Abstract

Diffraction gratings are transversally inscribed in the bulk of monolithic crystalline silicon with infrared nanosecond laser pulses. Nanoscale material analyses of the modifications composing the gratings show that they rely on laser-induced stress associated with a positive refractive index change as confirmed with phase-shift interferometry. Characterizations of the optical properties of the gratings, including the diffraction angles and the efficiency of the different orders, are carried out. The refractive index change obtained from these measurements is in good agreement with the phase-shift measurements. Finally, we show that the grating diffraction efficiency depends strongly on the laser writing speed.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (2)

2017 (4)

H. Iwata, D. Kawaguchi, and H. Saka, Microscopy 66, 328 (2017).
[Crossref]

O. Tokel, A. Turnalı, G. Makey, P. Elahi, T. Çolakoğlu, E. Ergeçen, Ö. Yavuz, R. Hübner, M. Z. Borra, I. Pavlov, A. Bek, R. Turan, D. K. Kesim, S. Tozburun, S. Ilday, and F. Ö. Ilday, Nat. Photonics 11, 639 (2017).
[Crossref]

M. Chanal, V. Yu. Fedorov, M. Chambonneau, R. Clady, S. Tzortzakis, and D. Grojo, Nat. Commun. 8, 773 (2017).
[Crossref]

I. Pavlov, O. Tokel, S. Pavlova, V. Kadan, G. Makey, A. Turnali, Ö. Yavuz, and F. Ö. Ilday, Opt. Lett. 42, 3028 (2017).
[Crossref]

2016 (3)

2015 (2)

E. V. Zavedeev, V. V. Kononenko, and V. I. Konov, Laser Phys. 26, 016101 (2015).
[Crossref]

P. C. Verburg, L. A. Smillies, G. R. B. E. Römer, B. Haberl, J. E. Bradby, J. S. Williams, and A. J. Huis in ’t Veld, Appl. Phys. A 120, 683 (2015).
[Crossref]

2014 (1)

J. Zhang, M. Gecevičius, M. Beresna, and P. G. Kazansky, Phys. Rev. Lett. 112, 033901 (2014).
[Crossref]

2005 (1)

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, Nature 433, 725 (2005).
[Crossref]

1999 (1)

L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, Opt. Commun. 171, 279 (1999).
[Crossref]

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1989 (1)

1981 (1)

Bek, A.

O. Tokel, A. Turnalı, G. Makey, P. Elahi, T. Çolakoğlu, E. Ergeçen, Ö. Yavuz, R. Hübner, M. Z. Borra, I. Pavlov, A. Bek, R. Turan, D. K. Kesim, S. Tozburun, S. Ilday, and F. Ö. Ilday, Nat. Photonics 11, 639 (2017).
[Crossref]

Beresna, M.

J. Zhang, M. Gecevičius, M. Beresna, and P. G. Kazansky, Phys. Rev. Lett. 112, 033901 (2014).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, 1970), Chap. VIII.

Borra, M. Z.

O. Tokel, A. Turnalı, G. Makey, P. Elahi, T. Çolakoğlu, E. Ergeçen, Ö. Yavuz, R. Hübner, M. Z. Borra, I. Pavlov, A. Bek, R. Turan, D. K. Kesim, S. Tozburun, S. Ilday, and F. Ö. Ilday, Nat. Photonics 11, 639 (2017).
[Crossref]

Bradby, J. E.

P. C. Verburg, L. A. Smillies, G. R. B. E. Römer, B. Haberl, J. E. Bradby, J. S. Williams, and A. J. Huis in ’t Veld, Appl. Phys. A 120, 683 (2015).
[Crossref]

Brisset, F.

Cao, J.

Chambonneau, M.

Chanal, M.

Clady, R.

M. Chanal, V. Yu. Fedorov, M. Chambonneau, R. Clady, S. Tzortzakis, and D. Grojo, Nat. Commun. 8, 773 (2017).
[Crossref]

Cohen, O.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, Nature 433, 725 (2005).
[Crossref]

Çolakoglu, T.

O. Tokel, A. Turnalı, G. Makey, P. Elahi, T. Çolakoğlu, E. Ergeçen, Ö. Yavuz, R. Hübner, M. Z. Borra, I. Pavlov, A. Bek, R. Turan, D. K. Kesim, S. Tozburun, S. Ilday, and F. Ö. Ilday, Nat. Photonics 11, 639 (2017).
[Crossref]

Davis, K. M.

Elahi, P.

O. Tokel, A. Turnalı, G. Makey, P. Elahi, T. Çolakoğlu, E. Ergeçen, Ö. Yavuz, R. Hübner, M. Z. Borra, I. Pavlov, A. Bek, R. Turan, D. K. Kesim, S. Tozburun, S. Ilday, and F. Ö. Ilday, Nat. Photonics 11, 639 (2017).
[Crossref]

Ergeçen, E.

O. Tokel, A. Turnalı, G. Makey, P. Elahi, T. Çolakoğlu, E. Ergeçen, Ö. Yavuz, R. Hübner, M. Z. Borra, I. Pavlov, A. Bek, R. Turan, D. K. Kesim, S. Tozburun, S. Ilday, and F. Ö. Ilday, Nat. Photonics 11, 639 (2017).
[Crossref]

Fang, A.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, Nature 433, 725 (2005).
[Crossref]

Fedorov, V. Yu.

M. Chanal, V. Yu. Fedorov, M. Chambonneau, R. Clady, S. Tzortzakis, and D. Grojo, Nat. Commun. 8, 773 (2017).
[Crossref]

Franco, M.

L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, Opt. Commun. 171, 279 (1999).
[Crossref]

Gaylord, T.

Gecevicius, M.

J. Zhang, M. Gecevičius, M. Beresna, and P. G. Kazansky, Phys. Rev. Lett. 112, 033901 (2014).
[Crossref]

Glenn, W. H.

Goodman, J. W.

J. W. Goodman, An Introduction to Fourier Optics (McGraw-Hill, 1968).

Grojo, D.

Haberl, B.

P. C. Verburg, L. A. Smillies, G. R. B. E. Römer, B. Haberl, J. E. Bradby, J. S. Williams, and A. J. Huis in ’t Veld, Appl. Phys. A 120, 683 (2015).
[Crossref]

Hak, D.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, Nature 433, 725 (2005).
[Crossref]

Helbert, A.-L.

Hirao, K.

Hübner, R.

O. Tokel, A. Turnalı, G. Makey, P. Elahi, T. Çolakoğlu, E. Ergeçen, Ö. Yavuz, R. Hübner, M. Z. Borra, I. Pavlov, A. Bek, R. Turan, D. K. Kesim, S. Tozburun, S. Ilday, and F. Ö. Ilday, Nat. Photonics 11, 639 (2017).
[Crossref]

Huis in ’t Veld, A. J.

P. C. Verburg, L. A. Smillies, G. R. B. E. Römer, B. Haberl, J. E. Bradby, J. S. Williams, and A. J. Huis in ’t Veld, Appl. Phys. A 120, 683 (2015).
[Crossref]

Ilday, F. Ö.

O. Tokel, A. Turnalı, G. Makey, P. Elahi, T. Çolakoğlu, E. Ergeçen, Ö. Yavuz, R. Hübner, M. Z. Borra, I. Pavlov, A. Bek, R. Turan, D. K. Kesim, S. Tozburun, S. Ilday, and F. Ö. Ilday, Nat. Photonics 11, 639 (2017).
[Crossref]

I. Pavlov, O. Tokel, S. Pavlova, V. Kadan, G. Makey, A. Turnali, Ö. Yavuz, and F. Ö. Ilday, Opt. Lett. 42, 3028 (2017).
[Crossref]

Ilday, S.

O. Tokel, A. Turnalı, G. Makey, P. Elahi, T. Çolakoğlu, E. Ergeçen, Ö. Yavuz, R. Hübner, M. Z. Borra, I. Pavlov, A. Bek, R. Turan, D. K. Kesim, S. Tozburun, S. Ilday, and F. Ö. Ilday, Nat. Photonics 11, 639 (2017).
[Crossref]

Iwata, H.

H. Iwata, D. Kawaguchi, and H. Saka, Microscopy 67, 30 (2018).
[Crossref]

H. Iwata, D. Kawaguchi, and H. Saka, Microscopy 66, 328 (2017).
[Crossref]

Jones, R.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, Nature 433, 725 (2005).
[Crossref]

Kadan, V.

Kämmer, H.

Kawaguchi, D.

H. Iwata, D. Kawaguchi, and H. Saka, Microscopy 67, 30 (2018).
[Crossref]

H. Iwata, D. Kawaguchi, and H. Saka, Microscopy 66, 328 (2017).
[Crossref]

Kazansky, P. G.

J. Zhang, M. Gecevičius, M. Beresna, and P. G. Kazansky, Phys. Rev. Lett. 112, 033901 (2014).
[Crossref]

Kesim, D. K.

O. Tokel, A. Turnalı, G. Makey, P. Elahi, T. Çolakoğlu, E. Ergeçen, Ö. Yavuz, R. Hübner, M. Z. Borra, I. Pavlov, A. Bek, R. Turan, D. K. Kesim, S. Tozburun, S. Ilday, and F. Ö. Ilday, Nat. Photonics 11, 639 (2017).
[Crossref]

Kononenko, V. V.

E. V. Zavedeev, V. V. Kononenko, and V. I. Konov, Laser Phys. 26, 016101 (2015).
[Crossref]

Konov, V. I.

E. V. Zavedeev, V. V. Kononenko, and V. I. Konov, Laser Phys. 26, 016101 (2015).
[Crossref]

Lammers, K. A.

Lancry, M.

Li, Q.

Liu, A.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, Nature 433, 725 (2005).
[Crossref]

Makey, G.

O. Tokel, A. Turnalı, G. Makey, P. Elahi, T. Çolakoğlu, E. Ergeçen, Ö. Yavuz, R. Hübner, M. Z. Borra, I. Pavlov, A. Bek, R. Turan, D. K. Kesim, S. Tozburun, S. Ilday, and F. Ö. Ilday, Nat. Photonics 11, 639 (2017).
[Crossref]

I. Pavlov, O. Tokel, S. Pavlova, V. Kadan, G. Makey, A. Turnali, Ö. Yavuz, and F. Ö. Ilday, Opt. Lett. 42, 3028 (2017).
[Crossref]

Matthäus, G.

Meltz, G.

Miura, K.

Moharam, M.

Morey, W. W.

Mysyrowicz, A.

L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, Opt. Commun. 171, 279 (1999).
[Crossref]

Nolte, S.

Paniccia, M.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, Nature 433, 725 (2005).
[Crossref]

Pavlov, I.

O. Tokel, A. Turnalı, G. Makey, P. Elahi, T. Çolakoğlu, E. Ergeçen, Ö. Yavuz, R. Hübner, M. Z. Borra, I. Pavlov, A. Bek, R. Turan, D. K. Kesim, S. Tozburun, S. Ilday, and F. Ö. Ilday, Nat. Photonics 11, 639 (2017).
[Crossref]

I. Pavlov, O. Tokel, S. Pavlova, V. Kadan, G. Makey, A. Turnali, Ö. Yavuz, and F. Ö. Ilday, Opt. Lett. 42, 3028 (2017).
[Crossref]

Pavlova, S.

Poumellec, B.

Prade, B.

L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, Opt. Commun. 171, 279 (1999).
[Crossref]

Römer, G. R. B. E.

P. C. Verburg, L. A. Smillies, G. R. B. E. Römer, B. Haberl, J. E. Bradby, J. S. Williams, and A. J. Huis in ’t Veld, Appl. Phys. A 120, 683 (2015).
[Crossref]

Rong, H.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, Nature 433, 725 (2005).
[Crossref]

Saka, H.

H. Iwata, D. Kawaguchi, and H. Saka, Microscopy 67, 30 (2018).
[Crossref]

H. Iwata, D. Kawaguchi, and H. Saka, Microscopy 66, 328 (2017).
[Crossref]

Sanner, N.

Smillies, L. A.

P. C. Verburg, L. A. Smillies, G. R. B. E. Römer, B. Haberl, J. E. Bradby, J. S. Williams, and A. J. Huis in ’t Veld, Appl. Phys. A 120, 683 (2015).
[Crossref]

Sudrie, L.

L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, Opt. Commun. 171, 279 (1999).
[Crossref]

Sugimoto, N.

Tokel, O.

O. Tokel, A. Turnalı, G. Makey, P. Elahi, T. Çolakoğlu, E. Ergeçen, Ö. Yavuz, R. Hübner, M. Z. Borra, I. Pavlov, A. Bek, R. Turan, D. K. Kesim, S. Tozburun, S. Ilday, and F. Ö. Ilday, Nat. Photonics 11, 639 (2017).
[Crossref]

I. Pavlov, O. Tokel, S. Pavlova, V. Kadan, G. Makey, A. Turnali, Ö. Yavuz, and F. Ö. Ilday, Opt. Lett. 42, 3028 (2017).
[Crossref]

Tozburun, S.

O. Tokel, A. Turnalı, G. Makey, P. Elahi, T. Çolakoğlu, E. Ergeçen, Ö. Yavuz, R. Hübner, M. Z. Borra, I. Pavlov, A. Bek, R. Turan, D. K. Kesim, S. Tozburun, S. Ilday, and F. Ö. Ilday, Nat. Photonics 11, 639 (2017).
[Crossref]

Turan, R.

O. Tokel, A. Turnalı, G. Makey, P. Elahi, T. Çolakoğlu, E. Ergeçen, Ö. Yavuz, R. Hübner, M. Z. Borra, I. Pavlov, A. Bek, R. Turan, D. K. Kesim, S. Tozburun, S. Ilday, and F. Ö. Ilday, Nat. Photonics 11, 639 (2017).
[Crossref]

Turnali, A.

O. Tokel, A. Turnalı, G. Makey, P. Elahi, T. Çolakoğlu, E. Ergeçen, Ö. Yavuz, R. Hübner, M. Z. Borra, I. Pavlov, A. Bek, R. Turan, D. K. Kesim, S. Tozburun, S. Ilday, and F. Ö. Ilday, Nat. Photonics 11, 639 (2017).
[Crossref]

I. Pavlov, O. Tokel, S. Pavlova, V. Kadan, G. Makey, A. Turnali, Ö. Yavuz, and F. Ö. Ilday, Opt. Lett. 42, 3028 (2017).
[Crossref]

Tzortzakis, S.

M. Chanal, V. Yu. Fedorov, M. Chambonneau, R. Clady, S. Tzortzakis, and D. Grojo, Nat. Commun. 8, 773 (2017).
[Crossref]

Verburg, P. C.

P. C. Verburg, L. A. Smillies, G. R. B. E. Römer, B. Haberl, J. E. Bradby, J. S. Williams, and A. J. Huis in ’t Veld, Appl. Phys. A 120, 683 (2015).
[Crossref]

Vetter, C.

Watanabe, W.

Williams, J. S.

P. C. Verburg, L. A. Smillies, G. R. B. E. Römer, B. Haberl, J. E. Bradby, J. S. Williams, and A. J. Huis in ’t Veld, Appl. Phys. A 120, 683 (2015).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, 1970), Chap. VIII.

Yavuz, Ö.

O. Tokel, A. Turnalı, G. Makey, P. Elahi, T. Çolakoğlu, E. Ergeçen, Ö. Yavuz, R. Hübner, M. Z. Borra, I. Pavlov, A. Bek, R. Turan, D. K. Kesim, S. Tozburun, S. Ilday, and F. Ö. Ilday, Nat. Photonics 11, 639 (2017).
[Crossref]

I. Pavlov, O. Tokel, S. Pavlova, V. Kadan, G. Makey, A. Turnali, Ö. Yavuz, and F. Ö. Ilday, Opt. Lett. 42, 3028 (2017).
[Crossref]

Zavedeev, E. V.

E. V. Zavedeev, V. V. Kononenko, and V. I. Konov, Laser Phys. 26, 016101 (2015).
[Crossref]

Zhang, J.

J. Zhang, M. Gecevičius, M. Beresna, and P. G. Kazansky, Phys. Rev. Lett. 112, 033901 (2014).
[Crossref]

Appl. Opt. (1)

Appl. Phys. A (1)

P. C. Verburg, L. A. Smillies, G. R. B. E. Römer, B. Haberl, J. E. Bradby, J. S. Williams, and A. J. Huis in ’t Veld, Appl. Phys. A 120, 683 (2015).
[Crossref]

J. Opt. Soc. Am. (1)

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

Laser Phys. (1)

E. V. Zavedeev, V. V. Kononenko, and V. I. Konov, Laser Phys. 26, 016101 (2015).
[Crossref]

Microscopy (2)

H. Iwata, D. Kawaguchi, and H. Saka, Microscopy 66, 328 (2017).
[Crossref]

H. Iwata, D. Kawaguchi, and H. Saka, Microscopy 67, 30 (2018).
[Crossref]

Nat. Commun. (1)

M. Chanal, V. Yu. Fedorov, M. Chambonneau, R. Clady, S. Tzortzakis, and D. Grojo, Nat. Commun. 8, 773 (2017).
[Crossref]

Nat. Photonics (1)

O. Tokel, A. Turnalı, G. Makey, P. Elahi, T. Çolakoğlu, E. Ergeçen, Ö. Yavuz, R. Hübner, M. Z. Borra, I. Pavlov, A. Bek, R. Turan, D. K. Kesim, S. Tozburun, S. Ilday, and F. Ö. Ilday, Nat. Photonics 11, 639 (2017).
[Crossref]

Nature (1)

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, Nature 433, 725 (2005).
[Crossref]

Opt. Commun. (1)

L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, Opt. Commun. 171, 279 (1999).
[Crossref]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. Lett. (1)

J. Zhang, M. Gecevičius, M. Beresna, and P. G. Kazansky, Phys. Rev. Lett. 112, 033901 (2014).
[Crossref]

Other (2)

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, 1970), Chap. VIII.

J. W. Goodman, An Introduction to Fourier Optics (McGraw-Hill, 1968).

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Figures (5)

Fig. 1.
Fig. 1. Schematic description of the experimental arrangement. The red and pink beams correspond to the one employed for nanosecond writing and for analyzing the optical properties of the inscribed gratings, respectively. (a) Diffraction patterns recorded at the indicated relative z positions of the InGaAs array. (b) NIC micrograph of the cross section of a grating. (c) TEM image, including the material (1) modified and (2) unmodified by the laser, as well as (3) a cleaving-induced crack and electron diffraction image taken in (1).
Fig. 2.
Fig. 2. Interference traces obtained on the same iso-phase curve in a reference point unmodified by the nanosecond laser beam during the grating inscription (in blue) and one in the center of a line composing the grating (in red). The inset is a magnification at the center of the traces.
Fig. 3.
Fig. 3. Comparison between the theoretical values (circles) of the angle of diffraction for the different orders according to Eq. (1) and experimental measurements (squares) for gratings of period Λ = 100 (red) and 50 μm (blue).
Fig. 4.
Fig. 4. (a) Diffraction patterns normalized to the 0th order obtained on gratings with indicated periods Λ for an incident polarization indicated by the vector E . The orders of diffraction are indicated in green. The vector k shows the direction of propagation. The spatial scale applies to all images. (b) Diffraction efficiencies for a grating of period Λ = 50 μm, at indicated polarizations. 0° and 90° stand for a polarization parallel and perpendicular to the lines, respectively. The circles are measurements, and the empty red squares are calculations at 90° according to Ref. [18].
Fig. 5.
Fig. 5. (a) NIC micrograph of a cross section of one line composing a grating of period Λ = 100 μm written at 0.5 mm/s. (b) Diffraction pattern of the corresponding grating. The vector k shows the direction of propagation.

Equations (1)

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θ air = arcsin ( m λ / Λ ) .

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