Abstract

The phase of a standard Fresnel zone lens (FZL) is periodically modulated in the radial direction using the phase of a binary fraxicon. The resulting element (rf-FZL) focuses light into a ring. The ring is found to be quasi-achromatic, in that the diameter is wavelength independent but its location is not. The binary rf-FZL is fabricated using electron beam direct writing. Experimental results confirm the generation of a wavelength-independent ring pattern at the focus of the rf-FZL. An efficiency of 24% was obtained. The variation in radius of ring pattern was reduced from 61 μm to less than 10 nm for a corresponding wavelength variation from 532 to 633 nm.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2013 (3)

2012 (2)

V. Pavelyev, V. Osipov, D. Kachalov, S. Khonina, W. Cheng, A. Gaidukeviciute, and B. Chichkov, “Diffractive optical elements for the formation of ‘light bottle’ intensity distributions,” Appl. Opt. 51, 4215–4218 (2012).
[CrossRef]

A. Vijayakumar, M. Uemukai, and T. Suhara, “Phase-shifted Fresnel zone lenses for photomixing generation of coherent THz wave,” Jpn. J. Appl. Phys. 51, 070206 (2012).

2011 (1)

2007 (1)

X.-C. Yuan, B. P. S. Ahluwalia, W. C. Cheong, J. Bu, H. B. Niu, and X. Peng, “Direct electron beam writing of kinoform micro-axicon for generation of propagation-invariant beams with long non-diffracting distance,” J. Opt. 9, 329–334 (2007).

2006 (1)

2003 (1)

M. de Angeles, L. Cacciapuoti, G. Pierattini, and G. M. Tino, “Axially symmetric hollow beams using refractive conical lenses,” Opt. Lasers Eng. 39, 283–291 (2003).
[CrossRef]

1998 (1)

I. Amidror, “The Fourier-spectrum of circular sine and cosine gratings with arbitrary radial phases,” Opt. Commun. 149, 127–134 (1998).
[CrossRef]

1997 (1)

L. Niggl, T. Lanzl, and M. Maier, “Properties of Bessel beams generated by periodic gratings of circular symmetry,” J. Opt. Soc. Am. 14, 27–33 (1997).
[CrossRef]

1996 (1)

M. Ferstl and A. M. Frisch, “Static and dynamic Fresnel zone lenses for optical interconnections,” J. Mod. Opt. 43, 1451–1462 (1996).
[CrossRef]

1990 (1)

Q. Ren and R. Birngruber, “Axicon: a new laser beam delivery system for corneal surgery,” IEEE J. Quantum Electron. 26, 2305–2308 (1990).
[CrossRef]

1986 (1)

M. V. Perez, C. Gomez-Reino, and J. M. Cuadrado, “Diffraction patterns and zone plates produced by thin linear axicons,” Optica Acta 33, 1161–1176 (1986).
[CrossRef]

1982 (1)

1978 (1)

1974 (1)

1972 (1)

H. H. Barret, “Fresnel zone plate imaging in nuclear medicine,” J. Nucl. Med. 13, 382–385 (1972).

1961 (1)

Ahluwalia, B. P. S.

X.-C. Yuan, B. P. S. Ahluwalia, W. C. Cheong, J. Bu, H. B. Niu, and X. Peng, “Direct electron beam writing of kinoform micro-axicon for generation of propagation-invariant beams with long non-diffracting distance,” J. Opt. 9, 329–334 (2007).

Amidror, I.

I. Amidror, “The Fourier-spectrum of circular sine and cosine gratings with arbitrary radial phases,” Opt. Commun. 149, 127–134 (1998).
[CrossRef]

Barret, H. H.

H. H. Barret, “Fresnel zone plate imaging in nuclear medicine,” J. Nucl. Med. 13, 382–385 (1972).

Belanger, P. A.

Bhattacharya, S.

Birngruber, R.

Q. Ren and R. Birngruber, “Axicon: a new laser beam delivery system for corneal surgery,” IEEE J. Quantum Electron. 26, 2305–2308 (1990).
[CrossRef]

Bu, J.

X.-C. Yuan, B. P. S. Ahluwalia, W. C. Cheong, J. Bu, H. B. Niu, and X. Peng, “Direct electron beam writing of kinoform micro-axicon for generation of propagation-invariant beams with long non-diffracting distance,” J. Opt. 9, 329–334 (2007).

Cacciapuoti, L.

M. de Angeles, L. Cacciapuoti, G. Pierattini, and G. M. Tino, “Axially symmetric hollow beams using refractive conical lenses,” Opt. Lasers Eng. 39, 283–291 (2003).
[CrossRef]

Chebbi, B.

Cheng, W.

Cheong, W. C.

X.-C. Yuan, B. P. S. Ahluwalia, W. C. Cheong, J. Bu, H. B. Niu, and X. Peng, “Direct electron beam writing of kinoform micro-axicon for generation of propagation-invariant beams with long non-diffracting distance,” J. Opt. 9, 329–334 (2007).

Chichkov, B.

Cuadrado, J. M.

M. V. Perez, C. Gomez-Reino, and J. M. Cuadrado, “Diffraction patterns and zone plates produced by thin linear axicons,” Optica Acta 33, 1161–1176 (1986).
[CrossRef]

de Angeles, M.

M. de Angeles, L. Cacciapuoti, G. Pierattini, and G. M. Tino, “Axially symmetric hollow beams using refractive conical lenses,” Opt. Lasers Eng. 39, 283–291 (2003).
[CrossRef]

Fedotowsky, A.

Ferstl, M.

M. Ferstl and A. M. Frisch, “Static and dynamic Fresnel zone lenses for optical interconnections,” J. Mod. Opt. 43, 1451–1462 (1996).
[CrossRef]

Frisch, A. M.

M. Ferstl and A. M. Frisch, “Static and dynamic Fresnel zone lenses for optical interconnections,” J. Mod. Opt. 43, 1451–1462 (1996).
[CrossRef]

Gaidukeviciute, A.

Golub, I.

Gomez-Reino, C.

M. V. Perez, C. Gomez-Reino, and J. M. Cuadrado, “Diffraction patterns and zone plates produced by thin linear axicons,” Optica Acta 33, 1161–1176 (1986).
[CrossRef]

Gourley, K.

Kachalov, D.

Khonina, S.

Kobayashi, K.

Koyama, J.

Kress, B. C.

B. C. Kress and P. Meyrueis, Applied Digital Optics (Wiley, 2009).

Lanzl, T.

L. Niggl, T. Lanzl, and M. Maier, “Properties of Bessel beams generated by periodic gratings of circular symmetry,” J. Opt. Soc. Am. 14, 27–33 (1997).
[CrossRef]

Lehovec, K.

Maier, M.

L. Niggl, T. Lanzl, and M. Maier, “Properties of Bessel beams generated by periodic gratings of circular symmetry,” J. Opt. Soc. Am. 14, 27–33 (1997).
[CrossRef]

Meyrueis, P.

B. C. Kress and P. Meyrueis, Applied Digital Optics (Wiley, 2009).

Miyamato, K.

Niggl, L.

L. Niggl, T. Lanzl, and M. Maier, “Properties of Bessel beams generated by periodic gratings of circular symmetry,” J. Opt. Soc. Am. 14, 27–33 (1997).
[CrossRef]

Nishihara, H.

Niu, H. B.

X.-C. Yuan, B. P. S. Ahluwalia, W. C. Cheong, J. Bu, H. B. Niu, and X. Peng, “Direct electron beam writing of kinoform micro-axicon for generation of propagation-invariant beams with long non-diffracting distance,” J. Opt. 9, 329–334 (2007).

Osipov, V.

Pavelyev, V.

Peng, X.

X.-C. Yuan, B. P. S. Ahluwalia, W. C. Cheong, J. Bu, H. B. Niu, and X. Peng, “Direct electron beam writing of kinoform micro-axicon for generation of propagation-invariant beams with long non-diffracting distance,” J. Opt. 9, 329–334 (2007).

Perez, M. V.

M. V. Perez, C. Gomez-Reino, and J. M. Cuadrado, “Diffraction patterns and zone plates produced by thin linear axicons,” Optica Acta 33, 1161–1176 (1986).
[CrossRef]

Pierattini, G.

M. de Angeles, L. Cacciapuoti, G. Pierattini, and G. M. Tino, “Axially symmetric hollow beams using refractive conical lenses,” Opt. Lasers Eng. 39, 283–291 (2003).
[CrossRef]

Ren, Q.

Q. Ren and R. Birngruber, “Axicon: a new laser beam delivery system for corneal surgery,” IEEE J. Quantum Electron. 26, 2305–2308 (1990).
[CrossRef]

Rioux, M.

Suhara, T.

A. Vijayakumar, M. Uemukai, and T. Suhara, “Phase-shifted Fresnel zone lenses for photomixing generation of coherent THz wave,” Jpn. J. Appl. Phys. 51, 070206 (2012).

T. Suhara, K. Kobayashi, H. Nishihara, and J. Koyama, “Graded-index Fresnel zone lenses for integrated optics,” Appl. Opt. 21, 1966–1971 (1982).
[CrossRef]

Tino, G. M.

M. de Angeles, L. Cacciapuoti, G. Pierattini, and G. M. Tino, “Axially symmetric hollow beams using refractive conical lenses,” Opt. Lasers Eng. 39, 283–291 (2003).
[CrossRef]

Uemukai, M.

A. Vijayakumar, M. Uemukai, and T. Suhara, “Phase-shifted Fresnel zone lenses for photomixing generation of coherent THz wave,” Jpn. J. Appl. Phys. 51, 070206 (2012).

Vijayakumar, A.

Yuan, X.-C.

X.-C. Yuan, B. P. S. Ahluwalia, W. C. Cheong, J. Bu, H. B. Niu, and X. Peng, “Direct electron beam writing of kinoform micro-axicon for generation of propagation-invariant beams with long non-diffracting distance,” J. Opt. 9, 329–334 (2007).

Appl. Opt. (7)

IEEE J. Quantum Electron. (1)

Q. Ren and R. Birngruber, “Axicon: a new laser beam delivery system for corneal surgery,” IEEE J. Quantum Electron. 26, 2305–2308 (1990).
[CrossRef]

J. Mod. Opt. (1)

M. Ferstl and A. M. Frisch, “Static and dynamic Fresnel zone lenses for optical interconnections,” J. Mod. Opt. 43, 1451–1462 (1996).
[CrossRef]

J. Nucl. Med. (1)

H. H. Barret, “Fresnel zone plate imaging in nuclear medicine,” J. Nucl. Med. 13, 382–385 (1972).

J. Opt. (1)

X.-C. Yuan, B. P. S. Ahluwalia, W. C. Cheong, J. Bu, H. B. Niu, and X. Peng, “Direct electron beam writing of kinoform micro-axicon for generation of propagation-invariant beams with long non-diffracting distance,” J. Opt. 9, 329–334 (2007).

J. Opt. Soc. Am. (2)

L. Niggl, T. Lanzl, and M. Maier, “Properties of Bessel beams generated by periodic gratings of circular symmetry,” J. Opt. Soc. Am. 14, 27–33 (1997).
[CrossRef]

K. Miyamato, “The phase Fresnel lens,” J. Opt. Soc. Am. 51, 17–20 (1961).
[CrossRef]

Jpn. J. Appl. Phys. (1)

A. Vijayakumar, M. Uemukai, and T. Suhara, “Phase-shifted Fresnel zone lenses for photomixing generation of coherent THz wave,” Jpn. J. Appl. Phys. 51, 070206 (2012).

Opt. Commun. (1)

I. Amidror, “The Fourier-spectrum of circular sine and cosine gratings with arbitrary radial phases,” Opt. Commun. 149, 127–134 (1998).
[CrossRef]

Opt. Lasers Eng. (1)

M. de Angeles, L. Cacciapuoti, G. Pierattini, and G. M. Tino, “Axially symmetric hollow beams using refractive conical lenses,” Opt. Lasers Eng. 39, 283–291 (2003).
[CrossRef]

Opt. Lett. (2)

Optica Acta (1)

M. V. Perez, C. Gomez-Reino, and J. M. Cuadrado, “Diffraction patterns and zone plates produced by thin linear axicons,” Optica Acta 33, 1161–1176 (1986).
[CrossRef]

Other (1)

B. C. Kress and P. Meyrueis, Applied Digital Optics (Wiley, 2009).

Supplementary Material (1)

» Media 1: MP4 (2917 KB)     

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Figures (8)

Fig. 1.
Fig. 1.

Optics configuration for generation of a focused ring pattern at the image plane of a rf-FZL (uv configuration).

Fig. 2.
Fig. 2.

Generation of the phase profile of a rf-FZL (uv-configuration) from the phase profiles of a BFZL and a BF.

Fig. 3.
Fig. 3.

Variation in the focal length of a rf-FZL (f-configuration) as a function of incident wavelength.

Fig. 4.
Fig. 4.

Variation of the radius of the first-order ring patterns of a rf-FZL (f-configuration) (blue color) and a BF (dashed green color) when the wavelength is varied between 400 and 800 nm. Colors are available in the online version.

Fig. 5.
Fig. 5.

Optical microscope image of the outermost part of the rf-FZL (uv-configuration) fabricated by electron beam direct writing.

Fig. 6.
Fig. 6.

Optical microscope image of the rf-FZL (f-configuration) fabricated using electron beam direct writing.

Fig. 7.
Fig. 7.

(a) Image and (b) intensity profile of the ring pattern generated by the rf-FZL (uv-configuration).

Fig. 8.
Fig. 8.

(a) and (c) Image of the ring pattern generated by rf-FZL (f-configuration) for the wavelengths 635 and 532 nm, respectively, (b) and (d) give the normalized intensity profiles for these wavelengths. The ring pattern occurs at a different focal plane for each wavelength. This was captured by moving the position of a CCD through a distance of 5.9 mm. A video of the same can be seen in Media 1, online.

Equations (11)

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

k(un+vn)k(u+v)=2nπ,
ρn=[Cρ24u2v24(u2+v2+Cρ)]1/2,
ΦBFZL(ρ)={Φ1ρnρρn+120elsewheren=0,1,2,3,.
ΦBF(ρ)={Φ20ρΛ20Λ2ρΛΦBF(ρ)=ΦBF(ρ+lΛ)wherel=0,1,2.
Φrf-BFZL=[ΦBFZL+ΦBF]2π.
k(un+vn)k(u+v)=2nπΦ2.
ρn=[Cρ24u2v24(u2+v2+Cρ)]1/2,
r1=vλΛ2λ2.
f=ρn2n2λ22nλ.
r1=(ρn2n2λ2)2nΛ2λ2.
r1ρn22nΛ.

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