Abstract

We present, design and generate a new kind of vector optical fields with linear polarization distributions modeling to electric and magnetic field lines. The geometric configurations of “electric charges” and “magnetic charges” can engineer the spatial structure and symmetry of polarizations of vector optical field, providing additional degrees of freedom assisting in controlling the field symmetry at the focus and allowing engineering of the field distribution at the focus to the specific applications.

© 2013 OSA

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2013 (2)

2012 (1)

2010 (1)

2009 (3)

2008 (1)

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photon.2, 501–505 (2008).
[CrossRef]

2007 (4)

2006 (3)

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett.91, 233901 (2003).
[CrossRef] [PubMed]

2002 (2)

2000 (2)

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. A253, 358–379 (1959).
[CrossRef]

Arlt, J.

Bernet, S.

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

Biener, G.

Bokor, N.

N. Bokor and N. Davidson, “A three dimensional dark focal spot uniformly surrounded by light,” Opt. Commun.279, 229–234 (2007).
[CrossRef]

N. Bokor and N. Davidson, “Generation of a hollow dark spherical spot by 4π focusing of a radially polarized Laguerre-Gaussian beam,” Opt. Lett.31, 149–151 (2006).
[CrossRef] [PubMed]

Bomzon, Z.

Brown, T. G.

Chen, J.

X. L. Wang, Y. N. Li, J. Chen, C. S. Guo, J. P. Ding, and H. T. Wang, “A new type of vector fields with hybrid states of polarization,” Opt. Express18, 10786–10795 (2010).
[CrossRef] [PubMed]

X. L. Wang, J. P. Ding, J. Q. Qin, J. Chen, Y. X. Fan, and H. T. Wang, “Configurable three-dimensional optical cage generated from cylindrical vector beams,” Opt. Commun.282, 3421–3425 (2009).
[CrossRef]

Chen, W.

W. Chen and Q. Zhan, “Three-dimensional focus shaping with cylindrical vector beams,” Opt. Commun.265, 411–417 (2006).
[CrossRef]

Chong, C. T.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photon.2, 501–505 (2008).
[CrossRef]

Davidson, N.

N. Bokor and N. Davidson, “A three dimensional dark focal spot uniformly surrounded by light,” Opt. Commun.279, 229–234 (2007).
[CrossRef]

N. Bokor and N. Davidson, “Generation of a hollow dark spherical spot by 4π focusing of a radially polarized Laguerre-Gaussian beam,” Opt. Lett.31, 149–151 (2006).
[CrossRef] [PubMed]

Ding, J. P.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett.91, 233901 (2003).
[CrossRef] [PubMed]

Fan, Y. X.

X. L. Wang, J. P. Ding, J. Q. Qin, J. Chen, Y. X. Fan, and H. T. Wang, “Configurable three-dimensional optical cage generated from cylindrical vector beams,” Opt. Commun.282, 3421–3425 (2009).
[CrossRef]

Fürhapter, S.

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

Guo, C. S.

Hasman, E.

Jesacher, A.

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

Jiao, X. Y.

Kleiner, V.

Kozawa, Y.

Leger, J.

Lerman, G.

Lerman, G. M.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett.91, 233901 (2003).
[CrossRef] [PubMed]

Levy, U.

Li, P.

Li, Y. N.

Lilach, Y.

Liu, S.

Lukyanchuk, B.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photon.2, 501–505 (2008).
[CrossRef]

Maurer, C.

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

Ni, W. J.

Padgett, M.J.

Peng, T.

Qin, J. Q.

X. L. Wang, J. P. Ding, J. Q. Qin, J. Chen, Y. X. Fan, and H. T. Wang, “Configurable three-dimensional optical cage generated from cylindrical vector beams,” Opt. Commun.282, 3421–3425 (2009).
[CrossRef]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett.91, 233901 (2003).
[CrossRef] [PubMed]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. A253, 358–379 (1959).
[CrossRef]

Ritsch-Marte, M.

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

Sato, S.

Sheppard, C.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photon.2, 501–505 (2008).
[CrossRef]

Shi, L. P.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photon.2, 501–505 (2008).
[CrossRef]

Wang, H. F.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photon.2, 501–505 (2008).
[CrossRef]

Wang, H. T.

Wang, S. C.

Wang, X. L.

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. A253, 358–379 (1959).
[CrossRef]

Xie, X. S.

Yang, L. X.

Youngworth, K. S.

Zhan, Q.

Zhang, W.

Zhao, J. L.

Zhou, J. Y.

Adv. Opt. Photon. (1)

Nat. Photon. (1)

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photon.2, 501–505 (2008).
[CrossRef]

New J. Phys. (1)

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

Opt. Commun. (3)

W. Chen and Q. Zhan, “Three-dimensional focus shaping with cylindrical vector beams,” Opt. Commun.265, 411–417 (2006).
[CrossRef]

N. Bokor and N. Davidson, “A three dimensional dark focal spot uniformly surrounded by light,” Opt. Commun.279, 229–234 (2007).
[CrossRef]

X. L. Wang, J. P. Ding, J. Q. Qin, J. Chen, Y. X. Fan, and H. T. Wang, “Configurable three-dimensional optical cage generated from cylindrical vector beams,” Opt. Commun.282, 3421–3425 (2009).
[CrossRef]

Opt. Express (5)

Opt. Lett. (8)

Phys. Rev. Lett. (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett.91, 233901 (2003).
[CrossRef] [PubMed]

Proc. Roy. Soc. A (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. A253, 358–379 (1959).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Schematic of experimental setup for generating L-LP-VFs with their SoP distributions similar to the electric and magnetic field lines. The main configuration is a 4f system composed of a pair of identical lenses (L1 and L2). A spatial light modulator (SLM) is located at the input plane of the 4f system. Two λ/4 waveplates behind a spatial filter (SF) with two apertures are placed in the Fourier plane of the 4f system. A Ronchi phase grating (G) is placed in the output plane of the 4f system.

Fig. 2
Fig. 2

L-LP-VFs with their SoP distributions similar to the field lines of the electric dipole (first row) and the dual equal-positive charges (second row). First column shows the directions of the field lines or the SoP distributions of L-LP-VFs. Second and third columns (fourth and fifth columns) show the simulated and measured intensity patterns of the x-components (y-components), respectively. Any picture has a dimension of 6d × 6d.

Fig. 3
Fig. 3

L-LP-VFs with their SoP distributions similar to the field lines of the dual unequal charges. First, second, third and fourth columns show the cases of (p1, p2) = (+2, −1), (+3, −1), (+4, −1) and (+5, −1), respectively. The “charges” p1 and p2 are always located at (x1, y1) = (−d, 0) and (x2, y2) = (d, 0), respectively. First row shows the directions of the electric field lines or the SoP distributions. Second and third rows (fourth and fifth rows) show the simulated and measured intensity patterns of the x-components (y-components), respectively. Any picture has a dimension of 6d × 6d.

Fig. 4
Fig. 4

L-LP-VFs with their SoP distributions similar to the field lines of three charges (first and second columns) and four charges (third and four columns). First row shows the directions of the electric field lines or the SoP distributions. Second and third rows (fourth and fifth rows) show the simulated and measured intensity patterns of the x-components (y-components), respectively. Any picture has a dimension of 6d × 6d.

Fig. 5
Fig. 5

L-LP-VFs with their SoP distributions similar to the field lines of magnetic dipoles for six situations. First row shows the directions of the magnetic field lines or the SoP distributions. Second and third rows (fourth and fifth rows) show the simulated and measured intensity patterns of the x-components (y-components), respectively. Any picture has a dimension of 6d × 6d.

Fig. 6
Fig. 6

Intensity distributions of the tightly focused L-LP-VFs with the same SoP distributions as the field lines of dual charges. First and second rows correspond to the cases of electric dipoles and dual-positive charges, for different intervals between two “charges”, respectively. Any picture has a dimension of 4λ × 4λ.

Fig. 7
Fig. 7

Intensity distributions of the tightly focused L-LP-VFs with the same SoP distributions as the field lines of magnetic dipole with (m1, m2) = (1, 1), for different intervals between two singularities. Any picture has a dimension of 4λ × 4λ.

Fig. 8
Fig. 8

Intensity patterns of the tightly focused L-LP-VFs with the same SoP distributions as the magnetic field lines for different m1 when m2 ≡ 1 and d = 0.3 f. Any picture has a dimension of 4λ × 4λ.

Equations (6)

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E P ( x , y ) = j = 1 N p j ( x x j ) [ ( x x j ) 2 + ( y y j ) 2 ] 3 / 2 e ^ x + j = 1 N p j ( y y j ) [ ( x x j ) 2 + ( y y j ) 2 ] 3 / 2 e ^ y = E p x ( x , y ) e ^ x + E p y ( x , y ) e ^ y ,
E ( x , y ) = A 0 [ cos Δ ( x , y ) e ^ x + sin Δ ( x , y ) e ^ y ] ,
Δ ( x , y ) = tan 1 [ E p y ( x , y ) / E p x ( x , y ) ] ,
E ( x , y ) = A 0 [ cos δ ( x , y ) e ^ x + sin δ ( x , y ) e ^ y ] ,
B P ( x , y ) = B 0 [ 3 2 x y e ^ x + ( d 2 x 2 + 1 2 y 2 ) e ^ y ] = B p x ( x , y ) e ^ x + B p y ( x , y ) e ^ y ,
B P ( x , y ) = B 0 [ 3 2 x y e ^ x + ( d 2 m 1 x 2 + 1 2 m 2 y 2 ) e ^ y ] = B p x ( x , y ) e ^ x + B p y ( x , y ) e ^ y .

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