Abstract

Methods for generating beams with arbitrary polarization based on the use of liquid crystal displays have recently attracted interest from a wide range of sources. In this paper we present a technique for generating beams with arbitrary polarization and shape distributions at a given plane using a Mach-Zehnder setup. The transverse components of the incident beam are processed independently by means of spatial light modulators placed in each path of the interferometer. The modulators display computer generated holograms designed to dynamically encode any amplitude value and polarization state for each point of the wavefront in a given plane. The steps required to design such beams are described in detail. Several beams performing different polarization and intensity landscapes have been experimentally implemented. The results obtained demonstrate the capability of the proposed technique to tailor the amplitude and polarization of the beam simultaneously.

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  19. V. Arrizón, L. González, R. Ponce, and A. Serrano-Heredia, “Computer-generated holograms with optimum bandwidths obtained with twisted-nematic liquid-crystal displays,” Appl. Opt.44, 1625–1634 (2005).
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  21. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University Press, 1999).

2012 (3)

2011 (2)

H. Chen, J. Hao, B.F. Zhang, J. Xu, J. Ding, and H.T. Wang, “Generation of vector beam with space-variant distribution of both polarization and phase,” Opt. Lett.36, 3179–3181 (2011).
[CrossRef] [PubMed]

I. Moreno, C. Iemmi, J. Campos, and M.J. Yzuel, “Jones matrix treatment for optical fourier processors with structured polarization,” Opt. Lett.19, 4583–4594 (2011).

2010 (2)

2009 (1)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics1, 1–57 (2009).
[CrossRef]

2007 (2)

2006 (1)

2005 (2)

2004 (1)

R. Tudela, E. Martin-Badosa, I. Labastida, S. Vallmitjana, and A. Carnicer, “Wavefront reconstruction by adding modulation capabilities of two liquid crystal devices,” Opt. Eng.43, 2650–2657 (2004).
[CrossRef]

2003 (1)

2002 (1)

2001 (1)

R.L. Eriksen, P.C. Mogensen, and J. Glückstad, “Elliptical polarisation encoding in two dimensions using phase-only spatial light modulators,” Opt. Commun.187, 325–336 (2001).
[CrossRef]

2000 (1)

1997 (1)

E. Martín-Badosa, A. Carnicer, I. Juvells, and S. Vallmitjana, “Complex modulation characterization of liquid crystal devices by interferometric data correlation,” Meas. Sci. Technol.8, 764–772 (1997).
[CrossRef]

1993 (1)

Arrizón, V.

Bernet, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys.9, 78 (2007).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University Press, 1999).

Campos, J.

I. Moreno, C. Iemmi, J. Campos, and M.J. Yzuel, “Jones matrix treatment for optical fourier processors with structured polarization,” Opt. Lett.19, 4583–4594 (2011).

Carnicer, A.

R. Tudela, E. Martin-Badosa, I. Labastida, S. Vallmitjana, and A. Carnicer, “Wavefront reconstruction by adding modulation capabilities of two liquid crystal devices,” Opt. Eng.43, 2650–2657 (2004).
[CrossRef]

E. Martín-Badosa, A. Carnicer, I. Juvells, and S. Vallmitjana, “Complex modulation characterization of liquid crystal devices by interferometric data correlation,” Meas. Sci. Technol.8, 764–772 (1997).
[CrossRef]

Chen, H.

Chen, J.

Cottrell, D.M.

Dainty, C.

Davis, J.A.

Ding, J.

Eriksen, R.L.

R.L. Eriksen, P.C. Mogensen, and J. Glückstad, “Elliptical polarisation encoding in two dimensions using phase-only spatial light modulators,” Opt. Commun.187, 325–336 (2001).
[CrossRef]

Flores-Pérez, A.

Fürhapter, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys.9, 78 (2007).
[CrossRef]

Glückstad, J.

R.L. Eriksen, P.C. Mogensen, and J. Glückstad, “Elliptical polarisation encoding in two dimensions using phase-only spatial light modulators,” Opt. Commun.187, 325–336 (2001).
[CrossRef]

González, L.

Guo, C.S.

Hao, J.

Hernández-Hernández, J.

Iemmi, C.

I. Moreno, C. Iemmi, J. Campos, and M.J. Yzuel, “Jones matrix treatment for optical fourier processors with structured polarization,” Opt. Lett.19, 4583–4594 (2011).

Jáuregui, R.

Jesacher, A.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys.9, 78 (2007).
[CrossRef]

Jureller, J.E.

Juškaitis, R.

Juvells, I.

E. Martín-Badosa, A. Carnicer, I. Juvells, and S. Vallmitjana, “Complex modulation characterization of liquid crystal devices by interferometric data correlation,” Meas. Sci. Technol.8, 764–772 (1997).
[CrossRef]

Kenny, F.

Kim, G.H.

Kimura, W.D.

Labastida, I.

R. Tudela, E. Martin-Badosa, I. Labastida, S. Vallmitjana, and A. Carnicer, “Wavefront reconstruction by adding modulation capabilities of two liquid crystal devices,” Opt. Eng.43, 2650–2657 (2004).
[CrossRef]

Lara, D.

Li, P.

Li, Y.

Liu, S.

Martin-Badosa, E.

R. Tudela, E. Martin-Badosa, I. Labastida, S. Vallmitjana, and A. Carnicer, “Wavefront reconstruction by adding modulation capabilities of two liquid crystal devices,” Opt. Eng.43, 2650–2657 (2004).
[CrossRef]

Martín-Badosa, E.

E. Martín-Badosa, A. Carnicer, I. Juvells, and S. Vallmitjana, “Complex modulation characterization of liquid crystal devices by interferometric data correlation,” Meas. Sci. Technol.8, 764–772 (1997).
[CrossRef]

Massoumian, F.

Maurer, C.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys.9, 78 (2007).
[CrossRef]

McNamara, D.E.

Mogensen, P.C.

R.L. Eriksen, P.C. Mogensen, and J. Glückstad, “Elliptical polarisation encoding in two dimensions using phase-only spatial light modulators,” Opt. Commun.187, 325–336 (2001).
[CrossRef]

Moreno, I.

I. Moreno, C. Iemmi, J. Campos, and M.J. Yzuel, “Jones matrix treatment for optical fourier processors with structured polarization,” Opt. Lett.19, 4583–4594 (2011).

Neil, M.A.A.

Ni, W.J.

Park, S.P.

Peng, T.

Ponce, R.

Ritsch-Marte, M.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys.9, 78 (2007).
[CrossRef]

Rodríguez-Herrera, O.G.

Scherer, N.F.

Serrano-Heredia, A.

Sonehara, T.

Tidwell, S.C.

Toussaint, K.C.

S. Tripathi and K.C. Toussaint, “Versatile generation of optical vector fields and vector beams using a non-interferometric approach,” Opt. Lett.20, 10788–10795 (2012).

K.C. Toussaint, S.P. Park, J.E. Jureller, and N.F. Scherer, “Generation of optical vector beams with a diffractive optical element interferometer,” Opt. Lett.30, 2846–2848 (2005).
[CrossRef] [PubMed]

Tripathi, S.

S. Tripathi and K.C. Toussaint, “Versatile generation of optical vector fields and vector beams using a non-interferometric approach,” Opt. Lett.20, 10788–10795 (2012).

Tudela, R.

R. Tudela, E. Martin-Badosa, I. Labastida, S. Vallmitjana, and A. Carnicer, “Wavefront reconstruction by adding modulation capabilities of two liquid crystal devices,” Opt. Eng.43, 2650–2657 (2004).
[CrossRef]

Vallmitjana, S.

R. Tudela, E. Martin-Badosa, I. Labastida, S. Vallmitjana, and A. Carnicer, “Wavefront reconstruction by adding modulation capabilities of two liquid crystal devices,” Opt. Eng.43, 2650–2657 (2004).
[CrossRef]

E. Martín-Badosa, A. Carnicer, I. Juvells, and S. Vallmitjana, “Complex modulation characterization of liquid crystal devices by interferometric data correlation,” Meas. Sci. Technol.8, 764–772 (1997).
[CrossRef]

Volke-Sepúlveda, K.

Wang, H.T.

Wang, X.L.

Wilson, T.

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University Press, 1999).

Xu, J.

Yzuel, M.J.

I. Moreno, C. Iemmi, J. Campos, and M.J. Yzuel, “Jones matrix treatment for optical fourier processors with structured polarization,” Opt. Lett.19, 4583–4594 (2011).

Zhan, Q.

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics1, 1–57 (2009).
[CrossRef]

Zhang, B.F.

Zhao, J.

Zheng, Z.

Adv. Opt. Photonics (1)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics1, 1–57 (2009).
[CrossRef]

Appl. Opt. (3)

Meas. Sci. Technol. (1)

E. Martín-Badosa, A. Carnicer, I. Juvells, and S. Vallmitjana, “Complex modulation characterization of liquid crystal devices by interferometric data correlation,” Meas. Sci. Technol.8, 764–772 (1997).
[CrossRef]

New J. Phys. (1)

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys.9, 78 (2007).
[CrossRef]

Opt. Commun. (1)

R.L. Eriksen, P.C. Mogensen, and J. Glückstad, “Elliptical polarisation encoding in two dimensions using phase-only spatial light modulators,” Opt. Commun.187, 325–336 (2001).
[CrossRef]

Opt. Eng. (1)

R. Tudela, E. Martin-Badosa, I. Labastida, S. Vallmitjana, and A. Carnicer, “Wavefront reconstruction by adding modulation capabilities of two liquid crystal devices,” Opt. Eng.43, 2650–2657 (2004).
[CrossRef]

Opt. Express (3)

Opt. Lett. (9)

H. Chen, J. Hao, B.F. Zhang, J. Xu, J. Ding, and H.T. Wang, “Generation of vector beam with space-variant distribution of both polarization and phase,” Opt. Lett.36, 3179–3181 (2011).
[CrossRef] [PubMed]

I. Moreno, C. Iemmi, J. Campos, and M.J. Yzuel, “Jones matrix treatment for optical fourier processors with structured polarization,” Opt. Lett.19, 4583–4594 (2011).

S. Tripathi and K.C. Toussaint, “Versatile generation of optical vector fields and vector beams using a non-interferometric approach,” Opt. Lett.20, 10788–10795 (2012).

V. Arrizón, “Complex modulation with a twisted-nematic liquid-crystal spatial light modulator: double-pixel approach,” Opt. Lett.28, 1359–1361 (2003).
[CrossRef] [PubMed]

X.L. Wang, J. Ding, W.J. Ni, C.S. Guo, and H.T. Wang, “Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement,” Opt. Lett.32, 3549–3551 (2007).
[CrossRef] [PubMed]

H. Chen, Z. Zheng, B.F. Zhang, J. Ding, and H.T. Wang, “Polarization structuring of focused field through polarization-only modulation of incident beam,” Opt. Lett.35, 2825–2827 (2010).
[CrossRef] [PubMed]

M.A.A. Neil, F. Massoumian, R. Juškaitis, and T. Wilson, “Method for the generation of arbitrary complex vector wave fronts,” Opt. Lett.27, 1929–1931 (2002).
[CrossRef]

K.C. Toussaint, S.P. Park, J.E. Jureller, and N.F. Scherer, “Generation of optical vector beams with a diffractive optical element interferometer,” Opt. Lett.30, 2846–2848 (2005).
[CrossRef] [PubMed]

A. Flores-Pérez, J. Hernández-Hernández, R. Jáuregui, and K. Volke-Sepúlveda, “Experimental generation and analysis of first-order TE and TM Bessel modes in free space,” Opt. Lett.31, 1732–1734 (2006).
[CrossRef] [PubMed]

Other (1)

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University Press, 1999).

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Figures (6)

Fig. 1:
Fig. 1:

Sketch of the experimental setup.

Fig. 2:
Fig. 2:

(a) Modulation response M for the Holoeye displays SLM1 and SLM2. The Fig. also shows how Cnm can be accessed as a combination of M n m ( 1 ), M n m ( 2 ), E n m ( 1 ) and E n m ( 2 ). (b) Double pixel hologram approach: four pixels of the SLM that have values M n m ( 1 ) and M n m ( 2 ) are required to encode each complex value, Cnm.

Fig. 3:
Fig. 3:

Accessible values using the codification procedure (SLM1 in blue, SLM2 in red). The black dashed line delimits the useful values.

Fig. 4:
Fig. 4:

(a) Gaussian beam with radial polarization, (b) Gaussian beam with ‘star-like’ polarization, (c) L 1 0 Laguerre-Gauss beam displaying different polarizations in the external ring and in the inner disc and (d) doughnut-shaped beam with ϕ(x, y) = ±2tan−1(y/x).

Fig. 5:
Fig. 5:

Experimental intensity patterns for different positions of the analyzer P2. All the experimental images were recorded using an 8-bit CCD and displayed in false color using the hot colormap to help assess the imperfections of the experimental beam.

Fig. 6:
Fig. 6:

Experimentally measured Stoke parameters: (a) Radially polarized elliptically-shaped Gaussian beam, (b) S0, (c) S1, (d) S2, (e) S4, (f) P.

Equations (8)

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E out ( x , y ) = E in 1 ( x , y ) h 1 ( x , y ) e 1 + E in 2 ( x , y ) h 2 ( x , y ) e 2 = = A 1 ( x , y ) exp ( i ϕ 1 ( x , y ) ) e 1 + A 2 ( x , y ) exp ( i ϕ 2 ( x , y ) ) e 2 .
A s h ( x , y ) exp ( x 2 + y 2 w 0 2 ) L 1 0 ( x 2 + y 2 w 0 2 )
A s h ( x , y ) ( x 2 + y 2 ) 1 / 2 exp ( x 2 + y 2 w 0 2 )
S 0 = I ( 0 ° , 0 ) + I ( 90 ° , 0 )
S 1 = I ( 0 ° , 0 ) I ( 90 ° , 0 )
S 2 = I ( 45 ° , 0 ) I ( 135 ° , 0 )
S 3 = I ( 45 ° , π / 2 ) I ( 135 ° , π / 2 ) ,
P = S 1 2 + S 2 2 + S 3 2 S 0 .

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