The Fluorescence of Pr 3 + in Zinc Lithium Bismuth Borate Glasses with Large Stimulated Emission Cross Section

Glass sample of Zinc Lithium Bismuth Borate (25−x) Bi2O3:20Li2O:20ZnO:35B2O3:xPr6O11, (where x = 1, 1.5 and 2 mol%) has been prepared by melt-quenching technique. The amorphous nature of the prepared glass samples was confirmed by X-ray diffraction. The absorption spectra of three Pr3+ doped zinc lithium bismuth borate glasses have been recorded at room temperature. The observed optical spectra are discussed in terms of energy states and the intensity of the transitions. The various interaction parameters like Slater-Condon, Lande, bonding and Racah parameters have been computed. Judd-Ofelt intensity parameters and laser parameters have also been calculated. The stimulated emission cross section (σp) for the transition (3P0 → 3F2) is found to be in the range 3.12 10.43 × 10−20 cm2. The σp values are comparatively large suggesting the possible utilization of these materials in laser applications.


Introduction
Rare earth doped solid state materials have become an important class of solids, attracting much attention among researches as is evident from the abundance of studies that can be found in the literature.A substantial amount of work has been done on the lasing characteristics of rare earth doped solid state materials [1] [2].
Glasses are good host for rare earth ions, easy to make and at the same time they can be tailored for specific applications [3]- [5].Most of the glasses developed for laser action give suitable laser transition in NIR region whereas Pr 3+ doped glasses lase in visible region.Praseodymium doped glasses have wide application such as UV-VIS-NIR lasers, up converters, optical fiber amplifier etc. [6]- [8].
Since the spectroscopic properties of rare earth ions are strongly affected by glass composition the host glass composition were tailored with spectroscopic features of Pr 3+ ion suitable for efficient laser performance.Some spectral studies have been reported for Pr 3+ doped borate and phosphate glasses by Weber [9] [10], Riesfeld [11] [12], Lakshman [13] and Tandon et al. [14]- [16].Recently, such studies have been reported on Pr 3+ doped bismuth borate glasses by our group [17].
In this communication, these studies have been extended by adding higher mol% of Bi 2 O 3 in Pr 3+ doped zinc lithium bismuth borate glasses.
Large stimulated emission cross section is one of the most important parameters required for the design of high peak power solid state lasers.Thus, the variation of σ p with glass composition (e.g., borate, phosphates, silicates, etc.) has become the subject of intensive study because it is necessary to maximize σ p to achieve the best performance from an amplifier or laser system [18].
In the present work, the effect of bismuth borate matrix on the fluorescence properties of Pr 3+ is investigated.The compositional dependence of the stimulated emission cross section of the ( 3 P 0 → 3 F 2 ) transition of Pr 3+ is discussed.A comparative study of predicted laser action in borate, phosphate and bismuth borate glasses doped with Pr 3+ ions have also been discussed.The addition of higher mol% of Bi 2 O 3 in borate glasses enhances the value of stimulated emission cross section.

Preparation of Glasses
The following Pr 3+ doped bismuth borate glass samples ( Then melted at 1050˚C by an electrical muffle furnace for 2 hours.After complete melting, the melts were quickly poured in to a preheated stainless steel mould and annealed at temperature of 350˚C for 2 h to remove thermal strains and stresses.Every time fine powder of cerium oxide was used for polishing the samples.The glass samples so prepared were of good optical quality and were transparent.The chemical compositions of the glasses with the name of samples are summarized in Table 1.

XRD Study
Figure 1 represents the XRD pattern of the sample which shows no sharp Bragg's peak, but only a broad diffuse hump around low angle region.This is the clear indication of amorphous nature within the resolution limit of XRD instrument.
The amorphous nature of all samples was confirmed by the absence of Bragg's peak in X-ray diffraction pattern (Figure 1).

Energy Interaction Parameters
The energy E j can be expressed in terms of interaction parameters-(Slater-Condon) F k , and ξ 4f (Lande) by Taylor  series expansion for a small variation of energies ∆E j .In the first order approximation, the energy E j of the j th level is given by [19] [20].
( ) ( ) , 2, 4 6 , , , where, E oj is the zero order energy of j th level and ΔF k and Δξ 4f are the small changes in the corresponding parameters and these values have been calculated by partial regression method.
The value of F k and ξ 4f are then evaluated using equations.
where, 0 k F and 0 4 f ξ are zero order values of the parameters F k and ξ 4f , respectively.The Racah parameters E k (k = 1, 2, 3) can be expressed as linear combination of F k (k = 2, 4, 6) given by ( ) ( ) ( )

Oscillator Strength
The intensity of spectral lines are expressed in terms of oscillator strengths using the relation [21].
( ) where, ε(ν) is molar absorption coefficient at a given energy ν (cm −1 ), to be evaluated from Beer-Lambert law.Under Gaussian Approximation, using Beer-Lambert law, the observed oscillator strengths of the absorption bands have been experimentally calculated, using the modified relation [22].

Judd-Ofelt Intensity Parameters
According to Judd [23] and Ofelt [24] theory, independently derived expression for the oscillator strength of the induced forced electric dipole transitions between an initial J manifold ( )

N
f S L J level and the terminal J' manifold ( ) where, the line strength ( ) , S J J′ is given by the equation In the above equation m is the mass of an electron, c is the velocity of light, ν is the wave number of the transition, h is Planck's constant, n is the refractive index, J and J' are the total angular momentum of initial and final level respectively, Ω λ (λ = 2, 4 and 6) are known as Judd-Ofelt intensity parameters which contain the effect of the odd-symmetry crystal field terms, radial integrals and energy denominators.

Radiative Properties
The Ω λ parameters obtained using the absorption spectral results have been used to predict radiative properties such as spontaneous emission probability (A) and radiative life time (τ R ), and laser parameters like fluorescence branching ratio (β R ) and stimulated emission cross section (σ p ).
The spontaneous emission probability from initial manifold ( ) where, ( ) where, the sum is over all terminal manifolds.
The radiative life time is given by ( ) ( ) where, the sum is over all possible terminal manifolds.The stimulated emission cross -section for a transition from an initial manifold ( ) where, p λ the peak fluorescence wavelength of the emission band and Δ eff λ is the effective fluorescence line width.

Nephelauxetic Ratio (β') and Bonding Parameter (b 1/2 )
The nature of the R-O bond is known by the Nephelauxetic Ratio ( ) β ′ and Bonding Parameter (b 1/2 ), which are computed by using following formulae [27].The Nephelauxetic Ratio is given by where, ν a and ν g refer to the energies of the corresponding transition in the glass and free ion, respectively.The values of bonding parameter b 1/2 are given by where β is the average value of .β ′

Optical Properties Absorption Spectrum
The absorption spectra of these glasses were recorded between wavelengths range 400 -900 nm with a Spctro Scan 80D/80DV Spectrophotometer and 900 -2250 nm with a Perkin-Elmer Lambda 750 UV/VIS/NIR Spectrophotometer at room temperature.
The absorption spectra of Pr 3+ doped ZnLiBiB glass specimens have been represented in Figure 2 in terms of relative absorption (I/I 0 ) versus wavelength (nm), where I and I 0 are intensities of the radiation transmitted through doped specimens and undoped specimens of equal thickness.Eight absorption bands UV-VIS and NIR region have been observed from the ground state 3 H 4 to excited states 3 P 2 , 3 P 1 , 3 P 0 , 1 D 2 , 1 G 4 , 3 F 4 , 3 F 3 and 3 F 2 for Pr 3+ doped ZnLiBiB glasses.
The experimental and calculated oscillator strengths for Pr 3+ ions in zinc lithium bismuth borate glasses are given in Table 2. Racah parameters (E k ) have been deduced from F k parameters [29] (Table 3).The ratio of Racah parameters E 1 /E 3 and E 2 /E 3 are about 10 and 0.05 respectively.Which are almost equal to the hydrogenic ratio [30].This implies that Pr 3+ ions at different doping concentrations are subjected.
Further Judd-Ofelt intensity parameters Ω λ (λ = 2, 4 and 6) were calculated by using the fitting approximation of the experimental oscillator strengths to the calculated oscillator strengths with respect to their electric dipole contributions.In the present case the three Ω λ parameters follow the trend Ω 2 < Ω 4 < Ω 6 .The spectroscopic quality factor (Ω 4 /Ω 6 ) related with the rigidity of the glass system has been found to lie between 0.4 and 0.7 in the   4.
A comparison of calculated σ values for bismuth borate glasses with those reported [31] for borate, silicate, fluoroberyllate, phosphate and tellurite glasses (Figure 3) shows that bismuth borate glasses are best and tellurite glasses the next best.However, tellurite glasses have low transmission in the desired region (NIR) due to high value of refractive index.
Computed values of Slater-Condon, Lande, Racah, nephelauexetic ratio and bonding parameter for Pr 3+ doped ZnLiBiB glass specimens are given in Table 3.

Fluorescence Spectrum
The fluorescence spectrum of Pr 3+ doped in zinc lithium bismuth borate glass is shown in Figure 4.There are four broad bands ( 3 P 0 → 3 H 4 ), ( 3 P 0 → 3 H 5 ), ( 3 P 0 → 3 H 6 ) and ( 3 P 0 → 3 F 2 ), respectively for glass specimens.Out of four emission transition observed from 3 P 0 level, only three ( 3 P 0 → 3 H 4 , 3 H 6 and 3 F 2 ) are included in the fit.The transition 3 P 0 → 3 H 5 is excluded since the matrix elements for this transition are zero and the β is too weak to measure.The value of stimulated emission cross-section (σ p ) is found to be maximum for the transition ( 3 P 0 → 3 F 2 ) for glass ZnLiBiB PR 01, suggesting that glass ZnLiBiB PR01 is better compared to the other two glass systems (ZnLiBiB PR1.5 and ZnLiBiB PR02).The wavelengths of these bands along with their assignments are given in Table 5.Table 5. Emission peak wave lengths (λ p ), radiative transition probability (A rad ), branching ratio (β R ), stimulated emission crosssection (σ p ), andradiative life time (τ) for various transitions in Pr 3+ doped ZnLiBiB glasses.
c is the molar concentration of the absorbing ion per unit volume, I is the optical path length, 0 log I I is absorbtivity or optical density and 1 2 υ ∆ is half band width.
elements of the doubly reduced unit tensor operator calculated in intermediate coupling approximation.Ω λ parameter can be obtained from least square fitting method[25].The matrix element( ) 2 U λthat are insensitive to the environment of rare earth ions were taken from the literature[26].
The fluorescence branching ratio for the transitions originating from a specific initial manifold

Figure 3 .
Figure 3. Range of stimulated emission cross-section for different Pr 3+ doped glasses.

Table 1 .
Chemical composition of the glasses.

Table 3 .
Computed values of Slater-Condon, Lande, Racah, nephelauexetic ratio and bonding parameter for Pr 3+ doped ZnLiBiB glass specimens.The values of Judd-Ofelt intensity parameters are given in Table
In the present study, the glass samples of composition (25−x) Bi 2 O 3 :20Li 2 O:20ZnO:35B 2 O 3 :xPr 6 O 11 (where x = 1, 1.5, 2 mol%) have been prepared by melt-quenching method.The stimulated emission cross section (σ p ) and branching ratio (β R ) values are calculated for present glasses.It could be observed that glass ZnLiBiB (PR01) possessed better values when compared to the other two glass systems.The large stimulated emission cross section in bismuth borate glasses suggests the possibility of utilizing these systems as laser materials.