1. Introduction

Er³⁺ laser around 1.55 μm has many applications, such as range finding, optical communication, remote sensing, and medical treatment [1–5]. Yb³⁺ ions with large absorption cross-section around 980 nm, i.e. the emission wavelength of InGaAs diode laser, are generally co-doped as a sensitizer to improve the performance of the 1.55 μm laser via the efficient energy transfer from Yb³⁺ to Er³⁺ ions [1–4].

At present, Er³⁺ and Yb³⁺ co-doped borate crystals, such as YAl₃(BO₃)₄, YCa₄O(BO₃)₃, and Sr₃Lu₂(BO₃)₄ [2–4], have been demonstrated as a kind of the most efficient gain media for the 1.55 μm laser. However, for absorbing pump light around 980 nm efficiently and realizing high efficient 1.55 μm laser operation, high Yb³⁺ doping concentration is necessary for the above crystals [2–4]. Comparing with the Er³⁺/Yb³⁺ co-doped crystals, crystal defects related with the ion-substitution may be reduced when the Yb³⁺ is a matrix constitutive ion in a crystal. Generally, only low Er³⁺ doping concentration is needed in the Er³⁺ and Yb³⁺ co-doped borate crystals for realizing high efficient 1.55 μm laser operation. On the other hand, the radius of Er³⁺ ion (0.89 Å) is close to that of Yb³⁺ ion (0.87 Å) [6]. Therefore, the Er³⁺ doped YbAl₃(BO₃)₄ and Sr₃Yb₂(BO₃)₄ crystals have been studied in our group [7, 8]. Although the thermal properties on the input and output faces of a c-cut plate are isotropic for the uniaxial YbAl₃(BO₃)₄ crystal, which can only be obtained by the flux method with a long growing period. The biaxial Sr₃Yb₂(BO₃)₄ crystal can be obtained by the short-period and low-cost Czochralski method, but the strong anisotropy makes them easy cracked during laser operation. Therefore, finding new uniaxial borate laser crystals with Yb³⁺ as a matrix constitutive ion, which can be grown by the Czochralski method, is still necessary.

The Yb³⁺ doped Sr₃Y(BO₃)₃ (SYB) crystal, which belongs to trigonal system with the space group R$\overline{3}$ has been demonstrated as excellent crystal for solid-laser [9, 10]. However, the peak absorption cross-section of Yb³⁺ in the SYB crystal is relatively small (about 0.95 × 10⁻²⁰ cm² at 975 nm for σ polarization) [10]. Therefore, 1.55 μm laser operation of Er³⁺ and Yb³⁺ co-doped SYB crystal has not been reported till now. In addition to the SYB crystal, there is another member of this borate family, Sr₃Yb(BO₃)₃ [11], which has high Yb³⁺ concentration to make up for the small absorption cross-section but has not been investigated as laser crystal. In this paper, the polarized spectral properties and quasi-cw laser operation of an Er:Sr₃Yb(BO₃)₃ crystal are reported.

2. Spectral properties

An Er:Sr₃Yb(BO₃)₃ crystal was grown by the Czochralski method with a seed crystal along the c-axis, which is cut from an Er:Sr₃Yb(BO₃)₃ crystal grown by spontaneous nucleation. The Er³⁺ and Yb³⁺ concentrations in the grown crystal, cut around the samples for spectral and laser experiments, were determined to be 0.384 wt.% and 26.95 wt.%, respectively, by the inductively coupled plasma atomic emission spectrometry (ICP-AES, Ultima2, Jobin-Yvon). Therefore, the Er³⁺ concentration in the crystal in atomic percent can be calculated to be 1.45 at.% (7.04 × 10¹⁹ cm⁻³) by Er/(Er + Yb). Then the segregation coefficient of the Er³⁺ in the crystal was calculated to be 1.07 after the initial 1.35 at.% Er³⁺concentration in the melt was taken into account. The value is similar to those of Er:Sr₃Yb₂(BO₃)₄ (1.02) and Yb:Y₃Al₅O₁₂ (1.1) crystals [8, 12]. In fact, for realizing high efficient 1.55 μm laser, only low Er³⁺ concentration is needed in the crystal for avoiding the negative effect of re-absorption of Er³⁺. Therefore, about 1.45 at.% Er³⁺ concentration was selected in the Er:Sr₃Yb(BO₃)₃ crystal according to the current literature reports [1–5].

Room temperature (RT) polarized absorption spectra recorded with a spectrophotometer (Lambda 900, Perkin-Elmer) in a range from 280−1700 nm are shown in Fig. 1. It can be found that the crystal has weak anisotropy in spectra. Except the band around 976 nm, consisted with the ²F_7/2→²F_5/2 transition of Yb³⁺ ions and the ⁴I_15/2→⁴I_11/2 transition of Er³⁺ ions, the other bands are related to the transitions originated from the ⁴I_15/2 ground level to different excited levels of Er³⁺ ions. For the absorption band around 976 nm, the peak absorption wavelength and full width at half the maximum (FWHM) are 976 nm and 7 nm, respectively, for both σ and π polarizations. The peak absorption cross-sections of the Er:Sr₃Yb(BO₃)₃ crystal are 0.69 × 10⁻²⁰ and 0.86 × 10⁻²⁰ cm² for σ and π polarizations, respectively.

 

Fig. 1 RT polarized absorption spectra of the Er:Sr₃Yb(BO₃)₃ crystal from 280 to 1700 nm.

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Using BaSO₄ as a standard reference, a RT diffuse reflection spectrum of an undoped Sr₃Yb(BO₃)₃ polycrystalline powder, which was obtained by solid-state synthesis, was measured by a spectrophotometer (Lambda 950, Perkin-Elmer) in a range from 830 to1100 nm and is shown in Fig. 2. It can be found from Figs. 1 and 2 that the Er:Sr₃Yb(BO₃)₃ crystal and Sr₃Yb(BO₃)₃ polycrystalline powder have similar absorption bands from 850 to 1050 nm, which demonstrate that the absorption band around 976 nm of the Er:Sr₃Yb(BO₃)₃ crystal is mainly caused by the Yb³⁺ ions.

 

Fig. 2 RT diffuse reflection spectrum of the Sr₃Yb(BO₃)₃ polycrystalline powder from 830 to 1100 nm.

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The Judd-Ofelt (J-O) theory [13, 14] is an effective method for estimating spectral parameters of rare earth ions in crystals and glasses. Since the application of the J-O theory has been reported widely [15–17], only the calculation results about upper laser level ⁴I_13/2 are presented for brevity. The calculated spontaneous emission probabilities A for the ⁴I_13/2→⁴I_15/2 transition are 105.62 s⁻¹ and 146.58 s⁻¹ for σ and π polarizations, respectively, and then the radiative lifetime of the ⁴I_13/2 level can be calculated to be 8.38 ms. It is worth noting that the magnetic dipole probabilities for the ⁴I_13/2→⁴I_15/2 transition are 48.46 s⁻¹ and 50.44 s⁻¹ for σ and π polarizations, respectively, which implies that the contribution of the magnetic dipole for the ⁴I_13/2→⁴I_15/2 transition is important.

RT polarized fluorescence spectra from 1400 to 1700 nm under excitation at 976 nm were recorded using a spectrometer (FLS920, Edinburgh). Polarized emission cross-sections spectra, which were calculated from the recorded fluorescence spectra by the Fuchtbauer-Ladenburg (FL) method [18], are shown in Fig. 3. The peak emission cross-sections are 0.57 × 10⁻²⁰ cm² at 1539 nm and 0.67 × 10⁻²⁰ cm² at 1535 nm for σ and π polarizations, respectively.

 

Fig. 3 RT polarized emission cross-sections of the Er:Sr₃Yb(BO₃)₃ crystal from 1400 to 1700 nm.

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From the absorption and emission cross-sections, denoted as σ^abs and σ^em, respectively, a gain cross-section curve can be calculated by ${\sigma }^{\text{g}}(\lambda )=\beta {\sigma }^{em}(\lambda )-(1-\beta ){\sigma }^{abs}(\lambda )$ [19, 20], where β is the ratio of the number of Er³⁺ ions in the upper laser level ⁴I_13/2 to the total number of Er³⁺ ions. Considering that a c-cut Er:Sr₃Yb(BO₃)₃ crystal was used in the following laser experiment, only the curves for σ polarization with different values of β are shown in Fig. 4. It can be found that the gain curve is flat with FWHM of 46 nm and the possible wavelength for free running laser is between 1540 nm and 1549 nm when β = 0.5.

 

Fig. 4 Gain curves of the ⁴I_13/2→⁴I_15/2 transition of Er³⁺ ions in the Er:Sr₃Yb(BO₃)₃ crystal for σ polarization with different β.

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RT fluorescence decay curves at wavelengths of 1040 and 1535 nm, corresponding to the transitions of ²F_5/2→²F_7/2 and ⁴I_13/2→⁴I_15/2 of Yb³⁺ and Er³⁺ ions, respectively, were recorded using the spectrometer (FLS920, Edinburgh) when a tunable mid-band OPO laser (Vibrant 355II, OPOTEK) with pulse duration of ~5 ns was used as the exciting source and the exciting wavelengths were set at 930 and 976 nm, respectively. The signals were detected with an NIR PMT (R5509, Hamamatsu). It can be found from Fig. 2 that the Yb³⁺ has absorption around 930 nm. However, the Er³⁺ has not absorption around this wavelength, which can be deduced from the absorption spectra of Er³⁺:Sr₃Y(BO₃)₃ crystal [21]. The Sr₃Y(BO₃)₃ has the same structure as the Sr₃Yb(BO₃)₃. Therefore, the excitation wavelength was selected at 930 nm, where Er³⁺ has no absorption, for measuring the fluorescence lifetime of Yb³⁺ in the Er:Sr₃Yb(BO₃)₃ crystal. On the other hand, for measuring the fluorescence lifetime of ⁴I_13/2→⁴I_15/2 of Er³⁺, the excitation wavelength is 976 nm, where both Er³⁺ and Yb³⁺ have absorption.

To avoid the influence of re-absorption on the measured fluorescence lifetimes [22], all the decay curves were recorded from a powder sample of the crystal as reported in Ref [23]. RT fluorescence decay curves of Er³⁺ and Yb³⁺ ions in the Er:Sr₃Yb(BO₃)₃ crystal are shown in Fig. 5(a). The fitted fluorescence lifetime of the upper laser level ⁴I_13/2 of Er³⁺ ions in the Er:Sr₃Yb(BO₃)₃ crystal is 682.0 ± 3.0 μs, which is close to the fluorescence lifetime (700 μs) of the ⁴I_13/2 level of Er³⁺ ions in the Er³⁺/Yb³⁺:Sr₃Y(BO₃)₃ crystal [24]. Combining with the radiative lifetime calculated above, the fluorescence quantum efficiency of the ⁴I_13/2 level is estimated to be 8.1%. The short fluorescence lifetime and low quantum efficiency of the upper laser level ⁴I_13/2 are related to the high non-radiative transition probability caused by the high phonon energy (about 1400 cm⁻¹) in the borate crystals [25]. The fitted fluorescence lifetime of the ²F_5/2 level of Yb³⁺ ions in the Er:Sr₃Yb(BO₃)₃ crystal is 9.20 ± 0.02 μs.

 

Fig. 5 RT fluorescence decay curves of Er³⁺ and Yb³⁺ ions in the Er:Sr₃Yb(BO₃)₃ crystal (a) and Yb³⁺ ions in Sr₃Yb(BO₃)₃ polycrystalline powder (b).

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The efficiency of energy transfer from Yb³⁺ to Er³⁺ ions could be estimated by ${\eta }_{ET}=1-{\tau }_f/{\tau }_0$, where and are the fluorescence lifetimes of Yb³⁺ ions in the crystal co-doped with Er³⁺ ions and not, respectively [3]. Therefore, the fluorescence decay curve of the ²F_5/2 level of Yb³⁺ ions in the undoped Sr₃Yb(BO₃)₃ polycrystalline powder, was recorded and is shown in Fig. 5(b). The fitted fluorescence lifetime is about 677.6 ± 3.0 μs. Therefore, the efficiency of energy transfer in the Er:Sr₃Yb(BO₃)₃ crystal is about 98.6%.

For comparison, spectral parameters of the Er:Sr₃Yb(BO₃)₃, Er:Sr₃Yb₂(BO₃)₄, Er:YbAl₃(BO₃)₄, Er:Yb:YVO₄, and Er:Yb:YAG crystals are listed in Table 1. The Er:Sr₃Yb(BO₃)₃ crystal, grown by the Czochralski method, has a relatively wide FWHM for the absorption band around 976 nm, which is in favor of being pumped by diode laser even the emission bandwidth and temperature-dependent wavelength shift of diode laser are considered. Furthermore, the Er:Sr₃Yb(BO₃)₃ crystal has high energy transfer efficiency from Yb³⁺ to Er³⁺ ions, which is originated from the high effective phonon energy of the crystal. Strong energy transfer is a key to obtain efficient 1.55 μm laser operation. However, the Er:Sr₃Yb(BO₃)₃ crystal has a smaller peak absorption cross-section at 976 nm.

Table 1. Spectral parameters and laser performances of the Er:Sr₃Yb(BO₃)₃, Er:Sr₃Yb₂(BO₃)₄, Er:YbAl₃(BO₃)₄, Er:Yb:YVO₄, and Er:Yb:YAG crystals

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For absorbing 80% of the incident pump power in a single pass of the plate, the thickness of a c-cut Er:Sr₃Yb(BO₃)₃ crystal must be more than 500 μm. However, for realizing single longitudinal mode operation, the thickness of the microchip gain media is generally about less than 300 μm [7, 26]. Furthermore, it can be found from the condition for realizing single longitudinal mode operation that a crystal with broad gain bandwidth is not suitable to be used as a microchip gain medium [31]. Therefore, the Er:Sr₃Yb(BO₃)₃ crystal is not suitable to be used as a microchip gain media for single longitudinal mode operation even if Yb³⁺ is a matrix constitutive ion in the crystal.

3. Laser experiments

A 1.27-mm-thick c-cut Er:Sr₃Yb(BO₃)₃ crystal was used as gain medium in the laser experiment. The uncoated crystal was held in an aluminum slab and an end-pumped hemispherical laser cavity was adopted. The flat input mirror has 90% transmission at 970 nm and 99.8% reflectivity around 1.55 μm. Three output couplers with the same radius curvature of 100 mm and different transmissions of 0.6%, 1.0% and 1.8% around 1.55 μm were used. The reflectivities of the three output couplers at 970 nm were higher than 98%. The cavity length was kept at about 100 mm. A 970 nm diode laser coupled by a fiber with 800 μm diameter core (FAP-980, Coherent) was used as the pump source. After passing a simple telescopic lens system, the pump beam was focused to a spot with waist diameter of about 290 μm in the crystal. The absorption coefficient of the Er:Sr₃Yb(BO₃)₃ crystal at 970 nm for σ polarization is 11.73 cm⁻¹, therefore, about 77.5% of the incident pump power can be absorbed in a single pass of the plate. The thermal conductivity of the Sr₃Y(BO₃)₃ crystal has been reported to be 1.8 W m⁻¹ K⁻¹ [10]. For investigating the influence of thermal effect on laser performance of the Yb³⁺:Sr₃Y(BO₃)₃ crystal, the authors in Ref [10] found that the crystal underwent fracture when the diode power was set to its maximum value (10 W). The result shows that the thermal properties of the Sr₃Y(BO₃)₃ crystal is not very good. Considering that the Sr₃Yb(BO₃)₃ crystal has the same structure with Sr₃Y(BO₃)₃ crystal and no special device was used to control the cooling of the sample, the diode laser operated in a pulse mode for reducing the influence of the pump-induced thermal load on the laser performance and avoiding possible fracture of the sample. The pulse duration was 2 ms and the duty cycle was 2%.

Figure 6 shows the measured fundamental laser output power as a function of the absorbed pump power for the three output couplers. Because the duty cycle of the quasi-cw pulse laser was 2%, the values in the figure are the measured ones multiplied by 50. It can be found from Fig. 6 that the best laser performance is for the output coupler with 1.0% transmission. For this output coupler, the absorbed pump power threshold was 4.53 W, the slope efficiency was 15%, and up to 1.4 W output power was obtained when the absorbed pump power was 13.95 W. Laser performances of the Er:Sr₃Yb(BO₃)₃, Er:Sr₃Yb₂(BO₃)₄, Er:YbAl₃(BO₃)₄, Er:Yb:YVO₄, and Er:Yb:YAG crystals are compared in Table 1. It can be found that the output power and slope efficiency achieved in the Er:Sr₃Yb(BO₃)₃ crystal are the best. Compared with Er:Sr₃Yb₂(BO₃)₄ and Er:YbAl₃(BO₃)₄, crystals, the better laser performance obtained in the Er:Sr₃Yb(BO₃)₃ crystal may be originated from higher optical quality of this crystal and optimized concentration ratio of Er³⁺ and Yb³⁺ in it. In fact, the biaxial Er:Sr₃Yb₂(BO₃)₄ crystal must be glued on a 5-mm-thick pure YAG crystal for avoiding the fracture of sample during laser experiment, which was originated from the strong anisotropy of the crystal. Compared with Er:Yb:YVO₄ and Er:Yb:YAG crystals, the better laser performance obtained in the Er:Sr₃Yb(BO₃)₃ crystal should be originated from higher energy transfer efficiency from Yb³⁺ to Er³⁺ in this crystal. Furthermore, it is worth noting that the absorption cross-section of the Er:Sr₃Yb(BO₃)₃ crystal at 976 nm is nearly three times of that at the pump wavelength of 970 nm in this work (see Fig. 1). Therefore, if a pump source around 976 nm is used, the laser performance of a thinner Er:Sr₃Yb(BO₃)₃ medium may be improved. Therefore, the Er:Sr₃Yb(BO₃)₃ crystal is more suitable for 1.55 μm laser when the Yb³⁺ is a matrix constitutive ion in a crystal.

 

Fig. 6 1.55 μm laser output power as a function of absorbed pump power at 970 nm.

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Laser emission spectra for the three couplers, recorded with a monochromator (Triax 550, Jobin-Yvon) when the absorbed pump power was 13.95 W, are shown in Fig. 7. All the laser beams are un-polarized for the c-cut Er:Sr₃Yb(BO₃)₃ unaxial crystal. The laser wavelengths are around 1569, 1569, and 1547 nm when the transmissions of output coupler are 0.6%, 1.0%, and 1.8%, respectively, which are agreed with those estimated by the gain curves shown in Fig. 4. The blue shift of laser wavelength with the increment of output coupler transmission can be explained by the σ-polarized gain curve with different values of the population inversion β [32].

 

Fig. 7 Spectra of the Er:Sr₃Yb(BO₃)₃ laser around 1.55 μm when the absorbed pump power is 13.95 W and output coupler transmissions are: (a) T = 0.6%, (b) T = 1.0%, (c) T = 1.8%..

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4. Conclusion

Polarized spectral properties of a 1.45 at.% Er³⁺ doped Sr₃Yb(BO₃)₃ crystal, grown by the Czochralski method, were investigated. The fluorescence quantum efficiency of the ⁴I_13/2 level of Er³⁺ ions is about 8.1% and the efficiency of the energy transfer from Yb³⁺ to Er³⁺ ions is about 98.6% in the crystal.

End-pumped by a diode laser at 970 nm in a hemispherical cavity, 1.4 W quasi-cw laser around 1.55 μm with slope efficiency of 15% and absorbed pump power threshold of 4.53 W was achieved in a 1.27-mm-thick c-cut crystal. Compared with those of Er:Yb:YVO₄, Er:Yb:YAG, Er:YbAl₃(BO₃)₄ and Er:Sr₃Yb₂(BO₃)₄ crystals, a better laser performance was achieved in the Er:Sr₃Yb(BO₃)₃ crystal. Furthermore, compared with the Er:YbAl₃(BO₃)₄ and Er:Sr₃Yb₂(BO₃)₄ crystals, the uniaxial Er:Sr₃Yb(BO₃)₃ crystal have both advantages of isotropy on the c-cut plate and simple growing process. Therefore, the Er:Sr₃Yb(BO₃)₃ crystal may be a potential gain medium for the 1.55 μm laser.