1. Introduction

In the quest for the “perfect” laser medium for high energy, eye-safe solid state lasers, the Er³⁺:Sc₂O₃ (Er:ScO) sesquioxide is a promising candidate because it meets two major requirements imposed on such medium: (i) it can operate with a very low quantum defect (QD) and (ii) it has a high thermal conductivity, higher than that of YAG and of other prominent sesquioxides [1]. However, due to limited availability of high optical quality material, Er:ScO laser development started only very recently and relevant spectroscopic investigations are still relatively rare.

The most efficient eye-safe operation of an Er:ScO laser was observed on three major laser transitions: Y₁→Z₆ (~1604 nm), Y₁→Z₅ (~1581 nm), Y₁→Z₄ (~1558.4 nm). These transitions are shown on an energy level diagram in Fig. 1 , along with the Er³⁺ absorption and emission spectra at 77K. Relative to resonant pumping into the strongest absorption band around 1535 nm, these transitions correspond to 4.5%, 3% and 1.5% QD, respectively. For comparison, the smallest usable QD of an Er:YAG laser is 5.5% [2].

 

Fig. 1 Emission and absorption spectra of Er³⁺:Sc₂O₃ along with the Er³⁺ C₂ center energy levels diagram (all at 77K). Short arrows show the location of major transitions where lasing was achieved.

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To the best of our knowledge, the Er:ScO lasing in the eye-safe wavelength range was demonstrated first on the 1604 nm transition [3]. The first 1581 nm Er:ScO laser operating at room temperature was reported in [4]. The lowest 1.5% QD operation was demonstrated in [5] at cryogenic temperatures. Liquid nitrogen cooling was used not only for the population reduction of the terminal laser level, but also for improving thermo-optical properties of the laser medium required for high power operation with good beam quality. However, the 46% optical to optical efficiency of laser operation was lower than expected [5]. Partially, it was caused by high scattering losses in the under-developed laser ceramic material used in these experiments. Other possible reasons include up-conversion and energy migration between Er³⁺ ions occupying the two substitution sites with different point symmetry, C₂ and C_3i, which are known to co-exist in sesquioxide hosts structures [6]. The purpose of this effort is to study spectroscopic and laser features of Er:ScO with the ultimate goal of optimization of the laser efficiency.

2. Spectroscopy

Sc₂O₃ single crystals belong to a cubic sesquioxides (space group T_h ⁷, Ia3). The Sc₂O₃ unit cell has 24 sites of C₂ symmetry and 8 of C_3i symmetry into which Er³⁺ substitutes [6,7]. While C₂ centers allow electric dipole transitions [8,9], C_3i centers permit only magnetic dipole transitions.

Typically, magnetic dipole transitions in rare-earth ions are several orders of magnitude weaker than electric dipole ones. In sesquioxides, however, C_3i centers can be distinctly observed in the emission and absorption spectra even at cryogenic temperatures.

Figure 1 presents the emission and the absorption cross section spectra of Er³⁺ in Sc₂O₃ at 77K. The absorption spectrum was obtained using a Cary 6000i spectrometer with 0.1 nm resolution. The emission spectrum was obtained by exciting the ⁴I_11/2 multiplet with a 970 nm diode laser, and recording the ⁴I_13/2→⁴I_15/2 fluorescence using an Acton 2500 monochromator with an InGaAs detector. The broadband (3-4 nm full width at half maximum, FWHM) diode laser excites Er³⁺ ions in cites of both symmetries, which makes it difficult to distinguish the transitions due to their spectral proximity. Based on the collected spectra, we obtained an energy level scheme corresponding to transitions between the ⁴I_15/2 and ⁴I_13/2 manifolds of Er³⁺ in C₂ sites, which is consistent with the scheme at 300K presented in [8].

At low temperatures, the emission spectrum of C_3i centers can be studied using site-selective excitation [10]. From Fig. 1, one can notice that ⁴I_15/2→⁴I_13/2 absorption at 77K offers at least two lines which do not overlap. One is at 1527.6 nm, and published energy levels indicate that this is due to the Z₁→Y₂ transition of Er³⁺ in the C₂ site. The other is at 1529.3 nm, which does not correspond to any C₂ transition. The strength of the latter transition suggests that it most likely belongs to the C_3i center, rather than to Er³⁺ in any distorted (irregular [11]) site. By exciting into these lines with a narrow-bandwidth source (we used a Santec 207 diode laser) one can define the contribution of each site to the observed luminescence.

In Fig. 2 , the resulting emission spectra are plotted in blue for C₂ centers and in red for the presumed C_3i centers. Taking into account that the ratio of Er³⁺ ions in C₂ and C_3i sites is 3 to 1 [6], it is somewhat surprising that the strength of these emission transitions is very substantial, especially around 1552 nm.

 

Fig. 2 Er³⁺:Sc₂O₃ emission spectra at 77K when C₂ and C_3i-symmetry centers were excited selectively. C₂ center was excited into Z₁ →Y₂, 1527.6 nm absorption line. C_3i center was excited into 1529.3 nm. a. Ceramic sample with 0.25% Er-doping concentration; b. Single crystalline sample with 1.2% Er concentration. On the inset: I_13/2 → ⁴I_15/2 luminescence decay at T = 80 K in Er(0.25%):Sc₂O₃ (powder).

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We studied three samples with different Er-concentrations which were grown by different techniques: Er(0.25%):Sc₂O₃ laser ceramic, hydrothermally grown Er(0.3%):Sc₂O₃ crystal and Er(1.2%):Sc₂O₃ Czochralski grown crystal. We observed that while the growth method did not discernibly affect the emission spectra, Er³⁺ doping levels did. It was found that the excitation exchange between the two centers becomes stronger with concentration so that their emission spectra are almost undistinguishable in the highly-doped Er(1.2%):Sc₂O₃ crystal. For low Er³⁺ concentration, the emission spectra for the two excitation wavelengths are substantially different, but virtually all luminescent features are present for both C₂ and C_3i centers. This indicates that there is always some degree of concentration-dependent energy migration between the centers even at 77K.

The measurements of the fluorescence lifetime of the I_13/2 manifold were carried out on a pulverized Er(0.25%):Sc₂O₃ sample at 80 K and revealed clear two-exponential decay: 6.75 and 19.4 ms, Fig. 2a, inset. The shorter decay time is associated with C₂ centers while the longer one can be attributed to C_3i centers.

We also carefully studied the 1581- and the 1558-1560 nm emission bands, which participate in the two lowest-QD pump-laser schemes. The structure of the 1581 nm band is dominated by a single Y₁→Z₅ transition of the C₂ center and, thus, the 1581 nm laser behaved completely predictably. On the other hand, the 1558-1560 nm band, indicated by the dashed ellipse in Fig. 2a, has a rather complex structure. There are multiple transitions “hiding” underits emission envelope. These transitions are indicated by the blue dash and solid arrows on the energy level diagram in Fig. 1.

Simulations with the Lorentzian fitting reveal significant spectral overlap between the two strong transitions in the C₂ center: Y₄→Z₅ (1559.3 nm) and Y₁→Z₄ (1558.4 nm), shown in Fig. 3a , by bold solid lines. These two transitions are mostly responsible for lasing in the 1558-1560 nm band. The Lorentzian fitting also provided useful estimations of their cross sections which were later used in the modeling. The contribution of C_3i centers to integrated laser gain is small, though not insignificant. The position of the 1558.4 nm emission peak was almost independent of the sample temperature, see Fig. 3b. Between 80 and 150 K we found only a ~200 pm “red-shift”.

 

Fig. 3 Er^3+:Sc₂O₃ emission spectra in the 1558-1560 nm band: a. Simulation with Lorentzian curves. Transitions of the C₂-center - bold solid lines; those of C_3i center - dotted lines. Experimental data - dashed line. b. Temperature dependence of the 1558-1560 nm emission band.

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3. Modeling

The specifics of the energy levels in Er:ScO cause complex laser spectral behavior. Two major transitions Y₁→Z₅ (1581 nm) and Y₁→Z₄ (1558.4 nm) can lase with similar probability. Indeed, while the Y₁→Z₄ transition has a higher cross-section, its terminal laser level Z₄ has a higher thermal population. The proximity of a strong, overlapping transition Y₄→Z₅ (1559.3 nm) complicates the picture.

To understand all these effects, we have developed a model that includes two transitions at approximately 1558 nm and simultaneously one at 1581 nm. The criterion for laser oscillation at one wavelength or another (or simultaneously at both) is the calculated threshold pump power for every possible laser transition. The laser operates at the wavelength which corresponds to the transition with the lowest possible threshold pump power. The model is based on general quasi-four-level laser equations and takes into account the saturation effects of the pump intensity on the laser absorption coefficient, as was shown in [12]. This model also takes into account the pump-absorption spectral overlap, which noticeably varies with the pumping wavelength. We neglected the effect of up-conversion because our laser sample had relatively low Er³⁺ concentration of 0.25%. For more detailed modeling, the up-conversion can be taken into account by the reduction of the lifetime of the upper laser level.

Let N₂(λ_p,z,T) be the local population density of the upper energy manifold ⁴I_13/2 and λ_p be the pumping wavelength corresponding to the transition originating at the Stark level Z₁ of the lower energy manifold ⁴I_15/2 and terminating at the level Y₁ of the upper manifold ⁴I_13/2 (see energy level diagram, Fig. 1). In the steady state condition, before the laser threshold is reached, when only ⁴I_13/2 and ⁴I_15/2 manifolds are involved, the local population density N₂(λ_p,z,T) and the local pump intensity - I_p(λ, z) are connected by the equation:

Following [13], the pump saturated absorption coefficient can be expressed as:

Pump intensity I_p(λ, z) decreases with propagation along axis z in accordance with Eq. (5), and it can be determined at any point z from the numerical solution of the transcendental equation:

If I_p(λ, 0) = I_p0(λ) is the incident pump intensity, then by using Eq. (7) one can calculate the pump intensity at every point z along the laser axis. According to Eq. (4), the difference between the calculated values of the pump intensities ΔI(λ,z) = I_p(λ,z + dz)-I_p(λ,z) defines the absorbed pump power in every elementary volume dV = π(d_p)²dz /4. By integrating ΔI(λ,z) over the length of the active medium, l_a, and then over the wavelengths under the absorption contour and converting pump intensity into absorbed power, one can finally calculate the total population density N₂(λ_p,z,T) and the total absorbed pump power P_abs(P_p,T):

According to the energy level diagram (see Fig. 1), the 1581 nm laser emission corresponds to the transition originating at the lowest Stark level Y₁ of the upper laser manifold ⁴I_13/2 (ΔE = 0) and terminating at the level Z₅ of the lower laser manifold ⁴I_15/2 (ΔE = 189.5 cm⁻¹). The emission cross-section for this transition is measured to be σ_g1581 = 0.75∙10⁻²⁰ cm² (0.65∙10⁻²⁰ cm²). Here and below the open numbers correspond to 77 K, the numbers in parentheses correspond to 120 K. The laser gain coefficient α_g1581(P_p,T), for 1581 nm is defined by Eq. (10), where f_Yi = f_Y1 = 0.499 (0.393) and f_Zj = f_Z5 = 0.015 (0.042).

Two major transitions with slightly different wavelengths could contribute to the laser emission in the 1558-1560 nm band: one is Y₁→Z₄ (1558.4 nm, terminal ΔE = 97 cm⁻¹) and the other is Y₄→Z₅ (1559.3 nm, ΔE = 189.5 cm⁻¹), see Fig. 1, inset. For simplicity we denote them as 1558 and 1559 nm lines respectively. We will neglect contributions of the other, much weaker, transitions in this band.

The peak emission cross-section of the 1558-1560 nm band is σ_g1558 = 2.25∙10⁻²⁰ cm² (2.1∙10⁻²⁰ cm²). The laser gain coefficient, α_g(P_p,T), will be defined by a slightly more complicated expression than Eq. (10):

Figures 4a and 4b show calculated dependencies of the threshold pump power on the transmission of the output coupler, when the laser operates at 1581- or 1558.4 nm wavelengths (or both). Calculations are made for two temperatures of the laser crystal: 77 K (Fig. 4a) and 120 K (Fig. 4b). It was also assumed that the 1558 nm contour contains contributions only from the two transitions and determined by Eq. (12). Other parameters of the crystal, pump source and the laser resonator were taken as: N₀ = 6.1∙10²⁰ cm⁻³, τ = 6.75 ms, λ_p = 1535 nm, σ_p = 1.4∙10⁻¹⁹ cm², Δλ_pump = 0.3 nm, G_p(λ) – Gaussian shape, Δλ_abs = 0.35 nm (FWHM), g(λ) – Lorentzian shape, f_Z1 = 0.5181 (0.402), d_p = 0.47 mm, l_a = 10 mm, L = 0.1. One can see that at a lower temperature (77 K) and with low output coupling (low cavity losses), the threshold for operation at the 1581 nm line is somewhat lower than that of the 1558.4 nm and the laser operates exclusively at 1581 nm. Conversely, if the transmission of the output coupler is high, the threshold for operation around 1558.4 nm becomes lower and the laser operates only at 1558.4 nm. In intermediate cases of the output coupling (~0.15-0.22), the laser operates on both of these wavelengths simultaneously. Calculations show that similar wavelength behavior at low temperatures will be observed for a wide range of ratios between the emission cross-sections σ_gY4 and σ_gY1. Thus, this wavelength competition is not sensitive to the exact parameters needed to fit the behavior of the absorption and emission near 1558.4 nm. However, this wavelength competition is impossible to explain if just one Y₁→Z₄ major laser transition in 1558-1560 nm band is taken into account. If this were the case, the total gain at 1581 nm would always exceed that at 1558 nm since they share the same upper laser level Y₁ and the population inversion for both of them grows equally with increasing resonator losses.

 

Fig. 4 (a, b). Calculated threshold pump power of the resonantly pumped, CW Er³⁺:Sc₂O₃ laser vs transmission of the output coupler for two temperatures of the laser crystal: 77 K (a) and 120 K (b)

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The competition between lasing wavelengths occurs differently at higher crystal temperatures. Figure 4b shows that at 120 K, the threshold for laser operation at 1558.4 nm is lower than that for 1581 nm for almost any output coupling. This result seems to be counterintuitive, but can be easily explained. First, the population of the terminal laser level of the 1581 nm transition Y₁→Z₅ grows faster with temperature than that of the 1558.4 nm transition Y₁→Z₄. Secondly, there is another transition in the 1558-1560 nm wavelength band, Y₄→Z₅ (1559.3 nm), which should affect laser performance. This transition has the same terminal laser level as the 1581 nm one, so that the losses for both of them grow similarly with temperature, whereas the population of its upper level (and, hence, gain will grow faster than that of the 1581 nm.

4. Laser experiments

We have performed a set of cryogenic laser experiments on Er:ScO, aiming for a very low-QD laser operation for minimizing the heat deposition. Another specific motivation is to test the predicted output coupling and temperature dependence of laser wavelength given by our laser model, which indicates that the presence of multiple transitions near 1558.4 nm promotes the use of this line to minimize the QD.

Achieving very low-QD operation involves a very small separation between the pump and the lasing wavelengths. For the end pumped laser geometry, this puts severe requirements on the dielectric coatings of the cavity mirrors. It becomes practically impossible to create an AR/HR dichroic mirror, separating the 1535 nm pump and the lasing emission. Therefore, we used two alternative methods of wavelength separation.

One of them is to use narrowband wavelength-selective optics, like Volume Bragg Gratings (VBG), targeting specific laser transitions. This approach was used in our original work [5], where we utilized a VBG as a dichroic pump mirror in the cavity. This VBG was designed to operate as a high reflector (HR) at ~1558-1560 nm and had a limited temperature tuning rang. The VBG was 99% transparent to the 1535 nm pump emission.

The second option eliminates the forced wavelength selection imposed by a VBG. We modified the resonator by replacing the VBG with a “dot-mirror”. This mirror was a large diameter flat window, AR-coated at the 1535 nm pump wavelength, with the HR-coating in the 1550-1600 nm wavelength range applied to approximately a 3 mm-diameter central area. Thus, the HR mirror became non-discriminating, allowing lasing on both Y₁→Z₄ (1558 nm) and/or Y₁→Z₅ (1581 nm) laser transitions. The small HR-coated area introduces a small loss for the pump beam entering the cavity through the rest of the window area. As a pump source we used an Er-fiber laser delivering up to 60 W of CW emission at 1535 nm - the peak of the absorption in Er:ScO. This pump allowed nearly perfect mode-matching for clean experiment interpretation. The Er:ScO lasing wavelength was constantly monitored while we varied different parameters of the laser cavity - the transmission of the output coupler (OC), VBG temperature and the temperature of the Er:ScO crystal itself.

4.1 Resonator with non-selective “dot-mirror”

The Er:ScO laser input-output data obtained with the cavity formed by non-selective elements is presented in Fig. 5a . The highest laser output, ~12.5 W, and the best slope efficiency of about 56%, was achieved with R_OC = 77% output coupler. We directly measured round trip losses at ~10%, which include losses on cryostat windows. Under these conditions, the theoretical maximum slope efficiency should be 71%. With this cavity we observed that the output wavelength depended on the losses and also on the crystal temperature. At first, we kept the temperature of the laser crystal at around 80 K and monitored the output wavelength while changing output couplers. With weakly-transmitting couplers, R_OC = 98% and 95%, the laser operated exclusively at the Y₁→Z₅ (1581 nm) transition. With highly-transmitting couplers, R_OC = 80% and 77%, the laser emitted at the Y₁→Z₄ (1558.4 nm) transition. Intermediate couplings, R_OC = 90% and 85%, supported dual wavelength operation: at low pumping levels, the laser emitted at the 1581 nm, then, with stronger pumping, the 1558.4 nm lasing began to compete with the 1581 nm one and for sufficiently high power 1558.4 nm lasing took over.

 

Fig. 5 Performance of the Er:ScO cryo-laser with non-selective cavity: a. Laser output vs. absorbed pump power with output coupler reflectivities in the range of 77-95%. b. Laser output vs. temperature for the laser operating at 1581 nm (red) and 1558.4 nm (blue).

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The competition between these lines also takes place with varying the temperature of the laser crystal. At low temperatures, around 80 K, and when the cavity losses are rather low, the laser tends to operate at the Y₁→Z₅ (1581 nm) transition. When the temperature of the active medium grows to about 100-110K, the 1581 nm operation completely disappears, while lasing at the Y₁→Z₄ (1558.4 nm) transition starts and continues up to 200 K, gradually fading away, see Fig. 5b. It is worth mentioning that the rate of the decline of the 1581 nm lasing with temperature is much faster than that of the 1558.4 nm. Experimentally observed spectra of the laser output is entirely consistent with the results of our model, pointing to a complex structure of the 1558-1560 nm band.

4.2 Resonator with VBG

With the VBG used as the HR cavity mirror, there was not much difference in the overall efficiency of the laser compared with the non-selective “dot-mirror” case, see Fig. 6 . The slope efficiency was about 63%, but it is a significant improvement versus our original result46% [5]. In the case of the non-selective cavity, if the laser emits in the 1558-1560 nmband, it operates at the peak of the luminescent band envelope, which is dominated by the Y₁→Z₄ (1558.4 nm) transition, see Fig. 7a . If the VBG serves as the HR cavity mirror, the wavelength of the laser output could be tuned between 1558.2 nm and 1559.6 nm, simply by varying the VBG temperature, see Fig. 7b. The lasing wavelength simply follows the VBG transmission. Its overall “red” shift indicates that the Y₁→Z₄ transition was not the only one taking part in the Er:ScO lasing. There must have been another transition around 1559 nm strongly influencing the laser performance. This too, is fully consistent with the spectroscopy and the laser modeling reported in the preceding sections.

 

Fig. 6 Output versus absorbed pump power for the Er:ScO cryo-laser with VBG in a function of the dichroic pump mirror.

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Fig. 7 Er:ScO laser spectra at 80K in the 1558-1560 nm band: a. Laser cavity formed with non-selective mirrors; b. Cavity formed with VBG mirror. Depicted in b (dot-lines) is the VBG transmission at 10C and 45C obtained with the white light source. The emission spectrum in the 1558-1560 nm band at 80K is shown in solid grey lines. The laser wavelengths corresponding to different VBG temperatures are depicted in solid colored lines.

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5. Conclusions

We reported the results of a thorough investigation of a cryogenically cooled, eye-safe Er³⁺:Sc₂O₃ laser by studying its spectroscopic features in detail and analyzing its operation in the 1581- and 1558-1560 nm bands. It was shown that at least two transitions between the ⁴I_13/2 and ⁴I_15/2 manifolds are capable of providing laser operation in the ultra-low quantum defect mode. A numerical laser model, which takes into account the pump and laser saturation effects on laser performance, was developed. It predicted major details of lasing competition between the 1581- and 1558-1560 nm bands. The most striking modeling result is that overlapping transitions around 1559 nm strongly influence this competition. Cavity losses and the operating temperature affect the output wavelength as well.

Another important result of this study was the observation of a strong energy migration between Er³⁺ ions in C₂ sites and those in the second type of site (most likely, the C_3i site). Assuming that only ions in C₂ sites contribute to the laser gain at 1580 nm wavelength, this C₂→C_3i energy transfer reduces laser efficiency. All sesquioxides have the same types of cation sites, into which RE³⁺ can substitute, so this phenomenon has to be taken into account for all rare-earth doped sesquioxide lasers. However, when lasing occurs in the 1558-1560 nm band, we could not rule out the contribution of the ions in C_3i sites, although this contribution is relatively small.

The detail study of the energy migration between Er³⁺ ions in different sites and its influence on the laser performance was beyond the scope of this paper and requires separate investigation.