Abstract

In this paper, we generalize the concept of classical spiral zone plates (SZPs) to fractional spiral zone plates (FSZPs). By using an SZP with a fractional topological charge and controlling the starting orientation, we can break down the symmetry of the focusing process to give orientation-selective anisotropic vortex foci. Numerical results show that its binary structure gives additional high-order foci on the optical axis and the intensities in the foci can be controlled by properly choosing the fractional topological charge. Our study reveals the feasibility to control the intensity in the foci by means of FSZPs.

© 2013 Optical Society of America

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    [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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    [CrossRef]
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    [CrossRef]
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2010 (3)

2009 (1)

G. Situ, G. Pedrini, and W. Osten, “Spiral phase filtering and orientation-selective edge detection/enhancement,” J. Opt. Soc. Am. A. 26, 1788–1797 (2009).
[CrossRef]

2007 (1)

2006 (3)

D. Cojoc, B. Kaulich, A. Carpentiero, S. Cabrini, L. Businaro, and E. Di Fabrizio, “X-ray vortices with high topological charge,” Microelectron. Eng. 83, 1360–1363 (2006).
[CrossRef]

C.-S. Guo, Y. Zhang, Y.-J. Han, J.-P. Ding, and H.-T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259, 449–454 (2006).
[CrossRef]

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]

2005 (3)

2004 (2)

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A. 6, 259–268(2004).
[CrossRef]

A. G. Peele, K. A. Nugent, and A. P. Mancuso, “X-ray phase vortices: theory and experiment,” J. Opt. Soc. Am. A. 21, 1575–1584 (2004).
[CrossRef]

2001 (1)

2000 (1)

1998 (1)

1996 (1)

1994 (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

1993 (1)

Z. Jaroszewicz and A. Koodziejczyk, “Zone plates performing generalized Hankel transforms and their metrological applications,” Opt. Commun. 102, 391–396 (1993).
[CrossRef]

1992 (2)

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
[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]

Almazov, A. A.

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Bernet, S.

Berry, M. V.

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A. 6, 259–268(2004).
[CrossRef]

Businaro, L.

D. Cojoc, B. Kaulich, A. Carpentiero, S. Cabrini, L. Businaro, and E. Di Fabrizio, “X-ray vortices with high topological charge,” Microelectron. Eng. 83, 1360–1363 (2006).
[CrossRef]

Cabrini, S.

D. Cojoc, B. Kaulich, A. Carpentiero, S. Cabrini, L. Businaro, and E. Di Fabrizio, “X-ray vortices with high topological charge,” Microelectron. Eng. 83, 1360–1363 (2006).
[CrossRef]

Carpentiero, A.

D. Cojoc, B. Kaulich, A. Carpentiero, S. Cabrini, L. Businaro, and E. Di Fabrizio, “X-ray vortices with high topological charge,” Microelectron. Eng. 83, 1360–1363 (2006).
[CrossRef]

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Cojoc, D.

D. Cojoc, B. Kaulich, A. Carpentiero, S. Cabrini, L. Businaro, and E. Di Fabrizio, “X-ray vortices with high topological charge,” Microelectron. Eng. 83, 1360–1363 (2006).
[CrossRef]

Cottrell, D. M.

Davis, J. A.

Di Fabrizio, E.

D. Cojoc, B. Kaulich, A. Carpentiero, S. Cabrini, L. Businaro, and E. Di Fabrizio, “X-ray vortices with high topological charge,” Microelectron. Eng. 83, 1360–1363 (2006).
[CrossRef]

Ding, J.-P.

C.-S. Guo, Y. Zhang, Y.-J. Han, J.-P. Ding, and H.-T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259, 449–454 (2006).
[CrossRef]

Elfstrom, H.

Fak-aim, M.

M. Fak-aim, A. Seanton, and S. Kaitwanidvilai, “Automatic visual inspection of bump in flip chip using edge detection with genetic algorithm,” in the Proceedings of the International Multiconference of Engineers and Computer Scientists 2008 (International Association of Engineers, 2008), Vol. I, pp. 19–21.

Ferrari, J. A.

Flores, J. L.

Fürhapter, S.

S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Spiral phase contrast imaging in microscopy,” Opt. Express 13, 689–694 (2005).
[CrossRef]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Shadow effects in spiral phase contrast microscopy,” Phys. Rev. Lett. 94, 233902 (2005).
[CrossRef]

Guo, C.-S.

C.-S. Guo, Y. Zhang, Y.-J. Han, J.-P. Ding, and H.-T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259, 449–454 (2006).
[CrossRef]

Han, Y.-J.

C.-S. Guo, Y. Zhang, Y.-J. Han, J.-P. Ding, and H.-T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259, 449–454 (2006).
[CrossRef]

Heckenberg, N. R.

Heise, B.

Jaroszewicz, Z.

Z. Jaroszewicz and A. Koodziejczyk, “Zone plates performing generalized Hankel transforms and their metrological applications,” Opt. Commun. 102, 391–396 (1993).
[CrossRef]

Jesacher, A.

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Shadow effects in spiral phase contrast microscopy,” Phys. Rev. Lett. 94, 233902 (2005).
[CrossRef]

S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Spiral phase contrast imaging in microscopy,” Opt. Express 13, 689–694 (2005).
[CrossRef]

Kaitwanidvilai, S.

M. Fak-aim, A. Seanton, and S. Kaitwanidvilai, “Automatic visual inspection of bump in flip chip using edge detection with genetic algorithm,” in the Proceedings of the International Multiconference of Engineers and Computer Scientists 2008 (International Association of Engineers, 2008), Vol. I, pp. 19–21.

Kaulich, B.

D. Cojoc, B. Kaulich, A. Carpentiero, S. Cabrini, L. Businaro, and E. Di Fabrizio, “X-ray vortices with high topological charge,” Microelectron. Eng. 83, 1360–1363 (2006).
[CrossRef]

Khonina, S. N.

Koodziejczyk, A.

Z. Jaroszewicz and A. Koodziejczyk, “Zone plates performing generalized Hankel transforms and their metrological applications,” Opt. Commun. 102, 391–396 (1993).
[CrossRef]

Kotlyar, V. V.

Kovalev, A. A.

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Lin, J.

Liu, Y.

Lohmann, A. W.

Mancuso, A. P.

A. G. Peele, K. A. Nugent, and A. P. Mancuso, “X-ray phase vortices: theory and experiment,” J. Opt. Soc. Am. A. 21, 1575–1584 (2004).
[CrossRef]

Maurer, C.

McDuff, R.

McNamara, D. E.

Moh, K.

Moreno, I.

Nugent, K. A.

A. G. Peele, K. A. Nugent, and A. P. Mancuso, “X-ray phase vortices: theory and experiment,” J. Opt. Soc. Am. A. 21, 1575–1584 (2004).
[CrossRef]

Osten, W.

G. Situ, G. Pedrini, and W. Osten, “Spiral phase filtering and orientation-selective edge detection/enhancement,” J. Opt. Soc. Am. A. 26, 1788–1797 (2009).
[CrossRef]

Pedrini, G.

G. Situ, G. Pedrini, and W. Osten, “Spiral phase filtering and orientation-selective edge detection/enhancement,” J. Opt. Soc. Am. A. 26, 1788–1797 (2009).
[CrossRef]

Peele, A. G.

A. G. Peele, K. A. Nugent, and A. P. Mancuso, “X-ray phase vortices: theory and experiment,” J. Opt. Soc. Am. A. 21, 1575–1584 (2004).
[CrossRef]

Ritsch-Marte, M.

Sakdinawat, A.

Schausberger, S. E.

Seanton, A.

M. Fak-aim, A. Seanton, and S. Kaitwanidvilai, “Automatic visual inspection of bump in flip chip using edge detection with genetic algorithm,” in the Proceedings of the International Multiconference of Engineers and Computer Scientists 2008 (International Association of Engineers, 2008), Vol. I, pp. 19–21.

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]

Situ, G.

G. Situ, G. Pedrini, and W. Osten, “Spiral phase filtering and orientation-selective edge detection/enhancement,” J. Opt. Soc. Am. A. 26, 1788–1797 (2009).
[CrossRef]

Smith, C. P.

Soifer, V. A.

Stifter, D.

Swartzlander, G. A.

Turunen, J.

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]

Wang, H.-T.

C.-S. Guo, Y. Zhang, Y.-J. Han, J.-P. Ding, and H.-T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259, 449–454 (2006).
[CrossRef]

White, A. G.

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Yuan, X. C.

Zhang, N.

Zhang, Y.

C.-S. Guo, Y. Zhang, Y.-J. Han, J.-P. Ding, and H.-T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259, 449–454 (2006).
[CrossRef]

Appl. Opt. (3)

J. Mod. Opt. (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]

J. Opt. A. (1)

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A. 6, 259–268(2004).
[CrossRef]

J. Opt. Soc. Am. A (1)

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

A. G. Peele, K. A. Nugent, and A. P. Mancuso, “X-ray phase vortices: theory and experiment,” J. Opt. Soc. Am. A. 21, 1575–1584 (2004).
[CrossRef]

G. Situ, G. Pedrini, and W. Osten, “Spiral phase filtering and orientation-selective edge detection/enhancement,” J. Opt. Soc. Am. A. 26, 1788–1797 (2009).
[CrossRef]

Microelectron. Eng. (1)

D. Cojoc, B. Kaulich, A. Carpentiero, S. Cabrini, L. Businaro, and E. Di Fabrizio, “X-ray vortices with high topological charge,” Microelectron. Eng. 83, 1360–1363 (2006).
[CrossRef]

Opt. Commun. (3)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

C.-S. Guo, Y. Zhang, Y.-J. Han, J.-P. Ding, and H.-T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259, 449–454 (2006).
[CrossRef]

Z. Jaroszewicz and A. Koodziejczyk, “Zone plates performing generalized Hankel transforms and their metrological applications,” Opt. Commun. 102, 391–396 (1993).
[CrossRef]

Opt. Express (1)

Opt. Lett. (7)

Phys. Rev. Lett. (1)

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Shadow effects in spiral phase contrast microscopy,” Phys. Rev. Lett. 94, 233902 (2005).
[CrossRef]

Other (1)

M. Fak-aim, A. Seanton, and S. Kaitwanidvilai, “Automatic visual inspection of bump in flip chip using edge detection with genetic algorithm,” in the Proceedings of the International Multiconference of Engineers and Computer Scientists 2008 (International Association of Engineers, 2008), Vol. I, pp. 19–21.

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Figures (5)

Fig. 1.
Fig. 1.

(a) Computer-generated FSZPs with different TCs, and the upper-left parts are the enlargements of the central parts in the θ direction; the parameters of the FSZPs are below: 100 zones, r1=0.7mm; (b) diffraction patterns of FSZPs with λ=633nm at z=f=0.7741m.

Fig. 2.
Fig. 2.

Diffraction patterns of the FSZP with p=1/2 when (left) θ=0 and (right) θ=π/4. The arrows indicate the θ direction.

Fig. 3.
Fig. 3.

Intensity profile along the y axis on the first focal plane.

Fig. 4.
Fig. 4.

(a) Diffraction patterns with λ=633nm at z=f/3=0.2580m when p=1/2, 1/3, and 1/5, and the upper-right corners are the diffraction patterns with λ=633nm at z=f=0.7741m when p=1/2, 1/3, and 1/5; (b) diffraction patterns with λ=633nm at z=f=0.7741m when p=3/2, 1, and 3/5.

Fig. 5.
Fig. 5.

Log plots of y-axial intensity with (a) p=1/2, z=f/3 and p=3/2, z=f; (b) p=1/3, z=f/3 and p=1, z=f; and (c) p=1/5, z=f/3 and p=3/5, z=f.

Equations (11)

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SZPP(r,φ)=exp(ipφiπr2λf),
t(r2,φ)={0(2k1)πpφ(θ)πr2λf2kπ12kπpφ(θ)πr2λf(2k+1)πk=0,1,2,
r=2(1p)λf+r2
U(ρ,ϕ,z,θ)=1iλzexp(iπλzρ2)×0R02πexp[i2πλzρrcos(φ(θ)ϕ(θ))]×exp(iπr2λz)t(r2,φ(θ))rdrdφ(θ),
U(ρ,ϕ,z,θ)=1iλzexp(iπλzρ2)0Rexp(iπr2λz){πJ0(2πλzρr)+1πn=±1,±3,m=(i)mlnm(p)exp[i(mϕ(θ)nπr2λf)]Jm(2πλzρr)}rdr,
lnm(p)={exp[2πi(npm)]1n(npm)npis a fraction0npis an integer,andnpm2πinnp=m
t(r2,φ(θ))=121iπn1nexp[in(pφ(θ)πr2λf)],n=±1,±3,
exp[ixcosy]=m=+(i)mJm(x)exp[imy],
I(ρ=0,z=f/s)=|siλf0R1πexp(2πisp)1s2prdr|2=N2sinc2(sp),
Is,p(ρ,ϕ,z,θ)=|1iπλzexp(iπλzρ2)m=(i)mlsm(p)exp(imϕ(θ))×0Rexp[i(πr2λzsπr2λf)]Jm(2πλzρr)rdr|2
Is,p(ρ/s,ϕ,f/s,θ)=I1,ps(ρ,ϕ,f,θ),

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