Abstract

Application of the two-photon polymerization (2PP) technique for the fabrication of binary radial diffractive optical elements (DOEs) to form a bottle-like intensity distribution, or “light bottle,” is studied. Computer modeling and fabrication of a binary DOE for the formation of the desired light distributions are realized. The results of scanning electron microscopy analysis of the diffractive relief produced by the 2PP technique and an investigation of the optical properties of the fabricated elements are presented.

© 2012 Optical Society of America

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    [CrossRef]
  8. I. Manek, Yu. B. Ovchinnikov, and R. Grimm, “Generation of a hollow laser beam for atom trapping using an axicon,” Opt. Commun. 147, 67–70 (1998).
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  9. S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, K. Jefimovs, J. Simonen, and J. Turunen, “Rotation of microparticles with Bessel beams generated by diffractive elements,” J. Mod. Opt. 51, 2167–2184 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  20. D. G. Kachalov, V. S. Pavelyev, S. N. Khonina, R. V. Skidanov, and O. Yu. Moiseev, “Application of the direct search in solving a problem of forming longitudinal distribution of intensity,” J. Mod. Opt. 58, 69–76 (2011).
    [CrossRef]
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    [CrossRef]

2011 (2)

D. G. Kachalov, K. A. Gamazkov, V. S. Pavelyev, and S. N. Khonina, “Optimization of binary DOE for ‘light trap’ distribution forming,” (in Russian; English summary), Comput. Opt. 35, 70–76 (2011).

D. G. Kachalov, V. S. Pavelyev, S. N. Khonina, R. V. Skidanov, and O. Yu. Moiseev, “Application of the direct search in solving a problem of forming longitudinal distribution of intensity,” J. Mod. Opt. 58, 69–76 (2011).
[CrossRef]

2010 (1)

2007 (1)

H.-Y. Tsai, H. I. Smith, and R. Menon, “Fabrication of spiral-phase diffractive elements using scanning-electron-beam lithography,” J. Vac. Sci. Technol. B 25, 2068–2071 (2007).
[CrossRef]

2006 (1)

2005 (2)

S. N. Khonina, R. V. Skidanov, V. V. Kotlyar, V. A. Soifer, and J. Turunen, “DOE-generated laser beams with given orbital angular moment: application for micromanipulation,” Proc. SPIE 5962, 59622W (2005).
[CrossRef]

V. V. Kotlyar, A. A. Almazov, S. N. Khonina, V. A. Soifer, H. Elfstrom, and J. Turunen, “Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate,” J. Opt. Soc. Am. A 22, 849–861(2005).
[CrossRef]

2004 (3)

D. Yelin, B. E. Bouma, and G. J. Tearney, “Generating an adjustable three-dimensional dark focus,” Opt. Lett. 29, 661–663 (2004).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, K. Jefimovs, J. Simonen, and J. Turunen, “Rotation of microparticles with Bessel beams generated by diffractive elements,” J. Mod. Opt. 51, 2167–2184 (2004).
[CrossRef]

V. A. Soifer, V. V. Kotlyar, and S. N. Khonina, “Optical microparticle manipulation: advances and new possibilities created by diffractive optics,” Phys. Part. Nucl. 35, 733–766 (2004).

2002 (1)

M. Meister and R. J. Winfield, “Novel approaches to direct search algorithms for the design of diffractive optical elements,” Opt. Commun. 203, 39–49 (2002).
[CrossRef]

2000 (1)

1999 (1)

R. Ozeri, L. Khaykovich, and N. Davidson, “Long spin relaxation times in a single-beam blue-detuned optical trap,” Phys. Rev. A 59, R1750–R1753 (1999).
[CrossRef]

1998 (1)

I. Manek, Yu. B. Ovchinnikov, and R. Grimm, “Generation of a hollow laser beam for atom trapping using an axicon,” Opt. Commun. 147, 67–70 (1998).
[CrossRef]

1997 (1)

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

1996 (2)

1992 (1)

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

1986 (1)

Almazov, A. A.

Arlt, J.

Ashkin, A.

Bjorkholm, J. E.

Bouma, B. E.

Chichkov, B. N.

Chu, S.

Davidson, N.

R. Ozeri, L. Khaykovich, and N. Davidson, “Long spin relaxation times in a single-beam blue-detuned optical trap,” Phys. Rev. A 59, R1750–R1753 (1999).
[CrossRef]

Dziedzic, J. M.

Elfstrom, H.

Gahagan, K. T.

Gamazkov, K. A.

D. G. Kachalov, K. A. Gamazkov, V. S. Pavelyev, and S. N. Khonina, “Optimization of binary DOE for ‘light trap’ distribution forming,” (in Russian; English summary), Comput. Opt. 35, 70–76 (2011).

Grimm, R.

I. Manek, Yu. B. Ovchinnikov, and R. Grimm, “Generation of a hollow laser beam for atom trapping using an axicon,” Opt. Commun. 147, 67–70 (1998).
[CrossRef]

Hirano, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

Jefimovs, K.

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, K. Jefimovs, J. Simonen, and J. Turunen, “Rotation of microparticles with Bessel beams generated by diffractive elements,” J. Mod. Opt. 51, 2167–2184 (2004).
[CrossRef]

Kachalov, D. G.

D. G. Kachalov, V. S. Pavelyev, S. N. Khonina, R. V. Skidanov, and O. Yu. Moiseev, “Application of the direct search in solving a problem of forming longitudinal distribution of intensity,” J. Mod. Opt. 58, 69–76 (2011).
[CrossRef]

D. G. Kachalov, K. A. Gamazkov, V. S. Pavelyev, and S. N. Khonina, “Optimization of binary DOE for ‘light trap’ distribution forming,” (in Russian; English summary), Comput. Opt. 35, 70–76 (2011).

V. P. Osipov, V. S. Pavelyev, D. G. Kachalov, A. Zukauskas, and B. N. Chichkov, “Realization of binary radial diffractive optical elements by two-photon polymerization technique,” Opt. Express 18, 25808–25814 (2010).
[CrossRef]

Khaykovich, L.

R. Ozeri, L. Khaykovich, and N. Davidson, “Long spin relaxation times in a single-beam blue-detuned optical trap,” Phys. Rev. A 59, R1750–R1753 (1999).
[CrossRef]

Khonina, S. N.

D. G. Kachalov, V. S. Pavelyev, S. N. Khonina, R. V. Skidanov, and O. Yu. Moiseev, “Application of the direct search in solving a problem of forming longitudinal distribution of intensity,” J. Mod. Opt. 58, 69–76 (2011).
[CrossRef]

D. G. Kachalov, K. A. Gamazkov, V. S. Pavelyev, and S. N. Khonina, “Optimization of binary DOE for ‘light trap’ distribution forming,” (in Russian; English summary), Comput. Opt. 35, 70–76 (2011).

V. V. Kotlyar, S. N. Khonina, A. A. Kovalev, V. A. Soifer, H. Elfstrom, and J. Turunen, “Diffraction of a plane, finite-radius wave by a spiral phase plate,” Opt. Lett. 31, 1597–1599 (2006).
[CrossRef]

S. N. Khonina, R. V. Skidanov, V. V. Kotlyar, V. A. Soifer, and J. Turunen, “DOE-generated laser beams with given orbital angular moment: application for micromanipulation,” Proc. SPIE 5962, 59622W (2005).
[CrossRef]

V. V. Kotlyar, A. A. Almazov, S. N. Khonina, V. A. Soifer, H. Elfstrom, and J. Turunen, “Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate,” J. Opt. Soc. Am. A 22, 849–861(2005).
[CrossRef]

V. A. Soifer, V. V. Kotlyar, and S. N. Khonina, “Optical microparticle manipulation: advances and new possibilities created by diffractive optics,” Phys. Part. Nucl. 35, 733–766 (2004).

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, K. Jefimovs, J. Simonen, and J. Turunen, “Rotation of microparticles with Bessel beams generated by diffractive elements,” J. Mod. Opt. 51, 2167–2184 (2004).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

V. V. Koltyar and S. N. Khonina, “Multi-order diffractive optical elements to process data,” in Perspectives in Engineering OpticsK. Singh and V. K. Rastogi, eds. (Anita Publications, 2003), pp. 47–56.

Koltyar, V. V.

V. V. Koltyar and S. N. Khonina, “Multi-order diffractive optical elements to process data,” in Perspectives in Engineering OpticsK. Singh and V. K. Rastogi, eds. (Anita Publications, 2003), pp. 47–56.

Kotlyar, V. V.

V. V. Kotlyar, S. N. Khonina, A. A. Kovalev, V. A. Soifer, H. Elfstrom, and J. Turunen, “Diffraction of a plane, finite-radius wave by a spiral phase plate,” Opt. Lett. 31, 1597–1599 (2006).
[CrossRef]

V. V. Kotlyar, A. A. Almazov, S. N. Khonina, V. A. Soifer, H. Elfstrom, and J. Turunen, “Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate,” J. Opt. Soc. Am. A 22, 849–861(2005).
[CrossRef]

S. N. Khonina, R. V. Skidanov, V. V. Kotlyar, V. A. Soifer, and J. Turunen, “DOE-generated laser beams with given orbital angular moment: application for micromanipulation,” Proc. SPIE 5962, 59622W (2005).
[CrossRef]

V. A. Soifer, V. V. Kotlyar, and S. N. Khonina, “Optical microparticle manipulation: advances and new possibilities created by diffractive optics,” Phys. Part. Nucl. 35, 733–766 (2004).

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, K. Jefimovs, J. Simonen, and J. Turunen, “Rotation of microparticles with Bessel beams generated by diffractive elements,” J. Mod. Opt. 51, 2167–2184 (2004).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

Kovalev, A. A.

Kuga, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

Manek, I.

I. Manek, Yu. B. Ovchinnikov, and R. Grimm, “Generation of a hollow laser beam for atom trapping using an axicon,” Opt. Commun. 147, 67–70 (1998).
[CrossRef]

Meister, M.

M. Meister and R. J. Winfield, “Novel approaches to direct search algorithms for the design of diffractive optical elements,” Opt. Commun. 203, 39–49 (2002).
[CrossRef]

Menon, R.

H.-Y. Tsai, H. I. Smith, and R. Menon, “Fabrication of spiral-phase diffractive elements using scanning-electron-beam lithography,” J. Vac. Sci. Technol. B 25, 2068–2071 (2007).
[CrossRef]

Osipov, V. P.

Ovchinnikov, Yu. B.

I. Manek, Yu. B. Ovchinnikov, and R. Grimm, “Generation of a hollow laser beam for atom trapping using an axicon,” Opt. Commun. 147, 67–70 (1998).
[CrossRef]

Ozeri, R.

R. Ozeri, L. Khaykovich, and N. Davidson, “Long spin relaxation times in a single-beam blue-detuned optical trap,” Phys. Rev. A 59, R1750–R1753 (1999).
[CrossRef]

Pavelyev, V. S.

D. G. Kachalov, V. S. Pavelyev, S. N. Khonina, R. V. Skidanov, and O. Yu. Moiseev, “Application of the direct search in solving a problem of forming longitudinal distribution of intensity,” J. Mod. Opt. 58, 69–76 (2011).
[CrossRef]

D. G. Kachalov, K. A. Gamazkov, V. S. Pavelyev, and S. N. Khonina, “Optimization of binary DOE for ‘light trap’ distribution forming,” (in Russian; English summary), Comput. Opt. 35, 70–76 (2011).

V. P. Osipov, V. S. Pavelyev, D. G. Kachalov, A. Zukauskas, and B. N. Chichkov, “Realization of binary radial diffractive optical elements by two-photon polymerization technique,” Opt. Express 18, 25808–25814 (2010).
[CrossRef]

Piestun, R.

Sasada, H.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

Shamir, J.

Shimizu, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

Shinkaryev, M. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

Shiokawa, N.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

Simonen, J.

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, K. Jefimovs, J. Simonen, and J. Turunen, “Rotation of microparticles with Bessel beams generated by diffractive elements,” J. Mod. Opt. 51, 2167–2184 (2004).
[CrossRef]

Skidanov, R. V.

D. G. Kachalov, V. S. Pavelyev, S. N. Khonina, R. V. Skidanov, and O. Yu. Moiseev, “Application of the direct search in solving a problem of forming longitudinal distribution of intensity,” J. Mod. Opt. 58, 69–76 (2011).
[CrossRef]

S. N. Khonina, R. V. Skidanov, V. V. Kotlyar, V. A. Soifer, and J. Turunen, “DOE-generated laser beams with given orbital angular moment: application for micromanipulation,” Proc. SPIE 5962, 59622W (2005).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, K. Jefimovs, J. Simonen, and J. Turunen, “Rotation of microparticles with Bessel beams generated by diffractive elements,” J. Mod. Opt. 51, 2167–2184 (2004).
[CrossRef]

Smith, H. I.

H.-Y. Tsai, H. I. Smith, and R. Menon, “Fabrication of spiral-phase diffractive elements using scanning-electron-beam lithography,” J. Vac. Sci. Technol. B 25, 2068–2071 (2007).
[CrossRef]

Soifer, V. A.

V. V. Kotlyar, S. N. Khonina, A. A. Kovalev, V. A. Soifer, H. Elfstrom, and J. Turunen, “Diffraction of a plane, finite-radius wave by a spiral phase plate,” Opt. Lett. 31, 1597–1599 (2006).
[CrossRef]

S. N. Khonina, R. V. Skidanov, V. V. Kotlyar, V. A. Soifer, and J. Turunen, “DOE-generated laser beams with given orbital angular moment: application for micromanipulation,” Proc. SPIE 5962, 59622W (2005).
[CrossRef]

V. V. Kotlyar, A. A. Almazov, S. N. Khonina, V. A. Soifer, H. Elfstrom, and J. Turunen, “Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate,” J. Opt. Soc. Am. A 22, 849–861(2005).
[CrossRef]

V. A. Soifer, V. V. Kotlyar, and S. N. Khonina, “Optical microparticle manipulation: advances and new possibilities created by diffractive optics,” Phys. Part. Nucl. 35, 733–766 (2004).

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, K. Jefimovs, J. Simonen, and J. Turunen, “Rotation of microparticles with Bessel beams generated by diffractive elements,” J. Mod. Opt. 51, 2167–2184 (2004).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

V. A. Soifer, ed., Methods for Computer Design of Diffractive Optical Elements (Wiley, 2002).

Spektor, B.

Swartzlander, G. A.

Tearney, G. J.

Torii, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

Tsai, H.-Y.

H.-Y. Tsai, H. I. Smith, and R. Menon, “Fabrication of spiral-phase diffractive elements using scanning-electron-beam lithography,” J. Vac. Sci. Technol. B 25, 2068–2071 (2007).
[CrossRef]

Turunen, J.

V. V. Kotlyar, S. N. Khonina, A. A. Kovalev, V. A. Soifer, H. Elfstrom, and J. Turunen, “Diffraction of a plane, finite-radius wave by a spiral phase plate,” Opt. Lett. 31, 1597–1599 (2006).
[CrossRef]

V. V. Kotlyar, A. A. Almazov, S. N. Khonina, V. A. Soifer, H. Elfstrom, and J. Turunen, “Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate,” J. Opt. Soc. Am. A 22, 849–861(2005).
[CrossRef]

S. N. Khonina, R. V. Skidanov, V. V. Kotlyar, V. A. Soifer, and J. Turunen, “DOE-generated laser beams with given orbital angular moment: application for micromanipulation,” Proc. SPIE 5962, 59622W (2005).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, K. Jefimovs, J. Simonen, and J. Turunen, “Rotation of microparticles with Bessel beams generated by diffractive elements,” J. Mod. Opt. 51, 2167–2184 (2004).
[CrossRef]

Uspleniev, G. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

Winfield, R. J.

M. Meister and R. J. Winfield, “Novel approaches to direct search algorithms for the design of diffractive optical elements,” Opt. Commun. 203, 39–49 (2002).
[CrossRef]

Yelin, D.

Yu. Moiseev, O.

D. G. Kachalov, V. S. Pavelyev, S. N. Khonina, R. V. Skidanov, and O. Yu. Moiseev, “Application of the direct search in solving a problem of forming longitudinal distribution of intensity,” J. Mod. Opt. 58, 69–76 (2011).
[CrossRef]

Zukauskas, A.

Comput. Opt. (1)

D. G. Kachalov, K. A. Gamazkov, V. S. Pavelyev, and S. N. Khonina, “Optimization of binary DOE for ‘light trap’ distribution forming,” (in Russian; English summary), Comput. Opt. 35, 70–76 (2011).

J. Mod. Opt. (3)

D. G. Kachalov, V. S. Pavelyev, S. N. Khonina, R. V. Skidanov, and O. Yu. Moiseev, “Application of the direct search in solving a problem of forming longitudinal distribution of intensity,” J. Mod. Opt. 58, 69–76 (2011).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, K. Jefimovs, J. Simonen, and J. Turunen, “Rotation of microparticles with Bessel beams generated by diffractive elements,” J. Mod. Opt. 51, 2167–2184 (2004).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

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

J. Vac. Sci. Technol. B (1)

H.-Y. Tsai, H. I. Smith, and R. Menon, “Fabrication of spiral-phase diffractive elements using scanning-electron-beam lithography,” J. Vac. Sci. Technol. B 25, 2068–2071 (2007).
[CrossRef]

Opt. Commun. (2)

I. Manek, Yu. B. Ovchinnikov, and R. Grimm, “Generation of a hollow laser beam for atom trapping using an axicon,” Opt. Commun. 147, 67–70 (1998).
[CrossRef]

M. Meister and R. J. Winfield, “Novel approaches to direct search algorithms for the design of diffractive optical elements,” Opt. Commun. 203, 39–49 (2002).
[CrossRef]

Opt. Express (1)

Opt. Lett. (5)

Phys. Part. Nucl. (1)

V. A. Soifer, V. V. Kotlyar, and S. N. Khonina, “Optical microparticle manipulation: advances and new possibilities created by diffractive optics,” Phys. Part. Nucl. 35, 733–766 (2004).

Phys. Rev. A (1)

R. Ozeri, L. Khaykovich, and N. Davidson, “Long spin relaxation times in a single-beam blue-detuned optical trap,” Phys. Rev. A 59, R1750–R1753 (1999).
[CrossRef]

Phys. Rev. Lett. (1)

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

Proc. SPIE (1)

S. N. Khonina, R. V. Skidanov, V. V. Kotlyar, V. A. Soifer, and J. Turunen, “DOE-generated laser beams with given orbital angular moment: application for micromanipulation,” Proc. SPIE 5962, 59622W (2005).
[CrossRef]

Other (2)

V. A. Soifer, ed., Methods for Computer Design of Diffractive Optical Elements (Wiley, 2002).

V. V. Koltyar and S. N. Khonina, “Multi-order diffractive optical elements to process data,” in Perspectives in Engineering OpticsK. Singh and V. K. Rastogi, eds. (Anita Publications, 2003), pp. 47–56.

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Figures (7)

Fig. 1.
Fig. 1.

Optical scheme for the formation of a “light bottle” distribution.

Fig. 2.
Fig. 2.

Calculated longitudinal intensity distribution for the designed binary DOE (negative image).

Fig. 3.
Fig. 3.

Enlarged view of the light trap (computer simulation).

Fig. 4.
Fig. 4.

(a) Calculated phase of binary radial DOE (black, 0; white, π); (b) optical view of the realized diffractive microrelief; (c) SEM view of radial zone with minimum ring width.

Fig. 5.
Fig. 5.

Optical setup for investigation of light intensity distribution.

Fig. 6.
Fig. 6.

Transverse light intensity sections registered at defined points along the optical axis (bottom) compared with the numerical calculations (top).

Fig. 7.
Fig. 7.

(a) Three-dimensional view of the intensity distribution measured in the region of optical trap formation at a distance of 52.5 mm from the DOE and (b) its cross section.

Equations (2)

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F(ρ,z)=ikzeikzexp(ikρ22z)0Rexp(r2σ2)exp[iφ(r)+ikr22z]J0(krρz)rdr,
Φ(ρj,zi)={ci|exp[I¯(ρj,zi)I(ρj,zi)I¯(ρj,zi)]1|,ifI¯(ρj,zi)>0,ci{exp[I(ρj,zi)I¯norm]1},ifI¯(ρj,zi)=0,

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