Spectral Properties and Parameters Calculation of Er : LiGdF 4 Crystal

The absorption and fluorescence spectra of Er:LiGdF4 crystal was measured at room temperature. Base on the Judd-Ofelt theory, the intensity parameters of Er in LiGdF4 crystal were determined, 2  = 0.905 × 10 –20 cm, 4  = 2.47 × 10 cm and = 4.92 × 10 cm. The values of the radiative transition probabilities, branching ratios, integrated emission cross-section and radiative lifetimes of excited states of Er in LiGdF4 crystal were calculated. The stimulated emission cross-section was also evaluated for the I13/2→I15/2 transitions. In comparisons with other Er doped laser crystals, Er:LiGdF4 crystal has potential as a promising laser crystal. 6 


Introduction
Diode-pumped solid-state lasers operating in the eye-safe spectral region around 1.5 µm have been of increasing interest in recent years, for a mass of application fields such as eye-safe compact devices for laser medical, environmental detection, laser radar, electro-optical jamming, remote sensing, optical communication and laser ranging [1][2][3].During the last few years Er 3+ -doped materials have been widely investigated for possible laser applications, especially in spectral ranges around 1540 nm ( 4 I 13/2 → 4 I 15/2 ) , which have low in optical waveguide and are safe to human eyes [4].
1.5 μm laser emission of Er 3+ has been investigated in several hosts, both oxides [5,6] and fluorides [7,8].Furthermore, fluoride hosts possess a low phonon energy, lower emitted threshold, wide-in-wavelength transmission region, lower thermal effects [9,21], resulting in longer lifetimes with respect to oxide crystals, without significant decreasing of the emission cross section values.
In this work, The Judd-Ofelt (J-O) intensity par-ameters   (λ = 2, 4, 6) were determined by analyzing the room temperature absorption spectra of Er 3+ -doped LiGdF 4 crystal.And the radiative transition probabilities, branching ratios, integrated emission cross-sections and radiative lifetimes of excited states of Er 3+ in LiGdF 4 were calculated In addition, The stimulated emission cross-sections for selected transitions were also calculated.The results show that this crystal may be a preferable candidate for a tunable infrared laser media.

Experimental
The starting material was prepared from commercially available LiF and GdF 3 powders of high purity (> 99.999%).As dopants, high purity ErF 3 powder (> 99.999%) was used.The concentration of Er 3+ in the starting material was 2.1 mol%.As the LiGdF 4 compound melts slightly incongruent and a few LiF evaporate during process of Er:LiGdF 4 growth, the starting material was LiF:GdF 3 = 68:32.All the powders were purified by HF processing in order to prevent OH − contamination.
The growth of Er:LiGdF 4 crystal has been performed with a growth apparatus consisted of DJL-400 Czochralski furnace with conventional resistive heating, special care has been devoted to the quality of the vacuum system, which should have an ultimate pressure limit better under 10 −3 Pa, the growth process was carried out in a high purity(5N) argon atmosphere.Thereafter, the starting materials were melted at approximately 860˚C.The pull and the rotation rate were 0.16 mm/h and 3 rpm.After growth, the crystal was cooled to room temperature at a rate of 10˚C /h.The absorption spectrum of the square slice sample was measured with ultraviolet (UV) spectrophotometer (Model UV360, SHIMADZU Company, Japan) in the 300 -1800 nm range at room temperature.The fluorescence spectrum was measured with a fluorescence spectrometer (Model Fluoro-Log-3, Horiba Company, Japan) in the 900 -1700 nm range at room temperature, and with the wavelength of 532 nm excited by an excitation source.

Absorption Spectrum
Figure 1 shows the absorption spectrum of Er:LiGdF 4 crystal in room temperature.The spectrum consists of six resolved bands associating with the transitions from the ground state 4 I 15/2 to excited states 4 where α is the absorption coefficient, α = A/(L × log 10 e), A is the absorbance, L is the thickness of the polished crystal, and N 0 is the concentration of Er 3+ ions in Er 3+ :LiGdF 4 crystal.The absorption cross-section of 4 I 15/2 → 4 I 13/2 transiton can be observed in Figure 1.The full width at half maximum (FWHM) at 986 nm and 1540.9 nm is 2.469 nm and 5.0319 nm; the corresponding absorption cross-section is 0.43 × 10 -20 cm 2 and 1.09 × 10 -20 cm 2 , respectively.

Spectroscopic Analysis (J-O)
Rare-earth doped crystals and glasses analyzed with Judd-Ofelt theory was successfully, especially for determining the branching ratios (β) from one level to other levels [10].According to the Judd-Ofelt theory [11,12], electronic dipole transitions within the 4f n configuration of a rare-earth ion can be analyzed.The electronic dipole transition line strength S JJ' between two different J states can be expressed as: where J represents the quantum number of the initial state transition, J' represents the quantum number of the terminal state transition, f n represents the electronic configuration,  represents the electronic wave functions, U (λ) represents the unit tensor element of the J-J' transition, <f n  J‖U (λ) ‖f n '  'J'> represents the unit tensor reduced element of the J-J' transition and   represents the phenomenological strength parameters determined by the coordinated property of the host materials.
The relationship between the integral absorption intensity Γ and the spectral line intensity can ben described as follows: where λ represents the average wavelength of the J-J' transition, n represents the refractive index of the transition wavelength, 0  represents the vacuum dielectric constant, c represents the vacuum speed of the light, h represents the Plank's constant, e represents the electronic charge and σ represents the absorption cross-section.
The central wavelength absorption peaks correspond to each energy level, the unit tensor element of the J-J' transition.The integral absorption intensity and the spectral line intensity of the Er:LGdF 4 crystal sample absorption spectrum are shown in Table 2.According to the data in Table 2 and Formulas (2) and (3), the phenomenological strength parameters   were fitted out as follows: 2  = 0.905 × 10 -20 cm 2 , 4 = 2.47 × 10 -20 cm 2 and 6   = 4.92 × 10 -20 cm 2 .In formulas ( 2) and (3), J is equal to 15/2 as the 4 I 15/2 energy level of the Er 3+ ion.
Generally, the intensity parameters can reflect the crystal structure, coordinated symmetry and order properties.The higher the values of the intensity parameters and the stronger the covalent characteristic of the intensity parameters are, the stronger the ionic characteristic of the crystal is.
The spontaneous radiation probability can be determined by the absorption spectrum.In fact, the probability contains the contributions of all kinds of multi-pole moments.Here we only consider the electric dipole moment.In respect to the radiation transition of the multiple excited state αSLJ-α'S'L'J', the spontaneous radiation probability induced by the electric dipole moment transition can be expressed as follows: where α, S, L, J and α', S', L', J' represent the quantum numbers of the initial state and terminal state, respectively.
The J-O theory can be used to evaluate the radiative properties of the rare-earth ions by using J-O parameters.
The fluorescence branch ratio β JJ' , the fluorescence life τ and the integral emission cross-section can be expressed as follows: where A JJ' represents the probability of spontaneous ra ' ' ' ' diation transition from energy level J to J'. the calculation of the spontaneous radiative transition probability, fluorescence life, fluorescence branch ratio and integral emission cross-section for partial energy levels of Er 3+ ions are shown in Table 3.The results prove that the 4 I 13/2 → 4 I 15/2 transition corresponds to a larger integral emission cross-section, a higher fluorescence branch ratio and a longer fluorescence life, and which is the essential condition for generating laser oscillation.The laser output for generating laser oscillation.The laser output for the 4 I 13/2 → 4 I 15/2 transition waveband can be obtained at room temperature.

Fluorescence Spectrum
The fluorescence spectra ranging from 900 to 1700 nm at room temperature were obtained under the 532 nm pumping shown in Figure 2. The main peak around 1530.5 nm is due to the Er 3+ 4I13/2→4I15/2 transition.From Figure 2, we can see that the FWHM of the sample is about 52 nm.It is well known that the broad emission band is fit for tunable laser medium.Therefore, the fluorescence spectra indicates that Er:LiGdF4 crystal is a potential candidate for compact and efficient near-infrared lasers.
The stimulate emission cross-sections were calculated by the Fuchtbauer-Ladenburg (F-L) equation [20]: where c is the speed of light, n is the refractive index, η is the radiative efficiency that can be estimated from the  comparison between the theoretical radiative and the fluorescence lifetime, I(λ) represents the experimental emission intensity as a function of the wavelength.According to Eq. ( 8), the Er 3+ 4I13/2→4I15/2 IR transition is a broad emission band at about 1530.5 nm.The corresponding FWHM is 52 nm, and the maximum emission cross-section of the Er 3+ 4I13/2→4I15/2 transition is 2.127 ×10 -20 cm 2 near 1530.5 nm。

Conclusions
Er 3+ -doped LiGdF4 single crystal was grown successfully by Czochralski method.The absorption spectrum was measured at room temperature.The broad absorption band and relative high absorption cross-section around 986 and 1540.9 nm are suitable for laser diode pumping.The Judd-Ofelt theory has been applied to the analysis of the room temperature absorption spectrum.Three intensity parameters were obtained: 2 = 0.905 ×10 -20 cm 2 , 4   = 2.47 ×10 -20 cm 2 and 6 = 4.92 ×10 -20 cm 2 .The room temperature emission spectra were recorded.The Er 3+ 4I13/2→4I15/2 IR transition is a broad emission band at about 1530.5 nm; the corresponding FWHM is 52 nm.The stimulated emission cross-section around 1530.5 nm were calculated by the F-L equation.The maximum emission cross-section with the peak at 1530.5 nm is 2.127 × 10 -20 cm 2 .