Abstract

We present and demonstrate a novel method for engineering the radial-variant polarization on the incident field to achieve a needle of transversally polarized field without any pupil filters. We generate a new kind of localized linearly-polarized vector fields with distributions of states of polarization (SoPs) describing by the radius to the power p and explore its tight focusing, nonparaxial focusing, and paraxial focusing properties. By tuning the power p, we obtain the needle-like focal field with hybrid SoPs and give the formula for describing the length of the needle. Experimentally, we systematically investigate both the intensity distributions and the polarization evolution of the optical needle by paraxial focusing the generated vector field. Such an optical needle, which enhances the light-matter interaction, has intriguing applications in optical microma-chining and nonlinear optics.

© 2013 Optical Society of America

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    [CrossRef]
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2013

T. Grosjean and I. Gauthier, “Longitudinally polarized electric and magnetic optical nano-needles of ultra high lengths,” Opt. Commun.294, 333–337 (2013).
[CrossRef]

L. Guo, C. Min, S. Wei, and X. Yuan, “Polarization and amplitude hybrid modulation of longitudinally polarized subwavelength-sized optical needle,” Chin. Opt. Lett.11, 052601 (2013).
[CrossRef]

E. T. F. Rogers, S. Savo, J. Lindberg, T. Roy, M. R. Dennis, and N. I. Zheludev, “Super-oscillatory optical needle,” Appl. Phys. Lett.102, 031108 (2013).
[CrossRef]

H. Guo, X. Weng, M. Jiang, Y. Zhao, G. Sui, Q. Hu, Y. Wang, and S. Zhuang, “Tight focusing of a higher-order radially polarized beam transmitting through multi-zone binary phase pupil filters,” Opt. Express21, 5363–5372 (2013).
[CrossRef] [PubMed]

2012

2011

2010

2008

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. Photonics2, 501–505 (2008).
[CrossRef]

2007

2000

1959

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

April, A.

Brown, T. G.

Chen, H.

Chen, J.

X. L. Wang, J. Chen, Y. N. Li, J. P. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett.105, 253602 (2010).
[CrossRef]

Chen, W.

J. Wang, W. Chen, and Q. Zhan, “Three-dimensional focus engineering using dipole array radiation pattern,” Opt. Commun.284, 2668–2671 (2011).
[CrossRef]

J. Wang, W. Chen, and Q. Zhan, “Engineering of high purity ultra-long optical needle field through reversing the electric dipole array radiation,” Opt. Express18, 21965–21972 (2010).
[CrossRef] [PubMed]

Chen, Z.

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. Photonics2, 501–505 (2008).
[CrossRef]

Dehez, H.

Dennis, M. R.

E. T. F. Rogers, S. Savo, J. Lindberg, T. Roy, M. R. Dennis, and N. I. Zheludev, “Super-oscillatory optical needle,” Appl. Phys. Lett.102, 031108 (2013).
[CrossRef]

Ding, J. P.

Gauthier, I.

T. Grosjean and I. Gauthier, “Longitudinally polarized electric and magnetic optical nano-needles of ultra high lengths,” Opt. Commun.294, 333–337 (2013).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company, 2005), Sec. 5.

Grosjean, T.

T. Grosjean and I. Gauthier, “Longitudinally polarized electric and magnetic optical nano-needles of ultra high lengths,” Opt. Commun.294, 333–337 (2013).
[CrossRef]

Guo, C. S.

X. L. Wang, J. Chen, Y. N. Li, J. P. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett.105, 253602 (2010).
[CrossRef]

X. L. Wang, J. P. Ding, W. J. Ni, C. S. Guo, and H. T. Wang, “Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement,” Opt. Lett.32, 3549–3551 (2007).
[CrossRef] [PubMed]

Guo, H.

Guo, L.

Hao, J.

Hu, K.

Hu, Q.

Jiang, M.

Kitamura, K.

K. Kitamura, M. Nishimoto, K. Sakai, and S. Noda, “Needle-like focus generation by radially polarized halo beams emitted by photonic-crystal ring-cavity laser,” Appl. Phys. Lett.101, 221103 (2012).
[CrossRef]

Kotlyar, V. V.

Kovalev, A. A.

Li, Y.

Li, Y. N.

X. L. Wang, J. Chen, Y. N. Li, J. P. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett.105, 253602 (2010).
[CrossRef]

Lin, J.

Lindberg, J.

E. T. F. Rogers, S. Savo, J. Lindberg, T. Roy, M. R. Dennis, and N. I. Zheludev, “Super-oscillatory optical needle,” Appl. Phys. Lett.102, 031108 (2013).
[CrossRef]

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. Photonics2, 501–505 (2008).
[CrossRef]

Min, C.

Ni, W. J.

Nishimoto, M.

K. Kitamura, M. Nishimoto, K. Sakai, and S. Noda, “Needle-like focus generation by radially polarized halo beams emitted by photonic-crystal ring-cavity laser,” Appl. Phys. Lett.101, 221103 (2012).
[CrossRef]

Noda, S.

K. Kitamura, M. Nishimoto, K. Sakai, and S. Noda, “Needle-like focus generation by radially polarized halo beams emitted by photonic-crystal ring-cavity laser,” Appl. Phys. Lett.101, 221103 (2012).
[CrossRef]

Piché, M.

Pu, J.

Richards, B.

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

Rogers, E. T. F.

E. T. F. Rogers, S. Savo, J. Lindberg, T. Roy, M. R. Dennis, and N. I. Zheludev, “Super-oscillatory optical needle,” Appl. Phys. Lett.102, 031108 (2013).
[CrossRef]

Roy, T.

E. T. F. Rogers, S. Savo, J. Lindberg, T. Roy, M. R. Dennis, and N. I. Zheludev, “Super-oscillatory optical needle,” Appl. Phys. Lett.102, 031108 (2013).
[CrossRef]

Sakai, K.

K. Kitamura, M. Nishimoto, K. Sakai, and S. Noda, “Needle-like focus generation by radially polarized halo beams emitted by photonic-crystal ring-cavity laser,” Appl. Phys. Lett.101, 221103 (2012).
[CrossRef]

Savo, S.

E. T. F. Rogers, S. Savo, J. Lindberg, T. Roy, M. R. Dennis, and N. I. Zheludev, “Super-oscillatory optical needle,” Appl. Phys. Lett.102, 031108 (2013).
[CrossRef]

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. Photonics2, 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. Photonics2, 501–505 (2008).
[CrossRef]

Sui, G.

Tan, J.

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. Photonics2, 501–505 (2008).
[CrossRef]

Wang, H. T.

Wang, J.

J. Wang, W. Chen, and Q. Zhan, “Three-dimensional focus engineering using dipole array radiation pattern,” Opt. Commun.284, 2668–2671 (2011).
[CrossRef]

J. Wang, W. Chen, and Q. Zhan, “Engineering of high purity ultra-long optical needle field through reversing the electric dipole array radiation,” Opt. Express18, 21965–21972 (2010).
[CrossRef] [PubMed]

Wang, X. L.

X. L. Wang, J. Chen, Y. N. Li, J. P. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett.105, 253602 (2010).
[CrossRef]

X. L. Wang, J. P. Ding, W. J. Ni, C. S. Guo, and H. T. Wang, “Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement,” Opt. Lett.32, 3549–3551 (2007).
[CrossRef] [PubMed]

Wang, Y.

Wei, S.

Wei, S. B.

Weng, X.

Wolf, E.

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

Xu, J.

Yin, K.

Youngworth, K. S.

Yuan, G. H.

Yuan, X.

Yuan, X. C.

Zhan, Q.

J. Wang, W. Chen, and Q. Zhan, “Three-dimensional focus engineering using dipole array radiation pattern,” Opt. Commun.284, 2668–2671 (2011).
[CrossRef]

J. Wang, W. Chen, and Q. Zhan, “Engineering of high purity ultra-long optical needle field through reversing the electric dipole array radiation,” Opt. Express18, 21965–21972 (2010).
[CrossRef] [PubMed]

Zhang, B. F.

Zhao, Y.

Zheludev, N. I.

E. T. F. Rogers, S. Savo, J. Lindberg, T. Roy, M. R. Dennis, and N. I. Zheludev, “Super-oscillatory optical needle,” Appl. Phys. Lett.102, 031108 (2013).
[CrossRef]

Zhuang, S.

Appl. Phys. Lett.

K. Kitamura, M. Nishimoto, K. Sakai, and S. Noda, “Needle-like focus generation by radially polarized halo beams emitted by photonic-crystal ring-cavity laser,” Appl. Phys. Lett.101, 221103 (2012).
[CrossRef]

E. T. F. Rogers, S. Savo, J. Lindberg, T. Roy, M. R. Dennis, and N. I. Zheludev, “Super-oscillatory optical needle,” Appl. Phys. Lett.102, 031108 (2013).
[CrossRef]

Chin. Opt. Lett.

J. Opt. Soc. Am. A

Nat. Photonics

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. Photonics2, 501–505 (2008).
[CrossRef]

Opt. Commun.

T. Grosjean and I. Gauthier, “Longitudinally polarized electric and magnetic optical nano-needles of ultra high lengths,” Opt. Commun.294, 333–337 (2013).
[CrossRef]

J. Wang, W. Chen, and Q. Zhan, “Three-dimensional focus engineering using dipole array radiation pattern,” Opt. Commun.284, 2668–2671 (2011).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

X. L. Wang, J. Chen, Y. N. Li, J. P. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett.105, 253602 (2010).
[CrossRef]

Proc. R. Soc. A

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

Other

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company, 2005), Sec. 5.

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Figures (7)

Fig. 1
Fig. 1

Schematic of experimental setup for generating the radial-variant vector field and detecting the needle-like field. L1–L3: Lens; F: spatial filter; G: Ronchi phase grating; and P: polarizer.

Fig. 2
Fig. 2

Measured (top row) and simulated (lower row) intensity patterns passing through a horizontal polarizer of the radial-variant vector fields with different values of p. Any picture has a dimension of 6 mm×6 mm.

Fig. 3
Fig. 3

Intensity patterns of the tightly focused radial-variant vector fields in the XZ plane when β = 1, NA = 0.8, and different values of p. Any picture has a dimension of 5λ × 10λ.

Fig. 4
Fig. 4

The size of the optical needle generated by the tightly focused vector field with β = 1, p = 8, and NA = 0.8. (a) Intensity distribution in the focal region along the z-axis (x = y = 0). (b) Transverse component |Et|2, longitudinal component |Ez|2, and global intensity |Et|2 + |Ez|2 on the focal plane along the x-axis. The inset of (a) is the NA-dependent DOF. The inset of (b) is the contour plot of the global intensity pattern on the focal plane with the dimension of 2λ × 2λ.

Fig. 5
Fig. 5

The size of the optical needle generated by the nonparaxial focusing of a radial-variant vector field when r0 = 2.5 mm, f = 10 mm, and p = 8. (a) Intensity distribution on the focal region along the z-axis (x = y = 0). (b) Intensity distribution on the focal plane along the x-axis (y = 0). The inset of (a) is the f -dependent DOF. The inset of (b) is the contour plot of the intensity pattern on the focal plane with the dimension of 4λ × 4λ.

Fig. 6
Fig. 6

Optical needle generated by the paraxial focusing of a radial-variant vector field when r0 = 2.72 mm, f = 175 mm, and p = 8. (a) Intensity patterns through the focus in the XZ plane with a dimension of 12 mm×200 μm. Measured (b) and simulated (c) intensity patterns taken at planes (1–5) with d = 1 mm marked in (a).

Fig. 7
Fig. 7

Polarization evolution of the optical needle shown in Fig. 6(a). Measured (a, c) and simulated (b, d) intensity patterns with a polarizer taken at the planes (3, 5) marked in Fig. 6(a). (e) The simulated distribution of SoPs (Pink: LH polarization; Yellow: RH polarizaiton; White arrows: linear polarization) at planes (1–5).

Equations (14)

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E ( r , ϕ ) = A 0 circ ( r / r 0 ) ( cos δ e ^ x + sin δ e ^ y )
E x ( ρ , φ , z ) = c 0 i 0 α sin θ cos θ e i k z cos θ { cos [ 2 π β p ( sin θ sin α ) p ] ( 1 + cos θ ) J 0 ( k ρ sin θ ) + cos [ 2 π β p ( sin θ sin α ) p 2 φ ] ( 1 cos θ ) J 2 ( k ρ sin θ ) } d θ ,
E y ( ρ , φ , z ) = c 0 i 0 α sin θ cos θ e i k z cos θ { sin [ 2 π β p ( sin θ sin α ) p ] ( 1 + cos θ ) J 0 ( k ρ sin θ ) + sin [ 2 π β p ( sin θ sin α ) p 2 φ ] ( cos θ 1 ) J 2 ( k ρ sin θ ) } d θ ,
E z ( ρ , φ , z ) = 2 c 0 0 α sin 2 θ cos θ e i k z cos θ J 1 ( k ρ sin θ ) cos [ 2 π β p ( sin θ sin α ) p φ ] d θ ,
DOF = 4 λ / NA 2 .
E x ( ρ , φ , z ) = i k A 0 z e i k ξ ξ 2 0 r 0 cos δ exp ( i τ r 2 ) J 0 ( γ r ) r d r ,
E y ( ρ , φ , z ) = i k A 0 z e i k ξ ξ 2 0 r 0 sin δ exp ( i τ r 2 ) J 0 ( γ r ) r d r ,
E z ( ρ , φ , z ) = i k A 0 e i k ξ ξ 2 0 r 0 [ ρ J 0 ( γ r ) + i r J 1 ( γ r ) ] cos ( δ φ ) e i τ r 2 r d r ,
DOF = 4 f 2 λ / r 0 2 .
E x ( ρ , φ , z ) = i k A 0 e i k η η 0 r 0 cos δ exp ( i μ r 2 ) J 0 ( k ρ r η ) r d r ,
E y ( ρ , φ , z ) = i k A 0 e i k η η 0 r 0 sin δ exp ( i μ r 2 ) J 0 ( k ρ r η ) r d r ,
E ( ρ , φ , z ) = E + σ ^ + + E σ ^
E + = i k A 0 e i k η 2 η 0 r 0 exp ( i μ r 2 i δ ) J 0 ( k ρ r η ) r d r ,
E = i k A 0 e i k η 2 η 0 r 0 exp ( i μ r 2 + i δ ) J 0 ( k ρ r η ) r d r .

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