Spectroscopic properties of Er:BZMT ceramics for laser emission

Weichao Yao; Hengjun Chen; Hiyori Uehara; Hiyori Uehara; Ryo Yasuhara; Ryo Yasuhara

doi:10.1364/OME.408858

1. Introduction

Er³⁺-doped laser materials have attracted much attention in laser generation and amplification systems, owing to the demands of optical communication, LIDAR systems at around 1.6 µm, and remote sensing at 3 µm. Bulk and fiber gain materials are the main research directions in this area. For the Er³⁺-doped fibers, they are favorable for broadband and flexible wavelength selectivity [1,2], because of the spectral broadening induced by the glassy disordered structure. Ultra-short pulses can also be generated benefiting from the large gain bandwidth up to tens of nanometers in fibers. Up to now, femtosecond (fs) level pulse width has been generated from Er³⁺-doped fiber lasers [3,4]. However, despite the advantages in broad gain bandwidth in Er³⁺-doped fiber lasers, there are still obvious limitations. For example, in 1.6 µm Er,Yb fiber lasers, the wavelength is limited to less than ∼1625 nm [1]. Another limitation is that the fiber lasers have low damage threshold and obvious nonlinear effects, e.g., stimulated Raman scattering and self-phase modulation, which limit the output power of the ultra-fast lasers.

Some bulk Er³⁺-doped materials can also provide broadband gain bandwidth. More importantly, the nonlinear effects are usually negligible in bulk materials, which lead to less possibility of damage. Thus, these materials can not only be used directly for the generation of ultra-short laser pulses, but also can be employed in the amplifier to further increase the power level. In this case, the gain bandwidth of the bulk material is the principal limiting factor for efficient pulse amplification while maintaining the laser spectrum and the pulse width. At 1.5 µm, the Er:glass is typically used in mode-locked 1.5 µm solid state lasers. This material can support laser pulses shorter than 100 fs [5]. Nevertheless, the glass shows low damage threshold and relatively low thermal conductivity (<1 Wm^-1K^-1) [6], which will make them difficult for high power laser generation. Thus, a laser material with broad gain bandwidth and high damage threshold is necessary for a high power ultra-fast laser system.

Recently, a novel host material, transparent BZMT ceramic has been developed [7]. This type of ceramic has an ABO₃ perovskite structure. Since Zr⁴⁺, Mg²⁺, and Ta⁵⁺ have similar ionic radii (Zr⁴⁺: 72 pm, Mg²⁺: 72 pm, Ta⁵⁺: 64 pm), they can be randomly distributed in the B site of BZMT [8]. Coordination number in the A- and B-site is 12 and 6, respectively [7]. Meanwhile, the rare-earth active ions can be introduced into the B site with charge compensation being fulfilled by tuning the ratio of Zr⁴⁺, Mg²⁺, and Ta⁵⁺. Such disordered structure results in spectral broadening of the active ion. In the 1 µm wavelength region, a broadband emission spectrum has been observed from a Nd:BZMT ceramic [9], and a pulse width of 196 fs has been reported from a mode-locked Nd:BZMT laser [8]. Moreover, the thermal conductivity (3.1 Wm^-1K^-1) and thermal shock parameter (302 Wm^-1) of BZMT ceramics [7] are much higher than those of glass materials, which suggests a higher thermal damage threshold in BZMT. Therefore, BZMT based gain materials are excellent candidates for the high-power and ultra-fast laser systems. Further, the wide spectrum is also beneficial for achieving tunable laser wavelength.

In this work, the spectroscopic properties of the Er:BZMT ceramic were characterized, and Judd-Ofelt analysis was performed in order to evaluate the potential of Er:BZMT ceramic as gain medium, in both the 1.6 µm and the 3 µm spectral regions. To the best of our knowledge, this is the first study on the Er:BZMT laser gain medium.

2. Experimental results and discussions

The Er:BZMT ceramic provided by Murata Manufacturing Co., Ltd. has a composition of Ba(Er_0.05Zr_0.225Mg_0.225Ta_0.5)O₃. About 5 mol% Er³⁺ was substituted into the B site of BZMT. The detailed manufacturing process can be found in [7]. To characterize its spectral properties, a thin sample was cut from the ceramic with a cross-section of ∼5 mm × 5 mm and a thickness of 1 mm. Both two surfaces of the samples were well polished in order to reduce the scattering loss during the measurements.

First, the transmission spectrum was measured with a spectrophotometer (UV3600Plus, Shimadzu) at room temperature. Figure 1 shows the transmission spectrum of the Er:BZMT ceramic sample. As a comparison, the predicted Fresnel transmittance was also calculated according to:

(1)$$T = \frac{{{{\left( {1 - R} \right)}^2}}}{{1 - {R^2}}} $$

where R = (n-1)²/(n+1)² represents the theoretical reflectivity on the surface and n is the refractive index of BZMT ceramic [9]. Here multi-reflections between the two surfaces of the ceramic are taken into account since the thickness of the ceramic sample is only 1 mm. From Fig. 1, we can see that this ceramic has a wide transmission spectrum. At wavelengths above 600 nm, the measured transmittance is almost consistent with that of the predicted value. Taking the transmittance values at 1300 nm for instance, the measured transmittance is 78.8%, which is the same as the theoretical Fresnel transmittance, i.e., 78.8%, indicating that the scattering loss inside the ceramic sample is small and can be ignored, and high optical quality of the ceramic can be guaranteed. At shorter wavelength, a significant increase of the losses induced by the Rayleigh scattering was observed, which should be attributed to the inevitable small amount of defects, such as grain boundary pores in the ceramic.

Fig. 1. Transmission spectrum of the Er:BZMT ceramic.

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The absorption coefficient α(λ) was calculated by:

(2)$$\alpha \left( \lambda \right) = - \ln \left( {\frac{{ - {{\left( {1 - R} \right)}^2} + \sqrt {{{\left( {1 - R} \right)}^4} + 4T_\textrm{m}^2{R^2}} }}{{2{T_\textrm{m}}{R^2}}}} \right)/l$$

where T_m is the measured transmittance, l is the thickness of the sample. The net absorption coefficient is obtained after removing the baseline that caused by the slightly small scattering coefficient from the absorption. The absorption spectrum is shown in Fig. 2. A total of 14 absorption peaks can be observed, corresponding to the transitions from the ground level ⁴I_15/2 to the ⁴G_7/2 energy level. Different from typical Er:YAG crystal [10], the disordered structure of Er:BZMT has made the absorption spectrum to be broadened obviously. At typical pump wavelengths for the laser diodes, i.e., ∼976 nm and ∼1470 nm relating to the transitions of ⁴I_15/2 → ⁴I_11/2 and ⁴I_15/2 → ⁴I_13/2, the 3 dB absorption bandwidth is ∼19 nm and ∼60 nm, respectively, with absorption coefficient of ∼0.43 cm^-1 and ∼0.70 cm^-1, respectively. In this case, a relatively long sample is required to ensure the pump absorption for pumping with a 976 nm laser diode, but this kind of selectivity is unfavorable for the design of the laser because of the insufficient confocal parameter of the pump light in the ceramic. Therefore, in-band pumping scheme, i.e., pumping according to ⁴I_15/2 → ⁴I_13/2 at ∼1470 nm with a laser diode or at 1539 nm (3 dB bandwith: ∼23 nm) with an Er,Yb fiber laser is beneficial for the laser gain of 1.6 µm. In particular, a lower doping concentration will be allowed with a 1539 nm Er,Yb fiber laser pump source, which is also advantageous for improving the laser efficiency because of the reduction of energy transfer up-conversion process. On the other hand for the possible 3 µm emission pumped at ∼976 nm (⁴I_15/2 → ⁴I_11/2), a higher doping concentration is still necessary to achieve an effective pump absorption.

The nominal doping concentration of Er³⁺ in the BZMT can be calculated to be 6.9 × 10²⁰ cm^-3 from the cell parameters. We can therefore obtain the absorption cross-section according to the doping concentration. The absorption cross-section at 976 nm, 1470 nm and 1539 nm is 6.3 × 10⁻²⁰ cm², 1.0 × 10⁻²¹ cm², and 5.2 × 10⁻²⁰ cm², respectively, which are lower than that of Er:YAG [10], but have similar values with that of Er:glass [11,12]. Then, the parameters describing the spectroscopic properties of Er:BZMT, including the intensity parameters, theoretical oscillator strengths, radiative lifetimes, and branching ratios that relate to the 1.6 µm and 3 µm laser emissions are calculated using Judd-Ofelt analysis. Here, all the transitions in Fig. 2 were within consideration for the purpose to reduce the possible fitting errors. The experimental oscillator strengths f_exp can be given by [13]:

(3)$${f_{\exp }} = \frac{{4{\varepsilon _0}{m_\textrm{e}}{c^2}}}{{{N_\textrm{t}}{e^2}}}\int {\alpha \left( v \right)dv} $$

where ɛ₀ is the vacuum permittivity, m_e is the electron mass, c is the speed of light, N_t is the doping concerntration, e is the elementary charge, and α(v) represents the absorption coefficient at different wavenumber v.

Fig. 2. Absorption coefficient of Er:BZMT ceramic at different wavelength.

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The theoretical oscillator strengths for the electric-dipole (ED) and magnetic-dipole (MD) induced absorptions, $\left. {\left| {{l^N}SLJ} \right.} \right\rangle \to \left| {\left. {{l^N}{S^{\prime}}{L^{\prime}}{J^{\prime}}} \right\rangle } \right.$ and $\left. {\left| {{l^N}SLJ} \right.} \right\rangle \to \left| {\left. {{l^N}SL{J^{\prime}}} \right\rangle } \right.$, can be given by [13]:

(4)$$f_{\textrm{ED}}^{\textrm{abs}} = \frac{{8{\pi ^2}{m_\textrm{e}}}}{{3h}}\frac{{\overline v }}{{({2J + 1} )}}\frac{{{{({{n^2} + 2} )}^2}}}{{9n}}\sum\limits_{\lambda = 2,4,6} {{\Omega _{(\lambda )}}{{\left|{\left\langle {{l^N}SLJ\parallel {U^{(\lambda )}}\parallel {l^N}{S^{\prime}}{L^{\prime}}{J^{\prime}}} \right\rangle } \right|}^2}} $$

(5)$$f_{\textrm{MD}}^{\textrm{abs}} = \frac{{h\overline v }}{{6{m_\textrm{e}}{c^2}}}\frac{n}{{\left( {2J + 1} \right)}}{\left| {\left\langle {{l^N}SLJ\parallel L + gS\parallel {l^N}SL{J^{\prime}}} \right\rangle } \right|^2} $$

where h is the Planck’s constant, $\overline v $ is the average transition frequency, n is the refractive index of BZMT which can be found in [9], Ω₍_λ₎ are the intensity parameters, and U⁽^λ⁾ is the tensor operator. The values of squared reduced matrix elements were fitted via the total oscillator strengths expressed by $f_{\textrm{calc}}^{\textrm{abs}} = f_{\textrm{ED}}^{\textrm{abs}} + f_{\textrm{MD}}^{\textrm{abs}}$ and the experimental oscillator strengths using the program RELIC summarized in [13]. The intensity parameters Ω₍_λ₎ were further fitted and the fitting quality was calculated using the relative root mean square (RMS_rel):

(6)$$\textrm{RM}{\textrm{S}_{\textrm{rel}}} = \sqrt {\frac{1}{{N - p}}\sum\limits_{i = 1}^n {{{\left( {\frac{{f_i^{\exp } - f_i^{\textrm{calc}}}}{{f_i^{\exp }}}} \right)}^2}} } $$

where N is the number of transitions (N = 7) and p represents the number of fitted parameters (p = 3). Table 1 shows the oscillator strengths and the fitted intensity parameters Ω₍_λ₎ of Er:BZMT ceramic. The electrostatic intensity (F₍₂₎, F₍₄₎, F₍₆₎) and spin-orbit (ζ) parameters were fitted using RELIC program to be 429.33 cm^-1, 69.98 cm^-1, 7.22 cm^-1 and 2407.43 cm^-1, respectively, which are consistent with the statistical values [13]. The intensity parameters were fitted to be Ω₍₂₎ = 1.16×10⁻²⁰ cm², Ω₍₄₎ = 3.17×10⁻²¹ cm², and Ω₍₆₎ = 3.20×10⁻²¹ cm², with a RMS_rel of 0.19. Here the RMS_rel in this calculation is comparable with other Er³⁺-doped material [13], thus the calculation can be considered reasonable. Typically, Ω₍₂₎ is related to the degree of covalency between the Er³⁺ and the ligands. The Ω₍₂₎ value of Er:BZMT is smaller than that of some other Er³⁺-doped glasses such as ZBLAN (2.91 × 10⁻²¹ cm²) and silicate (4.23 × 10⁻²¹ cm²) [14], while is closer to that of some other Er³⁺-doped crystals such as YSGG (0.92 × 10⁻²¹ cm²) [15], YAP (0.95 × 10⁻²¹ cm²) [16], meaning more ionic and high symmetry of the Er:BZMT ceramic.

The spontaneous radiative decay rate A and branching ratio β for $\left| {{l^N}SLJ} \right\rangle \to \left| {{l^N}{S^{\prime}}{L^{\prime}}{J^{\prime}}} \right\rangle $ transition can be given by [13]:

(7)$$A_{SLJ \to {S^{\prime}}{L^{\prime}}{J^{\prime}}}^{\textrm{ED}(\textrm{MD})} = \frac{{2\pi {{\overline v }^2}{e^2}{n^2}}}{{{c^3}{m_\textrm{e}}{\varepsilon _0}}}f_{\textrm{ED}(\textrm{MD})}^{\textrm{abs}} $$

(8)$${\beta _{SLJ \to {S^{\prime}}{L^{\prime}}{J^{\prime}}}} = \frac{{A_{SLJ \to {S^{\prime}}{L^{\prime}}{J^{\prime}}}^{\textrm{ED}} + A_{SLJ \to {S^{\prime}}{L^{\prime}}{J^{\prime}}}^{\textrm{MD}}}}{{\sum\limits_{{S^{\prime}}{L^{\prime}}{J^{\prime}}} {\left( {A_{SLJ \to {S^{\prime}}{L^{\prime}}{J^{\prime}}}^{\textrm{ED}} + A_{SLJ \to {S^{\prime}}{L^{\prime}}{J^{\prime}}}^{\textrm{MD}}} \right)} }} $$

The calculated radiative transition rates, fluorescence branching ratios and radiative lifetimes from ⁴I_13/2, ⁴I_11/2, ⁴I_9/2 levels relating to the 1.6 µm and 3 µm laser emissions are shown in Table 2. The radiative lifetime of ⁴I_13/2 levels is 6.41 ms, which is comparable with that of Er-doped garnets [15] and glasses [12]. However, different from these materials, the radiative lifetime of ⁴I_11/2 level is longer than that of ⁴I_13/2. This can be explained by the fact that the MD interaction has a large contribution to the ⁴I_13/2 → ⁴I_15/2 transition while emission transitions from the ⁴I_11/2 manifold are dominated by ED interaction. It is known that the reduced matrix elements of MD transition do not vary much with host material. Therefore, the MD oscillator strength of the ⁴I_13/2 → ⁴I_15/2 transition is mainly impacted by refractive index. The large refractive index of BZMT (>2.0 at 1.6 µm) leads to a large A^MD and thus a short lifetime. Similar results can also be found from the Er:LaAlO₃ crystal [17].

To further characterize the two potential laser transitions at 3 µm and 1.6 µm, the fluorescence lifetimes (τ_f) of the ⁴I_11/2 and ⁴I_13/2 multiplets were measured excited by a 976 nm laser diode. The laser diode was run in quasi-continuous wave mode and the pulse durations for the fluorescence at 3 µm and 1.6 µm were set to be 100 µs and 2 ms, respectively, with rising and falling times less than 6 µs. The fluorescence decay curves were recorded by two fast detectors (Vigo FIP-1K-1G-F-ND, Thorlabs DET10D/M), respectively. Figure 3 shows the fluorescence decay curves for the transition of ⁴I_11/2 → ⁴I_13/2 and ⁴I_13/2 → ⁴I_15/2. The best fitted lifetime of ⁴I_11/2 and ⁴I_13/2 was 188 µs and 9.5 ms, respectively. We can therefore calculate the radiative quantum efficiency η_q by:

(9)$${\eta _\textrm{q}}\textrm{ = }{{{\tau _\textrm{f}}} / {{\tau _{\textrm{rad}}}}} $$

From Eq. (9), the radiative quantum efficiency for the 3 µm emission is only 2.3%, which is much lower than that of some other materials such as Er:Y₂O₃ [18] and Er:YAP [19]. The low quantum efficiency is believed to come from a high non-radiative relaxation induced by the high phonon energy (∼840 cm^-1 [9]). In this case, it is difficult for the Er:BZMT ceramic to produce the 3 µm laser emission. On the contrary, the fast non-radiative relaxation from ⁴I_11/2 is beneficial for 1.5 µm laser, because of the reduction of excited-state absorption (⁴I_11/2 → ⁴F_7/2), and energy transfer up-conversion (⁴I_11/2 + ⁴I₁₁_/2 → ⁴I_15/2 + ⁴F₇_/2) [20]. Further, for the 1.5 µm emission, the radiative quantum efficiency is over 100%. We believe that this error is caused by the reabsorption effect relating to ⁴I_15/2 → ⁴I_13/2, resulting in a longer fluorescence lifetime. In the further work, it is still possible to reduce the influence of re-absorption by reducing the doping concentration or adopting the pinhole method [21] to obtain more accurate results.

Fig. 3. Fluorescence lifetimes excited by a 976 nm laser diode. (a) ⁴I_11/2 → ⁴I_13/2; (b) ⁴I_13/2 → ⁴I_15/2.

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Table 1. Calculated Judd-Ofelt results of Er:BZMT ceramic.

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Table 2. Radiative transition rates, branching ratios and radiative lifetimes relating to 1.6 µm and 3 µm laser emissions.

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The fluorescence spectrum of the Er:BZMT sample for ⁴I_13/2 → ⁴I_15/2 is recorded with an optical spectrum analyzer (Q8381A, Advantest). Emission cross-section of the Er:BZMT ceramics can be further obtained according to the Füchtbauer–Ladenburg method [22]:

(10)$${\sigma _{\textrm{ems}}}\left( \lambda \right) = \frac{{\beta {\lambda ^5}I\left( \lambda \right)}}{{8\pi {n^2}c{\tau _{\textrm{rad}}}\int {\lambda I\left( \lambda \right)d\lambda } }} $$

where I(λ) is the fluorescence emission intensity at different wavelength. Figure 4 shows the emission cross-section in the 1.6 µm wavelength region. The peak emission cross-section is 0.37 × 10⁻²⁰ cm² at the wavelength of 1549 nm. This value is slightly lower than that of Er-glasses [12,23]. However, thanks to the disordered structure, the Er:BZMT ceramic has a broad emission spectra, i.e., from 1400 nm to 1700nm with a 3 dB bandwidth of ∼57 nm. This feature is favorable for the applications of tunable and ultra-fast laser systems.

The gain cross-section of the Er:BZMT for the 1.5 µm wavelength band was calculated according to:

(11)$${\sigma _{\textrm{gain}}}\left( \lambda \right) = P{\sigma _{\textrm{abs}}}\left( \lambda \right) - \left( {1 - P} \right){\sigma _{\textrm{ems}}}\left( \lambda \right) $$

where the inversion factor P is defined as P = N₁ / (N₀ + N₁), N₀ and N₁ are the populations on the ⁴I_15/2 and ⁴I_13/2 levels, respectively. Figure 5 shows the calculated gain cross-sections with different inversion factors. The gain cross-section as well as the gain bandwidth increase with the increasing of the inversion factor. If we consider ∼20% of inversion factor, the gain bandwidth (full width at half maximum) is ∼80 nm with a central wavelength of ∼1618 nm. In this case, in addition to a longer laser wavelength than the Er,Yb fiber laser [1] and Er:YAG laser [24], we can also obtain a laser pulse shorter than 100 fs from the Er:BZMT laser according to the Fourier transform-limit, assuming a Gaussian shape of laser pulse.

Fig. 4. Emission cross-section of the Er:BZMT ceramic sample.

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3. Summary

In conclusion, we have investigated the detailed spectroscopic properties of a high-quality transparent Er:BZMT ceramic. The disordered structure of the Er:BZMT ceramic leads to the broadening of the absorption and emission spectrum. Judd-Ofelt analysis was applied to calculate the spectroscopic parameters. The Judd-Ofelt intensity parameters of the Er:BZMT ceramic were estimated to be Ω₍₂₎ = 1.16 × 10⁻²⁰ cm², Ω₍₄₎ = 3.17×10⁻²¹ cm², and Ω₍₆₎ = 3.20 × 10⁻²¹ cm². The fluorescence lifetimes for the two typical emission bands, i.e., 1.6 µm and 3 µm were measured to be 9.5 ms and 188 µs, respectively. By comparing the measured and calculated lifetimes, we found that the ⁴I_11/2 level has a low radiative quantum efficiency of 2.3%. For the potential laser emission in the 1.6 µm wavelength region, the emission cross-section was calculated. Further calculation of the gain spectrum indicates that fs level ultra-short laser pulses were possible to be generated from the Er:BZMT laser system. Further work will be focused on the characterization of Er:BZMT laser performance.

Fig. 5. Gain cross-sections of Er:BZMT ceramic with different inversion factors.

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Funding

Japan Society for the Promotion of Science (15KK0245, 18H01204); National Institute for Fusion Science (UFEX5003, ULHH040).

Acknowledgements

The authors acknowledge Satoshi Kuretake and Koji Murayama in Murata Manufacturing Co., Ltd. for the fabrication of the Er:BZMT ceramic.

Disclosures

The authors declare no conflicts of interest.

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Transitions from ⁴I_15/2	$\bar{λ}$ (nm)	f_exp (× 10⁻⁶)	f_calc (× 10⁻⁶)
⁴I_13/2	1528	1.02	1.12 (0.64)^a
⁴I_11/2	968	0.20	0.24
⁴I_9/2	792	0.12	0.11
⁴F_9/2	652	0.60	0.71
⁴F_3/2 + ⁴F₅_/2 + ⁴F₇_/2 + ²H(2)_11/2 + ⁴S₃_/2	517	4.07	4.23
²G(1)_9/2	408	0.37	0.29
⁴G_7/2 + ⁴G₉_/2 + ²K₁₅_/2 + ⁴G₁₁_/2	377	6.38	5.99
F₍₂₎ = 429.33 cm^-1, F₍₄₎ = 69.98 cm^-1, F₍₆₎ = 7.22 cm^-1; ζ = 2407.43 cm^-1;
Ω₍₂₎ = 1.16 × 10⁻²⁰ cm², Ω₍₄₎ = 3.17×10⁻²¹ cm², Ω₍₆₎ = 3.20 × 10⁻²¹ cm²;
RMS_rel = 0.19

Transition		$\bar{λ}$ (nm)	A^ED (s^-1)	A^MD (s^-1)	β	τ_rad (ms)
Initial state	Final state	$\bar{λ}$ (nm)	A^ED (s^-1)	A^MD (s^-1)	β	τ_rad (ms)
⁴I_13/2	⁴I_15/2	1519	66.64	89.26	1	6.41
⁴I_11/2	⁴I_15/2	976	93.18	0	0.75	8.05
	⁴I_13/2	2727	11.38	19.71	0.25
⁴I_9/2	⁴I_15/2	801	77.68	0	0.70	8.99
	⁴I_13/2	1695	30.86	0	0.28
	⁴I_11/2	4480	0.46	2.25	0.02

Transitions from ⁴I_15/2	$\bar{λ}$ (nm)	f_exp (× 10⁻⁶)	f_calc (× 10⁻⁶)
⁴I_13/2	1528	1.02	1.12 (0.64)^a
⁴I_11/2	968	0.20	0.24
⁴I_9/2	792	0.12	0.11
⁴F_9/2	652	0.60	0.71
⁴F_3/2 + ⁴F₅_/2 + ⁴F₇_/2 + ²H(2)_11/2 + ⁴S₃_/2	517	4.07	4.23
²G(1)_9/2	408	0.37	0.29
⁴G_7/2 + ⁴G₉_/2 + ²K₁₅_/2 + ⁴G₁₁_/2	377	6.38	5.99
F₍₂₎ = 429.33 cm^-1, F₍₄₎ = 69.98 cm^-1, F₍₆₎ = 7.22 cm^-1; ζ = 2407.43 cm^-1;
Ω₍₂₎ = 1.16 × 10⁻²⁰ cm², Ω₍₄₎ = 3.17×10⁻²¹ cm², Ω₍₆₎ = 3.20 × 10⁻²¹ cm²;
RMS_rel = 0.19

Transition		$\bar{λ}$ (nm)	A^ED (s^-1)	A^MD (s^-1)	β	τ_rad (ms)
Initial state	Final state	$\bar{λ}$ (nm)	A^ED (s^-1)	A^MD (s^-1)	β	τ_rad (ms)
⁴I_13/2	⁴I_15/2	1519	66.64	89.26	1	6.41
⁴I_11/2	⁴I_15/2	976	93.18	0	0.75	8.05
	⁴I_13/2	2727	11.38	19.71	0.25
⁴I_9/2	⁴I_15/2	801	77.68	0	0.70	8.99
	⁴I_13/2	1695	30.86	0	0.28
	⁴I_11/2	4480	0.46	2.25	0.02

Spectroscopic properties of Er:BZMT ceramics for laser emission

Abstract

1. Introduction

2. Experimental results and discussions

3. Summary

Funding

Acknowledgements

Disclosures

References

Cited By

Figures (5)

Tables (2)

Equations (11)

Optical Materials Express