Abstract

The role of chirp on the light–matter interaction of femto- and pico-second laser pulses with functional structured surfaces is studied using drag-reducing riblets as an example. The three-dimensional, periodic microstructure naturally gives rise to a mutual interplay of (i) reflection, (ii) scattering, and (iii) diffraction phenomena of incident coherent light. Furthermore, for femtosecond pulses, the structure induces (iv) an optical delay equivalent to a consecutive temporal delay of 230 fs in places of the pulse. These features enable studying experimentally and numerically the effect of tuning both pulse duration τ and spectral bandwidth Δω on the features of the wide-angle scattering pattern from the riblet structure. As a result, we discovered a significant breakdown of fringes in the scattering pattern with decreasing pulse duration and/or increasing spectral bandwidth. This unique type of chirp control is straightforwardly explained and verified by numerical modeling considering the spectral and temporal interaction between different segments within the scattered, linearly chirped pulse and the particular geometric features of the riblet structure. The visibility of the fringe pattern can be precisely adjusted, and the off-state is achieved using τ<230  fs or Δω>2.85×1013  rad/s.

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References

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  1. M. M. Moslehi, “Sensor for semiconductor device manufacturing process control,” U.S. patent5,293,216 (March 8, 1994).
  2. M. M. Moslehi, “Apparatus for semiconductor device fabrication diagnosis and prognosis,” U.S. patent5,719,495 (February 17, 1998).
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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]
  19. J. P. Heritage, R. N. Thurston, W. J. Tomlinson, A. M. Weiner, and R. H. Stolen, “Spectral windowing of frequency-modulated optical pulses in a grating compressor,” Appl. Phys. Lett. 47, 87–89 (1985).
    [Crossref]
  20. J. P. Heritage, A. M. Weiner, and R. N. Thurston, “Picosecond pulse shaping by spectral phase and amplitude manipulation,” Opt. Lett. 10, 609–611 (1985).
    [Crossref]
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    [Crossref]
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    [Crossref]

2016 (1)

J. Tschentscher, S. Hochheim, H. Bruening, K. Brune, K.-M. Voit, and M. Imlau, “Optical riblet sensor: beam parameter requirements for the probing laser source,” Sensors 16, 458 (2016).
[Crossref]

2015 (1)

S. Odoulov, A. Shumelyuk, H. Badorreck, S. Nolte, K.-M. Voit, and M. Imlau, “Interference and holography with femtosecond laser pulses of different colours,” Nat. Commun. 6, 5866 (2015).
[Crossref]

2012 (1)

J.-H. Lee, J. P. Singer, and E. L. Thomas, “Micro-/nanostructured mechanical metamaterials,” Adv. Mater. 24, 4782–4810 (2012).
[Crossref]

2011 (2)

V. A. Ganesh, H. K. Raut, A. S. Nair, and S. Ramakrishna, “A review on self-cleaning coatings,” J. Mater. Chem. 21, 16304–16322 (2011).
[Crossref]

A. M. Weiner, “Ultrafast optical pulse shaping: a tutorial review,” Opt. Commun. 284, 3669–3692 (2011).
[Crossref]

2010 (1)

B. Dean and B. Bhushan, “Shark-skin surfaces for fluid-drag reduction in turbulent flow: a review,” Philos. Trans. R. Soc. London A 368, 4775–4806 (2010).
[Crossref]

2002 (1)

B. Kasemo, “Biological surface science,” Surf. Sci. 500, 656–677 (2002).
[Crossref]

2000 (1)

D. W. Bechert, M. Bruse, W. Hage, and R. Meyer, “Fluid mechanics of biological surfaces and their technological application,” Naturwissenschaften 87, 157–171 (2000).
[Crossref]

1997 (1)

D. W. Bechert, M. Bruse, W. Hage, J. G. T. van der Hoeven, and G. Hoppe, “Experiments on drag-reducing surfaces and their optimization with an adjustable geometry,” J. Fluid Mech. 338, 59–87 (1997).
[Crossref]

1990 (1)

M. J. Walsh, “Effect of detailed surface geometry on riblet drag reduction performance,” J. Aircr. 27, 572–573 (1990).
[Crossref]

1985 (2)

J. P. Heritage, R. N. Thurston, W. J. Tomlinson, A. M. Weiner, and R. H. Stolen, “Spectral windowing of frequency-modulated optical pulses in a grating compressor,” Appl. Phys. Lett. 47, 87–89 (1985).
[Crossref]

J. P. Heritage, A. M. Weiner, and R. N. Thurston, “Picosecond pulse shaping by spectral phase and amplitude manipulation,” Opt. Lett. 10, 609–611 (1985).
[Crossref]

1969 (1)

E. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. 5, 454–458 (1969).
[Crossref]

Badorreck, H.

S. Odoulov, A. Shumelyuk, H. Badorreck, S. Nolte, K.-M. Voit, and M. Imlau, “Interference and holography with femtosecond laser pulses of different colours,” Nat. Commun. 6, 5866 (2015).
[Crossref]

Bechert, D.

M. Bruse, D. Bechert, J. T. van der Hoeven, W. Hage, and G. Hoppe, “Experiments with conventional and with novel adjustable drag-reducing surfaces,” in Proceedings of the International Conference on Near-Wall Turbulent Flows, Tempe, Arizona (March 15–17, 1993), pp. 719–738.

Bechert, D. W.

D. W. Bechert, M. Bruse, W. Hage, and R. Meyer, “Fluid mechanics of biological surfaces and their technological application,” Naturwissenschaften 87, 157–171 (2000).
[Crossref]

D. W. Bechert, M. Bruse, W. Hage, J. G. T. van der Hoeven, and G. Hoppe, “Experiments on drag-reducing surfaces and their optimization with an adjustable geometry,” J. Fluid Mech. 338, 59–87 (1997).
[Crossref]

Bhushan, B.

B. Dean and B. Bhushan, “Shark-skin surfaces for fluid-drag reduction in turbulent flow: a review,” Philos. Trans. R. Soc. London A 368, 4775–4806 (2010).
[Crossref]

Brillouin, L.

L. Brillouin, Wave Propagation and Group Velocity (Academic, 2013), Vol. 8.

Bruening, H.

J. Tschentscher, S. Hochheim, H. Bruening, K. Brune, K.-M. Voit, and M. Imlau, “Optical riblet sensor: beam parameter requirements for the probing laser source,” Sensors 16, 458 (2016).
[Crossref]

M. Imlau, H. Bruening, K.-M. Voit, J. Tschentscher, and V. Dieckmann, “Riblet sensor—light scattering on micro structured surface coatings,” arXiv: 1601.04694 (2016).

Brune, K.

J. Tschentscher, S. Hochheim, H. Bruening, K. Brune, K.-M. Voit, and M. Imlau, “Optical riblet sensor: beam parameter requirements for the probing laser source,” Sensors 16, 458 (2016).
[Crossref]

M. Imlau, H. Brüning, K.-M. Voit, J. Tschentscher, S. Dieckhoff, U. Meyer, K. Brune, J. Derksen, and C. Tornow, “A method for quality control of a micro-structuring and apparatus therefor,” DE102013220006A1 (April 2, 2015).

Brüning, H.

M. Imlau, H. Brüning, K.-M. Voit, J. Tschentscher, S. Dieckhoff, U. Meyer, K. Brune, J. Derksen, and C. Tornow, “A method for quality control of a micro-structuring and apparatus therefor,” DE102013220006A1 (April 2, 2015).

Bruse, M.

D. W. Bechert, M. Bruse, W. Hage, and R. Meyer, “Fluid mechanics of biological surfaces and their technological application,” Naturwissenschaften 87, 157–171 (2000).
[Crossref]

D. W. Bechert, M. Bruse, W. Hage, J. G. T. van der Hoeven, and G. Hoppe, “Experiments on drag-reducing surfaces and their optimization with an adjustable geometry,” J. Fluid Mech. 338, 59–87 (1997).
[Crossref]

M. Bruse, D. Bechert, J. T. van der Hoeven, W. Hage, and G. Hoppe, “Experiments with conventional and with novel adjustable drag-reducing surfaces,” in Proceedings of the International Conference on Near-Wall Turbulent Flows, Tempe, Arizona (March 15–17, 1993), pp. 719–738.

Dean, B.

B. Dean and B. Bhushan, “Shark-skin surfaces for fluid-drag reduction in turbulent flow: a review,” Philos. Trans. R. Soc. London A 368, 4775–4806 (2010).
[Crossref]

Derksen, J.

M. Imlau, H. Brüning, K.-M. Voit, J. Tschentscher, S. Dieckhoff, U. Meyer, K. Brune, J. Derksen, and C. Tornow, “A method for quality control of a micro-structuring and apparatus therefor,” DE102013220006A1 (April 2, 2015).

Dieckhoff, S.

M. Imlau, H. Brüning, K.-M. Voit, J. Tschentscher, S. Dieckhoff, U. Meyer, K. Brune, J. Derksen, and C. Tornow, “A method for quality control of a micro-structuring and apparatus therefor,” DE102013220006A1 (April 2, 2015).

U. Meyer, S. Markus, and S. Dieckhoff, “Device for testing the quality of microstructurization,” U.S. patent8,842,271 (September 23, 2014).

Dieckmann, V.

M. Imlau, H. Bruening, K.-M. Voit, J. Tschentscher, and V. Dieckmann, “Riblet sensor—light scattering on micro structured surface coatings,” arXiv: 1601.04694 (2016).

Ganesh, V. A.

V. A. Ganesh, H. K. Raut, A. S. Nair, and S. Ramakrishna, “A review on self-cleaning coatings,” J. Mater. Chem. 21, 16304–16322 (2011).
[Crossref]

Hage, W.

D. W. Bechert, M. Bruse, W. Hage, and R. Meyer, “Fluid mechanics of biological surfaces and their technological application,” Naturwissenschaften 87, 157–171 (2000).
[Crossref]

D. W. Bechert, M. Bruse, W. Hage, J. G. T. van der Hoeven, and G. Hoppe, “Experiments on drag-reducing surfaces and their optimization with an adjustable geometry,” J. Fluid Mech. 338, 59–87 (1997).
[Crossref]

M. Bruse, D. Bechert, J. T. van der Hoeven, W. Hage, and G. Hoppe, “Experiments with conventional and with novel adjustable drag-reducing surfaces,” in Proceedings of the International Conference on Near-Wall Turbulent Flows, Tempe, Arizona (March 15–17, 1993), pp. 719–738.

Heritage, J. P.

J. P. Heritage, R. N. Thurston, W. J. Tomlinson, A. M. Weiner, and R. H. Stolen, “Spectral windowing of frequency-modulated optical pulses in a grating compressor,” Appl. Phys. Lett. 47, 87–89 (1985).
[Crossref]

J. P. Heritage, A. M. Weiner, and R. N. Thurston, “Picosecond pulse shaping by spectral phase and amplitude manipulation,” Opt. Lett. 10, 609–611 (1985).
[Crossref]

Hochheim, S.

J. Tschentscher, S. Hochheim, H. Bruening, K. Brune, K.-M. Voit, and M. Imlau, “Optical riblet sensor: beam parameter requirements for the probing laser source,” Sensors 16, 458 (2016).
[Crossref]

Holst, G. C.

G. C. Holst, CCD Arrays, Cameras, and Displays (JCD, 1998).

Hoppe, G.

D. W. Bechert, M. Bruse, W. Hage, J. G. T. van der Hoeven, and G. Hoppe, “Experiments on drag-reducing surfaces and their optimization with an adjustable geometry,” J. Fluid Mech. 338, 59–87 (1997).
[Crossref]

M. Bruse, D. Bechert, J. T. van der Hoeven, W. Hage, and G. Hoppe, “Experiments with conventional and with novel adjustable drag-reducing surfaces,” in Proceedings of the International Conference on Near-Wall Turbulent Flows, Tempe, Arizona (March 15–17, 1993), pp. 719–738.

Imlau, M.

J. Tschentscher, S. Hochheim, H. Bruening, K. Brune, K.-M. Voit, and M. Imlau, “Optical riblet sensor: beam parameter requirements for the probing laser source,” Sensors 16, 458 (2016).
[Crossref]

S. Odoulov, A. Shumelyuk, H. Badorreck, S. Nolte, K.-M. Voit, and M. Imlau, “Interference and holography with femtosecond laser pulses of different colours,” Nat. Commun. 6, 5866 (2015).
[Crossref]

M. Imlau, H. Bruening, K.-M. Voit, J. Tschentscher, and V. Dieckmann, “Riblet sensor—light scattering on micro structured surface coatings,” arXiv: 1601.04694 (2016).

M. Imlau, H. Brüning, K.-M. Voit, J. Tschentscher, S. Dieckhoff, U. Meyer, K. Brune, J. Derksen, and C. Tornow, “A method for quality control of a micro-structuring and apparatus therefor,” DE102013220006A1 (April 2, 2015).

Ion, J.

J. Ion, Laser Processing of Engineering Materials: Principles, Procedure and Industrial Application (Butterworth-Heinemann, 2005).

Kasemo, B.

B. Kasemo, “Biological surface science,” Surf. Sci. 500, 656–677 (2002).
[Crossref]

Lee, J.-H.

J.-H. Lee, J. P. Singer, and E. L. Thomas, “Micro-/nanostructured mechanical metamaterials,” Adv. Mater. 24, 4782–4810 (2012).
[Crossref]

Markus, S.

U. Meyer, S. Markus, and S. Dieckhoff, “Device for testing the quality of microstructurization,” U.S. patent8,842,271 (September 23, 2014).

Meyer, R.

D. W. Bechert, M. Bruse, W. Hage, and R. Meyer, “Fluid mechanics of biological surfaces and their technological application,” Naturwissenschaften 87, 157–171 (2000).
[Crossref]

Meyer, U.

M. Imlau, H. Brüning, K.-M. Voit, J. Tschentscher, S. Dieckhoff, U. Meyer, K. Brune, J. Derksen, and C. Tornow, “A method for quality control of a micro-structuring and apparatus therefor,” DE102013220006A1 (April 2, 2015).

U. Meyer, S. Markus, and S. Dieckhoff, “Device for testing the quality of microstructurization,” U.S. patent8,842,271 (September 23, 2014).

Moslehi, M. M.

M. M. Moslehi, “Sensor for semiconductor device manufacturing process control,” U.S. patent5,293,216 (March 8, 1994).

M. M. Moslehi, “Apparatus for semiconductor device fabrication diagnosis and prognosis,” U.S. patent5,719,495 (February 17, 1998).

Nair, A. S.

V. A. Ganesh, H. K. Raut, A. S. Nair, and S. Ramakrishna, “A review on self-cleaning coatings,” J. Mater. Chem. 21, 16304–16322 (2011).
[Crossref]

Nolte, S.

S. Odoulov, A. Shumelyuk, H. Badorreck, S. Nolte, K.-M. Voit, and M. Imlau, “Interference and holography with femtosecond laser pulses of different colours,” Nat. Commun. 6, 5866 (2015).
[Crossref]

Odoulov, S.

S. Odoulov, A. Shumelyuk, H. Badorreck, S. Nolte, K.-M. Voit, and M. Imlau, “Interference and holography with femtosecond laser pulses of different colours,” Nat. Commun. 6, 5866 (2015).
[Crossref]

Ramakrishna, S.

V. A. Ganesh, H. K. Raut, A. S. Nair, and S. Ramakrishna, “A review on self-cleaning coatings,” J. Mater. Chem. 21, 16304–16322 (2011).
[Crossref]

Raut, H. K.

V. A. Ganesh, H. K. Raut, A. S. Nair, and S. Ramakrishna, “A review on self-cleaning coatings,” J. Mater. Chem. 21, 16304–16322 (2011).
[Crossref]

Shumelyuk, A.

S. Odoulov, A. Shumelyuk, H. Badorreck, S. Nolte, K.-M. Voit, and M. Imlau, “Interference and holography with femtosecond laser pulses of different colours,” Nat. Commun. 6, 5866 (2015).
[Crossref]

Singer, J. P.

J.-H. Lee, J. P. Singer, and E. L. Thomas, “Micro-/nanostructured mechanical metamaterials,” Adv. Mater. 24, 4782–4810 (2012).
[Crossref]

Stolen, R. H.

J. P. Heritage, R. N. Thurston, W. J. Tomlinson, A. M. Weiner, and R. H. Stolen, “Spectral windowing of frequency-modulated optical pulses in a grating compressor,” Appl. Phys. Lett. 47, 87–89 (1985).
[Crossref]

Thomas, E. L.

J.-H. Lee, J. P. Singer, and E. L. Thomas, “Micro-/nanostructured mechanical metamaterials,” Adv. Mater. 24, 4782–4810 (2012).
[Crossref]

Thurston, R. N.

J. P. Heritage, R. N. Thurston, W. J. Tomlinson, A. M. Weiner, and R. H. Stolen, “Spectral windowing of frequency-modulated optical pulses in a grating compressor,” Appl. Phys. Lett. 47, 87–89 (1985).
[Crossref]

J. P. Heritage, A. M. Weiner, and R. N. Thurston, “Picosecond pulse shaping by spectral phase and amplitude manipulation,” Opt. Lett. 10, 609–611 (1985).
[Crossref]

Tomlinson, W. J.

J. P. Heritage, R. N. Thurston, W. J. Tomlinson, A. M. Weiner, and R. H. Stolen, “Spectral windowing of frequency-modulated optical pulses in a grating compressor,” Appl. Phys. Lett. 47, 87–89 (1985).
[Crossref]

Tornow, C.

M. Imlau, H. Brüning, K.-M. Voit, J. Tschentscher, S. Dieckhoff, U. Meyer, K. Brune, J. Derksen, and C. Tornow, “A method for quality control of a micro-structuring and apparatus therefor,” DE102013220006A1 (April 2, 2015).

Treacy, E.

E. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. 5, 454–458 (1969).
[Crossref]

Tschentscher, J.

J. Tschentscher, S. Hochheim, H. Bruening, K. Brune, K.-M. Voit, and M. Imlau, “Optical riblet sensor: beam parameter requirements for the probing laser source,” Sensors 16, 458 (2016).
[Crossref]

M. Imlau, H. Bruening, K.-M. Voit, J. Tschentscher, and V. Dieckmann, “Riblet sensor—light scattering on micro structured surface coatings,” arXiv: 1601.04694 (2016).

M. Imlau, H. Brüning, K.-M. Voit, J. Tschentscher, S. Dieckhoff, U. Meyer, K. Brune, J. Derksen, and C. Tornow, “A method for quality control of a micro-structuring and apparatus therefor,” DE102013220006A1 (April 2, 2015).

van der Hoeven, J. G. T.

D. W. Bechert, M. Bruse, W. Hage, J. G. T. van der Hoeven, and G. Hoppe, “Experiments on drag-reducing surfaces and their optimization with an adjustable geometry,” J. Fluid Mech. 338, 59–87 (1997).
[Crossref]

van der Hoeven, J. T.

M. Bruse, D. Bechert, J. T. van der Hoeven, W. Hage, and G. Hoppe, “Experiments with conventional and with novel adjustable drag-reducing surfaces,” in Proceedings of the International Conference on Near-Wall Turbulent Flows, Tempe, Arizona (March 15–17, 1993), pp. 719–738.

Voit, K.-M.

J. Tschentscher, S. Hochheim, H. Bruening, K. Brune, K.-M. Voit, and M. Imlau, “Optical riblet sensor: beam parameter requirements for the probing laser source,” Sensors 16, 458 (2016).
[Crossref]

S. Odoulov, A. Shumelyuk, H. Badorreck, S. Nolte, K.-M. Voit, and M. Imlau, “Interference and holography with femtosecond laser pulses of different colours,” Nat. Commun. 6, 5866 (2015).
[Crossref]

M. Imlau, H. Bruening, K.-M. Voit, J. Tschentscher, and V. Dieckmann, “Riblet sensor—light scattering on micro structured surface coatings,” arXiv: 1601.04694 (2016).

M. Imlau, H. Brüning, K.-M. Voit, J. Tschentscher, S. Dieckhoff, U. Meyer, K. Brune, J. Derksen, and C. Tornow, “A method for quality control of a micro-structuring and apparatus therefor,” DE102013220006A1 (April 2, 2015).

Walsh, M. J.

M. J. Walsh, “Effect of detailed surface geometry on riblet drag reduction performance,” J. Aircr. 27, 572–573 (1990).
[Crossref]

Weiner, A. M.

A. M. Weiner, “Ultrafast optical pulse shaping: a tutorial review,” Opt. Commun. 284, 3669–3692 (2011).
[Crossref]

J. P. Heritage, R. N. Thurston, W. J. Tomlinson, A. M. Weiner, and R. H. Stolen, “Spectral windowing of frequency-modulated optical pulses in a grating compressor,” Appl. Phys. Lett. 47, 87–89 (1985).
[Crossref]

J. P. Heritage, A. M. Weiner, and R. N. Thurston, “Picosecond pulse shaping by spectral phase and amplitude manipulation,” Opt. Lett. 10, 609–611 (1985).
[Crossref]

Adv. Mater. (1)

J.-H. Lee, J. P. Singer, and E. L. Thomas, “Micro-/nanostructured mechanical metamaterials,” Adv. Mater. 24, 4782–4810 (2012).
[Crossref]

Appl. Phys. Lett. (1)

J. P. Heritage, R. N. Thurston, W. J. Tomlinson, A. M. Weiner, and R. H. Stolen, “Spectral windowing of frequency-modulated optical pulses in a grating compressor,” Appl. Phys. Lett. 47, 87–89 (1985).
[Crossref]

IEEE J. Quantum Electron. (1)

E. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. 5, 454–458 (1969).
[Crossref]

J. Aircr. (1)

M. J. Walsh, “Effect of detailed surface geometry on riblet drag reduction performance,” J. Aircr. 27, 572–573 (1990).
[Crossref]

J. Fluid Mech. (1)

D. W. Bechert, M. Bruse, W. Hage, J. G. T. van der Hoeven, and G. Hoppe, “Experiments on drag-reducing surfaces and their optimization with an adjustable geometry,” J. Fluid Mech. 338, 59–87 (1997).
[Crossref]

J. Mater. Chem. (1)

V. A. Ganesh, H. K. Raut, A. S. Nair, and S. Ramakrishna, “A review on self-cleaning coatings,” J. Mater. Chem. 21, 16304–16322 (2011).
[Crossref]

Nat. Commun. (1)

S. Odoulov, A. Shumelyuk, H. Badorreck, S. Nolte, K.-M. Voit, and M. Imlau, “Interference and holography with femtosecond laser pulses of different colours,” Nat. Commun. 6, 5866 (2015).
[Crossref]

Naturwissenschaften (1)

D. W. Bechert, M. Bruse, W. Hage, and R. Meyer, “Fluid mechanics of biological surfaces and their technological application,” Naturwissenschaften 87, 157–171 (2000).
[Crossref]

Opt. Commun. (1)

A. M. Weiner, “Ultrafast optical pulse shaping: a tutorial review,” Opt. Commun. 284, 3669–3692 (2011).
[Crossref]

Opt. Lett. (1)

Philos. Trans. R. Soc. London A (1)

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Sensors (1)

J. Tschentscher, S. Hochheim, H. Bruening, K. Brune, K.-M. Voit, and M. Imlau, “Optical riblet sensor: beam parameter requirements for the probing laser source,” Sensors 16, 458 (2016).
[Crossref]

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M. Imlau, H. Brüning, K.-M. Voit, J. Tschentscher, S. Dieckhoff, U. Meyer, K. Brune, J. Derksen, and C. Tornow, “A method for quality control of a micro-structuring and apparatus therefor,” DE102013220006A1 (April 2, 2015).

M. Imlau, H. Bruening, K.-M. Voit, J. Tschentscher, and V. Dieckmann, “Riblet sensor—light scattering on micro structured surface coatings,” arXiv: 1601.04694 (2016).

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Figures (8)

Fig. 1.
Fig. 1. (a) Scanning electron microscope (SEM) image and schematic, three-dimensional representation of the riblet structure under study. (b) Scheme of the optical setup of the riblet sensor described in Refs. [8,9]: the laser beam is incident normal to the riblet sample’s surface, and the intensity distribution of the scattered light is detected in the 0° and ±45° directions. Degradation of the riblet structure is measured as a decrease in intensity around 45°. D1–D3, Si-PIN-diodes; BS, beam-splitter; M1, M2, mirrors; TS1–TS3, motorized translation stages.
Fig. 2.
Fig. 2. (a) Scheme of the pulse front reflected in the 45° direction and distinct pulse path lengths from next-neighboring riblet flanks. Period Λ of the riblet structure is 100 μm, and riblet height h is 50 μm. The spatial delay induced by the riblet structure is 70 μm, and the correlated temporal delay is about Δt=230  fs. (b) and (c) are discussed in the simulation section.
Fig. 3.
Fig. 3. (a) First setup: the laser beam is incident via mirrors M1–M3 normal to the riblet sample’s surface and the scattered intensity pattern is observed on a screen or detected via a photodiode array in the 45° direction. The initial pulse duration is τ=109  fs. In order to expand the pulse duration, blocks of borosilicate crown glass are placed into the beam path. (b) Second setup: the laser beam is adjusted into a grating stretcher built of BG1, BG2, and M4. Distance between the two blazed gratings of 176(1) cm results in τ2=2.4  ps. The variable slit VS allows for a limitation of the effective bandwidth Δω of the laser pulse. Its aperture a is varied from 1 to 7 mm. The D-shaped mirror DM separates incoming and stretched pulses. P1–P3 are pinholes to eliminate scattering.
Fig. 4.
Fig. 4. (a) Intensity patterns of the 45° signal obtained with the first setup for pulse durations of (1) 109 fs, (2) 234 fs, (3) 370 fs, (4) 680 fs, and (5) 900 fs, respectively. (b)–(e) Photographs of the intensity patterns (b), (c) at 900 fs and (d), (e) with a continuous-wave laser (λ=532  nm). (b) The 45° signal appears smoothly. This finding is in contrast to the observable substructure of the 45° signal well-known from continuous wave-experiments shown in (d). (c), (e) In 0° direction, both intensity patterns show distinct interference features with three prominent center peaks.
Fig. 5.
Fig. 5. Intensity pattern as a function of slit aperture a and accordingly labeled from 1 to 7. Smooth intensity distribution for a=7  mm as found in Fig. 4(a). With decreasing slit aperture and consequently decreasing pulse duration and bandwidth, the interference pattern appears. The results of the detected intensity patterns for a=1  mm and a=7  mm are fitted to the sum of two Gaussian functions. On the right, the respective visibilities ν are specified.
Fig. 6.
Fig. 6. Numeric energy pattern W(Δα) for 45° (a) for a constant bandwidth of Δω=3.41×1013  rad/s (Δλ=4.8  nm) and variable pulse duration τ and frequency gradient ω/t, and (b) for a constant frequency gradient ω/t=1.49×1025  rad/s2 and variable pulse duration τ and bandwidth Δω (N=13, M=5, b=15  μm, Λ=100  μm, R=0.36  m).
Fig. 7.
Fig. 7. Plot of frequency ω and power P versus time for two next-neighboring pulses with a mutual temporal delay of 230 fs. Slope of frequency is ω/t=Δω/τ. (a) Frequency detuning Ωa for overlapping pulses. (b) Same pulse duration as in (a), while bandwidth is decreased, which results in the appearance of a stationary interference pattern.
Fig. 8.
Fig. 8. Influence of structure period Λ on threshold values of (a) pulse duration τ and (b) bandwidth Δω for a vanishing interference pattern (ν<0.1). Characteristic period Λ=100  μm of the investigated riblet structure is marked, respectively.

Tables (1)

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Table 1. Slit Apertures a, Pulse Duration τ, and Spectral Bandwidth Δωa

Equations (11)

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ωt=Δωτ1(τ0τ)2Δωτ
ν=ImaxIminImax+Imin.
E(Δα,t)=n=1Nm=1MAn(tn)exp[i(knR(ω0+12ω˙tn)tn+ϕn+ϕm)],
An(tn)=exp{2{[n12(N+1)]Λ}2wr2}·exp[2(ln2)tn2τ2],
tn(t)=t(n1)·Δt,
ωn(tn)=ω0+ω˙·tn,
ϕn(ωn)=ωnc·sin(45°+Δα)Λ·sin45°·(n1),
ϕm(ωn)=ωnc·sin(45°+Δα)bM1·(m1).
W(Δα)=|E(Δα,t)|2dt.
Ω=Δωτ·Δt=ωt·Δt.
ΩτCΔωCΔt.

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