1. Introduction

Ultraviolet laser systems are powerful instruments for research, analytics [1–3] and industrial applications [4,5]. Most of materials and compounds exhibit a higher absorption coefficient at UV spectral range. UV laser systems provide a higher sensitivity in analytics [1] and a higher efficiency and accuracy in micromachining and cutting applications [4–6]. Particularly, ultrashort UV pulses appears to be advantageous for micromachining precision because of a low thermal loading and high power [7,8].

The main methods to obtain UV laser radiation are nonlinear and parametric conversion of IR or visible laser radiation. An alternative and prospective method is using fluoride crystals doped with Ce³⁺ ions [9]. The lasing is based on the interconfigurational 5d-4f transitions of Ce³⁺ ions significantly broadened in a host crystal lattice, allowing for amplification and generation of ultrashort pulses. Subnanosecond pulses generation was achieved earlier via Q-switching or mode-locking [10–12]. Promising materials are family of fluoride crystals with scheelite structure such as LiLuF₄ and LiYF₄ activated with Ce³⁺ [12]. The Ce³⁺ substitutes Y³⁺ or Lu³⁺ with no need of any charge compensation. Here, only one type of impurity center is formed, exploring the whole amplification band to generate ultrashort pulses, in contrast to multiple Ce³⁺ centers formation in Ce:LiCaAlF₆ crystal (Ce:LICAF). On the other hand, they exhibit strong solarization (color center formation under irradiation by pumping radiation), stipulated by excited state photoionization of activated ions and leading to rising losses at laser wavelengths [13,14]. The color center formation and the transient losses are functions of UV pumping rate, UV lasing energy density in the laser cavity and temperature [15–17]. Lowering intracavity losses due to color centers bleaching by laser radiation allows for Q-switching with the color centers acting as saturable absorber.

The aim of this work is to study short pulse laser oscillations in a Ce³⁺:LiLu_0.7Y_0.3F₄ (Ce:LYLF) crystal, homologous to LiLuF₄ and LiYF₄, with superior laser properties and modulation of dynamic processes via pumping radiation [15].

2. Energy levels scheme and model of active medium

Active medium doped by Ce³⁺ ions operates according to well-known 4-level scheme. The pumping photons are absorbed via a transition from the ²F_5/2 level of the 4f-configuration to the ²D_3/2 level of 5d-configuration. The energy of the pump photon is high enough to bridge the energy gap between the conduction and the ²D_3/2 level via a stepwise excitation ²F_5/2(4f)→²D_3/2(5d)→CB (Conduction Band) and formation of color centers. Color centers can be bleached via photoionization by laser radiation and/or additional illumination of the crystal. A simplified model of pump-induced dynamic processes is shown in Fig. 1.

 

Fig. 1 A simplified model of laser action in Ce³⁺:LiLu_0.7Y_0.3F₄. (1) – (4) – the Ce³⁺ ions levels (4f and 5d states). (5) is the state localized within the conduction band. (6) is the edge of the conduction band. (7) - is ground state of color centers. Straight lines indicate absorption and emission transitions, curved lines indicate nonradiative transitions.

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Following one photon absorption, Ce³⁺ from level 3 (Fig. 1) are excited within the conduction band by realizing one electron (Fig. 1) [14–18]. Following fast relaxation, to the bottom of conduction band (6 in Fig. 1) electrons can be trapped by defects (7 in Fig. 1) to form optically active centers (color centers), which subsequently absorb the laser photons. Further, the illumination of color centers may cause additional ionization that promotes electrons back to the conduction band. Free charges in the conduction band can be recombined following excitation of the 5d-states of Ce³⁺ ions or they can be re-trapped again by defective sites in the crystal host. By exploiting these photodynamic processes is possible to design multifunctional gain materials functioned as tunable saturable absorbers.

A mathematical model based on Fig. 1 is described by the following rate equations:

Equations (1) – (4) describe the population of 4f- and 5d-states of Ce³⁺ ions. Equations (3) and (4) include terms which describe excited state absorption and subsequent relaxation to the Ce³⁺ from conduction band [17,19,20]. Equations (5) – (7) reflect the evolution and relaxation paths of either free charges after ionization of Ce³⁺ ions or color centers. Equation (8) determines the number of stimulated emission (lasing) photons n₈ in the laser cavity, Eq. (9) describes the lifetime of photon in the cavity τ_q. N_pump(t) and N_pumpgr(t) are the temporal evolution of photons fluxes of pump radiation and any additional external radiation, respectively.

The absorption cross-section at the pump wavelength is σ_abs, σ_Em – laser emission cross-section of Ce:LYLF active medium, 1/τ₄₃ and 1/τ₂₁ – the nonradiative transitions rates from the (4) and the (2) Ce³⁺ ions states, correspondently, τ₅₆ – average time of electron thermalization in the conduction band, σ_ESA – cross-section of excited state absorption at pump wavelength, photoionization cross-section of color centers is σ₇₅ for laser emission wavelength and σ_75gr the same for any additional radiation (e.g. at 532 nm), 1/τ₇₅ is the thermal destruction rate of color centers, 1/τ₆₄ is the probability of recombination of free charges that repopulate the excited 5d-states parameters, β₁ and β₂ are the branching ratios of the transition from the 5d-state to the ²F_7/2 and ²F_5/2 states, respectively. Parameter τ₃ – the Ce³⁺ luminescence lifetime, was adjusted according to [21]. Here, short pulse operation by intracavity transients was obtained at low levels of pumping intensity, which is close to the laser threshold value. In this case and for a high gain cross-section value for 5d-4f transitions, the luminescence lifetime appears to be shorter than the radiative lifetime of the excited 5d-state due to the high radiative noise level.

Some parameters of these dynamic processes are known from spectroscopic studies. Namely it is known that Ce³⁺ upper laser level lifetime is almost the same for the series of LiY_1-xLu_xF₄:Ce mixed crystals [17]. The absorption cross-section of the 4f-5d transition of Ce³⁺ ions was calculated from the absorption spectrum taking into account the Ce³⁺ ions segregation in the LiY_0,3Lu_0,7F₄ host lattice [22]. Also, this host lattice supports only one type of substitution center for Ce³⁺ from the emission cross-section of the 5d-4f transition of Ce³⁺. Thus knowing the luminescence spectrum and luminescence lifetime we were able to calculate the emission cross-section of 5d-4f transition of Ce³⁺ with the use of Einstein equation and technique from work [23]. Parameters of color centers, i.e. absorption cross-section at laser wavelength (311 nm) and additional illumination wavelength (532 nm), probability of color centers formation, probability of recombination of an electron, were varied to fit experimental data.

4. Experimental configuration

LiLu_0.7Y_0.3F₄ (Ce:LYLF) mixed crystal with 1 at. % of Ce³⁺ ions were grown from melts. The Ce:LYLF active element was an all-side polished parallelepiped 10x5x5 mm.

The experimental setup presented in the Fig. 2 was used to obtain picosecond range UV laser pulses from a Ce:LYLF active medium with additional pumping. The Ce:LYLF active medium was pumped by a UV solid-state master-oscillator and power amplifier Ce:LICAF laser pumped by the 4th harmonic of Nd:YAG at 10 Hz. Ce:LICAF laser oscillated at 289 nm with pulse duration t = (6,37 ± 0,05) ns providing 3 mJ of energy per pulse with 10 Hz pulse repetition rate. The remaining part of 532 nm radiation proceeding from forth harmonic generator of the same Nd:YAG laser was used to irradiate Ce:LYLF active element.

 

Fig. 2 Experimental setup 1 – Nd:YAG laser, emitting at 532 and 266 nm; 2 - 266/532 nm beam separator; 3, 14 - reflectors (R = 99,9% at 532 nm), 4, 10, 13 - reflectors (R = 99,9% at 266 nm), 5, 11 –telescopes 1,5x, 6 – 50/50 beam splitter at 266 nm, 7, 12 – Ce:LICAF active elements, 8, 9 – rear (R = 99,9%) and output (R = 65%) couplers, 15, 16 – cylindrical lenses, 18 - Ce:LYLF active element, 17, 19 - rear (R = 99,9%) and output (R = 25%) couplers. In the dash box the Ce:LiCAF laser is shown.

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The Ce:LYLF crystal was transversely pumped. The Ce:LYLF laser cavity consisted of two plane mirrors (99,9% and 25% reflectivity at 270 nm – 350 nm). A small active medium length (25 mm) and significant output losses determine a low Q-factor of the laser cavity and the lifetime of photons in the cavity τ_c was 300 ps. Pumping and additional radiation were focused on the polished side of the active element by cylindrical lenses with focal lengths 5 cm and 20 cm, respectively. Pump radiation was focused into a spot with the size 0,15x3 mm². Spot of the additional pumping radiation covered the UV pumped area and its’ energy density was about 1 J/cm². Pulses of pump radiation and additional irradiation were superposed in time with a jitter of 4 ns.

Pulse shape measurements were performed with Alphalas photodiodes with 50 ps rise time coupled to a Tektronix oscilloscope with 3,5 GHz bandwidth.

5. Results

Short single laser pulse oscillation from Ce:LYLF was obtained at 311 nm having a pulse width 400 ± 50 ps, inset of Fig. 3(a). This was obtained without any additional irradiation at a pumping energy twice as high as the threshold energy. Because the laser pulse width appears to be greater than the photon lifetime in the cavity (τ_c = 303 ps) a multimode lasing was obtained. It is seen from the Fig. 3 that rise time of the laser pulse is shorter than its descending part which indicates about possible passive Q-switching.

 

Fig. 3 Temporal evolution of laser pulses with 400 ps from Ce:LYLF in a low Q-factor cavity. (a) – experimental, (b) – numerically calculated. Color lines represent UV pumping and UV with external additional pumping at 532 nm, respectively. Inset in fig. (a) shows a 400 ps single pulse. Inset in fig. (b) shows calculated dependence of pulse width on pumping energy taking into account the color center impact (grey open circles points and line) and without one (black points and line). Dashed boxes indicate single and double laser pulses modes, correspondingly.

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Pumping at higher energies is accompanied by a number of pulses of free multimode lasing. Additional irradiation of Ce:LYLF active medium at 532 nm has the consequence of generating an additional 600 ps laser pulses 2.5 ns apart from the main one, Fig. 3. This two-pulse operation appears at 1.5 times higher pumping energy above of the threshold. The slope efficiency of the lasing is higher under additional irradiation at 532 nm and the threshold energy is 17% lower (Fig. 4) The similar results for ns-pulse laser action regime were reported before in [16].

 

Fig. 4 Dependence of the output energy on the pump energy (a) and calculated color centers density (b) with and without external additional irradiation at 532 nm.

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Simulated results by using of rate Eqs. (1)-(9) are shown in Fig. 4(a). One can see two regions divided by fracture, which corresponds to the appearance of the second laser pulse. This fracture shifts to lower pumping energies when we apply additional irradiation to bleach the color centers and the two-pulse mode appears at lower pumping energies. Our calculations have shown that multiple pulse mode operation appears at pumping energies much lower when absorption of color centers is excluded. The inset in Fig. 3(b) shows the dependence of pulse width on the pumping energy, derived from simulation. It shows that when color centers are excluded from the model there is not a single pulse mode operation, while there are still present in experiments. When color centers are taken into consideration, single pulse mode operation at pumping energies up to 1,5 the threshold value is obtained. Thus color centers widen the region of single short pulse mode operation and stabilize the laser pulses in time.

The color centers density evolution is shown in Fig. 4(b). It demonstrates passive a Q-switch mode operation by color centers formed in Ce:LYLF active medium. During subnanosecond pulse generation, the color centers density drastically drops because of bleaching by laser radiation. It again grows almost to the initial level because the pump pulse is still acting on the active medium.

For additional irradiation of the active medium, the average amount of color centers descents. After laser pulse generation, the threshold value does not grow significantly and further laser pulses can be observed. It clearly demonstrates an opportunity to adjust the initial absorption coefficient of “saturable absorber”. Generally speaking there are several types of color centers being induced in the Ce³⁺:LiY_1-xLu_xF₄ family of crystals during UV pumping and additional irradiation could either lower or increase the amount of color centers absorbing the laser radiation. The last one can be achieved by redistribution of accumulated energy between different types of CC or by additional illumination of the sample at the 266 nm, which corresponds to a maximum of Ce³⁺ ions excited-state photoionization band [16]. The simulated results presented at Figs. 3, 4 were obtained at following variable parameters values: probability of capture of an electron by defect from CB 1/τ₆₇ (7.1 ± 0.9)·10⁹ s⁻¹, probability of recombination of an electron at the site of Ce³⁺ 1/τ₆₄ (2.5 ± 1.2)·10⁹ s⁻¹, color centers absorption cross section at the wavelength 532 nm σ_75gr (2.7 ± 0.7)·10⁻¹⁸ cm², color centers absorption cross section at the wavelength 311 nm σ₇₅ (4.0 ± 1.2)·10⁻¹⁸ cm².

6. Conclusion

The 400 ± 50 ps single short laser pulses were obtained in Ce:LiY_0.3Lu_0.7F₄ crystals at 311 nm with slope efficiency as high as 6% for low Q-factor cavity under 6 ns pulses at 10 Hz pumping by Ce:LiCAF laser at 289 nm. Intracavity losses modulation alike Q-switching was demonstrated by laser color centers bleaching. Ce:LYLF single crystals can be operated as active media and Q-switching device at the same time. The results demonstrate a “saturated absorber” operation. Additional irradiation of active medium at 532 nm increases the slope efficiency up to 6.2% and it is accompanied by a 600 ps second laser pulse generated 2.5 ns after the first one. Bleaching of color centers is accompanied by lowering the average losses in the cavity and increasing the slope efficiency. Also, loss modulation provides an opportunity to regulate the temporal distribution of laser pulses.