Abstract

Under certain exposure conditions, femtosecond lasers create nanogratings in the bulk of fused silica for which the orientation is governed by the laser polarization. Such nanostructure induces stress that affects optical and chemical properties of the material. Here, we present a method based on optical retardance measurement to quantify the stress around laser affected zones. Further, we demonstrate stress dependence on the nanogratings orientation and we show that the stress within single nanogratings lamellae can locally be as high as several gigapascals.

© 2013 OSA

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  1. C. Hnatovsky, J. R. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica,” Appl. Phys. Lett.87(1), 014104–014106 (2005).
    [CrossRef]
  2. Y. Bellouard, E. Barthel, A. A. Said, M. Dugan, and P. Bado, “Scanning thermal microscopy and Raman analysis of bulk fused silica exposed to low-energy femtosecond laser pulses,” Opt. Express16(24), 19520–19534 (2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. A. Marcinkevi Ius, S. Juodkazis, M. Watanabe, M. Miwa, S. Matsuo, H. Misawa, and J. Nishii, “Femtosecond laser-assisted three-dimensional microfabrication in silica,” Opt. Lett.26(5), 277–279 (2001).
    [CrossRef] [PubMed]
  5. Y. Shimotsuma, P. G. Kazansky, J. R. Qiu, and K. Hirao, “Self-organized nanogratings in glass irradiated by ultrashort light pulses,” Phys. Rev. Lett.91(24), 247405 (2003).
    [CrossRef] [PubMed]
  6. V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, “Optically produced arrays of planar nanostructures inside fused silica,” Phys. Rev. Lett.96(5), 057404–1 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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  17. S. Kiyama, S. Matsuo, S. Hashimoto, and Y. Morihira, “Examination of etching agent and etching mechanism on femotosecond laser microfabrication of channels inside vitreous silica substrates†,” J. Phys. Chem. C113(27), 11560–11566 (2009).
    [CrossRef]

2013 (2)

2012 (1)

2011 (1)

2010 (1)

2009 (1)

S. Kiyama, S. Matsuo, S. Hashimoto, and Y. Morihira, “Examination of etching agent and etching mechanism on femotosecond laser microfabrication of channels inside vitreous silica substrates†,” J. Phys. Chem. C113(27), 11560–11566 (2009).
[CrossRef]

2008 (1)

2006 (2)

V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, “Optically produced arrays of planar nanostructures inside fused silica,” Phys. Rev. Lett.96(5), 057404–1 (2006).
[CrossRef] [PubMed]

Y. Bellouard, T. Colomb, C. Depeursinge, M. Dugan, A. A. Said, and P. Bado, “Nanoindentation and birefringence measurements on fused silica specimen exposed to low-energy femtosecond pulses,” Opt. Express14(18), 8360–8366 (2006).
[CrossRef] [PubMed]

2005 (1)

C. Hnatovsky, J. R. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica,” Appl. Phys. Lett.87(1), 014104–014106 (2005).
[CrossRef]

2003 (2)

B. Poumellec, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Femtosecond laser irradiation stress induced in pure silica,” Opt. Express11(9), 1070–1079 (2003).
[CrossRef] [PubMed]

Y. Shimotsuma, P. G. Kazansky, J. R. Qiu, and K. Hirao, “Self-organized nanogratings in glass irradiated by ultrashort light pulses,” Phys. Rev. Lett.91(24), 247405 (2003).
[CrossRef] [PubMed]

2001 (1)

1997 (1)

A. Agarwal and M. Tomozawa, “Correlation of silica glass properties with the infrared spectra,” J. Non-Cryst. Solids209(1-2), 166–174 (1997).
[CrossRef]

1996 (1)

1972 (1)

T. N. Vasudevan and R. S. Krishnan, “Dispersion of the stress-optic coefficient in glasses,” J. Phys. D Appl. Phys.5(12), 2283–2287 (1972).
[CrossRef]

1948 (1)

C. J. Tranter, “The use of the Mellin transform in finding the stress distribution in an infinite wedge,” Q. J. Mech. Appl. Math.1(1), 125–130 (1948).
[CrossRef]

Agarwal, A.

A. Agarwal and M. Tomozawa, “Correlation of silica glass properties with the infrared spectra,” J. Non-Cryst. Solids209(1-2), 166–174 (1997).
[CrossRef]

Bado, P.

Barthel, E.

Bellouard, Y.

Beresna, M.

Bhardwaj, V. R.

V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, “Optically produced arrays of planar nanostructures inside fused silica,” Phys. Rev. Lett.96(5), 057404–1 (2006).
[CrossRef] [PubMed]

C. Hnatovsky, J. R. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica,” Appl. Phys. Lett.87(1), 014104–014106 (2005).
[CrossRef]

Brisset, F.

Canning, J.

Champion, A.

Colomb, T.

Cook, K.

Corbari, C.

Corkum, P. B.

V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, “Optically produced arrays of planar nanostructures inside fused silica,” Phys. Rev. Lett.96(5), 057404–1 (2006).
[CrossRef] [PubMed]

C. Hnatovsky, J. R. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica,” Appl. Phys. Lett.87(1), 014104–014106 (2005).
[CrossRef]

Davis, K. M.

Depeursinge, C.

Dugan, M.

Franco, M.

Gecevicius, M.

Hashimoto, S.

S. Kiyama, S. Matsuo, S. Hashimoto, and Y. Morihira, “Examination of etching agent and etching mechanism on femotosecond laser microfabrication of channels inside vitreous silica substrates†,” J. Phys. Chem. C113(27), 11560–11566 (2009).
[CrossRef]

Hirao, K.

Y. Shimotsuma, P. G. Kazansky, J. R. Qiu, and K. Hirao, “Self-organized nanogratings in glass irradiated by ultrashort light pulses,” Phys. Rev. Lett.91(24), 247405 (2003).
[CrossRef] [PubMed]

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett.21(21), 1729–1731 (1996).
[CrossRef] [PubMed]

Hnatovsky, C.

V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, “Optically produced arrays of planar nanostructures inside fused silica,” Phys. Rev. Lett.96(5), 057404–1 (2006).
[CrossRef] [PubMed]

C. Hnatovsky, J. R. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica,” Appl. Phys. Lett.87(1), 014104–014106 (2005).
[CrossRef]

Juodkazis, S.

Kazansky, P. G.

Kiyama, S.

S. Kiyama, S. Matsuo, S. Hashimoto, and Y. Morihira, “Examination of etching agent and etching mechanism on femotosecond laser microfabrication of channels inside vitreous silica substrates†,” J. Phys. Chem. C113(27), 11560–11566 (2009).
[CrossRef]

Krishnan, R. S.

T. N. Vasudevan and R. S. Krishnan, “Dispersion of the stress-optic coefficient in glasses,” J. Phys. D Appl. Phys.5(12), 2283–2287 (1972).
[CrossRef]

Lancry, M.

Marcinkevi Ius, A.

Matsuo, S.

S. Kiyama, S. Matsuo, S. Hashimoto, and Y. Morihira, “Examination of etching agent and etching mechanism on femotosecond laser microfabrication of channels inside vitreous silica substrates†,” J. Phys. Chem. C113(27), 11560–11566 (2009).
[CrossRef]

A. Marcinkevi Ius, S. Juodkazis, M. Watanabe, M. Miwa, S. Matsuo, H. Misawa, and J. Nishii, “Femtosecond laser-assisted three-dimensional microfabrication in silica,” Opt. Lett.26(5), 277–279 (2001).
[CrossRef] [PubMed]

Misawa, H.

Miura, K.

Miwa, M.

Morihira, Y.

S. Kiyama, S. Matsuo, S. Hashimoto, and Y. Morihira, “Examination of etching agent and etching mechanism on femotosecond laser microfabrication of channels inside vitreous silica substrates†,” J. Phys. Chem. C113(27), 11560–11566 (2009).
[CrossRef]

Mysyrowicz, A.

Nishii, J.

Poumellec, B.

Prade, B.

Qiu, J. R.

Y. Shimotsuma, P. G. Kazansky, J. R. Qiu, and K. Hirao, “Self-organized nanogratings in glass irradiated by ultrashort light pulses,” Phys. Rev. Lett.91(24), 247405 (2003).
[CrossRef] [PubMed]

Rajeev, P. P.

V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, “Optically produced arrays of planar nanostructures inside fused silica,” Phys. Rev. Lett.96(5), 057404–1 (2006).
[CrossRef] [PubMed]

C. Hnatovsky, J. R. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica,” Appl. Phys. Lett.87(1), 014104–014106 (2005).
[CrossRef]

Rajesh, S.

Rayner, D. M.

V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, “Optically produced arrays of planar nanostructures inside fused silica,” Phys. Rev. Lett.96(5), 057404–1 (2006).
[CrossRef] [PubMed]

C. Hnatovsky, J. R. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica,” Appl. Phys. Lett.87(1), 014104–014106 (2005).
[CrossRef]

Said, A. A.

Shimotsuma, Y.

Y. Shimotsuma, P. G. Kazansky, J. R. Qiu, and K. Hirao, “Self-organized nanogratings in glass irradiated by ultrashort light pulses,” Phys. Rev. Lett.91(24), 247405 (2003).
[CrossRef] [PubMed]

Simova, E.

V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, “Optically produced arrays of planar nanostructures inside fused silica,” Phys. Rev. Lett.96(5), 057404–1 (2006).
[CrossRef] [PubMed]

C. Hnatovsky, J. R. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica,” Appl. Phys. Lett.87(1), 014104–014106 (2005).
[CrossRef]

Sudrie, L.

Sugimoto, N.

Takebe, H.

Taylor, J. R.

C. Hnatovsky, J. R. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica,” Appl. Phys. Lett.87(1), 014104–014106 (2005).
[CrossRef]

Taylor, R. S.

V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, “Optically produced arrays of planar nanostructures inside fused silica,” Phys. Rev. Lett.96(5), 057404–1 (2006).
[CrossRef] [PubMed]

Tomozawa, M.

A. Agarwal and M. Tomozawa, “Correlation of silica glass properties with the infrared spectra,” J. Non-Cryst. Solids209(1-2), 166–174 (1997).
[CrossRef]

Tranter, C. J.

C. J. Tranter, “The use of the Mellin transform in finding the stress distribution in an infinite wedge,” Q. J. Mech. Appl. Math.1(1), 125–130 (1948).
[CrossRef]

Vasudevan, T. N.

T. N. Vasudevan and R. S. Krishnan, “Dispersion of the stress-optic coefficient in glasses,” J. Phys. D Appl. Phys.5(12), 2283–2287 (1972).
[CrossRef]

Watanabe, M.

Weickman, A.

Yang, W.

Zhang, J.

Appl. Phys. Lett. (1)

C. Hnatovsky, J. R. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica,” Appl. Phys. Lett.87(1), 014104–014106 (2005).
[CrossRef]

J. Non-Cryst. Solids (1)

A. Agarwal and M. Tomozawa, “Correlation of silica glass properties with the infrared spectra,” J. Non-Cryst. Solids209(1-2), 166–174 (1997).
[CrossRef]

J. Phys. Chem. C (1)

S. Kiyama, S. Matsuo, S. Hashimoto, and Y. Morihira, “Examination of etching agent and etching mechanism on femotosecond laser microfabrication of channels inside vitreous silica substrates†,” J. Phys. Chem. C113(27), 11560–11566 (2009).
[CrossRef]

J. Phys. D Appl. Phys. (1)

T. N. Vasudevan and R. S. Krishnan, “Dispersion of the stress-optic coefficient in glasses,” J. Phys. D Appl. Phys.5(12), 2283–2287 (1972).
[CrossRef]

Opt. Express (6)

Opt. Lett. (2)

Opt. Mater. Express (2)

Phys. Rev. Lett. (2)

Y. Shimotsuma, P. G. Kazansky, J. R. Qiu, and K. Hirao, “Self-organized nanogratings in glass irradiated by ultrashort light pulses,” Phys. Rev. Lett.91(24), 247405 (2003).
[CrossRef] [PubMed]

V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, “Optically produced arrays of planar nanostructures inside fused silica,” Phys. Rev. Lett.96(5), 057404–1 (2006).
[CrossRef] [PubMed]

Q. J. Mech. Appl. Math. (1)

C. J. Tranter, “The use of the Mellin transform in finding the stress distribution in an infinite wedge,” Q. J. Mech. Appl. Math.1(1), 125–130 (1948).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Left: Transverse and top view of a single nanograting made of porous material [11] Right: Top view of three lines with different nanograting orientation according to the writing direction and different σθ.(α is the angle between the writing direction and nanogratings orientation).

Fig. 2
Fig. 2

Left: top view of the laser pattern to investigate the dependence of the stress on nanogratings orientations. The laser beam is linearly polarized and the polarization is kept the same for all writing directions. Right: close-up three-dimensional view of two segments of the laser-written pattern shown in the left figure. (LAZ) stands for laser affected zones.

Fig. 3
Fig. 3

Wedge model used for finding analytically the stress distribution in an angular section of the sun-pattern. To capture the stress resulting from the expansion of the laser-written lines, we consider homogeneous force distribution (F1, F2) distributed along edges from a to b.

Fig. 4
Fig. 4

Finite element simulation for the homogeneous case. (i.e without taking into account the nanogratings) Left: plane-strain problem definition and boundary conditions (forces are indicated with blue arrows) and right, simulated stress for identical forces applied on each line. (Here, for the sake of clarity, the polarization state is assumed to be the same for each line.)

Fig. 5
Fig. 5

Left: Measured profile between two laser written lines versus simulations to define a range of pressure, in which the maximum principal stress fits best. The measurement error bars are not shown on this graph for clarity but are shown on the right graph. Right: Comparison of analytical model, finite element model and measurement.

Fig. 6
Fig. 6

Left: Effect of the polarization on the retardance distribution around the sun pattern. In this experiment, the polarization is kept unchanged while writing the lines at 1 mm/s. Right: the same image but this time with dots to help visualizing the maximum measured retardance as a function of the angle.

Fig. 7
Fig. 7

Multi-scale approach for investigating the effect of nanogratings orientation on stress distribution. Step 1 – ‘nanoscale description’, a uniform pressure σNG (black arrows) is applied around a single lamellae (red segment) that constitutes the nanogratings for different lamellae orientation. Step 2 – ‘microscale description’, the resulting principal stress σR (blue arrows) is applied on the equivalent rectangles, representing the nanogratings. This technique is then applied to the full patterns as can be seen on Fig. 7 right.

Fig. 8
Fig. 8

Left (graph): pink, blue and black dots represent the simulated retardance and black squares the measured one. The lines connecting simulation data-points are just added to help visualizing the distribution of data point. We clearly see two maxima and two minima according to the angle. Right: schematic showing the location of the maximum measured and simulated stress along a line profile.

Fig. 9
Fig. 9

Scanning Electron Microscope images of the nanogratings according to the energy deposition. The periodicity is about 275 +/− 5 nm and the size of the features is 100 +/− 5 nm.

Equations (6)

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

σ 1 σ 2 = R T( C 1 C 2 )
σ θ = 1 2πi ci c+i p(p+1)ϕ r p2 dp σ r = 1 2πi ci c+i [ d 2 ϕ d θ 2 pϕ ] r p2 dp },
σ θ σ r =F(r){ 2b r [ sin(α)cos(θ) 2α+sin(2α) 1 π 0 G(ξ)sin{ ξlog( b r ) }dξ ] 2a r [ sin(α)cos(θ) 2α+sin(2α) 1 π 0 G(ξ)sin{ ξlog( a r ) }dξ ] },
G(ξ)= sin(αθ)cosh(α+θ)ξ+sin(α+θ)cosh(αθ)ξ ξsin(2α)+sinh(2αξ)
f a (r,θ,α,a)= 0 G(ξ)sin{ ξlog( a r ) } dξ f b (r,θ,α,b)= 0 G(ξ)sin{ ξlog( b r ) } dξ }
F( r,α )= σ θ σ r κ{ 2b r [ sin( α )cos( θ ) 2α+sin( 2α ) f b π ] 2a r [ sin( α )cos( θ ) 2α+sin( 2α ) f a π ] }

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