Abstract

We propose an approach for implementation of an arbitrary vector beam based on a vector spatial light modulator (VSLM), which is simply composed by a phase-only spatial light modulator (SLM) and a composed half-wave plate with checkerboard structure. In combination with a four-phase encoding algorithm, the VSLM can transform a linear polarized Gaussian beam or a plane wave into a vector beam with both arbitrary spatial polarization and complex amplitude distributions in two dimensions. It is demonstrated that the VSLM can directly transform pure phase values into two orthogonal polarized complex values with high-diffraction efficiency. Compared with the existing methods for generation of vector beams with SLMs, our approach is on-axis and common-path with simple structure and only involves the zero-order diffraction. The proposed structure is also easier to make an integration and design portable device since it abstains from using optical elements such as special gratings, prisms, and reflectors.

© 2014 Optical Society of America

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H. Chen, J. Hao, B. F. Zhang, J. Xu, J. Ding, and H. T. Wang, Opt. Lett. 36, 3179 (2011).
[CrossRef]

M. Beresna, M. Gecevicius, P. G. Kazansky, and T. Gertus, Appl. Phys. Lett. 98, 201101 (2011).
[CrossRef]

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, J. Opt. 13, 064001 (2011).
[CrossRef]

B. Ma, B. Yao, Z. Li, and T. Ye, Appl. Opt. 50, 2588 (2011).
[CrossRef]

2010 (4)

J. L. Martínez, I. Moreno, J. A. Davis, T. J. Hernandez, and K. P. McAuley, Appl. Opt. 49, 5929 (2010).
[CrossRef]

X. L. Wang, Y. Li, J. Chen, C. S. Guo, J. Ding, and H. T. Wang, Opt. Express 18, 10786 (2010).
[CrossRef]

X. L. Wang, J. Chen, Y. Li, J. Ding, C. S. Guo, and H. T. Wang, Phys. Rev. Lett. 105, 253602 (2010).
[CrossRef]

Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, and K. Hamamoto, IEEE Photon. Technol. Lett. 22, 721 (2010).

2009 (1)

2008 (2)

T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Opt. Lett. 33, 122 (2008).
[CrossRef]

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

2007 (5)

2006 (2)

Q. Zhan, Opt. Lett. 31, 1726 (2006).
[CrossRef]

H. Wang, L. Shi, G. Yuan, X. Miao, W. Tan, and T. Chong, Appl. Phys. Lett. 89, 171102 (2006).
[CrossRef]

2005 (1)

2003 (2)

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

V. Arrizón, Opt. Lett. 28, 2521 (2003).
[CrossRef]

2001 (1)

R. L. Eriksen, P. C. Mogensen, and J. Glückstad, Opt. Commun. 187, 325 (2001).
[CrossRef]

1978 (1)

Arrizón, V.

Beresna, M.

M. Beresna, M. Gecevicius, P. G. Kazansky, and T. Gertus, Appl. Phys. Lett. 98, 201101 (2011).
[CrossRef]

Bernet, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
[CrossRef]

Carnicer, A.

Chen, H.

Chen, J.

X. L. Wang, Y. Li, J. Chen, C. S. Guo, J. Ding, and H. T. Wang, Opt. Express 18, 10786 (2010).
[CrossRef]

X. L. Wang, J. Chen, Y. Li, J. Ding, C. S. Guo, and H. T. Wang, Phys. Rev. Lett. 105, 253602 (2010).
[CrossRef]

Cheng, W.

Chong, C. T.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Chong, T.

H. Wang, L. Shi, G. Yuan, X. Miao, W. Tan, and T. Chong, Appl. Phys. Lett. 89, 171102 (2006).
[CrossRef]

Clegg, J. H.

Cottrell, D. M.

Dainty, C.

Davis, J. A.

Ding, J.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Duelk, M.

Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, and K. Hamamoto, IEEE Photon. Technol. Lett. 22, 721 (2010).

Erdei, G.

Eriksen, R. L.

R. L. Eriksen, P. C. Mogensen, and J. Glückstad, Opt. Commun. 187, 325 (2001).
[CrossRef]

Feurer, T.

M. Meier, V. Romano, and T. Feurer, Sci. Process 86, 329 (2007).

Fürhapter, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
[CrossRef]

Gecevicius, M.

M. Beresna, M. Gecevicius, P. G. Kazansky, and T. Gertus, Appl. Phys. Lett. 98, 201101 (2011).
[CrossRef]

Gertus, T.

M. Beresna, M. Gecevicius, P. G. Kazansky, and T. Gertus, Appl. Phys. Lett. 98, 201101 (2011).
[CrossRef]

Glückstad, J.

R. L. Eriksen, P. C. Mogensen, and J. Glückstad, Opt. Commun. 187, 325 (2001).
[CrossRef]

Göröcs, Z.

Guo, C. S.

Hamamoto, K.

Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, and K. Hamamoto, IEEE Photon. Technol. Lett. 22, 721 (2010).

Han, W.

Hao, J.

Heckenberg, N. R.

Hernandez, T. J.

Hernandez, T. M.

Hinokuma, Y.

Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, and K. Hamamoto, IEEE Photon. Technol. Lett. 22, 721 (2010).

Hsueh, C. K.

Jackel, S.

Jesacher, A.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
[CrossRef]

Jureller, J. E.

Juvells, I.

Karimi, E.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, J. Opt. 13, 064001 (2011).
[CrossRef]

Kazansky, P. G.

M. Beresna, M. Gecevicius, P. G. Kazansky, and T. Gertus, Appl. Phys. Lett. 98, 201101 (2011).
[CrossRef]

Kenny, F.

Koppa, P.

Lara, D.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Li, P.

Li, Y.

X. L. Wang, J. Chen, Y. Li, J. Ding, C. S. Guo, and H. T. Wang, Phys. Rev. Lett. 105, 253602 (2010).
[CrossRef]

X. L. Wang, Y. Li, J. Chen, C. S. Guo, J. Ding, and H. T. Wang, Opt. Express 18, 10786 (2010).
[CrossRef]

Li, Z.

Liu, S.

Lörincz, E.

Lukyanchuk, B.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Lumer, Y.

Ma, B.

Machavariani, G.

Maluenda, D.

Marrucci, L.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, J. Opt. 13, 064001 (2011).
[CrossRef]

Martínez, J. L.

Maurer, C.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
[CrossRef]

McAuley, K. P.

Meier, M.

M. Meier, V. Romano, and T. Feurer, Sci. Process 86, 329 (2007).

Meir, A.

Miao, X.

H. Wang, L. Shi, G. Yuan, X. Miao, W. Tan, and T. Chong, Appl. Phys. Lett. 89, 171102 (2006).
[CrossRef]

Minato, T.

Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, and K. Hamamoto, IEEE Photon. Technol. Lett. 22, 721 (2010).

Mogensen, P. C.

R. L. Eriksen, P. C. Mogensen, and J. Glückstad, Opt. Commun. 187, 325 (2001).
[CrossRef]

Moreno, I.

Moshe, I.

Nagali, E.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, J. Opt. 13, 064001 (2011).
[CrossRef]

Navaretti, P.

Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, and K. Hamamoto, IEEE Photon. Technol. Lett. 22, 721 (2010).

Neil, M. A. A.

Ni, W. J.

Nieminen, T. A.

Park, S. P.

Peng, T.

Piccirillo, B.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, J. Opt. 13, 064001 (2011).
[CrossRef]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Reményi, J.

Ritsch-Marte, M.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
[CrossRef]

Rodríguez-Herrera, O. G.

Rodríguez-Herrera, R.

Romano, V.

M. Meier, V. Romano, and T. Feurer, Sci. Process 86, 329 (2007).

Rubinsztein-Dunlop, H.

Sand, D.

Santamato, E.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, J. Opt. 13, 064001 (2011).
[CrossRef]

Sarkadi, T.

Sawchuk, A. A.

Scherer, N. F.

Sciarrino, F.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, J. Opt. 13, 064001 (2011).
[CrossRef]

Sheppard, C.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Shi, L.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

H. Wang, L. Shi, G. Yuan, X. Miao, W. Tan, and T. Chong, Appl. Phys. Lett. 89, 171102 (2006).
[CrossRef]

Slussarenko, S.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, J. Opt. 13, 064001 (2011).
[CrossRef]

Tan, W.

H. Wang, L. Shi, G. Yuan, X. Miao, W. Tan, and T. Chong, Appl. Phys. Lett. 89, 171102 (2006).
[CrossRef]

Toussaint, K. C.

Ujhelyi, F.

Velez, C.

Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, and K. Hamamoto, IEEE Photon. Technol. Lett. 22, 721 (2010).

Wang, H.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

H. Wang, L. Shi, G. Yuan, X. Miao, W. Tan, and T. Chong, Appl. Phys. Lett. 89, 171102 (2006).
[CrossRef]

Wang, H. T.

Wang, X. L.

Xu, J.

Yang, Y.

Yao, B.

Ye, T.

Yuan, G.

H. Wang, L. Shi, G. Yuan, X. Miao, W. Tan, and T. Chong, Appl. Phys. Lett. 89, 171102 (2006).
[CrossRef]

Zang, Z.

Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, and K. Hamamoto, IEEE Photon. Technol. Lett. 22, 721 (2010).

Zhan, Q.

Zhang, B. F.

Zhao, J.

Adv. Opt. Photon. (1)

Appl. Opt. (3)

Appl. Phys. Lett. (2)

H. Wang, L. Shi, G. Yuan, X. Miao, W. Tan, and T. Chong, Appl. Phys. Lett. 89, 171102 (2006).
[CrossRef]

M. Beresna, M. Gecevicius, P. G. Kazansky, and T. Gertus, Appl. Phys. Lett. 98, 201101 (2011).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, and K. Hamamoto, IEEE Photon. Technol. Lett. 22, 721 (2010).

J. Opt. (1)

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, J. Opt. 13, 064001 (2011).
[CrossRef]

Nat. Photonics (1)

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

New J. Phys. (1)

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
[CrossRef]

Opt. Commun. (1)

R. L. Eriksen, P. C. Mogensen, and J. Glückstad, Opt. Commun. 187, 325 (2001).
[CrossRef]

Opt. Express (6)

Opt. Lett. (9)

Phys. Rev. Lett. (2)

X. L. Wang, J. Chen, Y. Li, J. Ding, C. S. Guo, and H. T. Wang, Phys. Rev. Lett. 105, 253602 (2010).
[CrossRef]

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Sci. Process (1)

M. Meier, V. Romano, and T. Feurer, Sci. Process 86, 329 (2007).

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Figures (4)

Fig. 1.
Fig. 1.

Principle schematic of the double-channel VSLM. (a) Cell structure of the VSLM. (b) Example of the system for generation of vector beams based on the VSLM.

Fig. 2.
Fig. 2.

(a) Example of four-phase encoding patterns (only enlarged part is shown). (b) Checkerboard pattern displayed on a TN-LCD adjusted to its intensity modulating mode to form the required CHWP in experiments.

Fig. 3.
Fig. 3.

Experimental setup for demonstration of the feasibility of the VSLM.

Fig. 4.
Fig. 4.

Experimental results. (a) Intensity distribution of the output vector beam directly recorded by a CCD camera. (b)–(d) Intensity patterns when a linear analyzer placed before the CCD camera is oriented, respectively, at 45 deg, horizontally and vertically. (e) and (f) Interference patterns between a reference beam and two orthogonal polarization components of the vector beam.

Equations (9)

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E⃗(x,y)=[axexp[jφx(x,y)]ayexp[jφy(x,y)]],
u⃗(x,y)=[ux1(x,y)+ux2(x,y)uy1(x,y)+uy2(x,y)],
ux1=m,nexp[jϕx1(m,n)]w(xmpΔa,ynpΔb),ux2=m,nexp[jϕx2(m,n)]w(xmp+Δa,ynp+Δb),uy1=m,nexp[jϕy1(m,n)]w(xmpΔa,ynp+Δb),uy2=m,nexp[jϕy2(m,n)]w(xmp+Δa,ynpΔb),
U⃗(ξ,η)=sinc(aξ,bη)[Ux1(ξ,η)+Ux2(ξ,η)Uy1(ξ,η)+Uy2(ξ,η)],
Ux1=exp[j2πΔ(ξ+η)]m,nΦx1(ξm/p,ηn/p),Ux2=exp[j2πΔ(ξ+η)]m,nΦx2(ξm/p,ηn/p),Uy1=exp[j2πΔ(ξ+η)]m,nΦy1(ξm/p,ηn/p),Uy2=exp[j2πΔ(ξη)]m,nΦy1(ξm/p,ηn/p),
w(ξH,ηH)U(ξ,η)[Φx1(ξ,η)+Φx2(ξ,η)Φy1(ξ,η)+Φy2(ξ,η)],
u⃗o(x,y)=[exp[jϕx1(x,y)]+exp[jϕx2(x,y)]exp[jϕy1(x,y)]+exp[jϕy2(x,y)]].
ϕx1(r⃗)=φx(r⃗)+dxcos1[ax(r⃗)],ϕx2(r⃗)=φx(r⃗)dxcos1[ax(r⃗)],ϕy1(r⃗)=φy(r⃗)+dycos1[ay(r⃗)],ϕy2(r⃗)=φy(r⃗)dycos1[ay(r⃗)],
E⃗(r⃗)=[(r/Rx)exp[(r/Rx)2]exp[jlxθ](r/Ry)exp[(r/Ry)2]exp[jlyθ]],

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