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Abstract
Quasi-continuous-wave laser operation of 20 at.% Tm:LiYF4 thin films (84–240 μm) grown by Liquid Phase Epitaxy (LPE) on undoped LiYF4 substrates is achieved. The 240 μm-thick Tm:LiYF4 active layer pumped at 793 nm with a simple double-pass scheme generated 152 mW (average power) at 1.91 μm with a slope efficiency of 34.4% with respect to the absorbed pump power. A model of highly-doped Tm:LiYF4 lasers accounting for cross-relaxation, energy-transfer upconversion and energy migration is developed showing good agreement with the experiment. The pump quantum efficiency for Tm3+ ions is discussed and the energy-transfer parameters are derived. These results show that LPE-grown Tm:LiYF4 thin films are promising for ~1.9 μm thin-disk lasers.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Laser emission at ~2 µm falls in the so-called eye-safe spectral region which makes such lasers very attractive for free-space applications such as range-finding or wind mapping (Light Detection and Ranging - LIDAR), gas sensing and direct optical communications [1]. Moreover, water absorption at 2 μm defines the potential applications of such lasers in medicine, e.g., for cutting biological tissues. As absorption bands of several relevant atmospheric gases (H2O, CO2, N2O) spectrally overlaps with the emission of 2 µm laser sources, they can be used for atmosphere sensing and spectroscopy. 2 µm lasers are also suitable for soft materials (plastic) processing and they are routinely used as pump sources for optical parametric oscillators (OPOs) based on chalcogenide crystals emitting in the mid-IR (2-5 µm) [2].
2 µm lasers are typically based on Thulium (Tm3+) or Holmium (Ho3+) ions. Due to the typically large Stark splitting of the ground-state of Tm3+ (3H6), Tm lasers give access to a wide spectral tunability according to the 3F4 → 3H6 transition [3]. They can be pumped at ~0.8 µm, e.g., by commercially available AlGaAs laser diodes, while an efficient cross-relaxation (CR) process, 3H4 + 3H6 → 3F4 + 3F4, can raise the theoretical pump quantum efficiency up to 2 [4]. Due to the broadband emission characteristics, Tm3+-doped materials are also suitable for femtosecond (fs) pulse generation in mode-locked (ML) oscillators [5].
One efficient approach for power scaling in solid-sate bulk lasers is based on the thin-disk laser (TDL) geometry [6] which implies a disk-shaped active element with one of its faces being in thermal contact with a heat sink and serving as a highly-reflective mirror. Such a design results in a unidirectional heat flow. The disk thickness is typically substantially smaller than the size of the pump or laser beams. Such an approach allows one to overcome limitations related to thermal effects which is an important advantage to target power scaling of continuous-wave (CW) and ML laser oscillators [7,8]. The thin-disk laser elements are typically fabricated from bulk materials that are mechanically thinned (polished) down to few hundreds of microns. The main disadvantage of this method is the fragility of the thin disks and their mechanical deformation (bulging) under intense pumping.
An alternative approach is to grow directly a few hundred μm-thick rare-earth-doped active crystalline layer on a bulk crystalline substrate with a mm-range thickness in order to improve the thin-disk mechanical strength, and to reduce the deformation under high pump powers [9]. The active layer in this case is directly attached to the heat sink. The growth of such structures can be performed, e.g., by Liquid Phase Epitaxy (LPE). This approach has been recently demonstrated for monoclinic double tungstate crystals doped with Yb3+, Tm3+ and Ho3+ ions [9–11].
Regarding the thin-disk lasers emitting at ~2 μm and based on Tm3+ ions, there are only few reports in the literature. The first demonstration [12] based on a 10 at.% Tm:YAG crystal provided 2 W of output power with a slope efficiency of 20%. Later on, other materials have been implemented for Tm thin-disk lasers, namely, Tm:LiLuF4, Tm:Lu2O3 or Tm:KLu(WO4)2 [7,9,13–15]. Very recently, the group of O. Pronin reported on a 300 μm-thick 4 at.% Tm:YAG thin-disk laser with a multi-pass (72-passes) pumping yielding 24 W at 2014 nm with an optical-to-optical efficiency of 31% [16]. There is only one reported Tm thin-disk laser based on the LPE approach [9]. It consisted in a 250 μm thick 5 at.% Tm:KLu(WO4)2 TDL pumped with only 4 pump passes and delivering 5.9 W at 1855 nm with a slope efficiency of 47%.
In the present paper, we aimed to demonstrate proof-of-the-principle of a Tm:LiYF4 thin-disk laser based on LPE approach. LiYF4 is a well-known crystal for Tm3+ doping featuring advantageous spectroscopic properties, i.e., long lifetime of the upper laser level and efficient CR [17,18]. Efficient bulk and waveguide Tm:LiYF4 lasers have been reported [19–21], including waveguides based on LPE-grown films [21]. Moreover, the tetragonal LiYF4 host crystal possesses good thermal and thermo-mechanical properties, as compared, e.g., to monoclinic KLu(WO4)2 for which the thermo-optic effects were found to be notable even in the thin-disk configuration [22].
2. Epitaxy growth and spectroscopy
The 20 at.% Tm:LiYF4 layers were grown by LPE on undoped LiYF4 substrates previously grown by the Czochralski method [23]. The double-side polished 3.0 mm-thick substrates were oriented with their surface being parallel to the (001) crystallographic plane. The films were grown using a batch with a composition of 73 mol% LiF – 27 mol% YF3 with 20 at.% Tm3+ replacing the Y3+ ions. LiF served both as a solvent and as a solute. The grown layers were isostructural to LiYF4 (tetragonal space group C64h – I41/a). The growth was performed at the temperature of 731 °C for 1-3 h, slightly below the saturation point. The growth rate was 1-2 µm/min. As a result, colorless, transparent and crack-free layers with a thickness ranging from 80 to 240 μm and a surface area of 7 × 10 mm2 were obtained.
The grown layers were inspected with a confocal microscope Sensofar (model S-neox), all studies were done in bright field at 405 nm in reflection. First, the morphology of the top surface of the as-grown Tm:LiYF4 layers was studied, Fig. 1(a). This surface is not perfectly flat and its morphology resembles a hilly landscape in the μm-scale, with a peak-valley of few μm. Such a morphology can be explained by thermodynamical considerations: the surface energy of a curved surface is less than that of a perfectly flat one. As a consequence, the growth front takes the more stable configuration at the atomic scale during the LPE growth process. Thin dendritic structures of LiF can also be observed onto the layer. They come from crystallization of the residual solvent when the substrate is slowly removed from the molten bath.
Fig. 1 Bright-field microscope images of 20 at.% Tm:LiYF4 / (001) LiYF4 epitaxy: (a) top surface of the as-grown layer, arrow indicates surface dendritic LiF structures; (b) laser-grade polished top surface of the active layer (thickness: 100 μm); (c) growth defects at the substrate / layer interface (indicated by an arrow) due to striation defects in bulk LiYF4 substrate; (d) growth defect at the layer surface (indicated by an arrow).
After polishing to laser-grade quality, the central part of the sample is clean and transparent, Fig. 1(b). It contained no cracks or inclusions. Two types of defects were observed. The first defects appeared at the substrate / layer interface as slightly non-transparent “clouds”, Fig. 1(c). They are related to growth striation defects present in the bulk LiYF4 substrates and they are formed during the Czochralski crystal growth. The second type of defects appeared at the layer surface as squared holes with a lateral size of tens of μm and a depth of a few μm. They are typical for thick LiYF4 epitaxial layers. The defects described above were relatively rare and thus it was easy to find a large-aperture area of the sample which was suitable for laser operation.
A side facet of the sample was additionally polished after polishing of its top surface. The side facet was studied using an optical microscope and crossed polarizers, Fig. 2. The grown Tm:LiYF4 layer (thickness: 100 μm) is uniform and the substrate / layer interface is clean. The residual black dots in the substrate are due to the imperfect side polishing.
Fig. 2 Optical microscope image of the polished side facet of the 20 at.% Tm:LiYF4 / (001) LiYF4 epitaxy. The arrow indicates the crystallographic [001] direction.
For the laser experiments, the top surface of all grown epitaxies was polished to laser-grade quality. The surface roughness (few nm) was inspected using the same microscope as described above, in an interferometric configuration. The thickness of the substrate was reduced to 1.0 mm and the substrate face was also polished. The parallelism of the surfaces was better than 15”. No dielectric coatings were used.
The samples were tested for light propagation perpendicular to their surface (i.e., along the crystallographic c-axis). LiYF4 is an optically uniaxial crystal with its optical axis being parallel to the c-axis. Thus, there exist two principal light polarizations, π (E || c) and σ (E ⊥ c). For the indicated sample cut, any light wave propagating along the cavity axis will correspond to σ-polarization.
Absorption spectra of the 20 at.% Tm:LiYF4 layer (thickness: 210 μm) measured with a Lambda 1050 Perkin-Elmer spectrophotometer are shown in Fig. 3(a). They are compared with the absorption cross-section, σabs, spectra for a 3 at.% Tm:LiYF4 single-crystal. The spectra are similar in shape. The actual Tm3+ concentration NTm = αabs/σabs is 28.0 × 1020 cm−3 (or, equivalently, 20.0 at.%). The composition of the active layer is LiY0.8Tm0.2F4 and the segregation coefficient for Tm3+ ions KTm = Ncrystal/Nsolution is close to unity. The preferred pump wavelength is 793 nm corresponding to σabs = 0.38 × 10−20 cm2.
Fig. 3 Spectroscopy of 20 at.% Tm:LiYF4 thin films: (a) Absorption spectra for the 3H6 → 3H4 and 3H6 → 3F4 transitions (in black) compared with the absorption cross-section, σabs, spectra for a 3 at.% Tm:LiYF4 single-crystal (in red), both for σ-polarization; (b) luminescence spectra for the 3F4 → 3H6 transition and π and σ polarizations, the excitation wavelength is 780 nm.
The polarized luminescence spectra for the Tm:LiYF4 layer measured using an optical spectrum analyzer (OSA, model AQ6375B, Yokogawa) are shown in Fig. 3(b) for π and σ polarizations. The luminescence was collected from the edge of the sample using a Glan-Taylor polarizer and an optical fiber. A broad emission band spanning from 1.6 to 2.1 μm is due to the 3F4 → 3H6 transition. For σ-polarization in the spectral range where laser operation is expected, the peak stimulated-emission (SE) cross-section σSE is 0.25 × 10−20 cm2 at 1907 nm [17].
High Tm3+ concentration will affect the lifetimes of the 3H4 pump level and the 3F4 upper laser level. The corresponding luminescence decay curves are shown in Figs. 4(a)-4(b). Both decay curves are well-fitted with a single-exponential law yielding the luminescence lifetimes τlum of 2.2 μs (3H4) and 1.31 ms (3F4). These values are much shorter as compared to the radiative lifetimes τrad = 1.51 ms and 9.33 ms (estimated from the Judd-Ofelt theory [17]), respectively.
Fig. 4 Decay of luminescence from the 3H4 (a) and 3F4 (b) states of Tm3+ ions for 20 at.% Tm:LiYF4 thin films: circles – experimental data, black lines – single-exponential fits.
For very low Tm3+ doping concentration (when the reabsorption, CR and energy-migration are almost negligible), the luminescence lifetimes of the excited states are called intrinsic (unquenched). In general, they are shorter than the radiative ones because of non-radiative (NR) relaxation. The effect of NR relaxation is stronger for the 3H4 state as compared to the 3F4 one, due to the smaller energy-gap to the lower-lying multiplet. The shortening of the intrinsic lifetime of the 3H4 state with respect to the radiative one is significant for oxide materials with large phonon energies hνph. Typically, for Tm:LiYF4 crystals, due to the low maximum phonon energy of the host, hνph = 446 cm−1 [24], the NR relaxation from both the 3H4 and 3F4 states is weak [25] and their intrinsic lifetimes are close to the radiative ones τrad.
For highly Tm3+-doped LiYF4 LPE films, the observed shortening of the 3F4 luminescence lifetime is due to energy-migration to impurities (e.g., OH- groups) and other rare-earth ions. The 3H4 lifetime is shortened mostly due to the CR and partially due to energy-migration.
A simple approach to determine the theoretical pump quantum efficiency ηq(theor) (the ratio of the number of ions excited to the upper laser level, 3F4, to the number of absorbed pump photons) of a Tm3+-doped material is (i) to assume no bleaching of the ground-state, 3H6 (small-signal regime) and (ii) to consider solely cross-relaxation among all possible energy-transfer processes [26]. The CR rate is determined by the Tm3+ doping concentration. In this way, ηq(theor) is a value being dependent only on the Tm3+ concentration (for a certain material). For our case of 20 at.% Tm3+ doping, ηq(theor) should approach 2.
During the laser operation, the actual value of ηq may significantly deviate from ηq(theor). This is because the actual population of the upper laser level is determined by several energy-transfer processes, such as CR, energy-transfer upconversion (ETU) or energy migration to impurities. Moreover, the upper laser level population depends on the inversion level defined by the condition “gain is equal to losses”, which includes cavity parameters such as output coupling. This also means that the condition of zero ground-state bleaching is not applicable for many laser geometries. In the present paper, we want to show that for the case of very high Tm3+ doping levels, energy-transfer processes other than CR (i.e., energy-migration to impurities) may significantly affect the actual ηq value and, consequently, the laser efficiency.
3. Experimental results
3.1 Laser set-up
The hemipsherical laser cavity was composed by a flat pump mirror (PM) coated for high transmission (HT, T > 98%) at 0.79 μm and for high reflection (HR) at 1.9 µm, and a set of concave output couplers (OCs) with radius of curvature (RoC) of 100 mm and a transmission TOC of 2%, 5%, 8% or 10% at 1.9 μm (Fig. 5). All OCs provided partial reflection of the pump (Rp = 55%). The sample was placed close to the PM with the active layer facing the pump beam. The geometrical cavity length was 100 mm.
Fig. 5 (a) Scheme of the laser based on 20 at.% Tm:LiYF4 / LiYF4 epitaxy: P – Glan-Taylor polarizer, PM – pump mirror, OC – output coupler; (b) typical oscilloscope traces of the laser emission showing relaxation oscillations and the incident pump radiation; (c) typical laser emission spectrum (unpolarized output).
The pump source was a CW Ti:Sapphire laser (model 3900S, Spectra Physics) delivering up to 4 W at 793 nm. The incident pump power was varied using a Glan-Taylor polarizer and a rotatory λ/2 plate. The pump radiation was focused into the crystal through the PM using a spherical lens (focal length: f = 50 mm). The pump beam was modulated with a mechanical chopper (duty cycle: 1:2, pulse duration: ~10 ms). The measured pump spot size 2wp was 34 μm. The confocal parameter 2zR was 3.4 mm. The samples were attached to a passively cooled Cu-holder using a high-purity silver paint (SPI Supplies) for better heat removal. Quasi-CW pumping was used to avoid thermal fracture of the passively-cooled epitaxies.
A typical oscilloscope trace of the laser output at ~1.91 μm measured using a fast InGaAs photodetector (model UPD-5N-IR2-P, Alphalas, rise time: <200 ps) and an 8 GHz digital oscilloscope (model DSA7080B, Tektronix) as shown in Fig. 5(b). The temporal waveform exhibits relaxation oscillations which are inherent to Tm:LiYF4 lasers [27]. The oscilloscope trace of the incident pump radiation is also shown for comparison.
The laser operated at the TEM00 mode. The example evaluation of the beam quality factors M2x,y is shown in Fig. 6. We used an ISO-standard method to calculate M2x,y [28]. The laser beam was focused using a spherical lens (f = 50 mm) positioned at 1 cm after the OC. The beam diameters (at 1/e2 level) were measured along the horizontal (x) and vertical (y) directions using the optical knife method. The obtained beam quality factors are M2x = 1.29 ± 0.1 and M2y = 1.04 ± 0.1. The 2D beam profile was captured with a thermal imaging screen, see inset in Fig. 6. The beam profile was nearly circular.
Fig. 6 Evaluation of the beam quality factors M2x,y for output beam of the laser based on 20 at.% Tm:LiYF4 / LiYF4 epitaxy: symbols – experimental data on the squared beam diameters, curves – their parabolic fits. Layer thickness: 240 μm, TOC = 5%, Pinc = 2.2 W. Inset – 2D profile of the laser beam in the far-field captured with a thermal imaging screen.
The laser spectra were measured using an optical spectrum analyzer (model AQ6375B, Yokogawa).
3.2 Laser performance
The laser input-output features for the 20 at.% Tm:LiYF4 active layers are presented in Fig. 7. The laser emission was unpolarized. The results for the thickest layer (240 μm) and various OCs are shown in Fig. 7(a). The best laser performance corresponded to TOC = 2%: the laser delivered a maximum average output power of 152 mW with a slope efficiency η of 8.9% (with respect to the incident pump power Pinc). For higher TOC, the laser performance deteriorated. For all OCs, the laser emission occurred around 1.91 μm, see Fig. 5(c), in agreement with the gain spectra for σ-polarization.
Fig. 7 Input-output dependences for the 20 at.% Tm:LiYF4 active layers (quasi-CW operation, duty cycle: 1:2): (a) layer thickness: 240 µm, various TOC; (b) TOC = 2%, various layer thickness. η – slope efficiency. The vertical axis corresponds to the averaged peak output power.
In Fig. 7(b), we show the laser performance achieved with different thicknesses of the active layer, ranging from 84 to 240 μm (for the same optimum TOC = 2%). The output power gradually decreased and the laser threshold increased for thinner layers due to the lower pump absorption.
4. Modeling of the laser
The experimental results enabled us to determine the efficiency of the laser system. The laser performance can be compared with that predicted by a quasi-three-level laser model suitable for Tm3+-ion-based laser to determine parameters linked to the spectroscopic properties of the material. To account for the highly-doped laser-active material used in the experiments, the three following mechanisms were taken into account: CR, ETU and energy migration.
For quasi-three-level lasers pumped by a Gaussian laser beam, the input-output dependence is non-linear near the threshold due to the spatially nonuniform ground-state bleaching. This is observed in our case of Tm:LiYF4 laser, Fig. 7. Above the laser threshold (typically, from about 3 times of the threshold power), i.e., well into the saturated regime, the input-output dependence becomes linear. The slope efficiencies shown in Fig. 7 have been determined by fitting only the linear part of the output dependences. This part can be well described within the plane wave approximation (i.e., neglecting the spatial dependence of the excitation distribution).
In a quasi-three-level Tm3+ system, laser output power is given by Pout = η(Pinc – Pth), where η and Pth (the laser threshold) are given by [29]:
where, h is the Planck constant, νL and νP are the laser and pump frequencies, respectively, so that ηSt = hνL/hνP is the Stokes efficiency, ηq is the pump quantum efficiency, ηabs is the pump absorption efficiency, L is the passive loss, σLabs and σLSE are the absorption and SE cross-sections at νL for laser polarization (σ), τ2 is the lifetime of the 3F4 state and l is the geometrical length of the active layer.The energy-level diagram of Tm3+ ions in LiYF4, Fig. 8(a), can be approximated to a 3-level system due to the proximity of 3H5 and 3F4 levels, Fig. 8(b). Level 3 is considered to be much less populated than levels 1 and 2. Thus, we have: N1 + N2 ≈NTm.
Fig. 8 (a) Simplified scheme of energy levels of Tm3+ ions in LiYF4 showing possible spectroscopic processes (pump, laser, CR – cross-relaxation, black arrows – radiative decay, NR – non-radiative relaxation, ETU – energy-transfer upconversion, EM – energy migration); (b) Quasi-three-level scheme of a Tm:LiYF4 laser used for modeling.
CW lasers can be modeled with a set of equations in which the population inversion is coupled to the laser intensity. For a low-gain laser architecture such as thin-disk one, assuming a linear cavity with low passive losses, we have (gain is equal to losses):
In order to estimate the laser slope efficiency versus the absorbed pump power Pabs, one need to determine ηabs. In the case of thin active medium, populations can be considered to be constant over l. Hence, for a single-pass, ηabs is given by:
where N1 is determined by Eq. (2). For the case of OC providing a partial reflection (Rp) at the pump wavelength, the total pump absorption is determined as:Let us study the behavior of η as a function of the different spectroscopic parameters. The populations N1, N2 and N3 are related within the following set of rate equations:
where, IL and IP are light intensities at νL and νP, respectively, expressed in photons/(s∙cm2), σPabs is the absorption cross-section at νP for laser polarization (σ), CCR and KETU are the CR and ETU parameters expressed in cm3s−1 and Wd is the rate of migration to defects expressed in s−1. In Eq. (5a), the rate of energy migration from the 3F4 state W'd is directly included into the τ2 lifetime, cf. Figure 4(b), as 1/τ2 = 1/τ20 + W'd. At high concentration, the term representing the spontaneous radiative decay from level 3 could be neglected because this process is much weaker as compared to CR, ETU and energy migration. We will keep this term in the following expressions to remain general.For Tm:LiYF4, the CR was studied by Razumova et al. [30] by monitoring the shortening of the τ3 (3H4) lifetime with the Tm3+ doping concentration. From these data, CCR was calculated as 6.4 × 10−17 cm3s−1.
Considering the definition of pump quantum efficiency, ηq, it can be expressed as a ratio of the total number of photons emitted from the upper laser level by spontaneous and stimulated-emission to the number of absorbed pump photons:
Using the rate-equation, Eq. (5a), at the steady-state (dN2/dt = 0), the following expression is derived:The 3H4 population is then obtained by using the rate-equation, Eq. (5b), at the steady-state (dN3/dt = 0):By using Eqs. (7)-(8), the quantum efficiency can be written:From Eqs. (6), (9) and (1b), we finally obtain:At low pump power, the pump quantum efficiency depends on the output power Pout, so the whole Eq. (10) has to be taken into account. It shows that, near the laser threshold, the slope efficiency is lower than at high output power and it depends on the ratio between ETU, 2KETUN22, and spontaneous radiative decay from the upper laser level, N2/τ2.
When the laser is operated well above the laser threshold, ηq is a constant term:
This equation shows that the pump quantum efficiency depends on the ratio between CR and migration to defects. ηq decreases as Wd increases because migration depopulates the upper laser level 2. On the other hand, as expected, ηq increases with the enhanced CR. Note that Eq. (11) agrees well with the previous work of Honea et al. [26] which derived the following equation for ηq:As explained above, τ30 (unquenched) ≈τ3rad for Tm:LiYF4 and assuming small β32 (the luminescence branching ratio for the 3H4 → 3F4 + 3H5 transitions) and zero Wd, Eq. (12) takes the form of Eq. (11).In [31], van Dalfsen et al. used another definition of ηq:
This expression was used for oxide materials, e.g., Tm:KY(WO4)2, featuring strong NR relaxation from the 3H4 pump level. This equation can be obtained from more general Eq. (12) by assuming τ30 << τ3rad.According to Eq. (12), the transmission of the OC still affects ηq. Indeed, N1 decreases with increased TOC, because higher inversion population is needed to compensate for the output-coupling losses and thus ηq decreases accordingly. Thus, a lower laser threshold leading to higher N1 is an advantage for reaching a high pump quantum efficiency at high pump power. The value of ηq is thus close to 2 when CR is very efficient. On the other hand, when energy-migration to defects is notable, ηq is clearly lower than 2.
From Eqs. (2) and (11), the dependence of the pump quantum efficiency on output coupling is expressed as:
The influence of the transmission of the OC and energy-migration coefficient Wd on the pump quantum efficiency is shown in Fig. 9. ηq decreases with increasing TOC because of increased population inversion. Wd has to be as small as possible (Wd << CCRNTm) to reach high ηq values.
Fig. 9 Pump quantum efficiency ηq for 20 at.% Tm:LiYF4 well above the laser threshold as a function of TOC for energy-migration rates Wd varying from 28 to 280 × 103 s−1, l = 240 µm, L = 0.2%. Calculation with Eq. (14). CCR = 6.4 × 10−17 cm3s−1, τ30 = 1.51 ms, σLSE = 2.48 × 10−21 cm2 and σLabs = 0.31 × 10−21 cm2.
The dependence of ηq on the incident pump power Pinc can be calculated using Eq. (10) where Pout is represented as η(Pinc – Pth) and expressions for the slope efficiency and the laser threshold, Eq. (1), are substituted.
In a similar way, we analyse the effect of spectroscopic parameters (Wd and KETU) on the laser threshold Pth which is given by Eq. (1b) where the pump quantum efficiency is determined from Eq. (10) under the condition of Pout = 0. The results are shown in Fig. 10. The increase of both Wd and KETU is responsible for an increase of the laser threshold as these processes depopulates the upper laser level 2. In Eq. (1b), the laser threshold Pth depends on transmission of the OC directly. Additional dependence originates from ηq and ηabs. This atypical behaviour changes the standard Findlay-Clay analysis for which a linear fit of the dependence of Pth versus the output-coupling losses gives passive losses L [32]. In our case, the non-linear Pth(TOC) dependence makes it difficult to extract L because both ηq and ηabs are not constant with TOC. Consequently, in our modified approach, a fit using the slope efficiency and the laser threshold as a function of TOC gives Wd, KETU and L.
Fig. 10 Modified Findlay-Clay analysis for 20 at.% Tm:LiYF4: laser threshold Pth as a function of transmission of the output coupler TOC (a) for KETU varying from 0 to 6.0 × 10−18 cm3s−1 and fixed Wd = 170 × 103 s−1 and (b) for Wd varying from 28 to 280 × 103 s−1 and fixed KETU = 1.0 × 10−18 cm3s−1. Modeling parameters: l = 240µm, L = 0.2%, CCR = 6.4 × 10−17 cm3s−1, and wp = 17 µm.
5. Discussion
We report the first laser based on a Tm3+-doped fluoride LPE-grown active layer oriented for normal incidence. The best output performance was obtained for small TOC of 2% and it deteriorated for higher output coupling. This can be explained by the developed model. Two combined effects are responsible for this behaviour: saturation of pump absorption and decrease of the pump quantum efficiency ηq with increased TOC.
The quantum efficiency of a Tm3+-doped material is a function of the doping level as shown by Honea et al. [26]. For Tm:LiYF4, an increase of ηq with NTm was observed up to at least 6 at.% where this value is reaching ~2 [18,30]. For the Tm3+ doping levels higher than 3 at.%, the intensity of the 3F4 → 3H6 luminescence tend to decrease [30,33]. This corresponds to the effect of concentration-quenching of luminescence related to energy migration. For such a high doping level as 20 at.% Tm3+, energy-migration to defects and impurities is strong and it affects both populations of the 3H4 and 3F4 levels. This is confirmed by the short measured luminescence lifetime for the 3F4 state, Fig. 4(a), as well as the relatively low pump quantum efficiency ηq ≈1 (see below).
The model described in Section 4 allowed us to express inverse of the slope efficiency 1/η as a function of inverse of the output coupling 1/TOC by using the general formula given by Eq. (1a) and the expressions for ηabs and ηq given by Eq. (3) and Eq. (14), respectively. This corresponds to a modified Caird diagram [34], Fig. 11. When the pump absorption is not saturated, 1/η should vary according to a linear law (black solid line). The solid curve shows the effect of absorption saturation when ηq = 2 and there is no ETU nor energy-migration (KETU = 0 and Wd = 0). The dashed curves represent the effect of absorption saturation and energy-migration for various Wd. Finally, the dotted curve includes all three effects, namely absorption saturation and non-zero KETU and Wd. It gives the best agreement between the calculated and the experimental data. The best-fit spectroscopic parameters are Wd = 170 × 103 s−1, KETU = 1.0 × 10−18 cm3s−1 and the passive losses L are 0.2%.
Fig. 11 Modified Caird diagram for the laser based on 240 μm-thick 20 at.% Tm:LiYF4 active layer: inverse of the laser slope efficiency, 1/η, plotted as a function of inverse of the output coupling, 1/TOC. Black solid line and curve: no absorption saturation (ηabs = const, standard Caird plot) or absorption saturation (ηabs ≠ const) for KETU = 0 and Wd = 0; dashed colour curves - ηabs ≠ const, Wd varying from 28 to 280 × 103 s−1 and KETU = 0; dotted red curve - ηabs ≠ const, Wd = 170 × 103 s−1 and KETU = 1.0 × 10−18 cm3s−1; circles – experimental data.
From the determined values of L, Wd and KETU, we deduced the pump absorption ηabs, the pump quantum efficiency ηq and the laser threshold Pth. Figure 12 shows the calculated Pth vs. the output coupling within three approximations, namely (i) without ETU and energy-migration (KETU = 0 and Wd = 0), (ii) only with energy-migration and KETU = 0 and (iii) with both effects. Again, there is a good agreement with the experimental data for the (iii) model and the parameters determined above. The determined KETU parameter is in agreement with the value reported by So et al. [18], 5.5 × 10−18 cm3s−1 for 6 at.% Tm3+ (KETU has a linear dependence on the doping concentration, KETU = CETU∙NTm [35]).
Fig. 12 Modified Findlay-Clay diagram for the laser based on 240 μm-thick 20 at.% Tm:LiYF4 active layer: laser threshold, Pth, plotted as a function of output coupling, TOC. Black line: KETU = 0 and Wd = 0; dashed green curve - Wd = 170 × 103 s−1 and KETU = 0; dotted red curve - Wd = 170 × 103 s−1 and KETU = 1.0 × 10−18 cm3s−1; circles – experimental data. The passive loss L is 0.2%. For all curves, ηabs ≠ const.
The same analysis for η and Pth has been performed for lasers based on 84, 100 and 210 µm-thick active layers showing good agreement with the model for the same Wd and KETU values. The only parameter changed in the simulations was the passive loss (L = 0.2% for l = 210 µm and L = 0.7% for l = 84 and 100 µm) which accounts for different optical quality of the grown active layers. These values are much lower than Fresnel losses expected at ~1.91 μm for LiYF4 (3.3% per face). This is because despite the fact that no dielectric coatings were used, the epitaxy was polished with a good parallelism of its faces thus acting as an etalon. Note that due to the small thickness of the grown layers, it was not possible to determine the passive losses directly.
In Table 1, we summarized the experimental results described in Section 3.2 and the results of the calculation with the model presented in Section 4, namely the values of the pump absorption efficiency ηabs, laser slope efficiency with respect to the absorbed pump power η' and pump quantum efficiency ηq. Let’s first analyse ηabs. With the decrease of the layer thickness from 240 to 84 μm, it decreases from 25.9% to 8.4% accordingly (for TOC = 2%). For the same layer thickness of 240 μm, ηabs decreases with increased output coupling as expected for quasi-three-level lasers, namely from 25.9% to 20.0% for TOC ranging from 2% to 10%. This decrease originates from depopulation of the ground-state 1. As all the studied OCs were partially reflective for the pump, we were able to estimate the pump absorption by measuring the residual pump. The obtained values were in agreement with Table 1.
Table 1. Output Characteristicsa of Lasers Based on Highly-Doped Tm:LiYF4 Active Layers.
As explained above, the slope efficiency vs. the incident pump power (η) decreases with increased output coupling (due to absorption saturation, ETU and energy-migration) and with the decrease of the layer thickness. Concerning the efficiency vs. the absorbed pump power, η', it is also maximum for the smallest TOC of 2% (34.4%) and slightly decreases for higher output coupling reaching 27.4% for TOC = 10% (all values are specified for the 240 μm-thick active layer). This is accompanied by a decrease of ηq from 0.92 to 0.68.
The developed model can be extrapolated to a multi-pass pump configuration which is typical for thin-disk lasers. In Fig. 13, we plotted the optical-to-optical efficiency, ηopt = Pout/Pinc, for 5 at.% Tm: and 20 at.% Tm:LiYF4 active layers vs. the number of pump passes Np (assuming a perfect overlap of the pump modes due to the multiple passes). The following parameters are used: 2wp = 200 µm, Pinc = 1 kW, l = 240 µm, L = 0.2% and TOC = 2%. Note that for 5 at.% Tm3+, Wd is almost zero.
Fig. 13 Optical-to-optical efficiency, ηopt, versus the number of pump passes Np for 5 at.% Tm: and 20 at.% Tm:LiYF4 active layers. Modeling parameters: 2wp = 200 µm, Pinc = 1 kW, l = 240 µm, L = 0.2% and TOC = 2%.
Figure 13 shows an asymptotic behavior of ηopt towards 35% and more than 55% for 20 at.% and 5 at.% Tm3+-doped layers, respectively. In order to absorb almost all pump radiation, both samples require >45 passes. When all the pump is absorbed, the 5 at.% Tm3+-doped sample should lead to a higher optical-to-optical efficiency than the other one. This is because of decrease of ηq with the doping concentration under the same lasing conditions. However, the curves in Fig. 13 crosses at about 18 passes. So for small number of pump passes, 20 at.% Tm:LiYF4 is more promising than a sample with lower doping. Particularly LPE-based thin-disk laser elements have been found to be suitable for simplified pump geometries with small number of passes [11].
6. Conclusions
To conclude, we report on the first laser operation with highly-doped (20 at.% Tm) LiYF4 thin films with the thickness in the range of hundreds of μm grown by LPE on undoped bulk LiYF4 substrates. Pumped at 793 nm, a passively-cooled 240 μm-thick active layer generated 152 mW (average power) at 1.91 μm with a slope efficiency of 8.9% and 34.4% vs. the incident and absorbed pump power, respectively.
To explain the output performance of the 20 at.% Tm:LiYF4 lasers, we developed a model accounting for the key spectroscopic effects, namely, CR, ETU and energy-migration both from the pump and upper laser levels. This model allowed us to propose a modified Caird (for inverse of the laser slope efficiency) and Findlay-Clay plots (for the laser threshold) yielding not only the passive losses, but also ETU parameter KETU and energy-migration rate Wd. For 20 at.% Tm3+, Wd = 170 × 103 s−1 and KETU = 1.0 × 10−18 cm3s−1. This model can be used for any highly-doped Tm3+-ion-based active material.
Both ETU and energy-migration affects the laser threshold, by increasing it at a fixed output coupling. The slope efficiency (vs. the incident pump power) for highly-doped Tm:LiYF4 decreases with output coupling. This is related to (i) saturation of pump absorption related to depopulation of the ground-state needed to overcome the output-coupling losses, and (ii) decrease of the pump quantum efficiency due to the detrimental action of ETU and energy-migration. The latter effect has a dominant impact on ηq at high pump powers (well above the laser threshold). Near the laser threshold, the impact of ETU becomes more evident. Moreover, near the laser threshold, ηq is a function of the output power.
Our studies indicate the suitability of LPE-grown Tm:LiYF4 films for applications in thin-disk lasers with a simplified pump geometry (with reduced number of pump passes). High pump quantum efficiency in such lasers is expected to be achieved by optimization of the Tm3+ doping level between 3 and 20 at.%, so that the effect of efficient CR is not violated by detrimental ETU and energy-migration. For this, a concentration-dependent study of KETU and Wd is required. Further improvement of laser performance is expected by optimization of the quality of the grown films by removing the possible rare-earth impurities and defects.
Funding
French Agence Nationale de la Recherche (ANR) through the LabEx EMC3 (ANR-10-LABX-09-01), the European Community funds FEDER and the Normandie region.
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