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Nonlinear optical properties such as the nonlinear refractive index and nonlinear absorption are characterized by z-scan measurements for a series of silicate glasses upon irradiation with laser pulses of 130 fs duration and 800 nm center wavelength. The stoichiometry of the silicate glasses is varied systematically to reveal the influence of the glass composition on the nonlinear optical properties. Additionally, the thermal properties such as glass–transformation temperature and thermal expansion coefficient are obtained from dilatometric measurements. It is found that the nonlinear refractive index is mainly related to the silica matrix. The nonlinear absorption is increased with the addition of network–forming ions.
© 2013 Optical Society of America
1. Introduction
For more than three decades, the nonlinear optical properties of dielectrics have been studied in order to understand and optimize the properties, such as damage threshold and nonlinear refraction of optical components in high–power laser systems [1–3]. At high intensities, the laser–induced damage in dielectrics can be significantly affected by self–focusing and beam filamentation when intense laser beams induce changes in the refractive index of the material. Along with the advent of ultrafast laser sources, the optical nonlinearities of glasses have been investigated for some specific glasses, e.g., soda lime [4], lead oxide [5], alkali silicate [6], borosilicate [7], and crown [8] glasses. For the characterization of the nonlinear optical properties of transparent materials different approaches have been used, including the z-scan technique [4–9], three-wave frequency mixing [10] or investigating the emission spectrum of the laser-induced filament [11]. An empirical model for the calculation of the nonlinear refractive index was established by Boling et al. [12]. In recent studies the femtosecond (fs)-laser pulsed irradiation of silicate glasses of varying chemical composition was investigated at fluence levels above the surface damage threshold with respect to permanent structural changes in the glass material [13–16]. However, even though the influence of the glass stoichiometry on the nonlinear properties of glasses has been explored intensively for many commercial glasses of discrete chemical composition [10,17] the influence of the composition of the glass on nonlinear properties is still not completely understood.
This work aims to investigate a series of silicon dioxide (SiO2) based binary and ternary silicate glasses with different kinds and varying concentrations of network–modifying oxides (Li2O, Na2O, K2O, MgO) for the nonlinear optical properties at fluences below the damage threshold systematically. Important characteristics of the glasses, such as glass-transformation temperatures, coefficients of thermal expansion, band–gap energies and refractive indices were investigated. A z–scan experiment was set up for the measurement of nonlinear refractive indices and nonlinear absorption coefficients. The experimental results obtained for the glasses will be discussed and compared to the literature.
2. Experimental methods
Several binary and ternary silicate and alkaline earth silicate glasses were manufactured at the Fraunhofer IKTS. Fused silica was used as commercial standard (Suprasil, Heraeus GmbH, Germany). Table 1 lists the stoichiometric composition of the investigated glass materials along with their names used in this publication.
Table 1. Stoichiometric batch-composition of the glass samples.
In the glass manufacturing process, reagent grade raw materials of silicon oxide (SiO2) and the network–modifiers supplied in the form of carbonate powders were mixed to obtain the required stoichiometry. The powder mixture was then homogenized and molten in an oven at ≈1500 K. Subsequently, it was refined for one hour while bubbled with gaseous nitrogen to homogenize the melt and to remove the residual gases (e.g. CO2) and contaminations. The glass melt was then cast between two steel–plates where it cooled with a rate of several 100 K/s down to temperatures below the glass–transformation temperature (Tg). In order to releases mechanical stress in the glass it was subsequently tempered about 10 K above Tg for 60 minutes and then cooled down with 1 - 2 K/min to room temperature. The glass was cut and polished in a water free process to an optical grade surface quality. The sample thickness was typically 1.5 – 2 mm. To avoid hygroscopic reactions or degradation the samples were stored in a desiccator.
For characterization of the glasses, several chemical and physical constants were determined. The glass–transformation temperature Tg was experimentally measured with a horizontal dilatometer (Netzsch 404 E). The corresponding linear thermal expansion coefficient (ζ) was deduced from the same measurements. To determine the optical band–gap energies (Eg) of the individual glass samples, the transmission spectra of the samples were acquired by means of an optical spectrometer (Lambda 9, Perkin Elmer). The values of Eg were then calculated from the Tauc–plot as explained in [18]. The refractive indices (nd) were estimated from the commercially available Glass Property Information System [19]. These thermal and optical sample characteristics are compiled in Table 2.
Table 2. Thermal and optical properties of the glass samples
The Kerr-type nonlinear refractive indices (n2) were determined for the mentioned silicate glasses by z–scan measurements. These measurements have been performed with a commercial Ti:sapphire femtosecond laser system (Spitfire, Spectra Physics) at a pulse repetition rate of 1 kHz (τ = 130 fs pulse duration, λ = 800 nm central wavelength). In the z-scan setup, the beam was focused with a lens of 300 mm focal length. A partly closed aperture was placed in the far–field of the focused laser beam allowing for S ≈33% transmission of the signal beam with no sample placed. Both signals were detected with photodiodes and fed to an analog divider calculating the signal–to–reference ratio. The readout was obtained via Lock–in technique. The selected glass samples were investigated for absorption changes and nonlinear refractive index changes with open and closed aperture, respectively, while moving them along the beam propagation axis through the focal region without lateral displacement. The photodiode signal measured with the closed aperture was normalized by the one obtained with the open aperture.
In all z–scan measurements, the peak laser fluences F0 at the sample surface were kept below the single-pulse surface damage threshold Fth of the glass samples (F0 ≈0.02 × Fth) in order to avoid any permanent material modification upon multi–pulse irradiation. Incubation effects are known to increase the absorption rate upon repeated irradiation of the same spot in the ablative regime [20,21]. The incubation is usually described as the generation of defect states of the Si-O bond [22] or as color centers [23]. Modeling and experimental results show that the multi-pulse damage (ablation) threshold fluence decreases to and saturates at approx. 20% of the single-pulse value Fth. As the symmetry of the z-scan traces did not show any difference upon scanning in forward or reverse z-direction and the inspection of the material via optical microscopy did not show any visible damage, significant contributions due to incubation effects or damage can be excluded here.
To retrieve the nonlinear refractive index n2 the detector signal ratio (normalized transmission) was evaluated with a method described by Sheik–Bahae and co–workers. The normalized transmission TCA can be written in terms of the on–axis phase shift ∆Φ0 and the sample position z as [9]:
where (: the Rayleigh length of the focused laser beam) and |∆Φ0| is the phase shift which can be expressed as [24]:∆TP-V is the difference between the normalized peak and valley values of transmission and S is the aperture transmission. Then the nonlinear refractive index n2 can be calculated [25]:where I0 is the maximum laser beam intensity at the focus, and L is the thickness of the sample (~2 mm). The nonlinear on–axis phase shift was kept below 1.3 rad to fulfill the condition .3. Results and discussion
Figure 1 exemplifies the closed aperture z–scan results of the normalized transmission for fused silica recorded at three different intensities I0 between 0.7 × 1011 and 1.65 × 1011 W/cm2. The three solid lines represent the corresponding least–squares–fits using Eq. (1). With ∆Φ0 obtained from Eq. (1), the n2 can be calculated by Eq. (3) to be 2.3 × 10−16 cm2/W. Following the same procedure, the nonlinear refractive indices of the other glasses were evaluated. The results are compiled in Table 3.A statistical error of ± 10% is estimated for the measurement campaign (see Fig. 1 inset). All values listed in Tab. 3 have been obtained during the same measurement campaign to ensure a reliable comparability of the different glasses. The values of the measured nonlinear refractive index n2 do not show a strong variation with the chemical composition and lie between 2.2 and 2.8 × 10−16 cm2/W for the lithium, sodium and magnesium containing glasses - all close to the value of fused silica (2.3 × 10−16 cm2/W). This leads to the assumption, that the nonlinear refraction is determined by the Si-O matrix. It was already underlined by Adair et al. [10] that the polarizability of oxygen determines the value of n2 in silicates. This is in agreement with Scholze [26] that the polarizability of glasses is dominated by the electron shells of the large oxygen anions. Only the potassium containing glass KMg20Si60 exhibits a somewhat larger n2 of 3.4 × 10−16 cm2/W. This might be assigned to the higher polarizability of the (comparatively) large potassium cation, which, according to [27], can exceed the polarizability of oxygen.
Fig. 1 Closed aperture z–scan transmission for fused silica at three different laser intensities I0 between 0.7 and 1.65 × 1011 W/cm2. The solid lines represent least–squares–fits using Eq. (1). The inset displays the deduced values of the n2 for five peak intensities I0 with the dashed line as the average of the measured values.
Table 3. Nonlinear refractive index (n2) and three–photon absorption (3–PA) coefficient α3 for several silicate based glasses (λ = 800 nm).
As three photons of 1.55 eV energy (800 nm wavelength) are needed to overcome the band gap energy of ≈4.2 eV for all glasses except fused silica (see Table 2), it is assumed here that the three–photon absorption (3–PA) is the dominant mechanism in the glass close the focal region. The fs–laser beam propagation along the z – axis can then be written as
I (z) is the laser beam intensity at the position z and α3 is the three–photon absorption coefficient. Assuming a spatially Gaussian beam profile, the normalized energy transmittance can be approximated for small values of transmission change [28] as [29]:
where . After normalization by the open aperture measurement, the z–scan data set can be fitted to Eq. (5) to yield the 3–PA coefficient α3 for different peak intensities I0 incident to the respective glass samples.Figure 2 exemplifies the normalized transmission data for the LiMg10Si60 glass measured at four different peak intensities I0 between 1.9 and 4.3 × 1011 W/cm2 along with the corresponding least squares fits. The data provide 3–PA absorption coefficient values of α3 = 1.4, 1.5, and 2.1 × 10−23 cm3/W2, respectively. Note that in the measurement α3 rises with the incident laser intensity (see the inset of Fig. 2) indicating a contribution of a higher order absorption processes.
Fig. 2 Open aperture z–scan transmission for LiMg10Si60 glass at four different laser peak intensities I0 between 1.9 and 4.3 × 1011 W/cm2. The lines represent least squares fits to Eq. (5). The inset displays the deduced values of α3 for three peak intensities I0.
In analogy, the 3–PA coefficients for the other glass materials were determined. The results are summarized in Table 3. For all glasses, the values of the measured 3–PA coefficient α3 vary by less than a factor of two and are between 1.7 and 3.4 × 10−23 cm3/W2 - all significantly different from an estimated α3 of fused silica in the applied intensity regime (<1 × 10−23 cm3/W2). This is not surprising, as fused silica has a larger band–gap energy of ~7.8 eV and requires at least a five–photon absorption (5–PA) process [30] to overcome the optical band gap. However, there is a trend that with the addition of network–modifying ions with large radii the 3–PA coefficient increases. The large value of 3-PA value of LiSi66 may be assigned to the di-silicate type of its composition as during the laser treatment the di-silicate glass structure tends to transform towards a more crystalline phase. Thus, a formation of precursor-like clusters of the crystalline ion order in the glass structure might contribute to the higher 3-PA coefficient measured here.
Rearranging Eq. (5) and taking the natural logarithm operation at both sides yields the following relation [29]:
Equation (6) allows for a direct test of the hypothesis of a 3–PA process, as this would suggest that the slope σ of a linear fit is close to σ = 2 when the experimental data of are plotted versus , i.e., for the implicitly varied z–positions of a scan trace.
As an example, Fig. 3 shows the corresponding data for the LiMg10Si60 glass measured at maximum intensities I0 = 3.3, 3.8, and 4.3 × 1011 W/cm2. The slope of σ = 2 refers to a 3–photon absorption process while σ = 3 is indicative of four–photon absorption (4–PA), as shown by solid black lines. For intensities up to ≈□3 × 1011 W/cm2 the data agree well with the slope of σ = 2. This is consistent with the band–gap energies of around ≈4.2 eV listed in Table 2, as at least 3 photons with an energy of 1.55 eV each are required to overcome the band-gap in an optical excitation process. However, higher order effects become relevant at intensities above 3 × 1011 W/cm2. Note that some authors consider higher order ionization mechanisms, e.g. collisional ionization and optical field ionization as the dominant ionization processes at intensities in order of 1012 W/cm2 to 1014 W/cm2 [31]. Alternatively, the deviation in the slopes is a signature of other mechanisms than multi-photon excitation adding the absorption, caused by the absorption by the electrons promoted to the conduction band [32]. Boudebs et al. [33] also described an intensity dependent (effective) absorption coefficient in tellurium based chalcogenide glasses. However, for mixed higher order absorption a more complex modelling needs to be used [4,33] which is beyond the scope of this work.
Fig. 3 Plot of vs. I for LiMg10Si60 upon z–variation, measured for three different peak intensities I0. Note that the apparent scatter in the data at low transmission change values arises from the logarithmic data representation.
Similar results can be obtained for the KMg20Si60, LiMg20, LiSi66, NaSi66 and LiNa22Si66 glass samples.
The results listed in Table 3 are in reasonable agreement with the few data available for some specific glasses available in literature. The nonlinear refractive index for fused silica was measured to be in the order of 2.5 × 10−16 cm2/W [34] or 3.5 × 10−16 cm2/W [35]. For B270 crown glass, [8] gives the nonlinear refractive index in the order of 2.3 × 10−16 cm2/W, which has a similar SiO4-matrix compared to the glasses investigated in this paper [36].
Jamshidi–Galeh et al. measured the 3–PA coefficients to be 0.5 to 2 × 10−24 cm3/W2 for alkali silicate glasses and BK7 [6,7]. Linear and two–photon absorption are taken into account in their modeling which might lower the estimated values for the 3–PA coefficient. Evaluating the z–scan data of [8] performed on B270 crown glass by the method described here an absorption coefficient of α3 ≈□2 × 10−23 cm3/W2 is obtained – in good agreement with our measurements.
4. Conclusion
In summary, the Kerr-type nonlinear refractive indices of the binary and ternary alkaline and alkaline earth silicate glasses are measured very similar and close to the one of fused silica, i.e., n2 ≈(2.5 ± 0.3) × 10−16 cm2/W (except for the KMg20Si60 glass, see Table 3). As SiO2 is the main constituent in all glasses it is supported that the Si–O network is determining the n2 for all glasses. The addition of K2O can increase n2 by ≈50% which might be induced by the much larger radius of the potassium ion (compared to lithium ion) which comes along with an increase the polarizability of the glass. All investigated binary and ternary glasses have very similar optical band–gap energies Eg around ≈4.2 eV. Their 3–PA coefficients are gathered around α3≈(2.3 ± 0.6) × 10−23 cm3/W2. The parameters Eg and α3 are significantly different from pure (fused) silica and determined by the additional chemical constituents and the resulting structural modification of the glass network. The higher 3-PA value of LiSi66 might be attributed to the di-silicate type of the glass material.
Acknowledgments
The authors would like to thank R. Schadrack (BAM) for the dilatometric measurements. The authors acknowledge the funding of the German Research Foundation DFG (grants no. EB 248/4–2; EI 110/30–2; RO 2074/8–2).
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