Effects of Zr4+ co-doping on the spectroscopic properties and yellow light emissions of Dy3+ in LiNbO3 single crystals

S. W. Long; D. C. Ma; Y. Z. Zhu; S. P. Lin; B. Wang

doi:10.1364/OME.6.003354

1. Introduction

Lithium niobate (LN) is one of the most widely used integrated optical materials thanks to the excellent electro-optical and nonlinear optics properties. There are extensive applications of this material in holographic storage [1] and optoelectronic devices [2]. With the high optical transparency from 350nm to 1800nm, Lithium niobate could work as a promising solid state lasing material at the visible and infrared wavelength range, when co-doped with trivalent lanthanide rare earth ions. Therefore, Considerable researches on spectroscopy and level structure of a variety of rare earth ions (such as Er³⁺, Nd³⁺, Tm³⁺, Eu³⁺ and Pr³⁺) in LN have been carried out for deeper insight into the laser system with high efficiency [3–9].

Compared to the rare earth ions mentioned above, far less work had been focused on the Dy³⁺ doped solid state materials. Earlier researches on Dy³⁺ doped solid state materials were concentrated in near-infrared (1.3 1.55 [10] and 1.7μm [11]) and mid-infrared (3μm [12]) emissions. Despite several current successful approaches to generate yellow laser, absence of appropriate active medium still restricted the development of all new compact solid state yellow laser source which could be pumped with commercially accessible operation wavelength. As a consequence, with the efficient energy level transition of Dy³⁺ from ⁴F_9/2 to ⁶H_13/2, researchers recently have been more inclined to study the potential of Dy³⁺ operating as yellow luminescence center [13–18].

In both scientific research and commercial application, congruent LiNbO₃ (CLN) (molar ratio [Li]/[Nb] = 0.946) is preferred than the near stoichiometric LiNbO₃ (SLN) because of the better uniformity and easier accessibility. Nevertheless, due to intrinsic defects resulting from deviation of Li-Nb ratio and Li-deficiency, CLN has relatively low optical damage resistance when exposed to high laser intensity, which severely limits the performance of Dy:CLN. One effective approach to suppress optical damage, which attracts many researchers’ interest, consists in co-doping with optical damage resistant ions, such as Mg²⁺, Zn²⁺, In³⁺, Sc³⁺, Hf⁴⁺ and Zr⁴⁺ [19–24]. Among all the optical damage resistant ions, tetravalent Zr⁴⁺ presents the lowest threshold concentration of 2mol% and a distribution coefficient closer to one [25, 26], guaranteeing the quality of optical crystals. It is therefore of interest to know the spectroscopic and structural properties of Dy:CLN after co-doping with Zr⁴⁺.

In the present work, the effects of Zr⁴⁺ co-doping on the yellow light emissions of Dy³⁺ in LN single crystals have been extensively studied by preparing a series of Zr:Dy:CLN single crystals with the Czochralski technique. Based on X-ray diffraction patterns and UV absorption spectra, a brief location analysis of Zr⁴⁺ was given. Detailed Judd-Ofelt theory analysis was carried out to study the influence of Zr⁴⁺ co-doping on the spectroscopic properties of Dy³⁺ in LiNbO₃ single crystals. Besides, with the analysis of the measured fluorescence characteristics, the relation between yellow luminescence emissions and structure transmutation in Dy³⁺ and Zr⁴⁺ co-doped CLN crystals were discussed.

2. The Judd-Ofelt theory

The Judd-Ofelt theory (J-O theory) was put forward by Judd [27] and Ofelt [28] separately in 1962. This theory is the most effective way to study 4f-4f transition of rare earth ions in crystal field, with which spectral intensity parameters of rare earth ions in a variety of host materials have been calculated and analyzed. There are some important formulas as follows:

The experimental oscillator strength for transition from ground state to excited state:

f_{\exp} = \frac{m c^{2}}{N π {\bar{λ}}^{2} e^{2}} \int α (λ) d λ;

where

\bar{λ}

is mean wavelength of absorption band; N is the doping concentration of dopant in crystals, such as Dy³⁺; m and e are the mass and charge of electron respectively; c is the velocity of light; α(λ) is the absorption coefficient, the integration of which can be figured out according to the UV-Vis-NIR absorption spectroscopy.

The oscillator strength for electric dipole transition from state $4 f^{N} J$ to $4 f^{N} J^{'}$ :

f_{e d} = \frac{8 π^{2} m c}{3 h (2 J + 1) \bar{λ}} \frac{{(n^{2} + 2)}^{2}}{9 n} \sum_{δ = 2, 4, 6} Ω_{δ} {〈 4 f^{N} φ J | | U^{δ} | | 4 f^{N} φ^{'} J^{'} 〉}^{2};

where h is Planck constant; n is refractive index, the values of which were obtained in the [29, 30]; Ω_δ are the oscillator strength parameters; δ is only 2, 4 or 6 which is resulted from the transition selection rule of electric dipole; $〈 4 f^{N} φ J ‖ U^{δ} ‖ 4 f^{N} φ^{'} J^{'} 〉$ , which is inert to crystal field, are reduced matrix elements of unit tensor operators U^δ. They were cited from [31]. and [32]. to make calculation of oscillator strength parameters Ω_δ and fluorescence branching ratios respectively.

The oscillator strength for magnetic dipole transition from state $4 f^{N} J$ to $4 f^{N} J^{'}$ :

f_{m d} = \frac{n h}{6 m c (2 J + 1) \bar{λ}} {〈 4 f^{N} φ J ‖ L + 2 S ‖ 4 f^{N} φ^{'} J^{'} 〉}^{2};

where

〈 4 f^{N} φ J ‖ L + 2 S ‖ 4 f^{N} φ^{'} J^{'} 〉

is the reduced matrix element of magnetic dipole operator L + 2S. For the transitions ⁴F_9/2 → ⁶F_7/2, ⁴F_9/2 → ⁶H_7/2, ⁴F_9/2 → ⁶F_9/2, ⁴F_9/2 → ⁶H_9/2, ⁴F_9/2 → ⁶F_11/2 and ⁴F_9/2 → ⁶H_11/2 of Dy³⁺ ions, magnetic-dipole component makes a significant contribution and should be taken into account.

For Dy³⁺, transition of electric dipole and magnetic dipole dominate the 4f-4f transition:

f_{c a l} \approx f_{\exp} = f_{m d} + f_{e d};

According with other formulas above, oscillator strength parameters Ω_δ would be computed by least square method and then used to calculate f_cal.

The root mean square deviation of fitting is defined as:

Δ f_{r m s} = \sqrt{\frac{\sum_{i = 1}^{N u m} {(f_{c a l} - f_{\exp})}^{2}}{N u m - 3}};

where Num is the number of absorption bands involved in calculation.

Transition probability of electric dipole (A_ed), magnetic dipole (A_md) and total 4f-4f (A):

A = A_{e d} + A_{m d} = \frac{8 π^{2} e^{2} n^{2}}{m c {\bar{λ}}^{2}} f_{e d} + \frac{8 π^{2} e^{2} n^{2}}{m c {\bar{λ}}^{2}} f {}_{m d};

The radiant lifetime τ of excited level i:

τ_{i} = \frac{1}{\sum_{k} A_{i k}} (i - > k);

where A_ik is the radiative transition probability from level i to level k.

The fluorescence branching ratios β for transitions originating from level i:

β_{i k} = A_{i k} τ_{i} (i - > k);

3. Experimental

CLN crystals of good quality with fixed Dy³⁺ concentration (1mol%) and varied Zr⁴⁺ concentration (0mol%, 1mol%, 2mol%, 3mol%) have been grown along the c axis from congruent melt (molar ratio [Li]/[Nb] = 0.946) by using the Czochralski method. The Homogeneous single crystal Zr(1mol%):Dy(1mol%):CLN, showing typical appearance of Zr:Dy:CLN crystals, was showed in Fig. 1(a). Wafers oriented perpendicular to c axis with the thickness of 2.5mm were cut from the central part of crystals and polished for further optical analysis, as shown in Fig. 1(b). The sample wafers with Zr-doped concentration from 0mol% to 3mol% were referred as Zr-0, Zr-1, Zr-2 and Zr-3 respectively thereinafter.

Fig. 1 (a) The as-grown single crystal of Zr(1mol%):Dy(1mol%):CLN with a diameter of 25 mm approximately, displaying the typical appearance of Zr:Dy:CLN crystals. (b) The polished Zr:Dy:CLN wafers oriented perpendicular to c axis with different Zr⁴⁺ concentration from 0mol% to 3mol%.

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The polarized absorption spectra of the wafers (spanning wavelengths from 350 to 2000nm) and the ultraviolet absorption spectra were recorded using a Lambda 950 UV-Vis-NIR Spectrophotometer at room temperature. Prior to the measurement of polarized absorption spectra, except for the wafers Zr-0~3 oriented perpendicular to c axis mentioned above, the wafers oriented parallel to c axis had been also obtained from the same crystals.

The fluorescence emission spectra were acquired using an EDINBURGH FLSP980 Photoluminescence Spectrometer. Fluorescence lifetime decay curves were measured with an EDINBURGH FLSP920 spectrometer pumped by a μF900 flash lamp.

X-ray diffraction patterns from 20deg to 80deg were measured by a D-MAX 2200 VPC X-Ray Diffractometer.

4. Results and discussion

4.1 Location analysis of doping ions and shift of absorption edge

LiNbO₃ has a trigonal crystal structure with the space group R3c and the point group 3m at room temperature. As a consequence of Li-deficiency in CLN, Nb⁵⁺ will enter Li-vacancy and exist in the form of ${Nb}_{Li}^{4+}$ [33]. The XRD patterns of CLN (JCPDS 78-0251) and Zr:Dy:CLN crystals were showed in Fig. 2(a). The diffraction peaks attributed to CLN were marked with the indices of the corresponding crystallographic planes. There was no new diffraction peak in the XRD patterns of all the samples, which indicated no remarkable change in the lattice structure after doping with Dy³⁺ and Zr⁴⁺. Dy³⁺ would be located at Li⁺ site or Nb⁵⁺ site after Zr⁴⁺ entered the lattice. According to the Li vacancy defect model of CLN [33], damage resistant ion Zr⁴⁺ enters into the lattice in 2 different forms in sequence: firstly replacing ${Nb}_{Li}^{4+}$ , then replacing Li⁺ after reaching the thresholds. Below the threshold concentration of Zr⁴⁺, Zr⁴⁺ would substitute ${Nb}_{Li}^{4+}$ in the form of ${Zr}_{Li}^{3+}$ , repelling ${Nb}_{Li}^{4+}$ and reducing the vacancies $V_{Li}^{-}$ , followed by evidently increasing of the unit cell volume on account of the lower polarization ability of Zr⁴⁺ than that of Nb⁵⁺ [34, 35]. This increase would stop when Zr⁴⁺ substituted normal Li⁺ in Li site with a minor increase of Li vacancies after threshold achieved. Lattice parameters and cell volumes of Zr:Dy:CLN crystals were calculated by least square method. The unit cell volumes plotted in Fig. 2(b) agreed well with the model above.

Fig. 2 (a) X-ray powder diffraction patterns of CLN (JCPDS 78-0251) and Zr:Dy:CLN polycrystalline powders which were obtained from the as-grown Zr:Dy:CLN crystals. (b) The cell volumes of Zr:Dy:CLN crystals with fixed concentrations of Dy³⁺ (1mol%) and different concentrations of Zr⁴⁺.

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The absorption edge position, which is an important reflection to structure and defects of CLN, is defined as the UV wavelength position where absorption coefficient α(λ) is equal to 20 cm⁻¹. As showed in Fig. 3 and the inset, there were first violet shifts from 315.88nm to 313.80nm and from 313.80nm to 313.14nm for the absorption edge, followed by a red shift from 313.14nm to 313.93nm. The Zr⁴⁺ concentration had reached the threshold at 2mol%, which corresponded to the minimum of absorption edge position [24]. The Zr⁴⁺ threshold concentration can be explained with the change of valence electron transition energy from 2p orbits of O²⁻ to 4d orbits of Nb⁵⁺, which directly affects the absorption edge position [35–37]: Replacement with ions of higher (lower) polarizability would increasing (decreasing) polarization ability of O²⁻ and decreasing (increasing) the energy gap, resulting in a red (violet) shift of the absorption edge. Therefore, since the polarizability of Nb⁵⁺ was much stronger than Li⁺, the energy gap would be decreased to cause a red shift in CLN deviating from 303nm [38] of stoichiometric LiNbO₃ (SLN). When ${Nb}_{Li}^{4+}$ was replaced by Zr⁴⁺, the polarizability of which is between Li⁺ and Nb⁵⁺ (Li⁺ < Zr⁴⁺ < Nb⁵⁺), there would be a violet shift for the absorption edge but not reaching 303nm. After reaching the threshold concentration of Zr⁴⁺, all ${Nb}_{Li}^{4+}$ had been substituted. Additional Zr⁴⁺ would substitute Li⁺, with red shift dominating. Hence, with the minimum wavelength value of absorption edge, we drew the inference that ${Nb}_{Li}^{4+}$ had been replaced completely and the covalent bonding closest to SLN had been formed at 2mol% Zr⁴⁺ threshold concentration [38].

Fig. 3 Ultraviolet absorption spectra of Zr:Dy:CLN crystals from 310nm to 350nm at room temperature. The inset is the partial enlarged figure, showing the absorption edge positions.

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4.2 Optical properties and Judd-Ofelt analysis

The UV-VIS-NIR absorption spectra, measured in the 350-2000nm wavelength range at room temperature, were presented in Fig. 4. Seven absorption bands in the UV-Vis-NIR absorption spectra related to transitions of Dy³⁺ from ground state ⁶H_15/2 to excited states ⁶H and ⁶F terms were marked up. Significant absorption line broadening could be observed.

Fig. 4 The polarized absorption spectra of Zr:Dy:CLN crystals from 350nm to 2000nm at room temperature.

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Besides electric dipole transitions, magnetic dipole transitions should be taken into account for ⁶H_15/2→⁴I_15/2 transition of Dy³⁺. For simplicity, we chose the six absorption bands at longer wavelength region for J-O analysis mentioned above. f_exp, f_cal and ∆f_rms were derived and listed in Table 1. Since the oscillator strength parameters Ω_δ, introduced to give a good fit with the experimental data by Judd [27], are important structure and laser characteristics: Ω₂ often plays only a minor role in determining the oscillator strengths [27] but is sensitive to the symmetry and the covalent bonding of the RE sites. The ratio Ω₄/Ω₆ allows for a prediction of the stimulated emission probability [39, 40]. The oscillator strength parameters Ω_δ and quality factor X = Ω₄/Ω₆ of Dy³⁺ and Zr⁴⁺ co-doped CLN were derived and presented in Table 2. The J-O analysis results of Zr-0 were consistent with those reported in [41]. The differences could be explained with the Li-deficiency in CLN, different concentration of Dy³⁺ and different test environments.

Table 1. Measured and calculated oscillator strengths, root mean square deviation of Zr:Dy:CLN crystals.

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Table 2. The oscillator strength parameters Ω_δ and quality factors X of Zr:Dy:CLN crystals.

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As showed in Table 2, Ω₆ was insensitive to the transmutation of crystal structure which was resulted from different Zr⁴⁺ concentrations. The minimum of Ω₄ occurred at threshold concentration of Zr⁴⁺. Then the value of Ω₄ recovered to 1.31 with the concentration of Zr⁴⁺ exceeding up to 3mol%. The quality factors presented a similar trend of change as Ω₄. The relation Ω₂> Ω₆ >Ω₄ always existed despite the change of Zr⁴⁺ concentration and the values of Ω₂ were about several times higher than those of Ω₄ and Ω₆. This could be explained with consideration of the peculiarity of the hypersensitive transition ⁶H_15/2→⁶F_11/2 + ⁶F_9/2 in absorption spectra. According to the hypersensitive mechanism [42] and “ligand polarization” theory [43] developed by Judd and Mason respectively, the hypersensitive transition arose with the “pseudo-quadrupole” transition, which originated from the asymmetry of ligand environment and local asymmetry of rare-earth ions. Specific types of site symmetry of rare earth ions were required for hypersensitive transitions. Besides, the parameter Ω₂ was rather sensitive to the asymmetry of ligand environment. The Dy³⁺ in octahedral sites in CLN exhibited C3 or C1 site symmetry only [44], which are of the right symmetry to excite quadrupole transitions. The exceptionally large oscillator strength of the transition ⁶H_15/2→⁶H_9/2 + ⁶F_11/2 in Table 1 clearly indicated the arising of the hypersensitive transition phenomenon [45]. In view of the above, Ω₂ of Zr-2 which is significantly lower indicated that the hypersensitive transition ⁶H_15/2→⁶F_11/2 + ⁶F_9/2 was weakened. The central positive ions in oxygen octahedral formed an alternating sequence Li⁺-Dy³⁺-Li⁺, ${Nb}_{Li}^{4+}$ -Dy³⁺-Li⁺ (Dy³⁺ at Nb⁵⁺ site) or Nb⁵⁺-Dy³⁺- Nb⁵⁺ (Dy³⁺ at Li⁺ site) in Dy:CLN. The sequence ${Nb}_{Li}^{4+}$ -Dy³⁺-Li⁺ would be aligned in a new way ${Zr}_{Li}^{3+}$ -Dy³⁺-Li⁺ when the Zr⁴⁺ was co-doped. As discussed in section 4.1, polarization ability of O²⁻ increased with central ions of higher polarizability (Li⁺ < Zr⁴⁺ < Nb⁵⁺). It was obvious that the oxygen octahedral environment of Dy³⁺ showed higher symmetry when ${Nb}_{Li}^{4+}$ -Dy³⁺-Li⁺ transformed to ${Zr}_{Li}^{3+}$ -Dy³⁺-Li⁺. So, when all the ${Nb}_{Li}^{4+}$ ions were removed at threshold concentration of Zr⁴⁺, the highest symmetry occurred in the crystal field, resulting in the changed covalent chemical bonding and the lowest hypersensitive transition probability. The similar decrease of Ω₂ was also observed in the Dy³⁺ and Zn²⁺ (6mol%) co-doped LiNbO₃ crystal [46]. At the exceeding Zr³⁺ concentration, the transformation from Li⁺-Dy³⁺-Li⁺ to ${Zr}_{Li}^{3+}$ -Dy³⁺-Li⁺ dominated and the value of Ω₂ increased, improving the hypersensitive transition probability, which was beneficial for the spectral absorption.

Transition probabilities, fluorescence branching ratios and radiant lifetime of ⁴F_9/2 were figured out with the corresponding oscillator strength parameters by Eq. (6)-(8). These results were tabulated in Table 3. The fluorescence branching ratio of the transition ⁴F_9/2→⁶H_15/2 (blue fluorescence) increased, while the branching ration of the transition ⁴F_9/2→⁶H_13/2 (yellow fluorescence) decreased at threshold concentration of Zr⁴⁺. These results of fluorescence branching ratios showed a negative correlation between the yellow fluorescence branching ratio and symmetry.

Table 3. Transition probabilities, fluorescence branching ratios and radiant lifetimes of the excited level ⁴F_9/2 in Zr:Dy:CLN crystals.

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For efficient laser emission, integrated emission cross-section σ_i ( $σ_{i} = \sum (J \to J^{'}) = λ^{2} A_{J J^{'}} / (8 π c n^{2})$ ) is supposed to be greater than 10⁻¹⁸ cm [47]. The integrated emission cross-section σ_i of transition from ⁴F_9/2 to ⁶H_13/2 in Zr-3 was determined to be 1.81 × 10⁻¹⁸ cm, while the value of Zr-2 was 1.72 × 10⁻¹⁸ cm. Since optical damage resistance dramatically increased only when threshold concentration of Zr⁴⁺ was reached or exceeded [26], from the results above, only the transition from ⁴F_9/2 to ⁶H_13/2 of Zr-3 could realize laser operation with high optical damage resistance.

Except for the absorption band centered at 806nm, the absorption band at 450nm related to the transition from ⁶H_15/2 to ⁴I_15/2 was suitable for optical pumping, especially when the commercialization of blue laser diodes offered convenient access to 450nm pump sources. The fluorescence spectra were recorded under 450nm excitation and displayed in Fig. 5(a). We neglected the weak fluorescence bands in infrared region and evaluated the experimental fluorescence ratios. The experimental and calculated fluorescence ratios of transition ⁴F_9/2^→6H_13/2 were plotted in Fig. 5(b). The experimental fluorescence ratios were higher than those determined by Judd-Ofelt theory, which could be partly explained with the disregard of infrared fluorescence bands. The ratios β_exp decreased at threshold concentration and then increased at exceeding concentration, consistently with the Judd-Ofelt theory analysis. The stimulated emission cross sections σ_em were determined by the formula: $σ_{e m} = λ^{5} β I (λ) / (8 π c n^{2} τ \int λ I (λ) d λ)$ , where I(λ) is the fluorescence intensity. The dependence on Zr⁴⁺ concentration of the maximum emission cross sections σ_em(10⁻²⁰cm²) of the transition ⁴F_9/2^→6H_13/2 was showed in Fig. 5(c). As shown, the Zr⁴⁺, which we co-doped in Dy:CLN crystals to suppress optical damage, had a negative impact on the stimulated emission cross-section at threshold concentration. The negative impact on stimulated emission cross-section was significantly reduced at exceeding concentration of Zr⁴⁺. The fluorescence decay curves corresponding to the ⁴F_9/2 → ⁶H_13/2 transition of Zr:Dy:CLN crystals were showed in Fig. 6. By single exponential fitting, fluorescence lifetimes were found to be 192.37μs, 196.13μs, 197.81μs and 195.41μs with increasing of Zr⁴⁺ concentration. The corresponding R-Square was 0.997, 0.998, 0.998 or 0.997 respectively. Doping with Zr⁴⁺ induced a small increase to lifetime until reaching threshold concentration. The fluorescence quantum efficiency (η = τ_f/τ) was 68.87% and 71.04% for Zr-2 and Zr-3 respectively. This result also showed the excessive doping of Zr⁴⁺ was necessary.

Fig. 5 (a) Fluorescence spectra of Zr:Dy:CLN wafers at room temperature under 450nm excitation. (b) The experimental and calculated fluorescence branching ratios of the transition ⁴F_9/2^→6H_13/2. (c) The maximum stimulated emission cross sections σ_em corresponding to the transition ⁴F_9/2^→6H_13/2 of Zr:Dy:CLN crystals.

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Fig. 6 The fluorescence decay curves of the ⁴F_9/2 →⁶H_13/2 transition in Zr:Dy:CLN crystals.

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5. Conclusion

Zr:Dy:CLN single crystals with the fixed concentration of Dy³⁺(1mol%) and varied concentrations of Zr⁴⁺ (0, 1, 2, 3mol%) have been grown by the Czochralski technique. The XRD patterns and UV absorption spectra of Zr:Dy:CLN crystals have been recorded. According to the analysis on location of Zr⁴⁺ and shift of absorption edge position, ${Nb}_{Li}^{4+}$ had been replaced completely and the number of Li vacancies reached its minimum at threshold concentration (2mol% Zr⁴⁺). Based on the UV-Vis-NIR absorption spectra and fluorescence spectra, systematic Judd-Ofelt theory analysis has been carried out. The oscillator strength parameters, fluorescence branching ratios and radiant lifetimes of ⁴F_9/2 have been determined and stimulated emission cross sections of transition ⁴F_9/2→⁶H_13/2 have been evaluated. It turned out that the defects, resulting from Li-deficiency or exceeding Zr⁴⁺-doping, would improve the hypersensitive transition probability of ⁶H_15/2→⁶F_11/2 + ⁶F_9/2 and have a great impact on Ω₂ .A negative correlation between the yellow fluorescence branching ratio and the symmetry in crystal field was also observed. The concentration of Zr⁴⁺ was found to have little influence on fluorescence lifetime. These results above suggested that Zr:Dy:CLN wafers can be a candidate material for yellow laser and this work is considered to be promotive for understanding the impact of optical damage resistant ion Zr⁴⁺ on optical properties of Dy³⁺ doped materials.

Funding

National Natural Science Foundation of China (NSFC) (Nos. 11372361, 11302268, 11232015, 11472321, 11572355); Fundamental Research Funds for the Central Universities; and the Doctoral Program of Higher Education of China (20130171130003).

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Transition	Zr-0			Zr-1			Zr-2			Zr-3
Transition	The oscillator strength f (10⁻⁶)
⁶H_15/2→	f_exp	f_cal	∆f_rms	f_exp	f_cal	∆f_rms	f_exp	f_cal	∆f_rms	f_exp	f_cal	∆f_rms
⁴I_15/2	0.79	0.88	0.32	0.76	0.86	0.33	0.69	0.83	0.27	0.74	0.85	0.28
⁶F_3/2	0.36	0.29		0.36	0.28		0.35	0.28		0.36	0.28
⁶F_5/2	1.95	1.55		1.96	1.48		1.90	1.45		1.92	1.48
⁶F_7/2	3.48	3.21		3.32	3.10		2.99	2.96		3.13	3.04
⁶H_7/2 + ⁶F_9/2	3.65	3.73		3.60	3.67		3.29	3.31		3.41	3.44
⁶H_9/2 + ⁶F_11/2	9.12	9.09		9.16	9.13		8.20	8.18		8.76	8.74
⁶H_11/2	1.63	1.85		1.59	1.79		1.60	1.72		1.63	1.78

Crystal	Ω₂(10⁻²⁰cm²)	Ω₄(10⁻²⁰cm²)	Ω₆(10⁻²⁰cm²)	*X (Ω₄/Ω₆)*
Zr-0	5.52	1.53	2.20	0.69
Zr-1	5.56	1.58	2.12	0.75
Zr-2	5.09	1.21	2.08	0.58
Zr-3	5.45	1.31	2.11	0.62

Transition		Zr-0		Zr-1		Zr-2		Zr-3
⁴F_9/2 →	λ_em	A	β	A	β	A	β	A	β
⁴F_9/2 →	(nm)	(S⁻¹)	(%)	(S⁻¹)	(%)	(S⁻¹)	(%)	(S⁻¹)	(%)
⁶F_5/2	1156	21.23	0.57	21.27	0.57	19.37	0.56	20.81	0.57
⁶F_7/2	992	76.37	2.03	76.06	2.04	74.23	2.13	75.14	2.07
⁶H_5/2	918	9.52	0.25	9.59	0.26	7.96	0.23	8.44	0.23
⁶H_7/2	836	56.01	1.49	55.54	1.49	49.70	1.43	52.03	1.43
⁶F_9/2	831	264.34	7.04	263.82	7.09	259.07	7.44	261.87	7.20
⁶F_11/2	748	109.33	2.91	109.05	2.93	102.27	2.94	106.48	2.93
⁶H_9/2	747	54.91	1.46	54.49	1.46	49.79	1.43	52.64	1.45
⁶H_11/2	661	220.23	5.87	219.70	5.91	201.60	5.79	215.11	5.92
⁶H_13/2	576	2251.80	59.97	2241.04	60.25	2075.79	59.62	2187.39	60.17
⁶H_15/2	486	691.06	18.40	669.05	17.99	641.93	18.44	655.28	18.03
		τ = 266.33μs		τ = 268.84μs		τ = 287.22μs		τ = 275.09μs

Transition	Zr-0			Zr-1			Zr-2			Zr-3
Transition	The oscillator strength f (10⁻⁶)
⁶H_15/2→	f_exp	f_cal	∆f_rms	f_exp	f_cal	∆f_rms	f_exp	f_cal	∆f_rms	f_exp	f_cal	∆f_rms
⁴I_15/2	0.79	0.88	0.32	0.76	0.86	0.33	0.69	0.83	0.27	0.74	0.85	0.28
⁶F_3/2	0.36	0.29		0.36	0.28		0.35	0.28		0.36	0.28
⁶F_5/2	1.95	1.55		1.96	1.48		1.90	1.45		1.92	1.48
⁶F_7/2	3.48	3.21		3.32	3.10		2.99	2.96		3.13	3.04
⁶H_7/2 + ⁶F_9/2	3.65	3.73		3.60	3.67		3.29	3.31		3.41	3.44
⁶H_9/2 + ⁶F_11/2	9.12	9.09		9.16	9.13		8.20	8.18		8.76	8.74
⁶H_11/2	1.63	1.85		1.59	1.79		1.60	1.72		1.63	1.78

Crystal	Ω₂(10⁻²⁰cm²)	Ω₄(10⁻²⁰cm²)	Ω₆(10⁻²⁰cm²)	*X (Ω₄/Ω₆)*
Zr-0	5.52	1.53	2.20	0.69
Zr-1	5.56	1.58	2.12	0.75
Zr-2	5.09	1.21	2.08	0.58
Zr-3	5.45	1.31	2.11	0.62

Effects of Zr⁴⁺ co-doping on the spectroscopic properties and yellow light emissions of Dy³⁺ in LiNbO₃ single crystals

Abstract

1. Introduction

2. The Judd-Ofelt theory

3. Experimental

4. Results and discussion

4.1 Location analysis of doping ions and shift of absorption edge

4.2 Optical properties and Judd-Ofelt analysis

5. Conclusion

Funding

References and links

Cited By

Figures (6)

Tables (3)

Equations (8)

Optical Materials Express