Abstract

The focal field of high NA lens axicon with a binary-phase optical component is calculated by using vector diffraction theory. Numerical results show that for a radially polarized Bessel Gaussian input field, the proposed system generates a subwavelength (0.395λ) longitudinally polarized beam with large uniform depth of focus (approximately 6 λ).

© 2010 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
    [CrossRef]
  2. E. Yew and C. Sheppard, “Second harmonic generation polarization microscopy with tightly focused linearly and radially polarized beams,” Opt. Commun. 275(2), 453–457 (2007).
    [CrossRef]
  3. N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85(25), 6239–6241 (2004).
    [CrossRef]
  4. R. D. Romea and W. D. Kimura, “Modeling of inverse Čerenkov laser acceleration with axicon laser-beam focusing,” Phys. Rev. D 42(5), 1807–1818 (1990).
    [CrossRef] [PubMed]
  5. C. J. R. Sheppard and A. Choudhury, “Annular pupils, radial polarization, and superresolution,” Appl. Opt. 43(22), 4322–4327 (2004).
    [CrossRef] [PubMed]
  6. L. E. Helseth, “Roles of polarization, phase and amplitude in solid immersion lens systems,” Opt. Commun. 191(3-6), 161–172 (2001).
    [CrossRef]
  7. C. Liu and S.-H. Park, “Numerical analysis of an annular-aperture solid immersion lens,” Opt. Lett. 29(15), 1742–1744 (2004).
    [CrossRef] [PubMed]
  8. Y. Xu, J. Singh, C. J. R. Sheppard, and N. Chen, “Ultra long high resolution beam by multi-zone rotationally symmetrical complex pupil filter,” Opt. Express 15(10), 6409–6413 (2007).
    [CrossRef] [PubMed]
  9. N. Davidson, A. A. Friesem, and E. Hasman, “Holographic axilens: high resolution and long focal depth,” Opt. Lett. 16(7), 523–525 (1991).
    [CrossRef] [PubMed]
  10. Z. Jaroszewicz, J. Sochacki, A. Kolodziejczyk, and L. R. Staroński, “Apodized annular-aperture logarithmic axicon: smoothness and uniformity of intensity distributions,” Opt. Lett. 18(22), 1893–1895 (1993).
    [CrossRef] [PubMed]
  11. J. Sochacki, S. Bará, Z. Jaroszewicz, and A. Kołodziejczyk, “Phase retardation of the uniform-intensity axilens,” Opt. Lett. 17(1), 7–9 (1992).
    [CrossRef] [PubMed]
  12. J. Sochacki, A. Kołodziejczyk, Z. Jaroszewicz, and S. Bará, “Nonparaxial design of generalized axicons,” Appl. Opt. 31(25), 5326–5330 (1992).
    [CrossRef] [PubMed]
  13. G. Mikula, Z. Jaroszewicz, A. Kolodziejczyk, K. Petelczyc, and M. Sypek, “Imaging with extended focal depth by means of lenses with radial and angular modulation,” Opt. Express 15(15), 9184–9193 (2007).
    [CrossRef] [PubMed]
  14. D. Mas, J. Espinosa, J. Perez, and C. Illueca, “Three dimensional analysis of chromatic aberration in diffractive elements with extended depth of focus,” Opt. Express 15(26), 17842–17854 (2007).
    [CrossRef] [PubMed]
  15. W. H. Steel, P. Mollet ed. (Pergamon, Oxford, UK), 181 − 192(1960)
  16. Z. Jaroszewicz and J. Morales, “Lens axicons: systems composed of a diverging aberrated lens and a perfect converging lens,” J. Opt. Soc. Am. A 15(9), 2383–2390 (1998).
    [CrossRef]
  17. Z. Jaroszewicz and J. Morales, “Lens axicons: systems composed of a diverging aberrated lens and a converging aberrated lens,” J. Opt. Soc. Am. A 16(1), 191–197 (1999).
    [CrossRef]
  18. J. Pu, H. Zhang, and S. Nemoto, “Lens axicons illuminated by Gaussian beams for generation of uniform-axial intensity Bessel fields,” Opt. Eng. 39(3), 803–806 (2000).
    [CrossRef]
  19. A. Burvall, K. Kołacz, Z. Jaroszewicz, and A. T. Friberg, “Simple lens axicon,” Appl. Opt. 43(25), 4838–4844 (2004).
    [CrossRef] [PubMed]
  20. K. B. Rajesh and P. M. Anbarasan, “Generation of sub-wavelength and super-resolution longitudinally polarized non-diffraction beam using lens axicon,” Chin. Opt. Lett. 6(10), 785–787 (2008).
    [CrossRef]
  21. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems, II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
    [CrossRef]
  22. 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(2), 99–101 (2003).
    [CrossRef] [PubMed]
  23. T. G. Jabbour and S. M. Kuebler, “Vector diffraction analysis of high numerical aperture focused beams modified by two- and three-zone annular multi-phase plates,” Opt. Express 14(3), 1033–1043 (2006).
    [CrossRef] [PubMed]
  24. K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000).
    [CrossRef] [PubMed]
  25. J. Chen and Y. Yu, “The focusing property of vector Bessel–Gauss beams by a high numerical aperture objective,” Opt. Commun. 283(9), 1655–1660 (2010).
    [CrossRef]
  26. 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(8), 501–505 (2008).
    [CrossRef]

2010 (1)

J. Chen and Y. Yu, “The focusing property of vector Bessel–Gauss beams by a high numerical aperture objective,” Opt. Commun. 283(9), 1655–1660 (2010).
[CrossRef]

2008 (2)

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(8), 501–505 (2008).
[CrossRef]

K. B. Rajesh and P. M. Anbarasan, “Generation of sub-wavelength and super-resolution longitudinally polarized non-diffraction beam using lens axicon,” Chin. Opt. Lett. 6(10), 785–787 (2008).
[CrossRef]

2007 (4)

2006 (1)

2004 (4)

2003 (1)

2001 (1)

L. E. Helseth, “Roles of polarization, phase and amplitude in solid immersion lens systems,” Opt. Commun. 191(3-6), 161–172 (2001).
[CrossRef]

2000 (3)

J. Pu, H. Zhang, and S. Nemoto, “Lens axicons illuminated by Gaussian beams for generation of uniform-axial intensity Bessel fields,” Opt. Eng. 39(3), 803–806 (2000).
[CrossRef]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
[CrossRef]

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000).
[CrossRef] [PubMed]

1999 (1)

1998 (1)

1993 (1)

1992 (2)

1991 (1)

1990 (1)

R. D. Romea and W. D. Kimura, “Modeling of inverse Čerenkov laser acceleration with axicon laser-beam focusing,” Phys. Rev. D 42(5), 1807–1818 (1990).
[CrossRef] [PubMed]

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems, II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[CrossRef]

Anbarasan, P. M.

Bará, S.

Brown, T. G.

Burvall, A.

Chen, J.

J. Chen and Y. Yu, “The focusing property of vector Bessel–Gauss beams by a high numerical aperture objective,” Opt. Commun. 283(9), 1655–1660 (2010).
[CrossRef]

Chen, N.

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(8), 501–505 (2008).
[CrossRef]

Choudhury, A.

Davidson, N.

Dorn, R.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
[CrossRef]

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
[CrossRef]

Espinosa, J.

Friberg, A. T.

Friesem, A. A.

Glöckl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
[CrossRef]

Hasman, E.

Hayazawa, N.

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85(25), 6239–6241 (2004).
[CrossRef]

Helseth, L. E.

L. E. Helseth, “Roles of polarization, phase and amplitude in solid immersion lens systems,” Opt. Commun. 191(3-6), 161–172 (2001).
[CrossRef]

Illueca, C.

Jabbour, T. G.

Jaroszewicz, Z.

Kawata, S.

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85(25), 6239–6241 (2004).
[CrossRef]

Kimura, W. D.

R. D. Romea and W. D. Kimura, “Modeling of inverse Čerenkov laser acceleration with axicon laser-beam focusing,” Phys. Rev. D 42(5), 1807–1818 (1990).
[CrossRef] [PubMed]

Kolacz, K.

Kolodziejczyk, A.

Kuebler, S. M.

Leuchs, G.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
[CrossRef]

Liu, C.

Liu, C.-K.

Lukyanchuk, B.

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(8), 501–505 (2008).
[CrossRef]

Mas, D.

Mikula, G.

Morales, J.

Nemoto, S.

J. Pu, H. Zhang, and S. Nemoto, “Lens axicons illuminated by Gaussian beams for generation of uniform-axial intensity Bessel fields,” Opt. Eng. 39(3), 803–806 (2000).
[CrossRef]

Park, S.-H.

Perez, J.

Petelczyc, K.

Pu, J.

J. Pu, H. Zhang, and S. Nemoto, “Lens axicons illuminated by Gaussian beams for generation of uniform-axial intensity Bessel fields,” Opt. Eng. 39(3), 803–806 (2000).
[CrossRef]

Quabis, S.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
[CrossRef]

Rajesh, K. B.

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. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[CrossRef]

Romea, R. D.

R. D. Romea and W. D. Kimura, “Modeling of inverse Čerenkov laser acceleration with axicon laser-beam focusing,” Phys. Rev. D 42(5), 1807–1818 (1990).
[CrossRef] [PubMed]

Saito, Y.

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85(25), 6239–6241 (2004).
[CrossRef]

Sheppard, C.

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(8), 501–505 (2008).
[CrossRef]

E. Yew and C. Sheppard, “Second harmonic generation polarization microscopy with tightly focused linearly and radially polarized beams,” Opt. Commun. 275(2), 453–457 (2007).
[CrossRef]

Sheppard, C. J. R.

Shi, L.

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(8), 501–505 (2008).
[CrossRef]

Singh, J.

Sochacki, J.

Staronski, L. R.

Sun, C.-C.

Sypek, M.

Wang, H.

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(8), 501–505 (2008).
[CrossRef]

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. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[CrossRef]

Xu, Y.

Yew, E.

E. Yew and C. Sheppard, “Second harmonic generation polarization microscopy with tightly focused linearly and radially polarized beams,” Opt. Commun. 275(2), 453–457 (2007).
[CrossRef]

Youngworth, K. S.

Yu, Y.

J. Chen and Y. Yu, “The focusing property of vector Bessel–Gauss beams by a high numerical aperture objective,” Opt. Commun. 283(9), 1655–1660 (2010).
[CrossRef]

Zhang, H.

J. Pu, H. Zhang, and S. Nemoto, “Lens axicons illuminated by Gaussian beams for generation of uniform-axial intensity Bessel fields,” Opt. Eng. 39(3), 803–806 (2000).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85(25), 6239–6241 (2004).
[CrossRef]

Chin. Opt. Lett. (1)

J. Opt. Soc. Am. A (2)

Nat. Photonics (1)

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(8), 501–505 (2008).
[CrossRef]

Opt. Commun. (4)

J. Chen and Y. Yu, “The focusing property of vector Bessel–Gauss beams by a high numerical aperture objective,” Opt. Commun. 283(9), 1655–1660 (2010).
[CrossRef]

L. E. Helseth, “Roles of polarization, phase and amplitude in solid immersion lens systems,” Opt. Commun. 191(3-6), 161–172 (2001).
[CrossRef]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
[CrossRef]

E. Yew and C. Sheppard, “Second harmonic generation polarization microscopy with tightly focused linearly and radially polarized beams,” Opt. Commun. 275(2), 453–457 (2007).
[CrossRef]

Opt. Eng. (1)

J. Pu, H. Zhang, and S. Nemoto, “Lens axicons illuminated by Gaussian beams for generation of uniform-axial intensity Bessel fields,” Opt. Eng. 39(3), 803–806 (2000).
[CrossRef]

Opt. Express (5)

Opt. Lett. (5)

Phys. Rev. D Part. Fields (1)

R. D. Romea and W. D. Kimura, “Modeling of inverse Čerenkov laser acceleration with axicon laser-beam focusing,” Phys. Rev. D 42(5), 1807–1818 (1990).
[CrossRef] [PubMed]

Proc. R. Soc. Lond. A Math. Phys. Sci. (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems, II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[CrossRef]

Other (1)

W. H. Steel, P. Mollet ed. (Pergamon, Oxford, UK), 181 − 192(1960)

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Schematic diagram of Lens Axicon with binary phase element.

Fig. 2
Fig. 2

(a) Intensity profile of the radial component (Er 2), longitudinal component (Ez 2), and the total field (Er 2 + Ez 2) of the focal plane of the high NA lens for radial polarized Bessel-Gaussian beam. (b) Contour plot for the total intensity distribution.

Fig. 3
Fig. 3

Contour plots for the electric field density distributions in the yz-plane for lens after additional phase modulation. (a) Total energy density distribution. (b). Radial component.

Fig. 4
Fig. 4

Intensity profile of the radial component(Er 2), longitudinal component(Ez 2), and the total field (Er 2 + Ez 2) of the focal plane of the high NA lens axicon for radial polarized Bessel-Gaussian beam (b) Contour plot for the total intensity distribution.

Fig. 5
Fig. 5

Intensity profile of the radial component (Er 2), longitudinal component (Ez 2), and the total field (Er 2 + Ez 2) of the focal plane of the high NA lens axicon for radial polarized Bessel-Gaussian beam with additional phase modulation. (b) Contour plot for the total intensity distribution.

Fig. 6
Fig. 6

Contour plots for the electric field density distributions in the yz-plane for lens axicon after additional phase modulation. (a). Radial component. (b). Longitudinal component.

Equations (5)

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

E r ( r , z ) = 0 α cos ( θ ) sin ( 2 θ ) l ( θ ) J 1 ( k r sin ( θ ) ) exp ( i k z cos ( θ ) ) d θ E z ( r , z ) = 0 α cos ( θ ) sin 2 ( θ ) l ( θ ) J 0 ( k r sin ( θ ) ) exp ( i k z cos ( θ ) ) d θ ,
l ( θ ) = [ exp [ ξ 2 ( sin ( θ ) sin ( α ) ) 2 ] J 1 ( 2 ξ ( sin ( θ ) sin ( α ) ) ) ] ,
A ( θ ) = exp ( i k ( β sin ( θ ) sin ( α ) ) 4 + 1 2 f ( sin ( θ ) sin ( α ) ) 2 ) ,
T ( θ ) = { 1 , f o r 0 θ < θ 1 , θ 2 θ < θ 3 , θ 4 θ < α 1 f o r θ 1 θ < θ 2 , θ 3 θ < θ 4 .
( η = j z / ( j z + j r ) ) .   where   ϕ z = 2 π 0 r 0 | E z ( r , 0 ) | 2 r d r   and   ϕ r = 2 π 0 r 0 | E r ( r , 0 ) | 2 r d r .

Metrics