Abstract

Generation of vectorial optical fields with complex spatial distribution in the cross section is of great interest in areas where exotic optical fields are desired, including particle manipulation, optical nanofabrication, beam shaping and optical imaging. In this work, a vectorial optical field generator capable of creating arbitrarily complex beam cross section is designed, built and tested. Based on two reflective phase-only liquid crystal spatial light modulators, this generator is capable of controlling all the parameters of the spatial distributions of an optical field, including the phase, amplitude and polarization (ellipticity and orientation) on a pixel-by-pixel basis. Various optical fields containing phase, amplitude and/or polarization modulations are successfully generated and tested using Stokes parameter measurement to demonstrate the capability and versatility of this optical field generator.

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2013

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2008

2007

2006

2005

2004

2002

2000

1995

C. Ye, “Construction of an optical rotator using quarter-wave plates and an optical retarder,” Opt. Eng.34(10), 3031–3035 (1995).
[CrossRef]

Ahmed, M. A.

Barnett, S.

Bernet, S.

C. Maurer, A. Jesacher, S. Furhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys.9(3), 78 (2007).
[CrossRef]

Biss, D. P.

Bisson, J. F.

Brown, T. G.

Bu, J.

Campos, J.

Carnicer, A.

Chang, R. S.

Cheng, W.

Cižmár, T.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics5(6), 335–342 (2011).
[CrossRef]

Cottrell, D. M.

Courtial, J.

Dainty, C.

Davis, J. A.

Dholakia, K.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics5(6), 335–342 (2011).
[CrossRef]

Ding, J.

Franke-Arnold, S.

Furhapter, S.

C. Maurer, A. Jesacher, S. Furhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys.9(3), 78 (2007).
[CrossRef]

Gao, B. Z.

Gibson, G.

Graf, T.

Guo, C.-S.

Han, W.

Haus, J. W.

Hell, S. W.

S. W. Hell, “Far-field optical nanoscopy,” Science316(5828), 1153–1158 (2007).
[CrossRef] [PubMed]

Hernandez, T. M.

Iemmi, C.

Jesacher, A.

C. Maurer, A. Jesacher, S. Furhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys.9(3), 78 (2007).
[CrossRef]

Jureller, J. E.

Juvells, I.

Kenny, F.

Kozawa, Y.

Lara, D.

Leger, J.

Leger, J. R.

Levy, U.

Li, J.

Maluenda, D.

Martínez-Herrero, R.

Maurer, C.

C. Maurer, A. Jesacher, S. Furhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys.9(3), 78 (2007).
[CrossRef]

McNamara, D. E.

Moh, K. J.

Moreno, I.

Nesterov, A. V.

Ni, W.-J.

Niziev, V. G.

Padgett, M.

Park, S.

Pas’ko, V.

Ritsch-Marte, M.

C. Maurer, A. Jesacher, S. Furhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys.9(3), 78 (2007).
[CrossRef]

Rodríguez-Herrera, O. G.

Sand, D.

Sato, S.

Scherer, N. F.

Senatsky, Y.

Sonehara, T.

Toussaint, K. C.

Tripathi, S.

Ueda, K.

Vasnetsov, M.

Vogel, M. M.

Voss, A.

Wang, H.-T.

Wang, X.-L.

Yanai, A.

Ye, C.

C. Ye, “Construction of an optical rotator using quarter-wave plates and an optical retarder,” Opt. Eng.34(10), 3031–3035 (1995).
[CrossRef]

Youngworth, K. S.

Yuan, X.-C.

Yzuel, M. J.

Zhan, Q.

Zhu, S. W.

Adv. Opt. Photon.

Appl. Opt.

Nat. Photonics

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics5(6), 335–342 (2011).
[CrossRef]

New J. Phys.

C. Maurer, A. Jesacher, S. Furhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys.9(3), 78 (2007).
[CrossRef]

Opt. Eng.

C. Ye, “Construction of an optical rotator using quarter-wave plates and an optical retarder,” Opt. Eng.34(10), 3031–3035 (1995).
[CrossRef]

Opt. Express

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express12(22), 5448–5456 (2004).
[CrossRef] [PubMed]

Q. Zhan and J. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express10(7), 324–331 (2002).
[CrossRef] [PubMed]

W. Cheng, J. W. Haus, and Q. Zhan, “Propagation of vector vortex beams through a turbulent atmosphere,” Opt. Express17(20), 17829–17836 (2009).
[CrossRef] [PubMed]

Y. Kozawa and S. Sato, “Optical trapping of micrometer-sized dielectric particles by cylindrical vector beams,” Opt. Express18(10), 10828–10833 (2010).
[CrossRef] [PubMed]

I. Moreno, C. Iemmi, J. Campos, and M. J. Yzuel, “Jones matrix treatment for optical Fourier processors with structured polarization,” Opt. Express19(5), 4583–4594 (2011).
[CrossRef] [PubMed]

J. F. Bisson, J. Li, K. Ueda, and Y. Senatsky, “Radially polarized ring and arc beams of a neodymium laser with an intra-cavity axicon,” Opt. Express14(8), 3304–3311 (2006).
[CrossRef] [PubMed]

K. J. Moh, X.-C. Yuan, J. Bu, S. W. Zhu, and B. Z. Gao, “Surface plasmon resonance imaging of cell-substrate contacts with radially polarized beams,” Opt. Express16(25), 20734–20741 (2008).
[CrossRef] [PubMed]

A. Yanai and U. Levy, “Plasmonic focusing with a coaxial structure illuminated by radially polarized light,” Opt. Express17(2), 924–932 (2009).
[CrossRef] [PubMed]

I. Moreno, J. A. Davis, T. M. Hernandez, D. M. Cottrell, and D. Sand, “Complete polarization control of light from a liquid crystal spatial light modulator,” Opt. Express20(1), 364–376 (2012).
[CrossRef] [PubMed]

S. Tripathi and K. C. Toussaint., “Versatile generation of optical vector fields and vector beams using a non-interferometric approach,” Opt. Express20(10), 10788–10795 (2012).
[CrossRef] [PubMed]

F. Kenny, D. Lara, O. G. Rodríguez-Herrera, and C. Dainty, “Complete polarization and phase control for focus-shaping in high-NA microscopy,” Opt. Express20(13), 14015–14029 (2012).
[CrossRef] [PubMed]

D. Maluenda, I. Juvells, R. Martínez-Herrero, and A. Carnicer, “Reconfigurable beams with arbitrary polarization and shape distributions at a given plane,” Opt. Express21(5), 5432–5439 (2013).
[CrossRef] [PubMed]

Opt. Lett.

Science

S. W. Hell, “Far-field optical nanoscopy,” Science316(5828), 1153–1158 (2007).
[CrossRef] [PubMed]

Other

B. E. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley-Interscience, 2007).

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Figures (11)

Fig. 1
Fig. 1

Illustration of the spatially variant Polarization Rotator setup. (a) The Polarization Rotator comprised of QWP and reflective SLM; (b) Illustration of the effective rotation of the QWP fast axis for the incident (upper) and the reflected (lower) beams due to the mirror imaging of the laboratory coordinates in dashed lines.

Fig. 2
Fig. 2

Flow chart of the VOF-Gen. Modulations of all degree of freedom are realized in four SLM sections.

Fig. 3
Fig. 3

Schematic diagram of the experimental setup for the proposed VOF-Gen.

Fig. 4
Fig. 4

Pure phase modulation with spiral phase of topological charge 1 (left), 10 (middle) and 15 (right). The images are captured at the focal plane of a lens.

Fig. 5
Fig. 5

x-polarized “EO” logo coded in amplitude.

Fig. 6
Fig. 6

Far field intensities captured at the focal plane of a lens. (a) Radially polarized beam without pre-compensation phase; (b) radially polarized beam with pre-compensation phase.

Fig. 7
Fig. 7

Radially polarized beam generated by the VOF-Gen. (a) the total field; (b) shows the fields after a polarizer with transmission axis orientation indicated by black arrows at 0°, 45°, 90° and 135°, respectively; (c) intensity distribution of radially polarized beam superimposed with the polarization map.

Fig. 8
Fig. 8

Taiji pattern coded in circular polarization. The total field (left), the upper half Taiji pattern (upper right) in RCP and the lower half Taiji pattern (lower right) in LCP.

Fig. 9
Fig. 9

Ring structure with SOP continuously varying from azimuthal to radial direction as radius increases.

Fig. 10
Fig. 10

Double ring structure with amplitude and polarization rotation modulation. (a) The total field; (b) the linear polarization components with polarizer at 0°, 135° and 90°; (c) the polarization map.

Fig. 11
Fig. 11

Optical field with constant ellipticity and elevation angle along radial direction: (a) simulation, (b) experimental results and (c) histogram of ellipticity.

Equations (11)

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E d ( x,y )= A d ( x,y ) e j ϕ d ( x,y ) ( E xd ( x,y ) E yd ( x,y ) e j δ d ( x,y ) ),
M PR = M QWP_135° M refl M SLM M QWP_45° = 1 4 ( 1j 1j 1j 1j )( 1 0 0 1 )( e iδ( x,y ) 0 0 1 )( 1j 1+j 1+j 1j ) = e j δ( x,y ) 2 ( sin( δ( x,y ) 2 ) cos( δ( x,y ) 2 ) cos( δ( x,y ) 2 ) sin( δ( x,y ) 2 ) ) = e j( δ( x,y ) 2 ) R( 3π 2 δ( x,y ) 2 ),
J 1 ( x,y )= e j ϕ 1 ( x,y ) E 0 ( x,y )( 1 0 ),
J 2 ( x,y )= e j( ϕ 1 ( x,y )+ ϕ 2 ( x,y ) 2 +π ) sin( ϕ 2 ( x,y ) 2 ) E 0 ( x,y )( 1 0 ),
ϕ 2 ( x,y )=2 sin 1 ( A d ( x,y ) ).
J 3 ( x,y )= E 0 ( x,y ) e j( ϕ 1 ( x,y )+ ϕ 2 ( x,y ) 2 + ϕ 3 ( x,y ) 2 +π ) sin( ϕ 2 ( x,y ) 2 )( cos( ϕ 3 ( x,y ) 2 + π 2 ) sin( ϕ 3 ( x,y ) 2 + π 2 ) ).
ϕ 3 ( x,y )=2 tan 1 ( | E yd ( x,y ) | | E xd ( x,y ) | )π.
J 4 ( x,y )= E 0 ( x,y ) e j( ϕ 1 ( x,y )+ ϕ 2 ( x,y ) 2 + ϕ 3 ( x,y ) 2 +π ) sin( ϕ 2 ( x,y ) 2 )( cos( ϕ 3 ( x,y ) 2 + π 2 ) e j ϕ 4 ( x,y ) sin( ϕ 3 ( x,y ) 2 + π 2 ) ),
ϕ 4 ( x,y )= δ d ( x,y ),
ϕ output ( x,y )= ϕ 1 ( x,y )+ ϕ 2 ( x,y ) 2 + ϕ 3 ( x,y ) 2 +π.
ϕ 1 ( x,y )= ϕ d ( x,y )+ ϕ c ( x,y ),

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