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Abstract
We are grateful to Ballato et al. [Opt. Mater. Express 13, 2338 (2023) [CrossRef] ] for their comment on our recently published paper. The optical model and simulation of optical fiber materials are important to design new materials systems and to further improve the fiber laser performance. However, accurate calculation of the non-crystal fiber materials is still challenging, both from the methodology and from the needed calculating resources. The recently published paper [Opt. Mater. Express 13, 935 (2023) [CrossRef] ] has sparked interest, which gives us the opportunity to explain the difference between the modeled data and the well-established experimental results.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
Firstly, previous results show that the refractive index of the SiO2-BPO4 join remarkably increased when the doping concentration of the [BPO4]° increases [1]. Here, we further calculate this dependence with 3.33, 3.45, 3.57 mole percent in SiO2, without changing the cell volume. Figure 1 clearly shows the same trend with a smaller increase in the refractive index [1–3].
Fig. 1. The calculated refractive indices of the SiO2-BPO4 when doping [BPO4]° into the fused silica with 0, 3.23, 3.33, 3.45, 3.57 mole percent.
As for the calculation method, ab initio molecular dynamics (AIMD) simulation based on density functional theory is widely used in the modeling of SiO2 [4–6]. The generalized gradient corrected (GGA) exchange-correlation functional in the Perdew-Burke Ernzerhof (PBE) form is adopted to describe the electron correlation [7–11], is used to calculate the optical materials properties [11–13]. We take the parameter settings, such as cut-off energy, k-point grid, etc., from several theoretical papers [4,5,14–17].
Adding AlPO4 reduces the refractive index of SiO2, which has been reported in many experiments [18–23]. In the manuscript [24], [AlPO4]° is doped by replacing the two SiO4/2 groups without changing the supercell volume. This assumption is used by Feng et al. They established the SiO2 model with 96 atoms and 2.2 g/cm3 without changing the volume when doping the Cu, Ca, K, Fe, and Ce impurities [7–9,11]. Michael Nolan and Graeme W. Watson studied the hole localization of Al-doped SiO2, and the volume remained unchanged when Al2O3 was doped [10].
We have to point out that the conclusions in the manuscript were discussed under constraints of lighter doping and volume invariance, which caused the refractive index result to be somehow inconsistent with the experimental results. There are some factors that may cause deviations:
- 1) The limitations of the PBE algorithm. PBE is fast but not so accurate. G0W0 + BSE and HSE06 hybrid functional calculation methods can more accurately describe the dielectric function of the material but the calculation is slow and expensive;
- 2) The density may change under doping, and further models should consider the change of the supercell volume. . Ballato et al. fitted the experimental data [1] and described: “Due to some variation in the data, a range of densities 2640 ± 300 kg/m3 around nBPO4 = 1.545 best fits the data” [25]. The density of fused silica is reported to be 2200 kg/m3 [13,14]. This shows that doping [BPO4]° into the silica will increase its density. In terms of doping AlPO4 unit, the two structures AlPO4 and 2SiO2 have the same volume, though AlPO4, unit has slightly more mass [18]. Therefore, doping either [AlPO4]° or [BPO4]° does change the density of the fused silica. Referring to the calculated refractive indices, some disagreement may exist between SiO2-BPO4 and SiO2-AlPO4, if density variations are not considered. In order to improve the model accuracy, density variations of fused silica should be taken into account in future calculations.
- 3) The model accuracy is mainly limited by the computing speed and memory. A wider doping concentration may be calculated to accommodate the experimental results.
We thank Ballato et al. for their constructive suggestion to improve our understanding. There is still a gap between the model accuracy and the experimental results. We hope more research efforts can be delivered to narrow this gap in the future.
Funding
The Science and Technology Innovation Program of Hunan Province (2021RC3083); National Natural Science Foundation of China (12004432).
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available but may be obtained from the authors upon reasonable request.
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