1 Introduction

Diode-pumped all-solid-state laser sources, with the advantages including compactness, high efficiency, low maintenance, and low cost, have aroused great research interest and developed rapidly in the last few decades. Nd-doped crystals, as the most famous laser gain medium at 1.06 μm pumped by laser diode (LD), have been applied in many fields such as medicine, industry, submarine communications, and so on [1–4]. Among traditional Nd3+-doped single crystals, Nd:YAG and Nd-doped vanadates attract most of the attention and are widely used. However, Nd:YAG [5] shows a strong sensitivity to the pumping wavelength due to its narrow absorption bandwidth at around 808 nm. Nd-doped vanadates [6] tend to form color centers during the growth process due to the component volatility, resulting in difficulty to obtain large-size and high-quality crystals, and their applications in high-power lasers are very limited. Therefore, many efforts are made to search for new favorable solid-state laser materials.

Orthotantalate LnTaO4 (Ln = Sc, Y, La, Gd, Lu) is a kind of efficient luminescence material. Particularly for GdTaO4, it is proved to be an efficient host material by doping Bi, Eu, and Tb ions [7–10]. Eu-doped GdTaO4 is a commonly used red phosphor. Tb-doped GdTaO4 is an excellent X-ray phosphor with green emission. Recently, the growth of bulk GdTaO4 single crystal has been realized by our group using Cz method [11]. There was no component volatility in the growth procedure, which seems more favorable than Nd-doped vanadates, and high-quality single crystal was obtained. The as-grown crystal was proved to be M-type, belonging to monoclinic system with space group I2/a. The site symmetry of Gd ion is C 2. The low symmetry is advantageous for relaxing the parity-forbidden rule and improving the photoluminescence efficiency [12]. Also, it is well known that polarized laser can be easily realized in crystals with low symmetry. Hence, we chose GdTaO4 as the laser host material and studied the laser performance of Nd-doped GdTaO4 single crystal.

In this work, we report the spectroscopic characterization of Nd3+-doped GdTaO4 single crystal. The spectral parameters are calculated by Judd–Ofelt theory with three perpendicular unpolarized absorption spectra (referred to as TPM method) [13]. The continuous-wave (CW) laser operation of Nd:GdTaO4 at 1,066 nm is realized by LD pumping.

2 Experimental details

An Nd3+-doped GdTaO4 single crystal was grown by conventional Czochralski method. The details of the growth procedure were described in previous work [14]. The initial ratio of Nd3+ ion in the raw materials is 2 at.%. The seed is oriented along a-axis, and the as-grown crystal is shown in Fig. 1. It can be seen that the dimensions of the crystal are Ф30 mm × 50 mm, and the whole crystal is transparent and crack-free. There are no scattering points when the crystal is irradiated by a 5 mW He–Ne laser. The crystal structure was studied by X-ray powder diffraction (XRD) using CuKα radiation (X’pert PRO), with data of 2θ collected from 10° to 90° at a step rate of 0.2° min−1. The concentrations of Nd, Gd, and Ta elements in the as-grown crystal were measured by X-ray fluorescence analysis (XRF-1800). The measured sample was cut from the shoulder part of the crystal and ground into powder.

Fig. 1
figure 1

Photograph of the as-grown Nd:GdTaO4 single crystal

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The samples for the spectroscopy experiments were cut from the as-grown crystal in three mutually perpendicular directions (one of them was a direction) with dimensions of 10 mm × 10 mm × 2 mm, and the two 10 mm × 10 mm faces were polished. The absorption spectra were recorded at room temperature by a PerkinElmer Lambda-950 UV/VIS/NIR spectrophotometer with a spectral interval of 0.2 nm. An FLSP-920 spectrophotometer (Edingburger instrument Ltd, UK) was used to measure the photoluminescence spectrum with a 808 nm LD excitation source, and the fluorescence decay curve was obtained by excitation with an Opolette 355 I OPO laser (OPOTEK, Inc, USA).

A simple plano–plano resonator was employed to generate the 1,066 nm laser, as shown in Fig. 2. The pump source used in the experiment was a fiber-coupled LD with a maximum output power of 30 W at 808 nm. The spectral bandwidth is 3 nm, and the core size of the fiber-coupled laser diode is 200 μm. The pump light was collimated and focused on the crystal through the focusing optics (NA = 0.22) with the focus length of 6 cm. The laser medium was an Nd:GdTaO4 single crystal with dimensions of 2 mm × 2 mm × 6 mm, in which the 2 × 2 mm2 faces were perpendicular to a direction and the 6-mm edge was along a direction. The two 2 × 2 mm2 faces were polished and anti-reflection (AR) coated for 808 and 1,066 nm. M1 is a plano mirror, AR coated at 808 nm at the pump side, high-reflection (HR) coated at 1.06 μm, and high-transmission (HT) coated at 808 nm on the other side. Two plane mirrors with different transmissions of 2.6 or 5.2 % at 1.06 μm were used as the output couplers (M2). During the experiments, the crystal was wrapped with indium foil and mounted in a water-cooled copper block. The cooling water was maintained at 20 °C throughout the experiments. The output power was measured with an OPHIR 30A-BB-18 power meter, and the laser spectrum was recorded with a FLSP-920 spectrophotometer.

Fig. 2
figure 2

Configuration of the experimental laser setup

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3 Results and discussion

3.1 Crystal structure and effective segregation coefficient

The XRD pattern of the Nd:GdTaO4 crystal is shown in Fig. 3. All the diffraction peaks are sharp and can be well indexed with the JCPDS card file 24–441 of GdTaO4, which indicates the high quality of the single crystal. The as-grown crystal belongs to I2/a space group. Using the general structure analysis software (GSAS), the unit cell parameters of Nd:GdTaO4 are fitted to be: a = 5.405 Å, b = 11.061 Å, c = 5.082 Å, α = γ = 90°, β = 95.62°.

Fig. 3
figure 3

XRD pattern of the Nd:GdTaO4 single crystal

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Using the XRF analysis, the concentration of Nd, Gd, and Ta ions in the as-grown crystal is measured to be 1.34, 98.42, and 100.2 at.%, respectively. According to the equation

$$k_{\text{eff}} = C_{S} /C_{L} ,$$

where C s and C L are the respective concentrations of the ions in crystal and melt. The effective segregation coefficient of Nd3+ is determined approximately to be 0.67, which is in accordance with that in Ref. [14].

3.2 Optical properties

The absorption spectra of Nd:GdTaO4 from 320 to 950 nm at room temperature are shown in Fig. 4. The absorption coefficient of samples in three directions shows distinct difference. There are nine absorption bands that correspond to the transitions from the ground state 4I9/2 of Nd3+ ions to different excited states. All the final states are assigned and marked in Fig. 4. The absorption of Nd:GdTaO4 at 808 nm in a direction is very strong with an absorption coefficient of 11.7263 cm−1 and a full width at half maximum (FWHM) of about 6 nm. The FWHM of Nd:GdTaO4 around 808 nm absorption band is much wider than 2 nm of Nd:YAG. Considering the diode laser bandwidth (3 nm), Nd:GdTaO4 can be better matched with the diode laser than Nd:YAG, which decreases the temperature dependence of the diode laser and is advantageous for improving laser efficiency. The absorption cross section σ can be determined with σ = α(λ)/N c, where α(λ) is the absorption coefficient, and N c is the concentration of Nd3+ ions in Nd:GdTaO4 crystal, which is measured to be 2.3 × 1020 cm−3 by XRF. Then, the absorption cross section of Nd:GdTaO4 in a direction is 5.098 × 10−20 cm2.

Fig. 4
figure 4

Absorption spectra of Nd:GdTaO4 in three mutually perpendicular directions; the red line denotes sample in a direction; the blue and black lines indicate samples in the other two directions, respectively

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The Judd–Ofelt (J–O) theory [15, 16], which is widely used for the calculation of spectroscopic parameters of rare earth ion-doped crystals and glasses, is applied to calculate the spectral parameters of Nd:GdTaO4. Nine absorption spectral bands at room temperature are used to fit the transition strength parameters Ω t (t = 2, 4, 6). According to the TPM method, α(λ) is the average of absorption coefficient of the crystal in three perpendicular directions. n is the average refractive index, which is calculated with the Sellmeier equation reported in Ref. [10]. In this work, the calculated values of the square of the reduced matrix element of the absorption transition were cited from Ref. [17]. The detailed calculation procedure is similar to that reported in Ref. [18]; thus, only the calculated results including the experimental oscillator strength f exp, the experimental electric dipole line strength S exp, and the calculated electric dipole line strength S cal are presented and summarized in Table 1. By a least squares fitting to the experimental line strength S exp, the three intensity parameters Ω t (t = 2, 4, 6) were fitted to be 4.05 ± 0.18 × 10−20, 2.82 ± 0.22 × 10−20, and 2.67 ± 0.18 × 10−20 cm2. The relative square deviation R is given by

$$R = \left\{ {\frac{{\sum {\left( {f_{ \exp } - f_{\text{cal}} } \right)^{2} } }}{{\sum {f_{ \exp }^{2} } }}} \right\}$$
(1)

Here, R is 5.52 %, which indicates the good consistency between the calculated and experimental values.

Table 1 Spectral parameters of Nd:GdTaO4 crystal
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The Ω 2 parameter depends on the crystal structure and coordination symmetry [19]. Generally, the higher value of Ω 2, the lower local environment symmetry exists. That is the reason why the value of Ω 2 for GdTaO4 crystal is so high [20]. In addition, according to J–O theory, the electric dipole line strength S of 4F3/2 → 4I9/2, 4F3/2 → 4I11/2 transitions can be expressed as follows:

$$S\left[ {^{ 4} {\text{F}}_{ 3/ 2} \to^{ 4} {\text{I}}_{ 9/ 2} } \right] \, = \, 0. 2 2 9 5\varOmega_{ 4} + \, 0.0 5 7 4\varOmega_{ 6}$$
(2)
$$S\left[ {^{ 4} {\text{F}}_{ 3/ 2} \to^{ 4} {\text{I}}_{ 1 1/ 2} } \right] \, = \, 0. 1 4 2 3\varOmega_{ 4} + \, 0. 40 4 2\varOmega_{ 6}$$
(3)

The value of Ω 2 has no practical influence on the emission properties of the crystal from the 4F3/2 state, as they mainly rely on the Ω 4 and Ω 6 parameters [19]. The value of S [4F3/2 → 4I11/2] is larger than that of S [4F3/2 → 4I9/2] (shown in Table 2), which indicates that the emission to the 4I11/2 state is more efficient than to the ground state.

Table 2 Spectral parameters of Nd:GdTaO4 for the radiative 4F3/2 → 4I J′ transition
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Using the calculated transition intensity parameters, the radiative properties of the excited states of Nd3+ ions can be predicted, including the radiative transition rate A (J′′→J′), the fluorescence branching ratio β (J′′→J′), and the radiative lifetime τ rad.

The calculated results of the radiative 4F3/2 → 4I J′ transition are listed in Table 2. The radiative lifetime of 4F3/2 is estimated to be 191.1 μs. Figure 5 shows the fluorescence decay curve at 1,066 nm corresponding to 4F3/2 → 4I11/2 transition excited by 808 nm. From Fig. 5, we see that it shows a single exponential decay behavior. The fluorescence lifetime is fitted to be 178.4 μs; thus, the radiative quantum efficiency of the 4F3/2 state is about η = 178.4/191.1 = 93.4 %, indicating a high laser efficiency of the crystal. The fluorescence branching ratio for the 4F3/2 → 4I11/2 transition is 46.5 %, which is favorable for laser operation around 1.06 μm. In addition, the fluorescence branching ratio for the 4F3/2 → 4I9/2 transition reaches 44.4 %, which means that Nd:GdTaO4 may be an efficient laser medium at 920 nm.

Fig. 5
figure 5

Fluorescence decay curve of Nd:GdTaO4 crystal

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The photoluminescence spectrum at room temperature is shown in Fig. 6. The strongest emission peak is located at 1,066.5 nm. Obviously, it results from the surrounding crystal field of Nd3+ ions induced by the GdTaO4 host. It is more notable that the emission intensity of 4F3/2 → 4I9/2 transition is very weak compared with that of 4F3/2 → 4I11/2 transition even though the fluorescence branching ratio of the former is 44.4 %. The explanation for this phenomenon should be based on two points. Firstly, the lower energy level 4I9/2 is the ground state of Nd3+ 4f energy levels, so the reabsorption exists at room temperature. On the other hand, the fluorescence spectrum has not been corrected. Because the InGaAs detector in the FLSP-920 spectrophotometer shows weak response in 850–950 nm, the signal-to-noise ratio (SNR) in this wavelength range is very weak and the spectrometer does not provide correction curve.

Fig. 6
figure 6

Fluorescence spectra of Nd:GdTaO4 excited by 808 nm at room temperature (not corrected for the spectral response of the detector)

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The stimulated emission cross section σ e can be determined with the measured fluorescence spectrum at room temperature according to the Füchtbauer–Ladenburg (F–L) method [21]:

$$\sigma_{\text{e}} \left( \lambda \right) = \frac{{\lambda^{5} \beta_{{J^{''} \to J^{'} }} I(\lambda )\eta }}{{8\pi n^{2} c\tau_{ \exp } \mathop \smallint \nolimits \lambda I(\lambda ){\text{d}}\lambda }}.$$
(4)

The stimulated emission cross section at 1,066 nm for 4F3/2 → 4I11/2 transition is calculated to be 3.9 × 10−19 cm2. Compared with other Nd3+-doped crystals, as listed in Table 3, Nd:GdTaO4 single crystal shows good comprehensive performance and can be expected as an excellent laser material.

Table 3 Comparison of the spectroscopic properties of Nd:GdTaO4 with other Nd3+-doped crystals
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3.3 Laser performance

For laser crystals, the thermal properties are very important for their laser operation. Due to the low doping concentration of Nd3+ ions, it will not bring noticeable influence on the thermal properties of GdTaO4. The thermal properties of Nd:GdTaO4, including specific heat, thermal conductivity, and thermal expansion coefficient, are expected to be similar to those of GdTaO4 single crystal [11]. The thermal conductivity of GdTaO4 single crystal along a, b, and c-axis is 7.3, 6.2, and 8.2 W/mK, and the thermal expansion coefficient along a, b, and c-axis is 6.17 × 10−6, 12.12 × 10−6, and 13.4 × 10−6 K−1. Considering the thermal effect and the anisotropy of absorption at 808 nm, it is apparent that Nd:GdTaO4 single crystal along a-axis is more suitable for laser operation.

Figure 7 shows the output power of Nd:GdTaO4 versus the incident power with two different output couplers. The length of the cavity is set to be 12 mm. As can be seen from Fig. 7, the threshold pump power (P th) is 0.339 and 0.347 W with the output coupler of 5.2 and 2.6 %, respectively. When the output coupler transmission is 5.2 %, a maximum output power of 2.5 W is achieved at a pump power of 7.2 W. Linear fitting results show the optical-to-optical conversion efficiency of 34.6 % and the slope efficiency of 36 %, which are better than those obtained at T = 2.6 %. The laser spectrum is presented in the inset of Fig. 7.

Fig. 7
figure 7

Output power of Nd:GdTaO4 versus incident power with different transmission of the output coupler. Inset the laser spectrum of Nd:GdTaO4

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The dependence of the laser performance on cavity length is investigated. Figure 8 shows the laser output of Nd:GdTaO4 versus incident power at T = 5.2 %, with the cavity length of 12, 14, and 20 mm. Obviously, the laser output power and the slope efficiency decrease with increasing the cavity length. This phenomenon is mainly due to the thermal lens effect in the Nd:GdTaO4 crystal, leading to more diffraction losses in longer cavity [24]. Therefore, more efficient laser output can be realized by optimizing the sample and the cavity design.

Fig. 8
figure 8

Laser output power of Nd:GdTaO4 versus incident power for different cavity lengths

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4 Conclusions

We report the spectroscopic and diode end-pumped laser properties of Nd:GdTaO4 single crystal for the first time. The effective segregation coefficient of Nd3+ in GdTaO4 is 0.67. The spectral parameters of Nd:GdTaO4 crystal are investigated using J–O theory. The calculated intensity parameters are 4.05 × 10−20, 2.82 × 10−20, and 2.67 × 10−20 cm2. The crystal exhibits strong absorption at 808 nm with the absorption cross section of 5.098 × 10−20 cm2 and a FWHM of 6 nm. The stimulated emission cross section at 1,066 nm is 3.9 × 10−19 cm2, and the fluorescence lifetime is 178.4 μs. The maximum output power is 2.5 W with an optical-to-optical conversion efficiency of 34.6 % and slope efficiency of 36 %. These results indicate that the Nd:GdTaO4 crystal is a new LD-pumped laser medium of 1,066 nm.