Abstract

We propose a comprehensive analysis of the effects that spherical aberration may have on the process of ultrafast laser photowriting in bulk transparent materials and discuss the consequences for the generated refractive index changes. Practical aspects for a longitudinal photowriting configuration are emphasized. Laser-induced index variation in BK7 optical glass and fused silica (a-SiO2) affected by spherical aberration are characterized experimentally using phase-contrast optical microscopy. Experimental data are matched by analytical equations describing light propagation through dielectric interfaces. Corrective solutions are proposed with a particular focus on the spatial resolution achievable and on the conditions to obtain homogeneously photo-induced waveguides in a longitudinal writing configuration.

© 2007 Optical Society of America

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References

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  1. B. N. Chichkov, C. Momma, S. Nolte, F. von Albenstein and A. Tünnermann, "Femtosecond, picosecond and nanosecond laser ablation of solids," Appl. Phys. A 63, 109 (1996).
  2. S. Valette, R. Le Harzic, N. Huot, E. Audouard and R. Fortunier, "2-D calculations of the thermal effects due to femtosecond laser-metal interaction," Appl. Surf. Sci. 247, 238-242 (2005).
    [CrossRef]
  3. K Miura, J. Qiu, H. Inouye, T. Mitsuyu and K. Hirao, "Photowritten optical waveguides in various glasses with ultrashort pulse laser," Appl. Phys. Lett. 71, 3329-3331 (1997).
    [CrossRef]
  4. D. Homoelle, S. Wielandy, A. L. Gaeta, N. F. Borrelli and C. Smith, "Infrared photosensitivity in silica glasses exposed to femtosecond laser pulses," Opt. Lett. 24, 1311-1313 (1999).
    [CrossRef]
  5. C. B. Schaffer, A. Brodeur, J. F. Garcia and E. Mazur, "Micromachining bulk glass by use of femtosecond laser pulses with nanojoule energy," Opt. Lett. 23, 93-95 (2001).
    [CrossRef]
  6. A. Mermillod-Blondin, I. M. Burakov, R. Stoian, A. Rosenfeld, E. Audouard, N. M. Bulgakova and I. V. Hertel, "Direct observation of femtosecond laser induced modifications in the bulk of fused silica by phase contrast microscopy," J. Laser Micro/Nanoeng. 1, 155-160 (2006).
    [CrossRef]
  7. S. Juodkasis, S. Matsuo, H. Misawa, V. Mizeikis, A. Marcinkevicius, H. B. Sun, Y. Tokuda, M. Takahashi, T. Yoko and J. Nishii, "Application of femtosecond laser pulses for microfabrication of transparent media," Appl. Surf. Sci. 197, 705-709 (2002).
    [CrossRef]
  8. K. Minoshima, A.M. Kowalevicz, I. Hartl, E.P. Ippen and J.G. Fujimoto, "Photonic device fabrication in glass by use of nonlinear materials processing with a femtosecond laser oscillator," Opt Lett. 26, 1516-1518 (2001).
    [CrossRef]
  9. M. H. Hong, B. Luk’Yanchuk, S. M. Huang, T. S. Ong, L. H. Van, andT. C. Chong, "Femtosecond laser application for high capacity optical data storage," Appl. Phys. A 79, 791-794 (2004).
  10. J. P. McDonald, V. R. Mistry, K. E. Ray, and S. M. Yalisove, "Femtosecond pulsed laser direct write production of nano- and microfluidic channels," Appl. Phys. Lett. 88, 183113-183115 (2006).
    [CrossRef]
  11. N. Takeshima, Y. Narita, S. Tanaka, Y. Kuroiwa and K. Hirao, "Fabrication of high-efficiency diffraction gratings in glass," Opt. Lett. 30, 352-354 (2005).
    [CrossRef] [PubMed]
  12. H. Zhang, S. M. Eaton, J. Li, A. H. Nejadmalayeri and P. R. Herman, "Type II high-strength Bragg grating waveguides photowritten with ultrashort laser pulses," Opt. Express 15, 4182-4191 (2007).
    [CrossRef] [PubMed]
  13. A. Marcinkevicius, V. Mizeikis, S. Juodkasis, S. Matsuo and H. Misawa, "Effects of refractive index-mismatch on laser microfabrication in silica glass," Appl. Phys. B 76, 257-260 (2003).
  14. D. Liu, Y. Li, R. An, Y. Dou, H. Yang and Q. Gong, "Influence of focusing depth on the microfabrication of waveguides inside silica glass by femtosecond laser direct writing," Appl. Phys. A 84, 257-260 (2006).
  15. C. Hnatovsky, R. S. Taylor, E. Simova, V. R. Bhardwaj, D. M. Rayner and P. B. Corkum, "High-resolution study of photoinduced modification in fused silica produced by a tightly focused femtosecond laser beam in the presence of aberrations," J. Appl. Phys. 98, 013517 1-5 (2005).
    [CrossRef]
  16. Q. Sun, H. Jiang, Y. Liu, Y. Zhou, H. Yang and Q. Gong, "Effect of spherical aberrations on the propagation of a tightly focused femtosecond laser pulse inside fused silica," Pure Appl. Opt. 7, 655-659 (2005).
    [CrossRef]
  17. P. Török, P. Vagra and G. Németh, "Analytical solution of the diffraction integrals and interpretation of wavefront distortion when light is focused through a planar interface between materials of mismatched refractive indices," J. Opt. Soc. Am. A 12, 2660-2671 (1995).
    [CrossRef]
  18. J. S. H. Wiersma, T. D. Visser and P. Török, "Annular focusing through a dielectric interface: scanning and confining the intensity," Pure Appl. Opt. 7, 1237-1248 (1998).
    [CrossRef]
  19. M. J. Booth and T. Wilson, "Refractive-index-mismatch induced aberrations in single-photon and two-phton microscopy and the used of aberration correction," J. Biomed. Opt. 6, 266-272 (2001).
    [CrossRef] [PubMed]
  20. M. J. Booth, M. A. A. Neil and T. Wilson, "Aberration correction for confocal imaging in refractive-index-mismatched-media," J. Microsc. 192, 90-98 (1998).
    [CrossRef]
  21. M. J. Booth, M. Schwertner, T. Wilson, M. Nakano, Y. Kawata, M. Nakabayashi and S. Miyata, "Predictive aberration correction for multilayer optical data storage," Appl. Phys. Lett. 88, 031109-031111 (2006).
    [CrossRef]
  22. M. A. A. Neil, R. Juskaitis, M. J. Booth, T. Wilson, T. Tanaka and S. Kawata, "Active aberration correction for the writing of three-dimensional optical memory device," Appl. Opt. 41, 1374-1379 (2002).
    [CrossRef] [PubMed]
  23. Z. Wu, H. Jiang, H. Yang and Q. Gong, "The refocusing behaviour of a focused femtosecond laser pulse in fused silica," Pure Appl. Opt. 5, 102-107 (2003).
    [CrossRef]
  24. A. Maréchal, Imagerie géométrique, aberrations, (Edition de la revue d’optique théorique et instrumentale, Paris 1952).
  25. M. Born and E. Wolf, Principle of Optics, 4th ed. (Pergamon, Oxford 1970).
  26. I. M. Burakov, N. M. Bulgakova, R. Stoian, A. Mermillod-Blondin, E. Audouard, R. Rosenfeld, A. Husakou and I. V. Hertel, "Spatial distribution of refractive index variations induced in bulk fused silica by single ultrashort and short laser pulses," J. Appl. Phys. 101, 043506 1-7 (2007).
    [CrossRef]
  27. L. Sudrie, M. Franco, B. Prade and A. Mysyrowicz, "Study of damage in fused silica induced by ultra-short IR laser pulses," Opt. Commun. 191, 333-339 (2001).
    [CrossRef]
  28. N. Sanner, N. Huot, E. Audouard, C. Larat, P. Laporte and J. P. Huignard, "100 kHz diffraction-limited femtosecond laser machining," Appl. Phys. B 80, 27-30 (2005).
  29. N. Sanner, N. Huot, E. Audouard, C. Larat, B. Loiseau and J. P. Huignard, "Programmable spatial beam shaping of a 100 kHz amplified femtosecond laser," Opt. Lett. 30, 1479-1481 (2005).
    [CrossRef] [PubMed]
  30. N. Sanner, N. Huot, E. Audouard, C. Larat and J. P. Huignard, "Direct ultrafast microstructuring of materials using programmable beam shaping," Opt. Laser Eng. 45, 737-741 (2007).
    [CrossRef]

2007

H. Zhang, S. M. Eaton, J. Li, A. H. Nejadmalayeri and P. R. Herman, "Type II high-strength Bragg grating waveguides photowritten with ultrashort laser pulses," Opt. Express 15, 4182-4191 (2007).
[CrossRef] [PubMed]

N. Sanner, N. Huot, E. Audouard, C. Larat and J. P. Huignard, "Direct ultrafast microstructuring of materials using programmable beam shaping," Opt. Laser Eng. 45, 737-741 (2007).
[CrossRef]

2006

M. J. Booth, M. Schwertner, T. Wilson, M. Nakano, Y. Kawata, M. Nakabayashi and S. Miyata, "Predictive aberration correction for multilayer optical data storage," Appl. Phys. Lett. 88, 031109-031111 (2006).
[CrossRef]

J. P. McDonald, V. R. Mistry, K. E. Ray, and S. M. Yalisove, "Femtosecond pulsed laser direct write production of nano- and microfluidic channels," Appl. Phys. Lett. 88, 183113-183115 (2006).
[CrossRef]

D. Liu, Y. Li, R. An, Y. Dou, H. Yang and Q. Gong, "Influence of focusing depth on the microfabrication of waveguides inside silica glass by femtosecond laser direct writing," Appl. Phys. A 84, 257-260 (2006).

2005

Q. Sun, H. Jiang, Y. Liu, Y. Zhou, H. Yang and Q. Gong, "Effect of spherical aberrations on the propagation of a tightly focused femtosecond laser pulse inside fused silica," Pure Appl. Opt. 7, 655-659 (2005).
[CrossRef]

N. Takeshima, Y. Narita, S. Tanaka, Y. Kuroiwa and K. Hirao, "Fabrication of high-efficiency diffraction gratings in glass," Opt. Lett. 30, 352-354 (2005).
[CrossRef] [PubMed]

S. Valette, R. Le Harzic, N. Huot, E. Audouard and R. Fortunier, "2-D calculations of the thermal effects due to femtosecond laser-metal interaction," Appl. Surf. Sci. 247, 238-242 (2005).
[CrossRef]

N. Sanner, N. Huot, E. Audouard, C. Larat, P. Laporte and J. P. Huignard, "100 kHz diffraction-limited femtosecond laser machining," Appl. Phys. B 80, 27-30 (2005).

N. Sanner, N. Huot, E. Audouard, C. Larat, B. Loiseau and J. P. Huignard, "Programmable spatial beam shaping of a 100 kHz amplified femtosecond laser," Opt. Lett. 30, 1479-1481 (2005).
[CrossRef] [PubMed]

2004

M. H. Hong, B. Luk’Yanchuk, S. M. Huang, T. S. Ong, L. H. Van, andT. C. Chong, "Femtosecond laser application for high capacity optical data storage," Appl. Phys. A 79, 791-794 (2004).

2003

A. Marcinkevicius, V. Mizeikis, S. Juodkasis, S. Matsuo and H. Misawa, "Effects of refractive index-mismatch on laser microfabrication in silica glass," Appl. Phys. B 76, 257-260 (2003).

Z. Wu, H. Jiang, H. Yang and Q. Gong, "The refocusing behaviour of a focused femtosecond laser pulse in fused silica," Pure Appl. Opt. 5, 102-107 (2003).
[CrossRef]

2002

M. A. A. Neil, R. Juskaitis, M. J. Booth, T. Wilson, T. Tanaka and S. Kawata, "Active aberration correction for the writing of three-dimensional optical memory device," Appl. Opt. 41, 1374-1379 (2002).
[CrossRef] [PubMed]

S. Juodkasis, S. Matsuo, H. Misawa, V. Mizeikis, A. Marcinkevicius, H. B. Sun, Y. Tokuda, M. Takahashi, T. Yoko and J. Nishii, "Application of femtosecond laser pulses for microfabrication of transparent media," Appl. Surf. Sci. 197, 705-709 (2002).
[CrossRef]

2001

K. Minoshima, A.M. Kowalevicz, I. Hartl, E.P. Ippen and J.G. Fujimoto, "Photonic device fabrication in glass by use of nonlinear materials processing with a femtosecond laser oscillator," Opt Lett. 26, 1516-1518 (2001).
[CrossRef]

C. B. Schaffer, A. Brodeur, J. F. Garcia and E. Mazur, "Micromachining bulk glass by use of femtosecond laser pulses with nanojoule energy," Opt. Lett. 23, 93-95 (2001).
[CrossRef]

M. J. Booth and T. Wilson, "Refractive-index-mismatch induced aberrations in single-photon and two-phton microscopy and the used of aberration correction," J. Biomed. Opt. 6, 266-272 (2001).
[CrossRef] [PubMed]

L. Sudrie, M. Franco, B. Prade and A. Mysyrowicz, "Study of damage in fused silica induced by ultra-short IR laser pulses," Opt. Commun. 191, 333-339 (2001).
[CrossRef]

1999

1998

M. J. Booth, M. A. A. Neil and T. Wilson, "Aberration correction for confocal imaging in refractive-index-mismatched-media," J. Microsc. 192, 90-98 (1998).
[CrossRef]

J. S. H. Wiersma, T. D. Visser and P. Török, "Annular focusing through a dielectric interface: scanning and confining the intensity," Pure Appl. Opt. 7, 1237-1248 (1998).
[CrossRef]

1997

K Miura, J. Qiu, H. Inouye, T. Mitsuyu and K. Hirao, "Photowritten optical waveguides in various glasses with ultrashort pulse laser," Appl. Phys. Lett. 71, 3329-3331 (1997).
[CrossRef]

1996

B. N. Chichkov, C. Momma, S. Nolte, F. von Albenstein and A. Tünnermann, "Femtosecond, picosecond and nanosecond laser ablation of solids," Appl. Phys. A 63, 109 (1996).

1995

Appl. Opt.

Appl. Phys. A

B. N. Chichkov, C. Momma, S. Nolte, F. von Albenstein and A. Tünnermann, "Femtosecond, picosecond and nanosecond laser ablation of solids," Appl. Phys. A 63, 109 (1996).

M. H. Hong, B. Luk’Yanchuk, S. M. Huang, T. S. Ong, L. H. Van, andT. C. Chong, "Femtosecond laser application for high capacity optical data storage," Appl. Phys. A 79, 791-794 (2004).

D. Liu, Y. Li, R. An, Y. Dou, H. Yang and Q. Gong, "Influence of focusing depth on the microfabrication of waveguides inside silica glass by femtosecond laser direct writing," Appl. Phys. A 84, 257-260 (2006).

Appl. Phys. B

A. Marcinkevicius, V. Mizeikis, S. Juodkasis, S. Matsuo and H. Misawa, "Effects of refractive index-mismatch on laser microfabrication in silica glass," Appl. Phys. B 76, 257-260 (2003).

N. Sanner, N. Huot, E. Audouard, C. Larat, P. Laporte and J. P. Huignard, "100 kHz diffraction-limited femtosecond laser machining," Appl. Phys. B 80, 27-30 (2005).

Appl. Phys. Lett.

M. J. Booth, M. Schwertner, T. Wilson, M. Nakano, Y. Kawata, M. Nakabayashi and S. Miyata, "Predictive aberration correction for multilayer optical data storage," Appl. Phys. Lett. 88, 031109-031111 (2006).
[CrossRef]

J. P. McDonald, V. R. Mistry, K. E. Ray, and S. M. Yalisove, "Femtosecond pulsed laser direct write production of nano- and microfluidic channels," Appl. Phys. Lett. 88, 183113-183115 (2006).
[CrossRef]

K Miura, J. Qiu, H. Inouye, T. Mitsuyu and K. Hirao, "Photowritten optical waveguides in various glasses with ultrashort pulse laser," Appl. Phys. Lett. 71, 3329-3331 (1997).
[CrossRef]

Appl. Surf. Sci.

S. Valette, R. Le Harzic, N. Huot, E. Audouard and R. Fortunier, "2-D calculations of the thermal effects due to femtosecond laser-metal interaction," Appl. Surf. Sci. 247, 238-242 (2005).
[CrossRef]

S. Juodkasis, S. Matsuo, H. Misawa, V. Mizeikis, A. Marcinkevicius, H. B. Sun, Y. Tokuda, M. Takahashi, T. Yoko and J. Nishii, "Application of femtosecond laser pulses for microfabrication of transparent media," Appl. Surf. Sci. 197, 705-709 (2002).
[CrossRef]

J. Biomed. Opt.

M. J. Booth and T. Wilson, "Refractive-index-mismatch induced aberrations in single-photon and two-phton microscopy and the used of aberration correction," J. Biomed. Opt. 6, 266-272 (2001).
[CrossRef] [PubMed]

J. Microsc.

M. J. Booth, M. A. A. Neil and T. Wilson, "Aberration correction for confocal imaging in refractive-index-mismatched-media," J. Microsc. 192, 90-98 (1998).
[CrossRef]

J. Opt. Soc. Am. A

Opt Lett.

K. Minoshima, A.M. Kowalevicz, I. Hartl, E.P. Ippen and J.G. Fujimoto, "Photonic device fabrication in glass by use of nonlinear materials processing with a femtosecond laser oscillator," Opt Lett. 26, 1516-1518 (2001).
[CrossRef]

Opt. Commun.

L. Sudrie, M. Franco, B. Prade and A. Mysyrowicz, "Study of damage in fused silica induced by ultra-short IR laser pulses," Opt. Commun. 191, 333-339 (2001).
[CrossRef]

Opt. Express

Opt. Laser Eng.

N. Sanner, N. Huot, E. Audouard, C. Larat and J. P. Huignard, "Direct ultrafast microstructuring of materials using programmable beam shaping," Opt. Laser Eng. 45, 737-741 (2007).
[CrossRef]

Opt. Lett.

Pure Appl. Opt.

J. S. H. Wiersma, T. D. Visser and P. Török, "Annular focusing through a dielectric interface: scanning and confining the intensity," Pure Appl. Opt. 7, 1237-1248 (1998).
[CrossRef]

Q. Sun, H. Jiang, Y. Liu, Y. Zhou, H. Yang and Q. Gong, "Effect of spherical aberrations on the propagation of a tightly focused femtosecond laser pulse inside fused silica," Pure Appl. Opt. 7, 655-659 (2005).
[CrossRef]

Z. Wu, H. Jiang, H. Yang and Q. Gong, "The refocusing behaviour of a focused femtosecond laser pulse in fused silica," Pure Appl. Opt. 5, 102-107 (2003).
[CrossRef]

Other

A. Maréchal, Imagerie géométrique, aberrations, (Edition de la revue d’optique théorique et instrumentale, Paris 1952).

M. Born and E. Wolf, Principle of Optics, 4th ed. (Pergamon, Oxford 1970).

I. M. Burakov, N. M. Bulgakova, R. Stoian, A. Mermillod-Blondin, E. Audouard, R. Rosenfeld, A. Husakou and I. V. Hertel, "Spatial distribution of refractive index variations induced in bulk fused silica by single ultrashort and short laser pulses," J. Appl. Phys. 101, 043506 1-7 (2007).
[CrossRef]

C. Hnatovsky, R. S. Taylor, E. Simova, V. R. Bhardwaj, D. M. Rayner and P. B. Corkum, "High-resolution study of photoinduced modification in fused silica produced by a tightly focused femtosecond laser beam in the presence of aberrations," J. Appl. Phys. 98, 013517 1-5 (2005).
[CrossRef]

A. Mermillod-Blondin, I. M. Burakov, R. Stoian, A. Rosenfeld, E. Audouard, N. M. Bulgakova and I. V. Hertel, "Direct observation of femtosecond laser induced modifications in the bulk of fused silica by phase contrast microscopy," J. Laser Micro/Nanoeng. 1, 155-160 (2006).
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

Focusing geometry in an overcorrected case (n2>n1). A: focal point in a matched medium whose position defines the focusing depth x = S A ¯ ; A ' P : : paraxial focus; AM: marginal focus; l: longitudinal spherical aberration defined by l = A ' P A ' M ¯ . The best focus A is located somewhere between A P and A M .

Fig. 2.
Fig. 2.

Longitudinal spherical aberration (LSA) as a function of NA for a fixed depth x=3 mm in fused silica: red: deduced from the vectorial approach [16,17], solid line: using Eq. (1), dashed: using Seidel approximation, dots: using Eq. (7,8) [18], blue: confocal parameter.

Fig. 3.
Fig. 3.

Distance from paraxial to best focus given by Eq. (10) (solid line) and half Seidel LSA (dashed line) for fused silica as a function of depth for different NA. For low NA, the two curves are identical.

Fig. 4.
Fig. 4.

Observation of index variation in SiO2 (a) and BK7 (b) as a function of depth. Single shot (Num=1) and multishot (Num=1000) regimes are depicted at different input energies for different physical depths with respect to the sample surface, 200 µm (left) and 500 µm (right). The laser pulse is coming from the left and observations are made perpendicular to the propagation axis. The position of the best focus is given by the dot line and is located within the central region of the structure.

Fig. 5.
Fig. 5.

Relative length of the refractive index variation trace (taken as the dimension of the continuous trace) as a function of depth for different pulse numbers (Num) for fused silica together with theoretical predictions (solid black line). Dashed red: confocal parameter of the incident beam. Triangles: Num=1, circles: Num=10, squares: Num=1000. The input energy is 2.7 µJ. Data are normalized to the length measured for x=2 mm (see text for detail).

Fig. 6.
Fig. 6.

Distance from paraxial to best focus as a function of depth for different pulse numbers (Num) for fused silica with theoretical predictions (black line) given by Eq. (10). The experimental paraxial focus is supposed to coincide with the beginning of the modified area. Close to the surface, its distance to the best focus is then mainly given by half of the confocal parameter. Dashed red: half confocal parameter of the incident beam. Triangles: Num=1, circles: Num=10, squares: Num=1000. The input energy is 2.7 µJ.

Fig. 7.
Fig. 7.

Minimum spot diameter achievable as a function of depth for fused silica (solid line) and BK7 (dotted line). N is the order of the last corrected Zernike polynomial. The red line is a guideline for the typical working distance of corresponding objectives. NA values above 0.7 are not considered, corresponding to a mimimum spot diameter of 0.7 µm.

Fig. 8.
Fig. 8.

Maximum tolerable NA that gives a constant peak index variation from the surface up to a given depth in fused silica (full line) and BK7 (dotted line). N is the order of the last corrected Zernike polynomial. The red line is a guideline for the typical working distance of corresponding objectives.

Tables (1)

Tables Icon

Table 1. First Zernike polynomials R0n (ρ).

Equations (12)

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

l = x n 2 n 1 { cos α ' [ 1 ( n 2 n 1 ) 2 sin 2 α ' ] 1 2 1 }
Δ 2 = 0 α ' l ( u ) sin u d u
Δ aberr n 1 Δ 1 = n 1 x [ cos α ( n 2 n 1 ) 2 cos α ' ]
a = 1 2 x . n 2 n 1 . n 2 2 n 1 2 n 1 2 > 0
Δ aberr = x NA [ csc 2 α ρ 2 n 2 n 1 csc 2 α ' ρ 2 ] = x NA [ A 00 + 1 2 n = 2 A n 0 R n 0 ( ρ ) ]
A n 0 = 2 ( n + 1 ) [ B n ( α ) n 2 n 1 B n ( α ' ) ]
u 1 u 2 I ( u ) d u = ε I ( u ) d u
u = ( 8 π n 1 z λ ) sin 2 ( α 2 )
l confocal = 4 n 2 λ N A 2
d z = 2 2 n 1 n 2 N A x . A 2 , 0
R S = 1 4 π 2 λ 2 σ 2 Δ = 1 1 2 ( 2 π λ x N A ) 2 j > 1 A 2 j , 0 2 2 j + 1
Δ remain = x N A 1 2 n = N + 2 A n 0 R n 0 ( ρ ) , n even

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