1. Introduction

The Yb³⁺ doped hosts have been extensively studied as possible competitors of the Nd³⁺ activated crystals. As it is well known [1,2], the Yb³⁺ two manifolds ²F_5/2 and ²F_7/2, which degeneracy is removed by interaction with the host crystalline electric field, leads to a low quantum defect producing a very low thermal energy dissipation. As a result the achievable optical-optical efficiency is very high but, on the other hand, the absorption and the emission-fluorescence spectra are partially overlapped and the re-absorption of the emitted fluorescence substantially increases the threshold level.

In presence of a birefringent medium, as in the case of the host material YLiF₄ (YLF), the absorption and emission spectra depend on the polarization of the electromagnetic wave in respect of the optical axes of the crystal. The use of Yb:YLF as active medium has already made possible the realization of efficient laser systems such as regenerative amplifiers [3,4] and passive mode-locked oscillators [5], mainly exploiting the π-polarization emission and a comprehensive characterization that includes the behaviour of σ-polarization has been proposed only in [6] for Yb concentration up to 10%. In this latter paper a maximum slope efficiency of 33% and a maximum power of 0.36W for π-polarization are reported, while the corresponding values relative to σ-polarization are 29% and 0.27W. Concerning the tunability, tuning ranges from 1010 to 1070nm for π-polarization and from 1010 to 1060nm for σ-polarization are reported in [3], while a tuning range 1020-1075nm is reported for π-polarization in [2]. In this work we present a complete characterization of the π and σ-polarization operation concerning the efficiency and the tunability of laser oscillators, based on a heavily doped (30% at.) Yb:YLF crystal. The comparison of the experimental results with the theoretical model provides indications about the influence of the factors which limit the tuning range in Yb based laser systems. The choice of a highly doped crystal allows to obtain a significant absorption of the pump even on the wings of the absorption band (e.g. at 940nm), and therefore permits to pump thin crystals at this wavelength.

2. Experimental set-up

The Yb:YLF crystal is a 1.4 mm thick, high quality sample, cut for normal incidence with the c-axis parallel to the input face. It has been obtained by the Chocralsky method with the 30% at. of Yb concentration in the melt (see [2] for a comprehensive description of the optical properties and of the growth technique). The crystal is welded with Indium on a copper heat sink stabilized at 20°C and it is longitudinally pumped by a fiber coupled laser diode. The pump beam is focused on the crystal through the cavity end mirror EM by means of two achromatic doublets with a 1:1 magnification. The maximum deliverable pump power is 21W; we employed a quasi-CW pump regime with repetition frequency of 10 Hz, duty factor 20% in order to limit the thermal load on the crystal. The waist radius of the pump beam, measured with a CCD camera, is w_p = 150μm at 1/e².

The cavity (see Fig. 1 ) is folded by means of a HR mirror (FM). The crystal is positioned near the dichroic EM. The transmission of the output couplers (OC) spans between 1.5% and 13.5%. A prism at the Brewster angle is inserted near the OC to achieve tuning (see the inset in Fig. 1). The desired polarization of the laser emission has been selected, for the non-tunable cavity, by an intra-cavity fused silica slab set at the Brewster angle of incidence (not reported in Fig. 1). For the dispersive cavity, the crystal has been rotated with the desired orientation with respect to the polarization direction where the polarization plane is determined by the plane of incidence on the prism. Polarization ratios exceeding 100:1 have been observed for all the configurations.

 

Fig. 1 Scheme of the experimental set-up. In the inset the tunable cavity arrangement. The laser diode emits at 940nm, fiber core diameter and NA are 200μm and 0.22 respectively. The doublets focal length is 60mm. The radius of curvature of FM is 150mm, EM and OC are flat.

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The distance D₁ between the EM and the FM has been set to 78mm. The mode size inside the laser crystal can be changed by varying the distance D₂ between the FM and the OC. In consequence, the matching of the pump and laser beam size inside the crystal has been optimised for maximum output power by adjusting the length D₂. We found that a values of D₂ = 435mm optimizes the output power for both π- and σ-polarization. By using an ABCD matrix simulation, we have calculated a waist radius w_L of 46μm for the TEM₀₀ cavity mode at the input facet of the active medium. This calculation neglects the weak astigmatism introduced by the cavity folding and by the intra-cavity prism, and the effect of the thermal lens into the crystal, which cannot be evaluated theoretically due to the lack of reliable thermo-optical parameters for highly doped YLF materials.

3. Results and discussion

3.1 Single wavelength operation

In this section, we show the results obtained for the not tunable laser operation. We reported in Fig. 2 the output power as a function of the absorbed pump power for both polarizations and for three different OC with transmission at the lasing wavelength λ_L between 1.5% and 13.5%. The maximum absorbed pump power is 8.8W, and the absorption in lasing conditions ranges between 59% and 61% (i.e. the maximum power incident on the crystal is 14.8W)

 

Fig. 2 Output power as function of the effectively absorbed pump power for the π and σ-polarization for three different OC.

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We remark that the experimental data shown in Fig. 2 are corrected with the actual pump absorption in lasing conditions, as discussed in [7,8], in order to properly evaluate the efficiency of the laser. We mention that this effect has also been observed to influence the thermal load in the crystal and the thermal lensing effect as well [9].

We obtain different lasing wavelength λ_L depending on both the lasing polarizations and the OC transmissions. The results are reported in the Table 1 . It can be noted that, for lower OC transmissions, σ-polarization shows a reduction of about 13% of P_max respect to π-polarization, while the slope efficiency η_sl is substantially unaffected. A consistent variation of the laser performances for the two polarizations can be observed for the higher transmission OC due to the relevant difference between the transmissions at the two lasing wavelengths (9.5% at 1049nm while 13.5% at 1025nm). The threshold power for σ-polarization increases by a factor between 1.3 and 1.6 respect to the π-polarization. The high ratio between the effective pump beam waist w_p and the TEM₀₀ cavity mode waist w_c leads to a multimode laser operation.

Table 1. Slope efficiency η_sl, maximum output power P_max and threshold power P_th obtained 
for σ and π-polarization with three different OC.

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3.2 Laser tuning

We report in Fig. 3(a) and 3(b) respectively the tuning curves for σ and π-polarization emission obtained with the wavelength dispersive set-up (see inset in Fig. 1) employing various OCs. In Fig. 4 we report the transmission spectra of the employed OC and of the EM.

 

Fig. 3 Tuning curves of Yb:YLF laser with various T_OC for a) σ-polarization and b) π-polarization. DF = 20%, P_abs = 8.8W.

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Fig. 4 OC transmission (solid line, left axis) and EM reflectivity (dash line, right axis).

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For π-polarization the largest tuning range is 80nm, from 996 to 1076nm, obtained with T_OC = 2% nominal. The maximum output power of 2.3W has been obtained at 1026nm employing an OC with higher transmission (T_OC = 20%), while, on the higher wavelength side, the maximum output power has been obtained with T_OC = 10% nominal. Similarly, for σ-polarization we obtain a tuning range as large as 66nm (from 998 to1064nm) with T_OC = 2% nominal and a maximum output power of about 1.5W at 1021nm, with corresponding OC transmissions.

We have also employed a commercial OC with a transmission spectrum, decreasing from short to long wavelength, that turns out to optimise the π-polarization emission (T_OC = π-optimized in Fig. 3 and Fig. 4) on both the short and long wavelength side of the tuning curve. It can be observed in Fig. 3(b) the tuning curve obtained with this OC the cavity coupling is optimized on both the small and long wavelength side up to 1060nm.

In order to address this point more quantitatively, we have evaluated the spectrum of the small signal amplification experienced by the laser fundamental mode, for different incident pump power levels. Referring to [10] for the basic theory, for given pump intensities at π and σ polarization $I_P^{\pi ,\sigma }$ and negligible laser intensity, the population densities in the lower and upper manifold are

In the longitudinal pumping scheme, the pump beam at the entrance facet for the i polarization (π or σ), is assumed to have a Gaussian intensity distribution with radius w_P. For a small laser intensity, the pump intensity distribution along the crystal can then be determined by solving the differential equation

The laser mode in the crystal is assumed Gaussian with radius w_L. The small signal gain distribution for a wavelength λ_L and for a polarization i is then given by

The overall small signal power amplification at the wavelength λ_L with polarization i in the double pass across the crystal length L_c is then given by

To describe our experimental situation, we assume λ_P = 940nm, ${\sigma }_a^{\pi }\left({\lambda }_P\right)$ = 1.54 × 10⁻²¹ cm ², ${\sigma }_a^{\sigma }\left({\lambda }_P\right)$ = 2.67 × 10⁻²¹ cm ², ${\sigma }_e^{\pi }\left({\lambda }_P\right)$ = 0.24 × 10⁻²¹ cm ², ${\sigma }_e^{\sigma }\left({\lambda }_P\right)$ = 0.44 × 10⁻²¹ cm ², L_c = 1.4mm, w_P = 154μm, w_L = 46μm and $I_P^{\pi }$ = $I_P^{\sigma }$ = $I_P/2$ (i.e. unpolarized pump source). The data for the absorption and emission cross section ${\sigma }_{a,e}^{\pi ,\sigma }\left(\lambda \right)$ have been obtained from [2]. The laser oscillation can occur only for wavelengths where A_i(λ)>1/(1-L(λ)), where L is the fraction of intracavity circulating energy lost over a cavity roundtrip, due to the output coupling plus parasitic losses and the term 1-L(λ) represents the round trip attenuation of the circulating power. Figure 5 shows the resulting small signal amplification spectrum calculated for the pump power used in the experiment. The figure also reports the level of the quantity 1/(1-L(λ)) calculated considering the reflectivity of the cavity mirrors and an overall loss level of 5% due to spurious reflection on the crystal and tuning prism surfaces. For each mirror set, the expected tuning range boundaries are located at the intersection of the amplification curve with the cavity losses curve.

 

Fig. 5 Round trip power amplification for different pumping levels, a) for σ and b) for π-polarization and value of the factor 1/(1-L(λ)) with the mirrors sets used in the experiment.

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It can be seen from Table 2 that the predicted tuning ranges for the different mirror sets are in good agreement with the experimental findings. On the short λ side, the experimental tuning ranges are slightly less extended than the prediction. This can be due to some unaccounted loss (for instance, on the prism surfaces). We notice that on the side of short λ the tuning range is limited by the steep rise of the losses due to cutoff in the reflectivity of EM.

Table 2. - Comparison between the experimental and modeled tuning ranges, with different output couplers.

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From the analysis of Fig. 5 it appears that, for a given pump power, the long wavelength limit of the tuning range can be strongly influenced by the cavity losses, because the small signal amplification is smoothly vanishing for increasing λ. A small reduction of the losses on this side can then determine a large shift of the boundary of the tuning range. On the other hand, on the short wavelength side the tuning range limit is less dependent on the intra-cavity losses, because A(λ) has a steep descent toward 1 for decreasing λ (in particular for the π polarization). This is due to the onset of the ground level absorption of the laser transition, which becomes the main loss path of the laser cavity at short wavelength.

4. Conclusions

We have reported a comprehensive characterization for the σ- and π-polarization emission of a Yb:YLF based laser with a maximum output power of 4.5W and a 80nm wide tuning range between 996 and 1076nm. We use a model, applicable to other Yb-based active media, for the evaluation of the tuning range of this active medium, whose results are in good agreement with the experimental findings. We show that a higher inversion pump level, obtainable by the improvement of the heat removal e.g. by reducing the crystal temperature, could considerably enlarge the Yb:YLF tuning range on the short wavelength side, while on the long wavelength side the tuning range can be extended by a careful optimization of the cavity parasitic losses. We also show the optimization of the output power over the main part of the tuning range, by means of a commercial OC with a suitable transmission spectrum.