appl. Phys. Lett. 94, 011104 (2009).
[CrossRef]

Dändliker, R.

Fernández-Alonso, M.

L. Martínez-León, P. Clemente, E. Tajahuerce, G. Mínguez-Vega, O. Mendoza-Yero, M. Fernández-Alonso, J. Lancis, V. Climent, and P. Andrés, Appl. Phys. Lett. 94, 011104 (2009).
[CrossRef]

Gorecki, C.

I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, Jpn. J. Appl. Phys. 34, 6423 (1995).
[CrossRef]

Herzig, H. P.

Hirao, K.

Iemmi, C.

Juday, R. D.

Kuittinen, M.

Kuroiwa, Y.

Lancis, J.

L. Martínez-León, P. Clemente, E. Tajahuerce, G. Mínguez-Vega, O. Mendoza-Yero, M. Fernández-Alonso, J. Lancis, V. Climent, and P. Andrés, Appl. Phys. Lett. 94, 011104 (2009).
[CrossRef]

Levy, U.

Lizana, A.

A. Lizana, A. Marquez, I. Moreno, C. Iemmi, J. Campos, and M. J. Yzuel, J. Eur. Opt. Soc. Rapid Publ. 3, 08012(2008).
[CrossRef]

Marom, E.

Marquez, A.

A. Lizana, A. Marquez, I. Moreno, C. Iemmi, J. Campos, and M. J. Yzuel, J. Eur. Opt. Soc. Rapid Publ. 3, 08012(2008).
[CrossRef]

Márquez, A.

Martínez-León, L.

L. Martínez-León, P. Clemente, E. Tajahuerce, G. Mínguez-Vega, O. Mendoza-Yero, M. Fernández-Alonso, J. Lancis, V. Climent, and P. Andrés, Appl. Phys. Lett. 94, 011104 (2009).
[CrossRef]

Mendlovic, D.

Mendoza-Yero, O.

L. Martínez-León, P. Clemente, E. Tajahuerce, G. Mínguez-Vega, O. Mendoza-Yero, M. Fernández-Alonso, J. Lancis, V. Climent, and P. Andrés, Appl. Phys. Lett. 94, 011104 (2009).
[CrossRef]

Mínguez-Vega, G.

L. Martínez-León, P. Clemente, E. Tajahuerce, G. Mínguez-Vega, O. Mendoza-Yero, M. Fernández-Alonso, J. Lancis, V. Climent, and P. Andrés, Appl. Phys. Lett. 94, 011104 (2009).
[CrossRef]

Moreno, I.

A. Lizana, A. Marquez, I. Moreno, C. Iemmi, J. Campos, and M. J. Yzuel, J. Eur. Opt. Soc. Rapid Publ. 3, 08012(2008).
[CrossRef]

I. Moreno, C. Iemmi, A. Márquez, J. Campos, and M. J. Yzuel, Appl. Opt. 43, 6278 (2004).
[CrossRef]

I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, Jpn. J. Appl. Phys. 34, 6423 (1995).
[CrossRef]

Morris, G. M.

Narita, Y.

Rosen, J.

Ruffieux, P.

Scharf, T.

Schlup, P.

Seitz, P.

Tajahuerce, E.

L. Martínez-León, P. Clemente, E. Tajahuerce, G. Mínguez-Vega, O. Mendoza-Yero, M. Fernández-Alonso, J. Lancis, V. Climent, and P. Andrés, Appl. Phys. Lett. 94, 011104 (2009).
[CrossRef]

Takeshima, N.

Tanaka, S.

Wilson, J. W.

Yzuel, M. J.

A. Lizana, A. Marquez, I. Moreno, C. Iemmi, J. Campos, and M. J. Yzuel, J. Eur. Opt. Soc. Rapid Publ. 3, 08012(2008).
[CrossRef]

A. Márquez, C. Iemmi, J. Campos, and M. J. Yzuel, Opt. Lett. 31, 392 (2006).
[CrossRef]

I. Moreno, C. Iemmi, A. Márquez, J. Campos, and M. J. Yzuel, Appl. Opt. 43, 6278 (2004).
[CrossRef]

I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, Jpn. J. Appl. Phys. 34, 6423 (1995).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Characterization of the LCD-SLM used in the experiments. (a) Phase modulation p(φ) of each tested wavelength (the inset shows the maximum phase modulation as a function of the wavelength), (b) phase modulation of each wavelength when the broadband optimized encoding is addressed to the LCD-SLM. Both (a) and (b) are represented versus the addressed phase φ.

Fig. 2.
Fig. 2.

ηm versus wavelength (a) in the range 454 to 633 nm (lines represent calculated values, whereas single points represent experimental results) and (b) in the range 454 to 514 nm.

Fig. 3.
Fig. 3.

Images of the measured diffracted orders.

Equations (7)

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

m(x,y)=a[φ(x,y)]exp{ip[φ(x,y)]},
m(φ)=a(φ)exp[ip(φ)]=α=Gαexp(iαφ),
Gα=12π02πa(φ)exp[ip(φ)]exp(iαφ)dφ.
ηm=|G1|2=sinc2(c),
p(φ)={φφ<εεε<φ<ε/2+π0φ>ε/2+π.
ηm=|G1|2=[ε2π1πsin(ε2)]2.
ηm(λ)=[(εopt2π)sinc(ελεopt2π)+2πcos(εopt4)sin(ελ2εopt4)]2,

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