We report the first laser operation based on Ho3+-doped LuLiF4 single crystal, which is directly pumped with 1.15-μm laser diode (LD). Based on the numerical model, it is found that the “two-for-one” effect induced by the cross-relaxation plays an important role for the laser efficiency. The maximum continuous wave (CW) output power of 1.4 W is produced with a beam propagation factor of M2 ~2 at the lasing wavelength of 2.066 μm. The slope efficiency of 29% with respect to absorbed power is obtained.
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Lasers based on trivalent holmium ion materials have been extensively investigated because of the capability of offering 2 μm and 2.9 μm coherent radiation [1–4]. Most of Ho-doped lasers have been researched widely with the pump sources of Tm3+-doped lasers, which are effective around 1.9 μm pump wavelength [5,6]. Diode pumping at ~1.9 μm for Ho-doped lasers was also performed, and generated 40 W of output power from a Ho:YAG laser with 150-W pump power . But the electro-optical efficiency of long wavelength laser diode is restricted and the emission linewidth is usually larger than the absorption peak of the Ho3+-doped crystal, leading to comparatively low absorption efficiency . Another available pump wavelength for Ho3+-doped lasers is around 1.15 μm . Directly diode pumping of Ho3+-doped fibers in 1.148 μm was also explored. The output power of 55 mW with a slope efficient of 27% was achieved through a 0.5 wt.% Ho3+-doped silica fiber . Directly diode pumped Ho3+-doped crystal at 1.15-μm wavelength has rarely been reported.
Compared with oxide crystals, fluoride crystals possess lower phonon energies and much longer lifetimes of upper laser levels, potential for achieving high-energy Q-switched laser operation . High efficient in-band pumped continuous wave and Q-switched 2-μm Ho:LuLiF4 (Ho:LLF) crystal lasers have been reported recently [1,4]. The advantages of LLF also make it an attractive candidate for directly diode pumped Ho3+-doped lasers, which can be advantageous in many ways such as efficiency, simplicity or compactness for Ho:LLF crystal laser.
In this work, we reported the results of a Ho:LLF crystal laser directly pumped with a LD at ~1.15 μm. Compared with 1.9-μm LDs, currently developed 1.15-μm LDs can provide much higher pump power, higher electrical efficiency and longer using lifetime. Furthermore, the cross relaxation of the Ho3+ ion with 1.15-μm pumping reveals the possibility of the “two-for-one” effect, which will enhance the pumping efficiency. Therefore, pumping Ho3+ bulk laser materials with 1.15-μm LDs has the potential to achieve higher laser performance. Besides, pumping Ho3+ laser materials with 1.15-μm LDs can also realize laser emission at the wavelength region of 2.9 μm.
2. Theoretical model and experimental laser setup
For better understanding the dynamics of this pump scheme, a model based on a set of rate equations to characterize Ho3+-doped fiber laser has been introduced . The simulation and experiment related five lowest energy levels, with corresponding energy transfer processes of Ho3+ ions in LLF pumped from 5I8 to 5I6 level, and the unpolarized absorption spectrum from 1100 to 1200 nm of Ho:LLF (1.0 at.%) are shown in Fig. 1.
Since the wavelength of pump light is near the exciting band from 5I7 to 5I4, the excited state absorption (ESA: 5I7→5I4) is included. The energy transfer processes between two Ho3+ ions, i.e., cross-relaxation (CR: 5I5, 5I8→5I7, 5I7 and 5I6, 5I8→5I7, 5I7) and energy transfer upconversion (ETU: 5I7, 5I7→5I5, 5I8 and 5I7, 5I7→5I6, 5I8), are also displayed . By donating the population density of the i-th energy level as Ni (i.e., N0 for 5I8, N1 for 5I7, etc.), the effects of ESA (WESA), CR, ETU in the time-independent rate equations in the CW regime for the two lowest energy levels are as follows:
The cross-relaxation and energy transfer upconversion mechanisms for Ho3+ ions pumped at ~1.15 μm can be described by
Note that the influence of cross relaxation on the pump efficiency is determined mainly by the ratio between the coefficients of k2101(k3101) and k1012(k1013). Thus choosing a laser crystal with a large ratio of k2101(k3101) and k1210(k1013) is important to enhance the “two-for-one” pumping effect.
Because of the geometric difference between bulk and optical fiber, the pumping intensity can be assumed uniform along the bulk crystal, and the laser oscillation in the gain media should be rewritten in the form of ,
The single crystal of Ho:LLF with a doping concentration of 1 at.% used in our experiments was grown by the Czochralski method. The Ho:LLF crystal laser was pumped by a fiber coupled LD (Idrive~5.8A, Pout ~10W CW, 400 μm core, NA ~0.2), and the experimental setup is shown in Fig. 2. The slab was cut along the a-axis with a dimension of 3 × 3 × 30 mm3. The unpolarized pump light was focused through the 3 × 3 mm2 facet into the crystal with a spot radius of ~0.35 mm, the Rayleigh length of the pump light inside the Ho:LLF crystal was calculated to be ~2.8 mm. Both the pump and output facets of the crystal was anti-reflection (AR) coated (R<0.2% at 2066 nm and R< 0.4% at 1148 nm). The sample was conductively cooled by a micro-channel copper heat sink with circulating water of 15 °C. The laser cavity was formed by a plane mirror M1 (AR at 1148 nm, highly reflective at 2066 nm) and a 250 mm radius-of-curvature (ROC) partially reflective output coupler M2 (98%, 95%, and 90% reflectivities at 2066 nm, respectively). Neglecting thermal lensing, with a cavity length of ~130 mm the TEM00 beam radius in the Ho:LLF slab was calculated to be 0.288 mm. A dichroic mirror M3 (R>99.5% at 1148 nm and AR at 2066 nm) was placed to remove residual pump light. The laser output power was measured with a FieldMate power meter (Coherent Co.), and the laser spectrum was measure with a mid-infrared spectrometer (SandHouse Co.).
3. Results and discussion
The parameters used in the numerical simulations are listed in Table 1 [2,14,15] and the values of the absorption cross-section σ01 at wavelength of 2066 nm calculated from Ref . are also shown in Table 1. Note that the ratio of k2101(k3101) and k1012(k1013) of Ho:LLF is one order of magnitude higher than that of Ho-doped silica glass.
As mentioned above, the excited state absorption (ESA) is believed to occur in pump scheme between 5I8 and 5I6 levels, however, the role of ESA has never been addressed. To better understand and quantify the effect of ESA, we investigated the dependence of the output power on ESA using Ho-doped (1.0 at.%) LLF crystal with a length of 30 mm. The simulated results are compared with the experimental observation in Fig. 3(a). The simulation including ESA was consistent with the experimental measurement. However, by inputting the corresponding parameters but without ESA term included, the simulation brought a higher slope efficiency. Therefore, the laser efficiency is obviously compromised by the ESA. Furthermore, by using output coupler with higher transmission, the population N1 should be kept at the raised value to overcome higher output losses. In such a case, the increasing of output coupler transmission will magnify the impact introduced by ESA [see Fig. 3(b)].
As it is well known, the cross-relaxation (CR) is a significant effect in Tm3+ laser with pumping between 3H6→3F4 levels . The effect, so-called as “two-for-one” effect, allows one pump photon excite two ions to the upper laser level, greatly enhancing the pump efficiency. The energy transfer upconversion (ETU) is a process making ions transmit in a reverse direction and thus undermining the population inversion.
In Ho3+ laser pumped at 1148 nm, the cross-relaxation (k2101, k3101) and energy transfer upconversion (k1013, k1012) also occur . The efficiency of the Ho-doped LLF laser is severely determined by the CR-ETU process. The role of CR-ETU in the laser efficiency depended not only on the ratio between coefficients k2101(k3101) and k1012(k1013), but also on the population of involved energy levels 5I5, 5I6 and 5I7. The influence of the CR-ETU in Ho:LLF (1.0 at.%) laser with 10% output coupler is shown in Fig. 4(a). Under low pumping intensity, the populations N2 and N3 are low while N1 is almost constant. The contribution to the population inversion by the CR is weaker than that by the ETU. As a result, the impact of CR-ETU on the laser efficiency is negative. As seen from Fig. 4(a), when the absorbed pump power is less than 1.21 W, the output power is observable lower in comparison with the value if the CR-ETU process is ignored from the model.
In the condition near the threshold, the contribution of the ETU process was the main effect. With increasing the output coupling, the population N1 increased and the ETU was more likely to occur. In Fig. 4(b), the influence of CR-ETU process is plotted with the absorbed pump power near the threshold. It can be seen that increasing the output coupler transmission leads to higher threshold pump power and bigger difference in the output power between the cases when the CR-ETU process is turned on and off.
On the other hand, when the absorbed pump power was increased, the populations N2 and N3 increased rapidly. Above 1.21 W, the weighting factors of CR and ETU were reversed. Consequently, the influence of CR-ETU made a positive contribution to the laser performance. The output power is improved with the CR-ETU processes.
The slope efficiencies with respect to the absorbed pump power versus various transmissions of couplers are shown in Fig. 4(c). Compared with the effect of ESA, the influence of CR-ETU is more instructive in the Ho:LLF bulk lasers.
The performance of Ho:LLF crystal lasers is plotted in Fig. 5(a) as a function of absorbed pump power. The maximum power of 1.4 W was generated with the 10% output coupler, corresponding to a slope efficiency of 29% with respect to the absorbed pump power and the threshold pump power was around 0.6 W. The output laser beam was π-polarized with the degree of polarization >25 dB. The experimental measurement agrees quite well with the calculation based on the theoretical model, indicated that the ESA and CR-ETU processes play important roles in the performances of Ho:LLF lasers.
The laser emission spectrum is presented in Fig. 5(b). The center wavelength of the emission peak was 2066 nm. The emission bandwidth (FWHM) was ~7 nm, which was slightly broader than that pumped at 1.9 μm wavelength .
The M2 factor of the 2.066 μm laser was measured at the maximum output power with a beam profile analyzer. The beam was collimated and focused with a 100-mm focal length lens. The beam spot size and divergence angel were recorded by the scanning method. The measured beam quality factor M2 value was ~2.
The quantum defect based on pumping and emission wavelength is ~56% for the 1.15-μm pumping of Ho:LLF crystal lasers. However, the CR-ETU process in Ho:LLF crystal provides an opportunity for the “two-for-one” effect, enhancing the pump efficiency of laser. Considering the electro-optical efficiency of 50% for 1.15-μm pump source, the electro-optical efficiency of whole system is likely greater than that of the traditional pumping scheme, in which Ho:LLF lasers are pumped by Tm-doped lasers.
The first demonstration of Ho3+-doped LLF lasers directly diode pumped at ~1.15 μm is reported. This Ho3+-doped laser has generated 1.4W CW output power at 2.066 μm with a slope efficiency of 29% with respect to absorbed pump power. The pump efficiency of the Ho3+:LLF crystal is enhanced through the “two-for-one” effect by the CR processes. The experimental results show that Ho:LLF lasers directly diode pumped at ~1.15 μm can be efficient sources for 2.1-μm radiation and particularly promising for Q-switched modes of operation owing to the long fluorescence lifetime and low saturation intensity. Higher power and efficiency should be possible to scale through optimizing crystal length, holmium doping concentration and minimizing detrimental thermal effects. The laser source can be comparable with other pump schemes for numerous applications.
This work was partially supported by National Natural Science Foundation of China (No. 61138006 and No. 61275136).
References and links
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