The interaction of focused 800 nm femtosecond (fs) laser pulses at low (1–45 kHz) and moderate (50–250 kHz) repetition rates with fluoride (ZBLAN-type) bulk glass is investigated in detail. It is shown that at repetition rates lower than ~50 kHz and low pulse energies, the refractive index change induced by pulse filamentation is mainly negative at the irradiated zone. At repetition rates above 50 kHz, structures are formed as a result of the fs laser pulse induced heat accumulation and subsequent melting of the glass. The refractive index profile of the structures produced in this regime is influenced by the laser writing conditions (repetition rate, pulse energy and translation speed). It is shown that waveguides with large circular cross sections and smooth positive index changes can be formed through a precise control of glass exposure. Those waveguides can exhibit low propagation losses (~0.4–2 dB/cm) and are thus good candidates for the development of mid-IR integrated photonic devices. Both absorbed energy and repetition rate thresholds for heat accumulation are determined experimentally.
© 2013 OSA
Direct writing of waveguides and other integrated photonic components inside the bulk of transparent materials by focused femtosecond (fs) laser pulses has attracted much attention in the last decade. Such process is simple, flexible and relatively low-cost, allowing for the fabrication of efficient three-dimensional index-modified structures without the need for a photolithographic process. In addition to mere waveguides [1,2], a variety of devices such as directional couplers, amplifiers, Bragg gratings, and waveguide lasers were successfully integrated in bulk glass using this technique [3–6]. Numerous studies of laser-induced modifications have been carried out in a wide variety of transparent materials, ranging from fused silica to exotic multi-component glasses, and have shown many potential applications for the integrated photonic industry [7–10].
Nonlinear absorption of high intensity focused fs-laser pulses can lead to an increase, decrease or a combination of both, of the refractive index. The dependence of the refractive index spatial profile on fs-laser writing conditions in multi-component glasses was investigated in . It has been observed that glasses defined by a low melting point, slow electronic relaxation and high thermal expansion usually undergo a refractive index decrease due to volume expansion and material rarefaction. Still, several strategies can be used to form efficient waveguides in those types of transparent materials. Through optimization of translation speed, repetition rate and pulse energy, Osellame et al.  reported the formation of a smooth positive index change in co-doped phosphate glass. Furthermore, a recent study has shown that a temporally shaped burst of fs-pulses produced by a moderate repetition rate laser can invert the regular material response resulting in a substantial refractive index increase .
Zirconium-fluoride glasses, from the broader fluoride glass family, represent an attractive material possessing a reduced phonon energy allowing for an extended transparency window from UV to the mid-infrared . Zirconium-fluoride glasses have been demonstrated as efficient gain media with a number of transition lines suitable for laser amplification and up-conversion processes in the visible and infrared regions. In addition, these glasses are characterized by a strong thermal expansion and a low melting point, and thus, should allow for control over the refractive index change through variation of the laser writing conditions. It was recently demonstrated that a significant decrease of the refractive index of fluoride glass can be induced and precisely controlled so as to fabricate key photonic components such as depress-clad waveguide lasers and fiber Bragg gratings [14,15]. To our knowledge, since the early demonstration of Miura et al.  showing how guiding structures can be inscribed in fluoride glass, there has been no further report on the formation of waveguides in fluoride glass.
In this paper, we report what we believe is the first detailed study of the photosensitivity of fluoride glasses to 800 nm femtosecond laser pulses at low (from 1 to 45 kHz) and moderate (from 50 to 250 kHz) repetition rates. At low repetition rates, small tracks of lowered refractive index are formed. At moderate repetition rates, we demonstrate the possibility of overcoming the material’s natural tendency and inducing a smooth positive refractive index change by translating the sample longitudinally through a loosely focused beam. The resulting waveguides are showing promising features for the development of integrated photonic devices operating in the mid-infrared.
2. Experimental setup and procedure
Two laser systems were used to generate the fs-pulses used during the experiments. First, a chirped-pulse-amplification (CPA) Ti:sapphire laser system (Coherent RegA) was used. The system operates at a central wavelength of 792 nm with a variable repetition rate ranging from 10 to 300 kHz with corresponding maximum pulse energies ranging from 7 to 5.5 μJ, respectively. The temporal FWHM width of the pulses was inferred from a scanning optical autocorrelator to be ~70 fs assuming a Gaussian pulse shape. Experiments at low repetition rate were carried out using a 1-kHz Coherent Legend-Elite USP laser amplifier system producing fs-pulses with a central wavelength of 806nm, a maximum pulse energy of 3.5 mJ and a pulse duration of ~35 fs inferred from a single-shot autocorrelator. Both laser beams were horizontally polarized and have diameters of 6 and 8.5 mm (at 1/e2), respectively. The beams were focused using a 5X (f = 25.4 mm, NA = 0.1) magnifying achromatic microscope objective resulting in focused spot sizes inside the glass sample estimated, assuming a diffraction-limited aberration-free focusing, to be 2w0 ~3.1 and 4.2 μm respectively. The pulse energy measured after the objective lens was controlled using a half-wave plate and a polarizer from 50 nJ up to 12 μJ. The samples were translated with scanning speeds ranging from 2 μm/s to 5 mm/s along the beam propagation axis using a motorized stage (Newport XML210). For the static exposure experiments, an electro-mechanical shutter was used to control the number of incident pulses.
The beam was focused inside 10 mm thick polished bulk samples. Three different fluoride glass samples were obtained from Le Verre Fluoré. Glass compositions of the three fluoride glass samples (in mol. %) used in the experiment, are presented in Table 1.After inscription, the waveguides end facets were polished and their transverse and longitudinal sections were examined under a phase contrast optical microscope (Olympus, IX71). The quantitative phase microscopy (QPM) method was used to obtain the radial refractive index profile of the waveguides . A QPM commercial software (Iatia Ltd.) was used to extract the phase images and the corresponding radial refractive index profile of the modified structures were retrieved by applying an inverse Abel transform to the phase images . Note that this process imposes symmetry on the resulting refractive index profiles.
A 5x microscope objective was used to couple a 633 nm He-Ne laser beam into the input facet of the inscribed tracks. The power transmitted out of the waveguide was coupled in a multimode optical fiber (Thorlabs GIF625) and measured with a power meter (Newport 818). Propagation losses of the waveguides were estimated by comparing the transmitted output with the input power. The near-field intensity profile of the waveguides was measured by imaging the end surface onto a CCD device (U-Eye SE) using a 10x objective. The far-field pattern of the red light exiting the waveguides was observed ~50 cm away from the sample on a white screen.
3. Results and discussions
Results presented in the following sections were obtained using the A3103 fluoride glass sample. Similar experiments were also performed using both the A3101 and 3104 samples and no significant difference was observed.
3.1 Static exposure to fs-pulses
The response of the fluoride glass to fs-pulses in the single-pulse regime was first investigated. The sample was translated transversally with respect to the laser beam propagation axis at a scanning speed of 50 mm/s while the laser repetition rate was set to 1 kHz. In this way, isolated structures induced by the absorption of a single pulse are formed every 50 μm along the translation axis. Microscope phase contrast images of typical single-pulse-induced structures with various pulse energies are illustrated in Fig. 1.At low pulse energy (<1.0 μJ), the beam collapses in a cylindrically shaped filament with a diameter of ~2 μm and a length of ~70 μm. Increasing the pulse energy results in the creation of merging filaments. It has been reported that beam ellipticity may affect the onset and orientation of multiple filaments . In our case, the multi-filaments are oriented along the major axis of the slightly elliptic beam. The formation of irregular modified zones and structural damage were observed at pulses energies in excess of 2 μJ.
The QPM technique was used to estimate the refractive index change of single-pulse-induced structures. The structures are considered as cylinders of length l along the beam propagation direction and the refractive index is inferred directly from the phase image using , where λ = 630 nm is the center wavelength of a 25 nm-bandwidth filter inserted in the microscope optical path and Δφ is the phase delay. The refractive index profile of a structure inscribed with pulse energy of 0.5 μJ is presented in Fig. 2.The induced refractive index profile shows a smooth negative index change of ~0.25 x 10−3. This confirms that the fluoride glass material response to non-linear absorption of a fs pulse consists in a decrease of its refractive index at the irradiated zone due to structural expansion. Fluoride glasses like ZBLAN have indeed a large thermal expansion coefficient of ~17.2 x 10-6 °C−1, a low glass transition temperature (Tg) of ~265 °C and exhibits a low thermal conductivity . These properties suggests that fluoride glasses used in our experiment fit in the same category of multi-component glasses prone to fs-induced decreases of their refractive index [10,11,20]. Mermillod-Blondin et al. related the laser induced expansion and material rarefaction of BK7, a representative borosilicate glass with strong thermal expansion, to the thermo-elastic dynamics and the structural relaxation of the material into a low-density phase after laser irradiation .
In order to characterize the heat accumulation effect associated with the waveguide inscription process in fluoride glasses, we performed static exposures of the bulk samples using multiple pulses. The sample was exposed to a number of shots N = 102, 103, 104 and 105, with pulse energies ranging from 0.1 to 3 μJ and repetition rates ranging from 10 to 250 kHz. The beam was focused ~500 μm below the sample surface to minimize beam aberrations. Phase contrast microscope images of the cross sections of the resulting index-modified zones for 104 shots are depicted in Fig. 3.At repetition rates below 50 kHz and low pulse energy, we observe index-modified structures of circular cross section with a diameter of ~2 μm which corresponds to a single filament (see Fig. 1b). Similarly to single-pulse exposure, higher pulse energies yield irregular and asymmetric structures characterized by multiple closely-spaced lobes of contrasting index change. At repetition rates above 50 kHz, another type of interaction is initiated. Bright index-modified zones of circular cross sections that extend beyond the diameter of a single filament are formed. Considering the low glass transition temperature of ZBLAN (used as a representative Zirconium-fluoride glass) and its low thermal diffusivity (2.4 x 10−3 cm2/s), it is expected that, given sufficiently high pulse energy, repetition rate and number of pulses, the cumulative temperature of the glass at the focal volume should eventually exceed the glass melting temperature [2,21–23] (see also section 3.2).
The diameter of the index modified structures was measured for different numbers of shots, repetition rates and pulse energies. We observed that the interaction of 103 successive pulses is sufficient to saturate the inscription process. That is, increasing the number of pulses from 103 to 104 does not yield larger modified structures. A further increase from 104 to 105 shots even results in a slight decrease of the modified structure cross section. The diameter of structures inscribed with 104 pulses and various repetition rates are plotted versus the pulse energy in Fig. 4.Irrespective of pulse energy, modified structures induced at a repetition rate of 10 kHz have a constant diameter of ~2 μm (this remains true even for exposition up to 105 pulses). At repetition rates of and above 50 kHz, the diameters of the index modified structures increase linearly up to ~3 times the focused beam size with increasing pulse energies. For a given pulse energy, the diameter of the modified structure reaches a maximum value for a repetition rate of ~175 kHz.
To complete the analysis, the pulse energy thresholds for both heat accumulation and index modification were measured for static exposure to 104 pulses at different repetition rates. The heat accumulation threshold was defined as the minimum energy required to initiate the formation of a structure with a diameter larger than 2 μm. The laser fluence F is defined by , where E is the pulse energy, N is the number of pulses and A is the circular cross section (r = 1 μm) of a single filament. The results are shown in Fig. 5.We first note that the heat accumulation threshold shows a sharp increase for rep rates below 75 kHz, in agreement with our previous results. The corresponding fluence values range between 160 and 350 kJ/cm2, which falls in the transient irradiation regime observed during waveguide inscription (see section 3.4, Fig. 10a). The index modification threshold, defined as the minimum pulse energy needed to induce an observable index change, slightly increases between 0.22 and 0.35 μJ for repetition rates increasing from 10 to 250 kHz. The energy threshold is actually linked to the critical power for self-focusing. Assuming a pulse duration of 70 fs and a pulse energy of 250 nJ, the calculated peak power is 3.6 MW which is close to the critical peak power for self-focusing in fluoride glass (Pcr ~3.1 MW, estimated with n2 ~2.1 x 10−16 cm2/W ). The slight increase in the energy threshold is explained by a variation of ~5 – 10% of the pulse duration over the range of repetition rates used in the experiment. The onset of self-focusing is thus the underlying physical process triggering glass modification.
3.2 Numerical modeling of thermal diffusion
To further investigate the heat accumulation effect and support the relevant experimental results, the spherical heat diffusion equation was numerically solved for fluoride glass parameters to obtain laser-induced temperature profiles T(r,t) near the focal volume, similarly to the work reported by Eaton et al.  for Schott AF45 glass. To simplify the calculations, we assumed a spherically symmetric heat diffusion process originating from the ellipsoidal-shape focal volume formed by the 5X objective.
The glass temperature as a function of the number of incident pulses was calculated at a specific radial position for different repetition rates. Calculations were made at r = 2.3 μm, a radius that is 10% greater than the calculated beam radius. The temperature curves were calculated by setting the absorbed energy in our routine to 0.6 μJ. This value corresponds to 55% of the 1.1 μJ incident pulse energy required to drive the heat accumulation process during static exposure to N = 104 pulses at a repetition rate of 50 kHz (see Fig. 5). Simulation results are presented in Fig. 6.A good agreement between the calculated and experimental values for the onset of heat accumulation is found. Indeed, although the glass experiences cycles of rapid heating and cooling upon receiving each pulse, no heat accumulation occurs at 10 kHz and the average temperature stays below Tg (dashed line). At 50 kHz or more and for a sufficient number of incident pulses, the average temperature rises up and stabilizes at values higher than Tg.
3.3 Linear traces of structural modifications in the absence of heat accumulation
For the remainder of the paper, dynamic exposures were performed by moving the laser focus inside the bulk sample at different speeds in order to inscribe continuous linear structures required to form waveguides.
First, the glass sample was translated longitudinally with respect to the beam propagation direction at low repetition rate (1–45 kHz). In this regime, the delay between each arriving pulse in the material is considerably longer than the characteristic thermal diffusion time (~μs). Therefore, temperature in the vicinity of the focal volume is maintained above Tg only for a short duration and the material undergoes a succession of melting and re-solidification cycles. At repetition rates lower than ~50 kHz and for input pulse energies ranging between 0.5 and 1.25 μJ, a single track of negative refractive index change with a nearly circular cross section of diameter comparable to the filament size is formed. The phase contrast image and the corresponding refractive index profile of the resulting tracks inscribed with a repetition rate of 10 kHz, a translation speed of 0.5 mm/s and pulse energy of 0.5 μJ are presented in Fig. 7.Such negative symmetrically shaped index profile appears to confirm what we observed for the static case. A maximum refractive index change amplitude value of 2.25 x 10−3 was measured for a track inscribed with a pulse energy of 1.25 μJ and translation speed of 0.05 mm/s. For higher input energies, the index profile evolved to a more complicated shape consisting of many closely-spaced positive and negative lobes distributed irregularly around the focal volume
3.4 Inscription of optical waveguides in the heat accumulation irradiation regime
In the following experiment, we combined, as proposed in , the heat accumulation effect to the longitudinal translation with a loosely focused beam (f = 25mm, 0.1 NA) to flip the negative refractive index change to a smooth positive one in fluoride glasses. Transverse writing geometry is usually preferred since it is not limited by the lens working distance. We have observed that a smooth positive index change cannot be induced in this writing configuration and therefore is not suited for waveguide inscription in fluoride glass within the range of the exposure parameters used in this work.
Phase contrast microscope images of tracks written with 0.5, 1 and 1.7 μJ, at repetition rates of 100 and 250 kHz and for various translation speeds are illustrated in Fig. 8. The laser fluence F is now calculated using: , where is the number of pulses impinging over a segment corresponding to the filament length (Lfil ~70μm (see section 3.1, Fig. 1)), A is its circular cross section (r = 1 μm) and td is the delay between pulses.Waveguides inscribed in this irradiation regime are characterized by a smooth circular cross section extending several microns away from the irradiated region. The structures observed for high pulse energy are typical of waveguides inscribed in the heat accumulation regime .
The diameters of the refractive index modified regions are depicted in Fig. 9 as a function of repetition rate and translation speed for various pulse energies.As expected, waveguide diameter increases with repetition rate and decreases with translation speed. Interestingly, the diameters of waveguides inscribed with a pulse energy of 0.5 μJ do not exceed 2 μm independently of repetition rate and translation speed. In agreement with the static exposure experiment, this confirms the existence of a pulse energy threshold lying between 0.5 and 0.75 μJ for the heat accumulation in fluoride glasses, for the range of repetition rates used in this work.
Next, the resulting refractive index change of waveguides inscribed at repetition rates of 50 kHz and above was investigated. Depending mainly on laser fluence, different refractive index morphologies are observed. Figure 10a summarizes the relative refractive index changes measured at the center of the exposed area (r = 0) as a function of the incident fluence and Fig. 10b depicts the corresponding radial refractive index profiles inscribed under different fluence regimes.Three distinct irradiation regimes are apparent depending on laser fluence. In the first regime (1), the laser fluence is low (F < 100 kJ/cm2) and there is no evidence of heat accumulation. The material undergoes multiple melting and re-solidification cycles. The structural change is confined to the region defined by the filament and results in a localized decrease of the refractive index caused by material rarefaction . Under those conditions, small anti-waveguides characterized by a sharp refractive index decrease in the center surrounded by positives side lobes are formed (profile E in Fig. 10b).The refractive index change also varies greatly from one track to another. Indeed, fewer pulses are deposited during the inscription process and the combination of pulse energy and translation speed has a greater impact on the resulting refractive index change.
At fluence ranging between 100 and 1000 kJ/cm2, a transient regime is initiated (denoted (2) in Fig. 10a). Tracks written in this range of fluence show a radial profile characterized by a weak index change that can be either positive or negative with a small dip in the center of the exposed area (Profiles C and D in Fig. 10b are typical examples).
Under high fluence (denoted (3) in Fig. 10a), the heat accumulation effect dominates the inscription process and the diameter of the tracks largely exceeds the size of a single filament. In this irradiation regime, waveguides with a smooth positive refractive index profile are formed. Depending on pulse energy and translation speed, two different kinds of waveguides are obtained. Profile A in Fig. 10b is a representative index profile of waveguides inscribed with moderate pulse energies (1-1.5 μJ) and low translation speeds (≤ 20 μm/s). These waveguides have a diameter ranging from 8 to 15 μm and a maximum refractive index change between + 0.6 and + 1.2 x 10−3. Under high pulse energies (>1.75 μJ) and moderate translation speeds (0.05-1 mm/s), large waveguides of diameters ranging from 20 to 50 μm and maximum refractive index change ranging from + 0.4 and + 0.7 x 10−3 are formed. Profile B in Fig. 10b is a typical index profile for such waveguides.
As mentioned above, the heat accumulation process is initiated for repetition rates higher than ~50 kHz. It was evidenced in our work that good quality waveguides, in terms of the observed near field profile, morphology of the index change and propagation losses were actually formed for repetition rates ranging from 100 to 250 kHz. Moreover, it has been shown that under large fluence, it is possible to optimize the waveguide sizes and refractive index change by a precise adjustment of both the scanning speed and the pulse energy. The propagation losses of optimized waveguides were estimated by coupling a He-Ne laser at λ = 0.633 μm in the waveguide and by measuring the output power through a multimode optical fiber. Fresnel losses and mode mismatch between the beam waist at the input surface and the effective waveguide diameter were taken into account giving an upper value to the propagation losses of the waveguides. Propagation losses as low as 0.4 dB/cm were measured. The majority of tested waveguides had propagation loss ranging between 0.5 and 2 dB/cm. Waveguides evidenced in our work exhibits slightly higher propagation losses than the best result of 0.2 dB/cm recorded by Zhang et al. for waveguides formed in fused silica glass .
Figure 11 shows the near field intensity profile of guided 633 nm light, phase contrast image of both side view and cross section and the refractive index profile of an optimized waveguide written under heat accumulation regime at moderate energy and low translation speed (corresponding to regime (3)).The 1.4 cm long waveguide shown in Fig. 11 was inscribed with a repetition rate of 175 kHz, a pulse energy of 1 μJ and a scan speed of 0.1 mm/s corresponding to a fluence of 3.9 MJ/cm2. The waveguide has a refractive index change of 0.5 x 10−3, a diameter of 12.2 μm and is showing single mode confinement at λ = 633 nm (V = 2.34). A total insertion loss of 1.8 dB was measured for this waveguide. By taking into account the 16% power loss from both the Fresnel reflections (4% at both facets) and mode mismatch (8%) between the beam waist and the waveguide mode field diameter, the upper bound for the propagation losses of the waveguide is estimated at 0.75 dB/cm. This underlines the possibility of low-loss waveguiding in bulk fluoride glass based on the optimization of the heat accumulation process through laser writing parameters. Moreover, since optimized waveguides evidenced in this work shows a wide range of size and refractive index change, we believe that it is possible to inscribe single-mode low-loss waveguides operating at various wavelengths in the mid-infrared where standard optical materials are not transparent.
We have demonstrated the formation of fs laser-induced refractive index change structures in bulk fluoride glasses at low and moderate repetition rates. Three different fluoride glass samples were used and no significant difference in the resulting index modified structures was observed. We showed that the primary response of the material to a single-pulse is a decrease of the refractive index. At repetition rates below ~50 kHz, a similar refractive index decrease is observed at the irradiated zone. The mechanism responsible for such index change is believed to be structural modifications in the form of local expansion of the irradiated region accompanied by stress-induced compression of the surrounding unexposed areas. At repetition rates above ~50 kHz, the refractive index modification process is dominated by a heat accumulation effect which drives glass melting. In this regime, longitudinal translation of the sample through a loosely focused beam results in the formation of large diameter waveguides characterized by a smooth positive refractive index change. Careful adjustment of the writing parameters allowed for the direct inscription of low-loss (~0.4–2 dB/cm) optical waveguides with near-circular mode profile and controllable diameter. Static exposure of the bulk sample has revealed that a specific amount of energy must be absorbed in order to initiate heat accumulation in the material. This energy threshold depends on the repetition rate of the fs laser source and varies from 1.1 to 0.5 μJ for repetition rates ranging from 50 to 250 kHz respectively. A simple numerical calculation of the laser-induced temperature profiles was used to support the main features of the experiment. Flexibility and control over waveguide characteristics combined with fluoride glass’ unique properties opens up new grounds for the fabrication of Mid-IR integrated 3D photonics devices.
This research was supported by the Canadian Institute for Photonic Innovations (CIPI), the Natural Science and Engineering Research Council of Canada (NSERC), the Canada Foundation for Innovation (CFI), the Fonds de recherche du Québec - Nature et technologies (FRQ.NT).
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