1. Introduction

Glassy materials play an important technological role, as they can be manufactured in different shapes and sizes, as well as their properties can be tailored by doping and compositional changes. They have great transparency in the visible and promising nonlinear optical properties [1, 2]. Furthermore, glasses can be easily microstructured, which makes them interesting materials for photonic applications [3]. Corning Gorilla Glass is an alkali aluminosilicate glass commonly used as protective cover on mobile devices. Such glass undergoes an ion exchange process [4], where sodium ions from the matrix are substituted by potassium ions from a hot bath, resulting in the creation of a compression layer that extends ~150 μm below surface and is responsible for improving the glass mechanical properties [5]. Lapointe et al. [6] showed the possibility of micromachining Gorilla Glass by Direct Laser Writing (DLW) with femtosecond laser pulses [7, 8], demonstrating the fabrication of ultra-long waveguides with high quality modes and low propagation losses, prompting such material for integrated photonic/electronic devices [9], as well as applications in supercontinuum generation [10], mid-infrared laser [11], etc. Aiming at such applications, it is important to study the nonlinear features of Gorilla Glass and their laser-inscribed waveguides. Recently, the nonlinear refractive index n₂ of Gorilla Glass was characterized [12] by Z-scan [13]. The authors found that $n_2$ is approximately constant through the studied range (490-1500 nm) with a mean value of 3.3 × 10⁻²⁰ m²/W. Even though Z-scan measurements revealed that Gorilla Glass has similar features to common glasses [14], the nonlinear characterization of laser-written waveguides is still necessary, since the effects of the DLW process on the nonlinearity are not totally understood [15]. However, the nonlinear characterization of waveguides can be quite challenging, being usually performed by interferometry and pump-probe techniques [16, 17]. An alternative technique, that has the advantage of using a single beam, is the Dispersive-scan (D-scan) method [18–20]. Such approach is based on the spectral modifications caused by self-phase modulation of an ultrafast pulse that passes through a material, as a function of the excitation pulse dispersion, which is varied by a dispersive line. The output spectra are collected and the spectral width and/or peak intensity are plotted as a function of the input pulse dispersion, from which one can obtain the magnitude and signal of $n_2$. D-scan was initially applied to glasses and optical fibers [18, 19] and it has recently been shown as an interesting method to determine the nonlinear properties of silicon waveguides [21]. Here we report on the first use of the D-scan to characterize the nonlinear optical properties of waveguides produced by DLW with fs-pulses. We characterized waveguides produced in Gorilla Glass with different writing parameters. Micro Raman measurements were performed in the microstructured material in order to better understand the mechanisms of laser modification.

2. Materials and methods

Waveguides were produced in Gorilla Glass by DLW using a Ti:Sapphire laser amplifier, emitting 150 fs pulses centered at ~780 nm with 1 kHz of repetition rate. The laser beam was focused with a microscope objective (NA = 0.65) approximately 100 μm beneath the glass surface, right in the compression layer. The glass sample was moved at 200 μm/s by computer controlled translation stages in order to produce 15 mm long waveguides. More details about the waveguides fabrication can be found in [12]. Here, we performed the nonlinear characterization of two types of waveguides, fabricated using pulse energies of 250 nJ (type A) and 500 nJ (type B), both presenting a Gaussian mode intensity profile [12].

Nonlinear characterization of Gorilla Glass waveguides was performed by D-scan [18, 19], whose experimental setup is shown in Fig. 1(a). As excitation source we used a Ti:Sapphire laser amplifier (50 fs, ~780 nm and 1 kHz). The beam was directed to a dispersive line (two prisms) that allows changing the pulse second-order dispersion (ϕ⁽²⁾). A fraction of the input beam is directed to a FROG (Frequency Resolved Optical Gating) for pulse characterization. The beam is coupled to the waveguide by a microscope objective (NA = 0.25) and the guided light is collected by another microscope objective (NA = 0.40). Both objectives and the sample are mounted on moving platforms to optimize coupling. The guided light is then directed to a spectrometer and a power-meter. In a D-scan measurement, the spectrum of the guided light is collected for different pulse second-order dispersions, achieved through the dispersive line. In Fig. 1(b), we can observe the collected output spectra of a type A waveguide for different values of the input pulse dispersion. Further processing of the spectra is required for the determination of their width, represented in this paper by the Standard Deviation (σ) of the spectral distribution. This way, we can build the D-scan curve of σ as function of ϕ⁽²⁾. The waveguides guided modes, as shown in Fig. 1(a), were analyzed by projecting the image of the waveguide output on a camera. To determine n₂, the experimental data were adjusted using numerical simulations performed in Lab2 [22]. In our simulations, the Nonlinear Schrödinger Equation is solved by a Split-step Fourier Transform algorithm [22], considering dispersion and self-phase modulation and assuming ultrashort pulses with a Gaussian spatial profile. The input pulse second-order dispersion (ϕ⁽²⁾) is varied and the output spectral width (σ) is recorded.

 

Fig. 1 – (a) Experimental setup of D-Scan showing the image of the guided mode of a type A waveguide and a scheme of the sample geometry. (b) Output spectra of a type A waveguide for different ϕ⁽²⁾.

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The characterization of the structural properties of the fs-laser fabricated waveguides was carried out by Raman spectroscopy using a LabRAM HR Evolution micro-Raman system that uses a 532 nm laser as excitation source with a 0.9 NA objective and a thermoelectrically cooled CCD detector. Raman spectra were recorded from the sample surface up to 120 μm beneath the surface, passing through the microstructured region, in steps of 2 μm, with the aid of a motorized translation stage to move the sample. For better contrast in the Raman measurements, we used waveguides fabricated with 5μJ of pulse energy (type C). Such waveguides were not characterized by D-scan because of their complex mode profile.

3. Results and discussion

In Fig. 1(b), we can observe the transmitted spectra of a type A waveguide (produced with $250 nJ$ energy pulses) for different values of second-order dispersion ϕ⁽²⁾. We can observe that as ϕ⁽²⁾ approaches zero from negative values the spectrum gets narrower and the peak intensity gets higher. As ϕ⁽²⁾ reaches positive values the spectrum gets broader and there is a decrease in the peak intensity. This behavior is typical for materials with a positive nonlinear index of refraction. For large values of |ϕ⁽²⁾|, the spectrum is similar for both negative and positive dispersion, meaning that there is so much second-order dispersion added to the pulse, leading to its temporal broadening, that no spectral modifications due to nonlinear effects are observed. Further processing of these spectra was performed to obtain the spectral width $\sigma$ as a function of ϕ⁽²⁾. The results are shown in Fig. 2(a) (circles), where the typical D-scan curve is observed. In order to extract the nonlinear refractive index $n_2$ from our experimental data, we performed a numerical simulation (solid line) as described in the previous section. The input pulse energy (E = 20.5 nJ), central wavelength (λ₀ = 785 nm) and spectral FWHM bandwidth (Δλ = 20 nm) were carefully determined experimentally and inserted in our simulations. The mode diameter $d$ at $1/e^2$ of the intensity profile was carefully determined through the analysis of an image of the waveguide output and set as d = 32.5 µm. The nonlinear refractive index of the type A waveguide, determined by fitting the experimental data, is n₂ = 9.0 × 10⁻²¹ m²/W, with an error of approximately 30%. A Type B waveguide, produced with 500 nJ energy pulses, was also subjected to D-scan measurements and the results are shown in Fig. 2(b) (circles). The input pulse features and mode size were set as follows: E = 25.6 nJ, λ₀ = 785 nm, Δλ = 29.5 nm and d = 19 µm. By means of our numerical simulation (solid line) we found n₂ = 7.0 × 10⁻²² m²/W. Both waveguides are far from tight confinement regime. A linear behavior was observed for the peak to valley change of the D-scan curves with the input intensity, which indicates a third-order electronic nonlinearity.

 

Fig. 2 – D-scan curves of Gorilla Glass waveguides produced by DLW with femtosecond pulses of energy of (a) 250 nJ (type A) and (b) 500 nJ (type B).

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According to [12], the nonlinear index of refraction of bulk Gorilla Glass is (3.3 ± 0.6) × 10⁻²⁰ m²/W, a value similar to the ones found in the literature for common glasses [14]. According to our D-scan measurements in Gorilla Glass waveguides, for the type A waveguide n₂ is more than 3 times lower than the n₂ of the bulk material. For type B waveguides, fabricated with higher pulse energy, the n₂ is approximately 47 times lower than the one for the bulk glass. Therefore, such results indicate that the microfabrication led to a significant reduction of the nonlinear index of refraction of the material, which in fact depends on the writing pulse energy.

The reduction of the nonlinear refractive index in fs-laser irradiated glasses when compared to the pristine material has been recently observed. This effect was first reported by Blömer et al. [15] in waveguides produced by DLW in fused silica. The waveguides exhibited $n_2$ values up to 4 times lower than the bulk material. Furthermore, the authors also have shown that $n_2$ is lower when higher energy per point is used in the fabrication process. Royon et al. [23] performed Third Harmonic Generation Microscopy on femtosecond laser exposed silica samples and also observed that their third order susceptibility is lower than the one for the non-irradiated material. Demetriou et al. [24] evaluated the nonlinear refractive index of ultrafast laser written waveguides fabricated in gallium lanthanum sulphide, a type of calchogenide glass, and observed a nonlinear refractive index 4-5 times lower than the bulk material index.

In order to get a better understanding of the structural modifications caused by fs-laser irradiation that may lead to the reduction of $n_2$, we performed Raman spectroscopy measurements in Gorilla Glass waveguides. Type C waveguides, produced with 5 µJ of pulse energy, were used as they presented more noticeable changes in the Raman spectrum. Figure 3(a) displays the Raman spectrum of the pristine Gorilla Glass (black line) measured at 40 µm below the surface. A spectrum of the microfabricated region measured at 76 µm deep is also shown in Fig. 3(a) (blue line). Both Raman spectra shown in Fig. 3(a) correspond to typical ones for alkali aluminosilicate glasses [25–27]. One can observe that for the modified region there is a decrease in intensity for the band centered at 479 cm⁻¹ (indicated by an arrow in Fig. 3(a)). As mentioned before, Raman spectra were collected at distinct sample depths, from the surface up to 120 µm below the surface, in steps of 2 µm. Each spectrum was individually processed. Baseline extraction was performed using the region without peaks above 1400 cm⁻¹ as reference. The spectra were then normalized by their area, and a multigaussian fit was performed for the low frequency (400 - 600 cm⁻¹) and high frequency (900 - 1200 cm⁻¹) regions separately. In the inset of Fig. 3(a) we can observe the peak intensity for the low frequency band centered at 479 cm⁻¹ as a function of the depth. As it can be seen, there is a significant signal decrease in the region centered around 75 µm that has more than 30 µm of width. This region corresponds to the waveguide profile, which is elongated due to the self-focusing that occurs during the fabrication.

 

Fig. 3 – (a) Raman spectra of the pristine Gorilla Glass measured at 40 µm of depth (black line) and the waveguide region at 76 µm (blue line). Inset: Peak intensity of the band centered at 479 cm⁻¹ as a function of the sample depth. (b) Intensity of the band centered at 1078 cm⁻¹ as a function of the depth.

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According to Fig. 3(a) there is a reduction of the 479 cm⁻¹ band and an increase of the 590 cm⁻¹ band due to the fs-laser irradiation. This observation was confirmed by the multi-gaussian fit of the low frequency region. These bands are known as D1 and D2 bands, respectively, and are related to 4 and 3-membered ring structures of $T{O}_4$ ($T=Si or Al)$ tetrahedra [27]. This way, we can conclude that the fs-laser irradiation leads to the depolymerization of the glass matrix, favoring 3-membered ring structures over 4-membered rings. Muniz et al. [28] performed the Raman structural analysis of calcium aluminosilicate glasses under high pressure and observed that for silica-rich glasses the densification process leads to an increase of 3-membered ring structures. Bressel et al. [29] studied the modifications caused by fs-laser pulses in $Ge{O}_2$ glass and also observed a reduction of the D1 band with an increase of the D2 band. This phenomenon was once again attributed to the densification of the material.

For the high frequency region we observed an intensity decrease of the 1078 cm⁻¹ band, as shown in Fig. 3(b), from the surface to the volume of the glass. This band can be associated with the presence of non-bridging oxygens (NBOs) [30–32]. Its decrease from the surface to the volume can be attributed to the ion exchange process that occurs mainly on the surface and leads to a greater concentration of potassium ions and NBOs [32]. However, around 75 µm, which is the center of the microstructured region, there is a more pronounced decrease in the signal intensity that can be attributed to the fs-laser irradiation. We also observed that the 1078 cm⁻¹ band becomes larger in the microstructured region. According to Boling et al. [33] NBOs are the main contributors to the optical nonlinearities of glasses, as they are much more polarizable than bridging oxygens (BOs). The intensity decrease of the 1078 cm⁻¹ band may represent a reduction of the number of NBOs and the band broadening can mean a greater heterogeneity on the NBOs bonding angles. Both spectral modifications related to the NBOs can explain the reduction of the nonlinear refractive index in the Gorilla Glass waveguides when compared to the pristine bulk material.

4. Conclusion

In this work, we performed the nonlinear characterization of fs-laser written waveguides in Gorilla Glass using the D-scan technique. The nonlinear refractive index n₂ measured in the waveguides is lower than the one for the pristine material and its value depends on the writing pulse energy. For waveguides fabricated with pulse energy of 250 nJ, n₂ is more than 3 times lower than the one for the pristine sample, while for waveguides fabricated with 500 nJ, n₂ was found to be approximately 47 times lower than the value for the pristine material. Raman spectroscopy measurements revealed the reduction and broadening of the high-frequency band related to non-bridging oxygens (NBOs), which can explain the decrease of the n₂ value. Therefore, given that Gorilla Glass may be an interesting material for device fabrication via fs-laser micromachining, the reduction of n₂ caused by such processing method should be considered when designing photonic devices, either in the case in which nonlinearities are important or in situations where they should be reduced.