The role of the optical filamentation of ultra-short infrared pulses at 800nm in the inscription of highly reflective and low loss fundamental order fiber Bragg gratings is investigated. The onset of the filamentation process is first evidenced through the observation of the spectra of both supercontinuum generation and plasma emission as well as through the precise measurement of the plasma-induced refractive index change. Typical samples of FBG obtained with this approach are presented.
©2011 Optical Society of America
The fabrication of fiber Bragg gratings (FBGs) based on the use of ultraviolet (UV) exposure either holographically  or through a phase mask  has significantly evolved during the two last decades. The underlying physical process relies on the activation of a resonant defect associated with the presence of germanium in the fiber core. More recently, refractive index modifications of a different type (i.e. non-resonant) have been produced in various transparent materials based on the use of intense infrared femtosecond pulses. This approach has shown great promise for the fabrication of versatile photonic structures, such as waveguides, couplers, and gratings, in two or three dimensions [3,4]. For instance, long period gratings were fabricated by focusing infrared pulses in single mode fibers using the point-by-point (PbP) irradiation technique . Index changes as high as 6 x 10−3 were achieved in standard Ge-doped telecom fibers . This technique was further developed and the writing of FBGs was also demonstrated . An alternative approach based on the interference of ultrashort pulses was developed to inscribe periodic structures in glass through a precise control of the interference pattern. Surface relief holographic gratings were first recorded on silica glass by interfering two infrared femtosecond pulsed beams . The use of a phase-mask was further demonstrated to be an efficient and robust method to write FBGs using 266nm , 400nm  and 800nm  femtosecond pulses. Some interesting properties of this approach were demonstrated such as the capability of writing FBGs in various transparent materials such as pure and germanium-doped silica, phosphate, sapphire, lithium niobate, borosilicate , doped and undoped fluoride , germanate, tellurite  and more recently in ytterbium-doped silica  for high-power fiber laser purposes. The high refractive index modulation (up to 5x10−3) resulting from this approach allowed the writing of high-reflectivity (95%) ultrabroadband (310 nm) FBGs in standard silica fibers . FBGs of type I associated with glass densification and type II associated with induced damage were fabricated in silica fiber using the phase-mask technique and infrared femtosecond pulses under different input beam energies .
In parallel to this, the optical filamentation of intense femtosecond pulses has attracted a lot of interest in the scientific community. The possibility of self-guiding a laser beam in air confined at a scale of 80 µm over 20 meters was first demonstrated by Braun et al  and was explained by a balance between Kerr self-focusing and defocusing by laser-induced electron plasma. It was further proposed that such phenomenon could be interpreted as the result of a moving focus along the filament . The emission of white light intimately associated with the filamentation process was also interpreted as the result of nonlinear effects that cause the conical emission of light . The filamentation of infrared femtosecond pulses in condensed matter was also investigated. The self-guided propagation of the beam was first observed in fused silica  and the resulting plasma-channel was associated with a permanent refractive index modification of type I inside of the bulk silica . It was further reported that depending on the focusing conditions and the input beam energy, different regimes can take place. Accordingly, a filamentation regime resulting in a smooth refractive index modification (type I) is likely to occur for loose focusing conditions whereas damage is generally induced inside of the bulk (type II) for tight focusing . A detailed description of the filamentation process and its consequences on optical media was also reported . When the input pulse power is sufficiently large compared to the critical power for self-focusing, the multi-filamentation process takes place resulting in a generally erratic spatial distribution of the filaments. However, it was found that the input beam ellipticity could affect the positioning of each filament  so that the use of a highly elliptical input beam could lead to the formation of a quasi-periodic arrangement of the filaments . Based on this idea, it was shown that the multi-filamentation process could be precisely controlled by superimposing an interference pattern to the elliptical input beam with the use of a 1-D diffractive element. In this manner permanent refractive index modifications were induced in fused silica blocks with a perfectly controlled pitch size of 47 µm .
In this paper, we demonstrate that the multi-filamentation of a highly elliptical focused beam can be precisely controlled in a periodic fashion using an interference pattern of short period (~0.5 µm). Loose focusing (i.e. f = 112mm) of ultrashort (34 fs) infrared femtosecond pulses at 1kHz in conjunction with a phase-mask will be shown to produce low loss and high-reflectivity first-order FBGs at 1.55 µm in standard SMF28 fibers as well as in fluoride fibers.
A Ti-sapphire regenerative amplifier system (Coherent, model Legend-HE) that produced pulses with 3.5 mJ of energy at 1 kHz repetition rate with a central wavelength of λ = 806 nm was used. Temporal width of the Fourier-transform limited pulses was measured to be ~34 fs. The pulse width was enlarged to ~60 fs due to the group velocity dispersion when passing through the beam steering optical components. The laser beam was enlarged to ~8.5 mm x 20 mm size (at 1/e2) thanks to a cylindrical telescope. The beam was then focused using a cylindrical lens with a focal length of 112 mm through a uniform silica phase mask onto the fiber positioned along the focal line and in close proximity to the phase mask. The uniform phase mask with a pitch of 1070nm was fabricated by holographic lithography on a UV-grade fused silica substrate. The zero order of diffraction at 800 nm for polarization perpendicular to the grooves is 14%. Such a bad zero-order nullification is hindered by the group velocity walk-off effect  that spatially separates the zero from the ± 1 orders after a short propagation distance of the fs laser pulses beyond the phase-mask. A pure two beam interference pattern can be obtained after a propagation of about 50-75 μm from the phase-mask. We place the fiber at 125 μm from the phase mask to ensure that the walk-off condition is respected. Based on Gaussian beam optics, the width of the focal spot is 2w ~1.27f λ/2w0 ~14 μm, where λ is the wavelength, f is the focal length, and w0 represents the input beam radius (8.5mm at 1/e2) perpendicular to the fiber axis. Figure 1 shows the sketch of the experimental setup used to write the FBGs.
Transmission and reflection spectra were measured in real-time using a broadband ASE light source together with an optical circulator and spectrum analyzer. After exposure, the fibers were cut through the center of the gratings and an optical fiber analyzer (NR-9200HR, EXFO) operating at 657 nm based on the refracted-near-field (RNF) technique was utilized to measure the cross-sectional (i.e. across the cleaved end-face) index profile averaged over a depth of approximately 1200 grating periods. The variation of refractive index modulation as a function of the annealing temperature was also measured using a specially designed fiber optic oven (ASP-500C).
3. Analysis of the Filamentation Process in a Coreless Fiber
In order to characterize the photo-induced refractive index change as well as its link to the filament formation process, a coreless silica-pure multimode fiber (Thorlabs, BFL48-200) with a diameter of 200 µm was first used. The basic idea here was to preserve the basic fiber geometry while avoiding any interference effect from the fiber core on the filament formation.
3.1 Spectra Emitted during Filamentation Process
Two distinct types of light emission are associated with the filamentation process in condensed matter: supercontinuum generation which is almost collinear with the pump pulse and plasma emission  which results from electron recombination within the filament. These two types of light emission were thus analyzed as a function of the input pulse energy. Supercontinuum light emission was monitored along beam propagation using both a camera and a screen whereas plasma emission was detected from the light guided through the coreless fiberoptic. In both cases an optical spectrum analyzer OSA (Ando AQ-6315A) was used to monitor the spectra. Figure 2 presents the far-field images of the two diffracted beams after their propagation through the 200 µm diameter fiber. Note that a pump rejection filter (absorbing from 750nm to 900nm) was introduced in order to observe only the new frequencies generated by the nonlinear processes. Starting at pulse energies of 0.5 mJ the two diffracted beams (corresponding to orders ± 1 of the phase mask) take the form of a rather typical although distorted conical emission.
The supercontinuum emission was coupled into an OSA so as to measure its spectral extent for different input pulse energies. The resulting spectra are presented in Fig. 3(a) . In this case, the pump rejection filter was removed. Although we note the absence of spectral modulation, which is likely blurred by other nonlinear and dispersive processes, the observed spectral broadening is rather typical of a self-phase modulation (SPM) driven process which becomes more pronounced for energies larger than 0.25mJ. At higher energies one also notes a slightly asymmetrical broadening that is broader on the blue side in agreement with previous reports .
The plasma emission spectra resulting from the filamentation process were also analyzed. Now since plasma emits light in an isotropic fashion, the emitted spectra were simply collected by the 200 µm coreless fiber. Two distinct phenomena are clearly observed in the plasma emission spectra. First, the onset of two broad emission peaks around 450nm and 650nm which occur for pulse energies larger than ~0.25mJ. Note that these two emission peaks were previously reported to be related to point defects that are created through photochemical reactions initiated by the multiphoton absorption process in silica . A second phenomenon which is characterized by an asymmetric broadening (red-shifted) of the laser line is observed for pulse energies larger than ~1.5mJ. In fact, the side-diffused laser line is no longer detected for energies of 1.5mJ and higher which would lead us to think that electron densities significantly increased in the focal region. In fact, our observations are consistent with previous observations according to which the continuum generation process is triggered by a catastrophic self-focusing process involving an SPM process enhanced with multiphoton excitation .
3.2 Direct Observation of the filaments
The dc refractive index change induced by the periodic filaments was characterized using a refracted near-field based instrument (EXFO, NR-9200HR) allowing a spatial resolution of 0.4 µm and a refractive index change resolution of about 5x10−5. Prior to measurement the 200 µm diameter coreless fiber was cleaved in the middle of its exposed region. The measurement performed on the resulting cleaved facet then provides the dc refractive index change averaged over a depth of ~600 µm (i.e. ~1200 grating periods). Two sets of measurements were carried out: 1) as a function of input pulse energy for a fixed exposure time; 2) as a function of exposure time for fixed input pulse energy. Figure 4 presents the results obtained for different input pulse energies at 60 s exposure. A relatively short filament is first observed (marked with a red arrow which also indicates laser propagation direction) for a pulse energy of 0.5mJ. The filament rapidly lengthens while the energy per pulse is increased until a splitting occurs for E≥1.0mJ. A closer view of the bifurcated filament obtained for E = 1.0mJ is shown on Fig. 5(a) .
One first notes that a maximum refractive index change of the order of 2x10−3 is reached prior to the trace splitting. Two asymmetrical branches result from the splitting, with one bearing a significantly reduced refractive index change. Clearly, the trace left by the femtosecond pulse arises from an asymmetrical spatial splitting. At this point, the precise mechanism leading to such pulse break-up is not fully understood. Clearly though, the overall extent of the trace is of the order of 100µm, for the case shown here, whereas its width appears to remain essentially constant throughout the entire propagation distance, therefore evidencing the filamentary nature of the process. In fact, the filament width is always of the order of 1µm and does not appear to vary much, neither along the filament nor as a function of the pulse energy or exposure time. Figure 5(b) shows a typical transverse profile of a filament obtained for 30s exposure at 1.0mJ.
We have performed an exhaustive analysis of the filament parameters for various inscription conditions. The maximum dc refractive index change as well as the filament length are shown on Fig. 6 .
The maximum dc refractive index change is shown to increase with the input pulse energy reaching a maximum at 1.0mJ (Fig. 6(a)). The reason for such roll-off of the refractive index change at higher energy pulses is most probably related to the filament breakup previously discussed that eventually leads to three sub-filaments at 2mJ (cf. Fig. 4). In contrast, we note that the filament length increases monotonically with pulse energy over the whole range of values (cf. Fig. 6(b)). Interestingly though, filament length does not appear to depend on exposure (Fig. 6(d)) i.e. from the very beginning of exposure, a full-length filament is formed, from which a refractive index trace eventually builds up through the photosensitivity process. From Fig. 6(c) one can infer that this underlying photosensitivity process starts to saturate, for the current inscription conditions, for exposure times of the order of 60s. A few interesting observations follow from the previous results. First, there exists a relatively narrow range in pulse energy that will lead to both an appreciable refractive index change while maintaining the filament at a reasonably short length. In fact, for practical reasons pertaining to subsequent fiber mechanical robustness, the filament should ideally be located so as to avoid touching fiber surfaces (cf. section 4). For the actual conditions of our experiment, the pulse energy range would therefore lie between 0.5 and 1.0 mJ and exposure time limited to less than 60s. A second observation relates to the filament width which is significantly smaller than a typical fiber core. Now, it is important to recall that this ~1 µm width is a value that is imposed by light-matter interaction and not by the focusing conditions (cf. section 5). A full interaction of the filament with the core mode therefore requires that the latter be appropriately scanned across the core area. Finally, it should be stressed that although the traces shown here correspond to the average dc part of the periodic refractive index change that is inscribed in the fiber, it is intimately related to the ac counterpart that is responsible for the actual FBG writing. This aspect will be exemplified in the following.
4. Filamentation in a Core Fiber
The filamentation process previously introduced for the ideal case of a coreless fiber is likely to be perturbed by various factors when a standard fiber is used. In this section we address some of these perturbing factors such as the fiber geometry and the presence of the core. Regarding the fiber geometry, it is reasonable to assume that the dioptric or lensing effect from the fiber is playing a role in the transverse focusing of the beam. According to basic calculations, this effect would reduce the beam by a factor of two over a distance corresponding to the fiber diameter. So, it will be shown in the next section that this lensing effect arising from the fiber cylindrical geometry is overwhelmed by the highly nonlinear self-focusing effect. Accordingly, we did not observe significant difference between the position of the filament in the 200µm diameter coreless fiber as compared to those obtained with the standard 125 µm diameter fibers. In fact, it was observed that under the focusing conditions described above, the maximum refractive index change occurs at about 60 µm from the input fiber face (see for example Fig. 4). This position fortunately corresponds to the core location in a 125 µm diameter fiber.
We have thus exposed standard SMF28 fibers under similar inscription conditions. Prior to exposure, the focus was precisely positioned with respect to the fiber core. We exposed SMF28 fiber samples to different input pulse energies and measured the induced dc refractive index change in the same manner as described for the coreless fiber case. Figure 7 shows the photo-induced refractive index variations for input energies of 0.5, 1.25 and 2.0 mJ. Note that the size of the elliptical beam incident on the cylindrical focusing lens was slightly smaller than that used in the coreless fiber case (i.e 5mm X 7.5mm). A relatively short filament is first observed for a pulse energy of 0.5mJ. Now this filament is not positioned so as to overlap with the fiber core so that it does not actually contribute to the inscription of an FBG but simply to a periodic modulation of the refractive index within the cladding. (Note that since the core and the cladding are both photosensitive to intense femtosecond pulses (as opposed to the UV radiation case) the threshold of the underlying photosensitive process does not necessarily correspond to the experimentally observed onset of FBG writing.) For a pulse energy of 1.25mJ the filament length is of the order of 70 µm but is barely touching the core. At 2.0mJ multi-filamentation is taking place at the fiber’s rear surface but one of the sub-filaments is subsequently hitting the core and vanishing soon after. Now it was observed that the fiber samples are weakened when the filament reaches the glass surface so that we can conclude that, for the current focusing geometry, energy per pulse should remain of the order of 1mJ in agreement with the results previously obtained for the coreless fiber. A corollary to this is that the filament propagation is affected by the core which contributes to reduce its length. This phenomenon is actually enhanced in the case of a hydrogen-loaded core as shown on Fig. 8 .
One sees that upon crossing the fiber core the filament is not only broadened but essentially stopped by it. The presence of germanium in the fiber core would most likely explain this behavior. Accordingly, one notes that the refractive index change is of the order of 10x10−3 in the core area whereas it is limited to 5x10−3 in the cladding supporting the idea that both glass densification and color centers are contributing to the femtosecond pulse-induced photosensitive process.
It is important to recall that the previous results were obtained under loose focusing conditions involving a 112 mm focal length cylindrical lens. Under such conditions the beam waist (2wy) actually impinging on the fiber along the y-axis was of the order of 20 µm. It is thus through a strong self-focusing process that the beam actually reduces to about 2 µm within a few tens of µm of highly nonlinear propagation within the glass, as depicted on Fig. 9 . This ten-fold reduction in size of the beam evidently results in a ten-fold increase in intensity. Note that the 1 µm width of the trace of refractive index change is consistent with such a 2 µm optical beam, recalling that the underlying nonlinear absorption process is scaling with the sixth power of the intensity.
Interestingly, the filamentation process is self-regulated so that light intensity is clamped to a certain value that essentially prevents catastrophic optical breakdown . It is essentially for this reason that this process leads to a smooth refractive index change (i.e. safe from optical damage) resulting in type I FBG with minimal losses. This point will be further illustrated at section 6. But the most important point is that, because of the periodic constraints imposed on the electric field along the z axis by the diffractive element, the previous self-focusing process is actually forced to occur along one dimension only, that is within each interference fringe. Figure 10 illustrates the interference fringe pattern that results from this 1D self-focusing.
The fiber exposed area is thus characterized by a series of periodically spaced and elliptically shaped optical filaments. In fact, we have checked by side diffraction inspection that the spacing of the resulting FBG planes is indeed of the order 0.5 µm corresponding to half the phase mask pitch, thus confirming that first-order gratings are indeed inscribed. To interpret the previous results we first note that our set-up is somehow similar to that used by Barthelemy et al. for the first demonstration of spatial solitons . In fact, within each fringe the 1D Nonlinear Shroedinger equation should apply leading initially to spatial self-compression under conditions for high order soliton. Now, based on simple assumptions, one can establish that the soliton order is in the range of 4-6 in the central portion of the beam which would readily lead to a ten-fold spatial pulse compression over distances of the order of a few tens of µm . Note that as we move away from beam maximum along the z axis, the energy contained in a given fringe is decreasing down below the threshold intensity for such nonlinear pulse compression (Fig. 10). As a result, the plasma density required for glass modification cannot be reached and inscription stops. Accordingly, it should be noted that a complete description of this problem would require that nonlinear terms arising from the electron plasma be also accounted for in a generalized version of NLS. It is therefore not appropriate to interpret the filament splitting that we observed simply in terms of high order soliton propagation.
6. FBGs In Silica and Fluoride Fibers based on the Filamentation Process
The inscription of an FBG was used to characterize the maximum refractive index modulation attainable with our set-up. The FBG exposure length was limited to L = 10mm (over a total length of 20mm at 1/e2) with a calibrated slit to obtain an almost uniform intensity profile in order to obtain a regular FBG spectral shape. Note that the FBGs presented in this section were inscribed using the same experimental conditions as for the coreless experiments (cf. section 2). Since the measured filament is about 1 µm in width as compared to the 8 µm fiber core diameter, the focusing lens was mounted on a piezoelectric translation stage and the beam was scanned transversally to the fiber section at a frequency of 0.05 Hz with scanning amplitude set to 20 µm. This ensured a maximal overlap between the grating and the propagating mode to be reflected. According to the results of the previous sections, the pulse energy was set to 1.0mJ to obtain the maximal refractive index change localized at the fiber core position and we exposed two pieces of SMF28 fibers, one hydrogen-free and the other hydrogen-loaded to measure the maximum refractive index modulation attainable in both cases. Figure 11(a) and 11(b) presents the reflection spectra of saturated FBGs written in both hydrogen-free and hydrogen-loaded fibers written under the same experimental conditions.
Maximum refractive index modulations of 2.7x10−3 and 5.5x10−3 are obtained in hydrogen-free and hydrogen-loaded fibers respectively. One can observe that the maximum refractive index modulation (ac component) in hydrogen-free SMF28 fiber is close to the maximum dc refractive index change obtained under the same exposure conditions in pure silica fibers (cf. Fig. 6(c)). We also proceeded to a thermal annealing of FBGs inscribed in both hydrogen-loaded and hydrogen-free fiber using a fiber optic oven up to 500°C. The annealing curves are presented at Fig. 12 . The normalized refractive index modulation (inferred from the FBG transmission spectrum) corresponding to the H2-loaded case shows a rapid drop for temperatures up to 300°C whereas, beyond this temperature, the two curves decrease with the same slope. This would indicate that a fraction of about 40% of the refractive index change in the H2-loaded case arises from color centers. Also note that 80% of the index modulation remains at 500°C in the unloaded case which is consistent with glass densification pertaining to Type I grating.
In order to inscribe improved quality FBGs, the length of the exposure beam was increased from 20mm to 50mm and the corresponding input beam energy was consequently increased from 1.0mJ to 2.5mJ in order to maintain the same writing conditions. The FBG exposure length was limited to L = 25mm (over a total length of 50mm at 1/e2) with a calibrated slit to obtain an almost uniform intensity profile in order to obtain a uniform FBG spectral shape.
Figure 13(a) shows the reflection and transmission spectra of an unsaturated FBG written in a hydrogen-free SMF28 fiber for an exposure time of 10s and input pulse energy of 2.5mJ. An FBG was also inscribed under the same exposure conditions in a 2000ppm Tm3+-doped ZBLAN fiber for 20s. The corresponding transmission spectrum is presented in Fig. 13(b).
The gray losses of these two −50dB reflectivity FBGs are lower than 0.02dB and 0.35 dB for the silica and the fluoride fibers respectively. Also note that, as a direct consequence of the photosensitivity of the cladding to femtosecond pulses, cladding-mode losses remain very low with less than 1.0dB and 0.5dB for the silica and the fluoride fibers respectively. The preceding results represent quite well the huge potential of femtosecond pulses in the filamentation regime to write high quality first-order FBGs in various materials.
We have provided a new physical insight on the 1D filamentation process allowing for the inscription of high quality first-order FBGs with femtosecond pulses and a phase mask. Average photo-induced dc and ac refractive index changes of the order of 5x10−3 were shown to arise from this process. The validity of the approach is illustrated with the inscription of −50dB FBGs in both silica and fluoride glass fibers.
This research was supported by the Canadian Institute for Photonic Innovations (CIPI), the Fonds Quebecois de la Recherche sur la Nature et les Technologies (FQNRT), the Natural Science and Engineering Research Council of Canada (NSERC) and the Canada Foundation for Innovation (CFI). The authors would also like to thank Prof. See Leang Chin for helpful discussions, Martin Laprise and Michael Dallaire for technical support.
References and links
2. K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett. 62(10), 1035–1037 (1993). [CrossRef]
4. 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(3-6), 333–339 (2001). [CrossRef]
5. Y. Kondo, K. Nouchi, T. Mitsuyu, M. Watanabe, P. G. Kazansky, and K. Hirao, “Fabrication of long-period fiber gratings by focused irradiation of infrared femtosecond laser pulses,” Opt. Lett. 24(10), 646–648 (1999). [CrossRef] [PubMed]
6. E. Fertein, C. Przygodzki, H. Delbarre, A. Hidayat, M. Douay, and P. Niay, “Refractive-index changes of standard telecommunication fiber through exposure to femtosecond laser pulses at 810cm,” Appl. Opt. 40(21), 3506–3508 (2001). [CrossRef] [PubMed]
7. A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Direct writing of fiber Bragg gratings by femtosecond laser,” Electron. Lett. 40(19), 1170–1172 (2004). [CrossRef]
8. K. I. Kawamura, N. Sarukura, M. Hirano, and S. Hosono, “Holographic encoding of fine-pitched micrograting structures in amorphous SiO2 thin films on silicon by a single femtosecond laser pulse,” Appl. Phys. Lett. 78(8), 1038–1040 (2001). [CrossRef]
9. A. Dragomir, D. N. Nikogosyan, K. A. Zagorulko, P. G. Kryukov, and E. M. Dianov, “Inscription of fiber Bragg gratings by ultraviolet femtosecond radiation,” Opt. Lett. 28(22), 2171–2173 (2003). [CrossRef] [PubMed]
10. M. Bernier, R. Vallée, B. Morasse, C. Desrosiers, A. Saliminia, and Y. Sheng, “Ytterbium fiber laser based on first-order fiber Bragg gratings written with 400 nm femtosecond pulses and a phase-mask,” Opt. Express 17(21), 18887–18893 (2009). [CrossRef] [PubMed]
11. S. J. Mihailov, C. W. Smelser, P. Lu, R. B. Walker, D. Grobnic, H. Ding, G. Henderson, and J. Unruh, “Fiber bragg gratings made with a phase mask and 800-nm femtosecond radiation,” Opt. Lett. 28(12), 995–997 (2003). [CrossRef] [PubMed]
12. S. J. Mihailov, D. Grobnic, C. W. Smelser, P. Lu, R. B. Walker, and H. Ding, “Induced Bragg gratings in optical fibers and waveguides using an ultrafast infrared laser and a phase mask,” Laser Chem. 2008, 416251 (2008). [CrossRef]
13. M. Bernier, D. Faucher, R. Vallée, A. Saliminia, G. Androz, Y. Sheng, and S. L. Chin, “Bragg gratings photoinduced in ZBLAN fibers by femtosecond pulses at 800 nm,” Opt. Lett. 32(5), 454–456 (2007). [CrossRef] [PubMed]
14. R. Suo, J. Lousteau, H. Li, X. Jiang, K. Zhou, L. Zhang, W. N. MacPherson, H. T. Bookey, J. S. Barton, A. K. Kar, A. Jha, and I. Bennion, “Fiber Bragg gratings inscribed using 800nm femtosecond laser and a phase mask in single- and multi-core mid-IR glass fibers,” Opt. Express 17(9), 7540–7548 (2009). [CrossRef] [PubMed]
15. M. Bernier, Y. Sheng, and R. Vallée, “Ultrabroadband fiber Bragg gratings written with a highly chirped phase mask and infrared femtosecond pulses,” Opt. Express 17(5), 3285–3290 (2009). [CrossRef] [PubMed]
16. C. W. Smelser, S. J. Mihailov, and D. Grobnic, “Formation of Type I-IR and Type II-IR gratings with an ultrafast IR laser and a phase mask,” Opt. Express 13(14), 5377–5386 (2005). [CrossRef] [PubMed]
18. A. Brodeur, C. Y. Chien, F. A. Ilkov, S. L. Chin, O. G. Kosareva, and V. P. Kandidov, “Moving focus in the propagation of ultrashort laser pulses in air,” Opt. Lett. 22(5), 304–306 (1997). [CrossRef] [PubMed]
19. O. G. Kosareva, V. P. Kandidov, A. Brodeur, C. Y. Chien, and S. L. Chin, “Conical emission from laser plasma interactions in the filamentation of powerful ultrashort laser pulses in air,” Opt. Lett. 22(17), 1332–1334 (1997). [CrossRef] [PubMed]
20. S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86(24), 5470–5473 (2001). [CrossRef] [PubMed]
21. K. Yamada, W. Watanabe, T. Toma, K. Itoh, and J. Nishii, “In situ observation of photoinduced refractive-index changes in filaments formed in glasses by femtosecond laser pulses,” Opt. Lett. 26(1), 19–21 (2001). [CrossRef] [PubMed]
22. N. T. Nguyen, A. Saliminia, W. Liu, S. L. Chin, and R. Vallée, “Optical breakdown versus filamentation in fused silica by use of femtosecond infrared laser pulses,” Opt. Lett. 28(17), 1591–1593 (2003). [CrossRef] [PubMed]
23. S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Theberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83(9), 863–905 (2005). [CrossRef]
25. D. Majus, V. Jukna, G. Valiulis, and A. Dubietis, “Generation of periodic filament arrays by self-focusing of highly elliptical ultrashort pulsed laser beams,” Phys. Rev. A 79(3), 033843 (2009). [CrossRef]
26. J. P. Bérubé, R. Vallée, M. Bernier, O. G. Kosareva, N. Panov, V. Kandidov, and S. L. Chin, “Self and forced periodic arrangement of multiple filaments in glass,” Opt. Express 18(3), 1801–1819 (2010). [CrossRef] [PubMed]
27. C. W. Smelser, D. Grobnic, and S. J. Mihailov, “Generation of pure two-beam interference grating structures in an optical fiber with a femtosecond infrared source and a phase mask,” Opt. Lett. 29(15), 1730–1732 (2004). [CrossRef] [PubMed]
28. A. Brodeur and S. L. Chin, “Ultrafast white-light continuum generation and self-focusing in transparent condensed media,” J. Opt. Soc. Am. B 16(4), 637–650 (1999). [CrossRef]
29. H. B. Sun, S. Juodkazis, M. Watanabe, S. Matsuo, H. Misawa, and J. Nishii, “Generation and recombination of defects in vitreous silica induced by irradiation with a near-infrared femtosecond laser,” J. Phys. Chem. B 104(15), 3450–3455 (2000). [CrossRef]
30. W. Liu, S. Petit, A. Becker, N. Aközbek, C. M. Bowden, and S. L. Chin, “Intensity clamping of a femtosecond laser pulse in condensed matter,” Opt. Commun. 202(1-3), 189–197 (2002). [CrossRef]
31. A. Barthelemy, S. Maneuf, and C. Froehly, “Soliton propagation and self-trapping of laser beams by a Kerr optical nonlinearity,” Opt. Commun. 55(3), 201–206 (1985). [CrossRef]
32. G. P. Agrawal, Applications of Nonlinear Fiber Optics (Academic Press, 2001).