The formation of two grating types in SMF-28 fiber by focusing 125 fs, 0.5–2 mJ pulses through a phase mask onto a fiber sample is studied. The first type, specified as type I-IR, occurs below the damage threshold of the medium. The scaling behavior of the type I-IR gratings with field intensity and annealing properties suggests that their formation is related to nonlinear absorption processes, possibly resulting in color center formation. The second type, denoted as type II-IR, occurs coincidentally with white light generation within the fiber. These type II-IR gratings are stable at temperatures in excess of 1000 °C and are most likely a consequence of damage to the medium following ionization.
©2005 Optical Society of America
Femtosecond pulse duration (fs) IR lasers have proven themselves to be useful sources for non-linear laser-material processing for photonic device fabrication. Direct-write imbedded waveguides with large induced index changes (Δn) were made in bulk and Ge-doped silica using these sources . Recently two regimes of ultrafast IR induced Δn in bulk silica were identified, which in terms of their magnitude and annealing properties, were similar to the Δn for UV induced Type I and II fiber Bragg gratings (FBG) . Two power thresholds were established, one for a reversible index change that could be annealed out at 900 °C (referred to in  as Type I damage). The second higher power threshold was the self-focusing threshold above which the induced index change was likely a result of multiphoton and avalanche ionization causing plasma formation. The resultant index change, referred to in  as Type II damage, would not anneal out at 900 °C.
Ultrafast IR pulses have been used to induce index changes in existing waveguides. Long-period grating structures were fabricated in optical fiber . More recently several groups have made retro-reflective FBGs with both IR and UV femtosecond sources and a phase mask [4–8] or via a point-by-point exposure with a femtosecond IR source. When ultrafast IR laser exposures were made with the optical fiber in close proximity to the phase mask (within a fiber diameter), good quality high index modulation FBGs (Δn mod>10-3) were easily achieved in SMF-28 and single mode silica core fibers without special photosensitization such as H2 loading . The resultant FBG structures were retro-reflective higher order gratings that had resonances in the telecommunication band and were stable at temperatures in excess of 1000 °C. White light emission was observed visually during the formation of these gratings. More recently high quality cladding mode suppressed gratings were made with 125 fs pulses and the SMF-28 fiber placed remotely from the phase mask (>3 mm distance) in order to have a pure two-beam interference pattern [10, 11]. In this instance however, no white light generation was observed during the grating formation and when the Ge-doped fiber was loaded with Hydrogen  the FBG had annealing properties similar to standard UV gratings.
In this work, the properties of fiber gratings written with a 125 femtosecond IR laser, a phase mask and different peak intensities at the fiber are presented. Two intensity dependent regimes of induced index change, separated by an intensity value that generates white light, are observed and using a variation of the nomenclature given in  are here referred to as Type I-IR and Type II-IR induced index change. The annealing properties of these two types of gratings are then investigated. Finally, the Type I-IR gratings are shown to scale nonlinearly with the incident field intensity suggesting that the Type I-IR index change process is related to a multiphoton absorption process, possibly resulting in color center generation.
2. Threshold Study
FBGs were written in Ge-doped Corning SMF-28 using 800 nm 125 fs pulses from an amplified Ti:sapphire system with a 1/e Gaussian beam radius, wo, of 3.2 mm and a maximum output energy of ~2 mJ. This system has a maximum repetition rate of 1 kHz. The beam was focused using a cylindrical lens with a focal length f=30 mm through a silica zero-order-nulled phase mask with a period Λm=3.213 µm onto the fiber. The entire incident beam was centered onto the fiber core and then scanned vertically over the fiber cross-section using a piezo-actuated translation stage with a±10 µm travel and a 20 s period. This ensured maximum coverage of the core region. The focus was always adjusted so that it remained at the fiber core. Transmission spectra were obtained using an Erbium source and a spectrum analyzer.
The fiber was placed at a fixed distance of 5 mm from the phase mask such that diffracted order walk-off from the mask would generate a 2-beam interference pattern from only the ±1 orders . For the determination of the Type I-IR threshold, the beam energy was increased until a multiple pulse exposure of ~100,000 pulses produced an index modulation that could be observed by monitoring the grating response in reflection. The pulse energy threshold at which grating formation could be observed was 500 µJ.
Because of the complex nature of the multiple beam interference field that is generated near the mask , it is difficult to obtain a quantitative estimate of the peak intensity in this region. In previous work [4, 5] the peak intensity seen at the fiber was solely based on the Gaussian beam approximation of the focal spot size. In  the beam diameter was mistakenly treated as the beam radius in the calculation. Considering only the focal spot size underestimates the peak intensity seen at the fiber, as the interference between phase mask orders should cause an increase in peak intensity . Improved understanding of the multiple beam interference patterns generated through the interaction of the incident pulse and the phase mask as well as the discovery of order walk off effects has allowed for a much more accurate determination of the field intensity impinging on the fiber. Phase mask order walk off can be exploited to produce an interference pattern comprised of only the ±1 phase mask orders . Considering that the 2-beam interference field produces a less complicated sinusoidal intensity modulation along the fiber length the peak intensity of the field is more easily calculated. The intensity threshold of index change in all-silica core fiber measured with this technique was consistent with studies in bulk media . In this instance transverse walk-off of the diffracted beams was not considered. It is considered in the treatment presented here.
The ±1 orders contained 77.6 % of the beam energy incident on the mask . 5 mm from a 3.21 µm mask, the diffraction angle θ ±1=14.4° produces a lateral separation of 2.6 mm between the peaks of the +1 and -1 order Gaussian beams. In this location (red) the magnitude of the envelope of the ±1 interference field is reduced by a factor of 0.86 as shown in Fig. 1. Also, shown is the envelope after 10 mm (blue). There is a significant reduction in peak intensity. There should also be a reduction in fringe visibility towards the edge of the profile due to incomplete overlap of the orders.
Considering free space Gaussian beam optics, a 30 mm focal length cylindrical lens and an input beam diameter of 6.4 mm results in a focal area of 4.8 µm×6.4 mm=3×10-4 cm2. Due to the tight focusing geometry the impact of the fiber on the spot size is reduced. The error in the pulse energy, focal area and pulse duration was estimated to be ±10%, 6% and 8% respectively. The spot size used here is consistent with observations under a microscope. The intensity threshold for Type I-IR grating formation is then estimated to be:
With the same exposure conditions and set up, only the pulse energy was increased until white light generation occurred coincident with Type II-IR grating formation. The white light generation threshold pulse energy was 1.3 mJ which when using Equation (1) yielded the intensity threshold for Type II-IR grating formation of 4.6±1.1×1013 W/cm2.
In bulk silica, the Gaussian beam peak power threshold levels for Type I and Type II damage observed by Sudrie et al. were 0.6 MW and 1.9 MW respectively . To compare these peak powers with the peak intensities obtained here, one can determine the peak power of the interference field. The peak power of the interference field is the energy contained in the central peak of the interference field divided by the temporal pulse length. The energy contained in the central peak can be determined by comparing the area under the central interference peak to the area under whole interference field. By integrating the field intensity for the central peak, and dividing by the area under the whole curve for ±1 orders that have traveled 5 mm away from the phase mask, it is found that the central peak contains ~1/4100th of the total energy. The peak power is now determined by:
The energy here is the total input energy and τ is the temporal pulse length. The factor of 0.776 determines the total energy contained in the ±1 orders. For an input energy of 1.3 mJ the peak power is 2±0.4 MW. These peak powers compare favorably to the thresholds for Type I and Type II index change found by Sudrie et al.
3. Annealing Study
The next study involved long term annealing of gratings written with and without coincident white light generation. Using a lower power amplifier system (maximum energy of 1 mJ) and the 19 mm focusing lens (beam diameter of 4.9 mm), gratings were fabricated either in close proximity to the mask or at 5 mm distance where two-beam interference would occur. For 125 fs pulses, the complex interference field near the phase mask had high peak intensities. It was therefore possible to create Type II-IR gratings using pulse energies lower than that required to produce Type II-IR gratings in the two-beam interference region. Interestingly this was also the case if an order of magnitude lower intensity Fourier transform-limited 1.6 ps pulse was used. To investigate the annealing characteristics of the Type I and Type II-IR gratings, three grating structures were fabricated. For the Type I-IR grating, the two-beam interference pattern was used with an estimated peak intensity of 3×1013 W/cm2. After several thousand 125 fs pulses the grating with the transmission spectrum shown in Fig. 2 (a) was produced. Using a commercial software package the index modulation corresponding to the -25 dB transmission at λBragg is Δn mod=1.1×10-3. Some assumptions have been made when calculating the index modulation. Firstly the Bragg resonance λBragg is assumed to be a fundamental resonance rather than higher order, and secondly the index modulation is to be a pure sinusoid with a 50/50 duty cycle.
With fibers placed within a fiber diameter of the mask, two Type II-IR FBGs were fabricated with 125 fs and 1.6 ps pulses each with incident pulse energies on the mask of 1 mJ. Transmission spectra for the 125 fs and 1.6 ps gratings are shown in Fig 2 (b) and 2 (c) respectively. The Δn mod were determined to be 1.5×10-3 and 1.7×10-3 respectively. In both cases the gratings were written after exposure to only a few dozen pulses. Considering the spectra presented in Fig. 2 (a), (b) and (c) it should be noted that the observed bandwidth respectively increases. This increase in bandwidth results from a reduction in the effective length of the grating. The strong cladding mode structures are a result of the non-uniform index change across the core as is seen in the observed optical microscope images of the index modulation in the fiber (see Fig 3). The fs and ps Type II-IR gratings shown in Fig. 3 (b) and (c) generally have an irregular structure in regions where the Gaussian beam profile tapers to zero, often resulting in missing grating lines. These missing fringes are a result of the threshold behavior of the Type II-IR induced index change. Being a damage-like process, fiber inhomogeneities or slight variations in beam uniformity can result in certain fringe lines being above threshold while others are not.
The grating growth rate for Type II-IR FBGs using both femtosecond and picosecond pulse durations is extremely rapid. A 30 dB loss at the Bragg wavelength could be achieved with as few as 20 shots. Type I-IR FBGs written with 125 fs pulses at large phase mask-fiber distances (>5 mm) exhibited regular monotonic growth and required several thousands of shots to produce a 30 dB loss at the Bragg wavelength. For picosecond pulses, only extremely small index changes (<10-6) could be produced with phase mask fiber separations in excess of 1 mm.
The annealing curves of the three FBGs are presented in Fig 4. For comparison a Type I-UV FBG was inscribed in H2-loaded SMF-28 fiber (3000 psi, 85 °C, 24 hr) using a frequency doubled Argon ion laser and a phase mask which produced a Δn mod=5×10-4. In Fig. 4 (a) the initial Δn mod of each of the FBGs are normalized to 1. For increasing temperature the Δn mod of the UV grating, denoted by the white circles, is seen to decrease and completely disappear when the grating temperature approaches 1000 °C. As well, the Type I-IR grating (denoted by black squares in Fig.4 (a)) undergoes an order of magnitude reduction in its Δn mod with a final value after 1 hour at 1000 °C of 1×10-4.
For the Type II-IR gratings, some interesting effects are observed. For the Type II-IR device written with 125 fs pulses, denoted by white squares in Fig.4 (a), the Δn mod is seen to increase as the temperature increases. This increase may be a result of the two kinds of index change being written simultaneously. In the peaks of the complex interference pattern, sufficient intensity exists to ultimately ionize the glass in the fiber producing an index change that is durable with temperature. In the valleys of the interference pattern the power is below the Type II-IR threshold however some Type I-IR index change may occur. As the device is annealed the Type II-IR index change remains fixed while the Type I-IR component is erased resulting in a higher Δn mod. For the Type II-IR grating written with the 1.6 ps pulse (denoted by black circles) the initial reduction and then stabilization of the Δn mod is likely due to a component of the initial total index change coming from a Type I-IR index change.
In Fig. 4 (b), long term annealing tests at 1000 °C were performed on the 125 fs and 1.6 ps Type II-IR gratings. The calculated Δn mod determined from the transmission spectra are plotted versus annealing time. After 260 hours there is only a slight reduction in the Δn mod of the fs FBG from its peak value to 1.6×10-3 while for the ps FBG, after an initial erasure during the first 50 hours, the Δn mod stabilized to a value of 1×10-3.
From the intensity threshold measurements and the annealing study it is clear that there are two regimes of ultrafast IR induced index change that appear similar in properties to Type I-UV and Type II-UV induced index change. As no white light generation (self focusing/ionization) is observed for the Type I-IR induced index change, it is likely that the index change is a result of highly nonlinear defect formation resulting from a multi-photon absorption process. These defects, like those associated with Type I-UV exposures, can be annealed out below the tg of the fiber. The Type II-IR gratings appear similar to the Type II-UV “damage” gratings. The white light generation that occurs concurrently with Type II-IR grating formation suggests that these gratings likely result from an ionization process, perhaps triggered by self focusing. Because of the ultrafast nature of the beam however, multiple pulse exposures can result in high index modulation within the fiber without the collateral damage to the interstitial material between high intensity zones. In the single pulse Type IIUV process, which utilizes longer time duration high peak power UV irradiation, there is material disruption around the high intensity portions of the beam producing laser-induced damage at the core-cladding interface . Subsequent UV-irradiation of such damage sites would result in catastrophic failure of the glass.
4. Scaling behavior of Type I-IR gratings.
The mechanism associated with formation of type I-UV fiber Bragg gratings (FBG) in standard telecommunications fiber is the photoexcitation of free electrons, by dissociating the GeO defect, that are subsequently trapped at defect sites. The resulting change in absorption would manifest in a change in the index of refraction via the Kramers-Kronig relations. The original Hill gratings were shown to result from the absorption of two 488 nm photons by the 242 nm GeO absorption band. Later, gratings were commonly written by UV excimer, doubled Argon ion or quadrupled YAG sources. With these lasers the index change is related to the linear absorption of UV photons. For fibers with low Ge dopant concentration the index change produced with an ArF 193 nm excimer source was shown to be the result of a two photon process. It was thought that this was the result of the absorption of two photons to bridge the band gap of silica. The Type I-IR gratings exhibit grating growth and annealing behavior similar to that observed with Type I-UV gratings. It would seem reasonable that the mechanism for fabrication of Type I-IR gratings may result from color center formation as well. The 800 nm wavelength or 1.55 eV photon energy is far removed from the typical bandgap of Ge doped silica or silica, thought to be 7.1 and 9.3 eV, respectively[18,19]. It is important to question whether the formation of Type I-IR Bragg gratings with ultrafast sources results from a highly nonlinear absorption process. This can be determined through a study of the growth of the index modulation as a function of interference field intensity. If a nonlinear absorption process is involved in the index growth, the growth rate should scale with intensity as Ic, where I is the peak interference field intensity and c is a real constant >1.
The exposure conditions are the same as described in the threshold study except that the repetition rate of the laser was maintained at 100 Hz. The transmission loss at the Bragg wavelength was measured continuously (>1 Hz) for input energies of 850, 900, 950, 1000, 1100 and 1200 µJ. Several spectra were taken at each energy increment and the spectral response of the grating was then modeled with a commercial FBG software package. A typical spectrum for a 1200 µJ input energy is shown in Fig. 5.
The grating length typically becomes larger as a function of incident intensity and has been considered in all simulations.
The ripple observed in the growth curves is a result of scanning the beam across the fiber core. The total number of pulses for each sweep is constant. The slope of ~5 in Fig. 6 (b) suggests that the growth rate scales with I5. This suggests a 5 photon absorption process. This behavior seems reasonable in Ge doped silica as 5 photons would bridge a gap of 7.75 eV, comparable to that of Ge doped silica. It is possible, considering the scaling behavior and annealing properties, that this process is similar to that observed during the formation of Type I-UV gratings.
There are some interesting features of the spectrum in Fig. 5 (a) that are important. As has been reported previously there is commonly a significant reduction in the cladding modes on the short wavelength side of the transmission spectrum. If the 1/e beam diameter of the Gaussian writing beam is 6.4 mm then a modeled 3 dB bandwidth of ~450 pm and an index modulation of ~4.1×10-4 would be expected for the transmission loss of 27 dB shown in Fig. 5. The wavelength shift would then be ~280 pm for this index change, similar to the actual shift in Fig 5 (b). The actual 3 dB bandwidth in Fig. 5 (a) is ~600 pm, a difference of 150 pm. To model this bandwidth it was necessary to reduce the width of the Gaussian by a factor of 1.4 and increase the index modulation to ~5.7×10-4 for the same transmission loss. As the wavelength shift should scale linearly with the index modulation a wavelength shift of ~400 pm should be expected. Clearly in Fig. 5 (b) the wavelength shift for Type I-IR gratings is only about 300 pm.
The nonlinear dependence of the index change on the input field intensity provides a possible explanation for the observed bandwidth and wavelength shift of Type I-IR gratings. In Fig. 7 (a) there is a comparison between the interference field intensity for the same parameters as Fig. 1 (blue) and the same field raised to the power of 5 (red). The pitch of the grating has been greatly exaggerated in Fig. 7 (a) for clarity. Fig. 7 (b) illustrates the relative area under the central peak for a grating that depends on I (blue) and a grating that depends on I5 (red).
There are two main differences between the profiles in Fig. 7 (a). The width of the profile becomes considerably narrower and the area under each interference peak (Fig. 7 (b)) becomes smaller. The smaller contribution these peaks would have to the average index would cause a reduction in wavelength shift and minimize the impact of the apodization profile on the spectral response. The narrower profile would result in an increase in spectral bandwidth. The nonlinear profile appears to be consistent with the spectral observations. As mentioned earlier the grating profiles appeared to become larger as a function of energy. This observation is not consistent with the nonlinear dependence of the index on the intensity field as the effective length of the grating should remain the same. A threshold effect could also mimic some of the spectral properties of Type I-IR gratings such as the observed wavelength shift. However, the scaling behavior does not seem to be consistent with such a model. It is possible that the grating growth is both nonlinear and threshold like. A direct measurement of the index profile of Type I-IR gratings will help determine the relative contribution of each effect to the structure of the index profile.
Two types of grating structure have been fabricated with an ultrafast laser and a phase mask. These gratings, referred to as Type I-IR and Type II-IR, exhibit different intensity thresholds, annealing behavior and grating structure. White light generation delineates the two grating types. The intensity thresholds and annealing behavior appear to be consistent with previous studies in bulk media  where self focusing triggered the transition. Type I-IR gratings are shown to scale highly nonlinearly with the input field intensity. This coupled with annealing behavior suggests that the grating growth mechanism is related to some form of color center formation. The white light and high temperature stability of Type II-IR gratings suggest that the dominant index change mechanism is that of ionization and damage.
References and Links
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