1. Introduction

The availability of ultrafast laser pulses is a basic requirement in most of the research fields of physics, chemistry, and biology. To date this purpose is achieved in the UV spectral range by means of frequency conversion of visible and infrared mode-locked solid-state or synchronously pumped dye laser sources. These widely used techniques are limited by the phase-matching condition of the nonlinear crystal, which has to be optimized each wavelength, and also by the low overall efficiency of the whole chain of pumping and harmonic generation. For these reasons, an ultraviolet (UV), broadband, all-solid-state cw laser would be a very desirable goal, especially for the generation of ultrashort pulses in the mode-locking oscillation regime. Cerium-activated colquiriite crystals have been used to obtain all-solid-state pulsed lasers that are directly tunable in the near-UV range [1–6]. These materials exhibit high optical-optical efficiency, wide tunability (270–380 nm), and the possibility of pulse generation at tens of femtoseconds. Despite several well-known applications for UV pulsed lasers, studies on the possible realization of a cw UV tunable laser are very scarce in literature [1,7]. In this work we present an experimental technique for the determination of the cw lasing threshold and the slope efficiency of a Ce:LiCAF laser that employs the pulsed regime. The method is based on the analysis of the temporal profile of the pulsed output of a Ce:LiCAF laser pumped with long pulses, which determines a quasi-stationary behavior. To make our analysis more reliable, we have applied it on two different cavity geometries. Section 2 reports the theory supporting our experimental technique.

2. Technique description

In this section we want to find the conditions on the pump pulse temporal profile that determine a quasi-stationary behavior of the pumped laser system, i.e., an oscillation regime where the instantaneous laser output power follows the instantaneous input power as it would in true cw conditions.

Assuming an unsaturated pump absorption of the pump radiation in the active medium, the population inversion density N_ex can be written as follows, in the approximation of Gaussian beam profile and cylindrical symmetry:

where n(t) represents the population inversion density on the axis of the pump beam and at the injection surface of the crystal. In the hypothesis of the pump spot radius w_p smaller than the laser cavity mode w_c , the laser dynamics are described by means of the coupled rate equations for n(t) and the circulating power P_c (t)

where t_c is the round-trip time; τ_c is the photon cavity lifetime; σ_em and σ_ESA, are, respectively, the stimulated emission and the excited-state absorption (ESA) cross sections; η_p and α_p are the pumping efficiency and the absorption coefficient at the pump frequency v_p ; v_c is the laser frequency; τ_f is the lifetime of the excited level; and I_sat = (τ_f σ_em)/(ħω_c ) is the saturation intensity. To simplify the notation we define the nondimensional circulating power p(t) and population inversion q(t) and the normalized pump power F(t) as follows:

Equations (2a) and (2b) can then be written as

In the cw regime the first members in Eq. (4) are identically zero, obtaining the usual steady-state expressions for the population inversion q_cw and the circulating power p_cw :

Now we want to discuss the conditions on the pump pulse evolution that make negligible the first term of Eq. (4) even in the presence of a time-dependent pump. If these conditions are fulfilled in the experiment, the temporal evolution of the output power as a function of the input power can be analyzed to determine the cw threshold and slope efficiency of the laser system under investigation. We introduce the small perturbation β(t) to the steady-state quantity p_cw :

By substituting Eq. (6) in Eq. (4b), and assuming that q̇(t) can be neglected in Eq. (4b) [that is well verified for smooth pump pulse and in the absence of laser spiking, because the population inversion remains very near to its saturated value expressed by Eq. (5)], we obtain the following rate equations for the perturbations to the pure cw regime:

where we have considered that above threshold Fτ_f >1 and we have assumed β≪1. By substituting Eqs. (6) and (7) into Eq. (4b), and neglecting the terms of the second order in β, we obtain a linear differential equation for β(t):

which can be integrated to give the solution

where t₀ ≤θ≤t. We can choose the initial time t₀ such that both the following conditions are true: β(t₀ )=0 [i.e., either the analysis starts from a completely stationary regime, or at some instant its intracavity power is equal to the value determined by Eq. (5), as it occurs during relaxation oscillations], and the integration interval involves the decreasing tail of the pump pulse, where we have Ḟ(t) <0 and F(t)<F(θ). We can then write

Well above the threshold γ͂(t) → ${\tau }_c^{-1}$ and if we assume that |Ḟ(t)| is slowly varying with respect to τ_c , the integral in the Eq. (9) can be approximated with

We express the requested condition on |Ḟ(t)| defining τ _p2 as follows:

Finally, from Eqs. (11) and (5), we can find the condition that ensures that the perturbation due to the time-varying excitation is small with respect to the quasi-stationary value determined by Eq. (5) with the instantaneous pump intensity F(t), i.e., β(t) ≪ p_cw (F(t)). We obtain the following condition for F(t) and its derivative defining τ _p1 as follows

To summarize, under the above conditions on the temporal derivatives of the excitation, expressed by Eqs. (12a) and (12b), the intracavity circulating power follows quasi statically the variation of the pump intensity and the laser instantaneously behaves as a cw system with the output power determined by the second part of Eq. (5). In this condition a linear dependence between the instantaneous laser and pump power can be observed and the time-resolved measurement of these two quantities allows the determination of the cw threshold pump intensity and the slope efficiency. We observe in Eqs. (12a) and (12b) that the time scale on which the pump variation has to be compared is given by the cavity photon lifetime τ_c . Moreover we note that the validity of Eqs. (12a) and (12b), obtained in the case of normal incidence of the pump beam on the crystal chosen for sake of simplicity in the calculation, can be extended to the case of Brewster incidence. In fact the pump geometry does not affect the physical considerations on the time domain.

3. Experiment

The system under investigation is based on a single crystal of LiCaAlF₆ (LiCAF) doped with 1% at. Ce³⁺, grown in a computer-controlled Czochralski furnace under high-purity argon atmosphere. As starting materials we used LiCaAlF₆ powder mixed with CeF₃ and NaF₃, respectively, as dopant and charge compensator. To avoid the OH^- impurities, the powders were purified at the AC Materials (Orlando, Fla.) at a high purity level (99.999%). The pulling rate was 0.8 mm/h, the rotation rate was 12 rpm, and the temperature of the melt was 825 °C. For the experiment the crystal was cut at the Brewster angle with the c axis tilted at 36° relative to the optically polished faces.

These crystals are good candidates for the investigation of the lowest limit of lasing threshold because of their high optical quality, leading to excellent laser performance and, to the best of our knowledge, the highest slope efficiency (49%) ever shown by a Ce:LiCAF laser, as described in Ref [8]. The sample was pumped by a Q-switched, continuously lamp-pumped, Nd:YLF laser with intracavity generation of the fourth harmonic (at 263.25 nm). The maximum average power is 700 mW generated at 1 kHz with a full-width at half-maximum (FWHM) pulse duration ranging from 100 to 122 ns while the repetition rate (RR) was increased from 100 Hz to 2 kHz. The pump pulse rise time (10 to 90%) also increases from 35 to 50 ns in the same range of RR. To obtain an experimental measurement of the threshold intensity $I_{\mathit{\text{cw}}}^{\mathit{\text{th}}}$

 

Fig. 1. Setup of the Ce:LiCAF tunable laser with residual pump reinjection. Dark colored beam, laser beam; light colored beam, pump beam.

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for a typical cavity scheme used in Ce:LiCAF lasers (see, for instance, Ref. [6]), we have used the dispersive cavity shown in Fig. 1.

The cavity is constituted by a high reflector (HR) with radius of curvature (ROC) of 20 cm and the output coupler (OC) with ROC=25 cm and transmittance T=22.2% at 289 nm. The pump is injected with a small angle (≂15 mrad) with respect to the laser mode. The single pass optical length of the resonator is l_c =12.5 cm, and the 6.3-mm-long Brewster-cut Ce:LiCAF crystal is positioned with the waist of the calculated Gaussian mode in its center. The calculated TEM₀₀ mode waist radius is w_c =95 μm in the direction perpendicular to the cavity plane, and the pump spot radius measured in air is w_p =65 μm.

 

Fig. 2. (a) Typical temporal evolution of the pump P_in (t) and laser pulse P_out (t) at RR=1 kHz. (b) P_out (t) as function of P_in (t): experimental data (symbols) and linear fit of the steady state of the laser pulse (solid lines) for RR = 1.0 kHz; 1.5 kHz; 2.0 kHz. Absorbed pump energies are 640 μJ, 420 μJ, and 280 μJ, respectively. Numbered arrows indicate the three phases of the laser and the pump pulse.

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In Fig. 2(a) we report the incident pump pulse and the corresponding laser pulse at the emission wavelength of maximum gain (289 nm) and at RR=1 kHz. We can observe that the laser pulse dynamics undergoes three distinct phases: (1) (t<30 ns) the laser is switched off while the population inversion increases; (2) (30 ns < t <100 ns) the laser switches on and the gain-switching peak appears, followed by the relaxation oscillations; (3) (t > 100 ns) the laser follows the tail of the pump pulse. We now apply all the considerations explained in the previous section to this last phase in order to obtaining information about the cw behavior of the Ce:LiCAF laser.

To do this, in Fig. 2(b) we report the instantaneous output power P_out (t) as a function of the time-correlated absorbed input power P_in (t) for three couples of laser and pump pulse acquired with a different RR (1.0 kHz; 1.5 kHz; 2.0 kHz). The three phases we already described are well recognizable, represented by numbered arrows. We observe that in phase 3, P_out is linearly correlated with the instantaneous pump power as predicted by Eq. (5). It is worth noting that even though the shape of the pump pulse changes in response to the different RR as specified a the beginning of this section, the slope and the threshold determined by the linear behavior of P_out as function of P_in do not change significantly. In fact they depend only on the resonator characteristics and the physical properties of the active medium. We obtain $p_{\mathit{\text{cw}}}^{\mathit{\text{th}}}$ =430±20 W corresponding to a threshold intensity $I_{\mathit{\text{cw}}}^{\mathit{\text{th}}}$ =4.5±0.2 MW/cm² and a cw slope efficiency η_cw =39%, with respect to the absorbed pump power

To obtain an experimental estimation of $I_{\mathit{\text{cw}}}^{\mathit{\text{th}}}$ for a more favorable Ce:LiCAF laser setup, we have applied the same technique to a 70 mm-long nondispersive cavity, with longitudinal pumping and low output coupling. The cavity we used is constituted by an end mirror with R>99% at the laser wavelength and T=70% at the pump wavelength, with ROC=20 cm. The output coupler is flat with T = 13.5% at 289 nm. The crystal is located at the center of the resonator, out of the cavity waist that is situated at the OC, and it is longitudinally pumped through the end mirror. The shorter cavity balances the effect of the lower transmittance of the OC so that the photon lifetime is the same (τ_c ≈ 3.5 ns) as that of the dispersive laser previously described. The condition of the pump beam focalization is also unchanged with respect to the previous case. In Fig. 3 we show the output power P_out in relation to the absorbed pump power P_in for three different pump pulse energies at the repetition rate of 2 kHz. We used a λ/2 plate and a polarizing cube to adjust the pump pulse energy to the desired level without affecting the transverse spatial distribution of the pump beam.

 

Fig. 3. P_out (t) as function of the absorbed input power for three different pump pulse energies at the repetition rate of 2 kHz. Experimental data (symbols) and linear fit (solid line) of the cw laser action are shown. The indicated values of $P_{\mathit{\text{cw}}}^{\mathit{\text{th}}}$ and η_cw are obtained by the linear fit.

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Fig. 4. τ _p1 and τ _p2 (right scale) as function of time as obtained for a typical pump pulse.

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We observe, again, that the linear parts of the experimental curves are well superimposed, reflecting the insensibility of the technique to the pump pulse temporal profile and energy. The threshold power obtained by the linear fit of the experimental data is $P_{\mathit{\text{cw}}}^{\mathit{\text{th}}}$ =183±20 W corresponding to a threshold intensity $I_{\mathit{\text{cw}}}^{\mathit{\text{th}}}$ =1.9±0.2 MW/cm² of incident pump power.

In order to evaluate in the experimental conditions τ _p1 and τ _p2 defined in the Eq. (12a) and Eq. (12b), we report in Fig. 4 a typical temporal profile of the pump pulse (left scale) from which these quantities have been calculated numerically (right scale). In our experimental condition the photon lifetime τ_c=3.5 ns is at least one order of magnitude smaller than τ_pl and τ_p2 over the pump pulse tail so that the conditions of Eqs. (12a) and (12b) are fulfilled. In Section 4 we compare the obtained experimental results with the available theoretical estimations.

4. Comparison with theoretical estimations

The only theoretical estimation of the threshold intensity for a cw Ce:LiCAF laser is given by Marshall and co-workers in Ref. [1] for longitudinal pumping conditions, assuming Gaussian pump and laser beams with pump spot radius much smaller than the laser mode radius (w_p ≪w₀ ), small output coupling (T=1%), negligible single-pass losses (L=0), and a unit quantum efficiency (η_p =1). They also assume the total absence of ESA due to the low population of the excited laser level in the cw pumping regime. The value they obtained for the absorbed intensity was $I_{\mathit{\text{cw}}}^{\mathit{\text{th}}}$ =12 kW/cm². Actually, we believe that the ESA cannot be neglected for any value of the population inversion because its effect is equivalent to a reduction of the single-ion-emission cross section and then to a reduction of the gain, as exemplified in Eq. (2a).

A more accurate estimation of the threshold power that takes into account the laser and pump beam spot sizes can be obtained using the more complete derivation of Payne in Ref. [9] for the quasi-three-level system Cr³⁺:LiCAF in the approximation of Gaussian pump and laser beams:

The final factor, where θ_BR and θ_t are, respectively, the Brewster incidence and the transmission angles at the crystal interface, takes into account the beams’ expansion inside the crystal due to the Brewster incidence. In the same picture the slope efficiency can be expressed in the approximation w_p ≪ w_c as

We have calculated the threshold power and the slope efficiency for our experiments using both models, with the parameter values corresponding to our experimental situation; we set η_p =1, σ _em =6.6×10^-18 cm² (from the emission cross section spectrum obtained for our crystal with the β-τmethod in Ref. [8]) and σ_ESA=3.6×10^-18 cm² (from Ref. [1]); we also assumed L=2% for the linear cavity and L=4% for the dispersive cavity (due to the prism losses).

Table 1. Summary of experimental and theoretical values of threshold power, threshold intensity and slope efficiency

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The experimental and calculated threshold power, intensity, and slope efficiency are summarized in the Table 1.

We observe that the values of the threshold calculated with Eq. (13) are in very good agreement with the experimental values for the nondispersive laser, while in the case of the dispersive laser they only match the right order of magnitude, underestimating the experimental ones. This fact can be explained by the presence in the dispersive laser of the quasi-collinear pumping that reduces the overlap between the laser and the pump mode. This is not considered in the model leading to Eq. (13). On the other hand, the calculated slope efficiency is in agreement with the experimental value for the dispersive cavity, while it is overestimated for the nondispersive one. As a matter of fact we have w_p /w_c ≈ 0.68 for both lasers we have presented so that the hypothesis of w_p ≤ w_c used in the derivation of Eq. (13) is not well verified, possibly leading to the observed discrepancy between the calculated and the experimental values of η_cw . Within the case of longitudinal pumping with normal incidence we can then use the Eq. (13) to extrapolate the threshold power in the optimized conditions of tight focusing of the pump beam with matched laser and pump spot radii w_p =w_c =20 μm, and low output coupling and losses (T+L=1%). We obtain for the absorbed pump radiation at the peak of gain the following values: $P_{\mathit{\text{cw}}}^{\mathit{\text{th}}}$ =590 mW and $I_{\mathit{\text{cw}}}^{\mathit{\text{th}}}$ =93 kW/cm².

It is worth noting that the model leading to Eqs. (13) and (14) does not take into account some parasitic effects that could influence the behavior of the crystal, such as the formation of long-lived color centers (CC) under intense pumping because of unwanted impurities or lattice defects (see Ref [1]). This is consistent with our experimental conditions: in fact the performance of the lasers here described (i.e., their cw slope and threshold) is not affected by the variation of the average pumping level; this suggests that the intensity-dependent absorption, induced by CC formation in the crystal, is negligible for the average pump intensity range used in the experiments, up to 10 kW/cm². Furthermore, we have observed stable performance of the crystals over ~100 hours of operation, indicating the absence of long-term solarization effects; nonetheless, it is clear that the stability of the performance at the pumping level required for cw operation requires samples with very low concentration of defects and uncontrolled impurities.

In the design of a true cw laser, the thermal lens effect induced in the LiCAF crystal must be considered as well. A first estimate (based on the analysis reported in Ref. [11]) shows that in the extrapolated conditions for cw laser operation, the thermal lens should have a focal length of approximately 5–10 cm (diverging because of the negative value of dn/dT in the LiCAF). Although not negligible, this effect can be compensated by a proper cavity design.

We conclude by observing that at the present state, commercial devices for generation of cw UV radiation in the absorption band of Ce:LiCAF provide a maximum power level of ~200 mW. Thus far this has hampered the realization of a true cw laser source. However, some examples of devices recently described in the literature can reach the required power level: for example, a laser source exceeding 5W has been obtained by means of fourth-harmonic generation of a single longitudinal mode, cw Nd:YAG laser in a locked ring cavity (see Ref. [10]). This technique can provide pump power high enough to obtain efficient cw UV tunable radiation from a Ce:LiCAF based all-solid-state laser.

These results demonstrate the feasibility of the all-solid-state cw laser source with direct UV emission, which in turn would allow development toward the realization of a tunable laser source directly generating femtosecond UV pulses.

5. Conclusion

We have presented a technique that allows direct measurement of the cw lasing threshold. When applied to two Ce:LiCAF-based laser configurations pumped with a long excitation pulse, the technique allows us to determine the threshold value in the cw regime for this material. We obtained experimental values of the threshold intensities $I_{\mathit{\text{cw}}}^{\mathit{\text{th}}}$ =4.5±0.2 MW/cm² and 1.9±0.2 MW/cm² for a dispersive laser with quasi-collinear pumping and a nondispersive laser with longitudinal pumping, respectively. To the best of our knowledge, these are the only experimental measurements of this quantity for a Ce:LiCAF laser. The experimental values are in disagreement with the theoretical model given in Ref. [1] applied to our experimental conditions, while a more accurate model by Payne et al. [9] adapted to the present laser system can reproduce quite well the measured values in the case of longitudinal pumping. On the basis of this model, experimentally validated for the Ce:LiCAF system, we extrapolate the value Ict $I_{\mathit{\text{cw}}}^{\mathit{\text{th}}}$ =93 kW/cm² as the lower limit of the threshold intensity. In this picture the cw lasing action of Ce:LiCAF is obtainable with 590 mW of absorbed cw power tightly focused in a 20 μm spot radius. Our results demonstrate the possibility of making a cw tunable UV all-solid-state laser source.