1. Introduction

Lanthanide rare-earth orthophosphates, with a common chemical formula of RePO₄, have been studied extensively for several decades, in their structural, solid-state chemical, optical, and physical properties. Depending on the atomic number of lanthanide element, these orthophosphates fall into two categories: the light-rare-earth phosphates from LaPO₄ to EuPO₄ exist in the monoclinic monazite structure (space group P2₁/n), whereas the heavy-rare-earth ones from HoPO₄ to the end member LuPO₄ can only be found with the tetragonal zircon structure (space group I4₁/amd). The rare-earth phosphates of zircon structure have proven to enable other lanthanide ions to be incorporated into their crystal lattice in large amounts, substituting for the original lanthanide ions that occupy the lattice site with local symmetry of D_2d [1]. These phosphates, which are also known to be of very high chemical stability, can therefore serve as ideal host crystals for the active rare-earth ions commonly in use, including Nd³⁺, Yb³⁺, Er³⁺, Tm³⁺, Ho³⁺, and Pr³⁺. Unfortunately, however, being incongruently melting, these crystals cannot be grown from melt by the conventional Czochralski method, making it extremely difficult to produce high-quality single crystals in large sizes [1]. It must be due to this reason that, up to now, little progress has been made in developing laser crystals based on these rare-earth orthophosphates; the only work reported in the past long period was on Nd:LuPO₄, in which 0.3 W of output power was generated with a 1-mm-thick crystal, which was grown in high-temperature solution [2].

In principle, LuPO₄, as a host crystal, seems to be more suitable for the Yb rather than for the Nd ion, owing to the closeness in both ionic radius and atomic mass between the Yb and Lu elements. In as early as 1984, crystal field analysis was already made for the Yb ion doped in LuPO₄ crystal [3]; some preliminary limited results on the spectroscopy of Yb:LuPO₄ crystal were also reported in the early days of Yb lasers [4]. Very recently crystals of Yb:LuPO₄, with their largest size amounting to 6 mm × 2 mm × 0.5 mm, were grown by the high-temperature solution method [5]. With these thin crystal plates, polarized absorption and emission spectra were obtained, and continuous-wave (cw) laser operation was demonstrated [6]. However, due to their very limited thickness, such thin Yb:LuPO₄ crystals seem not to enable high power to be generated from an end-pumped compact laser.

In this paper, we report a distinct type of columnar or acicular crystal of Yb:LuPO₄, which was also grown in high-temperature solution. Efficient cw laser action was realized with a 2-mm long rod sample cut from such a columnar crystal in a very compact resonator, generating a maximum output power in excess of 5 W. The laser performance demonstrated here reveals the potential of this sort of columnar Yb:LuPO₄ crystal in making high-power miniature rod lasers.

2. Description of experiment

The columnar Yb:LuPO₄ crystal was grown in high-temperature solution, along its crystallographic c axis starting from spontaneous nucleation. The crystal growth was conducted in a 50-ml platinum crucible containing a mixture of Yb₂O₃, Lu₂O₃, and PbHPO₄, which was placed in a furnace that was kept at a temperature of 1350 °C for 16 hours, and was then cooled down to 1000 °C at a rate of 1 °C/hour. After that, the furnace was rapidly cooled to room-temperature, and columnar crystals of Yb:LuPO₄ were obtained. Shown in Fig. 1 are some crystals grown in the process, with their transverse sizes being less than 0.8 mm and lengths at most 15 mm.

 

Fig. 1 Columnar crystals of Yb:LuPO₄ grown starting from spontaneous nucleation in high-temperature solution.

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To study the laser performance of such columnar Yb:LuPO₄ crystals, a tiny rod sample of 2 mm in length was cut and polished, the Yb-ion concentration was 5 at. % (6.15 × 10²⁰ cm⁻³). A very compact plano-concave resonator, having a cavity length of 13 mm, as illustrated schematically in Fig. 2, was employed to fabricate the experimental Yb:LuPO₄ miniature rod laser. The plane reflector (M1) was coated for high reflectance at 1020−1200 nm and high transmittance at 808−980 nm; while the concave mirror (M2), having a radius-of-curvature of 15 mm, served as the output coupler, whose transmission could be chosen from 0.5% to 62%. The uncoated miniature rod sample was fitted into a copper heat sink, which was cooled by use of cycling cooling water that was maintained at a temperature of 5 °C. A high-brightness fiber-coupled diode laser (fiber core diameter of 100 μm and NA of 0.22) was utilized as the pump source, whose emission wavelength was 976 nm (bandwidth of less than 0.5 nm), matching with the strongest zero-phonon-line absorption peak of Yb:LuPO₄ crystal for σ polarization [6]. The pump radiation from the fiber was delivered by a focusing optics into the crystal rod, with a spot radius of about 70 μm.

 

Fig. 2 Schematic diagram of the experimental setup for the Yb:LuPO₄ miniature crystal rod laser.

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3. Results and discussion

Continuous-wave operation was achieved of the Yb:LuPO₄ miniature rod laser operating in free-running mode, with the output coupling (T) changed over a wide range from 0.5% to 62%. The laser output was unpolarized, because of the isotropic gain for the electric field E lying in the transverse section of the Yb:LuPO₄ rod. Figure 3 shows the output power versus absorbed pump power measured with different output couplings. The absorbed pump power, P_abs, is estimated from the incident pump power, P_in, by P_abs = η_pP_in, with η_p denoting the small-signal or unsaturated absorption of the crystal at the pumping wavelength. For the crystal rod used in the experiment (2 mm long, Yb-ion doping of 5 at. %), η_p was measured to be 0.94. From the σ-polarized absorption spectrum one reads a cross section of 2.5 × 10⁻²⁰ cm² at 976 nm [6], leading to an absorption coefficient of 15.4 cm⁻¹, from which η_p is calculated to be 0.95, nearly the same as the measured value. The absorption for the rod sample was 3.6 times higher than reached with the thin Yb:LuPO₄ crystal plate studied in our previous work [6], a result arising from their distinct combinations of crystal thickness with Yb-ion doping level (0.3 mm thick and 10 at. %, for the thin crystal plate).

 

Fig. 3 Output power versus P_abs for the Yb:LuPO₄ miniature rod laser, obtained with the output coupling changed from 0.5% to 62%.

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As can be seen from Fig. 3(a), the lasing threshold was reached at P_abs = 0.43 W for T = 0.5%, which seems to be rather high, given such a low output coupling used. This might suggest significant dissipative losses arising from absorption and/or scattering by imperfections existing in the crystal. Indeed, substantial inhomogeneity of the crystal rod was noticed during the adjustment of the laser. The threshold measured here proved to be much higher than that for the Yb:LuPO₄ crystal plate laser, which amounted only to 0.17 W for T = 1.3% [6]. Apart from the less resonant absorption losses in connection with the small thickness, the optical quality of the crystal plate was found to be considerably higher than the rod sample. It is also worth pointing out that the uncoated end faces of the crystal rod, were not likely to introduce appreciable losses, as the Fresnel reflections would be greatly diminished by the etalon effects existing inside the resonator (e.g., formed by the inner surface of M1 and the front end face of the crystal). Due to the broad emission band of the Yb:LuPO₄ crystal, the free-running laser oscillation actually occurred at the wavelengths corresponding to the transmission peaks of the etalons formed, at which the Fresnel reflection losses were essentially negligible compared to other internal losses or the output coupling. The discrete oscillation lines appearing in the laser emission spectra (Fig. 4) provide a clear evidence for the presence of internal etalons. One sees that while the laser action in the case of T = 0.5% was less efficient, the laser efficiency could be increased greatly by increasing the output coupling of the resonator; with T changed from 0.5% to 5.7%, the slope efficiency could be increased steadily, from η = 11% to η = 41%. In fact, the laser could operate efficiently over an output coupling range from 5.7% to 40%, with slope efficiencies in excess of 40%, while the optimum output coupling proved to be T = 12%. The output power produced with the optimum output coupling, as presented in Fig. 3(b), scaled roughly linearly with P_abs, reaching 5.3 W at P_abs = 13.2 W, resulting in an optical-to-optical efficiency of 40%; whereas the slope efficiency, estimated for an intermediate operational region of P_abs = 4−11 W, amounts to η = 50%. One notes that the laser action became less efficient when P_abs was increased exceeding about 11 W, a common tendency observed also in cases with other output couplings, which resulted from the strengthening of thermally induced losses.

 

Fig. 4 Emission spectrum of the Yb:LuPO₄ miniature rod laser, measured at P_abs = 7.0 W for different output couplings.

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It is worthwhile to stress that the absorbed pump power, which is calculated from the unsaturated absorption, might be applicable accurately only for the cases of small output couplings. In the case of large output coupling, higher inversion and hence higher population density in the upper manifold would be expected for steady-state laser oscillation. As a result, the absorption for the pump radiation, which is caused by the zero-phonon-line transition, would be reduced largely by the presence of strong emission. This means that the actual absorbed pump power might be overestimated in this case. It should also be noted that the absorbed pump power, determined in this manner for high pump levels, might also be overestimated due to the decrease of absorption cross section with increasing temperature.

The laser performance, achieved with the Yb:LuPO₄ crystal rod, turns out to differ significantly from that for the previous thin crystal plate [6]. In contrast to the optimal output coupling determined here, T = 12%, the most efficient laser action in the case of the Yb:LuPO₄ crystal plate, was generated under the condition of T = 1.3% [6]. Such a low optimal output coupling was mainly attributed to the very limited round-trip gain available from the 0.3 mm thick laser crystal, as well as the very low overall internal losses. One may also notice that the laser efficiency achieved with the thin crystal plate (optical conversion efficiency of 67% and slope efficiency of 75% [6]), proved to be considerably higher than for the crystal rod. Besides the much lower overall internal losses of the plate laser, its closer mode matching with the pump beam (fundamental mode radius of about 50 μm, compared to 40 μm for the rod laser) was also responsible for the more efficient laser operation. As a further comparison, one can note that under nearly the same output coupling conditions, the two lasers exhibited quite different output characteristics. For instance, the most efficient oscillation of the present crystal rod laser was achieved with T = 12%; for the thin crystal plate laser, however, the output coupling of T = 11% led to a laser operation that was much less efficient when compared to its optimal case [6]. Among other factors such as the difference in the resonator configuration, in the thickness as well as the optical quality of the laser crystal, an important reason for such an appreciable change in the output behavior was the distinct polarization states: the laser oscillation generated with the Yb:LuPO₄ crystal plate was linearly polarized with E // c axis (π-polarized); while the crystal rod, which was along the c axis, could allow only unpolarized laser oscillation (with E ⊥ c axis). Consequently, the laser gain for the crystal plate is dependent upon the π-polarized gain cross section, whereas that for the crystal rod depends on the σ-polarized gain cross section, which, respectively, are determined by the π- and σ-polarized absorption and emission cross sections. Due to the strong anisotropy in the absorption and emission spectra of the Yb:LuPO₄ crystal [6], the gain nature differs for E // c and for E ⊥ c, resulting in different laser oscillation behavior for the plate and rod crystals.

Figure 4 shows the emission spectra of the Yb:LuPO₄ laser for three different output couplings of T = 0.5%, 12%, and 62%, which were measured at an intermediate pump level of P_abs = 7.0 W. Each spectrum comprises several discrete emission lines, which is typical for free-running quasi-three-level lasers possessing broad emission bands. It is also a usual feature for such lasers that the emission spectrum tends to shift towards the short-wavelength side, upon increasing the output coupling. One sees that in the case of T = 0.5%, the laser oscillation occurred at 1035.5−1041.3 nm, just within the broad emission band centered at 1037 nm in the σ-polarized emission spectrum of Yb:LuPO₄ [6]; while for T = 62% the oscillation wavelengths shifted to 1002.6−1005.1 nm, corresponding to the strong short-wavelength emission band of the crystal, which is centered at 1002 nm in the σ-polarized emission spectrum [6].

To gain further insight into the output characteristics of the Yb:LuPO₄ miniature rod laser, a theoretical calculation is carried out for the laser operating under conditions of the optimum output coupling (T = 12%), in accordance with a space-dependent rate-equation model for quasi-three-level lasers [7]. The parameters involved in the calculation are listed as follows (using the same symbols as in [7]): σ_e = 0.53 × 10⁻²⁰ cm² (the averaged value for 1017 and 1021 nm, which were the actual lasing wavelengths, read from the σ-polarized emission spectrum [6]); σ_a = 0.10 × 10⁻²⁰ cm² (read from the σ-polarized absorption spectrum [6]); τ = 0.83 ms [4], hν_p = 2.04 × 10⁻¹⁹ J (λ_p = 976 nm); hν = 1.96 × 10⁻¹⁹ J (λ = 1019 nm), l = 0.2 cm; N_t = 6.15 × 10²⁰ cm⁻³ (5 at. %, crystal density of 5.53 g/cm³ is used [4]), γ_i = 0.035; γ₂ = 0.128 (T = 12%); γ = 0.10, B = σ_aN_tl/γ = 1.24, w_p = 70 μm; w₀ = 40 μm (calculated for the cavity used), α = (w₀/w_p)² = 0.33, P_mth = 0.30 W; P_s = 0.06 W. The calculated results of output power as a function of P_abs are plotted as a solid curve in Fig. 3(b), from which one sees a good agreement between the theoretical calculation and the experimental measurement, and only in the high-power region exceeding P_abs ≈11 W can noticeable discrepancy be found, this, as mentioned above, is due to the enhancement of thermally induced losses occurring inside the laser crystal, which have not been taken into account in the theoretical model [7].

The pump power absorbed at lasing threshold (P_th) can be accurately measured, owing to the absence of internal laser field that has significant influence on the extent of absorption saturation. Table 1 shows a comparison between the measured and calculated P_th for T = 0.5%, 2.1%, 5.7%, 12%, 40%, and 62%. The calculation is made by using the same parameters given above, except for γ (γ₂) and B, which are dependent on the value of T. One notes that a fair agreement exists between the measured results and the theoretical predictions.

Table 1. Absorbed Pump Power Measured and Calculated for Reaching Laser Threshold (P_th) Under Different Output Coupling Conditions

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The beam quality of the Yb:LuPO₄ miniature rod laser was also examined in the experiment. Shown in Fig. 5 are a beam pattern (a) and its spatial intensity distributions (b), measured at an intermediate pump power of P_abs = 7.0 W in the case of T = 12%. The beam quality factor (M²) was determined to be 2.29 and 2.33, for the horizontal and vertical directions, respectively. Such fairly large M² values imply the presence of higher-order transverse mode oscillation, which was attributed to the fundamental mode radius that is calculated to be about 40 μm, considerably smaller than the pump beam spot radius (70 μm).

 

Fig. 5 Laser beam pattern (a) and its intensity distributions (b), measured at P_abs = 7.0 W in the case of T = 12% for the Yb:LuPO₄ miniature rod laser.

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4. Conclusion

In summary, the laser performance of a sort of columnar crystal of Yb:LuPO₄ was studied. Efficient cw laser action was achieved with a miniature crystal rod in a very compact resonator, producing a maximum output power of 5.3 W with an optical-to-optical efficiency of 40%, while the slope efficiency was 50%. It seems to be quite feasible, given the excellent host properties, to scale the output power to a 10-W level with still higher efficiencies, by improving the crystal rod quality, by optimizing the Yb-ion concentration, and by properly designing the compact resonator. Possessing the advantages of no need for orientation determining, no limit on sample length, and strong absorption at the readily available 976 nm emission wavelength of diode lasers, these columnar Yb:LuPO₄ crystals are desirable for making high-power miniature rod lasers, which may find some practical applications in developing very compact coherent sources.