Abstract

The effects of polarization and frequency chirp of femtosecond laser pulses focused inside silica glass on plasma density generated in a femtosecond modification process are numerically studied. The vector four-dimensional nonlinear Schrödinger equation coupled with the Drude plasma equation are simultaneously solved for that purpose. The evolution of polarization along the filament is investigated for different polarizations of the incident pulse. It is observed that there is a sharp variation of polarization ellipse at the vicinity of the focus for an incident pulse with elliptical polarization. For a linearly or circularly polarized incident beam the polarization along the filament remains unchanged. On the other hand, it is found that the magnitude and the sign of the frequency chirp of the incident pulse effectively change the plasma density generated in the process of laser-induced modification. In particular, for incident peak powers near the threshold, by changing the sign of the input chirp, maximum plasma density can be altered by several orders of magnitude. Furthermore, by adjusting the value of the input chirp, the magnitude and the location of plasma density can be adjusted. The results reveal that polarization and frequency chirp of the incident femtosecond laser pulses are two appropriate parameters for controlling the plasma density in the process of laser-induced modification.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Della Valle, R. Osellame, and P. Laporta, “Micromachining of photonic devices by femtosecond laser pulses,” J. Opt. A 11, 013001 (2009).
    [CrossRef]
  2. R. Osellame, R. M. Vazquez, C. Dongre, R. Dekker, H. Hoekstra, M. Pollnau, R. Ramponi, and G. Cerullo, “Femtosecond laser fabrication for the integration of optical sensors in microfluidic lab-on-chip devices,” in Ultrafast Phenomena XVI, Vol. 92 of Springer Series in Chemical Physics (Springer, 2009), pp. 973–975.
  3. M. Kim, D. J. Hwang, H. Jeon, K. Hiromatsu, and C. P. Grigoropoulos, “Single cell detection using a glass-based optofluidic device fabricated by femtosecond laser pulses,” Lab Chip 9, 311–318 (2009).
    [CrossRef]
  4. W. J. Chen, S. M. Eaton, H. Zhang, and P. R. Herman, “Broadband directional couplers fabricated in bulk glass with high repetition rate femtosecond laser pulses,” Opt. Express 16, 11470–11480 (2008).
    [CrossRef]
  5. J. Liu, Z. Zhang, S. Chang, C. Flueraru, and C. P. Grover, “Directly writing of 1-to-N optical waveguide power splitters in fused silica glass using a femtosecond laser,” Opt. Commun. 253, 315–319 (2005).
    [CrossRef]
  6. H. Zhang, S. M. Eaton, and P. R. Herman, “Single-step writing of Bragg grating waveguides in fused silica with an externally modulated femtosecond fiber laser,” Opt. Lett. 32, 2559–2561 (2007).
    [CrossRef]
  7. G. Cheng, Y. Wang, J. D. White, Q. Liu, W. Zhao, and G. Chen, “Demonstration of high-density three-dimensional storage in fused silica by femtosecond laser pulses,” J. Appl. Phys. 94, 1304–1307 (2003).
    [CrossRef]
  8. T. Shih, R. R. Gattass, C. R. Mendonca, and E. Mazur, “Faraday rotation in femtosecond laser micromachined waveguides,” Opt. Express 15, 5809–5814 (2007).
    [CrossRef]
  9. M. Kamata, M. Obara, R. R. Gattass, L. R. Cerami, and E. Mazur, “Fabrication of waveguide-based vibration sensors by femtosecond laser micromachining,” in Conference on Lasers and Electro-Optics (2005), paper CThCC3.
  10. C. B. Schaffer, A. Brodeur, J. F. García, and E. Mazur, “Micromachining bulk glass by use of femtosecond laser pulses with nanojoule energy,” Opt. Lett. 26, 93–95 (2001).
    [CrossRef]
  11. R. R. Gattass, “Femtosecond-laser interactions with transparent materials: applications in micromachining and supercontinuum generation,” Ph.D. thesis (Harvard University, 2006).
  12. A. Ferrer, V. Diez-Blanco, A. Ruiz, J. Siegel, and J. Solis, “Deep subsurface optical waveguides produced by direct writing with femtosecond laser pulses in fused silica and phosphate glass,” Appl. Surf. Sci. 254, 1121–1125 (2007).
    [CrossRef]
  13. M. Ams, G. D. Marshall, and M. J. Withford, “Study of the influence of femtosecond laser polarisation on direct writing of waveguides,” Opt. Express 14, 13158–13163 (2006).
    [CrossRef]
  14. A. H. Nejadmalayeri and P. R. Herman, “Ultrafast laser waveguide writing: lithium niobate and the role of circular polarization and picosecond pulse width,” Opt. Lett. 31, 2987–2989 (2006).
    [CrossRef]
  15. D. J. Little, M. Ams, P. Dekker, G. D. Marshall, J. M. Dawes, and M. J. Withford, “Femtosecond laser modification of fused silica: the effect of writing polarization on Si-O ring structure,” Opt. Express 16, 20029–20037 (2008).
    [CrossRef]
  16. R. S. Taylor, E. Simova, and C. Hnatovsky, “Creation of chiral structures inside fused silica glass,” Opt. Lett. 33, 1312–1314 (2008).
    [CrossRef]
  17. J. M. Guay, A. Villafranca, F. Baset, K. Popov, L. Ramunnom, and V. R. Bhardwaj, “Polarization-dependent femtosecond laser ablation of poly-methyl methacrylate,” New J. Phys. 14, 085010 (2012).
    [CrossRef]
  18. J. Yu, H. Jiang, H. Yang, and Q. Gong, “Polarization effect during propagation of a femtosecond laser pulse in fused silica glass,” J. Opt. Soc. Am. B 29, 1937–1941 (2012).
    [CrossRef]
  19. D. Liu, Y. Li, M. Liu, H. Yang, and Q. Gong, “The polarization-dependence of femtosecond laser damage threshold inside fused silica,” Appl. Phys. B 91, 597–599 (2008).
    [CrossRef]
  20. B. Poumellec, M. Lancry, A. Chahid-Erraji, and P. G. Kazansky, “Modification thresholds in femtosecond laser processing of pure silica: review of dependencies on laser parameters,” Opt. Mater. Express 1, 766–782 (2011).
    [CrossRef]
  21. E. Louzon, Z. Henis, S. Pecker, Y. Ehrlich, D. Fisher, M. Fraenkel, and A. Zigler, “Reduction of damage threshold in dielectric materials induced by negatively chirped laser pulses,” Appl. Phys. Lett. 87, 241903 (2005).
    [CrossRef]
  22. J. A. Dharmadhikari, K. Pradyna, A. Bhatnagar, D. Mathur, and A. K. Dharmadhikari, “Effect of chirp on the index contrast of waveguides written in BK7 glass with ultrashort laser pulses,” Opt. Commun. 287, 122–127 (2013).
    [CrossRef]
  23. A. S. Arabanian and R. Massudi, “Modeling of femtosecond pulse propagation inside x-cut and z-cut MgO doped LiNbO3 anisotropic crystals,” Appl. Opt. 52, 4212–4222 (2013).
    [CrossRef]
  24. R. W. Boyd, Nonlinear Optics (Academic, 2007).
  25. K. Okamoto, Fundamentals of Optical Waveguides (Elsevier Academic, 2006).
  26. J. Strikwerda, Finite Difference Scheme and Partial Differential Equations (SIAM, 2004).
  27. Q. Sun, H. Jiang, Y. Liu, Z. Wu, H. Yang, and Q. Gong, “Diagnose parameters of plasma induced by femtosecond laser pulse in quartz and glasses,” Front. Phys. China 1, 67–71 (2006).
    [CrossRef]

2013 (2)

J. A. Dharmadhikari, K. Pradyna, A. Bhatnagar, D. Mathur, and A. K. Dharmadhikari, “Effect of chirp on the index contrast of waveguides written in BK7 glass with ultrashort laser pulses,” Opt. Commun. 287, 122–127 (2013).
[CrossRef]

A. S. Arabanian and R. Massudi, “Modeling of femtosecond pulse propagation inside x-cut and z-cut MgO doped LiNbO3 anisotropic crystals,” Appl. Opt. 52, 4212–4222 (2013).
[CrossRef]

2012 (2)

J. Yu, H. Jiang, H. Yang, and Q. Gong, “Polarization effect during propagation of a femtosecond laser pulse in fused silica glass,” J. Opt. Soc. Am. B 29, 1937–1941 (2012).
[CrossRef]

J. M. Guay, A. Villafranca, F. Baset, K. Popov, L. Ramunnom, and V. R. Bhardwaj, “Polarization-dependent femtosecond laser ablation of poly-methyl methacrylate,” New J. Phys. 14, 085010 (2012).
[CrossRef]

2011 (1)

2009 (2)

G. Della Valle, R. Osellame, and P. Laporta, “Micromachining of photonic devices by femtosecond laser pulses,” J. Opt. A 11, 013001 (2009).
[CrossRef]

M. Kim, D. J. Hwang, H. Jeon, K. Hiromatsu, and C. P. Grigoropoulos, “Single cell detection using a glass-based optofluidic device fabricated by femtosecond laser pulses,” Lab Chip 9, 311–318 (2009).
[CrossRef]

2008 (4)

2007 (3)

2006 (3)

2005 (2)

E. Louzon, Z. Henis, S. Pecker, Y. Ehrlich, D. Fisher, M. Fraenkel, and A. Zigler, “Reduction of damage threshold in dielectric materials induced by negatively chirped laser pulses,” Appl. Phys. Lett. 87, 241903 (2005).
[CrossRef]

J. Liu, Z. Zhang, S. Chang, C. Flueraru, and C. P. Grover, “Directly writing of 1-to-N optical waveguide power splitters in fused silica glass using a femtosecond laser,” Opt. Commun. 253, 315–319 (2005).
[CrossRef]

2003 (1)

G. Cheng, Y. Wang, J. D. White, Q. Liu, W. Zhao, and G. Chen, “Demonstration of high-density three-dimensional storage in fused silica by femtosecond laser pulses,” J. Appl. Phys. 94, 1304–1307 (2003).
[CrossRef]

2001 (1)

Ams, M.

Arabanian, A. S.

Baset, F.

J. M. Guay, A. Villafranca, F. Baset, K. Popov, L. Ramunnom, and V. R. Bhardwaj, “Polarization-dependent femtosecond laser ablation of poly-methyl methacrylate,” New J. Phys. 14, 085010 (2012).
[CrossRef]

Bhardwaj, V. R.

J. M. Guay, A. Villafranca, F. Baset, K. Popov, L. Ramunnom, and V. R. Bhardwaj, “Polarization-dependent femtosecond laser ablation of poly-methyl methacrylate,” New J. Phys. 14, 085010 (2012).
[CrossRef]

Bhatnagar, A.

J. A. Dharmadhikari, K. Pradyna, A. Bhatnagar, D. Mathur, and A. K. Dharmadhikari, “Effect of chirp on the index contrast of waveguides written in BK7 glass with ultrashort laser pulses,” Opt. Commun. 287, 122–127 (2013).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 2007).

Brodeur, A.

Cerami, L. R.

M. Kamata, M. Obara, R. R. Gattass, L. R. Cerami, and E. Mazur, “Fabrication of waveguide-based vibration sensors by femtosecond laser micromachining,” in Conference on Lasers and Electro-Optics (2005), paper CThCC3.

Cerullo, G.

R. Osellame, R. M. Vazquez, C. Dongre, R. Dekker, H. Hoekstra, M. Pollnau, R. Ramponi, and G. Cerullo, “Femtosecond laser fabrication for the integration of optical sensors in microfluidic lab-on-chip devices,” in Ultrafast Phenomena XVI, Vol. 92 of Springer Series in Chemical Physics (Springer, 2009), pp. 973–975.

Chahid-Erraji, A.

Chang, S.

J. Liu, Z. Zhang, S. Chang, C. Flueraru, and C. P. Grover, “Directly writing of 1-to-N optical waveguide power splitters in fused silica glass using a femtosecond laser,” Opt. Commun. 253, 315–319 (2005).
[CrossRef]

Chen, G.

G. Cheng, Y. Wang, J. D. White, Q. Liu, W. Zhao, and G. Chen, “Demonstration of high-density three-dimensional storage in fused silica by femtosecond laser pulses,” J. Appl. Phys. 94, 1304–1307 (2003).
[CrossRef]

Chen, W. J.

Cheng, G.

G. Cheng, Y. Wang, J. D. White, Q. Liu, W. Zhao, and G. Chen, “Demonstration of high-density three-dimensional storage in fused silica by femtosecond laser pulses,” J. Appl. Phys. 94, 1304–1307 (2003).
[CrossRef]

Dawes, J. M.

Dekker, P.

Dekker, R.

R. Osellame, R. M. Vazquez, C. Dongre, R. Dekker, H. Hoekstra, M. Pollnau, R. Ramponi, and G. Cerullo, “Femtosecond laser fabrication for the integration of optical sensors in microfluidic lab-on-chip devices,” in Ultrafast Phenomena XVI, Vol. 92 of Springer Series in Chemical Physics (Springer, 2009), pp. 973–975.

Della Valle, G.

G. Della Valle, R. Osellame, and P. Laporta, “Micromachining of photonic devices by femtosecond laser pulses,” J. Opt. A 11, 013001 (2009).
[CrossRef]

Dharmadhikari, A. K.

J. A. Dharmadhikari, K. Pradyna, A. Bhatnagar, D. Mathur, and A. K. Dharmadhikari, “Effect of chirp on the index contrast of waveguides written in BK7 glass with ultrashort laser pulses,” Opt. Commun. 287, 122–127 (2013).
[CrossRef]

Dharmadhikari, J. A.

J. A. Dharmadhikari, K. Pradyna, A. Bhatnagar, D. Mathur, and A. K. Dharmadhikari, “Effect of chirp on the index contrast of waveguides written in BK7 glass with ultrashort laser pulses,” Opt. Commun. 287, 122–127 (2013).
[CrossRef]

Diez-Blanco, V.

A. Ferrer, V. Diez-Blanco, A. Ruiz, J. Siegel, and J. Solis, “Deep subsurface optical waveguides produced by direct writing with femtosecond laser pulses in fused silica and phosphate glass,” Appl. Surf. Sci. 254, 1121–1125 (2007).
[CrossRef]

Dongre, C.

R. Osellame, R. M. Vazquez, C. Dongre, R. Dekker, H. Hoekstra, M. Pollnau, R. Ramponi, and G. Cerullo, “Femtosecond laser fabrication for the integration of optical sensors in microfluidic lab-on-chip devices,” in Ultrafast Phenomena XVI, Vol. 92 of Springer Series in Chemical Physics (Springer, 2009), pp. 973–975.

Eaton, S. M.

Ehrlich, Y.

E. Louzon, Z. Henis, S. Pecker, Y. Ehrlich, D. Fisher, M. Fraenkel, and A. Zigler, “Reduction of damage threshold in dielectric materials induced by negatively chirped laser pulses,” Appl. Phys. Lett. 87, 241903 (2005).
[CrossRef]

Ferrer, A.

A. Ferrer, V. Diez-Blanco, A. Ruiz, J. Siegel, and J. Solis, “Deep subsurface optical waveguides produced by direct writing with femtosecond laser pulses in fused silica and phosphate glass,” Appl. Surf. Sci. 254, 1121–1125 (2007).
[CrossRef]

Fisher, D.

E. Louzon, Z. Henis, S. Pecker, Y. Ehrlich, D. Fisher, M. Fraenkel, and A. Zigler, “Reduction of damage threshold in dielectric materials induced by negatively chirped laser pulses,” Appl. Phys. Lett. 87, 241903 (2005).
[CrossRef]

Flueraru, C.

J. Liu, Z. Zhang, S. Chang, C. Flueraru, and C. P. Grover, “Directly writing of 1-to-N optical waveguide power splitters in fused silica glass using a femtosecond laser,” Opt. Commun. 253, 315–319 (2005).
[CrossRef]

Fraenkel, M.

E. Louzon, Z. Henis, S. Pecker, Y. Ehrlich, D. Fisher, M. Fraenkel, and A. Zigler, “Reduction of damage threshold in dielectric materials induced by negatively chirped laser pulses,” Appl. Phys. Lett. 87, 241903 (2005).
[CrossRef]

García, J. F.

Gattass, R. R.

T. Shih, R. R. Gattass, C. R. Mendonca, and E. Mazur, “Faraday rotation in femtosecond laser micromachined waveguides,” Opt. Express 15, 5809–5814 (2007).
[CrossRef]

R. R. Gattass, “Femtosecond-laser interactions with transparent materials: applications in micromachining and supercontinuum generation,” Ph.D. thesis (Harvard University, 2006).

M. Kamata, M. Obara, R. R. Gattass, L. R. Cerami, and E. Mazur, “Fabrication of waveguide-based vibration sensors by femtosecond laser micromachining,” in Conference on Lasers and Electro-Optics (2005), paper CThCC3.

Gong, Q.

J. Yu, H. Jiang, H. Yang, and Q. Gong, “Polarization effect during propagation of a femtosecond laser pulse in fused silica glass,” J. Opt. Soc. Am. B 29, 1937–1941 (2012).
[CrossRef]

D. Liu, Y. Li, M. Liu, H. Yang, and Q. Gong, “The polarization-dependence of femtosecond laser damage threshold inside fused silica,” Appl. Phys. B 91, 597–599 (2008).
[CrossRef]

Q. Sun, H. Jiang, Y. Liu, Z. Wu, H. Yang, and Q. Gong, “Diagnose parameters of plasma induced by femtosecond laser pulse in quartz and glasses,” Front. Phys. China 1, 67–71 (2006).
[CrossRef]

Grigoropoulos, C. P.

M. Kim, D. J. Hwang, H. Jeon, K. Hiromatsu, and C. P. Grigoropoulos, “Single cell detection using a glass-based optofluidic device fabricated by femtosecond laser pulses,” Lab Chip 9, 311–318 (2009).
[CrossRef]

Grover, C. P.

J. Liu, Z. Zhang, S. Chang, C. Flueraru, and C. P. Grover, “Directly writing of 1-to-N optical waveguide power splitters in fused silica glass using a femtosecond laser,” Opt. Commun. 253, 315–319 (2005).
[CrossRef]

Guay, J. M.

J. M. Guay, A. Villafranca, F. Baset, K. Popov, L. Ramunnom, and V. R. Bhardwaj, “Polarization-dependent femtosecond laser ablation of poly-methyl methacrylate,” New J. Phys. 14, 085010 (2012).
[CrossRef]

Henis, Z.

E. Louzon, Z. Henis, S. Pecker, Y. Ehrlich, D. Fisher, M. Fraenkel, and A. Zigler, “Reduction of damage threshold in dielectric materials induced by negatively chirped laser pulses,” Appl. Phys. Lett. 87, 241903 (2005).
[CrossRef]

Herman, P. R.

Hiromatsu, K.

M. Kim, D. J. Hwang, H. Jeon, K. Hiromatsu, and C. P. Grigoropoulos, “Single cell detection using a glass-based optofluidic device fabricated by femtosecond laser pulses,” Lab Chip 9, 311–318 (2009).
[CrossRef]

Hnatovsky, C.

Hoekstra, H.

R. Osellame, R. M. Vazquez, C. Dongre, R. Dekker, H. Hoekstra, M. Pollnau, R. Ramponi, and G. Cerullo, “Femtosecond laser fabrication for the integration of optical sensors in microfluidic lab-on-chip devices,” in Ultrafast Phenomena XVI, Vol. 92 of Springer Series in Chemical Physics (Springer, 2009), pp. 973–975.

Hwang, D. J.

M. Kim, D. J. Hwang, H. Jeon, K. Hiromatsu, and C. P. Grigoropoulos, “Single cell detection using a glass-based optofluidic device fabricated by femtosecond laser pulses,” Lab Chip 9, 311–318 (2009).
[CrossRef]

Jeon, H.

M. Kim, D. J. Hwang, H. Jeon, K. Hiromatsu, and C. P. Grigoropoulos, “Single cell detection using a glass-based optofluidic device fabricated by femtosecond laser pulses,” Lab Chip 9, 311–318 (2009).
[CrossRef]

Jiang, H.

J. Yu, H. Jiang, H. Yang, and Q. Gong, “Polarization effect during propagation of a femtosecond laser pulse in fused silica glass,” J. Opt. Soc. Am. B 29, 1937–1941 (2012).
[CrossRef]

Q. Sun, H. Jiang, Y. Liu, Z. Wu, H. Yang, and Q. Gong, “Diagnose parameters of plasma induced by femtosecond laser pulse in quartz and glasses,” Front. Phys. China 1, 67–71 (2006).
[CrossRef]

Kamata, M.

M. Kamata, M. Obara, R. R. Gattass, L. R. Cerami, and E. Mazur, “Fabrication of waveguide-based vibration sensors by femtosecond laser micromachining,” in Conference on Lasers and Electro-Optics (2005), paper CThCC3.

Kazansky, P. G.

Kim, M.

M. Kim, D. J. Hwang, H. Jeon, K. Hiromatsu, and C. P. Grigoropoulos, “Single cell detection using a glass-based optofluidic device fabricated by femtosecond laser pulses,” Lab Chip 9, 311–318 (2009).
[CrossRef]

Lancry, M.

Laporta, P.

G. Della Valle, R. Osellame, and P. Laporta, “Micromachining of photonic devices by femtosecond laser pulses,” J. Opt. A 11, 013001 (2009).
[CrossRef]

Li, Y.

D. Liu, Y. Li, M. Liu, H. Yang, and Q. Gong, “The polarization-dependence of femtosecond laser damage threshold inside fused silica,” Appl. Phys. B 91, 597–599 (2008).
[CrossRef]

Little, D. J.

Liu, D.

D. Liu, Y. Li, M. Liu, H. Yang, and Q. Gong, “The polarization-dependence of femtosecond laser damage threshold inside fused silica,” Appl. Phys. B 91, 597–599 (2008).
[CrossRef]

Liu, J.

J. Liu, Z. Zhang, S. Chang, C. Flueraru, and C. P. Grover, “Directly writing of 1-to-N optical waveguide power splitters in fused silica glass using a femtosecond laser,” Opt. Commun. 253, 315–319 (2005).
[CrossRef]

Liu, M.

D. Liu, Y. Li, M. Liu, H. Yang, and Q. Gong, “The polarization-dependence of femtosecond laser damage threshold inside fused silica,” Appl. Phys. B 91, 597–599 (2008).
[CrossRef]

Liu, Q.

G. Cheng, Y. Wang, J. D. White, Q. Liu, W. Zhao, and G. Chen, “Demonstration of high-density three-dimensional storage in fused silica by femtosecond laser pulses,” J. Appl. Phys. 94, 1304–1307 (2003).
[CrossRef]

Liu, Y.

Q. Sun, H. Jiang, Y. Liu, Z. Wu, H. Yang, and Q. Gong, “Diagnose parameters of plasma induced by femtosecond laser pulse in quartz and glasses,” Front. Phys. China 1, 67–71 (2006).
[CrossRef]

Louzon, E.

E. Louzon, Z. Henis, S. Pecker, Y. Ehrlich, D. Fisher, M. Fraenkel, and A. Zigler, “Reduction of damage threshold in dielectric materials induced by negatively chirped laser pulses,” Appl. Phys. Lett. 87, 241903 (2005).
[CrossRef]

Marshall, G. D.

Massudi, R.

Mathur, D.

J. A. Dharmadhikari, K. Pradyna, A. Bhatnagar, D. Mathur, and A. K. Dharmadhikari, “Effect of chirp on the index contrast of waveguides written in BK7 glass with ultrashort laser pulses,” Opt. Commun. 287, 122–127 (2013).
[CrossRef]

Mazur, E.

Mendonca, C. R.

Nejadmalayeri, A. H.

Obara, M.

M. Kamata, M. Obara, R. R. Gattass, L. R. Cerami, and E. Mazur, “Fabrication of waveguide-based vibration sensors by femtosecond laser micromachining,” in Conference on Lasers and Electro-Optics (2005), paper CThCC3.

Okamoto, K.

K. Okamoto, Fundamentals of Optical Waveguides (Elsevier Academic, 2006).

Osellame, R.

G. Della Valle, R. Osellame, and P. Laporta, “Micromachining of photonic devices by femtosecond laser pulses,” J. Opt. A 11, 013001 (2009).
[CrossRef]

R. Osellame, R. M. Vazquez, C. Dongre, R. Dekker, H. Hoekstra, M. Pollnau, R. Ramponi, and G. Cerullo, “Femtosecond laser fabrication for the integration of optical sensors in microfluidic lab-on-chip devices,” in Ultrafast Phenomena XVI, Vol. 92 of Springer Series in Chemical Physics (Springer, 2009), pp. 973–975.

Pecker, S.

E. Louzon, Z. Henis, S. Pecker, Y. Ehrlich, D. Fisher, M. Fraenkel, and A. Zigler, “Reduction of damage threshold in dielectric materials induced by negatively chirped laser pulses,” Appl. Phys. Lett. 87, 241903 (2005).
[CrossRef]

Pollnau, M.

R. Osellame, R. M. Vazquez, C. Dongre, R. Dekker, H. Hoekstra, M. Pollnau, R. Ramponi, and G. Cerullo, “Femtosecond laser fabrication for the integration of optical sensors in microfluidic lab-on-chip devices,” in Ultrafast Phenomena XVI, Vol. 92 of Springer Series in Chemical Physics (Springer, 2009), pp. 973–975.

Popov, K.

J. M. Guay, A. Villafranca, F. Baset, K. Popov, L. Ramunnom, and V. R. Bhardwaj, “Polarization-dependent femtosecond laser ablation of poly-methyl methacrylate,” New J. Phys. 14, 085010 (2012).
[CrossRef]

Poumellec, B.

Pradyna, K.

J. A. Dharmadhikari, K. Pradyna, A. Bhatnagar, D. Mathur, and A. K. Dharmadhikari, “Effect of chirp on the index contrast of waveguides written in BK7 glass with ultrashort laser pulses,” Opt. Commun. 287, 122–127 (2013).
[CrossRef]

Ramponi, R.

R. Osellame, R. M. Vazquez, C. Dongre, R. Dekker, H. Hoekstra, M. Pollnau, R. Ramponi, and G. Cerullo, “Femtosecond laser fabrication for the integration of optical sensors in microfluidic lab-on-chip devices,” in Ultrafast Phenomena XVI, Vol. 92 of Springer Series in Chemical Physics (Springer, 2009), pp. 973–975.

Ramunnom, L.

J. M. Guay, A. Villafranca, F. Baset, K. Popov, L. Ramunnom, and V. R. Bhardwaj, “Polarization-dependent femtosecond laser ablation of poly-methyl methacrylate,” New J. Phys. 14, 085010 (2012).
[CrossRef]

Ruiz, A.

A. Ferrer, V. Diez-Blanco, A. Ruiz, J. Siegel, and J. Solis, “Deep subsurface optical waveguides produced by direct writing with femtosecond laser pulses in fused silica and phosphate glass,” Appl. Surf. Sci. 254, 1121–1125 (2007).
[CrossRef]

Schaffer, C. B.

Shih, T.

Siegel, J.

A. Ferrer, V. Diez-Blanco, A. Ruiz, J. Siegel, and J. Solis, “Deep subsurface optical waveguides produced by direct writing with femtosecond laser pulses in fused silica and phosphate glass,” Appl. Surf. Sci. 254, 1121–1125 (2007).
[CrossRef]

Simova, E.

Solis, J.

A. Ferrer, V. Diez-Blanco, A. Ruiz, J. Siegel, and J. Solis, “Deep subsurface optical waveguides produced by direct writing with femtosecond laser pulses in fused silica and phosphate glass,” Appl. Surf. Sci. 254, 1121–1125 (2007).
[CrossRef]

Strikwerda, J.

J. Strikwerda, Finite Difference Scheme and Partial Differential Equations (SIAM, 2004).

Sun, Q.

Q. Sun, H. Jiang, Y. Liu, Z. Wu, H. Yang, and Q. Gong, “Diagnose parameters of plasma induced by femtosecond laser pulse in quartz and glasses,” Front. Phys. China 1, 67–71 (2006).
[CrossRef]

Taylor, R. S.

Vazquez, R. M.

R. Osellame, R. M. Vazquez, C. Dongre, R. Dekker, H. Hoekstra, M. Pollnau, R. Ramponi, and G. Cerullo, “Femtosecond laser fabrication for the integration of optical sensors in microfluidic lab-on-chip devices,” in Ultrafast Phenomena XVI, Vol. 92 of Springer Series in Chemical Physics (Springer, 2009), pp. 973–975.

Villafranca, A.

J. M. Guay, A. Villafranca, F. Baset, K. Popov, L. Ramunnom, and V. R. Bhardwaj, “Polarization-dependent femtosecond laser ablation of poly-methyl methacrylate,” New J. Phys. 14, 085010 (2012).
[CrossRef]

Wang, Y.

G. Cheng, Y. Wang, J. D. White, Q. Liu, W. Zhao, and G. Chen, “Demonstration of high-density three-dimensional storage in fused silica by femtosecond laser pulses,” J. Appl. Phys. 94, 1304–1307 (2003).
[CrossRef]

White, J. D.

G. Cheng, Y. Wang, J. D. White, Q. Liu, W. Zhao, and G. Chen, “Demonstration of high-density three-dimensional storage in fused silica by femtosecond laser pulses,” J. Appl. Phys. 94, 1304–1307 (2003).
[CrossRef]

Withford, M. J.

Wu, Z.

Q. Sun, H. Jiang, Y. Liu, Z. Wu, H. Yang, and Q. Gong, “Diagnose parameters of plasma induced by femtosecond laser pulse in quartz and glasses,” Front. Phys. China 1, 67–71 (2006).
[CrossRef]

Yang, H.

J. Yu, H. Jiang, H. Yang, and Q. Gong, “Polarization effect during propagation of a femtosecond laser pulse in fused silica glass,” J. Opt. Soc. Am. B 29, 1937–1941 (2012).
[CrossRef]

D. Liu, Y. Li, M. Liu, H. Yang, and Q. Gong, “The polarization-dependence of femtosecond laser damage threshold inside fused silica,” Appl. Phys. B 91, 597–599 (2008).
[CrossRef]

Q. Sun, H. Jiang, Y. Liu, Z. Wu, H. Yang, and Q. Gong, “Diagnose parameters of plasma induced by femtosecond laser pulse in quartz and glasses,” Front. Phys. China 1, 67–71 (2006).
[CrossRef]

Yu, J.

Zhang, H.

Zhang, Z.

J. Liu, Z. Zhang, S. Chang, C. Flueraru, and C. P. Grover, “Directly writing of 1-to-N optical waveguide power splitters in fused silica glass using a femtosecond laser,” Opt. Commun. 253, 315–319 (2005).
[CrossRef]

Zhao, W.

G. Cheng, Y. Wang, J. D. White, Q. Liu, W. Zhao, and G. Chen, “Demonstration of high-density three-dimensional storage in fused silica by femtosecond laser pulses,” J. Appl. Phys. 94, 1304–1307 (2003).
[CrossRef]

Zigler, A.

E. Louzon, Z. Henis, S. Pecker, Y. Ehrlich, D. Fisher, M. Fraenkel, and A. Zigler, “Reduction of damage threshold in dielectric materials induced by negatively chirped laser pulses,” Appl. Phys. Lett. 87, 241903 (2005).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

D. Liu, Y. Li, M. Liu, H. Yang, and Q. Gong, “The polarization-dependence of femtosecond laser damage threshold inside fused silica,” Appl. Phys. B 91, 597–599 (2008).
[CrossRef]

Appl. Phys. Lett. (1)

E. Louzon, Z. Henis, S. Pecker, Y. Ehrlich, D. Fisher, M. Fraenkel, and A. Zigler, “Reduction of damage threshold in dielectric materials induced by negatively chirped laser pulses,” Appl. Phys. Lett. 87, 241903 (2005).
[CrossRef]

Appl. Surf. Sci. (1)

A. Ferrer, V. Diez-Blanco, A. Ruiz, J. Siegel, and J. Solis, “Deep subsurface optical waveguides produced by direct writing with femtosecond laser pulses in fused silica and phosphate glass,” Appl. Surf. Sci. 254, 1121–1125 (2007).
[CrossRef]

Front. Phys. China (1)

Q. Sun, H. Jiang, Y. Liu, Z. Wu, H. Yang, and Q. Gong, “Diagnose parameters of plasma induced by femtosecond laser pulse in quartz and glasses,” Front. Phys. China 1, 67–71 (2006).
[CrossRef]

J. Appl. Phys. (1)

G. Cheng, Y. Wang, J. D. White, Q. Liu, W. Zhao, and G. Chen, “Demonstration of high-density three-dimensional storage in fused silica by femtosecond laser pulses,” J. Appl. Phys. 94, 1304–1307 (2003).
[CrossRef]

J. Opt. A (1)

G. Della Valle, R. Osellame, and P. Laporta, “Micromachining of photonic devices by femtosecond laser pulses,” J. Opt. A 11, 013001 (2009).
[CrossRef]

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

Lab Chip (1)

M. Kim, D. J. Hwang, H. Jeon, K. Hiromatsu, and C. P. Grigoropoulos, “Single cell detection using a glass-based optofluidic device fabricated by femtosecond laser pulses,” Lab Chip 9, 311–318 (2009).
[CrossRef]

New J. Phys. (1)

J. M. Guay, A. Villafranca, F. Baset, K. Popov, L. Ramunnom, and V. R. Bhardwaj, “Polarization-dependent femtosecond laser ablation of poly-methyl methacrylate,” New J. Phys. 14, 085010 (2012).
[CrossRef]

Opt. Commun. (2)

J. Liu, Z. Zhang, S. Chang, C. Flueraru, and C. P. Grover, “Directly writing of 1-to-N optical waveguide power splitters in fused silica glass using a femtosecond laser,” Opt. Commun. 253, 315–319 (2005).
[CrossRef]

J. A. Dharmadhikari, K. Pradyna, A. Bhatnagar, D. Mathur, and A. K. Dharmadhikari, “Effect of chirp on the index contrast of waveguides written in BK7 glass with ultrashort laser pulses,” Opt. Commun. 287, 122–127 (2013).
[CrossRef]

Opt. Express (4)

Opt. Lett. (4)

Opt. Mater. Express (1)

Other (6)

R. W. Boyd, Nonlinear Optics (Academic, 2007).

K. Okamoto, Fundamentals of Optical Waveguides (Elsevier Academic, 2006).

J. Strikwerda, Finite Difference Scheme and Partial Differential Equations (SIAM, 2004).

R. Osellame, R. M. Vazquez, C. Dongre, R. Dekker, H. Hoekstra, M. Pollnau, R. Ramponi, and G. Cerullo, “Femtosecond laser fabrication for the integration of optical sensors in microfluidic lab-on-chip devices,” in Ultrafast Phenomena XVI, Vol. 92 of Springer Series in Chemical Physics (Springer, 2009), pp. 973–975.

M. Kamata, M. Obara, R. R. Gattass, L. R. Cerami, and E. Mazur, “Fabrication of waveguide-based vibration sensors by femtosecond laser micromachining,” in Conference on Lasers and Electro-Optics (2005), paper CThCC3.

R. R. Gattass, “Femtosecond-laser interactions with transparent materials: applications in micromachining and supercontinuum generation,” Ph.D. thesis (Harvard University, 2006).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

Geometry of pulse focusing inside silica glass.

Fig. 2.
Fig. 2.

Polarization ellipse with the maximum amplitude along the x axis, |Ex|, the maximum amplitude along the y axis, |Ey|, the amplitude of the major semiaxis, a, and the amplitude of the minor semiaxis, b.

Fig. 3.
Fig. 3.

Variation of maximum plasma density versus ellipticities of the incident polarization ellipses. The cases r=0 and r=1 correspond to linear and circular polarization of the incident pulse, respectively. The peak power of the incident pulse is 4.5 MW.

Fig. 4.
Fig. 4.

Variation of ellipticity of polarization of elliptically polarized incident pulses along propagation axis at the vicinity of the focus with azimuth angle of θ=0 and ellipticity of (a) r=0.6 and (b) r=0.8. (c) Evolution of polarization ellipse along propagation axis for incident polarization with ellipticities of r=0.6 and r=0.8. (d) Plasma density distribution for r=0.6.

Fig. 5.
Fig. 5.

Plasma density distribution generated inside silica by different pulses with the same peak power at the entrance and different frequency chirp.

Fig. 6.
Fig. 6.

Variation of the plasma density along propagation axis for different values of the frequency chirp of the incident pulse and for two different input peak powers, which are, both, significantly higher than the threshold, i.e., of (a) 6.5 MW and (b) 11 MW.

Tables (1)

Tables Icon

Table 1. Physical Constants and Parameters Used in this Study

Equations (20)

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

E0=12(A0xe^x+A0ye^y),
A0x(x,y,t)=2Pinπwf2exp((x2+y2)[1r02+ik02f](1+icp)t2tp2)
A0y(x,y,t)=iA0x(x,y,t).
E0=A0x(1+r2)(e^x+ire^y),
zE=ik22t2E+i2k0T2E+ik02ε0nb2PNL12σ(1+iωτc)ρE12β(K)(|E|2)K1E.
PNL=3ε0χxxxx(3){23(E·E*)E+13(E·E)E*}.
Δn=Re(ΔnyΔnx)=2n23((|Ey|2|Ex|2)(sin2ψ).
Δn=Re(ΔnyΔnx)=2n23((|Ey|2|Ex|2)(sin2ψ).
tan2θ=2|Ex||Ey||Ex|2|Ey|2cosψ,
r=tanχ=ba,
sin2χ=2|Ex||Ey||Ex|2+|Ey|2sinψ.
ρt=ρEgσ|E|2+β(K)|E|2(K)Kω0.
t=t/tp,z=z/4zf,x=x/wf,y=y/wf,e=E/2Pin/πwf2,T2=wf2T2,ρ=ρ/ρBD,
ze=iδ2t2e+iT2e+icSF[{23(e·e*)e+13(e·e)e*}]γ(1+iωτc)ρeμ(|e|2)K1e
ρt=vρ(|e|2)+(|e|2e0)K,
cSF=8Pin/Pcr,δ=2zfk2/tp2,γ=2σρBDzfandμ=2zfβ(K)(2Pin/πwf2)(K1)e0=(KωρBDβ(K)tp)1/Kπwf22Pin,v=σtpEg2Pinπwf2.
Aexi,j,tmx+1/2exi+1,j,tmx+1/2exi1,j,tmx+1/2=Bexi,j,tm+C1(exi,j,t+1m+exi,j,t1m)=hi,j,tm,Cexi,j,tmy+1/2exi,j+1,tmy+1/2exi,j1,tmy+1/2=Dexi,j,tmx+1/2+C2(exi+1,j,tmx+1/2+exi1,j,tmx+1/2)=gi,j,tmx+1/2,Eexi,j,tm+1exi,j,t+1m+1exi,j,t1m+1=Fexi,j,tmy+1/2+C3(exi,j+1,tmy+1/2+exi,j1,tmy+1/2)=di,j,tmy+1/2,
el,j,tmx+1/2(l=i1,i,i+1)=(el,j,tm+el,j,tm+1)/2,ei,l,tmy+1/2(l=j1,j,j+1)=(ei,l,tm+ei,l,tm+1)/2,
A=2i(Δx)2Δz+2,B=2(Δx)2δ(Δt)2+iγ(1+iω0τc)ρ(Δx)22i(Δx)2Δz,C=2i(Δy)2Δz+2,D=2i(Δy)2Δz2(Δy)2(Δx)2,E=2i(Δt)2δΔz+2+iγ(1+iω0τc)ρ(Δt)2/δ,F=+2(Δt)2δ(Δy)2+2i(Δt)2δΔz,
C1=(Δx)2δ(Δt)2,C2=((Δy)2(Δx)2),C3=(Δt)2δ(Δy)2.

Metrics