[1] [1] Gattass, R. R. and Mazur, E., “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2, 219-225 (2008).

[2] [2] Schaffer, C. B., Brodeur, A., Garcia, J. F. and Mazur, E., “Micromachining bulk glass by use of femtosecond laser pulses with nanojoule energy,” Opt. Lett. 26, 93-95 (2001).

[3] [3] Eaton, S. M., Zhang, H., Herman, P. R., Yoshino, F., Shah, L., Bovatsek, J. and Arai, A. Y., “Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate,” Opt. Express 13, 4708-4716 (2005).

[4] [4] Osellame, R., Chiodo, N., Maselli, V., Yin, A., Zavelani-Rossi, M., Cerullo, G., Laporta, P., Aiello, L., De Nicola, S., Ferraro, P., Finizio, A. and Pierattini, G., “Optical properties of waveguides written by a 26MHz stretched cavity Ti:sapphire femtosecond oscillator,” Opt. Express 13, 612-620 (2005).

[5] [5] Gattass, R. R., Cerami, L. R. and Mazur, E., “Micromachining of bulk glass with bursts of femtosecond laser pulses at variable repetition rates,” Opt. Express 14, 5279-5284 (2006).

[6] [6] Eaton, S. M., Zhang, H., Ng, M. L., Li, J., Chen, W., Ho, S. and Herman, P. R., “Transition from thermal diffusion to heat accumulation in high repetition rate femtosecond laser writing of buried optical waveguides,” Opt. Express 16, 9443-9458 (2008).

[7] [7] Miese, C., Withford, M. J. and Fuerbach, A., “Femtosecond laser direct-writing of waveguide Bragg gratings in a quasi cumulative heating regime,” Opt. Express 19, 19542-19550 (2011).

[8] [8] Tamaki, T., Watanabe, W. and Itoh, K., “Laser micro-welding of transparent materials by a localized heat accumulation effect using a femtosecond fiber laser at 1558 nm,” Opt. Express 14, 10460-1048 (2006).

[9] [9] Miyamoto, I., Cvecek, K. and Schmidt, M., “Evaluation of nonlinear absorptivity in internal modification of bulk glass by ultrashort laser pulses,” Opt. Express 19, 10714-10727 (2011).

[10] [10] Miyamoto, I., Cvecek, K., Okamoto, Y., Schmidt, M. and Helvajian, H., “Characteristics of laser absorption and welding in FOTURAN glass by ultrashort laser pulses,” Opt. Express 19, 22961-22973 (2011).

[11] [11] Sugioka, K., Iida, M., Takai, H. and Micorikawa, K., “Efficient microwelding of glass substrates by ultrafast laser irradiation using a double-pulse train,” Opt. Lett. 36, 2734-2736 (2011).

[12] [12] Wu, S., Wu, D., Xu, J., Hanada, Y., Suganuma, R., Wang, H., Makimura, T., Sugioka, K. and Midorikawa, K., “Characterization and mechanism of glass microwelding by double-pulse ultrafast laser irradiation,” Opt. Express 20, 28893-28905 (2012).

[13] [13] Zimmermann, F., Richter, S., Doering, S., Tuennermann, A. and Nolte, S., “Ultrastable bonding of glass with femtosecond laser bursts,” Appl. Opt. 52, 1149-1154 (2013).

[14] [14] Sakakura, M., Shimizu, M., Shimotsuma, Y., Miura, K. and Hirao, K., “Temperature distribution and modification mechanism inside glass with heat accumulation during 250 kHz irradiation of femtosecond laser pulses,” Appl. Phys. Lett. 93, 231112 (2008).

[15] [15] Yoshino, T., Matsumoto, M., Ozeki, Y. and Itoh, K., “Energy-dependent temperature dynamics in femtosecond laser microprocessing clarified by Raman temperature measurement,” Proc. SPIE 8249, 82491D (2012).

[16] [16] Hermans, M., Gottmann, J. and Schiffer, A., “In-situ diagnostics on fs-laser induced modification of glasses for selective etching,” Proc. SPIE 8244, 82440E (2012).

[17] [17] Shimizu, M., Sakakura, M., Ohnishi, M., Shimotsuma, Y., Nakaya, T., Miura, K. and Hirao, K., “Mechanism of heat-modification inside a glass after irradiation with high-repetition rate femtosecond laser pulses,” J. Appl. Phys. 108, 073533 (2010).

[18] [18] Vogel, A., Novak, J., Hüttman, G. and Paltauf, G., “Mechanisms of femtosecond laser nanosurgery of cells and tissues,” Appl. Phys. B 81, 1015-1047 (2005).

[19] [19] Sudrie, L., Couairon, A., Franco, M., Lamouroux, B., Prade, B., Tzorzakis, S. and Mysyrowicz, A., “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89, 186601 (2002).

[20] [20] Arnold, C. L., Heisterkamp, A., Ertmer, W. and Lubatschowski, H., “Computational model for nonlinear plasma formation in high NA micromachining of transparent materials and biological cells,” Opt. Express 15, 10303-10317 (2007).

[21] [21] Popov, K. I., McElcheran, C., Briggs, K., Mack, S. and Ramunno, L., “Morphology of femtosecond laser modification of bulk dielectrics,” Opt. Express 19, 271-282 (2011).

[22] [22] Jiao, J. and Guo, Z., “Modeling of ultrashort pulsed laser ablation in water and biological tissues in cylindrical coordinates,” Appl. Phys. B 103, 195-205 (2011).

[23] [23] Rayner, D. M., Naumov, A. and Corkum, P. B., “Ultrashort pulse non-linear optical absorption in transparent media,” Opt. Express 13, 3208-3217 (2005).

[24] [24] Burakov, I. M., Bulgakova, N. M., Stoian, R., Mermillod-Blondin, A., Audouard, E., Rosenfeld, A., Husakou, A. and Hertel, I. V., “Spatial distribution of refractive index variations induced in bulk fused silica by single ultrashort and short laser pulses,” J. Appl. Phys. 101, 043506 (2007).

[25] [25] Sun, M., Eppelt, U., Russ, S., Hartmann, C., Siebert, C., Zhu, J. and Schulz, W., “Numerical analysis of laser ablation and damage in glass with multiple picosecond laser pulses,” Opt. Express 21, 7858-7867 (2013).

[26] [26] Kennedy, P. K., “A first-order model for computation of laser-induced breakdown thresholds in ocular and aqueous media: Part I – Theory,” IEEE J. Quant. Electron. 31, 2241-2249 (1995).

[27] [27] Yoshino, F., Shah, L., Fermann, M., Arai, A. and Uehara, Y., “Micromachining with a high repetition rate femtosecond laser,” J. Laser Micro/Nanoeng. 3, 157-162 (2008).

[28] [28] Schott D263 Material Information Sheet http://www.schott.com/advanced_optics/english/download/.

[29] [29] Sun, Q., Jiang, H., Liu, Y., Zhou, Y., Yang, H. and Gong, Q., “Relaxation of dense electron plasma induced by femtosecond laser in dielectric materials,” Chin. Phys. Lett. 23, 189-192 (2006).

[30] [30] Gulley, J. R., Winkler, S. W., Dennis, W. M., Liebig, C. M. and Stoian, R., “Interaction of ultrashort-laser pulses with induced undercritical plasmas in fused silica,” Phys. Rev. A 85, 013808 (2012).

[31] [31] Shimizu, M., Sakakura, M., Ohnishi, M., Yamaji, M., Shimotsuma, Y., Hirao, K. and Miura, K., “Threedimensional temperature distribution and modification mechanism in glass during ultrafast laser irradiation at high repetition rates,” Opt. Express 20, 934-940 (2012).

[32] [32] Hoehm, S., Rosenfeld, A., Krueger, J. and Bonse, J., “Femtosecond laser-induced periodic surface structures on silica,” J. Appl. Phys. 112, 014901 (2012).

[33] [33] Englert, L., Rethfeld, B., Hagg, L., Wollenhaupt, M., Sarpe-Tudoran, C. and Baumert, T., “Control of ionization processes in high band gap materials via tailored femtosecond pulses,” Opt. Express 15, 17855-17862 (2007).

[34] [34] Nagata, T., Kamata, M. and Obara, M., “Optical waveguide fabrication with double pulse femtosecond lasers,” Appl. Phys. Lett. 86, 251103 (2005).

[35] [35] Wortmann, D., Ramme, M. and Gottmann, J., “Refractive index modification using fs-laser double pulses,” Opt. Express 15, 10149-10153 (2007).