Abstract

A compact optics configuration for the generation of donut beams for trapping atoms at the micrometer scale using a multilevel spiral-phase Fresnel zone plate (FZP) and a semiconductor laser is proposed. A FZP is designed and a multilevel spiral phase is integrated into it. A spiral-phase FZP with a radius of 1 mm and with more than 1300 half-period zones is designed with multiple angular levels for integer and fractional topological charges, and the device is fabricated using electron-beam lithography direct writing. The performance of the device is evaluated, and the generation of symmetric and asymmetric donut beams is successfully demonstrated.

© 2012 Optical Society of America

Full Article  |  PDF Article

Errata

A. Vijaykumar and Shanti Bhattacharya, "Design, fabrication, and evaluation of a multilevel spiral-phase Fresnel zone plate for optical trapping: Erratum," Appl. Opt. 52, 1148-1148 (2013)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-52-6-1148

References

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2011 (1)

N. Gao, C. Xie, C. Li, C. Jin, and M. Liu, “Square optical vortices generated by binary spiral zone plates,” Appl. Phys. Lett. 98, 151106 (2011).
[CrossRef]

2010 (2)

2009 (1)

2008 (2)

K. C. Neuman and A. Nagy, “Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nat. Methods 5, 491–505 (2008).
[CrossRef]

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, “Holographic assembly workstation for optical manipulation,” J. Opt. A 10, 044009 (2008).
[CrossRef]

2007 (1)

M. Boyd, E. W. Streed, P. Medley, G. K. Campbell, J. Mun, W. Ketterle, and D. E. Pritchard, “Atom trapping with a thin magnetic film,” Phys. Rev. A 76, 043524 (2007).
[CrossRef]

2006 (4)

2005 (2)

2004 (2)

S. Bergamini, B. Darquie, M. Jones, L. Jacubowiez, A. Browaeys, and P. Grangier, “Holographic generation of microtrap arrays for single atoms by use of a programmable phase modulator,” J. Opt. Soc. Am. A 21, 1889–1894 (2004).
[CrossRef]

S. S. R. Oemrawsingh, J. A. W. van Houwelingen, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W. ’t Hooft “Production and characterization of spiral phase plates for optical wavelengths,” Appl. Opt. 43, 688–694 (2004).
[CrossRef]

2003 (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[CrossRef]

2002 (1)

J. E. Curtis, B. A. Koss, and D. J. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[CrossRef]

2001 (2)

H. Ott, J. Fortagh, G. Schlotterbeck, A. Grossmann, and C. Zimmermann, “Bose–Einstein condensation in a surface microtrap,” Phys. Rev. Lett. 87, 230401 (2001).
[CrossRef]

W. Hansel, P. Hommelhoff, T. W. Hansch, and J. Reichel, “Bose–Einstein condensation on a microelectronic chip,” Nature 413, 498–501 (2001).
[CrossRef]

1997 (2)

E. Fallman and O. Axner, “Design of fully steerable dual-trap optical tweezers,” Appl. Opt. 36, 2107–2113 (1997).
[CrossRef]

A. E. Chiou, W. Wang, G. J. Sonek, J. Hong, and M. W. Berns, “Interferometric optical tweezers,” Opt. Commun. 133, 7–10 (1997).
[CrossRef]

1991 (1)

T. Abe, S. Yamasaki, T. Yamaguchi, R. Yoshikawa, and T. Takigawa, “Representative figure method for proximity error correction [II],” Jpn. J. Appl. Phys. 30, 2965–2969 (1991).
[CrossRef]

1989 (2)

T. K. Lean, “Theory and practice of proximity correction by secondary exposure,” J. Appl. Phys. 65, 1776–1781 (1989).
[CrossRef]

H. G. Kraus, “Huygens-Fresnel-Kirchoff wave-front diffraction formulation: spherical waves,” J. Opt. Soc. Am. A 6, 1196–1205 (1989).
[CrossRef]

1987 (1)

S. A. Rishton and D. P. Kern, “Point exposure distribution measurements for proximity correction in electron beam lithography on a sub-100 nm scale,” J. Vac. Sci. Technol. B 5, 135–141 (1987).
[CrossRef]

1986 (1)

1979 (1)

J. E. Harvey, “Fourier treatment of near-field scalar diffraction theory,” Am. J. Phys. 47, 974–980 (1979).
[CrossRef]

1972 (1)

W. H. Carter, “Electromagnetic field of a Gaussian beam with an elliptical cross section,” J. Opt. Soc. Am. A 62, 1195–1201 (1972).
[CrossRef]

’t Hooft, G. W.

Abe, T.

T. Abe, S. Yamasaki, T. Yamaguchi, R. Yoshikawa, and T. Takigawa, “Representative figure method for proximity error correction [II],” Jpn. J. Appl. Phys. 30, 2965–2969 (1991).
[CrossRef]

Ahluwalia, B. P. S.

Almazov, A. A.

Ashkin, A.

Axner, O.

Bergamini, S.

S. Bergamini, B. Darquie, M. Jones, L. Jacubowiez, A. Browaeys, and P. Grangier, “Holographic generation of microtrap arrays for single atoms by use of a programmable phase modulator,” J. Opt. Soc. Am. A 21, 1889–1894 (2004).
[CrossRef]

Berns, M. W.

A. E. Chiou, W. Wang, G. J. Sonek, J. Hong, and M. W. Berns, “Interferometric optical tweezers,” Opt. Commun. 133, 7–10 (1997).
[CrossRef]

Bjorkholm, J. E.

Bowman, R.

Boyd, M.

M. Boyd, E. W. Streed, P. Medley, G. K. Campbell, J. Mun, W. Ketterle, and D. E. Pritchard, “Atom trapping with a thin magnetic film,” Phys. Rev. A 76, 043524 (2007).
[CrossRef]

Browaeys, A.

S. Bergamini, B. Darquie, M. Jones, L. Jacubowiez, A. Browaeys, and P. Grangier, “Holographic generation of microtrap arrays for single atoms by use of a programmable phase modulator,” J. Opt. Soc. Am. A 21, 1889–1894 (2004).
[CrossRef]

Campbell, G. K.

M. Boyd, E. W. Streed, P. Medley, G. K. Campbell, J. Mun, W. Ketterle, and D. E. Pritchard, “Atom trapping with a thin magnetic film,” Phys. Rev. A 76, 043524 (2007).
[CrossRef]

Carberry, D. M.

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, “Holographic assembly workstation for optical manipulation,” J. Opt. A 10, 044009 (2008).
[CrossRef]

Carter, W. H.

W. H. Carter, “Electromagnetic field of a Gaussian beam with an elliptical cross section,” J. Opt. Soc. Am. A 62, 1195–1201 (1972).
[CrossRef]

Cheong, W. C.

Chiou, A. E.

A. E. Chiou, W. Wang, G. J. Sonek, J. Hong, and M. W. Berns, “Interferometric optical tweezers,” Opt. Commun. 133, 7–10 (1997).
[CrossRef]

Chu, S.

Cooper, J.

Courtial, J.

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, “Holographic assembly workstation for optical manipulation,” J. Opt. A 10, 044009 (2008).
[CrossRef]

E. Schonbrun, R. Piesten, P. Jordan, J. Cooper, K. D. Wulff, J. Courtial, and M. Padgett, “3D interferometric optical tweezers using a single spatial modulator,” Opt. Express 13, 3777–3786 (2005).
[CrossRef]

Curtis, J. E.

J. E. Curtis, B. A. Koss, and D. J. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[CrossRef]

Darquie, B.

S. Bergamini, B. Darquie, M. Jones, L. Jacubowiez, A. Browaeys, and P. Grangier, “Holographic generation of microtrap arrays for single atoms by use of a programmable phase modulator,” J. Opt. Soc. Am. A 21, 1889–1894 (2004).
[CrossRef]

Ding, J.

C. S. Guo, D. M. Xue, Y. J. Han, and J. Ding, “Optimal phase steps of multi-level spiral phase plates,” Opt. Commun. 268, 235–239 (2006).
[CrossRef]

Dziedzic, J. M.

Elfstrom, H.

Eliel, E. R.

Fallman, E.

Fortagh, J.

H. Ott, J. Fortagh, G. Schlotterbeck, A. Grossmann, and C. Zimmermann, “Bose–Einstein condensation in a surface microtrap,” Phys. Rev. Lett. 87, 230401 (2001).
[CrossRef]

Gao, N.

N. Gao, C. Xie, C. Li, C. Jin, and M. Liu, “Square optical vortices generated by binary spiral zone plates,” Appl. Phys. Lett. 98, 151106 (2011).
[CrossRef]

Gibson, G.

R. Bowman, G. Gibson, and M. Padgett, “Particle tracking stereomicroscopy in optical tweezers: control of trap shape,” Opt. Express 18, 11785–11790 (2010).
[CrossRef]

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, “Holographic assembly workstation for optical manipulation,” J. Opt. A 10, 044009 (2008).
[CrossRef]

Golub, I.

Grangier, P.

S. Bergamini, B. Darquie, M. Jones, L. Jacubowiez, A. Browaeys, and P. Grangier, “Holographic generation of microtrap arrays for single atoms by use of a programmable phase modulator,” J. Opt. Soc. Am. A 21, 1889–1894 (2004).
[CrossRef]

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[CrossRef]

Grier, D. J.

J. E. Curtis, B. A. Koss, and D. J. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[CrossRef]

Grossmann, A.

H. Ott, J. Fortagh, G. Schlotterbeck, A. Grossmann, and C. Zimmermann, “Bose–Einstein condensation in a surface microtrap,” Phys. Rev. Lett. 87, 230401 (2001).
[CrossRef]

Guo, C. S.

C. S. Guo, D. M. Xue, Y. J. Han, and J. Ding, “Optimal phase steps of multi-level spiral phase plates,” Opt. Commun. 268, 235–239 (2006).
[CrossRef]

Han, Y. J.

C. S. Guo, D. M. Xue, Y. J. Han, and J. Ding, “Optimal phase steps of multi-level spiral phase plates,” Opt. Commun. 268, 235–239 (2006).
[CrossRef]

Hansch, T. W.

W. Hansel, P. Hommelhoff, T. W. Hansch, and J. Reichel, “Bose–Einstein condensation on a microelectronic chip,” Nature 413, 498–501 (2001).
[CrossRef]

Hansel, W.

W. Hansel, P. Hommelhoff, T. W. Hansch, and J. Reichel, “Bose–Einstein condensation on a microelectronic chip,” Nature 413, 498–501 (2001).
[CrossRef]

Harvey, J. E.

J. E. Harvey, “Fourier treatment of near-field scalar diffraction theory,” Am. J. Phys. 47, 974–980 (1979).
[CrossRef]

Hommelhoff, P.

W. Hansel, P. Hommelhoff, T. W. Hansch, and J. Reichel, “Bose–Einstein condensation on a microelectronic chip,” Nature 413, 498–501 (2001).
[CrossRef]

Hong, J.

A. E. Chiou, W. Wang, G. J. Sonek, J. Hong, and M. W. Berns, “Interferometric optical tweezers,” Opt. Commun. 133, 7–10 (1997).
[CrossRef]

Jackson, J. C.

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, “Holographic assembly workstation for optical manipulation,” J. Opt. A 10, 044009 (2008).
[CrossRef]

Jacubowiez, L.

S. Bergamini, B. Darquie, M. Jones, L. Jacubowiez, A. Browaeys, and P. Grangier, “Holographic generation of microtrap arrays for single atoms by use of a programmable phase modulator,” J. Opt. Soc. Am. A 21, 1889–1894 (2004).
[CrossRef]

Jin, C.

N. Gao, C. Xie, C. Li, C. Jin, and M. Liu, “Square optical vortices generated by binary spiral zone plates,” Appl. Phys. Lett. 98, 151106 (2011).
[CrossRef]

Jones, M.

S. Bergamini, B. Darquie, M. Jones, L. Jacubowiez, A. Browaeys, and P. Grangier, “Holographic generation of microtrap arrays for single atoms by use of a programmable phase modulator,” J. Opt. Soc. Am. A 21, 1889–1894 (2004).
[CrossRef]

Jordan, P.

Kern, D. P.

S. A. Rishton and D. P. Kern, “Point exposure distribution measurements for proximity correction in electron beam lithography on a sub-100 nm scale,” J. Vac. Sci. Technol. B 5, 135–141 (1987).
[CrossRef]

Ketterle, W.

M. Boyd, E. W. Streed, P. Medley, G. K. Campbell, J. Mun, W. Ketterle, and D. E. Pritchard, “Atom trapping with a thin magnetic film,” Phys. Rev. A 76, 043524 (2007).
[CrossRef]

Khonina, S. N.

Kloosterboer, J. G.

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. J. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[CrossRef]

Kotlyar, V. V.

Kovalev, A. A.

Kraus, H. G.

Leach, J.

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, “Holographic assembly workstation for optical manipulation,” J. Opt. A 10, 044009 (2008).
[CrossRef]

Lean, T. K.

T. K. Lean, “Theory and practice of proximity correction by secondary exposure,” J. Appl. Phys. 65, 1776–1781 (1989).
[CrossRef]

Li, C.

N. Gao, C. Xie, C. Li, C. Jin, and M. Liu, “Square optical vortices generated by binary spiral zone plates,” Appl. Phys. Lett. 98, 151106 (2011).
[CrossRef]

Lin, J.

Liu, M.

N. Gao, C. Xie, C. Li, C. Jin, and M. Liu, “Square optical vortices generated by binary spiral zone plates,” Appl. Phys. Lett. 98, 151106 (2011).
[CrossRef]

Medley, P.

M. Boyd, E. W. Streed, P. Medley, G. K. Campbell, J. Mun, W. Ketterle, and D. E. Pritchard, “Atom trapping with a thin magnetic film,” Phys. Rev. A 76, 043524 (2007).
[CrossRef]

Miles, M.

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, “Holographic assembly workstation for optical manipulation,” J. Opt. A 10, 044009 (2008).
[CrossRef]

Moh, K. J.

Mun, J.

M. Boyd, E. W. Streed, P. Medley, G. K. Campbell, J. Mun, W. Ketterle, and D. E. Pritchard, “Atom trapping with a thin magnetic film,” Phys. Rev. A 76, 043524 (2007).
[CrossRef]

Nagy, A.

K. C. Neuman and A. Nagy, “Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nat. Methods 5, 491–505 (2008).
[CrossRef]

Neuman, K. C.

K. C. Neuman and A. Nagy, “Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nat. Methods 5, 491–505 (2008).
[CrossRef]

Oemrawsingh, S. S. R.

Osten, W.

Ott, H.

H. Ott, J. Fortagh, G. Schlotterbeck, A. Grossmann, and C. Zimmermann, “Bose–Einstein condensation in a surface microtrap,” Phys. Rev. Lett. 87, 230401 (2001).
[CrossRef]

Padgett, M.

Pedrini, G.

Piesten, R.

Pritchard, D. E.

M. Boyd, E. W. Streed, P. Medley, G. K. Campbell, J. Mun, W. Ketterle, and D. E. Pritchard, “Atom trapping with a thin magnetic film,” Phys. Rev. A 76, 043524 (2007).
[CrossRef]

Reichel, J.

W. Hansel, P. Hommelhoff, T. W. Hansch, and J. Reichel, “Bose–Einstein condensation on a microelectronic chip,” Nature 413, 498–501 (2001).
[CrossRef]

Rishton, S. A.

S. A. Rishton and D. P. Kern, “Point exposure distribution measurements for proximity correction in electron beam lithography on a sub-100 nm scale,” J. Vac. Sci. Technol. B 5, 135–141 (1987).
[CrossRef]

Robert, D.

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, “Holographic assembly workstation for optical manipulation,” J. Opt. A 10, 044009 (2008).
[CrossRef]

Schlotterbeck, G.

H. Ott, J. Fortagh, G. Schlotterbeck, A. Grossmann, and C. Zimmermann, “Bose–Einstein condensation in a surface microtrap,” Phys. Rev. Lett. 87, 230401 (2001).
[CrossRef]

Schonbrun, E.

Situ, G. H.

Skidanov, R. V.

Soifer, V. A.

Sonek, G. J.

A. E. Chiou, W. Wang, G. J. Sonek, J. Hong, and M. W. Berns, “Interferometric optical tweezers,” Opt. Commun. 133, 7–10 (1997).
[CrossRef]

Streed, E. W.

M. Boyd, E. W. Streed, P. Medley, G. K. Campbell, J. Mun, W. Ketterle, and D. E. Pritchard, “Atom trapping with a thin magnetic film,” Phys. Rev. A 76, 043524 (2007).
[CrossRef]

Takigawa, T.

T. Abe, S. Yamasaki, T. Yamaguchi, R. Yoshikawa, and T. Takigawa, “Representative figure method for proximity error correction [II],” Jpn. J. Appl. Phys. 30, 2965–2969 (1991).
[CrossRef]

Tossavainen, N.

Turunen, J.

van Houwelingen, J. A. W.

Verstegen, E. J. K.

Wang, H.

Wang, W.

A. E. Chiou, W. Wang, G. J. Sonek, J. Hong, and M. W. Berns, “Interferometric optical tweezers,” Opt. Commun. 133, 7–10 (1997).
[CrossRef]

Whyte, G.

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, “Holographic assembly workstation for optical manipulation,” J. Opt. A 10, 044009 (2008).
[CrossRef]

Woerdman, J. P.

Wulff, K. D.

Xie, C.

N. Gao, C. Xie, C. Li, C. Jin, and M. Liu, “Square optical vortices generated by binary spiral zone plates,” Appl. Phys. Lett. 98, 151106 (2011).
[CrossRef]

Xue, D. M.

C. S. Guo, D. M. Xue, Y. J. Han, and J. Ding, “Optimal phase steps of multi-level spiral phase plates,” Opt. Commun. 268, 235–239 (2006).
[CrossRef]

Yamaguchi, T.

T. Abe, S. Yamasaki, T. Yamaguchi, R. Yoshikawa, and T. Takigawa, “Representative figure method for proximity error correction [II],” Jpn. J. Appl. Phys. 30, 2965–2969 (1991).
[CrossRef]

Yamasaki, S.

T. Abe, S. Yamasaki, T. Yamaguchi, R. Yoshikawa, and T. Takigawa, “Representative figure method for proximity error correction [II],” Jpn. J. Appl. Phys. 30, 2965–2969 (1991).
[CrossRef]

Yoshikawa, R.

T. Abe, S. Yamasaki, T. Yamaguchi, R. Yoshikawa, and T. Takigawa, “Representative figure method for proximity error correction [II],” Jpn. J. Appl. Phys. 30, 2965–2969 (1991).
[CrossRef]

Yuan, X. C.

Zhang, B.

Zhang, L. S.

Zhao, D.

Zimmermann, C.

H. Ott, J. Fortagh, G. Schlotterbeck, A. Grossmann, and C. Zimmermann, “Bose–Einstein condensation in a surface microtrap,” Phys. Rev. Lett. 87, 230401 (2001).
[CrossRef]

Am. J. Phys. (1)

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Figures (10)

Fig. 1.
Fig. 1.

Schematic of the setup for the generation of a donut intensity profile at the image plane using spiral-phase FZP and DBR laser. The quantities u and v are the object and image focal distances, and t is the thickness of glass substrate.

Fig. 2.
Fig. 2.

Schematic of the optics configuration for focusing a diverging wave with a FZP. un and vn are the optical path lengths traversed by the light rays from the laser source to the nth zone of the FZP and from the nth zone of FZP to the focal point in the image plane. rn is the radius of nth half-period zone.

Fig. 3.
Fig. 3.

Image of the beam cross section at the laser output and the plot of the intensity profiles along the x and y directions.

Fig. 4.
Fig. 4.

(a) Phase profile of a 16-level spiral-phase FZP and (b) the intensity profile at the focal plane.

Fig. 5.
Fig. 5.

Profile of resist thickness for different values of electron-beam dose.

Fig. 6.
Fig. 6.

Distribution of phase values, resist thickness and dose values for the 16 levels.

Fig. 7.
Fig. 7.

Optical microscope image of the (a) central part and (b) outer part of the fabricated spiral-phase FZP.

Fig. 8.
Fig. 8.

Comparison of calculated values of resist thicknesses and measured values of the resist thicknesses from the fabricated device.

Fig. 9.
Fig. 9.

Image of the donut beam at the image plane and plot of the intensity profiles along the x and y directions.

Fig. 10.
Fig. 10.

Image of the asymmetric donut beam at the image plane for topological charges L=0.25, L=0.5, and L=0.75.

Tables (1)

Tables Icon

Table 1. Simulated and Measured Values of Inner and Outer 1/e2 Radii along the x and y Directions

Equations (12)

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E(x,y,z)=E0(w0xw0y)1/2(wx(z)wy(z))1/2exp(x2wx2(z))exp(y2wy2(z))exp(ikz+iζ(z))exp(ikx22Rx(z))exp(iky22Ry(z)),
OPD=[(rn2+v2)1/2+(rn2+u2)1/2](u+v)=nλ2,
rn=[(n2λ24+nλ(u+v)+2uv)24u2v24(n2λ24+nλ(u+v)+2uv+u2+v2)]1/2.
ΦFZP(r)={Φ1,rnr<rn+10,rn+1r<rn+2.n=2p,p=0,1,2
ΦSPP(θ)=[Lθ]2π.
ΔΦ=(2πM)L.
ΦSPP(θ)=ΔΦfloor[M2πθ].
ΦspFZP(r,θ)={ΔΦ,floor[M2πθ]rnr<rn+10,rn+1r<rn+2.n=2p,p=0,1,2
w(z)=w0[1+(zλπw02)2]1/2.
PPtot=1Ptot0a0a[I0(W0xW0y)(Wx(z)Wy(z))exp(2x2Wx2(z))exp(2y2Wy2(z))2π(x2+y2)1/2]dxdy,
ΦspFZP(m)=(m1)0.125π,
t=λ(nrna).

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