Abstract

We describe the use of stress birefringence in the creation of vortex illumination. A trifold symmetric stress pattern will provide an annular region that exhibits polarization vortices when illuminated with linearly polarized light and scalar vortices when illuminated with circularly polarized light. A finite element plane-stress model is used to analyze the space-variant anisotropy.

© 2007 Optical Society of America

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References

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  1. F. Flossmann, U. T. Schwarz, M. Maier, and M. Dennis, "Polarization singularities from unfolding an optical vortex through a birefringent crystal," Phys. Rev. Lett. 95, 253901 (2005).
    [CrossRef] [PubMed]
  2. A. Estroff, Y. Fan, A. Bourov, and B. Smith, "Mask-induced polarization effects at high numerical aperture," J. Microlithogr. Microfabr. Microsyst. 4, 031107 (2005).
    [CrossRef]
  3. B. W. Smith and J. S. Cashmore, "Challenges in high NA, polarization, and photoresists," in Optical Microlithography XV, A. Yen, ed., Proc. SPIE 4691, 11-24 (2002).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  13. S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "The focus of light-theoretical calculation and experimental topographic reconstruction," Appl. Phy. B 72, 109-113 (2001).
  14. E. G. Churin, J. Hossfeld, and T. Tschudi, "Polarization configurations with singular point formed by computer-generated holograms," Opt. Commun. 99, 13-17 (1993).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  17. D. P. Biss, "Focal field interactions from cylindrical vector beams," Ph.D. dissertation (University of Rochester, 2005).
  18. K. S. Youngworth, "Inhomogeneous polarization in confocal microscopy," Ph.D. dissertation (University of Rochester, 2002).
  19. K. S. Youngworth, D. P. Bliss, and T. G. Brown, "Point spread functions for particle imaging using inhomogeneous polarization in scanning optical microscopy," in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing VIII, J.-A. Conchello, C. J. Cogswell, and T. Wilson, eds., Proc. SPIE 4261, 14-23 (2001).
    [CrossRef]
  20. Q. W. Zhan and J. R. Leger, "Focus shaping using cylindrical vector beams," Opt. Express 10, 324-331 (2002).
    [PubMed]
  21. K. B. Doyle, V. L. Genberg, and G. J. Michels, Integrated Optomechanical Analysis, Vol. TT58 of SPIE Tutorial Texts in Optical Engineering (SPIE Press, 2002).

2005 (2)

F. Flossmann, U. T. Schwarz, M. Maier, and M. Dennis, "Polarization singularities from unfolding an optical vortex through a birefringent crystal," Phys. Rev. Lett. 95, 253901 (2005).
[CrossRef] [PubMed]

A. Estroff, Y. Fan, A. Bourov, and B. Smith, "Mask-induced polarization effects at high numerical aperture," J. Microlithogr. Microfabr. Microsyst. 4, 031107 (2005).
[CrossRef]

2002 (3)

B. W. Smith and J. S. Cashmore, "Challenges in high NA, polarization, and photoresists," in Optical Microlithography XV, A. Yen, ed., Proc. SPIE 4691, 11-24 (2002).
[CrossRef]

T. Grosjean, D. Courjon, and M. Spajer, "An all-fiber device for generating radially and other polarized light beams," Opt. Commun. 203, 1-5 (2002).
[CrossRef]

Q. W. Zhan and J. R. Leger, "Focus shaping using cylindrical vector beams," Opt. Express 10, 324-331 (2002).
[PubMed]

2001 (3)

D. P. Biss and T. G. Brown, "Cylindrical vector beam focusing through a dielectric surface," Opt. Express 9, 490-497 (2001).
[CrossRef] [PubMed]

K. S. Youngworth, D. P. Bliss, and T. G. Brown, "Point spread functions for particle imaging using inhomogeneous polarization in scanning optical microscopy," in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing VIII, J.-A. Conchello, C. J. Cogswell, and T. Wilson, eds., Proc. SPIE 4261, 14-23 (2001).
[CrossRef]

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "The focus of light-theoretical calculation and experimental topographic reconstruction," Appl. Phy. B 72, 109-113 (2001).

2000 (2)

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

K. S. Youngworth and T. G. Brown, "Focusing of high numerical aperture cylindrical vector beams," Opt. Express 7, 77-87 (2000).
[CrossRef] [PubMed]

1999 (2)

1998 (1)

1996 (3)

1994 (1)

1993 (1)

E. G. Churin, J. Hossfeld, and T. Tschudi, "Polarization configurations with singular point formed by computer-generated holograms," Opt. Commun. 99, 13-17 (1993).
[CrossRef]

Biss, D. P.

D. P. Biss and T. G. Brown, "Cylindrical vector beam focusing through a dielectric surface," Opt. Express 9, 490-497 (2001).
[CrossRef] [PubMed]

D. P. Biss, "Focal field interactions from cylindrical vector beams," Ph.D. dissertation (University of Rochester, 2005).

Bliss, D. P.

K. S. Youngworth, D. P. Bliss, and T. G. Brown, "Point spread functions for particle imaging using inhomogeneous polarization in scanning optical microscopy," in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing VIII, J.-A. Conchello, C. J. Cogswell, and T. Wilson, eds., Proc. SPIE 4261, 14-23 (2001).
[CrossRef]

Bourov, A.

A. Estroff, Y. Fan, A. Bourov, and B. Smith, "Mask-induced polarization effects at high numerical aperture," J. Microlithogr. Microfabr. Microsyst. 4, 031107 (2005).
[CrossRef]

Brown, T. G.

K. S. Youngworth, D. P. Bliss, and T. G. Brown, "Point spread functions for particle imaging using inhomogeneous polarization in scanning optical microscopy," in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing VIII, J.-A. Conchello, C. J. Cogswell, and T. Wilson, eds., Proc. SPIE 4261, 14-23 (2001).
[CrossRef]

D. P. Biss and T. G. Brown, "Cylindrical vector beam focusing through a dielectric surface," Opt. Express 9, 490-497 (2001).
[CrossRef] [PubMed]

K. S. Youngworth and T. G. Brown, "Focusing of high numerical aperture cylindrical vector beams," Opt. Express 7, 77-87 (2000).
[CrossRef] [PubMed]

Cashmore, J. S.

B. W. Smith and J. S. Cashmore, "Challenges in high NA, polarization, and photoresists," in Optical Microlithography XV, A. Yen, ed., Proc. SPIE 4691, 11-24 (2002).
[CrossRef]

Churin, E. G.

E. G. Churin, J. Hossfeld, and T. Tschudi, "Polarization configurations with singular point formed by computer-generated holograms," Opt. Commun. 99, 13-17 (1993).
[CrossRef]

Courjon, D.

T. Grosjean, D. Courjon, and M. Spajer, "An all-fiber device for generating radially and other polarized light beams," Opt. Commun. 203, 1-5 (2002).
[CrossRef]

Dennis, M.

F. Flossmann, U. T. Schwarz, M. Maier, and M. Dennis, "Polarization singularities from unfolding an optical vortex through a birefringent crystal," Phys. Rev. Lett. 95, 253901 (2005).
[CrossRef] [PubMed]

Dorn, R.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "The focus of light-theoretical calculation and experimental topographic reconstruction," Appl. Phy. B 72, 109-113 (2001).

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Doyle, K. B.

K. B. Doyle, V. L. Genberg, and G. J. Michels, Integrated Optomechanical Analysis, Vol. TT58 of SPIE Tutorial Texts in Optical Engineering (SPIE Press, 2002).

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "The focus of light-theoretical calculation and experimental topographic reconstruction," Appl. Phy. B 72, 109-113 (2001).

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Estroff, A.

A. Estroff, Y. Fan, A. Bourov, and B. Smith, "Mask-induced polarization effects at high numerical aperture," J. Microlithogr. Microfabr. Microsyst. 4, 031107 (2005).
[CrossRef]

Fan, Y.

A. Estroff, Y. Fan, A. Bourov, and B. Smith, "Mask-induced polarization effects at high numerical aperture," J. Microlithogr. Microfabr. Microsyst. 4, 031107 (2005).
[CrossRef]

Flossmann, F.

F. Flossmann, U. T. Schwarz, M. Maier, and M. Dennis, "Polarization singularities from unfolding an optical vortex through a birefringent crystal," Phys. Rev. Lett. 95, 253901 (2005).
[CrossRef] [PubMed]

Genberg, V. L.

K. B. Doyle, V. L. Genberg, and G. J. Michels, Integrated Optomechanical Analysis, Vol. TT58 of SPIE Tutorial Texts in Optical Engineering (SPIE Press, 2002).

Glockl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "The focus of light-theoretical calculation and experimental topographic reconstruction," Appl. Phy. B 72, 109-113 (2001).

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Greene, P. L.

Grosjean, T.

T. Grosjean, D. Courjon, and M. Spajer, "An all-fiber device for generating radially and other polarized light beams," Opt. Commun. 203, 1-5 (2002).
[CrossRef]

Hall, D. G.

Hossfeld, J.

E. G. Churin, J. Hossfeld, and T. Tschudi, "Polarization configurations with singular point formed by computer-generated holograms," Opt. Commun. 99, 13-17 (1993).
[CrossRef]

Jordan, R. H.

Leger, J. R.

Leuchs, G.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "The focus of light-theoretical calculation and experimental topographic reconstruction," Appl. Phy. B 72, 109-113 (2001).

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Maier, M.

F. Flossmann, U. T. Schwarz, M. Maier, and M. Dennis, "Polarization singularities from unfolding an optical vortex through a birefringent crystal," Phys. Rev. Lett. 95, 253901 (2005).
[CrossRef] [PubMed]

Michels, G. J.

K. B. Doyle, V. L. Genberg, and G. J. Michels, Integrated Optomechanical Analysis, Vol. TT58 of SPIE Tutorial Texts in Optical Engineering (SPIE Press, 2002).

Quabis, S.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "The focus of light-theoretical calculation and experimental topographic reconstruction," Appl. Phy. B 72, 109-113 (2001).

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Saghafi, S.

Schadt, M.

Schwarz, U. T.

F. Flossmann, U. T. Schwarz, M. Maier, and M. Dennis, "Polarization singularities from unfolding an optical vortex through a birefringent crystal," Phys. Rev. Lett. 95, 253901 (2005).
[CrossRef] [PubMed]

Sheppard, C. J. R.

Smith, B.

A. Estroff, Y. Fan, A. Bourov, and B. Smith, "Mask-induced polarization effects at high numerical aperture," J. Microlithogr. Microfabr. Microsyst. 4, 031107 (2005).
[CrossRef]

Smith, B. W.

B. W. Smith and J. S. Cashmore, "Challenges in high NA, polarization, and photoresists," in Optical Microlithography XV, A. Yen, ed., Proc. SPIE 4691, 11-24 (2002).
[CrossRef]

Spajer, M.

T. Grosjean, D. Courjon, and M. Spajer, "An all-fiber device for generating radially and other polarized light beams," Opt. Commun. 203, 1-5 (2002).
[CrossRef]

Stalder, M.

Tschudi, T.

E. G. Churin, J. Hossfeld, and T. Tschudi, "Polarization configurations with singular point formed by computer-generated holograms," Opt. Commun. 99, 13-17 (1993).
[CrossRef]

Youngworth, K. S.

K. S. Youngworth, D. P. Bliss, and T. G. Brown, "Point spread functions for particle imaging using inhomogeneous polarization in scanning optical microscopy," in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing VIII, J.-A. Conchello, C. J. Cogswell, and T. Wilson, eds., Proc. SPIE 4261, 14-23 (2001).
[CrossRef]

K. S. Youngworth and T. G. Brown, "Focusing of high numerical aperture cylindrical vector beams," Opt. Express 7, 77-87 (2000).
[CrossRef] [PubMed]

K. S. Youngworth, "Inhomogeneous polarization in confocal microscopy," Ph.D. dissertation (University of Rochester, 2002).

Zhan, Q. W.

Appl. Phy. B (1)

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "The focus of light-theoretical calculation and experimental topographic reconstruction," Appl. Phy. B 72, 109-113 (2001).

J. Microlithogr. Microfabr. Microsyst. (1)

A. Estroff, Y. Fan, A. Bourov, and B. Smith, "Mask-induced polarization effects at high numerical aperture," J. Microlithogr. Microfabr. Microsyst. 4, 031107 (2005).
[CrossRef]

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

Opt. Commun. (3)

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

E. G. Churin, J. Hossfeld, and T. Tschudi, "Polarization configurations with singular point formed by computer-generated holograms," Opt. Commun. 99, 13-17 (1993).
[CrossRef]

T. Grosjean, D. Courjon, and M. Spajer, "An all-fiber device for generating radially and other polarized light beams," Opt. Commun. 203, 1-5 (2002).
[CrossRef]

Opt. Express (4)

Opt. Lett. (4)

Phys. Rev. Lett. (1)

F. Flossmann, U. T. Schwarz, M. Maier, and M. Dennis, "Polarization singularities from unfolding an optical vortex through a birefringent crystal," Phys. Rev. Lett. 95, 253901 (2005).
[CrossRef] [PubMed]

Proc. SPIE (2)

B. W. Smith and J. S. Cashmore, "Challenges in high NA, polarization, and photoresists," in Optical Microlithography XV, A. Yen, ed., Proc. SPIE 4691, 11-24 (2002).
[CrossRef]

K. S. Youngworth, D. P. Bliss, and T. G. Brown, "Point spread functions for particle imaging using inhomogeneous polarization in scanning optical microscopy," in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing VIII, J.-A. Conchello, C. J. Cogswell, and T. Wilson, eds., Proc. SPIE 4261, 14-23 (2001).
[CrossRef]

Other (3)

K. B. Doyle, V. L. Genberg, and G. J. Michels, Integrated Optomechanical Analysis, Vol. TT58 of SPIE Tutorial Texts in Optical Engineering (SPIE Press, 2002).

D. P. Biss, "Focal field interactions from cylindrical vector beams," Ph.D. dissertation (University of Rochester, 2005).

K. S. Youngworth, "Inhomogeneous polarization in confocal microscopy," Ph.D. dissertation (University of Rochester, 2002).

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Figures (8)

Fig. 1
Fig. 1

(a) Discrete tape-segmented λ / 2 wave plate photograph and (b) schematic illustrating the fast axis of each of the eight segments within the tape-segmented λ / 2 wave plate.

Fig. 2
Fig. 2

Two spatial symmetries producing polarized beams. (a) With the tape-segmented wave plate a radial beam is formed with incident linear polarization oriented in the vertical direction. (b) Counterrotating beam is formed with a different wave plate fast axis symmetry and incident linear polarization oriented in the vertical direction. Connecting the discrete wave plate pattern produces a continuous m = 3 pattern that has a smoothly varying fast axis orientation.

Fig. 3
Fig. 3

Generation of radial and azimuthal polarization vortex beams with counterrotating beams and a λ / 2 wave plate oriented in the vertical and 45° directions, respectively.

Fig. 4
Fig. 4

Schematic of stress-induced space-variant wave plate. The BK7 window at the center is placed under m = 3 stress by three set screws and an annular region of λ / 2 retardance is formed. A 3.175   mm thick copper sleeve surrounds the 12 .70   mm diameter, 9 .525   mm thick BK7 window.

Fig. 5
Fig. 5

(a) Finite element prediction of birefringence in a stress-induced space-variant wave plate. Arrows inside the wave plate represent the principal components of the diagonalized stress matrix. (b) Arrows of similar length represent isotropic regions of high stress while (c) arrows of different length represent regions with anisotropic stress.

Fig. 6
Fig. 6

(a) Contours of constant retardance predicted for a finite element model of an m = 3 stress-induced space-variant wave plate. Neighboring contours differ in retardance by one tenth of a wave. Arrow points to the contour of half-wave retardance. Gray outer diameter represents the copper sleeve and the inner region represents the BK7 window. (b) Photograph of stress-induced space-variant wave plate placed between circular polarizers to provide contours of equal retardance. Annular region of half-wave retardance is located where the dark band is observed. Triangles show where the external force is applied to the wave plate.

Fig. 7
Fig. 7

(a) Pupil image of stress-induced wave plate and (b) point-spread function of stress- induced wave plate in an imaging system viewed using a horizontal analyzer. Lobes rotate with the analyzer, illustrating the presence of a polarization vortex beam in the focal region.

Fig. 8
Fig. 8

Photographs of thermal compression stress-induced space-variant wave plate when illuminated with RHC light and viewed through a RHC analyzer. Rings of alternating RHC and left-hand circular (LHC) polarization are observed at the center of a window under m = 3 stress. Bright rings are rings of retardance equal to one wavelength and the dark rings are LHC and exhibit a vortex structure. Photograph (b) is an enlargement of the central part of photograph (a).

Equations (7)

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

[ R ( θ ) ] 1 [ σ x x σ x y σ y x σ y y ] [ R ( θ ) ] = [ σ 11 0 0 σ 22 ] ,
Δ n 1 = k 11 σ 11 + k 12 σ 22 ,
Δ n 2 = k 11 σ 22 + k 12 σ 11 .
M ( ρ , ϕ ) = [ cos θ sin θ sin θ cos θ ] [ e i δ / 2 0 0 e i δ / 2 ] [ cos θ sin θ sin θ cos θ ] .
M ( ρ , ϕ ) = i [ cos ( ϕ ) sin ( ϕ ) sin ( ϕ ) cos ( ϕ ) ] .
E out ( ρ , ϕ ) = i [ sin ϕ cos ϕ ] .
[ cos ϕ sin ϕ sin ϕ cos ϕ ] 1 2 [ 1 i ] = e i ϕ 1 2 [ 1 i ] .

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