1. Introduction

Ho³⁺-doped crystals have been widely studied for lasing around 2.0 μm via the ⁵I₇→⁵I₈ transition. The laser is eye-safe and matches well with the absorption lines of H₂O and CO₂. Therefore, a number of applications such as coherent lidar, atmospheric sensing, and surgery are possible [1–3]. Furthermore, the laser operating in ultrafast pulse regime can also be used in time-resolved spectroscopy and as pumping source for the optical parametric oscillator (OPO) in the mid-infrared region [4,5]. Research of gain media for realizing the pulse laser has recently attracted substantial attentions. Generally, Tm³⁺ or Yb³⁺ ions, which has large absorption cross section at the emitting wavelengths of the commercially available high power laser diodes (LD), is co-doped as sensitizer for improving pump absorption [6–9]. The processes of energy transfers from Tm³⁺ and Yb³⁺ to Ho³⁺ ions are schemed in Fig. 1 . Notably for the Tm³⁺/Ho³⁺ co-doped system, a maximal pump quantum efficiency close to 2 could be expected due to the cross relaxation (CR) of Tm³⁺ ions, ³H₄ + ³H₆→³F₄ + ³F₄.

 

Fig. 1 Schematic of energy transfer from Tm³⁺ to Ho³⁺ ions and Yb³⁺ to Ho³⁺ ions.

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Double tungstate and double molybdate crystals with a general formula of MT(XO₄)₂ (M = Li, Na, or K; T = Y, La, Gd, or Lu; X = W or Mo) have been proved to meet the requirement of hosts for ultrashort pulse laser [4,10]. Especially for the subgroup with M = Li or Na, which belongs to the tetragonal system with space group of $I\overline{4}$. Crystals with this structure are usually characterized by a high disordered local environment due to the monovalent alkali ions and trivalent rare earth ions randomly sharing two different S₄ lattice sites labeled as 2b and 2d [11]. When active ions of rare earths substitute the trivalent cations, inhomogeneous broadening for absorption and emission bands are beneficial to being pumped by LD and generating wide tunable and ultrashort pulse lasers. Recently, a pulse laser operation as short as 191 fs has been realized in a Tm³⁺/Ho³⁺ co-doped NaY(WO₄)₂ crystal [10]. Detailed spectroscopic and laser properties of another isostructural Tm³⁺ singly doped LiGd(MoO₄)₂ (LGM) crystal have been reported in our previous work [12]. In this work, Tm³⁺/Ho³⁺ co-doped LGM crystals are studied as the gain media for Ho³⁺ laser around 2.0 μm. The laser has been realized in a simple plano-concave cavity with a pulsed LD as pumping source.

2. Experimental procedure

Two Tm³⁺/Ho³⁺ and one Yb³⁺/Ho³⁺ co-doped LGM single crystals were grown by the Czochralski method in air at about 1030 °C. After growth the crystals were annealed at about 850 °C for 10 hours to reduce the residual stress. The doping concentrations measured by an inductively coupled plasma atomic emission spectrometer (Ultima 2, Jobin-Yvon) are 5.4/1.4 and 4.6/0.6 at.% for the two Tm³⁺/Ho³⁺ co-doped crystals and 7.7/1.4 at.% for the Yb³⁺/Ho³⁺ co-doped crystal (hereafter 5.4/1.4 TH, 4.6/0.6 TH and 7.7/1.4 YH for short, respectively). Oriented crystal samples were cut and polished for spectral experiments with dimensions (crystallographic a × b × c) of 2.70 × 10 × 10, 1.88 × 7 × 8, and 2.20 × 5 × 7 mm³, respectively. No gas bubbles or inclusions were found in these samples. The optical quality of the crystals was examined by a ZYGO GPI optical interferometer. The interference fringes are straight and have a uniform distribution which shows the crystals have good optical homogeneity. Figure 2 shows the result for the 4.6/0.6 TH. The polarized absorption spectra were measured using a UV/VIS/NIR spectrophotometer (Lambda 900, Perkin-Elmer) with a scanning step of 0.5 nm. A deuterium lamp (UV) and a tungsten-halogen lamp (VIS/NIR) were equipped as the light sources. The polarized fluorescence spectra were measured by a TE-cooled PbS detector in the NIR region associated with a monochromator (Triax 550, Jobin-Yvon) ahead of it, a Ti:sapphire laser operating at 795 nm and an InGaAs LD operating at 970 nm were used as exciting sources for the Tm³⁺ and Yb³⁺ ions, respectively, with a measured resolution of 1.0 nm. The fluorescence decay curves were measured by a spectrometer (FLSP920, Edinburgh) with a Hamamatsu R928 PMT and an InSb detectors in the VIS and NIR regions, respectively, a tunable mid-band OPO laser (Vibrant 355II, OPOTEK) with pulse duration of about 5 ns was adopted as the exciting source. In fluorescence experiments front-surface excitation-detection was used to measure fluorescence spectra of the crystal samples in order to minimize the impact of re-absorption. Additionally, the excitation intensity was always kept as low as possible to avoid some possible amplified spontaneous emission. All of the spectral experiments were carried out at room temperature.

 

Fig. 2 Interference fringes for 4.6/0.6 TH crystal sample.

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3. Results and discussion

3.1 Absorption and Judd-Ofelt analysis

Absorption spectra of the 7.7/1.4 YH in a range of 350−2200 nm were measured for two different polarizations of σ (E⊥c, E represents the electric field direction of incident light) and π (E//c) and are shown in Fig. 3 . It can be found that the absorption of Ho³⁺ ions exhibits a strong anisotropic behavior. The Yb³⁺ ions have only an intense absorption band around 980 nm and do not influence the absorption of Ho³⁺ ions in other measured spectral region. The Judd-Ofelt (J-O) theory [13,14] was applied to determine the intermultiplet spontaneous transition rates of Ho³⁺ ions in LGM crystal. The J-O intensity parameters Ω_t (t = 2, 4, 6) were fitted by adopting the six easily distinguishable absorption bands corresponding to the transitions from the ground ⁵I₈ multiplet to the excited ⁵I₇, ⁵I₆, ⁵F₅, ⁵F₄ + ⁵S₂, ⁵F₁ + ⁵G₆, and ³G₅ multiplets. The calculation procedure can be found in the literature [15,16] and the refractive index has been estimated in [17]. The contribution of the magnetic dipole (MD) transition of ⁵I₈→⁵I₇ was excluded before the calculation. The values of the reduced matrix elements of unit tensor operators and the coefficients of the intermediate coupling wavefunctions were taken from [18] and [19], respectively. The mean wavelength ($\overline{\lambda }$), the experimental oscillator strength ($f_{\text{ED}}^{\text{exp}}$), and the oscillator strength calculated from the J-O intensity parameters ($f_{\text{ED}}^{\text{calc}}$) for each band are listed in Table 1 . The root mean square (rms) deviations between the experimental and calculated oscillator strengths are 0.95 × 10⁻⁶ and 2.42 × 10⁻⁶ for σ and π polarizations, respectively. Both are in the typical error range of the J-O fitting [20]. The intensity parameters for Ho³⁺ ions in LGM crystal are listed in Table 2 and the effective J-O intensity parameters were calculated according to ${\Omega }_t^{\text{eff}}=\left(2{\Omega }_t^{\text{σ}}+{\Omega }_t^{\text{π}}\right)/3$. These parameters are comparable to those of Ho³⁺ in KGd(WO₄)₂ crystal [21].

 

Fig. 3 Polarized absorption spectra of 7.7/1.4 YH crystal in a range of 350−2200 nm.

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Table 1. Mean wavelengths and experimental and calculated absorption oscillator strengths for ED transitions of Ho³⁺ in LGM crystal

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Table 2. J-O intensity parameters of Ho³⁺ in LGM crystal (in unit of 10⁻²⁰ cm²)

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The intermultiplet electric dipole (ED) spontaneous transition rates ($A_{\text{ED}}^q$) of Ho³⁺ were calculated from the intensity parameters for both polarizations (q = σ and π) and are listed in Table 3 . Taking the MD transition rates ($A_{\text{MD}}^{}$) into account, the average spontaneous transition rates could be calculated by $A=\left(2A^{\text{σ}}+A^{\text{π}}\right)/3$ with $A^q=A_{\text{ED}}^q+A_{\text{MD}}^q$. Then the fluorescence branching ratios (β) and the radiative lifetimes (${\tau }_{\text{r}}$) could be further calculated and the results are also listed in Table 3.

Table 3. Spontaneous transition rates, fluorescence branching ratios, and radiative lifetimes of Ho³⁺ in LGM crystal

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The polarized absorption spectra were also measured for the Tm³⁺/Ho³⁺ co-doped LGM crystals in a range of 750−850 nm. Since the absorption cross sections corresponding to the ³H₆→³H₄ transition of Tm³⁺ ions are nearly identical for both 5.4/1.4 TH and 4.6/0.6 TH, only the spectra of the latter are shown in Fig. 4 for brevity. The peak absorption cross sections were 4.66 × 10⁻²⁰ cm² for σ polarization at 795 nm and 1.93 × 10⁻²⁰ cm² for π polarization at 781 nm, with band widths of 8 and 37 nm, respectively. Both the peak values are slightly larger than those of the Tm³⁺ singly doped LGM, respectively [12]. Taking into account the typical wavelength drift with temperature is about 0.3 nm/K and the spectral bandwidth is 3 to 6 nm for commercial LD pumping source, the stronger absorption of Tm³⁺/Ho³⁺ co-doped LGM in σ polarization should be ideal for LD pumping.

 

Fig. 4 Polarized absorption spectra of 4.6/0.6 TH crystal in a range of 750–850 nm.

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3.2 Fluorescence and stimulated emission cross sections

When the Yb³⁺ ions were excited to the ²F_5/2 multiplet at 970 nm, the polarized fluorescence spectra of 7.7/1.4 YH around 2.0 μm were measured and are shown in Fig. 5(a) . The emission bands in the range of 1900−2100 nm with peaks around 2050 nm are attributed to the ⁵I₇→⁵I₈ transition of Ho³⁺ ions. Under excitation at 795 nm, the Tm³⁺ ions were excited to the ³H₄ multiplet and the polarized fluorescence spectra of both 5.4/1.4 TH and 4.6/0.6 TH were measured and are shown in Figs. 5(b) and 5(c), respectively. The emission bands of Tm³⁺ ions corresponding to the transition of ³F₄→³H₆ can still be found in the range of 1650−1950 nm, which suggests that the energy transfer from Tm³⁺ to Ho³⁺ is not complete. Furthermore, the ratio of the integrated fluorescence intensity of Ho³⁺ ions to that of both Tm³⁺ and Ho³⁺ ions, i.e., ${\displaystyle {\int }_{{\text{Ho}}^{3+}}I\left(\lambda \right)}d\lambda /{\displaystyle {\int }_{{\text{Tm}}^{3+}{\text{+Ho}}^{3+}}I\left(\lambda \right)}d\lambda$, in the entire emission band of 1650−2100 nm in one co-doped crystal, can be used as a measure for the net energy transfer efficiency from Tm³⁺ to Ho³⁺. The ratio in 5.4/1.4 TH is larger compared with that for 4.6/0.6 TH just indicates a preferred energy distribution on Ho³⁺ ions in the higher co-doped case.

 

Fig. 5 Polarized fluorescence spectra of 7.7/1.4 YH (a) under excitation at 970 nm; 5.4/1.4 TH (b) and 4.6/0.6 TH (c) under excitation at 795 nm.

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The fluorescence decay curves for the ³H₄ multiplet of Tm³⁺ ions were measured for both 5.4/1.4 TH and 4.6/0.6 TH and are shown in Fig. 6 in semi-log scale. The exciting and monitoring wavelengths were 783 and 810 nm, respectively. Both decay curves display a departure from the single exponential behavior. The mean fluorescence lifetimes are estimated 18 and 28 μs for 5.4/1.4 TH and 4.6/0.6 TH, respectively, according to ${\tau }_{\text{f}}={\displaystyle {\int }_0^{\infty }tI\left(t\right)}dt/{\displaystyle {\int }_0^{\infty }I\left(t\right)}dt$ where $I\left(t\right)$ is the fluorescence intensity at time t [22]. Since an intrinsic lifetime τ₀ = 134 μs for the ³H₄ multiplet has been reported in a 0.79 at.% Tm³⁺ singly doped LGM crystal [12], the energy transfer efficiency (η) for Tm³⁺ ions on the ³H₄ multiplet were estimated 87% and 79% for 5.4/1.4 TH and 4.6/0.6 TH, respectively, by $\eta =1-{\tau }_{\text{f}}/{\tau }_{\text{0}}$ and the energy transfer should be firstly attributed to the cross relaxation (³H₄ + ³H₆→³F₄ + ³F₄) between Tm³⁺ ions.

 

Fig. 6 Fluorescence decay curves for the ³H₄ multiplet of Tm³⁺ ions for 5.4/1.4 TH and 4.6/0.6 TH. The exciting and monitoring wavelengths are 783 and 810 nm, respectively.

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The fluorescence decay curves for the ³F₄ multiplet of Tm³⁺ ions and the ⁵I₇ multiplet of Ho³⁺ ions were also measured for the Tm³⁺/Ho³⁺ co-doped LGM crystals and are shown in Fig. 7 . The exciting and monitoring wavelengths were 1700 (2000) nm and 1750 (2050) nm for the ³F₄ (⁵I₇) multiplet of Tm³⁺ (Ho³⁺) ions, respectively. Similar kinetic behaviors can be found for both the 5.4/1.4 TH and 4.6/0.6 TH. Notably for the curves of Tm³⁺ ions, a sharp decay in the early time was recorded responsible for the fast energy transfer of ³F₄(Tm³⁺) + ⁵I₈(Ho³⁺)→³H₆(Tm³⁺) + ⁵I₇(Ho³⁺). Since the energy transfer is nearly resonant and always accompanied by its inverse process of ⁵I₇(Ho³⁺) + ³H₆(Tm³⁺)→⁵I₈(Ho³⁺) + ³F₄(Tm³⁺), the two multiplets, ³F₄ and ⁵I₇, will share their excitations and be rapidly coupled into an equilibrium system after excitation [23]. Therefore, the decay rates of both the Tm³⁺ and Ho³⁺ ions become nearly identical in the late decay period. The mean fluorescence lifetimes were estimated 3.9 ms for the ³F₄ multiplet and 4.2 ms for the ⁵I₇ multiplet in 5.4/1.4 TH and 2.1 and 2.3 ms in 4.6/0.6 TH, respectively. By the way, the fluorescence decay curve for the ⁵I₇ multiplet of Ho³⁺ ions was also measured from the 7.7/1.4 YH and is shown in Fig. 8 . The lifetime fitted from the single exponential decay curve is 4.9 ms which is longer than the above Tm³⁺/Ho³⁺ co-doped systems. Meanwhile, the fluorescence lifetime for the ³F₄ multiplet of Tm³⁺ ions was previously reported about 1 ms in Tm³⁺ singly doped LGM crystals [12], the distinct coupled decay behaviors for the Tm³⁺/Ho³⁺ co-doped systems just embodies the energy transfers between Tm³⁺ and Ho³⁺ ions. The coupled lifetimes are closely related to the doping concentrations, especially, related to the ratio of Tm³⁺ to Ho³⁺ concentrations [24].The stimulated emission cross section (${\sigma }_{\text{EM}}^q$) for the ⁵I₇→⁵I₈ transition of Ho³⁺ ions is an important factor related to the 2.0 μm laser operation. According to the Füchtbauer-Ladenburg (F-L) formula [25]

 

Fig. 7 Fluorescence decay curves for the ³F₄ (⁵I₇) multiplet of Tm³⁺ (Ho³⁺) ions for 5.4/1.4 TH and 4.6/0.6 TH. The exciting and monitoring wavelengths are 1700 (2000) and 1750 (2050) nm, respectively.

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Fig. 8 Fluorescence decay curve for the ⁵I₇ multiplet of Ho³⁺ ions for 7.7/1.4 YH. The exciting and monitoring wavelengths are 2000 and 2050 nm, respectively.

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Fig. 9 Polarized emission cross sections for the ⁵I₇→⁵I₈ transition of Ho³⁺ ions derived by the F-L formula. The corresponding absorption cross sections for ⁵I₈→⁵I₇ transition are also plotted for comparison.

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Using the absorption and emission cross sections derived above, the wavelength dependence of the gain cross sections can be calculated by [26]

 

Fig. 10 Polarized gain cross sections for ⁵I₇→⁵I₈ transition of Ho³⁺ ions in LGM crystal with different values of population inversion P (P = 0.3, 0.4, …, 0.7).

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3.3 Laser demonstration

In order to assess the laser performance of the Tm³⁺/Ho³⁺ co-doped LGM, an end-pumped plano-concave resonator was adopted with a fiber-coupled pulsed LD emitting at 795 nm as the pumping source. The pump beam was modulated with a duty cycle of 2% and a modulation frequency of 10 Hz. It passed through an input coupler which had a 90% transmission at 795 nm and a reflectivity of R > 99% in the region between 1900 and 2100 nm. The crystal sample, without any antireflection coating, was held in an aluminum mount and positioned to the input coupler as close as possible. The diameter of pump beam inside the gain medium was about 115 μm. Three output couplers with transmissions T_OC = 0.7%, 2.4%, and 3.9% around 2.0 μm and the same curvature radius of 100 mm were adopted in the experiment, respectively. The length of the plano-concave cavity was set close to the curvature radius of the output couplers.

Taking into account the polarization-dependent absorption of the Tm³⁺ ions at the pump wavelength, the c-cut Tm³⁺/Ho³⁺ co-doped LGM crystal samples with dimensions (a × b × c) of 7 × 10 × 0.87 and 7 × 7 × 1.10 mm for 5.4/1.4 TH and 4.6/0.6 TH were used as laser gain media, respectively. However, the Ho³⁺ laser was only realized in the 4.6/0.6 TH with lasing wavelength at 2.05 μm. Within a low-power pump, the single-path pump absorption efficiency was measured about 80% which is in agreement with the calculated 79% from absorption cross section. The absorption efficiency was almost kept the same in our experiment. Figure 11 shows the average output power versus the average absorbed pump power at different output coupler transmissions, the laser operated at a relative low-power level. The maximum output power of 25 mW was achieved when the absorbed pump power was 138 mW for the T_OC = 3.9%. The related slope efficiency (η_S) was about 20%. Moreover, it can be found that, since the slope efficiency has monotonically increased from 10% to 20% with the increment of T_OC from 0.7% to 3.9%, a higher efficient laser can be expected by optimizing the output coupler transmission.

 

Fig. 11 Average output power versus average absorbed pump power for a c-cut 4.6/0.6 TH laser at different output coupler transmissions.

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The Ho³⁺ laser around 2.0 μm operating at room temperature is a quasi-three-level system. The reason for the lack of laser demonstration in the higher co-doped 5.4/1.4 TH sample may be mainly attributed to the stronger re-absorption loss.

4. Conclusion

A detailed description of the spectroscopic properties for the Ho³⁺ ions in LGM crystals was performed. Comparative study on the spectroscopic properties related to the 2.0 μm laser of Ho³⁺ has been carried out for the Tm³⁺/Ho³⁺ co-doped LGM crystals with concentrations of 5.4/1.4 and 4.6/0.6 at.%. Although the fluorescence spectra suggest that a more efficient energy transfer from Tm³⁺ to Ho³⁺ ions has occurred in the 5.4/1.4 TH, laser operation has been realized only in the 4.6/0.6 TH. The main reason for the lack of laser operation in the higher co-doped sample should be attributed to the stronger re-absorption loss as the Ho³⁺ concentration is more than twice as high in the lower co-doped case.

A 2.05 μm Ho³⁺ laser has been realized in a 1.10-mm-thick c-cut 4.6/0.6 TH sample with a fiber-coupled pulsed LD end-pumped at 795 nm. The slope efficiency of 20% was achieved at the output coupler transmission of 3.9% and the maximum average output power was 25 mW when the absorbed pump power was 138 mW. Since a continuous wave Ho³⁺ laser with slope efficiency as high as 48% has been realized in another isostructural 5/0.25 at.% Tm³⁺/Ho³⁺ co-doped NaY(WO₄)₂ crystal when a V-type astigmatically-compensated resonator has been adopted [27], a better result can be expected for the Tm³⁺/Ho³⁺ co-doped LGM crystal by further optimizing the concentrations of Tm³⁺/Ho³⁺ ions and configuration of laser cavity.