Abstract

We investigate the tight focusing properties of a double-ring-shaped, azimuthally polarized vector beam (DRS-APVB) by use of vectorial Debye theory. It is shown that a dark channel with an ultralong depth of focus (106λ) and subwavelength focal holes (0.5λ) can be generated by focusing a DRS-APVB through a dielectric interface with an annular high-numerical aperture (NA) objective lens. The influence of the NA of the objective, the relative refractive indices of two dielectric media, and the probe depth of the system on the focusing properties of the dark channel has been studied in detail. Such a non-diffracting dark channel could find potential applications in atom optical experiments, such as with atomic lenses, atom traps, and atom switches.

© 2014 Optical Society of America

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References

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  1. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
    [CrossRef]
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    [CrossRef]
  4. 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, 0526901 (2013).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. 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. Photonics 2, 501–505 (2008).
    [CrossRef]
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    [CrossRef]
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2014 (1)

2013 (3)

K. D. Leaked, A. R. Hawkins, and H. Schmidt, “All-optical particle trap using orthogonally intersecting beams,” Photon. Res. 1, 47–51 (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, 0526901 (2013).
[CrossRef]

S. N. Khonina and A. V. Ustinov, “Thin light tube formation by tightly focused azimuthally polarized light beams,” ISRN Opt. 2013, 185495 (2013).
[CrossRef]

2012 (2)

2011 (1)

C. Kuang, X. Hao, X. Liu, T. Wang, and Y. Ku, “Formation of sub-half-wavelength focal spot with ultralong depth of focus,” Opt. Commun. 284, 1766–1769 (2011).
[CrossRef]

2009 (1)

R. Zhou, B. Escamilla, J. Haus, P. Powers, and Q. Zhan, “Fiber laser generating switchable radially and azimuthally polarized beams with 140  mW output power at 1.6  μm wavelength,” Appl. Phys. Lett. 95, 191111 (2009).
[CrossRef]

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. Photonics 2, 501–505 (2008).
[CrossRef]

2005 (2)

2004 (1)

2003 (2)

E. Engel, N. Huse, T. A. Klar, and S. W. Hell, “Creating λ/3 focal holes with a Mach–Zehnder interferometer,” Appl. Phys. B 77, 11–17 (2003).
[CrossRef]

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

2002 (3)

2001 (3)

2000 (1)

1998 (1)

P. Ke and M. Gu, “Characterization of trapping force in the presence of spherical aberration,” J. Mod. Opt. 45, 2159–2168 (1998).
[CrossRef]

1959 (1)

E. Wolf, “Electromagnetic diffraction in optical systems I. An integral representation of the image field,” Proc. R. Soc. London 253, 349–357 (1959).
[CrossRef]

Anbarasan, P. M.

Biener, G.

Biss, D. P.

Bomzon, Z.

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge, 1999).

Brown, T. G.

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. Photonics 2, 501–505 (2008).
[CrossRef]

Dorn, R.

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

Engel, E.

E. Engel, N. Huse, T. A. Klar, and S. W. Hell, “Creating λ/3 focal holes with a Mach–Zehnder interferometer,” Appl. Phys. B 77, 11–17 (2003).
[CrossRef]

T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E 64, 066613 (2001).
[CrossRef]

Escamilla, B.

R. Zhou, B. Escamilla, J. Haus, P. Powers, and Q. Zhan, “Fiber laser generating switchable radially and azimuthally polarized beams with 140  mW output power at 1.6  μm wavelength,” Appl. Phys. Lett. 95, 191111 (2009).
[CrossRef]

Foley, J. T.

Gu, M.

P. Ke and M. Gu, “Characterization of trapping force in the presence of spherical aberration,” J. Mod. Opt. 45, 2159–2168 (1998).
[CrossRef]

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

Guo, L.

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, 0526901 (2013).
[CrossRef]

Hao, X.

C. Kuang, X. Hao, X. Liu, T. Wang, and Y. Ku, “Formation of sub-half-wavelength focal spot with ultralong depth of focus,” Opt. Commun. 284, 1766–1769 (2011).
[CrossRef]

Hasman, E.

Haus, J.

R. Zhou, B. Escamilla, J. Haus, P. Powers, and Q. Zhan, “Fiber laser generating switchable radially and azimuthally polarized beams with 140  mW output power at 1.6  μm wavelength,” Appl. Phys. Lett. 95, 191111 (2009).
[CrossRef]

Hawkins, A. R.

Hell, S. W.

E. Engel, N. Huse, T. A. Klar, and S. W. Hell, “Creating λ/3 focal holes with a Mach–Zehnder interferometer,” Appl. Phys. B 77, 11–17 (2003).
[CrossRef]

T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E 64, 066613 (2001).
[CrossRef]

Helseth, L. E.

L. E. Helseth, “Focusing of atoms with strongly confined light potentials,” Opt. Commun. 212, 343–352 (2002).
[CrossRef]

Hu, K.

Huse, N.

E. Engel, N. Huse, T. A. Klar, and S. W. Hell, “Creating λ/3 focal holes with a Mach–Zehnder interferometer,” Appl. Phys. B 77, 11–17 (2003).
[CrossRef]

Jaroszewicz, Z.

Jhe, W.

Ke, P.

P. Ke and M. Gu, “Characterization of trapping force in the presence of spherical aberration,” J. Mod. Opt. 45, 2159–2168 (1998).
[CrossRef]

Khonina, S. N.

S. N. Khonina and A. V. Ustinov, “Thin light tube formation by tightly focused azimuthally polarized light beams,” ISRN Opt. 2013, 185495 (2013).
[CrossRef]

Kim, J.

Kim, K.

Klar, T. A.

E. Engel, N. Huse, T. A. Klar, and S. W. Hell, “Creating λ/3 focal holes with a Mach–Zehnder interferometer,” Appl. Phys. B 77, 11–17 (2003).
[CrossRef]

T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E 64, 066613 (2001).
[CrossRef]

Kleiner, V.

Ku, Y.

C. Kuang, X. Hao, X. Liu, T. Wang, and Y. Ku, “Formation of sub-half-wavelength focal spot with ultralong depth of focus,” Opt. Commun. 284, 1766–1769 (2011).
[CrossRef]

Kuang, C.

C. Kuang, X. Hao, X. Liu, T. Wang, and Y. Ku, “Formation of sub-half-wavelength focal spot with ultralong depth of focus,” Opt. Commun. 284, 1766–1769 (2011).
[CrossRef]

Lalithambigai, K.

Leaked, K. D.

Leger, J.

Leuchs, G.

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

Li, T.

Liu, X.

C. Kuang, X. Hao, X. Liu, T. Wang, and Y. Ku, “Formation of sub-half-wavelength focal spot with ultralong depth of focus,” Opt. Commun. 284, 1766–1769 (2011).
[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. Photonics 2, 501–505 (2008).
[CrossRef]

Min, C.

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, 0526901 (2013).
[CrossRef]

Munro, P. R. T.

Noh, H.

Pillai, T. V. S.

Powers, P.

R. Zhou, B. Escamilla, J. Haus, P. Powers, and Q. Zhan, “Fiber laser generating switchable radially and azimuthally polarized beams with 140  mW output power at 1.6  μm wavelength,” Appl. Phys. Lett. 95, 191111 (2009).
[CrossRef]

Prabakaran, K.

Pu, J.

Quabis, S.

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

Rajesh, K. B.

Ravi, V.

Schmidt, H.

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. Photonics 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. Photonics 2, 501–505 (2008).
[CrossRef]

Shin, Y.

Suresh, P.

Török, P.

Ustinov, A. V.

S. N. Khonina and A. V. Ustinov, “Thin light tube formation by tightly focused azimuthally polarized light beams,” ISRN Opt. 2013, 185495 (2013).
[CrossRef]

Visser, T. D.

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. Photonics 2, 501–505 (2008).
[CrossRef]

Wang, T.

C. Kuang, X. Hao, X. Liu, T. Wang, and Y. Ku, “Formation of sub-half-wavelength focal spot with ultralong depth of focus,” Opt. Commun. 284, 1766–1769 (2011).
[CrossRef]

Wang, X.

Wang, Z.

Wei, S.

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, 0526901 (2013).
[CrossRef]

Wolf, E.

J. T. Foley and E. Wolf, “Wavefront spacing in the focal region of high-numerical-aperture systems,” Opt. Lett. 30, 1312–1314 (2005).
[CrossRef]

E. Wolf, “Electromagnetic diffraction in optical systems I. An integral representation of the image field,” Proc. R. Soc. London 253, 349–357 (1959).
[CrossRef]

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge, 1999).

Youngworth, K. S.

Yuan, X.

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, 0526901 (2013).
[CrossRef]

Zhan, Q.

R. Zhou, B. Escamilla, J. Haus, P. Powers, and Q. Zhan, “Fiber laser generating switchable radially and azimuthally polarized beams with 140  mW output power at 1.6  μm wavelength,” Appl. Phys. Lett. 95, 191111 (2009).
[CrossRef]

Q. Zhan and J. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10, 324–331 (2002).
[CrossRef]

Zhong, M.

Zhou, J.

Zhou, R.

R. Zhou, B. Escamilla, J. Haus, P. Powers, and Q. Zhan, “Fiber laser generating switchable radially and azimuthally polarized beams with 140  mW output power at 1.6  μm wavelength,” Appl. Phys. Lett. 95, 191111 (2009).
[CrossRef]

Appl. Phys. B (1)

E. Engel, N. Huse, T. A. Klar, and S. W. Hell, “Creating λ/3 focal holes with a Mach–Zehnder interferometer,” Appl. Phys. B 77, 11–17 (2003).
[CrossRef]

Appl. Phys. Lett. (1)

R. Zhou, B. Escamilla, J. Haus, P. Powers, and Q. Zhan, “Fiber laser generating switchable radially and azimuthally polarized beams with 140  mW output power at 1.6  μm wavelength,” Appl. Phys. Lett. 95, 191111 (2009).
[CrossRef]

Chin. Opt. Lett. (2)

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, 0526901 (2013).
[CrossRef]

M. Zhong, X. Wang, J. Zhou, Z. Wang, and T. Li, “Optimal beam diameter for lateral optical forces on microspheres at a water–air interface,” Chin. Opt. Lett. 12, 011403 (2014).
[CrossRef]

ISRN Opt. (1)

S. N. Khonina and A. V. Ustinov, “Thin light tube formation by tightly focused azimuthally polarized light beams,” ISRN Opt. 2013, 185495 (2013).
[CrossRef]

J. Mod. Opt. (1)

P. Ke and M. Gu, “Characterization of trapping force in the presence of spherical aberration,” J. Mod. Opt. 45, 2159–2168 (1998).
[CrossRef]

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

Nat. Photonics (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. Photonics 2, 501–505 (2008).
[CrossRef]

Opt. Commun. (2)

C. Kuang, X. Hao, X. Liu, T. Wang, and Y. Ku, “Formation of sub-half-wavelength focal spot with ultralong depth of focus,” Opt. Commun. 284, 1766–1769 (2011).
[CrossRef]

L. E. Helseth, “Focusing of atoms with strongly confined light potentials,” Opt. Commun. 212, 343–352 (2002).
[CrossRef]

Opt. Express (4)

Opt. Lett. (5)

Photon. Res. (1)

Phys. Rev. E (1)

T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E 64, 066613 (2001).
[CrossRef]

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]

Proc. R. Soc. London (1)

E. Wolf, “Electromagnetic diffraction in optical systems I. An integral representation of the image field,” Proc. R. Soc. London 253, 349–357 (1959).
[CrossRef]

Other (2)

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

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge, 1999).

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Figures (7)

Fig. 1.
Fig. 1.

Scheme of focusing optical system.

Fig. 2.
Fig. 2.

Intensity distribution for different values of β. (a) β=1.2 and (b) β=1.15. The parameters for calculations are A=1, n0=1, n1=1, n2=3.55, NA=0.6, d=13λ, and δ=0.76.

Fig. 3.
Fig. 3.

Phase distribution of Eφt(r,φ,z) near focus. (a) Along axis r in the plane of 36λ and 37λ, and (b) along optical axis z with r=0.485λ. β=1.2. The other parameters are the same as those in Fig. 2.

Fig. 4.
Fig. 4.

Intensity distribution for different rφ planes, in which arrows indicate the polarization direction of the focused field. (a) Plane z and (b) plane z+λ/2. λ is the wavefront spacing of focused, azimuthally polarized beams. β=1.2. The other parameters are the same as those in Fig. 2.

Fig. 5.
Fig. 5.

(a) An intensity profile across the plane of z=42λ. (b) Distribution of the FWHM of the focal hole and the wavefront spacing of focused, azimuthally polarized beams along the dark channel with r=0.485λ and β=1.2. The other parameters are the same as those in Fig. 2.

Fig. 6.
Fig. 6.

Influence of varying NA on the focusing properties of the dark channel. (a) Depth of focus of the dark channel, (b) FWHM of the focal hole, and (c) wavefront spacing in the middle of the dark channel with r=0.485λ and β=1.2. The other parameters are the same as those in Fig. 2.

Fig. 7.
Fig. 7.

Intensity distribution for different values of d. (a) d=15λ, (b) d=3λ. The white line represents the interface of the system. β=1.2; the other parameters are the same as those in Fig. 2.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

Eφr(r,φ,z)=2Aδ·ααexp[i2k1dcosθ1]rscosθ1sinθ1A(θ1)J1(k1rsinθ1)exp[izk1cosθ1]dθ1,
Eφt(r,φ,z)=2Aδ·ααexp[ik0Φ(θ1,θ2)]tscosθ1sinθ1A(θ1)J1(k1rsinθ1)exp[izk2cosθ2]dθ1,
rs=n1cosθ1n2cosθ2n1cosθ1+n2cosθ2,
ts=2sinθ2cosθ1sin(θ1+θ2).
Φ(θ1,θ2)=d(n1cosθ1n2cosθ2),
A(θ1)=β2sinθ1sin2αexp[(βsinθ1sinα)2]Lp1[2(βsinθ1sinα)2],

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