Abstract

We have shown experimentally that square-profile microsteps on a silica substrate, with square sides of 0.4, 0.5, 0.6, and 0.8 μm and height of 500 nm, illuminated through the substrate by a linearly polarized laser beam of wavelength λ=633nm, produce, near the surface, enhanced-intensity regions (termed photonic nanojects), with their intensity being six times higher than that of the incident light and their respective full width at half-maximum diameters being 0.44λ, 0.43λ, 0.39λ, and 0.47λ, which is below the diffraction limit of 0.51λ. It is worth noting that when the step side is smaller than the wavelength, the focus is found within the step; otherwise the focus is outside the step, which is similar to an optical candle.

© 2014 Optical Society of America

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References

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  1. Y. F. Lu, L. Zhang, W. D. Song, Y. W. Zheng, and B. S. Luk’yanchuk, “Laser writing of a subwavelength structure on silicon (100) surfaces with particle-enhanced optical irradiation,” JETP Lett. 72, 457–459 (2000).
    [Crossref]
  2. E. McLeod and C. B. Arnold, “Subwavelength direct-write nanopatterning using optically trapped microspheres,” Nat. Nanotechnol. 3, 413–417 (2008).
    [Crossref]
  3. X. Li, Z. G. Chen, A. Taflove, and V. Backman, “Optical analysis of nanoparticles via enhanced backscattering facilitated by 3-D photonic nanojets,” Opt. Express 13, 526–533 (2005).
    [Crossref]
  4. P. Ferrand, J. Wenger, A. Devilez, M. Pianta, B. Stout, N. Bonod, E. Popov, and H. Rigneault, “Direct imaging of photonic nanojets,” Opt. Express 16, 6930–6940 (2008).
    [Crossref]
  5. S.-C. Kong, A. Taflove, and V. Backman, “Quasi one-dimensional light beam generated by a graded-index microsphere,” Opt. Express 17, 3722–3731 (2009).
    [Crossref]
  6. A. Devilez, N. Bonod, J. Wenger, D. Gerard, B. Stout, H. Rigneault, and E. Popov, “Three-dimensional subwavelength confinement of light with dielectric microspheres,” Opt. Express 17, 2089–2094 (2009).
    [Crossref]
  7. Z. G. Chen, A. Taflove, and V. Backman, “Photonic nanojet enhancement of backscattering of light by nanoparticles: a potential novel visible-light ultramicroscopy technique,” Opt. Express 12, 1214–1220 (2004).
    [Crossref]
  8. D. McCloskey, J. J. Wang, and J. F. Donegan, “Low divergence photonic nanojets from Si3N4 microdisks,” Opt. Express 20, 128–140 (2012).
    [Crossref]
  9. http://optics.synopsys.com/rsoft/ .
  10. V. V. Kotlyar, S. S. Stafeev, Y. Liu, L. O’Faolain, and A. A. Kovalev, “Analysis of the shape of a subwavelength focal spot for the linearly polarized light,” Appl. Opt. 52, 330–339 (2013).
    [Crossref]
  11. V. V. Kotlyar, A. A. Kovalev, Y. O. Shuypova, A. G. Nalimov, and V. A. Soifer, “Subwavelength confinement of light in waveguide structures,” Comput. Opt. 34, 169–186 (2010) (in Russian).
  12. V. V. Kotlyar, S. S. Stafeev, and A. A. Kovalev, “Curved laser microjet in near field,” Appl. Opt. 52, 4131–4136 (2013).
    [Crossref]
  13. J. Martin, J. Proust, D. Gérard, J.-L. Bijeon, and J. Plain, “Intense Bessel-like beams arising from pyramid-shaped microtips,” Opt. Lett. 37, 1274–1276 (2012).
    [Crossref]
  14. S. S. Stafeev, V. V. Kotlyar, and L. O’Faolain, “Subwavelength focusing of laser light by microoptics,” J. Mod. Opt. 60, 1050–1059 (2013).
    [Crossref]

2013 (3)

2012 (2)

2010 (1)

V. V. Kotlyar, A. A. Kovalev, Y. O. Shuypova, A. G. Nalimov, and V. A. Soifer, “Subwavelength confinement of light in waveguide structures,” Comput. Opt. 34, 169–186 (2010) (in Russian).

2009 (2)

2008 (2)

E. McLeod and C. B. Arnold, “Subwavelength direct-write nanopatterning using optically trapped microspheres,” Nat. Nanotechnol. 3, 413–417 (2008).
[Crossref]

P. Ferrand, J. Wenger, A. Devilez, M. Pianta, B. Stout, N. Bonod, E. Popov, and H. Rigneault, “Direct imaging of photonic nanojets,” Opt. Express 16, 6930–6940 (2008).
[Crossref]

2005 (1)

2004 (1)

2000 (1)

Y. F. Lu, L. Zhang, W. D. Song, Y. W. Zheng, and B. S. Luk’yanchuk, “Laser writing of a subwavelength structure on silicon (100) surfaces with particle-enhanced optical irradiation,” JETP Lett. 72, 457–459 (2000).
[Crossref]

Arnold, C. B.

E. McLeod and C. B. Arnold, “Subwavelength direct-write nanopatterning using optically trapped microspheres,” Nat. Nanotechnol. 3, 413–417 (2008).
[Crossref]

Backman, V.

Bijeon, J.-L.

Bonod, N.

Chen, Z. G.

Devilez, A.

Donegan, J. F.

Ferrand, P.

Gerard, D.

Gérard, D.

Kong, S.-C.

Kotlyar, V. V.

V. V. Kotlyar, S. S. Stafeev, Y. Liu, L. O’Faolain, and A. A. Kovalev, “Analysis of the shape of a subwavelength focal spot for the linearly polarized light,” Appl. Opt. 52, 330–339 (2013).
[Crossref]

V. V. Kotlyar, S. S. Stafeev, and A. A. Kovalev, “Curved laser microjet in near field,” Appl. Opt. 52, 4131–4136 (2013).
[Crossref]

S. S. Stafeev, V. V. Kotlyar, and L. O’Faolain, “Subwavelength focusing of laser light by microoptics,” J. Mod. Opt. 60, 1050–1059 (2013).
[Crossref]

V. V. Kotlyar, A. A. Kovalev, Y. O. Shuypova, A. G. Nalimov, and V. A. Soifer, “Subwavelength confinement of light in waveguide structures,” Comput. Opt. 34, 169–186 (2010) (in Russian).

Kovalev, A. A.

Li, X.

Liu, Y.

Lu, Y. F.

Y. F. Lu, L. Zhang, W. D. Song, Y. W. Zheng, and B. S. Luk’yanchuk, “Laser writing of a subwavelength structure on silicon (100) surfaces with particle-enhanced optical irradiation,” JETP Lett. 72, 457–459 (2000).
[Crossref]

Luk’yanchuk, B. S.

Y. F. Lu, L. Zhang, W. D. Song, Y. W. Zheng, and B. S. Luk’yanchuk, “Laser writing of a subwavelength structure on silicon (100) surfaces with particle-enhanced optical irradiation,” JETP Lett. 72, 457–459 (2000).
[Crossref]

Martin, J.

McCloskey, D.

McLeod, E.

E. McLeod and C. B. Arnold, “Subwavelength direct-write nanopatterning using optically trapped microspheres,” Nat. Nanotechnol. 3, 413–417 (2008).
[Crossref]

Nalimov, A. G.

V. V. Kotlyar, A. A. Kovalev, Y. O. Shuypova, A. G. Nalimov, and V. A. Soifer, “Subwavelength confinement of light in waveguide structures,” Comput. Opt. 34, 169–186 (2010) (in Russian).

O’Faolain, L.

S. S. Stafeev, V. V. Kotlyar, and L. O’Faolain, “Subwavelength focusing of laser light by microoptics,” J. Mod. Opt. 60, 1050–1059 (2013).
[Crossref]

V. V. Kotlyar, S. S. Stafeev, Y. Liu, L. O’Faolain, and A. A. Kovalev, “Analysis of the shape of a subwavelength focal spot for the linearly polarized light,” Appl. Opt. 52, 330–339 (2013).
[Crossref]

Pianta, M.

Plain, J.

Popov, E.

Proust, J.

Rigneault, H.

Shuypova, Y. O.

V. V. Kotlyar, A. A. Kovalev, Y. O. Shuypova, A. G. Nalimov, and V. A. Soifer, “Subwavelength confinement of light in waveguide structures,” Comput. Opt. 34, 169–186 (2010) (in Russian).

Soifer, V. A.

V. V. Kotlyar, A. A. Kovalev, Y. O. Shuypova, A. G. Nalimov, and V. A. Soifer, “Subwavelength confinement of light in waveguide structures,” Comput. Opt. 34, 169–186 (2010) (in Russian).

Song, W. D.

Y. F. Lu, L. Zhang, W. D. Song, Y. W. Zheng, and B. S. Luk’yanchuk, “Laser writing of a subwavelength structure on silicon (100) surfaces with particle-enhanced optical irradiation,” JETP Lett. 72, 457–459 (2000).
[Crossref]

Stafeev, S. S.

Stout, B.

Taflove, A.

Wang, J. J.

Wenger, J.

Zhang, L.

Y. F. Lu, L. Zhang, W. D. Song, Y. W. Zheng, and B. S. Luk’yanchuk, “Laser writing of a subwavelength structure on silicon (100) surfaces with particle-enhanced optical irradiation,” JETP Lett. 72, 457–459 (2000).
[Crossref]

Zheng, Y. W.

Y. F. Lu, L. Zhang, W. D. Song, Y. W. Zheng, and B. S. Luk’yanchuk, “Laser writing of a subwavelength structure on silicon (100) surfaces with particle-enhanced optical irradiation,” JETP Lett. 72, 457–459 (2000).
[Crossref]

Appl. Opt. (2)

Comput. Opt. (1)

V. V. Kotlyar, A. A. Kovalev, Y. O. Shuypova, A. G. Nalimov, and V. A. Soifer, “Subwavelength confinement of light in waveguide structures,” Comput. Opt. 34, 169–186 (2010) (in Russian).

J. Mod. Opt. (1)

S. S. Stafeev, V. V. Kotlyar, and L. O’Faolain, “Subwavelength focusing of laser light by microoptics,” J. Mod. Opt. 60, 1050–1059 (2013).
[Crossref]

JETP Lett. (1)

Y. F. Lu, L. Zhang, W. D. Song, Y. W. Zheng, and B. S. Luk’yanchuk, “Laser writing of a subwavelength structure on silicon (100) surfaces with particle-enhanced optical irradiation,” JETP Lett. 72, 457–459 (2000).
[Crossref]

Nat. Nanotechnol. (1)

E. McLeod and C. B. Arnold, “Subwavelength direct-write nanopatterning using optically trapped microspheres,” Nat. Nanotechnol. 3, 413–417 (2008).
[Crossref]

Opt. Express (6)

Opt. Lett. (1)

Other (1)

http://optics.synopsys.com/rsoft/ .

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Figures (13)

Fig. 1.
Fig. 1. Schematic view of the step under study.
Fig. 2.
Fig. 2. Intensity pattern in the plane perpendicular to the incident wave polarization (xz) for a step of width (a) 0.4 μm, (b) 0.6 μm, and (c) 0.8 μm. White-dashed contour outlines the element’s boundary.
Fig. 3.
Fig. 3. Intensity pattern in the plane (yz) parallel to the incident beam polarization for a step of width (a) 0.4 μm, (b) 0.6 μm, and (c) 0.8 μm. White-dashed contour outlines the element’s boundary.
Fig. 4.
Fig. 4. Intensity profile along the z axis when using a diffraction step of width (a) 0.4 μm, (b) 0.6 μm, and (c) 0.8 μm. The black vertical line denotes the step’s top surface.
Fig. 5.
Fig. 5. Near-step intensity maximum profile as a function of the step width (square side).
Fig. 6.
Fig. 6. (a) AFM image of the microsteps under study with a 0.6 μm side and (b) their selected profiles. White-dashed line on (a) depicts the line along which the profile is taken.
Fig. 7.
Fig. 7. (a) AFM image of 2.5 μm side steps and (b) an exemplified step’s profile.
Fig. 8.
Fig. 8. Intensity distribution near the exit surface of a 0.6 μm side step, which was experimentally obtained under illumination with a linearly polarized 633 nm laser light: (a) half-tone intensity pattern and (b), (c) intensity profiles for the minimal and maximal focal spot’s diameter.
Fig. 9.
Fig. 9. (a) Minimal and (b) maximal FWHM size of the photonic nanojet’s cross section near the exit surface versus the side of the step’s square cross section. The curve shows the simulation results; the bars show the experimental results.
Fig. 10.
Fig. 10. Intensity profiles directly behind the step surface with the square side of 0.5 μm in the plane (a) perpendicular and (b) parallel to the input beam polarization axis.
Fig. 11.
Fig. 11. Intensity pattern in the plane perpendicular to the input radiation polarization (xz) for a microsphere of diameter (a) 0.4 μm, (b) 0.6 μm, and (c) 0.8 μm. The microsphere’s boundary is shown as a dashed circle.
Fig. 12.
Fig. 12. Intensity pattern in the plane parallel to the input radiation polarization (yz) for a microsphere of diameter (a) 0.4 μm, (b) 0.6 μm, and (c) 0.8 μm. The microsphere’s boundary is shown as a dashed circle.
Fig. 13.
Fig. 13. Intensity profile along the z axis for a sphere of diameter (a) 0.4 μm, (b) 0.6 μm, and (c) 0.8 μm. The sphere’s boundary is shown as a vertical line.

Tables (1)

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Table 1. Comparison of the Optical Nanojet Parameters: Silica Microspheres versus Square Steps (λ=633nm)

Equations (3)

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Ey={cos(αx),|x|L/2,cos(αL/2)exp[γ(|x|L/2)],|x|>L/2,
Δx=0.92λzn,
L=2·0.92λHn0.86μm.

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