Enhanced linear and nonlinear optical properties of erbium/ytterbium lead phosphate glass by gamma irradiation for optoelectronics applications

Herein, this study intends to reveal the impact of gamma irradiation on the structural, linear, and nonlinear optical characteristics of 47P2O5−23Na2O−6Al2O3−22PbO−0.5Er2O3−1.5Yb2O3 glass. The Er/Yb-doped lead phosphate glass samples were produced using the traditional melt quenching procedure and then treated to different doses of gamma irradiation (0, 20, 50, and 100) kGy. The amorphous phase structure of the Er/Yb-doped lead phosphate glass samples was verified through XRD patterns. Also, the shift of the FTIR peaks due to the change in bond angles, and the change in the bond length of the P–O–P bridges means the glass network stability against radiation. With increasing irradiation dosages, the energy gap dropped from 4.11 eV to 3.42 eV and then enhanced to 3.48 at 100 kGy. At the same time, the Urbach energy enhanced from 10.23 eV to 37.03 eV. The oscillator energy Eo was found between 1.55 and 1.62 eV. Also, the dispersion energy Ed varied between 2.11 eV at 100 kGy and 2.71 eV at the dose of 50 kGy. The percentage of free carrier ions to effective mass (N/m*) is in the range (4.82–8.66) × 1047 cm3/g. Besides, the lattice dielectric constant (εl\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varepsilon }_{l}$$\end{document}) increased from 5.54 to 6.63 as the gamma dosages increased. Furthermore, increasing gamma doses up to 50 kGy promotes susceptibility, which subsequently declines at 100 kGy, suggesting that increasing gamma doses over 50 kGy weakens polarizability potential. While the increasing gamma doses up to 50 kGy reduces the nonlinear refractive index and then improves at 100 kGy. Overall, the nonlinear and linear research revealed that Er/Yb lead phosphate glass is being used as a promising material for gain media and optical amplifiers.


Introduction
The scientific community has recently focused on manufacturing and analyzing optical glass systems doped with heavy metal oxide (HMO) and its special applications in optics, photonic devices, and nuclear engineering [1][2][3][4][5]. Synthesis and characterization of new materials are important for several applications [6][7][8][9][10][11]. Furthermore, doping such substances with rare-earth (Re 3+ ) ions enhances their optical and electronic properties, good stability, and flexibility characteristics, allowing an intake of elements in their formulation to be accepted. While also lasers, solid-phase lighting systems, fiber amplification, photodetectors, storage systems, dosimeters, and renewable power their uses are advancing [2,[12][13][14][15][16][17]. Moreover, trivalent rare-earth (Re 3+ ) ions in glasses contain a substantial percentage of absorption bands in the Vis-NIR areas, making them useful as practical photonic elements for various purposes. Specifically, Er 3+ / causes either the introduction of new active defects or the activation of existing defects and the repair of these defects by recombination or recovery. Irradiation causes changes in the glass matrix's structure, including defects [30,38]. Optical spectra (UV-Vis light) are used to investigate the impact of radiation on glasses modified with rare-earth oxides that produce distinct emission bands in the UV-visible region [39]. Liberated electrons can pass through the glass matrix during the irradiation process, generating electron-hole pairs that are predicted to interact with non-bridging oxygen that occurs as defects in the host glass to capture the positive holes or liberated radicals, causing color centers to form in the glass network [27]. Ramesh et al. showed that the nonlinear optical (NLO) features improved with gamma irradiation doses increasing, suggesting that high-dose irradiated glasses might be valuable for photonic devices, especially optical limiters. It is worth noting that this study shows how gamma irradiation affects the NLO characteristics of lead phosphate glasses having Re 3+ ions (Er 3+ /Yb 3+ doped and co-doped). Research on the performance of radiation on Re 3+ doped and co-doped glasses is increasing attention in the photonics and dosimetry investigation fields [1,40,41].
Herein, this study intends to reveal the impacts of gamma ir radiation on the str uctural, linear, and nonlinear optical character istics of glass. The Er/Yb-doped lead phosphate glass sample was produced using the traditional melt quenching procedure and then treated to different doses of gamma irradiation (0, 20, 50, and 100) kGy. Also, our study guides the commercial preparation of Er 3+ /Yb 3+ co-doped lead phosphate glasses and active optoelectronic devices.

Er 3+ /Yb 3+ doped lead phosphate glasses preparation
G l a s s s a m p l e w i t h t h e c o m p o s i t i o n o f was prepared by the quenching melting method at 1100 °C at a muffle furnace during the melting process, the molten sample was stirred two times to obtain homogeneity for the molten components of the glassy sample. The molten glassy sample was poured into preheated stainless steel frames, followed by transferring the poured sample into another furnace at 300 °C to avoid thermal stress and let to cool gradually till it reached room temperature after 24 h. The obtained sample was divided into rectangle pieces and power for different measurements [42,43]. According to the chemical composition formula, the sample has density of 4.15 g/ cm 3 . The raw materials used for preparation are ammonium dihydrogen phosphate, sodium carbonate, aluminum oxide, lead oxide, erbium oxide, and ytterbium oxide.

Fourier transform infra-red (FTIR) studies
Phosphorus pentoxide has a molecular formula, P 4 O 10, but its common name is derived from the empirical formula (P 2 O 5 ). Phosphate glass is inorganic polymeric [57]. Phosphate glasses have a tetrahedral structure surrounded by four oxygen atoms, and each pair can only share one oxygen ion with the other [58,59]. In the phosphorus tetrahedral structure, three oxygen atoms bridge to neighboring tetrahedral, and the fourth is considered non-bridging oxygen (P = O) [60]. It is based on the concept that phosphate glasses are constructed from the number of the building unit (phosphate tetrahedra) to form the structure. The PO 4 unit has three bridging oxygen, which is the Q 3 unit. PO 4 unit with two bridging oxygen is Q 2 unit (metaphosphate). PO 4 unit, which has one bridging oxygen, is Q 1 (pyrophosphate). However, the PO 4 unit with no bridging oxygen is Q 0 (orthophosphate) [61].
The tetrahedral form results from SP 3 hybrid orbitals by outer electrons (3S 2 , 3P 3 ), and the fifth ʹe is promoted to the third orbital to form a strong П bond with oxygen 2P electrons. The tetrahedral links from covalent bridging oxygen can form different phosphate anions. The classification of the different tetrahedral phosphate anions (Q n ) according to BOs can be represented in Ref. [62].  Figure 2 shows FTIR spectra of Er/Yb-doped lead phosphate glass, whereas Table 1 illustrates the IR absorption peaks assignment for the investigated sample and compares it with other previously prepared phosphate glasses [27,63,64]. The spectra show two main areas; one is specific for phosphate groups located in the range from 400 to 1600 cm −1 , and the other is specific for OH molecules from 1640 to 4000 cm −1 . Figure 3a-d shows deconvoluted FTIR spectra of Er/Yb-doped lead phosphate glass samples before and   [66], 501 cm −1 is for Pb-metaphosphate bond due to the presence of lead oxide inside the glass network, 534 cm −1 is for harmonic bending of P-O-P and PbO 6 vibration mode while 564 cm −1 is for AlO 6 group vibration mode [67]. Another peak at 617 cm −1 may be related to bonds of Pb-O and Pb-O-P vibration from the formed (PbO 4 ) pyramidal groups. Also, the extended peak from 710 to 890 cm −1 is observed to deconvoluted into three peaks at 712, 764, and 889 cm −1 , where the peak at 712 cm −1 is for vibration in AlO 4 units as a former oxide, 764 cm −1 is for symmetric vibrations of P-O-P bond in pyrophosphate (P 2 O 7 ) 4− units and 889 cm −1 is considered to be due to the asymmetric vibration of bridging oxygen in P-O-P bonds of different metaphosphate units in the form of a ring, terminal, and chain units.
Two deconvoluted peaks are given at 958 cm −1 , associated with symmetric PO 3 and Pb-O from pyramidal groups (PbO 4 ), while the other is at 1074 cm −1 for asymmetrical vibration of PO 3 bonds in pyrophosphate units; this high intensity is due to Na ions. The other two deconvoluted peaks at 1150 cm −1 and 1247 cm −1 are for symmetrical and asymmetrical O-P-O bonds, respectively. Besides two peaks, one at 1383 cm −1 for (PO 3 ) 2− a terminal group that contains the doubly bonded oxygen P = O Stretching mode and 1617 cm −1 for the P−O−H bridge. All these peaks are assigned in Table 1. FTIR spectra concluded that the revealed characteristic vibrational bands are related to the presence of metaphosphates (PO 2-) and pyrophosphate (PO 3-) units, with the first in higher intensity.
In general, FTIR spectra of phosphate glasses are known to have several overlapped peaks, while the position of these peaks can be shifted owing to additives or  Table 2. Various induced defects have been detected relying on the intensity of radiation exposure and charged particle irradiation [68,69]. Glasses often have a limited range of orders and suffer from defect sites. Suppose the energy of the photon is greater than the bandgap. In that case, electrons are liberated from the valence band, and the remaining energy will be transferred to kinetic energy if the glasses are irradiated to electromagnetic fields [68]. Consequently, the escaped electrons migrate through the glass network. They are either captured via pre-existing defects for generating induced defect centers in the glasses or generate secondary electron cascades through knock-on collision with the bound electrons throughout the terms of excess energy Compton electrons. The major vibrated groups appeared in almost the same numbers and positions upon irradiation to various gamma doses as they achieved in the non-treated sample. It reveals that the total phosphate structural units (metaphosphate (PO 2-) and pyrophosphate (PO 3-)) units of the investigated glasses continue to stay in overall with their arrangement typically [70]. The reduction in pyrophosphate groups and the corresponding rise in metaphosphate groups might be ascribed to the decrease in the peak intensity at 1074 cm -1 after progressive gamma irradiation doses. In addition, the shift of the peaks, which matched with a decrease in intensity at 764 cm −1 upon irradiation with different gamma doses, may be due to a change in bond angles besides the change in the bond length of the P-O-P bridges which means the glass network stability against radiation [64,[71][72][73]. Also, decreasing the intensity of the peaks in the area of 600-650 cm −1 and 900-1200 cm −1 may be attributed to the rearrangement of defects and NBO originated by irradiation that resulted in conversion from PO 4 (tetrahedral groups) to PO 3 units [5].

The absorption spectra behavior
The absorption spectra of Er-Yb lead phosphate glass samples are shown in Fig. 4. For the pristine glass sample (0 kGy), the absorption bands can be categorized into three mean regions; the first one is located in the range of 190-300 nm for the oxygen deficient center (ODC), which depends on the existence Table 2 Deconvolution parameters of the infra-red spectra of studied glasses; band center, relative area, and the amplitude for the samples bands  [74][75][76][77]. In general, irradiation causes the electrons that are already present in the glass matrix to get excited, and these excited electrons have the potential to eject themselves in accordance with the dosage, therefore, increasing the number of NBOs. Irradiation causes some of these electrons to get excited, and some of those electrons may be utilised to heal defects that are already present in the glass matrix. But in the other hand, Yb ions have the ability to captivate these electrons in during charge transfer (CT) process between Yb and Er, which will also assist in returning some of the NBOs to the BOs and beginning to form more covalent bonds between the cations and the O 2− as observed by a reduction in the intensity of the bands with a small lower shift in the wavelength in the first region upon 20 and 100 kGy. The second and third areas do not produce any shift in the wavelength; rather, a rise in the band intensities is the only change that can be seen.

The spectral distribution of absorption index
The extinction coefficient (k) can be deduced as a function of the absorbance coefficient α (λ) [78][79][80].
(1) k = 4 The extinction coefficient (k) spectra of Er/Yb lead phosphate glass samples are presented in Fig. 5. The spectral behavior of k has been observed to be influenced by gamma dosages. Irradiation of Er/Yb lead phosphate glass decreases the absorption index but has little effect on the spectra' peak position of absorption bands. Also, it is worth noting that the value of k has never approached zero. This behavior might be considered a unique feature of free carriers' appearances.

The refractive index spectra (n)
The refractive index (n), which is controlled by the interaction of light with the electrons of the component atoms of the glass, is another essential characteristic of the optoelectronic properties of the studied glass. It is influence by oxides in the glass sample, cationic polarizability, and radiation doses. The rise in NBOs, created due to the effect of gamma radiation, increases the refractive indices of a standard glass system.
The spectra of the refractive index, n, for Er/Yb lead phosphate glass samples are seen in Fig. 6. We found that the value of n changes slightly after irradiation in all wavelength ranges. Also, the absorption peaks were shifted to higher wavelengths with increasing gamma radiation doses. 5 The extinction coefficient (k) spectra of Er/Yb lead phosphate glass samples Fig. 6 The refractive index spectra, n, of Er/Yb lead phosphate glass samples.

Urbach and optical bandgap energies
The Urbach energy, Eu, may be derived in the low incident photons energy spectrum through graphing the relationship between lnα and hν (see Fig. 7) [81]: The Urbach energy (E u ) values of Er/Yb lead phosphate glass samples are summarized and tabulated in Table 3. We will see that enhanced doses of up to 50 kGy improve the Urbach energy of Er/Yb lead phosphate glass samples and then declines at a dose of 100 kGy. That means the increase in the depolymerization of the glassy network up to 50 kGy making the glass samples less compacted due to more formation of NBOs amount. The Eu of Er/Yb lead phosphate glass samples increases from 10.23 eV for the pristine glass sample to 37.03 eV at 50 kGy.
Using the Tauc relation, the optical band gap energy of Er/ Yb lead phosphate glass samples was related to and h [82]: in which A is a constant, t denotes the transition type, and E g represents the energy gap As shown in Fig. 8, the direct optical band gap energy, E g , may be calculated by graphing (αhν) 2 as a function of (hν) for Er/Yb lead phosphate glass samples. Table 3 lists the values of the energy band gaps for direct transitions. We note that by increasing the irradiation doses up to 50 kGy, a decrease in the energy gap was observed and then increased at the dose of 100 kGy. The direct optical band gap energy decreased from 4.11 eV for pristine Er/Yb lead phosphate glass to 3.42 eV at 50 kGy. These results agree with previous findings of Urbach's energy behavior. That may explained as by increasing gamma doses, the amount of created excited electrons and nonbridging oxygen increased and moved through the already excited defects inside lead phosphate glass sample that act as tunnels between energy levels till reach 100 kGy where the excited electrons being to be captured by converting NBOs to BO that reduce the amount of net empty defects.
A material's optical density (Dopt) is related to its thickness and absorption coefficient. The present glass system's optical density (Dopt) may be computed using the formula below [34]: in which, r is the thickness of the sample. Figure 9 illustrates the optical density (D opt ) spectrum of Er/Yb lead phosphate glass samples. The optical density of the synthetic glass rises as gamma radiation exposures rise. This rise caused the wide near-visible band to shift in the direction of a higher wavelength, which was generated by a reduction in the bandgap.

Dispersion and the dielectric performance
The dispersion behavior plays a very important role in assessing optical materials since it is a vital factor in optical communication and the manufacturing of spectral dispersion technologies. The single oscillator model could be used to calculate the oscillator energy E o , dispersion energy E d , and static dielectric constant (ε ∞ = n 2 ) for Er/Yb lead phosphate glass samples, which can then be expressed using Wemple and DiDomenico formula [83].
The relationship between (n 2 −1) −1 and (hν) 2 for Er/Yb lead phosphate glass samples is seen in Fig. 10. Table 3 validates the (E o , E d , and ε ∞ ) values. Increased the irradiated dosages up to 50 kGy resulted in a significant rise in these values, which subsequently reduced at 100 kGy. The oscillator energy Eo was found between 1.55 to 1.62 eV. Also, the dispersion energy E d ranged from 2.11 eV at 100 kGy to 2.71 eV at the dose of 50 kGy. We observed that the dispersion constants values had been empirically related to the bandgap variation [84]. Also, the static dielectric constant varied between 2.36 and 2.66.
The percentage of free carrier ions to effective mass (N/m*) is reliant on the lattice dielectric constant (ε), wavelength λ, and the refractive index [85]: The relationship between (n 2 −k 2 ) vs. λ 2 for Er/Yb lead phosphate glass samples is seen in Fig. 11. Table 4 lists the values for these parameters. The percentage of free carrier ions to effective mass (N/m*) increased with increasing gamma doses but declined at 50 kGy, where the N/m* values in the range (4.82-8.66) × 10 47 cm 3 /g. Besides, the lattice dielectric constant ( l ) increased from 5.54 to 6.63 with increasing the gamma doses.

Nonlinear optical properties
The following expression was used to compute the nonlinear third-order optical susceptibility (χ (3) ) for Er/Yb lead phosphate glass samples using linear refractive index and dispersion parameters (E o and Ed) [86][87][88]: where A ~ 1.7 × 10 -10 esu [89]. The relationship between χ (3) and h for Er/Yb lead phosphate glass samples is shown in Fig. 12. The susceptibility χ (3) is the outcome of the Er/Yb lead phosphate glass samples reaction to the impacted electric field of light. We can see from Fig. 12 that increasing gamma doses up to 50 kGy enhances the susceptibility χ (3) and then reduces at 100 kGy, so we assume that the increase of gamma doses beyond 50 kGy reduces polarizability ability. The electrical polarizability of the irradiated Er/Yb lead phosphate glass samples opens up the prospect of using them in optoelectronics applications. Figure 13 demonstrates the correlation between the nonlinear refractive index and for Er/Yb lead phosphate glass samples. The nonlinear susceptibility can be used to calculate the nonlinear refractive index, n 2 , using the formula [86,87]: We can see that from Fig. 13 that increasing gamma doses up to 50 kGy reduces the nonlinear refractive index, n 2 , and then improves at 100 kGy, The nonlinear absorption coefficient β C spectra for Er/Yb lead phosphate glass samples were based on their band structure. It controls the energy states and may well be derived using the formula [86,87]: K c is constant (3100 cm/GW), Ep is the Kane energy, and the dispersion of absorption coefficient is denoted by F, which is related to photon energy. The nonlinear absorption coefficient β C varied as the gamma doses enhanced (Fig. 14).

Conclusion
The purpose of this study was to reveal the effect of gamma rays on the Er/Yb lead phosphate glass system's physical, structural, linear, and nonlinear optical characteristics. The Er/Yb lead phosphate glass's amorphous nature was verified using XRD patterns. FTIR spectra likewise reveal the resistance of Er/Yb lead phosphate glass against radiation with slight adjustments in the intensities of specific bands. The Eu value of Er/Yb lead phosphate glass samples increases from 10.23 eV for the pristine glass sample to 37.03 eV at 50 kGy. Also, the direct optical band gap energy decreased from 4.11 eV for pristine Er/Yb lead phosphate glass to 3.42 eV at 50 kGy. The (2h ∕E g ) 5 . Fig. 12 The relationship between χ (3) and h for Er/Yb lead phosphate glass samples Fig. 13 The correlation between the nonlinear refractive index n 2 and for Er/Yb lead phosphate glass samples oscillator energy Eo was found between 1.55 and 1.62 eV. Also, the dispersion energy E d ranged from 2.11 eV at 100 kGy to 2.71 eV at the dose of 50 kGy. The free carrier concentration (N) increased with increasing gamma doses but declined at 50 kGy, where the percentage of free carrier ions to effective mass (N/m*) values in the range (4.82-8.66) × 10 47 cm 3 /g. Besides, the lattice dielectric constant ( l ) increased from 5.54 to 6.63 with increasing the gamma doses. Furthermore, increasing gamma doses up to 50 kGy enhances the susceptibility χ (3) and then reduces at 100 kGy, assuming that increasing gamma doses beyond 50 kGy reduces polarizability ability. While the increasing gamma doses up to 50 kGy reduces the nonlinear refractive index and then improves at 100 kGy. Altogether, the nonlinear and linear findings demonstrate that Er/Yb lead phosphate glass could be a potential candidate for optical applications such as gain media and optical amplifiers.
Funding Open access funding provided by The Science, Technology & Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB).

Conflict of interest
The authors declare that they have no conflict of interest.
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