Abstract

We present a highly efficient method of generating and shaping ellipse perfect vector beams (EPVBs) with a prescribed ellipse intensity profile and continuously variant linear polarization state. The scheme is based on the coaxial superposition of two orthogonally polarized ellipse laser beams of controllable phase vortex serving as the base vector components. The phase-only computer-generated hologram is specifically designed by means of a modified iteration algorithm involving a complex amplitude constraint, which is able to generate an EPVB with high diffraction efficiency in the vector optical field generator. We experimentally demonstrate that the efficiency of generating the EPVB has a notable improvement from 1.83% in the conventional complex amplitude modulation based technique to 11.1% in our method. We also discuss and demonstrate the simultaneous shaping of multiple EPVBs with independent tunable ellipticity and polarization vortex in both transversal (2D) and axial (3D) focusing structures, proving potentials in a variety of polarization-mediated applications such as trapping and transportation of particles in more complex geometric circumstances.

© 2018 Chinese Laser Press

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References

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2018 (2)

P. Pradhan, M. Sharma, and B. Ung, “Generation of perfect cylindrical vector beams with complete control over the ring width and ring diameter,” IEEE Photon. J. 10, 6500310 (2018).
[Crossref]

X. Z. Li, H. X. Ma, C. L. Yin, J. Tang, H. H. Li, M. M. Tang, J. G. Wang, Y. P. Tai, X. F. Li, and Y. S. Wang, “Controllable mode transformation in perfect optical vortices,” Opt. Express 26, 651–662 (2018).
[Crossref]

2017 (6)

2016 (6)

2015 (6)

S. H. Tao and W. X. Yu, “Beam shaping of complex amplitude with separate constraints on the output beam,” Opt. Express 23, 1052–1062 (2015).
[Crossref]

Z. Chen, T. Zeng, B. Qian, and J. Ding, “Complete shaping of optical vector beams,” Opt. Express 23, 17701–17710 (2015).
[Crossref]

C. Chang, J. Xia, L. Yang, W. Lei, Z. Yang, and J. Chen, “Speckle-suppressed phase-only holographic three-dimensional display based on double-constraint Gerchberg–Saxton algorithm,” Appl. Opt. 54, 6994–7001 (2015).
[Crossref]

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super-resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photon. Rev. 10, 147–152 (2015).
[Crossref]

S. Roy, K. Ushakova, Q. van den Berg, S. F. Pereira, and H. P. Urbach, “Radially polarized light for detection and nanolocalization of dielectric particles on a planar substrate,” Phys. Rev. Lett. 114, 103903 (2015).
[Crossref]

P. Chen, W. Ji, B. Y. Wei, W. Hu, V. Chigrinov, and Y.-Q. Lu, “Generation of arbitrary vector beams with liquid crystal polarization converters and vector-photoaligned q-plates,” Appl. Phys. Lett. 107, 241102 (2015).
[Crossref]

2014 (2)

2013 (3)

2012 (3)

2011 (3)

2010 (1)

2008 (2)

2007 (3)

2006 (2)

R. Chakraborty and A. Ghosh, “Generation of an elliptic Bessel beam,” Opt. Lett. 31, 38–40 (2006).
[Crossref]

H. W. Ren, Y. H. Lin, and S. T. Wu, “Linear to axial or radial polarization conversion using a liquid crystal gel,” Appl. Phys. Lett. 89, 051114 (2006).
[Crossref]

2003 (1)

2002 (1)

1999 (1)

1990 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Abeysinghe, D. C.

W. B. Chen, W. Han, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Generating cylindrical vector beams with subwavelength concentric metallic gratings fabricated on optical fibers,” J. Opt. 13, 015003 (2011).
[Crossref]

Abramochkin, E.

Alieva, T.

Arrizón, V.

Badham, K.

Beresna, M.

R. Drevinskas, J. Zhang, M. Beresna, M. Gecevičius, A. G. Kazanskii, and Y. P. Svirko, “Laser material processing with tightly focused cylindrical vector beams,” Appl. Phys. Lett. 108, 221107 (2016).
[Crossref]

Bhebhe, N.

C. Rosales-Guzmán, N. Bhebhe, N. Mahonisi, and A. Forbes, “Multiplexing 200 modes on a single digital hologram,” J. Opt. 19, 113501 (2017).
[Crossref]

Bhebheand, N.

Bu, J.

Calvo, M. L.

Cámara, A.

Campos, J.

Cao, Y. Y.

Carrada, R.

Castro, I.

Chakraborty, R.

Chang, C.

Chang, R. S.

C. Y. Han, R. S. Chang, and H. F. Chen, “Solid-state interferometry of a pentaprism for generating cylindrical vector beam,” Opt. Rev. 20, 189–192 (2013).
[Crossref]

Cheben, P.

Chen, H. F.

C. Y. Han, R. S. Chang, and H. F. Chen, “Solid-state interferometry of a pentaprism for generating cylindrical vector beam,” Opt. Rev. 20, 189–192 (2013).
[Crossref]

Chen, J.

Chen, P.

P. Chen, W. Ji, B. Y. Wei, W. Hu, V. Chigrinov, and Y.-Q. Lu, “Generation of arbitrary vector beams with liquid crystal polarization converters and vector-photoaligned q-plates,” Appl. Phys. Lett. 107, 241102 (2015).
[Crossref]

Chen, S. Z.

Chen, W. B.

W. B. Chen, W. Han, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Generating cylindrical vector beams with subwavelength concentric metallic gratings fabricated on optical fibers,” J. Opt. 13, 015003 (2011).
[Crossref]

Chen, Z.

Cheng, H.

Chigrinov, V.

P. Chen, W. Ji, B. Y. Wei, W. Hu, V. Chigrinov, and Y.-Q. Lu, “Generation of arbitrary vector beams with liquid crystal polarization converters and vector-photoaligned q-plates,” Appl. Phys. Lett. 107, 241102 (2015).
[Crossref]

Cottrell, D. M.

Cui, Y.

Davidson, N.

Davis, J. A.

Delaney, S. W.

Ding, J.

Dong, D.

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super-resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photon. Rev. 10, 147–152 (2015).
[Crossref]

Dou, X. J.

Drevinskas, R.

R. Drevinskas, J. Zhang, M. Beresna, M. Gecevičius, A. G. Kazanskii, and Y. P. Svirko, “Laser material processing with tightly focused cylindrical vector beams,” Appl. Phys. Lett. 108, 221107 (2016).
[Crossref]

Duparré, M.

Flamm, D.

Forbes, A.

Ford, D. H.

Fu, S.

Gao, C.

Gecevicius, M.

R. Drevinskas, J. Zhang, M. Beresna, M. Gecevičius, A. G. Kazanskii, and Y. P. Svirko, “Laser material processing with tightly focused cylindrical vector beams,” Appl. Phys. Lett. 108, 221107 (2016).
[Crossref]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Ghosh, A.

Gong, Q.

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super-resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photon. Rev. 10, 147–152 (2015).
[Crossref]

González, L. A.

Gu, B.

Gu, M.

Guo, C. S.

Guo, H. M.

Han, C. Y.

C. Y. Han, R. S. Chang, and H. F. Chen, “Solid-state interferometry of a pentaprism for generating cylindrical vector beam,” Opt. Rev. 20, 189–192 (2013).
[Crossref]

Han, L.

Han, W.

W. B. Chen, W. Han, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Generating cylindrical vector beams with subwavelength concentric metallic gratings fabricated on optical fibers,” J. Opt. 13, 015003 (2011).
[Crossref]

Hashimoto, N.

He, F.

Hernandez, T. M.

Hong, M. H.

Hu, Q.

Hu, W.

P. Chen, W. Ji, B. Y. Wei, W. Hu, V. Chigrinov, and Y.-Q. Lu, “Generation of arbitrary vector beams with liquid crystal polarization converters and vector-photoaligned q-plates,” Appl. Phys. Lett. 107, 241102 (2015).
[Crossref]

Hurtado, E.

Jackel, S.

Ji, W.

P. Chen, W. Ji, B. Y. Wei, W. Hu, V. Chigrinov, and Y.-Q. Lu, “Generation of arbitrary vector beams with liquid crystal polarization converters and vector-photoaligned q-plates,” Appl. Phys. Lett. 107, 241102 (2015).
[Crossref]

Ji, Z.

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super-resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photon. Rev. 10, 147–152 (2015).
[Crossref]

Kazanskii, A. G.

R. Drevinskas, J. Zhang, M. Beresna, M. Gecevičius, A. G. Kazanskii, and Y. P. Svirko, “Laser material processing with tightly focused cylindrical vector beams,” Appl. Phys. Lett. 108, 221107 (2016).
[Crossref]

Ke, Y.

Kimura, W. D.

Kotlyar, V. V.

A. A. Kovalev, V. V. Kotlyar, and A. P. Porfirev, “A highly efficient element for generating elliptic perfect optical vortices,” Appl. Phys. Lett. 110, 261102 (2017).
[Crossref]

Kovalev, A. A.

A. A. Kovalev, V. V. Kotlyar, and A. P. Porfirev, “A highly efficient element for generating elliptic perfect optical vortices,” Appl. Phys. Lett. 110, 261102 (2017).
[Crossref]

Kozawa, Y.

Lai, W. J.

Lei, W.

Li, H. H.

Li, P.

Li, X. F.

Li, X. P.

Li, X. Z.

Li, Y.

Lim, B. C.

Lin, Y. H.

H. W. Ren, Y. H. Lin, and S. T. Wu, “Linear to axial or radial polarization conversion using a liquid crystal gel,” Appl. Phys. Lett. 89, 051114 (2006).
[Crossref]

Ling, X. H.

Liu, J. S.

Liu, S.

Liu, Y.

Liu, Y. C.

Liu, Y. H.

Liu, Z.

Lu, Y.-Q.

P. Chen, W. Ji, B. Y. Wei, W. Hu, V. Chigrinov, and Y.-Q. Lu, “Generation of arbitrary vector beams with liquid crystal polarization converters and vector-photoaligned q-plates,” Appl. Phys. Lett. 107, 241102 (2015).
[Crossref]

Lumer, Y.

Luo, H.

Luo, H. L.

Ma, C.

Ma, H. X.

Machavariani, G.

Mahonisi, N.

C. Rosales-Guzmán, N. Bhebhe, N. Mahonisi, and A. Forbes, “Multiplexing 200 modes on a single digital hologram,” J. Opt. 19, 113501 (2017).
[Crossref]

Martínez-Matos, O.

Meir, A.

Min, C. J.

Miret, J. J.

Moreno, I.

Moshe, I.

Nelson, R. L.

W. B. Chen, W. Han, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Generating cylindrical vector beams with subwavelength concentric metallic gratings fabricated on optical fibers,” J. Opt. 13, 015003 (2011).
[Crossref]

Ni, W. J.

Peng, T.

Pereira, S. F.

S. Roy, K. Ushakova, Q. van den Berg, S. F. Pereira, and H. P. Urbach, “Radially polarized light for detection and nanolocalization of dielectric particles on a planar substrate,” Phys. Rev. Lett. 114, 103903 (2015).
[Crossref]

Phua, P. B.

Porfirev, A. P.

A. A. Kovalev, V. V. Kotlyar, and A. P. Porfirev, “A highly efficient element for generating elliptic perfect optical vortices,” Appl. Phys. Lett. 110, 261102 (2017).
[Crossref]

Pradhan, P.

P. Pradhan, M. Sharma, and B. Ung, “Generation of perfect cylindrical vector beams with complete control over the ring width and ring diameter,” IEEE Photon. J. 10, 6500310 (2018).
[Crossref]

Qi, Y.

Qian, B.

Ren, H. W.

H. W. Ren, Y. H. Lin, and S. T. Wu, “Linear to axial or radial polarization conversion using a liquid crystal gel,” Appl. Phys. Lett. 89, 051114 (2006).
[Crossref]

Rodrigo, J. A.

Rosales-Guzmán, C.

C. Rosales-Guzmán, N. Bhebhe, N. Mahonisi, and A. Forbes, “Multiplexing 200 modes on a single digital hologram,” J. Opt. 19, 113501 (2017).
[Crossref]

C. Rosales-Guzmán, N. Bhebheand, and A. Forbes, “Simultaneous generation of multiple vector beams on a single SLM,” Opt. Express 25, 25697–25706 (2017).
[Crossref]

Roy, S.

S. Roy, K. Ushakova, Q. van den Berg, S. F. Pereira, and H. P. Urbach, “Radially polarized light for detection and nanolocalization of dielectric particles on a planar substrate,” Phys. Rev. Lett. 114, 103903 (2015).
[Crossref]

Rui, G.

Ruiz, U.

Sánchez-López, M. M.

Sand, D.

Sato, S.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Schulze, C.

Sharma, M.

P. Pradhan, M. Sharma, and B. Ung, “Generation of perfect cylindrical vector beams with complete control over the ring width and ring diameter,” IEEE Photon. J. 10, 6500310 (2018).
[Crossref]

Shi, K.

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super-resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photon. Rev. 10, 147–152 (2015).
[Crossref]

Shu, W.

Svirko, Y. P.

R. Drevinskas, J. Zhang, M. Beresna, M. Gecevičius, A. G. Kazanskii, and Y. P. Svirko, “Laser material processing with tightly focused cylindrical vector beams,” Appl. Phys. Lett. 108, 221107 (2016).
[Crossref]

Taghizadeh, M. R.

Tai, Y. P.

Tan, Z. H.

Tanabe, A.

Tang, J.

Tang, M. M.

Tao, S. H.

Teo, H. H.

Tiaw, K. S.

Tidwell, S. C.

Ung, B.

P. Pradhan, M. Sharma, and B. Ung, “Generation of perfect cylindrical vector beams with complete control over the ring width and ring diameter,” IEEE Photon. J. 10, 6500310 (2018).
[Crossref]

Urbach, H. P.

S. Roy, K. Ushakova, Q. van den Berg, S. F. Pereira, and H. P. Urbach, “Radially polarized light for detection and nanolocalization of dielectric particles on a planar substrate,” Phys. Rev. Lett. 114, 103903 (2015).
[Crossref]

Ushakova, K.

S. Roy, K. Ushakova, Q. van den Berg, S. F. Pereira, and H. P. Urbach, “Radially polarized light for detection and nanolocalization of dielectric particles on a planar substrate,” Phys. Rev. Lett. 114, 103903 (2015).
[Crossref]

van den Berg, Q.

S. Roy, K. Ushakova, Q. van den Berg, S. F. Pereira, and H. P. Urbach, “Radially polarized light for detection and nanolocalization of dielectric particles on a planar substrate,” Phys. Rev. Lett. 114, 103903 (2015).
[Crossref]

Wang, H. T.

Wang, J. G.

Wang, T.

Wang, X. L.

Wang, Y.

Wang, Y. S.

Wei, B. Y.

P. Chen, W. Ji, B. Y. Wei, W. Hu, V. Chigrinov, and Y.-Q. Lu, “Generation of arbitrary vector beams with liquid crystal polarization converters and vector-photoaligned q-plates,” Appl. Phys. Lett. 107, 241102 (2015).
[Crossref]

Wen, S.

Wen, S. C.

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Figures (9)

Fig. 1.
Fig. 1. Reconstructed results of the ellipse beams with different topological charges [l1=2 for (a) and (b), l2=4 for (c) and (d)]. (a) and (c) are the intensity distributions. (b) and (d) are the phase distributions with differently marked topological charges.
Fig. 2.
Fig. 2. Intensity distributions at the filtering (Fourier) plane from the phase-only CGH calculated by (a) the grating encoding method and (b) the proposed F-DCGS method. (c) Flow chart of the proposed F-DCGS algorithm.
Fig. 3.
Fig. 3. Schematic representation of the experiment setup for generating an EPVB. P, polarizer; BE, beam expander; SLM, spatial light modulator; L, convex lenses (f1=400  mm, f2=300  mm, and f3=100  mm); QWP, quarter-wave plate; R, Ronchi grating; CCD, charge-coupled device.
Fig. 4.
Fig. 4. Generated intensity of the EPVB from the phase-only CGH calculated (a), (b) by the grating encoding method and (c), (d) by the F-DCGS method. The arrow marks in (b) and (d) indicate the polarization direction of an analyzer before the CCD.
Fig. 5.
Fig. 5. Experimental results of generating EPVBs under different ellipse modes and topological charges. The scaling factors are (a) a=1, b=0.5; (b) a=1, b=0.75; (c) a=1, b=1; (d) a=0.75, b=1; (e) a=0.5, b=1.
Fig. 6.
Fig. 6. Experimental intensity profiles of generating hybrid EPVBs after two analyzer directions.
Fig. 7.
Fig. 7. Experimental intensity patterns of the generated RPVBs. (a)–(d): RPVBs under different scaling modes of (a=1, b=0.5), (a=1, b=0.75), (a=0.75, b=1), and (a=0.5, b=1). (e) and (f) show hybrid RPVBs after two analyzer directions.
Fig. 8.
Fig. 8. Beam propagation in the xz and yz planes are displayed for the case of two beam shaping techniques. (a) Ellipse Bessel function method [3032]. (b) Our method. The beam intensity profiles before (z=1  cm) and at (z=0) the focal plane are also shown in each case. (c) The one-dimensional beam intensity profile of the two methods at z=0 (red and blue color lines, respectively).
Fig. 9.
Fig. 9. Experimental results of the generated hybrid EPVBs in two different types of three-dimensional layouts under different analyzer directions.

Equations (7)

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H(x,y)=0Tφ(x,y,t)[x0(t)]2+[y0(t)]2dt.
φ(x,y,t)=exp{iω02[yx0(t)xy0(t)]+iσω020τ[x0(τ)y0(τ)y0(τ)x0(τ)]dτ},
Etotal(x,y)=HL(x,y)·exp(i2πxsinθx/λ)+HR(x,y)·exp(i2πysinθy/λ).
φ(x,y)=Atotal(x,y)φtotal(x,y).
Ehybrid(x,y)=i=1nEtotali(x,y)·exp[ik(xuif+yvif)],
ϕi(x,y)=kzi1x2f2y2f2+k(xuif+yvif),
E3D(x,y)=i=1nEtotali(x,y)·exp[iφi(x,y)].