Franck Condon analysis of emission and excitation spectra of fused silica materials

. Analysis of defects in optical materials is essential for their applicability in cutting-edge optical components. Since fused silica (FS) counts among the most used materials, deep knowledge about the defects in FS is of high importance. These defects have been routinely identified by studying photoluminescence (PL) emission and its analysis via multiple Gaussian bands. Here we present an extended approach based on the Franck-Condon model to study the defects in FS and the connected pathways of charge carrier relaxation. First, we performed the optical characterization of the FS, including optical absorption, photoluminescence (PL) emission and excitation (PLE), and Fourier-transform infrared (FTIR) and Raman spectroscopy (RS). Based on the analysis of the PLE spectra and vibrational frequencies via RS and FTIR, we created a multi-transition Franck-Condon model, which is able to fully reproduce the PL and PLE spectra. Based on the experimental data and the Franck-Condon fit, we discuss two types of oxygen-deficient centres (ODC) present in this fused silica material and their emission pathways.


Introduction
Fused silica (SiO2) is an important material for optical applications.It is widely used to prepare optical elements, such as substrates, mirrors, or photonic crystals.The grade of fused silica and its applicability is set by the presence of defects, such as intrinsic defects or traces of impurities of various elements known as extrinsic defects [1].These defects can originate from the raw material or be generated during manufacturing [1,2].These defects enhance the optical absorption (OA) and the photoluminescence (PL) in the UV and visible regions, limiting their optical quality.Therefore, the study of these defects is an important task.For several years, the study of the defects in fused silica has been based on optical absorption and photoluminescence (PL) experiments.Analysis of such spectra has been vastly limited to fitting via Gaussian bands [3].However, this simple approach leaves the problem partially unsolved since some defects retain their asymmetric shape of spectra and cannot be well described by this model.In this work, we study the optical characterization of the fused silica sample including optical absorption, PL emission and PLE, and FTIR and Raman spectroscopy (RS).Subsequently, the multi-transition FC progression is used to reproduce the PL and PLE spectra.Based on the fitting parameters, we discuss the different types of defects present in the fused silica.

Absorbance and PL spectra
Figure 1 represents the fused silica (FS) absorbance spectrum.The fused silica sample, with a thickness of 3 mm, was supplied by Haian Baode Optical Glass Co., Ltd (type HS with high transmittance in the wavelength range of 260-3500 nm).It was polished by a continuous pitch polishing technique using Ceria (CeO2) water-based polishing slurry.The absorbance measurement reveals that the sample absorbs UV light with photon energy above 4.75 eV, which is significantly below the optical bandgap of FS and it indicates the presence of defects in the material.Having determined the absorbance, we turned to the measurement of the PLE and PL at emission energy 4.13 eV and excitation energy 5.28 eV, respectively, as shown in Figures 2 (a

FC analysis
To model the PLE and PL spectra, the FC progression was used [4,5]: Here,  is the photon energy and  0 is the transition energy from the lowest vibrational level of the electronic excited state to the lowest vibrational level of the ground state.The standard deviation σ characterizes the inhomogeneous broadening of  0 .The '+' and '-' signs refer to excitation and emission, respectively.The PLE spectrum was fitted by using two FC progressions (pink dashed lines in Fig. 2 (a)) with phonon modes of 0.0535 eV (432 cm -1 ) and 0.0985 eV (795 cm - 1 ).The energies of the phonon modes are taken from the Raman and FTIR spectra.
The first FC progression is centred at 4.97 eV with an FWHM equal to 0.35 eV and a PL0-0 transition energy (E0) equal to 4.7 eV.It is assigned to the twofold coordinated silicon, denoted as Si-ODC(II) defect.The second FC progression, which is centred at 5.18 eV with an FWHM equal to 0.43 eV, is assigned to the ODC defect affected by the Ge impurity, denoted as the Ge-ODC(II) defect.This data would not be sufficient to judge the use of specific phonon modes.However, since the PL emission and PL excitation spectra reflect the same physical model, hence the FC model was used to fit the PL spectra.By using a fourth FC progression-see Figure 2(b), we are able to reproduce the emission spectra.These progressions were associated with the energies of fourth different phonon modes: 54 meV (432 cm -1 ), and 131 meV (1060 cm -1 ), assigned to the I (singlet-singlet) and  (singlet-triplet) radiative transitions of the Si-ODC(II) defect and 99 meV (795 cm -1 ), 141 meV (1140 cm -1 ) assigned to the E (singlet-singlet), and  (singlet-triplet) radiative transitions of the Ge-ODC(II) defect.

Conclusion
This work presents a model based on a multi-FC progression to reproduce the fused silica's PL excitation and emission spectra.By reproducing these spectra, we were able to pinpoint the presence of two different variants of one ODC defect: Si-ODC(II) and Ge-ODC(II) defects Figure1represents the fused silica (FS) absorbance spectrum.The fused silica sample, with a thickness of 3 mm, was supplied by Haian Baode Optical Glass Co., Ltd (type HS with high transmittance in the wavelength range of 260-3500 nm).It was polished by a continuous pitch polishing technique using Ceria (CeO2) water-based polishing slurry.The absorbance measurement reveals that the sample absorbs UV light with photon energy above 4.75 eV, which is significantly below the optical bandgap of FS and it indicates the presence of defects in the material.Having determined the absorbance, we turned to the measurement of the PLE and PL at emission energy 4.13 eV and excitation energy 5.28 eV, respectively, as shown in Figures2 (a) and (b), where we observed multiple PL bands connected to different absorption bands.

Fig. 2 .
Fig. 2. (a) PL excitation spectra of FS (black dashed curve) corresponding to emission at 4.13 eV and their FC fit (blue solid curve) consisting of two components (dashed pink lines).(b) PL emission spectra of FS (black dashed curve) at excitation energy 5.28 eV and their FC fit (blue solid curve) consisting of a superposition of four different distinct FC progressions: S1-S0 radiative transitions (pink dashed lines), T1-S0 radiative transitions (red dashed lines).