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\begin{document}
\title{
Role of $\textnormal{PbO}$ and Up-conversion in RE doped $\textnormal{B}_{2}\textnormal{O}_{3}$- $\textnormal{P}_{2}\textnormal{O}_{5}$ glasses}

\author[a]{Harpreet Singh}
\author[b]{Devinder Singh}
\author[a]{Supreet Pal Singh^{*}}
\affil[a]{Department of Physics, Punjabi University Patiala, Punjab-147002}
\affil[b]{Department of Physics, Sri Guru Teg Bahadur Khalsa College, Anandpur Sahib, Punjab-140118}

\maketitle

\subsubsection*{Abstract} 
To investigate the role of PbO as a former or a modifier and effect of its compositional variation on the physical, structural and optical properties, lithium lead borophosphate glasses were synthesized by melt quenching technique. For physical properties of the prepared glasses, density was measured by the Archimedes principle and density showed an increasing trend with increasing concentration of lead oxide. The structural analysis were performed through X-ray diffraction and Fourier transform infrared spectroscopy. Structural units due to PbO, $\textnormal{P}_{2}\textnormal{O}_{5}$ and $\textnormal{B}_{2}\textnormal{O}_{3}$ were identified. Ultraviolet-visible absorption spectroscopy was performed for optical properties and increase in the indirect band gap from 4.80 eV to 4.90 eV was observed. One glass sample was chosen for doping of erbium, neodymium, thulium and ytterbium, for study of their up-conversion properties. All the prepared samples were excited at 980 nm and ytterbium being a sensitizer helps in up-converting infrared light to visible light. As up-conversion is a host dependent process, up-conversion results suggested that the rare earth doped lithium lead borophosphate glasses are great host for up-conversion and these glasses can find applications in display devices and lasers.

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{\bf Keywords}: Lead Borophosphate glasses, X-ray Diffraction, FTIR, UV-Vis-NIR Spectroscopy, Photoluminescence Spectroscopy, Up-conversion, RE doped glasses





\section{Introduction}
Glasses are characterized as non-crystalline materials that undergo glass transition. This phenomenon sets them apart from crystals which display extensive atomic regularity over long distances and possess a clearly defined melting point \cite{1}. Unlike crystals, the composition of glasses can be adjusted to attain specific properties that align with the requirements of particular applications. Consequently, glasses have played a pivotal role in numerous technological advancements such as lasers, scintillators, luminescent materials and bioactive glasses \cite{2}. In the last few years, lanthanides-doped glasses have garnered significant attention because of luminescence and up-conversion properties of lanthanides (Ln). These glasses are known for solid state lasers, optical amplifiers, color displays, scintillators, LEDs, temperature sensors, phosphors and dosimetric applications \cite{3,4}. The 4f orbitals of lanthanides are effectively shielded by the fully occupied $5s^{2}$ and $5p^{6}$ orbitals, rendering them less susceptible to external field of host material \cite{5}. This protective shielding is accountable for the unique optical characteristics exhibited by lanthanides. Up-conversion is a distinctive characteristic demonstrated by lanthanides, wherein they transform infrared light into visible light \cite{6}. Europium in its trivalent state ($\textnormal{Eu}^{3+}$) is recognized for emitting red light, while divalent europium ($\textnormal{Eu}^{2+}$) emits blue light. Terbium ($\textnormal{Tb}^{3+}$) releases green light, Samarium ($\textnormal{Sm}^{3+}$) gives off orange light, and Dysprosium ($\textnormal{Dy}^{3+}$) is notable for its white light emission. Erbium ($\textnormal{Er}^{3+}$), Neodymium ($\textnormal{Nd}^{3+}$), and Thulium ($\textnormal{Tm}^{3+}$) are distinguished for their luminescent and laser properties \cite{7,8,9}. When two rare earth (RE) ions are co-doped, they have the ability to exchange energy between each other, leading to up-conversion and an enhancement in photoluminescence efficiency. Ytterbium ($\textnormal{Yb}^{3+}$) serves as a fitting ion for this purpose, as it can efficiently transfer the absorbed infrared energy to its co-doped ion, resulting in visible region emission \cite{10}. Up-conversion (UC) is also dependent on the host material and for effective energy transfer and up-conversion to occur, the host material must have low phonon energy. The incorporation of heavy metal oxides (HMOs) like $\textnormal{Bi}_{2}\textnormal{O}_{3}$, $\textnormal{BaO}$ and $\textnormal{PbO}$ into glass structure leads to reduction in the phonon energy of the glass \cite{11}. PbO is known for increasing the moisture resistant capabilities and thermal stability of glass, have high density and high refractive index, and also influences the optical properties of the glasses \cite{12,13}. The stable oxidation state of Pb is +2, resulting in the formation of $\textnormal{Pb}^{2+}$ cations and can form both ionic and covalent bonds with oxygen. The ionic bond reflects its role as a modifier, while covalent bonding signifies its role as a constituent within the structure \cite{14}. $\textnormal{PbO}_{4}$ or $\textnormal{PbO}_{3}$ structural units are formed when PbO plays the role of the former in the structure  while $\textnormal{PbO}_{6}$ units are formed during its role as the modifier \cite{15,16}.\\
Up-conversion (UC), the process of converting low-energy photons into high-energy photons, presents a complexity not found in downconversion, where high-energy photons are converted into low-energy ones. Achieving UC demands a high-intensity excitation source due to its requirement for the simultaneous absorption of two or three photons \cite{17}. Additionally, the host material should possess low phonon energy to minimize non-radiative transitions and facilitate efficient energy transfer between dopant ions. The dopant ion's energy levels must be arranged in a ladder-like arrangement, providing multiple metastable states where excited electrons can absorb additional incoming photons and ascend to higher energy levels \cite{18,19,20}. Furthermore, UC is influenced by concentration of dopant ions; high concentrations lead to quenching, while low concentrations result in inefficient energy transfer. Therefore, successful up-conversion hinges on carefully considering all these factors and selecting an appropriate dopant-host combination \cite{21}. Considering the dual role of PbO and its property of enhancing luminescence, lithium lead borophosphate glasses were synthesized for investigation of their structural \& optical properties and their up-conversion efficiency. The impact of varying concentrations of lead oxide on the physical, structural, and optical characteristics of lithium borophosphate glasses (LBP) have been analysed. A single sample was chosen from the prepared LBP samples to undergo doping with Erbium ($\textnormal{Er}^{3+}$), Neodymium ($\textnormal{Nd}^{3+}$) and Thulium ($\textnormal{Tm}^{3+}$) ions, aimed at investigating the up-conversion properties of LBP glass.
\section{Sample preparation and experimental techniques}
Four different glass samples with composition  $(44-\textnormal{x})$ ${\textnormal{B}_{2}\textnormal{O}_{3}}$ - $20${\textnormal{P}_{2}\textnormal{O}_{5}} -  $(26+\textnormal{x})$\textnormal {PbO} - $10$\textnormal{Li}_{2}\textnormal{O}$, where $\textnormal{x}=2,4,6,$ and $8$ mol\% were prepared using the melt quenching technique. The detailed chemical composition and label of all the synthesised LBP samples is displayed in Table 1. Batch of 8g was prepared by taking appropriate amount of high purity $\textnormal{H}_{3}\textnormal{BO}_{3}$, $\textnormal{NH}_{4}\textnormal{H}_{2}\textnormal{PO}_{4}$, $\textnormal{PbO}$, $\textnormal{Li}_{2}\textnormal{CO}_{3}$. After properly weighed by electronic weighing balance, the powdered mixture was melted at 1100 \textdegree{C} in electric furnace in alumina crucible. The quenched samples were annealed at 400 \textdegree{C} for 10 hours to remove any thermal strain. As shown in Figure 1 glass samples are bubble free and transparent. The glasses were than ground to powder for structural and optical studies. Density was measured using the Archimedes' principle to observe the changes that occur with increasing concentration of PbO in the structure. The density value was used to calculate other physical parameters namely molar volume, ion concentration, polaron radius and inter-ionic distance. X-ray diffraction (XRD) and Fourier transform infrared spectroscopy (FTIR) are useful techniques to investigate the structure of the prepared glasses. The absence of sharp peaks in XRD spectra signify the non-crystalline nature of the prepared glass samples \cite{22}. XRD spectra were recorded using a Rigaku Miniflex 600-pro, employing CuK_{$\alpha$} radiation $(\lambda$=1.54 \r{A}) at 40 kV and 15 mA. FTIR is used to analyse the structure of the glass by identifying various structural units present in the glass structure. As different atoms/molecules absorb different energy/wavelength so they give a unique band in FTIR spectra \cite{23}. FTIR spectroscopy was conducted on the glass specimens using a Perkin Elmer Spectrum Two spectrometer equipped with a KBr window, $\textnormal{LiTaO}_{3}$ detector, and a resolution of 0.5 $\textnormal{cm}^{-1}$. Optical properties were studied with the help of UV-visible absorption spectroscopy in which the amount of light absorbed by the glass sample was observed from the absorption spectra \cite{24}. The various optical parameters like indirect band gap, refractive index, molar refractivity, molar polarizability, electronic polarizability and dielectric constant were calculated \cite{25,26,27,28}. To conduct optical analysis of the glass samples, ultraviolet-visible near-infrared (UV-Vis-NIR) absorption spectra were obtained using a Hitachi-UH 5700 spectrometer. This spectrometer has a resolution of 0.1 nm, utilizes a 50 W Tungsten-halogen and Deuterium lamp as a light source, and provides an accuracy of 0.1 nm for UV-visible measurements and 1.5 nm for the NIR region. Luminescence properties can be analyzed by exciting the sample at a specific wavelength, which is selected from the UV-Vis absorption spectra. To investigate the luminescent characteristics of the fabricated glass samples, photoluminescence (PL) spectroscopy was conducted using a Horiba Jobin Yvon Fluorolog-3 spectrofluorometer. This instrument utilized a 450 W continuous-wave Xenon arc lamp as an excitation source, offering an accuracy of 0.5 nm and a resolution of 0.2 nm.  All the studies were conducted at room temperature. The formulae and necessary details of calculation of physical, structural and optical parameters have been explained in our previous studies \cite{29,30,31}. 


\begin{table}
\label{table1}
\centering
\caption{Glass code and chemical composition of LBP glasses}\\
\vspace{1ex}
\begin{tabular*}{\columnwidth}{@{\extracolsep{\fill}}|CCCCC|}
\hline
 Glass code & $\textnormal{B}_2\textnormal{O}_3$ & $\textnormal{P}_2\textnormal{O}_5$ & $\textup{PbO}$ & $\textnormal{Li}_2\textnormal{O}$   \\
 
\hline
 
   LBP1 & $42$ & $20$ & $28$ & $10$  \\
   
   LBP2 & $40$ & $20$ & $30$ & $10$ \\
   

  LBP3 & $38 & $20$ & $32$ & $10$ \\
  
  LBP4 & $36$ & $20$ & $34$ & $10$ \\
  
  
  
  
  \hline
  



\end{tabular*}

\end{table}


\begin{figure} [H]
\begin{center}
\includegraphics[scale=0.6]{sam_image.jpg}
\caption{The prepared lithium lead borophosphate glass samples }
\end{center}
\end{figure}


\section{Results and Discussion}
\subsection{Lithium Lead Borophosphate glasses}
\subsubsection{Physical parameters}
The density and the physical parameters evaluated with its help are displayed in Table 2.  Addition of a chemical substance in the glass structure either helps in bond formation, making the structure stable and compact, or makes the structure open by creating non bridging oxygen atoms (NBOs). Bond formation leads to decrease in molar volume and consequently increase in density. With the increment of PbO, there is an increase in the overall molecular weight of each sample and consequently, this lead to an enhancement in the density upto LBP4 sample \cite{32}.  Decrease in molar volume signifies the increase in compactness due to bond formation by PbO in the structure because both oxygen and lead have higher electronegativity than other constituents. Ion concentration also showed linear behavior with increasing concentration of PbO. Polaron is a quantum unit of electron phonon interaction, when electron passes through the lattice, it distorts the region and this region is called polaron radius \cite{33}. From the results, polaron radius was observed to decreased; this infers that there is less distortion or more stable structure with increasing PbO concentration.  Results of increasing density and decreasing molar volume were also be verified from the decrease in inter ionic distance. Decrease in inter ionic distance make the structure more compact. Therefore, the involvement of PbO in the glass structure was affirmed by the physical parameters. 

\begin{table}[H]
\centering
\caption{Physical parameters of LBP glasses}
\vspace{1ex}
\begin{tabular}{|l|c|c|c|c|} 
\hline
 Physical parameters & LBP1 & LBP2 & LBP3 & LBP4  \\
\hline
 
   Density ($\rho$) (\textnormal{g}/\textnormal{cm}^{3}) & $3.13$ & $3.48$ & $4.13$ & $4.51$  \\  
   Molar volume ($V_{m}$) (\textnormal{cm}^{3}/mol) & $37.98$ & $35.08$ & $30.34$ & $28.49$ \\
   

   Ion concentration $(N)(\times10^{21})$ (ions/\textnormal{cm}^{3}) & $4.43$ & $5.41$ & $6.34$ & $7.18$ \\
  
  Polaron radius (r_{p})(\r {\textnormal A}) & $2.45$ & $2.29$ & $2.17$ & $2.09$ \\
  
  Inter-ionic distance (r_{i})(\r {\textnormal A}) & $6.08$ & $5.69$ & $5.40$ & $5.18$\\
  
  \hline
  

 

\end{tabular}

\end{table}





\subsubsection{X-ray diffraction (XRD)}
XRD spectra of the prepared LBP glass samples are shown in Figure 2. As the spectra show no sharp peaks, it confirmed the glassy nature of the prepared samples.  Nevertheless, in all samples, there is a noticeable small hump, which aligns with findings from our previous research \cite{29,30,31}. The significance of this hump lies in the existence of minor crystalline domains within the $25^{\circ}$-$30^{\circ}$ range in the glass cooling process during melt quenching.
\begin{figure} [H]
\begin{center}
\includegraphics[scale=0.9]{xrd_image.jpg}
\caption{X-ray diffraction spectra of prepared LBP glass samples }
\end{center}
\end{figure}

\subsubsection{Fourier transform infrared (FTIR) spectroscopy }
\begin{figure} [H]
\begin{center}
\includegraphics[scale=0.5]{ftir_image.jpg}
\caption{ FTIR spectra of prepared LBP glass samples  }
\end{center}
\end{figure}


The FTIR absorbance spectra of LBP glasses are shown in Figure 3. The vibrational bands are observed around 450-500 $\textnormal{c}\textnormal{m}^{-1}$, 500-565 $\textnormal{c}\textnormal{m}^{-1}$, 600-800 $\textnormal{c}\textnormal{m}^{-1}$, 800-1180 $\textnormal{c}\textnormal{m}^{-1}$, 1180-1280 $\textnormal{c}\textnormal{m}^{-1}$ and 1320-1390 $\textnormal{c}\textnormal{m}^{-1}$. The presence of $\textnormal{PbO}_{4}$ units due to $\textnormal{PbO}$ can be inferred from the band centred at 468 $\textnormal{c}\textnormal{m}^{-1}$ \cite{15,34,35}. Vibrations around 550 $\textnormal{c}\textnormal{m}^{-1}$ are due to presence of deformation vibration modes of P-O bonds in $\textnormal{PO}_{4}$ units \cite{36,37}. The bending vibrations of bridging oxygens in B-O-B, originating from penta-borate groups, are responsible for the band observed around 700 $\textnormal{c}\textnormal{m}^{-1}$. B-O stretching vibrations of $\textnormal{BO}_{4}$ units can be confirmed from vibrations around 1030 $\textnormal{c}\textnormal{m}^{-1}$ \cite{36,38,39,40}. The vibrational band around 1247 $\textnormal{c}\textnormal{m}^{-1}$ is linked to the asymmetric stretching vibration of the $\textnormal{PO}_{2}$ group, which corresponds to $\textnormal{P}^{2}$ units (where the superscript 2 signifies the number of bridging oxygen atoms attached to P) \cite{41,42}. It is important to mention that the symmetric stretching of $\textnormal{P=O}$, which relates to $\textnormal{P}^{3}$ units, can also be detected in the range of 1180-1280 $\textnormal{c}\textnormal{m}^{-1}$. Vibrations around 1362 $\textnormal{c}\textnormal{m}^{-1}$ are assigned to symmetric stretching vibrations of $\textnormal{P=O}$ bands \cite{35,36,37}. The FTIR spectra confirmed the structural units due to PbO, $\textnormal{P}_{2}\textnormal{O}_{5}$ and $\textnormal{B}_{2}\textnormal{O}_{3}$. As PbO is known for its dual role as a former or a modifier, presence of $\textnormal{PbO}_{4}$ units confirmed the role of PbO as a former in the structure in all LBP samples. The differences in intensity observed among various bands or vibrations are ascribed to the presence of bridging oxygen atoms and variations in molecular weights across the different LBP samples.  The peak positions of certain bands seem to shift as the concentration of PbO increases, suggesting that PbO is actively participating in the structure of the LBP glasses. Table 3 illustrates all the major bands/vibrations of thulium doped borophosphate glass as discussed above.


\begin{table} [H] 
\centering
\caption{Assignments of IR absorbance bands of lithium lead borophosphate glasses}
\vspace{1ex}
\begin{tabular*}{\columnwidth}{@{\extracolsep{\fill}}|c|c|}
\hline

Wavenumber ($\textnormal{cm}^{-1}$) & Band assignmnet \\
\hline

500-450 & Bending vibrations of $\textnormal{PbO}_{4}$ due to ${\textnormal{PbO}$ \\
565-500 & Deformation vibrations of P-O bond due to ${\textnormal{P}\textnormal{O}_{4}}$ units \\

600-800 &  B-O-B's bending vibrations\\

1180-800 & Stretching vibrations of tetrahedral $\textnormal{B}\textnormal{O}_4$ units\\

1280-1180 & Asymmetric and symmetric vibrations of P-O bonds in $\textnormal{PO}_{2}$ group \\
1390-1320 & Symmetric stretching vibrations of P=O \\
 
\hline
\end{tabular}
\end{table}



\subsubsection{Optical parameters}
The UV-visible absorption spectra of the LBP samples is shown in Figure 4 (a).   The optical parameters, indirect band gap, refractive index, molar refractivity, molar polarizability, electronic polarizability and dielectric constant  calculated from the absorption spectra are shown in Table 4.  Mott and Davis equation has been applied to evaluate the indirect optical band gap and is calculated by extrapolating the linear region of Tauc's curve \cite{26,27}. The Tauc's plots for evaluation of indirect band gap are shown in Figure 4 (b). The indirect band gap increased from 4.80 eV to 4.90 eV as the concentration of PbO in the glass structure increased. The increase in the indirect band gap is attributed to the formation of bridging oxygen atoms in the structure, which occurs as the concentration of PbO increases. The presence of bridging oxygen atoms results in a stronger hold on electrons, necessitating a substantial amount of energy to transfer them to excited states. Molar refractivity ($R_{m}$), molar polarizability ($\alpha_{m}$)  and electronic polarizability ($\alpha_{e}$) depict the polarized nature of the prepared glasses \cite{25}. Because of partial negative charge, NBO atoms exhibit greater polarizability compared to bridging oxygen atoms and due to this reason $R_{m}$, $\alpha_{m}$, $\alpha_{e}$ showed decreasing trend with increasing concentration of PbO. Refractive index decreased marginally with increasing concentration of PbO in the glass structure.

\begin{figure} [H]
\begin{center}
\includegraphics[scale=0.3]{uvbd_image.jpg}
\caption{ (a) UV-Vis absorption spectra of LBP glasses, (b) Tauc's plots for indirect band gap}
\end{center}
\end{figure}




\begin{table} [H] 
\centering
\caption{Optical parameters of LBP glasses}
\vspace{1ex}
\begin{tabular*} {\columnwidth}{@{\extracolsep{\fill}} |l|c|c|c|c|}
\hline
 Optical parameters & LBP1 & LBP2 & LBP3 & LBP4 \\
\hline

   Indirect band gap (eV) & $4.80$ & $4.83$ & $4.88$ & $4.90$  \\
   Refractive index (n) & 2.03& 2.02& 2.01& 2.01 \\

  Molar refractivity (R_{m}) & $19.36$ & $17.77$ & $15.37$ & $14.34$ \\
  
  Molar polarizability (a_{m})(\r {\textnormal A})^{3} & $7.67$ & $7.04$ & $6.09$ & $5.68$\\
  
  Electronic polarizability (\alpha_{e})(\r {\textnormal A})^{3} & $0.21$ & $0.20$ & $0.19$ & $0.19$ \\
  
  Dielectric constant (\epsilon) &4.12	&4.08	&4.04	&4.04\\
  \hline
  

\end{tabular*}

\end{table}







\subsection{Rare earth doped LBP glasses}
The up-conversion properties of rare earth doped lithium lead borophosphate glasses have been analyzed in this study. Due to highest concentration of PbO in LBP4 sample, it was selected for doping of Erbium ($\textnormal{Er}^{3+}$), Neodymium ($\textnormal{Nd}^{3+}$) and Thulium ($\textnormal{Tm}^{3+}$). Three different rare earth activated LBP samples were prepared using the melt quenching technique and the detailed composition of these glasses is shown in Table 5



\begin{table} [H]
\label{table1}
\centering
\caption{Glass code and chemical composition of erbium, neodymium and thulium doped lithium lead borophosphate glasses}\\
\vspace{1ex}
\begin{tabular*}{\columnwidth}{@{\extracolsep{\fill}}|CCCCCCCCC|}
\hline
 Glass code & $\textnormal{B}_2\textnormal{O}_3$ & $\textnormal{P}_2\textnormal{O}_5$ & $\textup{PbO}$ & $\textnormal{Li}_2\textnormal{O}$ & $\textnormal{Yb}_2\textnormal{O}_3$ & $\textnormal{Er}_2\textnormal{O}_3$ & $\textnormal{Nd}_2\textnormal{O}_3$ & $\textnormal{Tm}_2\textnormal{O}_3$  \\
 
\hline
 
   EBP & $35$ & $20$ & $34$ & $10$ & $0.5$ & $0.5$ & $0.0$ & $0.0$  \\
   
   NBP & $35$ & $20$ & $34$ & $10$ & $0.5$ & $0.0$ & $0.5$ & $0.0$ \\
   

  TBP & $35$ & $20$ & $34$ & $10$ & $0.5$ & $0.0$ & $0.0$ & $0.5$ \\
  \hline
  
\end{tabular*}

\end{table}





\subsubsection{Erbium doped lead borophosphate glass (EBP)}
\subsubsection*{UV-Vis-NIR absorption analysis}
The absorption spectrum of EBP glasses is shown in Figure 5. The absorption peaks/bands at $365$, $378$, $403$, $451$, $489$, $521$,  $544$, $651$ nm and $798$ corresponding to excited energy levels $^4\textnormal{G}_{9/2}$,$^4\textnormal{G}_{11/2}$,$^2\textnormal{G}_{9/2}$, $^4\textnormal{F}_{5/2}$, $^4\textnormal{F}_{7/2}$, $^2\textnormal{H}_{11/2}$, $^4\textnormal{S}_{3/2}$ and $^4\textnormal{F}_{9/2}$ and $^4\textnormal{I}_{9/2}$ obtained by absorption from ground state $^4\textnormal{I}_{15/2}$ of erbium \cite{43,44}. Of all the peaks, $^4\textnormal{G}_{11/2}$  and $^2\textnormal{H}_{11/2}$ possess maximum intensity due to their  hypersensitive nature. Ytterbium showed its characteristic absorption peak around 980 nm due to $^2\textnormal{F}_{7/2}$ \rightarrow $^2\textnormal{F}_{5/2}$ \cite{10}. From the absorption spectra, wavelength of 980 nm was chosen for studying UC studies. 


\begin{figure} [H]
\begin{center}
\includegraphics[scale=0.6]{eruv_image.jpg}
\caption{UV-Vis-NIR absorption spectrum of prepared EBP glass sample}
\end{center}
\end{figure}


\subsubsection*{UC spectrum of EBP sample under 980 excitation}
The PL emission spectrum of EBP sample, excited at 980 nm is shown in Figure 6 and the emission at 520 nm, 547 nm and 665 nm was observed. Figure 7 illustrates the detailed mechanism behind these emissions. The energy levels, specifically $^4\textnormal{I}_{11/2}$ of $\textnormal{Er}^{3+}$ and $^2\textnormal{F}_{5/2}$ of $\textnormal{Yb}^{3+}$, are in resonance, enabling efficient energy transfer between them \cite{45}. $\textnormal{Yb}^{3+}$ exhibits a higher absorption cross-section around 980 nm compared to $\textnormal{Er}^{3+}$, allowing it to absorb the excitation energy and subsequently transfer the absorbed energy to $\textnormal{Er}^{3+}$, called energy transfer up-conversion (ETU) \cite{17}. This energy transfer from ytterbium  results in excitation of electrons of $\textnormal{Er}^{3+}$ from ground state $^4\textnormal{I}_{15/2}$ to $^4\textnormal{I}_{11/2}$ (ETU1). This energy transfer is either radiative re-absorption by erbium, when excited $\textnormal{Yb}^{3+}$ ions return to the ground state and transfer their energy to erbium, or radiationless transfer, commonly known as Dexter energy transfer \cite{46,47} . Another energy transfer from ytterbium also further results in excited state absorption (ESA) at the $^4\textnormal{I}_{11/2}$ level, subsequently promoting the erbium ions to the $^4\textnormal{F}_{7/2}$ level (ETU2) \cite{47}. A non-radiative transition from the $^4\textnormal{F}_{7/2}$ level populates the $^2\textnormal{H}_{11/2}$ and $^4\textnormal{S}_{3/2}$ levels \cite{48,49}. Finally, a radiative transition from the $^2\textnormal{H}_{11/2}$ and $^4\textnormal{S}_{3/2}$ levels to the $^4\textnormal{I}_{15/2}$ level emits light at wavelengths of 520 nm and 547 nm, respectively. The emission at 665 nm occurs through a radiative transition from the $^4\textnormal{F}_{9/2}$ level to the $^4\textnormal{I}_{15/2}$ level \cite{50}. The $^4\textnormal{F}_{9/2}$ level is populated either by a non-radiative transition from the $^4\textnormal{S}_{3/2}$ level or by energy transfer from the $^4\textnormal{I}_{13/2}$ level to the $^4\textnormal{F}_{9/2}$ level facilitated by $\textnormal{Yb}^{3+}$ \cite{47}. The $^4\textnormal{I}_{13/2}$ level, in turn, is populated through a non-radiative transition from the $^4\textnormal{I}_{11/2}$ level during ETU1. Hence, wavelength of 980 nm is up-converted to 520 nm, 547 nm and 665 nm.


\begin{figure} [H]
\begin{center}
\includegraphics[scale=0.5]{eru_image.jpg}
\caption{Emission spectrum of EBP glass sample excited at 980 nm}
\end{center}
\end{figure}


\begin{figure} [H]
\begin{center}
\includegraphics[scale=0.6]{erm_image.jpg}
\caption{Up-conversion mechanism of EBP sample under 980 nm excitation}
\end{center}
\end{figure}





\subsubsection{Neodymium doped lead borophosphate glass (NBP)}
\subsubsection*{UV-Vis-NIR absorption studies}
The UV-Vis-NIR absorption spectrum of the prepared NBP glass is shown in Figure 8 and the transitions are observed at 806 nm (^4\textnormal{F}_{5/2}$+$^2\textnormal{H}_{9/2}$), 742 nm (^4\textnormal{F}_{7/2}$+$^4\textnormal{S}_{3/2}$), 684 nm (^4\textnormal{F}_{9/2}$), 626 nm (^2\textnormal{H}_{11/2}$), 581 nm (^4\textnormal{G}_{5/2}$+$^2\textnormal{G}_{7/2}$), 523 nm (^4\textnormal{G}_{7/2}$+$^4\textnormal{G}_{9/2}$+ $^2\textnormal{K}_{13/2}$) , 431 nm (^2\textnormal{D}_{5/2}$+$^2\textnormal{P}_{1/2}$), 358 nm (^4\textnormal{D}_{3/2}$+$^4\textnormal{D}_{5/2})$, 338 nm (^2\textnormal{I}_{11/2}$) and 315 nm ($^4\textnormal{D}_{7/2}+ $^2\textnormal{I}_{13/2}+ $^2\textnormal{L}_{15/2})$. All the transitions have taken place from the ground state $^4\textnormal{I}_{9/2}$ of $\textnormal{Nd}^{3+}$ \cite{51}. Among the various absorption transitions, 581 nm is hypersensitive transition and is the most intense. Peak around 977 nm is characteristic absorption by ytterbium.



\begin{figure} [H]
\begin{center}
\includegraphics[scale=0.9]{nduv_image.jpg}
\caption{UV-Vis-NIR absorption spectrum of prepared NBP glass sample}
\end{center}
\end{figure}


\subsubsection*{UC spectrum of NBP sample under 980 nm excitation}
The emission spectrum resulting from up-conversion ($\lambda_{exc}$ = 980 nm) and the underlying mechanism are depicted in the Figure 9 and Figure 10. As discussed earlier when excited by 980 nm,  the $\textnormal{Yb}^{3+}$ ions undergo a transition from the $^2\textnormal{F}_{7/2}$ to the $^2\textnormal{F}_{5/2}$ energy level. Subsequently, the energy is transferred to $\textnormal{Nd}^{3+}$ ions, causing them to transition to the $^4\textnormal{F}_{3/2}$ level \cite{52}. During the process of energy transfer, any surplus or deficit of energy is balanced through interactions with phonons (lattice vibrations), a phenomenon known as phonon-assisted energy transfer (PAET) \cite{46}. Upon reaching the $^4\textnormal{F}_{3/2}$ energy level, the $\textnormal{Nd}^{3+}$ ions undergo excited state absorption (ESA), leading to their transfer to the $^2\textnormal{G}_{9/2}$ level \cite{53}. Non-radiative transitions from $^2\textnormal{G}_{9/2}$ then cause the $\textnormal{Nd}^{3+}$ ions to shift down to the $^4\textnormal{G}_{9/2}$ energy level. The energy difference between $^4\textnormal{G}_{9/2}$ and $^4\textnormal{G}_{7/2}$ is 400 $\textnormal{c}\textnormal{m}^{-1}$, which promotes the population of $^4\textnormal{G}_{7/2}$ from $^4\textnormal{G}_{9/2}$ through non-radiative traansition. From the $^4\textnormal{G}_{7/2}$ level, radiative transitions to $^4\textnormal{I}_{9/2}$, $^4\textnormal{I}_{11/2}$, and $^4\textnormal{I}_{13/2}$ lead to the emission of light at 542 nm, 602 nm, and 660 nm, respectively \cite{53,54}. Among these transitions, the ground state $^4\textnormal{I}_{9/2}$ is the most stable, causing the 542 nm emission ($^4\textnormal{G}_{7/2}$ \rightarrow$^4\textnormal{I}_{9/2}$) to be more intense than the others. 
Hence, wavelength of 980 nm is up-converted to 542 nm, 602 nm and 660 nm.

\begin{figure} [H]
\begin{center}
\includegraphics[scale=0.4]{ndu_image.jpg}
\caption{Emission spectrum of NBP glass sample excited at 980 nm}
\end{center}
\end{figure}


\begin{figure} [H]
\begin{center}
\includegraphics[scale=0.6]{ndm_image.jpg}
\caption{Up-conversion mechanism of NBP sample under 980 nm excitation}
\end{center}
\end{figure}



\subsubsection{Thulium doped lead borophosphate glass (TBP)}
\subsubsection*{UV-Vis-NIR absorption investigations}
The UV-Vis-NIR absorption spectrum of TBP glass sample is shown in Figure 11 . The transitions were observed at 466 nm ($^1\textnormal{G}_{4}$), 684 nm ($^3\textnormal{F}_{3}$), 790 nm ($^3\textnormal{H}_{4}$) and 1210 nm ($^3\textnormal{H}_{5}$) and all these transitions are originating from ground state $^3\textnormal{H}_{6}$ of thulium \cite{55}. Peak around 978 nm is due to absorption by ytterbium ($^2\textnormal{F}_{7/2}$ \rightarrow $^2\textnormal{F}_{5/2}$). For UC studies, TBP glass sample is excited at 980 nm.


\begin{figure} [H]
\begin{center}
\includegraphics[scale=0.6]{tmuv_image.jpg}
\caption{UV-Vis-NIR absorption spectrum of prepared TBP glass sample}
\end{center}
\end{figure}


\subsubsection*{UC spectrum of TBP sample under 980 excitation}
The PL emission spectrum of TBP sample excited at 980 nm is shown in Figure 12 and the detailed mechanism of UC is shown in Figure 13. The peaks were observed at 488 nm, 521 nm and 649 nm and these peaks are due to energy transfer (ET) from $\textnormal{Yb}^{3+}$. Due to large absorption cross-section of $\textnormal{Yb}^{3+}$ ions around 980 nm,  only $\textnormal{Yb}^{3+}$ ions absorb the excitation energy of 980 nm; and three successive energy transfers populate the different excited levels of $\textnormal{Tm}^{3+}$ ions \cite{56}. During each instance of energy transfer from $\textnormal{Yb}^{3+}$ ions, the $\textnormal{Yb}^{3+}$ ions undergo a process of de-excitation from the $^2\textnormal{F}_{5/2}$ level to the $^2\textnormal{F}_{7/2}$ level \cite{57}. Phonons play a crucial role in energy transfer upconversion (ETU) as they help compensate for any excess or deficit energy between the two levels involved in the transfer \cite{46}. When the $\textnormal{Yb}^{3+}$ ions absorb energy at 980 nm, their electrons are excited from the $^2\textnormal{F}_{7/2}$ state to the $^2\textnormal{F}_{5/2}$ state. Subsequently, this excited energy is transferred to $\textnormal{Tm}^{3+}$ ions, causing the population of the $^3\textnormal{H}_{5}$ energy level (ET1). Through a non-radiative relaxation process, the $^3\textnormal{F}_{4}$ energy level of $\textnormal{Tm}^{3+}$ is populated. Another energy transfer from $\textnormal{Yb}^{3+}$ ions results in the excitation of electrons from the $^3\textnormal{F}_{4}$ energy level to the $^3\textnormal{F}_{2,3}$ energy level (ET2). This is followed by a non-radiative transition where the electrons are transferred from the $^3\textnormal{F}_{2,3}$ energy level to the $^3\textnormal{H}_{4}$ energy level \cite{58}. Finally, the $^1\textnormal{G}_{4}$ energy level is populated through another energy transfer from $\textnormal{Yb}^{3+}$ ions resulting in transferring of electrons from $^3\textnormal{H}_{4}$ to $^1\textnormal{G}_{4}$ level (ET3). Emission of wavelengths at 488 nm and 649 nm occurs through radiative transitions from the $^1\textnormal{G}_{4}$ energy level to the $^3\textnormal{H}_{6}$ energy level and the $^3\textnormal{F}_{4}$ energy level, respectively \cite{56,57,58}. Apart from energy transfer from $\textnormal{Yb}^{3+}$ ions, cross relaxation between two $\textnormal{Tm}^{3+}$ ions also occurs at the $^3\textnormal{F}_{3}$ level, with one being excited to $^1\textnormal{D}_{2}$ while the other returns to the ground, leading to the population of the $^1\textnormal{D}_{2}$ level \cite{59}. However, it is worth noting that energy transfer to the $^1\textnormal{D}_{2}$ level from the $^1\textnormal{G}_{4}$ level is not possible with $\textnormal{Yb}^{3+}$ ions due to a significant energy mismatch. Consequently, the emission at 521 nm is generated through the transition from the $^1\textnormal{D}_{2}$ energy level to the $^3\textnormal{H}_{5}$ energy level \cite{58,60}.





\begin{figure} [H] 
\begin{center}
\includegraphics[scale=0.45]{tmu_image.jpg}
\caption{Emission spectrum of TBP glass sample excited at 980 nm}
\end{center}
\end{figure}


\begin{figure} [H]
\begin{center}
\includegraphics[scale=0.72]{tmm_image.jpg}
\caption{Up-conversion mechanism of TBP sample under 980 nm excitation}
\end{center}
\end{figure}

The up-conversion results showed that the prepared lithium lead borophosphate glasses are capable of up-converting the infrared light to visible light with inclusion of rare earth; thus proving a suitable host for up-conversion. Moreover, the doping of $\textnormal{Er}^{3+}$, $\textnormal{Nd}^{3+}$ and $\textnormal{Tm}^{3+}$ the glasses useful in application of color displays and visible lasers. 

\section{Conclusions}
To study the role of PbO as a glass component, four lithium lead borophosphate glasses were synthesized by melt quenching technique by increasing the concentration of PbO is increased by 2 mol \%. Absence of sharp peaks in the XRD spectra of prepared glasses proved the non-crystalline nature of the glasses. Increase in overall molecular weight of the glass sample and bond formation by PbO in the structure, leads to increase in density and decrease in molar volume The polaron radius and inter-ionic distance also showed decreasing trend with increasing concentration of PbO, thereby proving the participation of PbO in the structure. The FTIR spectra validated the presence of distinct structural units due to $\textnormal{P}_{2}\textnormal{O}_{5}$, $\textnormal{B}_{2}\textnormal{O}_{3}$ and PbO. The vibrations occurring around 465 $\textnormal{c}\textnormal{m}^{-1}$, corresponding to $\textnormal{PbO}_{4}$ units, confirmed the role of PbO as a former in all the prepared samples. Indirect band gap was calculated from Tauc's plots and showed increasing trend (4.80 eV to 4.90 eV) with increasing concentration of PbO. This increase can be attributed to presence of bridging oxygen atoms in the structure. Lack of non-bridging oxygen atoms is responsible for the decreasing trend of refractive index, molar refractivity, molar polarizability, electronic polarizability and dielectric constant. As PbO is known for its influence on luminescence properties of glass as it lowers the phonon energy of the glass structure. The host with low phonon energies are great for up-conversion; so, from the prepared LBP samples, LBP4 sample was selected for doping $\textnormal{Er}^{3+}$, $\textnormal{Nd}^{3+}$ and $\textnormal{Tm}^{3+}$ and $\textnormal{Yb}^{3+}$ for up-conversion properties. Three different glass samples, EBP ($\textnormal{Er}^{3+}$-$\textnormal{Yb}^{3+}$), NBP ($\textnormal{Nd}^{3+}$-$\textnormal{Yb}^{3+}$) and TBP ($\textnormal{Tm}^{3+}$-$\textnormal{Yb}^{3+}$) were prepared using the melt quenching technique. The UV-Visible-NIR absorption spectra of EBP, NBP and TBP glass samples were recorded and wavelength of 980 nm was selected to excite the samples for UC studies.  The EBP sample upon excitation at 980 nm emitted wavelength of 520 nm, 547 nm and 665 nm. NBP glass radiated wavelength of 500 nm, 535 nm, 601 nm and 658 nm. TBP sample showed emission at 488 nm, 521 nm and 649 nm. The all prepared samples emit visible light through up-conversion when exposed to 980 nm light. Ytterbium served as the sensitizer, facilitating the transfer of its absorbed energy to the co-doped lanthanide ions. The LBP4 sample is a suitable host fot UC, and the UC ability of rare earth doped LBP glasses makes them a potential candidate for visible emission, color displays and laser applications.

\section*{Acknowledgments}
We are thankful to Sophisticated Analytical Instrument Facility (SAIF), IIT Bombay, for providing photoluminescence spectroscopy. 

\section*{Declarations}
\textbf{Availability of data and materials}\\
Data will be made available on request.\\
\\
\textbf{Conflict of Interest Statement }\\
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\\
\\
\textbf{Funding}\\
There are no funding sources.\\
\\
\textbf{Ethical approval}\\ This study did not require formal ethical approval as it did not involve human participants, animal subjects or sensitive data. The research adhered to the ethical guidelines and standards for conducting non-invasive and non-interventional research as outlined by Punjabi University, Patiala, Punjab, India.





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