Abstract

We propose a method to generate a vectorial focal field with reconfigurable distributions for both the intensity and polarization state. The three-dimensional focal volume was configured by modulating the phase and polarization of the incident light. The incident light yielding the desired field was determined based on an iterative scheme involving vectorial diffraction calculations and fast Fourier transforms. Optical experiments on vectorial field shaping were performed to validate the feasibility of our method. This method may have applications in optical tweezers, such as for realizing the optical manipulation of particles via polarization modulation in addition to phase control.

© 2014 Optical Society of America

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References

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2012 (4)

2011 (3)

2010 (3)

2009 (4)

2008 (2)

H. P. Urbach and S. F. Pereira, “Field in focus with a maximum longitudinal electric component,” Phys. Rev. Lett. 100, 123904 (2008).
[CrossRef]

K. A. Serrels, E. Ramsay, R. J. Warburton, and D. T. Reid, “Nanoscale optical microscopy in the vectorial focusing regime,” Nat. Photonics 2, 311–314 (2008).
[CrossRef]

2007 (1)

I. Iglesias and B. Vohnsen, “Polarization structuring for focal volume shaping in high-resolution microscopy,” Opt. Commun. 271, 40–47 (2007).
[CrossRef]

2006 (2)

A. F. Abouraddy and K. C. Toussaint, “Three-dimensional polarization control in microscopy,” Phys. Rev. Lett. 96, 153901 (2006).
[CrossRef]

M. R. Beversluis, L. Novotny, and S. J. Stranick, “Programmable vector point-spread function engineering,” Opt. Express 14, 2650–2656 (2006).
[CrossRef]

2005 (1)

2003 (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[CrossRef]

2002 (1)

Abouraddy, A. F.

A. F. Abouraddy and K. C. Toussaint, “Three-dimensional polarization control in microscopy,” Phys. Rev. Lett. 96, 153901 (2006).
[CrossRef]

Angelsky, O.

Audouard, E.

Bartels, R. A.

Bekshaev, A.

Beversluis, M. R.

Boruah, B. R.

B. R. Boruah, “Lateral resolution enhancement in confocal microscopy by vectorial aperture engineering,” Appl. Opt. 49, 701–707 (2010).
[CrossRef]

B. R. Boruah and M. A. A. Neil, “Focal field computation of an arbitrarily polarized beam using fast Fourier transforms,” Opt. Commun. 282, 4660–4667 (2009).
[CrossRef]

Brasselet, S.

Chen, H.

Chen, W.

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

Chenand, Z.

Dainty, J. C.

Dickey, F. M.

F. M. Dickey, S. C. Holswade, and D. L. Shealy, Laser Beam Shaping Applications (Taylor & Francis, 2006).

Ding, J.

Golub, I.

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[CrossRef]

Gu, M.

M. Gu, Advanced Optical Imaging Theory (Springer, 2000).

Hanson, S.

Hao, J.

Holswade, S. C.

F. M. Dickey, S. C. Holswade, and D. L. Shealy, Laser Beam Shaping Applications (Taylor & Francis, 2006).

Hu, K.

Huignard, J.

Huot, N.

Iglesias, I.

I. Iglesias and B. Vohnsen, “Polarization structuring for focal volume shaping in high-resolution microscopy,” Opt. Commun. 271, 40–47 (2007).
[CrossRef]

Kenny, F.

Khonina, S. N.

Kou, S. S.

Lara, D.

Larat, C.

Leger, J.

Lin, J.

Loiseaux, B.

Maksimyak, A.

Maksimyak, P.

Masihzadeh, O.

Neil, M. A. A.

B. R. Boruah and M. A. A. Neil, “Focal field computation of an arbitrarily polarized beam using fast Fourier transforms,” Opt. Commun. 282, 4660–4667 (2009).
[CrossRef]

Novotny, L.

Pereira, S. F.

H. P. Urbach and S. F. Pereira, “Field in focus with a maximum longitudinal electric component,” Phys. Rev. Lett. 100, 123904 (2008).
[CrossRef]

Pu, J.

Ramsay, E.

K. A. Serrels, E. Ramsay, R. J. Warburton, and D. T. Reid, “Nanoscale optical microscopy in the vectorial focusing regime,” Nat. Photonics 2, 311–314 (2008).
[CrossRef]

Reid, D. T.

K. A. Serrels, E. Ramsay, R. J. Warburton, and D. T. Reid, “Nanoscale optical microscopy in the vectorial focusing regime,” Nat. Photonics 2, 311–314 (2008).
[CrossRef]

Rodríguez-Herrera, O. G.

Sanner, N.

Schlup, P.

Serrels, K. A.

K. A. Serrels, E. Ramsay, R. J. Warburton, and D. T. Reid, “Nanoscale optical microscopy in the vectorial focusing regime,” Nat. Photonics 2, 311–314 (2008).
[CrossRef]

Shealy, D. L.

F. M. Dickey, S. C. Holswade, and D. L. Shealy, Laser Beam Shaping Applications (Taylor & Francis, 2006).

Sheppard, C. J. R.

Stranick, S. J.

Tang, W. T.

Toussaint, K. C.

A. F. Abouraddy and K. C. Toussaint, “Three-dimensional polarization control in microscopy,” Phys. Rev. Lett. 96, 153901 (2006).
[CrossRef]

Urbach, H. P.

H. P. Urbach and S. F. Pereira, “Field in focus with a maximum longitudinal electric component,” Phys. Rev. Lett. 100, 123904 (2008).
[CrossRef]

Vohnsen, B.

I. Iglesias and B. Vohnsen, “Polarization structuring for focal volume shaping in high-resolution microscopy,” Opt. Commun. 271, 40–47 (2007).
[CrossRef]

Wang, H. T.

Warburton, R. J.

K. A. Serrels, E. Ramsay, R. J. Warburton, and D. T. Reid, “Nanoscale optical microscopy in the vectorial focusing regime,” Nat. Photonics 2, 311–314 (2008).
[CrossRef]

Xu, J.

Yew, E. Y. S.

Yuan, X.-C.

Zenkova, C.

Zhan, Q.

Zhang, B. F.

Zheng, Z.

Adv. Opt. Photon. (2)

Appl. Opt. (1)

J. Opt. (1)

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

J. Opt. Soc. Am. A (1)

Nat. Photonics (1)

K. A. Serrels, E. Ramsay, R. J. Warburton, and D. T. Reid, “Nanoscale optical microscopy in the vectorial focusing regime,” Nat. Photonics 2, 311–314 (2008).
[CrossRef]

Nature (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[CrossRef]

Opt. Commun. (2)

I. Iglesias and B. Vohnsen, “Polarization structuring for focal volume shaping in high-resolution microscopy,” Opt. Commun. 271, 40–47 (2007).
[CrossRef]

B. R. Boruah and M. A. A. Neil, “Focal field computation of an arbitrarily polarized beam using fast Fourier transforms,” Opt. Commun. 282, 4660–4667 (2009).
[CrossRef]

Opt. Express (4)

Opt. Lett. (7)

Phys. Rev. Lett. (2)

A. F. Abouraddy and K. C. Toussaint, “Three-dimensional polarization control in microscopy,” Phys. Rev. Lett. 96, 153901 (2006).
[CrossRef]

H. P. Urbach and S. F. Pereira, “Field in focus with a maximum longitudinal electric component,” Phys. Rev. Lett. 100, 123904 (2008).
[CrossRef]

Other (2)

F. M. Dickey, S. C. Holswade, and D. L. Shealy, Laser Beam Shaping Applications (Taylor & Francis, 2006).

M. Gu, Advanced Optical Imaging Theory (Springer, 2000).

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Figures (8)

Fig. 1.
Fig. 1.

Focusing of incident light beams with space-variant phase and polarization.

Fig. 2.
Fig. 2.

Flow chart for iteratively searching for the optimal polarization and phase modulation of the incident light that can yield the desired focal field.

Fig. 3.
Fig. 3.

Simulation results of three intensity rings in the focal plane. The inner, middle, and outer rings have right-hand circular, x linear, and left-hand circular polarizations, respectively. (a) Intensity of the focal plane. (b) Phase difference of the right- and left-hand circular components. (c) and (d) Respective intensities of the right- and left-hand circular polarization components.

Fig. 4.
Fig. 4.

Experimentally generated vectorial field corresponding to Fig. 3. The inner, middle, and outer rings are right-hand circularly polarized, x linearly polarized, and left-hand circularly polarized, respectively. From left to right: intensity distribution recorded without an analyzer, and with an analyzer oriented at 0°, 45°, and 90° (as indicated by the arrow insets).

Fig. 5.
Fig. 5.

Phase distribution and experimental results that perform the spatially variant polarization distribution of the focal field. Inner ring and outer ring show right- and left-hand circular polarization, respectively. Middle ring indicates a radially polarized beam. The arrows show the orientation of the analyzer.

Fig. 6.
Fig. 6.

Recorded focal intensities of the four playing card patterns described in the text. From left to right: no analyzer, horizontal linear, vertical linear, right-hand circular, and left-hand circular analyzers have been employed (as indicated by the arrows insets).

Fig. 7.
Fig. 7.

Experimental demonstration of a polarization gradient distribution in the focal field. From left to right: no analyzer, right-hand circular, and left-hand circular analyzers have been applied (as indicated by the arrows insets).

Fig. 8.
Fig. 8.

Intensity distributions for the serial planes parallel to the focal plane. Top to bottom: experimental results with and without a polarization analyzer show that the light field in each image appeared in the specified position polarized as expected. The vertical linear polarization was assigned to “1, 2, and 3” and the horizontal linear polarization was assigned to “4, 5, and 6.”

Equations (5)

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Ei(x,y,z)=E02[eiδ+(x,y,z)(1i)+eiδ(x,y,z)(1i)]=E0eiδ+(x,y,z)+δ(x,y,z)2(cos(δ+(x,y,z)δ(x,y,z)2)sin(δ+(x,y,z)δ(x,y,z)2))=E0eiβ(x,y,z)(cosα(x,y,z)sinα(x,y,z)),
{Ei+(x0,y0)=E0+(x0,y0)[1i]Ei(x0,y0)=E0(x0,y0)[1i],
{E+(x,y,z)=AE0+(x0,y0)exp(i2πλf(xx0+yy0+zz0))P(x0,y0,z0)dx0dy0dz0E(x,y,z)=AE0(x0,y0)exp(i2πλf(xx0+yy0+zz0))P(x0,y0,z0)dx0dy0dz0.
P(x0,y0,z0)=δ(x02+y02+z02f)
{E+(x,y,z)=AE0+(x0,y0)exp(i2πf2(x02+y02)λfz)exp(i2πλf(xx0+yy0))dx0dy0E(x,y,z)=AE0(x0,y0)exp(i2πf2(x02+y02)λfz)exp(i2πλf(xx0+yy0))dx0dy0.

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