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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 15 — Jul. 28, 2003
  • pp: 1780–1786
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Fabrication of multi-core structures in an optical fiber using plasma self-channeling

Sung-Hak Cho, Hiroshi Kumagai, and Katsumi Midorikawa  »View Author Affiliations


Optics Express, Vol. 11, Issue 15, pp. 1780-1786 (2003)
http://dx.doi.org/10.1364/OE.11.001780


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Abstract

Fabrication of multi-core structures in an optical multimode fiber was first demonstrated by the scanning of plasma self-channeling excited by a femtosecond (110 fs) laser (λp=790 nm)

© 2003 Optical Society of America

1. Introduction

In the meantime, the interaction between ultrashort, high-intensity laser light and transparent solids has become a major concern since the advent of high-intensity femtosecond lasers. When a high-intensity laser beam is focused into bulk optically transparent materials at higher intensities than the self-focusing threshold, laser-induced solid-density plasma, plasma channeling, and small filaments are produced [4

4. N. Bloembergen, “The influence of electron plasma formation on superbroadening in light filaments,” Opt. Commun. 8, 285–288 (1973) [CrossRef]

]. Plasma channeling is an intensity-dependent nonlinear phenomenon, in which a laser beam is tightly focused and guided for the distance longer than the Rayleigh range. It is attributed to self-focusing due to the intensity-dependent refractive index change and to self-defocusing by the laser-induced plasma [5

5. S-H. Cho, H. Kumagai, I. Yokota, K. Midorikawa, and M. Obara, “Observation of self-channeled plasma formation and bulk modification in optical fibers using a high-intensity femtosecond laser,” Jpn. J. Appl. Phys. 37, L737–739 (1998) [CrossRef]

]. Plasma self-channeling in transparent materials has been known for many years by many researchers. This effect was used to fabricate structures in silica using a nanosecond pulsed laser [6

6. R. Pini, R. Salimbeni, M. Vannini, and Toci. “Mechanism of high aspect ratio high quality drilling on optical substrates by high repetition rate laser” CLEO (Optical Society of America, Washington, D.C., 1994) pp. 385–385

]. Recently, plasma induced structural modifications in bulk dielectrics by tight focusing of femtosecond laser pulses was demonstrated [7

7. K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21, 1729–31 (1996). [CrossRef] [PubMed]

]. Although the physical mechanisms responsible for infrared photosensitivity are still under investigation, many researchers have reported the selective induction of refractive-index changes in silica glass with tightly focused femtosecond laser pulses. This effect allows the precise fabrication of photonic devices such as waveguides, couplers, and gratings [8

8. E. N. Glezer, M. Milosavljevic, L. Huang, R. J. Finlay, T. -H. Her, J. P. Callan, and E. Mazur, “Three-dimensional optical storage inside transparent materials,” Opt. Lett. 21, 2023–2025 (1996). [CrossRef] [PubMed]

14

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

]. The integration technique of photonic devices in silica glass will open a new way for optical communication and information processing.

In this letter, we first report on the experimental results of the fabrication of multi-core structures with bulk refractive index modification in optical fibers using the scanning of plasma self-channeling excited by a high-intensity femtosecond laser.

2. Experimental setup

The schematic diagram of the experimental setup for plasma self-channeling-induced refractive index modification is shown in Fig. 1. The laser used in the experiment as an irradiation source is a Ti:sapphire oscillator-amplifier laser system (λp=790 nm) based on the chirped pulse amplification technique with a 110 fs pulse duration, 1 W average output power, and 1 kHz repetition rate. The linearly polarized laser beam has a Gaussian profile and is focused through a quartz lens with the focal-length of 60 mm. It is incident onto the input end face of the optical fiber located away from the breakdown point to avoid optical damage at the input end surface. The step-index optical multimode fibers used are composed of a pure silica core with 100/110 µm (Newport F-MCB-T) and 200/220 µm (Newport F-MCC-T) core/cladding diameter. Optical images of the temporal behavior of plasma self-channeling and photo-induced bulk modification are observed from a direction perpendicular to the optical z-axis by use of a trans-illuminated optical microscope (Leica M420) with a CCD camera (Pixera PVC 100C) connected to the computer.

Fig. 1. Experimental setup

3. Experimental results and Discussion

Intense ultrashort laser excitation of an optically transparent material causes a change in the refractive index of the material which is dependent on the intensity, which is written as n=n 0+n 2 E 2, and can thus induce self-focusing and plasma formation. Where n 0 is a linear refractive index of material and n 2 is a Kerr coefficient. Self-focusing occurs when the focusing effect exceeds the diffraction of the propagating beam. It is evident that self-focusing in silica glasses occurs at input intensity of 1×1012 W/cm2 where n 2 is 3.18×10-16 cm2/W in silica one [15

15. H. Kumagai, S-H. Cho, K. Ishikawa, K. Midorikawa, M. Fujimoto, S. Aoshima, and Y. Tsuchiya “Observation of the complex propagation of a femtosecond laser pulse in a dispersive transparent bulk materials,” J. Opt. Soc. Am. B , 20597–602 (2003) [CrossRef]

]. The complex refractive index variation in the created plasma is quantitatively described by means of the laser-induced plasma index modulation, Δnpl, defined as [16

16. N. Bloembergen, “Laser-induced electric breakdown in solids,” IEEE J. Quantum Electron. QE-10, 375–386 (1974) [CrossRef]

]

Δnpl=2n0e2τmω((1ω2τ3)+i(ω2τ2+ωτ)ω4τ4+1)N0exp{0tη(E)dt},
(1)

where τ is the electron collision time, ω is the light angular frequency, N 0 is the initial plasma density, m is the mass of electron, e is the electronic charge, and η(E) is the possibility per unit time for an electron to undergo an ionizing collision. The plasma formation causes a decrease in the real part of the medium refractive index explained by Eq. (1) and acts as a concave lens. The refractive index variation of the plasma can compensate for the self-focusing due to the optical Kerr effect in order to characterize the diameter of the pulsed laser beam where the permanent structural transformation can be induced. Plasma self-channeling is an intensity-dependent nonlinear phenomenon, in which a laser beam is tightly focused and guided for the distance longer than the Rayleigh range [5

5. S-H. Cho, H. Kumagai, I. Yokota, K. Midorikawa, and M. Obara, “Observation of self-channeled plasma formation and bulk modification in optical fibers using a high-intensity femtosecond laser,” Jpn. J. Appl. Phys. 37, L737–739 (1998) [CrossRef]

].

When the input intensity exceeds 1.5×1012 W/cm2, a uniform plasma channeling with a diameter of 12 – 15 µm was observed and reached a the length of 9 – 10 mm from the first self-focusing point in a bulk silica glass (Fig. 2(a)). The refractive index modification with a diameter of 5 µm was obtained at input intensities of 1.5×1012 W/cm2 after plasma self-channeling occurred (Fig. 2(b) and (c)). When the input intensity was 2.0×1012 W/cm2, the refractive index modification with the diameter of 6 µm and a length of 13 mm was obtained. The bulk modification with a diameter of 8 µm and the length of 15 mm was also formed at input an input intensity of 3.0×1012 W/cm2. In all cases, optical damage at the input end face of the optical fibers was not observed. The variation of the induced bulk modification profile as a function of distance was within 6% in the diameter of refractive index modification. However, when the input intensity exceeded 4.0×1012 W/cm2, the induced modification developed cracks indicating optical damage as seen in Fig. 2(d). The beam intensity of the plasma formation in an optical fluoride fiber reached 1.5×1014 W/cm2, which is the damage threshold for fused silica and several crystals, which is reported in recent damage studies with femtosecond laser pulses [17

17. O. M. Efimov, K. Gabel, S.V Garnov, L. B. Glebov, S. Grantham, M. Richardson, and M. J. Soileau, “Color-center generation in silicate glasses exposed to infrared femtosecond pulses,” J. Opt. Soc. Am. B. 15, 193–199 (1998). [CrossRef]

,18

18. B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Optical ablation by high-power short-pulse lasers,” J. Opt. Soc. Am, 13, 459–468 (1996). [CrossRef]

]. The refractive index modification induced in a pure silica multimode step-index fiber with a 100/110 µm core/cladding diameter reached a length of approximately 9 – 15 mm from the input surface of the optical fiber with the diameters ranging from 5 to 8 µm at input intensities more than 1.5×1012 W/cm2. In general, the length of photoinduced waveguides was limited by propagating dispersion in silica. However, it can be extended by the control of the chirped pulse technology of the irradiated femtosecond laser [19

19. T. Imahoko and M. Obara, “Frequency chirp and pulse width control of internal modification of transparent material using tailored femtosecond laser pulse,” LEOS’01 , 1, 304–305 (2001)

].

Fig. 2. Microscopic side views of plasma self-channeling (a) and photoinduced refractive index modification (b)×100, (c)×1000 magnified views. (d) Optical cracks (optical damage).
Fig. 3. The profiles of laser-induced refractive index in an optical multimode fiber. Before irradiation (a) and after irradiation of the pulses of 1×104 shots at input intensity of 1.5×1012 W/cm2 (b).

The measured refractive index profiles of bulk modification irradiated at input intensities of 1.5×1012 W/cm2 show clearly that the bulk modification provides the double core structure with graded refractive index profiles in an optical multimode fiber (Fig. 3(b)), in relation to the refractive index profile of an unmodified optical fiber (Fig. 3(a)). The graded refractive index profiles were fabricated to be a symmetric form from the center of a multimode fiber and the maximum value of refractive index change (Δn) was measured to be 2.1×10-2. From electron spin resonance (ESR) spectroscopic measurement, before laser irradiation, no defect was observed in an optical fiber (Fig. 4(a)). However, as a result of plasma self-channeling, the defect concentration of SiE’ (≡Si·, E’ center) was significantly increased in refractive index modified regions (Fig. 4(b)). The measured ESR signal in the modified regions agreed well with the absorption spectrum of SiE’, which has an unpaired electron in a dangling, tetrahedral (sp3) orbit of a single silicon which is bound to three oxygens in the glass. Other types of defects beside E’ center were not observed in refractive index modification. According to the electron spin resonance spectroscopic measurement, it was found that the defect concentration of SiE’ centers increased significantly in the modified region in relation to that of the region without modification. The plasma self-channeling would induce the refractive index modification with the defects.

Fig. 4. ESR spectroscopic measurement of optical fibers (a) before laser irradiation (b) after laser irradiation in laser-induced modification.

Figure 5(a) shows the intensity profile of an output beam (He-Ne) transmitted through an optical multimode fiber with a refractive index modification. Figure 5(b) shows the intensity profile of the output beam transmitted through a non-irradiated multimode fiber, which shows the general property of an output beam from an optical multimode fiber. The intensity profile of the output beam transmitted through the modified multimode fiber showed that the bulk modification produced a double core structure.

Fig. 5. The profiles of transmitted laser beam of 633 nm. (a) Profile transmitted from an optical multimode fiber with the modification. (b) Profile transmitted from a non-irradiation multimode fiber.

The measured NA from the refractive index modification was 0.17, in relation to the NA of 0.22 from the non-irradiated multimode one. The propagating loss through the refractive index modification is low (<0.15 dB/cm). It is found that the propagating beam of intensities higher than approximately 80 % is concentrated into the induced refractive index modified region in an optical multimode fiber. This means that the induced refractive index modification provides one core structure in a multimode fiber and serves as a lower-order mode converter for the propagating multimode beams. In our experiments, the maintenance of the polarization of the propagating laser beam and the birefringence effect in a photoinduced waveguide with refractive index modification was not observed.

By scanning an optical fiber using optical X-Y-Z stages, we fabricated multi-core structures in an optical fiber with 200/220 µm diameter which have a two-core and four-core structure (Fig. 6). The separated distance between bulk refractive index modifications with the diameter of 5 µm was 10 µm.

Fig. 6. Fabricated multi-core structures in an optical fiber. (a) Two-core (b) Four-core structure

The results of ESR spectroscopic measurements show that the concentration of defects is increased around the modified region. The formation of color centers changes both the absorption coefficient and density of the medium, leading to the change of refractive index. Although permanent structural changes on the lateral side of optical materials can be induced by the irradiation of the high-energy sources like e-beam, x-ray, or UV laser, the permanent structural transformation along the z-axis in optical fibers that can provide the singlemode waveguide structure is not obtainable by these methods. Although structural transformation along the z-axis could be also achieved by moving the laser focus, the technique of moving the laser focus was limited in distance on the z-axis from the input surface due to the working distance of the used objective lens [8

8. E. N. Glezer, M. Milosavljevic, L. Huang, R. J. Finlay, T. -H. Her, J. P. Callan, and E. Mazur, “Three-dimensional optical storage inside transparent materials,” Opt. Lett. 21, 2023–2025 (1996). [CrossRef] [PubMed]

,10

10. D. Homoelle, W. Wielandy, A. L. Gaeta, E. F. Borrelli, and C. Smith, “Infrared photosensitivity in silica glasses exposed to femtosecond laser pulses,” Opt. Lett. 24, 1311–1313 (1999). [CrossRef]

,14

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

]. In this letter, a novel scheme was used for producing optical waveguides, namely self-focused femtosecond pulse propagation in the optical fiber. The plasma self-channeling over a distance longer than the Rayleigh range provides a useful method to induce the structural transformation along the z-axis in an optical fiber due to characterization of the diameter of the pulsed laser beam. Although the physical mechanisms responsible for infrared photosensitivity in silica glasses are still under investigation, this technique can be applied to the fabrication of permanent structures of singlemode waveguides in optical fibers. The fabrication process relies on self-focusing and subsequent filament formation and can be used to demonstrate waveguides in any transparent glass including fluoride glass fibers. This process is not best suited only for high Kerr coefficient glasses. In general, singlemode fibers have a core diameter ranging from 4 to 10 µm, based on the laser wavelength regime. By considering the diameter of plasma self-channeling-induced refractive index modifications from 5 µm to 8 µm, it could be used as a multi-core structure in the end of an optical multimode fiber that has a single-mode waveguide in the range of the laser wavelengths from visible to infrared of 1.3–1.5 µm for optical communication.

4. Conclusion

As a new fabrication method for multi-core structures in optical multimode fibers, refractive index bulk modifications with the diameter of 5 – 8 µm were demonstrated in an optical fiber by the scanning of plasma self-channeling excited by a femtosecond laser. The plasma self-channeling occurred at an intensity higher than 1.5×1012 W/cm2 and it induced bulk refractive index modifications with color centers. The bulk modification had a graded refractive index profile and made a double core structure in optical multimode fibers. The plasma-induced refractive index modification will be a useful technique for the design of optical devices for such application as optical sensors and optical communications.

References and links

1.

S-H. Cho, H. Kumagai, and K. Midorikawa, “Fabrication of multi-core structure in optical fibers using plasma self-channeling excited by a femtosecond laser,” CLEO/Pacific Rim’01, July, (2001), Chiba (TuB2-4)

2.

J. M. Senior, Optical Fiber Communications: Principles and Practices -2nd. (Prentice Hall, New York, 1992) pp. 160–206

3.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-Mode Photonic Band Gap Guidance of Light in Air,” Science 285, 1537–1539 (1999) [CrossRef] [PubMed]

4.

N. Bloembergen, “The influence of electron plasma formation on superbroadening in light filaments,” Opt. Commun. 8, 285–288 (1973) [CrossRef]

5.

S-H. Cho, H. Kumagai, I. Yokota, K. Midorikawa, and M. Obara, “Observation of self-channeled plasma formation and bulk modification in optical fibers using a high-intensity femtosecond laser,” Jpn. J. Appl. Phys. 37, L737–739 (1998) [CrossRef]

6.

R. Pini, R. Salimbeni, M. Vannini, and Toci. “Mechanism of high aspect ratio high quality drilling on optical substrates by high repetition rate laser” CLEO (Optical Society of America, Washington, D.C., 1994) pp. 385–385

7.

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21, 1729–31 (1996). [CrossRef] [PubMed]

8.

E. N. Glezer, M. Milosavljevic, L. Huang, R. J. Finlay, T. -H. Her, J. P. Callan, and E. Mazur, “Three-dimensional optical storage inside transparent materials,” Opt. Lett. 21, 2023–2025 (1996). [CrossRef] [PubMed]

9.

D. Ashkenasi, H. Varel, A. Rosenfeld, S. Henz, J. Herrmann, and E. E. B. Cambell, “Application of self-focusing of ps laser pulses for three-dimensional microstructuring of transparent materials,” Appl. Phys. Lett. 72, 1442–1444 (1998). [CrossRef]

10.

D. Homoelle, W. Wielandy, A. L. Gaeta, E. F. Borrelli, and C. Smith, “Infrared photosensitivity in silica glasses exposed to femtosecond laser pulses,” Opt. Lett. 24, 1311–1313 (1999). [CrossRef]

11.

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. 26, 93–95 (2001). [CrossRef]

12.

K. Minoshima, A. M. Kowalevicz, E. P. Ippen, and J. G. Fujimoto, “Fabrication of coupled mode photonic devices in glass by nonlinear femtosecond laser materials processing,” Opt. Express 10, 645–652 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-15-645. [CrossRef] [PubMed]

13.

M. Li, M. Ishizuka, X. Liu, Y. Sugimoto, N. Ikeda, and K. Asakawa, “Nanostructuring in submicron-level waveguides with femtosecond laser pulses,” Opt. Commun. 212, 159–163 (2002). [CrossRef]

14.

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

15.

H. Kumagai, S-H. Cho, K. Ishikawa, K. Midorikawa, M. Fujimoto, S. Aoshima, and Y. Tsuchiya “Observation of the complex propagation of a femtosecond laser pulse in a dispersive transparent bulk materials,” J. Opt. Soc. Am. B , 20597–602 (2003) [CrossRef]

16.

N. Bloembergen, “Laser-induced electric breakdown in solids,” IEEE J. Quantum Electron. QE-10, 375–386 (1974) [CrossRef]

17.

O. M. Efimov, K. Gabel, S.V Garnov, L. B. Glebov, S. Grantham, M. Richardson, and M. J. Soileau, “Color-center generation in silicate glasses exposed to infrared femtosecond pulses,” J. Opt. Soc. Am. B. 15, 193–199 (1998). [CrossRef]

18.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Optical ablation by high-power short-pulse lasers,” J. Opt. Soc. Am, 13, 459–468 (1996). [CrossRef]

19.

T. Imahoko and M. Obara, “Frequency chirp and pulse width control of internal modification of transparent material using tailored femtosecond laser pulse,” LEOS’01 , 1, 304–305 (2001)

OCIS Codes
(140.3390) Lasers and laser optics : Laser materials processing
(220.0220) Optical design and fabrication : Optical design and fabrication

ToC Category:
Research Papers

History
Original Manuscript: April 14, 2003
Revised Manuscript: June 24, 2003
Published: July 28, 2003

Citation
Sung-Hak Cho, Hiroshi Kumagai, and Katsumi Midorikawa, "Fabrication of multi-core structures in an optical fiber using plasma self-channeling," Opt. Express 11, 1780-1786 (2003)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-15-1780


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References

  1. S-H. Cho, H. Kumagai, and K. Midorikawa, �??Fabrication of multi-core structure in optical fibers using plasma self-channeling excited by a femtosecond laser,�?? CLEO/Pacific Rim�??01, July, (2001), Chiba (TuB2-4)
  2. J. M. Senior, Optical Fiber Communications: Principles and Practices -2nd. (Prentice Hall, New York, 1992) pp. 160-206.
  3. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, �??Single-Mode Photonic Band Gap Guidance of Light in Air,�?? Science 285, 1537-1539 (1999). [CrossRef] [PubMed]
  4. N. Bloembergen, �??The influence of electron plasma formation on superbroadening in light filaments,�?? Opt. Commun. 8, 285-288 (1973). [CrossRef]
  5. S-H. Cho, H. Kumagai, I. Yokota, K. Midorikawa, and M. Obara, �??Observation of self-channeled plasma formation and bulk modification in optical fibers using a high-intensity femtosecond laser,�?? Jpn. J. Appl. Phys. 37, L737-739 (1998). [CrossRef]
  6. R. Pini, R. Salimbeni, M. Vannini, Toci. �??Mechanism of high aspect ratio high quality drilling on optical substrates by high repetition rate laser�?? CLEO (Optical Society of America, Washington, D.C., 1994) pp. 385-385.
  7. K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, �??Writing waveguides in glass with a femtosecond laser,�?? Opt. Lett. 21, 1729-31 (1996). [CrossRef] [PubMed]
  8. E. N. Glezer, M. Milosavljevic, L. Huang, R. J. Finlay, T. -H. Her, J. P. Callan, and E. Mazur, �??Three-dimensional optical storage inside transparent materials,�?? Opt. Lett. 21, 2023-2025 (1996). [CrossRef] [PubMed]
  9. D. Ashkenasi, H. Varel, A. Rosenfeld, S. Henz, J. Herrmann, and E. E. B. Cambell, �??Application of self-focusing of ps laser pulses for three-dimensional microstructuring of transparent materials,�?? Appl. Phys. Lett. 72, 1442-1444 (1998). [CrossRef]
  10. D. Homoelle, W. Wielandy, A. L. Gaeta, E. F. Borrelli, and C. Smith, �??Infrared photosensitivity in silica glasses exposed to femtosecond laser pulses,�?? Opt. Lett. 24, 1311-1313 (1999). [CrossRef]
  11. C. B. Schaffer, A. Brodeur, J. F. Garcia, E. Mazur, �??Micromachining bulk glass by use of femtosecond laser pulses with nanojoule energy,�?? Opt. Lett. 26, 93-95 (2001). [CrossRef]
  12. K. Minoshima, A. M. Kowalevicz, E. P. Ippen, and J. G. Fujimoto, �??Fabrication of coupled mode photonic devices in glass by nonlinear femtosecond laser materials processing,�?? Opt. Express 10, 645-652 (2002), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-15-645.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-15-645</a>. [CrossRef] [PubMed]
  13. M. Li, M. Ishizuka, X. Liu, Y. Sugimoto, N. Ikeda, K. Asakawa, �??Nanostructuring in submicron-level waveguides with femtosecond laser pulses,�?? Opt. Commun. 212, 159-163 (2002). [CrossRef]
  14. K. Miura, J. Qiu, H. Inoue, T. Mitsuyu, and K. Hirao, �??Photowritten optical waveguides in various glasses with ultrashort pulse laser,�?? Appl. Phys. Lett. 71, 3329-3331 (1997). [CrossRef]
  15. H. Kumagai, S-H. Cho, and K. Ishikawa, K. Midorikawa, M. Fujimoto, S. Aoshima, and Y. Tsuchiya �??Observation of the complex propagation of a femtosecond laser pulse in a dispersive transparent bulk materials,�?? J. Opt. Soc. Am. B, 20 597-602 (2003). [CrossRef]
  16. N. Bloembergen, �??Laser-induced electric breakdown in solids,�?? IEEE J. Quantum Electron. QE-10, 375-386 (1974). [CrossRef]
  17. O. M. Efimov, K. Gabel, S.V.Garnov, L. B. Glebov, S. Grantham, M. Richardson, and M. J. Soileau, �??Color-center generation in silicate glasses exposed to infrared femtosecond pulses,�?? J. Opt. Soc. Am. B. 15, 193-199 (1998). [CrossRef]
  18. B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, �??Optical ablation by high-power short-pulse lasers,�?? J. Opt. Soc. Am, 13, 459-468 (1996). [CrossRef]
  19. T. Imahoko, M. Obara, �??Frequency chirp and pulse width control of internal modification of transparent material using tailored femtosecond laser pulse,�?? LEOS�??01, 1, 304-305 (2001).

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