Abstract

Wavefront sensing under nonparaxial conditions was studied with Shack–Hartmann setups based on arrays of microaxicons. The robustness of the generated pseudonondiffracting subbeams against tilt and axial displacement was demonstrated for ultraflat Gaussian- and inverse-Gaussian-shaped elements in transmission and reflection. To characterize slight aberrations and to identify optimum parameter fields, spatial moments of intensity profiles were analyzed with high sensitivity. Reflective design enables for wavefront sensing at oblique incidence as necessary for low-feedback detection and phase diagnostics of ultrashort pulses.

© 2007 Optical Society of America

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  1. R. Grunwald, U. Griebner, F. Tschirschwitz, E. T. J. Nibbering, T. Elsaesser, V. Kebbel, H.-J. Hartmann, and W. Jüptner, Opt. Lett. 25, 981 (2000).
    [CrossRef]
  2. R. Grunwald, U. Neumann, V. Kebbel, H.-J. Kühn,K. Mann, U. Leinhos, H. Mischke, and D. Wulff-Molder, Opt. Lett. 29, 977 (2004).
    [CrossRef] [PubMed]
  3. J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
    [CrossRef] [PubMed]
  4. R. Grunwald, S. Woggon, U. Griebner, R. Ehlert, and W. Reinecke, Jpn. J. Appl. Phys., Part 1 37, 3701 (1998).
    [CrossRef]
  5. Z. Bouchal, J. Wagner, and M. Chlup, Opt. Commun. 151, 207 (1998).
    [CrossRef]
  6. T. Tanaka and S. Yamamoto, Opt. Commun. 184, 113 (2000).
    [CrossRef]
  7. R. Grunwald, U. Neumann, U. Griebner, K. Reimann, G. Steinmeyer, and V. Kebbel, Opt. Lett. 28, 2399 (2003).
    [CrossRef] [PubMed]
  8. R. Grunwald, S. Woggon, R. Ehlert, and W. Reinecke, Pure Appl. Opt. 6, 663 (1997).
    [CrossRef]
  9. R. Grunwald, H. Mischke, and W. Rehak, Appl. Opt. 38, 4117 (1999).
    [CrossRef]
  10. R. Grunwald, Thin Film Micro-Optics--New Frontiers of Spatio-Temporal Beam Shaping (Elsevier, 2007).
  11. R. Grunwald, V. Kebbel, U. Neumann, U. Griebner, and M. Piché, Opt. Eng. (Bellingham) 43, 2518 (2004).
    [CrossRef]

2004 (2)

2003 (1)

2000 (2)

1999 (1)

1998 (2)

R. Grunwald, S. Woggon, U. Griebner, R. Ehlert, and W. Reinecke, Jpn. J. Appl. Phys., Part 1 37, 3701 (1998).
[CrossRef]

Z. Bouchal, J. Wagner, and M. Chlup, Opt. Commun. 151, 207 (1998).
[CrossRef]

1997 (1)

R. Grunwald, S. Woggon, R. Ehlert, and W. Reinecke, Pure Appl. Opt. 6, 663 (1997).
[CrossRef]

1987 (1)

J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Bouchal, Z.

Z. Bouchal, J. Wagner, and M. Chlup, Opt. Commun. 151, 207 (1998).
[CrossRef]

Chlup, M.

Z. Bouchal, J. Wagner, and M. Chlup, Opt. Commun. 151, 207 (1998).
[CrossRef]

Durnin, J.

J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Ehlert, R.

R. Grunwald, S. Woggon, U. Griebner, R. Ehlert, and W. Reinecke, Jpn. J. Appl. Phys., Part 1 37, 3701 (1998).
[CrossRef]

R. Grunwald, S. Woggon, R. Ehlert, and W. Reinecke, Pure Appl. Opt. 6, 663 (1997).
[CrossRef]

Elsaesser, T.

Griebner, U.

R. Grunwald, V. Kebbel, U. Neumann, U. Griebner, and M. Piché, Opt. Eng. (Bellingham) 43, 2518 (2004).
[CrossRef]

R. Grunwald, U. Neumann, U. Griebner, K. Reimann, G. Steinmeyer, and V. Kebbel, Opt. Lett. 28, 2399 (2003).
[CrossRef] [PubMed]

R. Grunwald, U. Griebner, F. Tschirschwitz, E. T. J. Nibbering, T. Elsaesser, V. Kebbel, H.-J. Hartmann, and W. Jüptner, Opt. Lett. 25, 981 (2000).
[CrossRef]

R. Grunwald, S. Woggon, U. Griebner, R. Ehlert, and W. Reinecke, Jpn. J. Appl. Phys., Part 1 37, 3701 (1998).
[CrossRef]

Grunwald, R.

R. Grunwald, U. Neumann, V. Kebbel, H.-J. Kühn,K. Mann, U. Leinhos, H. Mischke, and D. Wulff-Molder, Opt. Lett. 29, 977 (2004).
[CrossRef] [PubMed]

R. Grunwald, V. Kebbel, U. Neumann, U. Griebner, and M. Piché, Opt. Eng. (Bellingham) 43, 2518 (2004).
[CrossRef]

R. Grunwald, U. Neumann, U. Griebner, K. Reimann, G. Steinmeyer, and V. Kebbel, Opt. Lett. 28, 2399 (2003).
[CrossRef] [PubMed]

R. Grunwald, U. Griebner, F. Tschirschwitz, E. T. J. Nibbering, T. Elsaesser, V. Kebbel, H.-J. Hartmann, and W. Jüptner, Opt. Lett. 25, 981 (2000).
[CrossRef]

R. Grunwald, H. Mischke, and W. Rehak, Appl. Opt. 38, 4117 (1999).
[CrossRef]

R. Grunwald, S. Woggon, U. Griebner, R. Ehlert, and W. Reinecke, Jpn. J. Appl. Phys., Part 1 37, 3701 (1998).
[CrossRef]

R. Grunwald, S. Woggon, R. Ehlert, and W. Reinecke, Pure Appl. Opt. 6, 663 (1997).
[CrossRef]

R. Grunwald, Thin Film Micro-Optics--New Frontiers of Spatio-Temporal Beam Shaping (Elsevier, 2007).

Hartmann, H.-J.

Jüptner, W.

Kebbel, V.

Kühn, H.-J.

Leinhos, U.

Mann, K.

Miceli, J. J.

J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Mischke, H.

Neumann, U.

Nibbering, E. T. J.

Piché, M.

R. Grunwald, V. Kebbel, U. Neumann, U. Griebner, and M. Piché, Opt. Eng. (Bellingham) 43, 2518 (2004).
[CrossRef]

Rehak, W.

Reimann, K.

Reinecke, W.

R. Grunwald, S. Woggon, U. Griebner, R. Ehlert, and W. Reinecke, Jpn. J. Appl. Phys., Part 1 37, 3701 (1998).
[CrossRef]

R. Grunwald, S. Woggon, R. Ehlert, and W. Reinecke, Pure Appl. Opt. 6, 663 (1997).
[CrossRef]

Steinmeyer, G.

Tanaka, T.

T. Tanaka and S. Yamamoto, Opt. Commun. 184, 113 (2000).
[CrossRef]

Tschirschwitz, F.

Wagner, J.

Z. Bouchal, J. Wagner, and M. Chlup, Opt. Commun. 151, 207 (1998).
[CrossRef]

Woggon, S.

R. Grunwald, S. Woggon, U. Griebner, R. Ehlert, and W. Reinecke, Jpn. J. Appl. Phys., Part 1 37, 3701 (1998).
[CrossRef]

R. Grunwald, S. Woggon, R. Ehlert, and W. Reinecke, Pure Appl. Opt. 6, 663 (1997).
[CrossRef]

Wulff-Molder, D.

Yamamoto, S.

T. Tanaka and S. Yamamoto, Opt. Commun. 184, 113 (2000).
[CrossRef]

Appl. Opt. (1)

Jpn. J. Appl. Phys., Part 1 (1)

R. Grunwald, S. Woggon, U. Griebner, R. Ehlert, and W. Reinecke, Jpn. J. Appl. Phys., Part 1 37, 3701 (1998).
[CrossRef]

Opt. Commun. (2)

Z. Bouchal, J. Wagner, and M. Chlup, Opt. Commun. 151, 207 (1998).
[CrossRef]

T. Tanaka and S. Yamamoto, Opt. Commun. 184, 113 (2000).
[CrossRef]

Opt. Eng. (Bellingham) (1)

R. Grunwald, V. Kebbel, U. Neumann, U. Griebner, and M. Piché, Opt. Eng. (Bellingham) 43, 2518 (2004).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. Lett. (1)

J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Pure Appl. Opt. (1)

R. Grunwald, S. Woggon, R. Ehlert, and W. Reinecke, Pure Appl. Opt. 6, 663 (1997).
[CrossRef]

Other (1)

R. Grunwald, Thin Film Micro-Optics--New Frontiers of Spatio-Temporal Beam Shaping (Elsevier, 2007).

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Figures (3)

Fig. 1
Fig. 1

Shack–Hartmann sensor with ultraflat microaxicons (transmission setup, schematically). The wavefront to be detected (WF) is split by an axicon array (AA) into needle-shaped pseudonondiffracting subbeams (“needle beam array,” NBA) of large DOF. Therefore, the system becomes tolerant against angular tilt and axial displacement. To analyze the wavefront, the transversal shift of the beams in the plane of interest (POI) is detected by means of an imaging system (IS) and camera (CCD). In transmission, convex axicon lenses were applied, whereas concave structures are used in reflective setup (not drawn here).

Fig. 2
Fig. 2

Arrays of pseudonondiffracting subbeams generated by three different types of axions detected at the same tilt angle of 25 ° : (a) conical diffractive axicons in transmission (axial position z = 7 mm ), (b) reflective thin-film axicons (inverse-Gaussian shape, structure depth 300 nm ) ( z = 8 mm ) , (c) continuous relief thin-film axicons (Gaussian shape, height 900 nm ) ( z = 7.85 mm ) . The average conical angles were 2.5 ° , 0.0015 ° , and 0.25 ° , respectively.

Fig. 3
Fig. 3

Tilt and displacement tolerance of needle-shaped Bessel-like subbeams in terms of (a) third-order (skewness) and (b) fourth-order moments (kurtosis) of the spatial intensity distribution [data corresponding to Fig. 2c]. The kurtosis indicates even very small aberrations by sensitively acquiring changes of the peakedness. The symmetry parameter skewness does not show comparable sensitivity. The wavefront of a diode laser beam after shaping with a glass lens ( f = 150 mm , distance from axicons 60 mm ) was detected at normal incidence (c) and an angle of incidence of 30 ° (d) (reference wavelength 822.7 nm ).

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