Abstract

It is a great challenge to create a needle-like field with properties of long beam length, narrow lateral width, uniformity, and high optical efficiency. Here we show a method that can realize these properties all at once. The key element is a 90° apex-angle concave conical mirror. By using this condenser along with a radially polarized incident beam of a specific field distribution, we numerically created a super slim, uniform, pure needle-like axially polarized field. This axially polarized field has a length of 50,000λ along the optical axis, and its lateral width still maintains a minimum 0.36λ size.

© 2014 Optical Society of America

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    [CrossRef]
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  8. Y. Kozawa, K. Yonezawa, and S. Sato, “Radially polarized laser beam from a Nd:YAG laser cavity with a c-cut YVO4 crystal,” Appl. Phys. B 88, 43–46 (2007).
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    [CrossRef]
  33. T. Cizmar and K. Dholakia, “Tunable Bessel light modes: engineering the axial propagation,” Opt. Express 17, 15558–15570 (2009).
    [CrossRef]
  34. H. Wang, L. 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]
  35. C. J. R. Sheppard and A. A. Choudhury, “Annular pupils, radial polarization, and superresolution,” Appl. Opt. 43, 4322–4327 (2004).
    [CrossRef]
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    [CrossRef]
  37. E. E. Ushakova and S. N. Kurilkina, “Formation of Bessel light pulses by means of a conical mirror,” J. Appl. Spectrosc. 77, 827–831 (2011).
    [CrossRef]
  38. K. B. Kuntz, B. Braverman, S. H. Youn, M. Lobino, E. M. Pessina, and A. I. Lvovsky, “Spatial and temporal characterization of a Bessel beam produced using a conical mirror,” Phys. Rev. A 79, 043802 (2009).
    [CrossRef]
  39. J. F. Fortin, G. Rousseau, N. McCarthy, and M. Piche, “Generation of quasi-Bessel beams and femtosecond optical X-waves with conical mirrors,” Proc. SPIE 4833, 876 (2003).
    [CrossRef]
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    [CrossRef]
  41. V. N. Belyi, N. S. Kazak, S. N. Kurilkina, and N. A. Khilo, “Generation of TE- and TH-polarized Bessel beams using one-dimensional photonic crystal,” Opt. Commun. 282, 1998–2008 (2009).
    [CrossRef]
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    [CrossRef]
  45. G. M. Lerman, A. Yanai, and U. Levy, “Demonstration of nanofocusing by the use of plasmonic lens illuminated with radially polarized light,” Nano Lett. 9, 2139–2143 (2009).
    [CrossRef]
  46. U. Schröter and D. Heitmann, “Surface-plasmon-enhanced transmission through metallic gratings,” Phys. Rev. B 58, 15419–15421 (1998).
    [CrossRef]
  47. J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845–2848 (1999).
    [CrossRef]
  48. P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A 2, 48–51 (2000).
    [CrossRef]
  49. Q. Cao and P. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88, 57403 (2002).
    [CrossRef]
  50. J. A. Hoffnagle and C. M. Jefferson, “Design and performance of a refractive optical system that converts a Gaussian to a flattop beam,” Appl. Opt. 39, 5488–5499 (2000).
    [CrossRef]

2013

J. Breuer and P. Hommelhoff, “Laser-based acceleration of nonrelativistic electrons at a dielectric structure,” Phys. Rev. Lett. 111, 134803 (2013).
[CrossRef]

T. Liu, J. Tan, J. Lin, and J. Liu, “Generating super-Gaussian light needle of 0.36 λ beam size and pure longitudinal polarization,” Opt. Eng. 52, 074104 (2013).
[CrossRef]

2012

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101, 041105 (2012).
[CrossRef]

X. Hao, C. Kuang, Y. Li, and X. Liu, “A method for extending depth of focus in STED nanolithography,” J. Opt. 14, 045702 (2012).
[CrossRef]

H. Dehez, A. April, and M. Piché, “Needles of longitudinally polarized light: guidelines for minimum spot size and tunable axial extent,” Opt. Express 20, 14891–14905 (2012).
[CrossRef]

2011

S. N. Khonina, N. L. Kazanskiy, and S. G. Volotovsky, “Vortex phase transmission function as a factor to reduce the focal spot of high-aperture focusing system,” J. Mod. Opt. 58, 748–760 (2011).
[CrossRef]

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

E. E. Ushakova and S. N. Kurilkina, “Formation of Bessel light pulses by means of a conical mirror,” J. Appl. Spectrosc. 77, 827–831 (2011).
[CrossRef]

2010

2009

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1–57 (2009).
[CrossRef]

T. Cizmar and K. Dholakia, “Tunable Bessel light modes: engineering the axial propagation,” Opt. Express 17, 15558–15570 (2009).
[CrossRef]

H. Dehez, M. Piché, and Y. De Koninck, “Enhanced resolution in two-photon imaging using a TM(01) laser beam at a dielectric interface,” Opt. Lett. 34, 3601–3603 (2009).
[CrossRef]

Z. Li, K. B. Alici, H. Caglayan, and E. Ozbay, “Generation of an axially asymmetric Bessel-like beam from a metallic subwavelength aperture,” Phys. Rev. Lett. 102, 143901 (2009).
[CrossRef]

G. M. Lerman, A. Yanai, and U. Levy, “Demonstration of nanofocusing by the use of plasmonic lens illuminated with radially polarized light,” Nano Lett. 9, 2139–2143 (2009).
[CrossRef]

V. N. Belyi, N. S. Kazak, S. N. Kurilkina, and N. A. Khilo, “Generation of TE- and TH-polarized Bessel beams using one-dimensional photonic crystal,” Opt. Commun. 282, 1998–2008 (2009).
[CrossRef]

K. B. Kuntz, B. Braverman, S. H. Youn, M. Lobino, E. M. Pessina, and A. I. Lvovsky, “Spatial and temporal characterization of a Bessel beam produced using a conical mirror,” Phys. Rev. A 79, 043802 (2009).
[CrossRef]

W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Plasmonic lens made of multiple concentric metallic rings under radially polarized illumination,” Nano Lett. 9, 4320–4325 (2009).
[CrossRef]

2008

H. Wang, L. 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]

O. Brzobohatý, T. Cizmár, and P. Zemánek, “High quality quasi-Bessel beam generated by round-tip axicon,” Opt. Express 16, 12688–12700 (2008).
[CrossRef]

2007

E. Y. S. Yew and C. J. R. Sheppard, “Second harmonic generation polarization microscopy with tightly focused linearly and radially polarized beams,” Opt. Commun. 275, 453–457 (2007).
[CrossRef]

H. Wang, G. Yuan, W. Tan, L. Shi, and T. Chong, “Spot size and depth of focus in optical data storage system,” Opt. Eng. 46, 065201 (2007).
[CrossRef]

K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, and D. H. Woo, “Vector field microscopic imaging of light,” Nat. Photonics 1, 53–56 (2007).
[CrossRef]

Y. Kozawa, K. Yonezawa, and S. Sato, “Radially polarized laser beam from a Nd:YAG laser cavity with a c-cut YVO4 crystal,” Appl. Phys. B 88, 43–46 (2007).
[CrossRef]

2004

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85, 6239–6241 (2004).
[CrossRef]

C. J. R. Sheppard and A. A. Choudhury, “Annular pupils, radial polarization, and superresolution,” Appl. Opt. 43, 4322–4327 (2004).
[CrossRef]

2003

C.-C. Sun and C.-K. Liu, “Ultrasmall focusing spot with a long depth of focus based on polarization and phase modulation,” Opt. Lett. 28, 99–101 (2003).
[CrossRef]

D. Ganic, X. Gan, and M. Gu, “Focusing of doughnut laser beams by a high numerical-aperture objective in free space,” Opt. Express 11, 2747–2752 (2003).
[CrossRef]

J. F. Fortin, G. Rousseau, N. McCarthy, and M. Piche, “Generation of quasi-Bessel beams and femtosecond optical X-waves with conical mirrors,” Proc. SPIE 4833, 876 (2003).
[CrossRef]

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

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90, 13903 (2003).
[CrossRef]

2002

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef]

Q. Cao and P. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88, 57403 (2002).
[CrossRef]

2001

C. J. Sheppard, “High-aperture beams,” J. Opt. Soc. Am. A 18, 1579–1587 (2001).
[CrossRef]

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
[CrossRef]

2000

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85, 4482–4485 (2000).
[CrossRef]

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A 2, 48–51 (2000).
[CrossRef]

J. A. Hoffnagle and C. M. Jefferson, “Design and performance of a refractive optical system that converts a Gaussian to a flattop beam,” Appl. Opt. 39, 5488–5499 (2000).
[CrossRef]

1999

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845–2848 (1999).
[CrossRef]

1998

U. Schröter and D. Heitmann, “Surface-plasmon-enhanced transmission through metallic gratings,” Phys. Rev. B 58, 15419–15421 (1998).
[CrossRef]

1995

Z. Bouchal and M. Olivík, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995).
[CrossRef]

W. Kimura, G. Kim, R. Romea, L. Steinhauer, I. Pogorelsky, K. Kusche, R. Fernow, X. Wang, and Y. Liu, “Laser acceleration of relativistic electrons using the inverse Cherenkov effect,” Phys. Rev. Lett. 74, 546–549 (1995).
[CrossRef]

1990

R. D. Romea and W. D. Kimura, “Modeling of inverse Čerenkov laser acceleration with axicon laser-beam focusing,” Phys. Rev. D 42, 1807–1818 (1990).
[CrossRef]

L. Cicchitelli, H. Hora, and R. Postle, “Longitudinal field components for laser beams in vacuum,” Phys. Rev. A 41, 3727–3732 (1990).
[CrossRef]

1987

J. Durnin and J. J. Miceli, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

1983

J. R. Fontana and R. H. Pantell, “A high-energy, laser accelerator for electrons using the inverse Cherenkov effect,” J. Appl. Phys. 54, 4285–4288 (1983).
[CrossRef]

1979

T. Tajima and J. M. Dawson, “Laser electron accelerator,” Phys. Rev. Lett. 43, 267–270 (1979).
[CrossRef]

1959

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. Ser. A 253, 358–379 (1959).

Abeysinghe, D. C.

W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Plasmonic lens made of multiple concentric metallic rings under radially polarized illumination,” Nano Lett. 9, 4320–4325 (2009).
[CrossRef]

Alici, K. B.

Z. Li, K. B. Alici, H. Caglayan, and E. Ozbay, “Generation of an axially asymmetric Bessel-like beam from a metallic subwavelength aperture,” Phys. Rev. Lett. 102, 143901 (2009).
[CrossRef]

April, A.

Astilean, S.

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A 2, 48–51 (2000).
[CrossRef]

Belyi, V. N.

V. N. Belyi, N. S. Kazak, S. N. Kurilkina, and N. A. Khilo, “Generation of TE- and TH-polarized Bessel beams using one-dimensional photonic crystal,” Opt. Commun. 282, 1998–2008 (2009).
[CrossRef]

Beversluis, M.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90, 13903 (2003).
[CrossRef]

Beversluis, M. R.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
[CrossRef]

Bouchal, Z.

Z. Bouchal and M. Olivík, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995).
[CrossRef]

Bouhelier, A.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90, 13903 (2003).
[CrossRef]

Braverman, B.

K. B. Kuntz, B. Braverman, S. H. Youn, M. Lobino, E. M. Pessina, and A. I. Lvovsky, “Spatial and temporal characterization of a Bessel beam produced using a conical mirror,” Phys. Rev. A 79, 043802 (2009).
[CrossRef]

Breuer, J.

J. Breuer and P. Hommelhoff, “Laser-based acceleration of nonrelativistic electrons at a dielectric structure,” Phys. Rev. Lett. 111, 134803 (2013).
[CrossRef]

Brown, T. G.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
[CrossRef]

Brzobohatý, O.

Caglayan, H.

Z. Li, K. B. Alici, H. Caglayan, and E. Ozbay, “Generation of an axially asymmetric Bessel-like beam from a metallic subwavelength aperture,” Phys. Rev. Lett. 102, 143901 (2009).
[CrossRef]

Cao, Q.

Q. Cao and P. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88, 57403 (2002).
[CrossRef]

Chen, W.

J. Wang, W. Chen, and Q. Zhan, “Engineering of high purity ultra-long optical needle field through reversing the electric dipole array radiation,” Opt. Express 18, 21965–21972 (2010).
[CrossRef]

W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Plasmonic lens made of multiple concentric metallic rings under radially polarized illumination,” Nano Lett. 9, 4320–4325 (2009).
[CrossRef]

Choi, S. B.

K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, and D. H. Woo, “Vector field microscopic imaging of light,” Nat. Photonics 1, 53–56 (2007).
[CrossRef]

Choi, W. J.

K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, and D. H. Woo, “Vector field microscopic imaging of light,” Nat. Photonics 1, 53–56 (2007).
[CrossRef]

Chong, C. T.

H. Wang, L. 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]

Chong, T.

H. Wang, G. Yuan, W. Tan, L. Shi, and T. Chong, “Spot size and depth of focus in optical data storage system,” Opt. Eng. 46, 065201 (2007).
[CrossRef]

Choudhury, A. A.

Cicchitelli, L.

L. Cicchitelli, H. Hora, and R. Postle, “Longitudinal field components for laser beams in vacuum,” Phys. Rev. A 41, 3727–3732 (1990).
[CrossRef]

Cizmar, T.

Cizmár, T.

Dawson, J. M.

T. Tajima and J. M. Dawson, “Laser electron accelerator,” Phys. Rev. Lett. 43, 267–270 (1979).
[CrossRef]

De Koninck, Y.

Dehez, H.

Dholakia, K.

T. Cizmar and K. Dholakia, “Tunable Bessel light modes: engineering the axial propagation,” Opt. Express 17, 15558–15570 (2009).
[CrossRef]

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[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]

Durnin, J.

J. Durnin and J. J. Miceli, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

Fernow, R.

W. Kimura, G. Kim, R. Romea, L. Steinhauer, I. Pogorelsky, K. Kusche, R. Fernow, X. Wang, and Y. Liu, “Laser acceleration of relativistic electrons using the inverse Cherenkov effect,” Phys. Rev. Lett. 74, 546–549 (1995).
[CrossRef]

Fontana, J. R.

J. R. Fontana and R. H. Pantell, “A high-energy, laser accelerator for electrons using the inverse Cherenkov effect,” J. Appl. Phys. 54, 4285–4288 (1983).
[CrossRef]

Fortin, J. F.

J. F. Fortin, G. Rousseau, N. McCarthy, and M. Piche, “Generation of quasi-Bessel beams and femtosecond optical X-waves with conical mirrors,” Proc. SPIE 4833, 876 (2003).
[CrossRef]

Fourmaux, S.

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of the setup and basic idea of the method. (a) Radially polarized incident beam of a specific intensity distribution and a 90° apex-angle concave conical mirror, where r0=104λ is the radius of the hole at the tip. (b) First stage of transmission, reflection. (c) Second stage of transmission, converging.

Fig. 2.
Fig. 2.

Electric energy density of the soft-edged electric field. (a) Er2(r,zcw) before reflection. (b) Ez2(r0,z) after reflection.

Fig. 3.
Fig. 3.

Electric density distributions of the field component Ez at the near axis. (a) Contour plot in the meridional plane. (b) Profile plot in the xy plane.

Fig. 4.
Fig. 4.

Diffraction results of scalar waves with different lateral intensity profile travel (z direction) through a 60,000λ wide (x direction) but infinitely long (y direction) opening in an opaque screen. Different incident scalar wave profiles: (a) rectangle profile, (c) super-Gaussian (2n=400) profile, (e) super-Gaussian (2n=16) profile and correspondingly different diffraction results on the output screen (z=60,000λ): (b) rectangle diffraction, (d) super-Gaussian (2n=400) diffraction, (f) super-Gaussian (2n=16) diffraction. Inserts in (b), (d), and (f) give a detailed view of each diffraction result.

Fig. 5.
Fig. 5.

(a) Intensity and (b) phase distribution profile of the diffracted super-Gaussian field (2n=16). Insert, detailed view of the phase oscillation starting at one end of the super-Gaussian field. The phase amplitude is smaller than 0.1 when intensity reaches 105 of the center intensity. The influence of the phase inhomogeneity that occurs at both ends of the super-Gaussian field can be ignored.

Equations (7)

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

Er(r,z)=f(r)·ejkzr^,
Ez(r,z)=g(z)r·ejkrz^,λrr0,
f(r)=g(z)r,
g(z)={e(zzcwΔw)2n0,zcw<z<zc+wotherwise.
f(r)={1re(rcrwΔw)2n0,rcw<r<rc+wotherwise.
U(P0)=14πS{GUnUGn}ds.
G=exp(jkr01)r01,

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