Judd-Ofelt Calculations for Nd³⁺-Doped Fluorozirconate-Based Glasses and Glass Ceramics

Abstract

A Judd-Ofelt analysis is performed to calculate the optical properties of Nd³⁺ ions embedded in a fluorozirconate glass matrix. The changes in the Judd-Ofelt parameters were determined as a function of the size of BaCl₂ nanocrystals grown inside the matrix. From these data, the radiative decay rates and the branching ratios of every transition in the energy range from 25.000 cm⁻¹ to the ground state are calculated. This was accomplished for samples containing nanocrystals with average sizes ranging from 10 to 40 nm.

1. Introduction

Photonic glasses doped with rare-earth ions such as erbium, neodymium, or europium gather widespread interest because of their applicability in photonic devices. Application as, for example, the active ion in a laser medium or as frequency converter in up- and downconverters [1, 2] requires efficient radiative decays of the ion with only minor losses to multiphonon relaxation (MPR). Therefore, the ion needs to be embedded in a low phonon energy environment which still remains both stable and transparent. Among appropriate materials are fluorozirconate (FZ) glasses with maximum phonon energies of less than 580 cm⁻¹ [3–5]. They have already proved to be a convenient choice for several applications.

As shown previously [6, 7], a uniform growth of BaCl₂ nanocrystals inside such glasses can be induced by thermal treatment as soon as additional chloride is introduced at the expense of fluoride. Since BaCl₂ has a maximum phonon energy on the order of 200 cm⁻¹ [3, 8], MPR is rendered even less probable and, thus, rare-earth ions tend to favor radiative decays [6, 7, 9].

The optical properties of Nd³⁺-doped fluorochlorozirconate (FCZ) glasses with differently sized BaCl₂ nanocrystals were studied with Judd-Ofelt theory. The sizes of the embedded nanocrystals were obtained from X-ray diffraction in combination with Scherrer analysis. It is known that Nd³⁺ ions are strongly affected by the BaCl₂ nanocrystals, but until now only speculations were possible as to the location of rare-earth ions at the edge of nanocrystals or even the possible inclusion into them [9, 10].

From Judd-Ofelt [11–13] analysis, the phenomenological Judd-Ofelt parameters can be determined. With them a quantitative measure for the influence of BaCl₂ nanocrystals on the Nd³⁺ can be established (see [14] for a detailed discussion). Here, the radiative decay rates for each transition were calculated and are given in a compressed form.

2. Methodology

Experimental details are as follows.The FCZ glass samples [14] investigated in this study are comprised of 52ZrF₄-10BaF₂-10BaCl₂-19NaCl-3.5LaF₃-3AlF₃-0.5InF₃-1KCl-1NdF₃ (values in mol%). The named chemicals were melted under an inert atmosphere, poured into a preheated (200°C) mold to avoid cracks, and then slowly cooled down to room temperature. Subsequently, the glasses were treated thermally at a temperature between 240°C and 270°C for 20 minutes to initiate the growth of BaCl₂ nanocrystals.

The visible and near-infrared transmittance spectra, from which the oscillator strengths were obtained, were recorded at room temperature with a double-beam spectrophotometer (Perkin Elmer Lambda 900).

Judd-Ofelt details are as follows. From the absorption cross-section spectra, the oscillator strengths 𝑓_meas are calculated with 𝑓_meas=4𝜋𝜀₀𝑒²𝑚_𝑒𝑐²𝜋^𝑘2_𝑘1𝜎(𝑘)𝑑𝑘, (1) where 𝑚_𝑒 is the mass of the electron; 𝑐, the speed of light; and 𝜎(𝑘), the absorption cross section.

The theoretical oscillator strengths feature contributions from electric, 𝑓_ed, and magnetic dipole transitions, 𝑓_md. Quadrupole effects are very weak and have been neglected. The dipolar oscillator strengths are of the following form: 𝑓_ed=4𝜋𝜀₀𝑒²8𝜋²𝑚_𝑒𝜈()𝜒3ℎ2𝐽+1^ed𝑆_ed,𝑓_md=4𝜋𝜀₀𝑒²8𝜋²𝑚_𝑒𝜈()𝜒3ℎ2𝐽+1^md𝑆_md, (2) where 𝜈 is the mean frequency and 𝐽 is the total angular momentum quantum number. From these, the line strengths, 𝑆_ed=_𝜆Ω_𝜆⟨𝑖𝑈_𝜆𝑗⟩²,𝑆_md=𝑒ℎ4𝜋𝑚_𝑒𝑐²⟨𝑖‖𝐿+2𝑆‖𝑗⟩², (3) are calculated, in which ⟨𝑖‖𝑈_𝜆‖𝑗⟩ are the doubly reduced matrix elements of the electric dipole tensor operator and ⟨𝑖‖𝐿+2𝑆‖𝑗⟩ are the elements of the magnetic dipole operator. These values do not depend much on the host and are given in the literature [13, 15–19]. The local field correction factors are 𝜒_ed=(𝑛²+2)² and 𝜒_md=𝑛 [20]. The Gaussian least-squares minimization of 𝑓_meas−𝑓_md=𝑓^(𝜆)_edΩ_𝜆 (4) yields the evaluation of the intensity parameters Ω_𝜆 (with 𝜆=2,4,6).

The effective refractive index 𝑛 of a composite material made of an FCZ glass matrix with inclusion of nanometric BaCl₂ crystallites has been calculated involving a Maxwell-Garnett approach [21]: 𝜀_eff=𝜀_𝑚𝜀_𝑖1+2𝛿_𝑖−𝜀_𝑚2𝛿_𝑖−2𝜀_𝑚2+𝛿_𝑖+𝜀_𝑖1−𝛿_𝑖, (5) where 𝜀_𝑚 and 𝜀_𝑖 are the dielectric constants of matrix and inclusion (data taken from [22, 23]).

The radiative emission rates are calculated [14] with 𝐴_𝑗𝑖=64𝜋⁴𝜈³3ℎ𝑐³2𝐽_𝑗𝜒+1^ed𝑆_ed+𝜒_md𝑆_md. (6) When 𝑖 is not only the ground state, the branching ratios 𝛽_𝑗𝑖=𝜏_𝑗𝐴_𝑗𝑖 define the percentage of the rate for each possible relaxation channel.

The tabular data given here are sectioned into samples with different BaCl₂ nanocrystal sizes. This starts with a determination for FZ glass and an untreated FCZ glass for reference and comparison. Then in order of increasing nanocrystal sizes, the different samples are given. For each source level |𝑖⟩, the target levels of the transition |𝑗⟩ along with the radiative decay rates 𝐴_rad and the corresponding branching ratio 𝛽_𝑖𝑗 are given. This is repeated for each sample.

3. Dataset Description

The dataset associated with this Dataset Paper consists of 6 items which are described as follows.

Dataset Item 1 (Table). Data of the radiative decay parameters in the FZ glass matrix.

• Column 1: |𝑖⟩
• Column 2: |𝑗⟩
• Column 3: 𝐴_rad (s^-1)
• Column 4: 𝛽_𝑖𝑗

Dataset Item 2 (Table). Data of the radiative decay parameters in the untreated FCZ glass matrix.

• Column 1: |𝑖⟩
• Column 2: |𝑗⟩
• Column 3: 𝐴_rad (s^-1)
• Column 4: 𝛽_𝑖𝑗

Dataset Item 3 (Table). Data of the radiative decay parameters in the FCZ glass matrix, thermally treated at 240°C. The average nanocrystal size was determined to be 12 nm [14].

• Column 1: |𝑖⟩
• Column 2: |𝑗⟩
• Column 3: 𝐴_rad (s^-1)
• Column 4: 𝛽_𝑖𝑗

Dataset Item 4 (Table). Data of the radiative decay parameters in the FCZ glass matrix, thermally treated at 250°C. The average nanocrystal size was determined to be 14 nm [14].

• Column 1: |𝑖⟩
• Column 2: |𝑗⟩
• Column 3: 𝐴_rad (s^-1)
• Column 4: 𝛽_𝑖𝑗

Dataset Item 5 (Table). Data of the radiative decay parameters in the FCZ glass matrix, thermally treated at 260°C. The average nanocrystal size was determined to be 25 nm [14].

• Column 1: |𝑖⟩
• Column 2: |𝑗⟩
• Column 3: 𝐴_rad (s^-1)
• Column 4: 𝛽_𝑖𝑗

Dataset Item 6 (Table). Data of the radiative decay parameters in the FCZ glass matrix, thermally treated at 270°C. The average nanocrystal size was determined to be 42 nm [14].

• Column 1: |𝑖⟩
• Column 2: |𝑗⟩
• Column 3: 𝐴_rad (s^-1)
• Column 4: 𝛽_𝑖𝑗

4. Concluding Remarks

A Judd-Ofelt analysis under consideration of the effective-𝑛 matrix in an FZ-based glass ceramic with BaCl₂ nanocrystals of different sizes has been performed in order to evaluate the optical properties of Nd³⁺ ions embedded therein. The radiative decay rates and the branching ratios of every transition in the energy range from 25.000 cm⁻¹ to the ground state are calculated. This is accomplished for samples containing nanocrystals with average sizes ranging from 10 to 40 nm. Using these data, the dynamics of these systems can be studied using rate equations.

Dataset Availability

The dataset associated with this Dataset Paper is dedicated to the public domain using the CC0 waiver and is available at http://dx.doi.org/10.1155/2013/236421/dataset.

Acknowledgments

This work was supported by the FhG Internal Programs under Grant no. Attract 692 034. In addition, the authors would like to thank the German Federal Ministry for Education and Research (Bundesministerium für Bildung und Forschung) for the financial support within the Centre for Innovation Competence SiLi-nano (Project no. 03Z2HN11).

Dataset Files

• 236421.item.1.xlsx

  Dataset Item 1 (Table). Data of the radiative decay parameters in the FZ glass matrix.

  • Column 1: |𝑖⟩
  • Column 2: |𝑗⟩
  • Column 3: 𝐴_rad (s^-1)
  • Column 4: 𝛽_𝑖𝑗

• 236421.item.2.xlsx

  Dataset Item 2 (Table). Data of the radiative decay parameters in the untreated FCZ glass matrix.

  • Column 1: |𝑖⟩
  • Column 2: |𝑗⟩
  • Column 3: 𝐴_rad (s^-1)
  • Column 4: 𝛽_𝑖𝑗

• 236421.item.3.xlsx

  Dataset Item 3 (Table). Data of the radiative decay parameters in the FCZ glass matrix, thermally treated at 240°C. The average nanocrystal size was determined to be 12 nm [14].

  • Column 1: |𝑖⟩
  • Column 2: |𝑗⟩
  • Column 3: 𝐴_rad (s^-1)
  • Column 4: 𝛽_𝑖𝑗

• 236421.item.4.xlsx

  Dataset Item 4 (Table). Data of the radiative decay parameters in the FCZ glass matrix, thermally treated at 250°C. The average nanocrystal size was determined to be 14 nm [14].

  • Column 1: |𝑖⟩
  • Column 2: |𝑗⟩
  • Column 3: 𝐴_rad (s^-1)
  • Column 4: 𝛽_𝑖𝑗

• 236421.item.5.xlsx

  Dataset Item 5 (Table). Data of the radiative decay parameters in the FCZ glass matrix, thermally treated at 260°C. The average nanocrystal size was determined to be 25 nm [14].

  • Column 1: |𝑖⟩
  • Column 2: |𝑗⟩
  • Column 3: 𝐴_rad (s^-1)
  • Column 4: 𝛽_𝑖𝑗

• 236421.item.6.xlsx

  Dataset Item 6 (Table). Data of the radiative decay parameters in the FCZ glass matrix, thermally treated at 270°C. The average nanocrystal size was determined to be 42 nm [14].

  • Column 1: |𝑖⟩
  • Column 2: |𝑗⟩
  • Column 3: 𝐴_rad (s^-1)
  • Column 4: 𝛽_𝑖𝑗