Growth, Structure, and Spectroscopic Properties of a Disordered Nd:SrLaGaO₄ Laser Crystal

Abstract

A disordered Nd:SrLaGaO₄ (Nd:SLG) laser crystal was successfully grown via the Czochralski (CZ) technique. The crystal structure, refractive index, polarized absorption spectra, and stimulated emission spectra were measured. The spectroscopic properties were studied intensively with the Judd–Ofelt (J-O) theory. The maximum absorption cross sections of π- and σ-polarization at 806 nm were calculated to be 3.73 × 10⁻²⁰ and 4.05 × 10⁻²⁰ cm², corresponding to FWHMs of 6.00 and 6.10 nm, respectively. The maximum emission cross sections of π- and σ-polarization at 1076 nm were 3.97 × 10⁻²⁰ and 4.12 × 10⁻²⁰ cm², with FWHMs of 30.21 and 19.44 nm, respectively. The decay life of the Nd³⁺:⁴F_3/2 energy level was fitted to be 0.152 ms, and the fluorescence quantum efficiency was 72.72%. The inhomogeneous broadening in spectra benefiting from the disordered structure indicates the Nd:SLG crystal is a promising gain medium for ultrafast laser and tunable laser generations in the near infrared region.

1. Introduction

Ultrafast and tunable lasers show extensive applications in intelligent processing [1], communication and remote sensing [2], national defense and military [3], medical beauty, and scientific research [4] because of the high pulse energy, high peak power, and short duration. In recent years, crystals with disordered structures have attracted extensive attention for ultrafast and tunable lasers gain media due to the wide emission band [5,6,7,8]. The random distribution of cations with different valences in the same lattice position leads to the disordered distribution of the lattice field, which leads to the uneven broadening of absorption and emission spectra [9,10].

For a 1.0 μm wavelength laser, Nd³⁺-doped laser crystals exhibit high pump efficiency and a low threshold due to the long upper\-level lifetime, large emission cross section, and no reabsorption loss of Nd³⁺ ions [8,9,10,11,12,13]. In recent years, many novel Nd³⁺-doped crystals have been reported to realize ultrashort or Q-switched pulsed lasers, such as Nd:GdSr₃(PO₄)₃ [5], Nd:LaMgAl₁₁O₁₉ [6], Nd:LuYPO₄ [8], Nd:Ca(Y, Gd)AlO₄ [9], and Nd:GdScO₃ [14]. Among those crystals, disordered aluminate (gallate) crystals present excellent thermal properties and spectral broadening, which is always regarded as the potential gain medium for high-power and ultrafast lasers [1,3,9,15,16,17,18,19,20]. In 2018, Lin et al. reported a new Nd:Gd₂SrAl₂O₇ crystal and achieved 1.55 W continuous-wave laser output at 1080 nm [16]. In 2020, Xu et al. demonstrated a high repetition rate passively Q-switched laser in the Nd:SrAl₁₁O₁₉ (Nd:SRA) crystal, corresponding to a high repetition rate of 201 kHz, a Q-switched pulse width of 346 ns, a peak power of 1.87 W, and a single pulse energy of 0.65 μJ [17]. Jia et al. reported spectroscopy and laser performance in a novel disordered crystal of Nd³⁺-doped CaYAl₃O₇ (CYAM) [18]. In 2021, Xu et al. reported a diode-pumped continuous-wave Nd:CaLaGa₃O₇ laser with a range of about 22 nm [19]. In 2023, Xu et al. successfully grown a disordered Nd:CaGdAl₃O₇ crystal via the optical floating zone method and made a detailed analysis of the disordered structure and the broad spectroscopic properties [20].

The ABCO₄ family crystallizes in the K₂NiF₄ tetragonal structure with a space group of I₄/mmm, has a complex and disordered lattice field, which causes a large inhomogeneous broadening of absorption and emission spectra. In general, rare-earth-doped CaYAlO₄, CaGdAlO₄, and SrLaAlO₄ laser crystals have been widely studied in ultrafast and tunable laser fields [7,9,15,21,22,23,24]. In 2016, Liu et al. reported a stable 458 femtosecond continuous-wave mode-locked pulse in the Nd:SrLaAlO₄ crystal at 1077.9 nm with an average power output of 520 mW [21]. In 2022, Yang et al. achieved a continuous single-frequency tunable laser at 1.08 µm with a tuning range of 60.72 GHz in the Nd:CaYAlO₄ crystal [24]. Chen et al. first reported a Nd-doped tunable laser beyond 1100 nm in the mixed Nd:CYGA crystal, where Gd³⁺ ions were introduced into the CaYAlO₄ crystal [15]. Among the ABCO₄ single crystal family, SrLaGaO₄ (SLG) crystal has been widely studied as a substrate material with epitaxial growth method for high-temperature superconducting thin films due to the low dielectric loss and good lattice matching with various superconducting coppers such as YBa₂Cu₃O_7−x [25]. The disordered environment formed by the random distribution of Sr³⁺ ions and La³⁺ ions may lead to a strong inhomogeneous broadening of the absorption and emission spectra. Thus, one could expect that the SrLaGaO₄ crystal may also be a potential laser material. However, research on rare-earth-doped SLG laser crystals is still limited. Dabkowski reported the Czochralski crystal growth of pure SrLaGaO₄ crystal in 1993 [26]. A brief study on the structure and absorption spectra properties of Nd:SrLaGaO₄ was first reported by Ryba-Romanowski in 1996 [27]. While there has been no systematic research on Nd:SrLaGaO₄ as a near-infrared laser gain medium in recent decades, it is necessary to study the crystal structure, refractive index, polarized absorption spectra, stimulated emission spectra, and decay life in detail to evaluate ultrafast and tunable laser performance in Nd:SrLaGaO₄. Nevertheless, these requirements have not been addressed thus far.

In this work, a detailed study on the Nd:SrLaGaO₄ crystal for ultrafast and tunable lasers in the near infrared region was presented. The pure and Nd-doped SLG crystals were grown by the Czochralski method in a rich Ga condition. The crystal structure was studied based on the Rietveld XRD refinement. The refractive index dispersion equations were fitted by the least squares method. The polarized spectroscopic properties and the fluorescence lifetime were studied intensively. Compared to the spectroscopic parameters of some other Nd³⁺-doped laser crystals, the broadening spectra characteristics indicated that Nd:SLG crystals are a good material for ultrafast and tunable lasers at 1.0 μm.

2. Experiment

In this paper, pure SLG and 1% Nd:SLG crystals were successfully grown by the Czochralski method in a rich Ga condition. The raw materials SrCO₃, La₂O₃, Ga₂O₃, and Nd₂O₃ with a purity of 4N were used without any treatment. According to a report in [26], SLG crystal grown in rich Ga conditions shows better crystallinity. Thus, more SrCO₃ and Ga₂O₃ and less La₂O₃ were weighed than the stoichiometric composition for the polycrystalline synthesis process in this work. After grinding and mixing the raw materials evenly, the plates were pressed and then sintered at 1250 °C for 3 days in a muffle furnace for high-temperature solid-phase reaction. Before crystal growth, the polycrystalline phase was proved to be pure by X-ray diffraction (XRD). For crystal growth, the polycrystalline raw material was loaded into a Φ60 mm iridium crucible with nitrogen protection. A c-cut pure SLG crystal was used as the seed for Nd:SLG crystal growth. During the crystal growth, the pulling rate was 1–2 mm/h and the rotation rate was 6–10 rpm/min, respectively. After crystal growth, in order to relieve the thermal stress, the crystal was cooled to room temperature slowly with a speed of 5–35 K/h. The dimension of the as-grown 1.0 at.%Nd:SLG crystal is about Φ25 mm × 35 mm. After annealing at 1000 °C for 48 h in a N₂ (98%)–H₂ (2%) atmosphere, the Nd:SLG crystal changed from atrovirens to purplish brown, indicating a color center defect in the crystal. Although treated in a reducing atmosphere, the color of the Nd:SLG crystal is still different from the usual Nd³⁺-doped laser crystals. There are some other color center defects in the Nd:SLG crystal compared with common O⁻ defects in the ABCO₄ family, which will be of great interest in further study.

The crystal structures were identified by powder XRD (Rigaku Miniflex 600 diffractometer, Rigaku, Tokyo, Japan). The patterns were collected in the range of 10–80° with a scanning speed of 2◦/min. The concentration of the Nd³⁺ ion in the Nd:SLG crystal was determined by inductively coupled plasma atomic emission spectrometry (ICP-AES, TPS-7000). A fully automatic high-precision refractometer (UV VIS SWIR IR 3-12 (Trioptics, Hamburg, Germany)) was used to test the refractive index. The crystallography c-axis of the Nd:SLG crystal was oriented by an X-ray direction finder (YX-Z). A small slice with a thickness of 2 mm was cut for polarized spectra. The incident surface was parallel to the c-axis and polished. Polarized absorption spectra were measured with a Perkin-Elmer UV-visible-near infrared spectrometer (Lambda-950, Perkin-Elmer, Waltham, MA, USA) in the range of 300–1000 nm. The polarized fluorescence spectra and fluorescence decay curve were recorded on an FLS920 fluorescence spectrometer (Edinburgh, Livingston, UK), with the xenon lamp as an excitation source. All the tests were recorded at room temperature.

3. Results and Discussion

3.1. Crystal Structure and Segregation

The structure of the Nd:SLG crystal was identified by powder XRD. As shown in Figure 1, all the diffraction peaks match well with the standard card (PDF#24-1208) with tetragonal phase, further indicating that the Nd³⁺ ions can be doped into the SLG host lattice by replacing the La³⁺ ions without any obvious variations to the host structure.

Based on the Rietveld XRD refinement, the structure of the Nd:SLG crystal was further studied in Figure 2. As shown in Figure 2a, the observed and calculated diffraction patterns match well with each other, revealing that the Nd:SLG crystal possesses a pure single tetragonal phase with a space group of I₄/mmm. The lattice parameters of the Nd:SLG crystal are calculated to be a = b = 3.84146 Å and c = 12.6813 Å. Because of the Nd³⁺ ions doping with a smaller cation radius than La³⁺ ions, the lattice parameters of the Nd:SLG crystal are slightly smaller than those of the pure SLG crystal (PDF #24-1208). The corresponding refined crystal structure parameters are presented in

Table 1. Crystal structure parameters of Nd:SLG obtained by Rietveld full-profile refinement.

Name	X	Y	Z	Wyckoff Site	Uiso
Sr1	0	0	0.3588	4e	0.00425
La1	0	0	0.3588	4e	0.00992
Ga1	0	0	0	2a	0.01715
O1	0	0	0.1680	4e	0.00914
O2	0	0.5	0	4c	0.01923
Nd6	0	0	0.3588	4e	0.00250

FirsCell parameters: a = b = 3.84146 Å, c = 12.6813 Å, α = β = γ = 90°. Cell volume: V = 187.135 ų, space group: tetragonal, I₄/mmm (139). Density: ρ = 6.398 g/cm³. Reliability factors (R-factor): GOF = 1.62, R_wp = 7.743%.

. Figure 2b displays a schematic structure of the Nd:SLG crystal. It can be seen that the Nd:SLG crystal is built up from GaO₆ layers, between which Nd³⁺ ions, Sr³⁺ ions, and La³⁺ ions are distributed randomly with C_4v symmetry.

The segregation coefficient is an important factor for laser crystals because it affects structure uniformity and laser output efficiency. With the help of the ICP-AES test, the lattice concentration of Nd³⁺ ions was calculated to be 1.27 × 10⁻²⁰ ions/cm³. The corresponding segregation coefficient was calculated to be 0.48, which was similar to the Nd:LuYPO₄ crystal [8].

3.2. Refractive Index

Refractive index is an important parameter for laser gain mediums. Since SLG crystal belongs to the tetragonal structure and uniaxial optical crystals, the minimum deviation technique with a right-angle prism sample, as shown in the inset in Figure 3, is used for the refractive index measurements of SLG crystal. The incident light must be perpendicular to the optic principal c-axis. With the help of a polarizer, o-light and e-light can be separated behind the prism. Based on the included angle to the incident light, n_o and n_e can be calculated, respectively.

Table 2. The refractive index test data of the SLG crystal.

λ (nm)	Refractive Index
	no	ne
546.0750	2.0159794	2.0329168
587.5620	2.0099844	2.0259665
643.8470	2.0039589	2.0184998
706.5190	1.9980698	2.0114033
768.1943	1.9931367	2.0079149
852.1100	1.9886278	2.0034969
1013.9800	1.9833680	1.9963757

shows the crystal refractive index test data. Seven test points with different wavelengths were selected, ranging from 546.07 nm to 1013.98 nm.

As shown in Figure 3, the refractive index dispersion equations (Sellmeier) are fitted by the least squares method as follows:

$${\mathrm{n}}_{\mathrm{o}}^2=-9.28518+\frac{13.17287{\lambda }^2}{{\lambda }^2-0.00401}-0.00615{\lambda }^2$$

$${\mathrm{n}}_{\mathrm{e}}^2=-7.16368+\frac{11.09283{\lambda }^2}{{\lambda }^2-0.00537}-0.00074{\lambda }^2$$

where $\lambda$ represents the wavelength and the unit is μm. It can be seen that the SLG crystal is a positive uniaxial crystal (n_o < n_e). The fitted refractive index dispersion equation is in good agreement with the actual measured value. The fitted refractive index dispersion equations can be used in the spectra and Judd–Ofelt (J-O) theory analyses next.

3.3. Absorption Spectra and Judd–Ofelt (J-O) Theory Analyses

Figure 4 shows the π- and σ-polarized absorption spectra of the Nd:SLG crystal at room temperature in the range of 500–1000 nm. All the absorption peaks have been marked. The peaks are located at 529, 589, 684, 751, 806, and 879 nm, corresponding to the transition of Nd³⁺ ions from the ground state ⁴I_9/2 to the excited state ⁴G_9/2 + ⁴G_7/2 + ²K_13/2, ⁴G_5/2 + ²G_7/2, ⁴F_9/2, ⁴S_3/2 + ²H_7/2, ⁴F_5/2 + ²H_9/2, and ⁴F_3/2. Due to the absorption of color center defects, a broad absorption peak instead of the characteristic absorption peak of Nd³⁺ ions appeared at wavelengths shorter than 500 nm. The characteristic absorption peak of Nd³⁺ ions located at 806 nm, corresponding to the transition ⁴I_9/2 → ⁴F_5/2 + ²H_9/2, is well matched with the emission band of commercial AlGaAs laser diodes. The absorption cross section can be calculated using the following formula:

$${\sigma }_{\mathrm{a}\mathrm{b}\mathrm{s}}\left(\lambda \right)=\frac{2.303\times \mathrm{O}\mathrm{D}\left(\lambda \right)}{N_0\times \mathrm{L}}$$

where $\mathrm{O}\mathrm{D}\left(\lambda \right)$ is the absorption optical density, $N_0$ is the lattice concentration (the number of Nd³⁺ ions per cubic centimeter), and $\mathrm{L}$ is the thickness of the sample. The maximum absorption cross sections of the Nd:SLG crystal for π-polarization and σ-polarization at 806 nm are calculated to be 3.73 × 10⁻²⁰ cm² and 4.05 × 10⁻²⁰ cm², which is larger than the disordered Nd:SrLaAlO₄ (2.45 × 10⁻²⁰ cm²) [21], Nd:SrLaGa₃O₇ (1.99 × 10⁻²⁰ cm²) [28], Nd:SrAl₁₂O₁₉ crystals (0.21 × 10⁻²⁰ cm² [π], 2.08 × 10⁻²⁰ cm² [σ]) [29], and comparable to Nd:CaYAl₃O₇ (3.51 × 10⁻²⁰ cm² [π], 5.34 × 10⁻²⁰ cm² [σ]) [18] and CaGdAl₃O₇ (3.78 × 10⁻²⁰ cm²) [20] crystals. The corresponding full width at half maximums (FWHMs) around 806 nm are 6.00 nm and 6.10 nm, respectively, which far exceed the Nd:YAG and Nd:YVO₄ crystals and are also close to some commonly disordered crystals such as Nd:CaYAlO₄ (5 nm) [23] and Nd:CaGdAlO₄ (5 nm) [22]. The large absorption cross sections and wide absorption bands resulting from the disordered structure of the crystal suggest that the Nd:SLG crystal is suitable for commercial AlGaAs laser diode pumping, which is beneficial to pump absorption efficiency and light-to-light conversion efficiency in laser operation.

The J-O theory is widely applied for systematic spectroscopic analysis of some rare earth-doped optical materials [8,20]. Based on the polarized absorption spectra, some important spectral parameters of the Nd:SLG crystal can be estimated, such as the oscillator strength, the J-O intensity parameters, the transition branching ratio, and the radiative lifetime.

The experimental absorption line intensity $S_{exp}$ is calculated through absorption spectroscopy using the following equation:

$$S_{exp}=\frac{9n}{{(n^2+2)}^2}·\frac{3hc(2J+1)}{8{\pi }^3{e}^2\overline{\lambda }{N}_0}\int \alpha \left(\lambda \right)d\lambda$$

where $e$, $n$, $h$, and $c$ are the electron charge, refractive index, Planck constant, and speed of light, respectively. $J$ is the initial total angular momentum quantum number, $\overline{\lambda }$ is the mean wavelength, $N_0$ is the concentration of the Nd³⁺ ion, and $\alpha \left(\lambda \right)$ is the absorption coefficient at the wavelength of $\lambda$.

Meanwhile, the calculated line intensity S_cal is obtained by the following equation:

$$S_{cal}=\sum _{\mathrm{2,4},6}{\Omega }_{\lambda }{\left|〈4f^n\psi J‖U^{\left(t\right)}‖4f^n{\psi }^{*}{J}^{*}〉\right|}^2$$

where the ${\Omega }_{\lambda }$ ($\lambda$ = 2,4,6) are the J-O strength parameters, and $U^{\left(t\right)}$ (t = 2,4,6) are the squared matrix elements. Then all the experimental absorption line intensity $S_{exp}$ and the calculated line intensity $S_{cal}$ are listed in

Table 3. The oscillator strength of the Nd:SLG crystal.

Nd3+ 5I8→	σ-Polarized			π-Polarized
	λ (nm)	${\mathit{S}}_{\mathit{e}\mathit{x}\mathit{p}}$	${\mathit{S}}_{\mathit{c}\mathit{a}\mathit{l}}$	λ (nm)	${\mathit{S}}_{\mathit{e}\mathit{x}\mathit{p}}$	${\mathit{S}}_{\mathit{c}\mathit{a}\mathit{l}}$
		10−20 cm2			10−20 cm2
4G9/2 + 4G7/2 + 2K13/2	529	7.059	6.032	529	6.099	4.673
4G5/2 + 2G7/2	586	18.68	18.74	589	20.93	21
4F9/2	684	1.08	0.549	684	0.616	0.633
4S3/2 + 2H7/2	751	7.239	6.627	751	9.355	8.583
4F5/2 + 2H9/2	806	6.126	7.086	806	5.755	6.922
4F3/2	883	2.909	2.653	879	1.629	1.2
RMSΔS	0.293			0.243

. The results show that the calculated oscillator strengths coincide well with the measured ones.

The root-mean-square deviation ($RMS∆S$) is calculated by the following equation:

$$RMS∆S=\sqrt{\frac{{\sum }_{J^{\prime }}{(S_{exp}-S_{cal})}^2}{N-3}}$$

where $N$ is the number of absorption bands used in the analysis. The root mean square deviation ($RMS∆S$) of π-polarized and σ-polarized strength parameters are 2.432 × 10⁻²¹ cm² and 2.932 × 10⁻²¹ cm², which confirms the agreement between the experimental and theoretical data within the error tolerance.

As listed in

Table 4. The J-O intensity parameters of Nd³⁺-doped crystals.

Crystal	Ω2,4,6 (10−20 cm2)				Ref.
	Ω2	Ω4	Ω6	Ω4/Ω6
Nd:SLG	3.28	2.97	3.61	0.82	This work
Nd:YAG	0.62	1.70	5.76	0.29	[31]
Nd:SrLaGa3O7	1.28	5.01	1.95	2.57	[28]
Nd:CaLaGa3O7	5.804	10.586	3.443	3.07	[32]
Nd:YVO4	5.88	4.08	5.11	0.80	[30]
Nd:CaYAlO4	2.19	8.16	8.57	0.95	[23]

, the J-O strength parameters Ω_2,4,6 are calculated as Ω₂ (3.28 × 10⁻²⁰ cm²), Ω₄ (2.97 × 10⁻²⁰ cm²), and Ω₆ (3.61 × 10⁻²⁰ cm²) by the formula Ω_eff = (2Ω_σ + Ω_π)/3. The large Ω₂ indicates that the crystal possesses lower symmetry and stronger covalent properties, further proving its disordered structure. The value of Ω₄/Ω₆ of 0.82, representing the spectroscopic quality factor, is comparable with that of Nd:YVO₄ (0.8) [30] and Nd:CaYAlO₄ (0.95) [23], which indicates highly feasible laser generation in the Nd:SLG crystal.

Table 5. The radiative transition rates A_ed, branching ratios β, and radiative lifetime τ_rad of Nd:SLG.

Transition		λ (nm)	Aed (s−1)	β (%)	τrad (ms)
4F3/2→					0.21
	4I15/2	1852	23.99864	0.51
	4I13/2	1333	465.4819	9.95
	4I11/2	1053	2290.509	48.95
	4I9/2	881	1898.881	40.58

shows the radiative transition rate, fluorescence branching ratio β, and radiation lifetime τ_rad. The transition ⁴F_3/2 → ⁴I_11/2 has the largest fluorescence branching ratio of 48.88%, indicating the most likely emission at 1.0 μm. The radiative lifetime of the crystal is fitted to be 0.21 ms.

3.4. Fluorescence Spectra

Figure 5 shows the polarized emission spectra of the Nd:SLG crystal, ranging from 820 to 1450 nm under 806 nm excitation. Three peaks with a central wavelength of 896, 1076, and 1360 nm are marked. The strongest peak at 1076 nm, corresponding to the transition of ⁴F_3/2 → ⁴I_11/2, is also consistent with the JO theoretical analysis. Moreover, the relative intensity of the peaks for π-polarization and σ-polarization is very similar. While the maximum emission of σ-polarization is about five times greater than that of π-polarization due to the anisotropy of the Nd:SLG crystal, the stimulated emission cross sections at 1076 nm are calculated as 3.97 × 10⁻²⁰ cm² for π-polarization and 4.12 × 10⁻²⁰ cm² for σ-polarization by the following formula:

$${\sigma }_{em}\left(\lambda \right)=\frac{{\lambda }^{5}I\left(\lambda \right)\beta }{8\pi c{n}^2\cdot {\tau }_r\int I\left(\lambda \right)\lambda d\lambda }$$

where $\beta$ is the fluorescence branching ratio, $\lambda$ is the emission wavelength, $I\left(\lambda \right)$ is the fluorescence intensity, $c$ is the speed of light in vacuum, $n$ is the refractive index, ${\tau }_r$ is the radiative lifetime, and $\frac{I\left(\lambda \right)}{\int I\left(\lambda \right)\lambda d\lambda }$ is the normalized line shape function of the emission spectrum. Because of the largest fluorescence branching ratio of ⁴F_3/2 → ⁴I_11/2 transition, the stimulated emission cross sections at 1076 nm are significantly larger than those of the emissions around 0.9 μm and 1.3 μm. Compared with some known disordered crystals, the emission cross sections of the Nd:SLG crystal at 1076 nm are a little larger than those of the Nd:SrGdGa₃O₇ (2.00 × 10⁻²⁰ cm²) [33] and comparable to those of the Nd:CaGdAl₃O₇ (4.94 × 10⁻²⁰ cm²) [20]. The corresponding FWHMs of the Nd:SLG crystal are 30.21 and 19.44 nm for π-polarization and σ-polarization, which is wider than most of the disordered crystals, such as Nd:CaYAl₃O₇ crystal (14.4 nm [σ]) [18], Nd:CaYAlO₄ crystal (12 nm [σ]) [23], and Nd:SrLaGa₃O₇ crystal (16.9 nm) [28]. The appropriate emission cross-sections and large emission bandwidth indicate a potential laser operation beyond 1.1 μm and are beneficial for wavelength-tunable and ultrashort pulse solid-state laser generations.

Figure 6 presents the fluorescence decay lifetime of the Nd³⁺:⁴F_3/2 energy level at the wavelength of 1076 nm under 806 nm excitation. The fluorescence lifetime is fitted to be 0.152 ms by a single exponential and linear function fit, which is longer than that of Nd:YVO₄ (0.084 ms) [34] and comparable to Nd:CaYAlO₄ (0.129 ms) [23], Nd:CaGdAlO₄ (0.123 ms) [22], and Nd:SrLaAlO₄ (0.138 ms) [35]. Due to the phonon relaxation between the host and Nd³⁺ ions, the fluorescence lifetime τ_f is always smaller than that of the calculated radiation lifetime τ_rad by the J-O theory. According to the formula η = τ_f/τ_rad, the fluorescence quantum efficiency η can be calculated as 72.72%. The long fluorescence lifetime and large fluorescence quantum efficiency reveal that the Nd:SLG crystal is suitable for high-power solid-state laser generation.

Table 6. A comparison of the Nd-doped spectroscopic properties between the common crystals and some disordered laser crystals.

Crystal	λabs (nm)	σabs (10−20 cm2)	FWHM (nm)	λem (nm)	σem (10−20 cm2)	FWHM (nm)	τf (μs)	Refs.
YAG	808	7.3	1	1064	28	0.8	230	[36,37]
YVO4	808.7(π)	38.7(π)	1.9(π)	1066(σ)	29.5(σ)	3.5(σ)	84.1	[34]
CaYAlO4	806(σ)	9.7(σ)	5(σ)	1080(σ)	10.44(σ)	12(σ)	129	[23]
CaGdAlO4	809(π)	6.8(π)	4(π)	1067(π)	12.5	18(π)	123	[22]
	809(σ)	7.5(σ)	5(σ)	1068(σ)		11(σ)
SrLaAlO4	808(σ)	2.44(σ)	17(σ)	1075(σ)	3.8(σ)	/	138	[35]
	808(π)	2.43(π)	17(π)	1065–1078(π)	5.2–5.5(π)	34(π)
CaYAl3O7	808(σ)	5.34(σ)	20.2(σ)	1062(σ)	4.55(σ)	14.4(σ)	261	[18]
	808(π)	3.51(π)	20.2(π)	1062(π)	5.97(π)	14(π)
CaGdAl3O7	808.5	3.78	19.3	1061.6	4.94	12.7	260.7	[20]
CaLaGa3O7	808(σ)	1.34(σ)	10(σ)	1061(σ)	6.9(σ)	27.8(σ)	250	[32]
	808(π)	3.18(π)	16(π)	1061(π)	7.23(π)	18.8(π)
Gd2SrAl2O7	808(σ)	11.84(σ)	3.4(σ)	1080	12.7(σ)	12.5(σ)	118	[16]
	807.5(π)	13.7(π)	3.3(π)	1080	15(π)	5.1(π)
SrLaGaO4	806(σ)	4.05(σ)	6.1(σ)	1076(σ)	4.12(σ)	19.44(σ)	152	This work
	806(π)	3.73(π)	6(π)	1076(π)	3.97(π)	30.21(π)

presents a brief comparison of Nd-doped spectroscopic properties between the common crystals and some disordered laser crystals. Compared with the spectroscopic parameters of the typical Nd:YAG and Nd:YVO₄ crystals, the disordered crystals always present broadening spectra characteristics, which is desirable for the generation of wavelength-tunable lasers and ultrashort pulse lasers. The large emission bandwidth, the appropriate emission cross-section, and the long fluorescence lifetime also indicate the Nd:SLG crystal as an effective gain material for 1.0 μm ultrafast and tunable lasers.

4. Conclusions

In short, a disordered Nd:SrLaGaO₄ crystal had been successfully grown by the Czochralski method in a rich Ga condition. The crystal structure, refractive index, polarized absorption spectra, and emission spectra were studied in detail.

• XRD was used to verify the unchanged tetragonal structure of the Nd³⁺-doped crystal. The Nd³⁺, Sr³⁺, and La³⁺ ions were distributed randomly with C_4v symmetry. The calculated lattice concentration and effective segregation coefficient of Nd³⁺ ions were 1.27 × 10⁻²⁰ ions/cm³ and 0.48.
• The refractive index of the Nd:SLG crystal was measured by the minimum deviation technique with a right-angle prism sample. The refractive index dispersion equation was fitted by the least squares method. The results reveal that the SLG crystal is a positive uniaxial crystal.
• The polarized absorption spectra of the Nd:SLG crystal were measured at room temperature. The maximum absorption cross sections of π- and σ-polarization at 806 nm were 3.73 × 10⁻²⁰ and 4.05× 10⁻²⁰ cm², and the corresponding FWHMs were 6.00 and 6.10 nm, respectively. Based on the J-O analysis, the ⁴F_3/2 → ⁴I_11/2 transition around 1.0 μm had the largest fluorescence branch ratio of 48.88%.
• The stimulated emission cross sections at 1076 nm were calculated as 3.97 × 10⁻²⁰ cm² for π-polarization and 4.12 × 10⁻²⁰ cm² for σ-polarization, and the corresponding FWHMs were 30.21 and 19.44 nm, respectively. The decay lifetime of the Nd³⁺:⁴F_3/2 energy level of Nd³⁺ ions at 1076 nm was fitted to 0.152 ms by a single exponential.

The broadening spectra characteristics resulting from the disordered crystal structure, as well as the appropriate emission cross-section and the long fluorescence lifetime, show the Nd:SLG crystal to be a good gain material for ultrafast and tunable lasers at 1.0 μm.