Abstract

Based on the properties of the dove prism and the Fourier optics approach, the coordinate relationships among four spatial light modulator (SLM) sections in a vectorial optical field generator are derived and experimentally verified. Taking the coordinate system of the first SLM section as a reference, the coordinate displacements between the first section and subsequent sections are determined via employing specially designed four-quadrant patterns, which enable the visualization of the degree of freedom controlled by each SLM section. A complex optical field could be accurately generated through combining the derived coordinate relationships and pre-compensation of the measured coordinate displacements. Several typical complex optical fields are experimentally generated to demonstrate the validity of the proposed transverse alignment method.

© 2017 Optical Society of America

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References

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2016 (1)

2015 (1)

2014 (1)

2013 (1)

2012 (1)

2010 (1)

W. Chen and Q. Zhan, “Diffraction limited focusing with controllable arbitrary three-dimensional polarization,” J. Opt. 12, 045707 (2010).
[Crossref]

2009 (2)

2007 (1)

2006 (1)

2004 (1)

2002 (2)

Barnett, S.

Chen, W.

W. Chen and Q. Zhan, “Diffraction limited focusing with controllable arbitrary three-dimensional polarization,” J. Opt. 12, 045707 (2010).
[Crossref]

Cheng, W.

Cottrell, D. M.

Courtial, J.

Davis, J. A.

Ding, J.

Franke-Arnold, S.

Gibson, G.

Guo, C.-S.

Han, W.

Haus, J. W.

Hernandez, T. M.

Jang, M.

Judkewitz, B.

Kim, T.

Leger, J. R.

Leportier, T.

Moreno, I.

Ni, W.-J.

Padgett, M.

Park, M.

Pas’ko, V.

Ruan, H.

Sand, D.

Vasnetsov, M.

Wang, H.-T.

Wang, X.-L.

Yang, C.

Yang, Y.

Zhan, Q.

Zhou, H.

Adv. Opt. Photon. (1)

Appl. Opt. (2)

J. Display Technol. (1)

J. Opt. (1)

W. Chen and Q. Zhan, “Diffraction limited focusing with controllable arbitrary three-dimensional polarization,” J. Opt. 12, 045707 (2010).
[Crossref]

Opt. Express (6)

Opt. Lett. (2)

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Figures (12)

Fig. 1.
Fig. 1.

(a) Diagram of the VOF-Gen system. (b)–(e) Illustration of the regions illuminated by the incident beam on SLM Sections 1–4, respectively.

Fig. 2.
Fig. 2.

Four-quadrant phase pattern for SLM Section 1.

Fig. 3.
Fig. 3.

Four-quadrant phase patterns and experimental results for measuring the coordinate displacements between SLM Sections 2 and 1. (a)–(c) Phase patterns for SLM Section 2 without coordinate shift, only with vertical coordinate shift, and with coordinate shifts in both directions, respectively. (d)–(f) Experimental results corresponding to patterns in (a)–(c), respectively.

Fig. 4.
Fig. 4.

Four-quadrant phase patterns and experimental results for measuring the coordinate displacements between SLM Sections 3 and 1. (a)–(c) Phase patterns for SLM Section 3 without coordinate shift, only with vertical coordinate shift, and with coordinate shifts in both directions, respectively. (d)–(f) Experimental results corresponding to patterns in (a)–(c), respectively.

Fig. 5.
Fig. 5.

Four-quadrant phase patterns and experimental results for measuring the coordinate displacements between SLM Sections 4 and 1. (a)–(c) Phase patterns for SLM Section 4 without coordinate shift, only with vertical coordinate shift, and with coordinate shifts in both directions, respectively. (d)–(f) Experimental results corresponding to patterns in (a)–(c), respectively.

Fig. 6.
Fig. 6.

Reference phase pattern applied to SLM Section 1.

Fig. 7.
Fig. 7.

Patterns (a) and (c) and experimental results (b) and (d) for the verification of the coordinate relationship between SLM Sections 2 and 1. The first and second rows are with and without using the derived relationship, respectively.

Fig. 8.
Fig. 8.

Patterns (a) and (c) and experimental results (b) and (d) for the verification of the coordinate relationship between SLM Sections 3 and 1. The first and second rows are with and without using the derived relationship, respectively.

Fig. 9.
Fig. 9.

Patterns (a) and (c) and experimental results (b) and (d) for the verification of the coordinate relationship between SLM Sections 4 and 1. The first and second rows are with and without using the derived relationship, respectively.

Fig. 10.
Fig. 10.

Phase patterns to generate the elliptically polarized beam with topological charge 1, elevation angle 30° and ellipticity π/10. (a) Without using the proposed transverse alignment method. (b) Using the proposed transverse alignment method. The numbers 1–4 stand for the phase pattern applied to SLM Sections 1–4, respectively.

Fig. 11.
Fig. 11.

Experimental results for the generation of the designed elliptically polarized beam. (a) Intensity distribution of the output beam with polarization map corresponding to the pattern without using the proposed transverse alignment method, histograms of (b) ellipticity and (c) elevation angle of the generated beam in (a). (d) Intensity distribution of the output beam with polarization map for the pattern using the proposed transverse alignment method, histograms of (e) ellipticity and (f) elevation angle of the generated beam in (d).

Fig. 12.
Fig. 12.

Experimental results for the generation of radially linear polarized beam. (a) Intensity distribution of the output beam with polarization map corresponding to the pattern without using the proposed transverse alignment method, histograms of (b) ellipticity and (c) elevation angle of the generated beam in (a). (d) Intensity distribution of the output beam with polarization map for the pattern using the proposed transverse alignment method, histograms of (e) ellipticity and (f) elevation angle of the generated beam in (d).

Equations (11)

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go(x,y)=F{F[gi(x,y)]}=gi(x,y),
E2(x,y)=F{F[E1(x,y)]}=E1(x,y).
E3(x,y)=F{F[E2(x,y)]}=E2(x,y)=E1(x,y).
E4(x,y)=F{F[E3(x,y)]}=E3(x,y)=E1(x,y).
Eo(x,y)=Ei(x,y)·exp[j(ϕ1(x,y)+ϕ2(x,y)2+ϕ3(x,y)2+π)]·sin[ϕ2(x,y)2]·[cos(ϕ3(x,y)2+π2)ejϕ4(x,y)sin(ϕ3(x,y)2+π2)],
Eo(x,y)=Ei(x,y)·exp[j(ϕ1(x,y)+ϕ2((xx2),(yy2))2+ϕ3((xx3),(y+y3))2+π)]·sin[ϕ2((xx2),(yy2))2]·[cos(ϕ3((xx3),(y+y3))2+π2)ejϕ4((x+x4),(yy4))sin(ϕ3((xx3),(y+y3))2+π2)].
Ed(x,y)=Ad(x,y)ejϕd(x,y)(Exd(x,y)Eyd(x,y)ejδd(x,y)),
ϕ2(x,y)=2sin1(Ad((xx2),(yy2))Ei((xx2),(yy2))),
ϕ3(x,y)=2tan1(|Eyd((xx3),(yy3))||Exd((xx3),(yy3))|)π,
ϕ4(x,y)=δd((xx4),(yy4)),
ϕ1(x,y)=ϕd(x,y)ϕ2((xx2),(yy2))2ϕ3((xx3),(y+y3))2π.

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