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Abstract
We have investigated the spectroscopic properties of Tm:YLF material around 1900 nm in detail to understand its amplification performance at cryogenic temperatures. Fluorescence lifetime and emission cross section (ECS) measurements are performed in the 78–300 K range using crystals with Tm doping levels of 0.5 and 2.5%. The radiative lifetime of the 3F4 level of Tm:YLF is found to be temperature dependent, and has a value of around 18 ms at 78 K, and 15.25 ms at 300 K, respectively. The emission measurements indicate the presence of rather strong and reasonably broadband peaks even at cryogenic temperatures. The 1877 nm emission peak of the E//c configuration has a strength of around 2.4 × 10−20 cm2 and a full-width half maximum (FWHM) of around 4 nm at 100 K. The E//a axis configuration possesses a broader emission around 1908 nm with a FWHM of around 19 nm at 100 K, but with a lower peak ECS value of 0.75 × 10−20 cm2. We have also investigated the temperature variation of fluorescence lifetime for the 3H4 level, and the results showed that the two-for-one cross-relaxation process is also quite effective at cryogenic temperatures. These findings clearly demonstrate that cryogenic Tm:YLF systems have the potential to reach kW level average powers and sub-1-ps pulsewidths.
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1. Introduction
High-average and peak power laser and amplifier systems near 2 µm region are attractive alternatives to their 1 µm counterparts due to wavelength scaling. As an example in high-harmonic generation, the highest extreme ultraviolet frequency (the maximum energy of the generated photons) scales with the square of the wavelength [1,2]. Frequency down conversion to mid-infrared region using crystals such as GaSe could achieve broader bandwidth phase matching when pumped around 2 µm [3]. In single-cycle terahertz generation by gas ionization, the peak field of the generated THz is shown to scale with λ4.6 ± 0.5 [4]. Moreover, the laser induced damage threshold of materials usually increase with increasing wavelength [5], and this enables usage of higher fluences on the sample, which can improve efficiencies of nonlinear interactions in general. As a result, we have been seeing increased interest toward development of high average and peak power laser and amplifier sources near 2 µm region in the last decades [6–14].
Among the alternatives for 2 µm gain media, Tm:YLF crystal owns strong emission bands in 2 µm region, has naturally polarized output, and possesses a smaller quantum defect due to weaker crystal field strength of YLF host. Moreover, unlike many other hosts, such as the well-known YAG, the YLF host has a negative thermo-optic (dn/dT) coefficient [15,16], and as a result the thermal lens observed in YLF based systems are comparatively small. This facilitates power scaling of Tm:YLF systems to multi-hundred Watt average power level even at room-temperature [17–24]. The material is usually pumped with well-developed high power AlGaAs laser diodes around 780 nm using the 3H6→3H4 transition (Fig. 1). The 3H4 level has a radiative lifetime of around 2 ms, and could be employed for broadband lasing in the 2200-2460 nm region in low Tm-doped samples (as the fluorescence lifetime of the 3H4 level reduces sharply with doping due to cross-relaxation) [25–27]. The 3F4 level has a much longer radiative lifetime of around 15 ms at room temperature, and acts as a reservoir for the ions that decay back from the higher lying laser levels. One can facilitate the metastable 3F4 level of Tm:YLF for broadly tunable laser operation in the 1772-2145 nm spectral region [28]. Note that the 3H5 multiplet decays directly to 3F4 by nonradiative multi phonon relaxation in microsecond time scale, and do not provide measurable level fluorescence [29,30].
Fig. 1. Energy level diagram of Tm3+ ion doped YLF. Zig-zagged lines represent nonradiative transitions. Stated fluorescence emission wavelengths are based on Stark sub-level energies, and exclude phonon coupling/broadening. Radiative lifetimes of the metastable laser active 3H4 and 3F4 levels are also indicated.
Note that, the cross-relaxation process which reduces the lifetime of the 3H4 level in highly-doped samples, can actually create an advantage while lasing from the 3F4 manifold. In this process, adjacent thulium ions interact with each other, and an excited ion in the 3H4 state decays non-radiatively to the 3F4 level, and the excess energy is used to excite an ion from the ground state (3H6) to the 3F4 state. The rate of the cross-relaxation process increases with thulium doping, and as a result it enables a pump quantum efficiency close to 2 in highly Tm-doped samples. Thus, the process is also known as two-for-one process, and it is used to increase the intrinsic laser slope efficiency of the system beyond the Stokes limit and it can also help to reduce the fractional thermal load on the crystal [18,31–34]. Note that, lasing via the 3F4 transition could also be achieved while in-line pumping the system (3H6→3F4) through the recently developed 1700 nm diodes [35,36]. As of today, these diodes still lack the maturity and the power levels that the 780 diode systems provide; however, in the coming years this route might become the standard pumping channel for 2 µm Tm systems.
Over the last decades, detailed studies performed with 1 µm laser systems showed that, due to improved spectroscopic and thermo-opto-mechanical properties, operating the laser/amplifier systems at cryogenic temperatures could enable an order of magnitude scaling in extractable average power levels and energies, and could improve the output beam quality significantly [15,37–39]. When we look at the state-of-the-art Tm:YLF laser systems, we see that multi-hundred Watt average power in continuous-wave (cw) operation [17–23] and multi-Joule level output energy in amplification [7,9,40,41] have already been demonstrated even at room-temperature. Hence, one expects that these average power and energy levels could be improved further via operating the Tm:YLF systems at cryogenic temperatures. Despite that, the potential of Tm:YLF lasers at cryogenic temperatures has not been investigated thoroughly yet.
In 1990, Nguyen et al. reported lasing of a cryogenic Tm:YLF system in the blue region (450-453 nm) via upconversion process, upon two-color pumping at 649 nm and 781 nm [42]. To our knowledge, first cryogenic lasing of Tm:YLF around 1900 nm is then reported by Ketteridge et al. in 1997 [43], where tunable cw operation in the 1850-1920 nm region with up to 7 W of cw laser power was demonstrated using 2 × 15 W 792 nm diode arrays. A cw cryogenic Tm:YLF laser emitting near 816 nm was reported by Aleshire et al. in 2017 with an output power of 350 mW and a slope efficiency of 46% (using the 3H4→3H6 transition) [44]. Recently, Yue et al. also reported cryogenic lasing around 1877 nm with a cw power up to 2.55 W and a slope efficiency of 22.8% [45].
In this work, we have investigated temperature dependence of spectroscopic properties of Tm:YLF crystals in detail to uncover its potential at cryogenic temperatures. Fluorescence lifetime and emission cross section measurements performed in the 78-300 K range showed that, the emission from the 3F4 manifold is broad enough to construct high-power laser and amplifiers systems with sub 1-2 ps pulsewidth. The measured dynamics of 3H4 level indicate that the two-for-one cross-relaxation process is also quite effective at cryogenic temperatures, and hence standard 780 nm pumping could ideally be used for efficient lasing near the 1900 nm region also for the cryogenic systems. Overall, our spectroscopic data confirms the usability of cryogenic Tm:YLF for generation and amplification of high average power ultrashort laser systems around 2 µm.
The paper is organized as follows: In Section 2, we outline our experimental methodology. Temperature dependent fluorescence lifetime and emission cross section measurements are presented in Sections 3 and 4, respectively. Then in Sections 5-6, we present temperature dependent absorption cross section and gain cross section calculations. Finally, in Section 7, we close with a brief discussion.
2. Experimental methodology
Figure 2 shows a schematic of temperature dependent (a) fluorescence lifetime and (b) emission cross section measurement setups. The experimental methodology employed is similar to what we have used recently for Yb:YLF [46,47] and room-temperature Tm:YLF [28]. In the experiments, two cuboid shaped Tm:YLF crystals are used. The first sample has a Tm doping of 0.5%, an aperture of 6 × 6 mm2 and a length of 10 mm. The second sample has a doping of 2.5%, a slightly larger aperture of 8 × 8 mm2 and a length of 10 mm. Both crystals are a-cut, and have antireflective coating on both sides, covering the 792 nm (AR < 0.5%) and 1800-1960 nm (AR < 0.2%) regions. The Tm:YLF crystals are indium soldered from their top side to a multi-stage pyramidal cold head, which was cooled to cryogenic temperatures by boiling liquid nitrogen using a vacuum sealed dewar system. Thermal sensors connected to the cold head near the crystal enabled real time measurement of temperature with ±0.1 K accuracy. For temperature dependent lifetime and emission measurements, the crystals are first cooled to 78 K by liquid nitrogen, then the slow heating cycle of the dewar is used to take temperature dependent spectroscopic data.
Fig. 2. A simplified schematic of the temperature dependent (a) fluorescence lifetime and (b) emission cross section measurements. (c) Sample curve showing the experimentally measured fluorescence signal from the 3F4 level. The time variation of the pump signal is also shown.
For fluorescence lifetime measurements (Fig. 2 (a)), a 4 W single-emitter multimode diode (MMD) is used as the excitation source. The diode has a central wavelength of 792 nm, and a FWHM of around 1.75 nm, which enables efficient excitation in the full temperature scan range (e.g. see Fig. 2 in [44]). The MMD output is first collimated with a 4.5 mm focal length aspheric lens, then a cylindrical lens with a focal length of 50 mm is employed in the fast axis to minimize the diode beams astigmatism. An achromatic doublet with a focal length of 60 mm is used to focus the pump beam to a waist of around 35 µm x 150 µm inside the Tm:YLF crystal. The Tm:YLF crystals are excited with up to 50 ms long pump pulses with 4 W peak power at repetition rate of 1 Hz (average incident power: 0.2 W). Note that here due to the relatively low peak power of our excitation source, we kept the length of the pump pulse rather long to improve the signal-to-noise-ratio in the experiments (pump pulse widths used was between 1 and 50 ms, depending on the signal level). As a result, to prevent internal heating of the crystal, we have used a rather low repetition rate in the experiments. Moreover, as it shown in Fig. 2 (c), the pump pulse we have used for excitation has a square shape in time with very sharp edges (rise/fall times below 20 µs). Hence, usage of long pump pulse length in this study does not affect the measured lifetime values, since the fall time of the square pump pulse is much faster than the measured lifetime of Tm:YLF material. Basically, a simple systems response approach could be used to prove that, by only analyzing the measured fluorescence signal in the decay stage (after turning the pump off, Fig. 2 (c)), one can determine the characteristic lifetime of the system without any loss of integrity.
During the lifetime measurements, the fluorescence decay signal is measured at 90° with respect to the direction of excitation beam, through the uncoated surface of the crystals via a side window of the dewar which is also uncoated. A 1000 nm high-pass filter (Thorlabs, FELH1000) is implemented to cut out the scattered pump signal. The 792 nm pump beam excites the Tm ions into the metastable 3H4 energy manifold, which then fills the 3F4 manifold via radiative transitions in the 1371-1509 nm and 2170-2460 nm spectral regions (Fig. 1). The 3F4 level, with a longer lifetime, decays back to the ground state (3H6) mainly via radiative emission in the 1674-1930 nm region [11]. In the experiments, we have measured temperature dependent fluorescence lifetimes of both the 3H4 and 3F4 levels in the 78-300 K range. The 3F4 level fluorescence lifetime is measured using an InGaAs detector (Thorlabs, DET10D2) with 25 ns rise time for 50 ohm termination and 30 µs rise time under 100 k ohm termination. Note that, the InGaAs detector is sensitive in a broad wavelength region (900-2600 nm). Hence, using the InGaAs detector one can measure the lifetime of the 3F4 and 3H4 levels simultaneously, or use adequate optical filters to select either of the transitions and look at the lifetimes separately (Fig. 2 (c)). For the 2.5% Tm-doped sample, the strength of the radiative emission from the 3H4 level is rather weak. Hence, for this case, the 3H4 level fluorescence lifetime is measured by monitoring the emission around 1500 nm with a free-space Ge detector that has higher sensitivity for the 3H4 emission (Thorlabs, DET30B, 800-1800 nm, a short pass filter is also employed). The Ge detector has a 650 ns rise time for 50 ohm termination, and sub-20 µs response time could be achieved while using a 5 k ohm termination. Moreover, we have performed a set of detailed lifetime measurements at room-temperature, where pinholes with diameters between 50 µm and 2 mm are used for the estimation of radiation-trapping free fluorescence lifetime [28,47].
The emission spectra for the 3F4→3H6 transition are similarly measured at a 90° angle (Fig. 2 (b)), while exciting the Tm:YLF sample with a home-build continuous-wave Ti:Sapphire laser with 1 W of output power at 780 nm (FWHM: 0.25 nm). In the emission measurements, the crystals are excited with a 100 µm beam from their edge to minimize self-absorption effects. To acquire the emission in both a and c axis, a thin film linear polarizer covering the 1000-3000 nm region is used (Thorlabs LPNIRA100-MP2 → extinction ratio:105, transmission: 86 ± 1% in the 1600-2600 nm range). The emission signal from the crystals is imaged into a set of 1 meter length low OH multimode fibers with core diameters between 50 µm and 550 µm using a 4 cm focal length uncoated lens. The fibers that are used for emission signal coupling provided relatively flat spectral response in the region of interest (1550-2150 nm); and hence no spectral correction was required: the fibers have a specified transmission above ∼97.5% in the 400-2150 nm range. A 1500-3400 nm optical spectrum analyzer (Yokogawa AQ6376) with a spectral resolution down to 0.1 nm is used for recording the fluorescence spectra. The Yokogawa spectrometer is purged with nitrogen gas to prevent the influence of air absorption on emission spectra. The effective resolution of the spectrometer is around 0.1 nm, 0.5 nm, 1 nm and 2 nm while using 50 µm, 100µm, 200 µm and 550 µm core fibers, respectively. A 1-2 nm resolution is sufficient at room temperature, whereas some of the peaks at cryogenic temperature required sub-0.5 nm resolution. The increased resolution at small core fibers comes at the expense of reduced signal to noise ratio, which increases the measurement time. As a result, at cryogenic temperatures, several sets of emission data are taken using different settings in the spectrometer, and the overall data is obtained by spectrally combining the emission data taken under different configurations.
The emission cross section is then calculated using the modified Füchtbauer–Ladenburg formula [48–50]:
McCumber relation is then used to calculate the absorption cross section from the measured emission cross section data using [53,54]:
Above Ehi and Eli are the corresponding individual intra-manifold energies of the higher and lower lying laser levels, respectively. In our calculations, we have used values reported in [56]: El1= 0 cm-1, El2= El3 = 30 cm-1, El4= 56 cm-1, El5= 270 cm-1, El6= 305 cm-1, El7= 319 cm-1, El8= El9 = 334 cm-1, El10 = 372 cm-1, El11= El12 = 407 cm-1, El13= 419 cm-1, Eh1= 5599 cm-1, Eh2= Eh3 = 5757 cm-1, Eh4= 5765 cm-1, Eh5= 5820 cm-1, Eh6= 5942 cm-1, Eh7= 5968 cm-1, Eh8= Eh9 = 5972 cm-1. The Zu/Zl ratio is temperature dependent and has a value of around 0.47 at 78K and 0.66 at 300K. The corresponding wavelength for the zero-phonon line energy (Ezl =5599 cm-1) is around 1785.5 nm (in air). The effective gain cross section (GCS) spectra (σg(λ,T)) of Tm:YLF is estimated using the measured emission cross section (${\sigma _e}({\lambda ,T} )$) and the calculated absorption cross section (${\sigma _a}({\lambda ,T} )$) data via:
In closing the experimental section, we present Fig. 3, which shows the details of the Stark level for the 3F4→3H6 transition of Tm:YLF. The graph includes calculated transition wavelengths in air, as well as calculated Boltzmann occupancy percentages of different levels at temperatures of 78 K and 300 K. We will refer to this energy level diagram later while trying to interpret the measured variation of emission spectra with temperature (the transitions are numbered and circled for easier future referencing). Note that, slightly different assignments for the Stark levels exist in literature [57,58], which might result in some small differences in the calculated wavelengths, and Boltzmann occupancy factors.
Fig. 3. A simplified energy level diagram of Tm:YLF for the 3F4→ 3H6 transition, along with the calculated Boltzmann occupancy percentages of Stark levels at 78 K and 300 K [56]. Optical transitions between different pairs of sub-levels and corresponding calculated absorption/emission wavelength/s are indicated/numbered. The emission wavelengths are calculated for air environment. The asterisk sign (*) in the wavelength range indicates transitions from collection of sub-levels with quite small energy difference.
3. Lifetime measurements
In this subsection, we will report our detailed temperature dependent fluorescence lifetime measurements with Tm:YLF for both the 3F4 and 3H4 manifolds. We would like to start the section by providing a representative example. For that, Fig. 4 (a) shows the measured emission decay for the 0.5% Tm-doped YLF sample at room temperature. Note that, as explained in the experimental part, the decay part of the recorded fluorescence signal is used for the determination of lifetime (the initial pumping state (population build-up state), that can be seen Fig. 2 (c), is excluded). The data in Fig. 4 (a) is a superposition of radiative decays from the 3F4 and 3H4 levels as it is apparent from the double exponential decay behavior. For this specific case, making a least mean squares fit to the experimental data, we have determined the fluorescence lifetimes of 3H4 and 3F4 levels as 2 ms and 15.5 ms, respectively. As it is illustrated in this sample case, we have collected several sets of temperature dependent decay data using samples with different doping levels, and made similar fits to determine the temperature dependence of fluorescence lifetime.
Fig. 4. (a) Sample experimentally measured lifetime decay curve and numerical best fit to the data. The data is taken with the 0.5%-doped Tm:YLF sample at room temperature. The lifetime of the 3F4 and 3H4 levels are determined to be 15.5 and 2 ms, respectively. (b) Measured variation of 3F4 level room-temperature fluorescence lifetime with pinhole diameter for the 0.5, and 2.5% Tm-doped YLF crystals. The radiation trapping free (intrinsic) fluorescence lifetime for the 3F4 manifold is estimated to be 15.25 ms and 15.8 ms for the 0.5, and 2.5% Tm-doped YLF crystals, respectively.
Before we present temperature dependent fluorescence lifetime data, we would like discuss the possible influence of radiation trapping on lifetime measurements. In Tm:YLF laser crystal, there is a significant spectral overlap between the absorption and emission bands at room temperature. Consequently, some portion of the spontaneously emitted photons get re-absorbed before it can leave the crystal, and as a result the measured fluorescence lifetime of the level is longer than its intrinsic fluorescence lifetime (we use the term intrinsic here for radiation trapping free lifetime). Moreover, this effect is temperature dependent as the spectral overlap of absorption and emission bands decrease at lower temperatures (as it will be discussed in more detail in the next section).
To minimize the effect of radiation trapping on measurements, we have taken our data while exciting crystals from their edges, but this still could not eliminate the radiation trapping effect fully, especially in highly doped samples (as in our 2.5% Tm-doped YLF crystal). It is possible to estimate the intrinsic fluorescence lifetime of a level by measuring the lifetime using pinholes of different sizes and by making a linear fit to the data [59]. To probe the strength of radiative trapping in Tm:YLF, we have looked at the variation of measured fluorescence lifetime with pinhole diameter for both the 0.5% and 2.5% Tm-doped YLF samples at room temperature (Fig. 4 (b)). As we see, for the 0.5% doped sample, there is only a slight increase of fluorescence lifetime, which clearly shows that the radiation trapping effect is minimal in this sample even at 300 K. On the other hand, the 2.5% Tm-doped sample shows an observable increase of fluorescence lifetime with pinhole dimeter, clearly showing the susceptibility of this crystal to radiation trapping. By making a linear fit to the measured data, we have estimated room-temperature intrinsic (absorption trapping free) fluorescence lifetimes of the 3F4 level as 15.25 ms and 15.8 ms for the 0.5% and 2.5% Tm-doped YLF crystals, respectively.
Ideally, one needs to perform sets of measurements as in Fig. 4 (b) at different temperatures to determine the variation of intrinsic fluorescence lifetime with temperature. For our case, the measurement setup size and geometry did not allow us sufficient signal to noise ratio to perform such measurements with the dewar at hand. Despite that, we have still tried to eliminate the influence of radiation trapping in our measurements as we will discuss now.
To start with, Fig. 5 (a) shows the measured variation of 3F4 energy level fluorescence lifetime with temperature in the 78-300 K range for both the 0.5% and 2.5% doped Tm:YLF crystals. For the 2.5% crystal we took two data sets, in the first set (2.5% Tm:YLF I) we have not used any pinholes in front of the detector, and this data is then naturally influenced by fluorescence trapping effect (but has a large SNR ratio). In the second data set (2.5% Tm:YLF II), we have tried to minimize the fluorescence trapping effect via usage of a 0.5 mm pinhole before the detector, at the expense of reduced SNR ratio and larger error bars. For the 0.5% doped crystal, as we discussed the fluorescence trapping effect is rather small due to the lower doping of the sample, and data is taken without using any pinholes (usage of pinholes results in quite low SNR in this lowly Tm-doped sample).
Fig. 5. (a) Measured variation of Tm:YLF fluorescence lifetime with temperature in the 78-300 K range, for the 3F4 energy level. The data is taken with the 0.5% and 2.5% Tm-doped YLF samples. The 2.5% Tm:YLF data is repeated twice: case I is taken without a pinhole, and case II is taken using a 0.5 mm pinhole. The data taken with the 0.5% doped YLF sample is used to estimate the temperature dependence of radiative lifetime via eliminating the contribution from radiation trapping. The empty red markers indicate an estimation for the intrinsic radiative lifetime. The red solid curve is a best fit to radiative lifetime of the 3F4 manifold. (b) Measured variation of Tm:YLF fluorescence lifetime with temperature in the 78-300 K range, for the 3H4 energy level. The data is taken with 0.5% and 2.5% Tm-doped YLF samples.
As we have expected, for the 2.5% doped Tm:YLF, we see that data taken with the 0.5 mm pinhole (shown by green markers in Fig. 5 (a)) resulted in shorter lifetimes compared to the case without the pinhole (shown with blue markers) as the pinhole eliminates some of the contribution from the radiation trapping effect. Looking at the data, we see that, as the temperature increases, the measured fluorescence lifetime of the 3F4 level in the 2.5% Tm-doped crystal first increase slightly, reach a maximum at around 150 K, and decrease slightly afterwards. We believe that, even the data taken with the 0.5 mm pinhole might be affected by radiation trapping in this relatively highly doped Tm:YLF sample. On the other hand, for temperatures below 150 K, the overlap of absorption and emission bands are rather limited in Tm:YLF and hence the radiation trapping effect itself is not sufficient to explain the measured trend. It is probable that Tm-ion doping density dependent processes such as cross relaxation, energy transfer upconversion and energy migration has a role in the observe temperature dependent behavior of the 2.5% Tm-doped sample (as the curve looks rather different for the 0.5% Tm-doped crystal) [60].
The measured temperature variation of 3F4 energy level fluorescence lifetime using the 0.5% Tm-doped YLF sample could provide a better hint for the variation of intrinsic fluorescence lifetime. As we see from Fig. 5 (a), the fluorescence lifetime which is around 18 ms at 80 K, gradually decreases to a value of 15.5 ms at 300 K. The decays from the 3F4 level is expected to be mostly via radiative transitions [30], and hence the observed change with temperature should be due to a change of radiative lifetime (an external quantum efficiency of 98% is measured for this transition in Tm:YLF recently proving the almost fully radiative nature of this transition in high purity samples [11]). The measured room-temperature lifetime without pinholes is 15.5 ms at 300 K, which is slightly above the intrinsic value 15.25 ms (Fig. 4 (b)). The small effect of radiation trapping on the measured fluorescence lifetimes for the 0.5% doped sample could be estimated via looking at the cross correlation of absorption and emission bands [61]. Using the measured emission data, we have eliminated the contribution of radiation trapping for the 0.5% doped sample and the resulting estimation for the intrinsic fluorescence lifetime is shown by the red solid line in Fig. 5 (a), that is slightly below the measured values at higher temperatures. A fit to the curve provides the following equation for the estimation of temperature dependence of radiative lifetime (${{\boldsymbol \tau }_{\boldsymbol r}}$) of the 3F4 level of Tm:YLF in the 80-300 K range:
where T is temperatures in Kelvins, and resulting lifetime is in ms units.The lifetime of the 3F4 level of Tm is known to reduce with energy migration to impurities [62,63], and as the highly Tm-doped samples has the tendency to have higher level of impurities, the reported fluorescence lifetime values in literature shows reduction of 3F4 lifetime with doping [32–46]. The measured room-temperature lifetime in this work (15.25 ms for 0.5% doped sample) is in good agreement with literature for the lowly Tm-doped crystals: 14.1 ms with 0.2% doping [64], 15 ms with 0.25% doping [62], 15 ms with 0.5% doping [50], 15.6 ms with 1% doping [65]. There is limited work on the lifetime of the 3F4 level at cryogenic temperatures. T.T. Basiev et al. reports the fluorescence lifetime of the 3F4 level as 18.05 ± 0.07 ms and 15.2 ± 0.1 ms at 78 K and 300 K, for a low thulium concentration, which is in very good agreement with our results [66]. An earlier study from 1988, also reports a radiative lifetime of 16.5 ms at 77 K and 13.5 ms at 300 K but the doping of the sample is not mentioned [30]. We believe the slightly lower radiative lifetimes reported in [30] might be due to the higher level of impurities of the sample.
We continue our discussion with Fig. 5 (b), which shows the measured variation of 3H4 level lifetime with temperature for the 0.5% and 2.5% Tm-doped samples. At room-temperature, we have measured the 3H4 level lifetime as 1.99 ms and as 0.5 ms for the 0.5%, and 2.5% Tm-doped YLF samples, respectively. As discussed earlier, the reduction of fluorescence lifetime of 3H4 level with doping is well studied [9,30,50,60,62,64,67–73] and is mostly due to two-for-one cross-relaxation process, which improves the lasing performance while lasing from the 3F4 manifold [32,74]. The measured values at room temperature are in quite good agreement with literature: 2 ms for 0.2% doping in [64], 2.05 ms for 0.5% doping in [30], 2.2 ms for 0.1% doping in [67], 0.84 ms for 2% doping in [73] and 0.37 ms for 3% doping in [73].
For the 0.5% doped Tm:YLF sample, the measured 3H4 level fluorescence lifetime does not vary much with temperature (except a small fluctuation in the 80-125 K range), and stays around 2 ms. For this lowly doped sample, cross-relaxation process is not yet quite effective and this value should be quite close to the radiative lifetime of this level. For the 2.5% Tm-doped sample, the measured lifetime is around 0.25 ms at 78K, which increases slowly and reaches a value of 0.5 ms at 300 K. We suspect that some of this increase in fluorescence lifetime with temperature might be due to the radiation trapping effect. In an earlier study, Armagan et al. measured temperature dependence of 3H4 fluorescence lifetime for a 6% doped sample and saw an increase from around 3 µs to 4.5 µs when the temperature is increased from around 50 K to 300 K [68]. The trend in [68] is similar to the trend we have observed for the 2.5% Tm-doped sample.
Overall, the measured lifetime of the 3H4 energy level does not show a significant change with temperature in the 78-300 K range. This indicates that, the two-for-one cross-relaxation process is also quite effective at cryogenic temperatures. We have also confirmed this via looking at the ratio of emission intensity around 1500 nm to the emission intensity around 1900 nm. For the 2.5% Tm-doped sample, the 1900 nm emission originating from the 3F4 level is much stronger than the 1500 nm emission originating from the 3H4 manifold at all temperature ranges. A more intense emission at 1900 nm compared to 1500 nm clearly demonstrates the presence of strong cross relaxation process [75]. Hence, we believe that, Tm:YLF cryogenic laser and amplifier systems could also use standard high power diode modules around 785 nm for pumping and obtain slope efficiencies above the Stokes limit as the cross relaxation process is also in play at cryogenic temperatures.
4. Emission cross section measurements
In this section, we will present our temperature dependent emission measurements for the 3F4 manifold. To start the discussion, Fig. 6 shows measured unpolarized emission intensity of Tm:YLF (Ia(λ)+Ic(λ) in Eqs. (1)-(2) at 78 K and 300 K in logarithmic scale. The data is normalized for both cases. In the figure, for the 78 K emission, we have also indicated the possible origin of the emission peaks. The numbers in Fig. 6 corresponds the transitions shown earlier in Fig. 3 between the different sub-levels of 3F4 and 3H6 manifolds. Transitions 1-7 are from the lowest lying Stark level of 3F4 manifold (Eh1) to different Stark levels of the 3H6 manifold. Transitions 8-14 and 15-21 correspond to decays from the higher lying levels of Eh2-4 and Eh5 (Fig. 3), respectively. At 78 K, lowest lying Stark level of 3F4 manifold (Eh1) has an estimated Boltzmann occupancy ratio of 84.9%. Hence, in the emission spectrum, transitions 1-7 is dominant compared to transitions 8-14 (Eh2-4 occupancy:4.6% at 78 K), which is dominant over transitions 15-21 (Eh5 occupancy: 1.44% at 78 K). At room-temperature, levels Eh1, Eh2-4, and Eh5 has estimated Boltzmann occupancy factors of 29.1%, 13.7% and 10.1% (Eh2, Eh3, Eh4 are Stark levels with very close energies [56]). Due to a more balanced distribution of excited thulium ions at room-temperature, the emission strengths from different Stark levels of the upper laser manifold equalizes. Moreover, due to the increased phonon energy, the phonon coupled emission lines get broader and smoother.
Fig. 6. Measured unpolarized emission spectra of Tm:YLF at 78 K and 300 K in normalized units. The data is taken using a 2.5% Tm-doped YLF crystal, and is shown in logarithmic units for better visibility of smaller strength emission peaks. Most of the emission peaks observed at 78 K could be matched to a transition in the energy level diagram (Fig. 3).
As the next step, in Figs. 7 and 8, we plot the measured variation of emission cross section with temperature for the E//c and E//a axis of Tm:YLF in normalized and absolute units, respectively. From Fig. 7, we see again that, the emission mostly originates from transitions from the lowest lying Stark level of 3F4 manifold at low temperatures (as we observed in Fig. 6 as well). As the temperature increases, other Stark levels of the upper laser manifold also start to contribute (strength of emission at shorter wavelengths increase) and we observe several broad lines with somewhat equal strength at room-temperature.
Fig. 7. Variation of normalized ECS spectra of Tm:YLF with temperature for (a) E//c and (b) E//a axes at selected crystal temperatures between 100 K and 300 K.
Fig. 8. Variation of emission cross section (ECS) spectra of Tm:YLF in absolute units with temperature for (a-c) E//c and (b-d) E//a axes from 78 K to 300 K. In graphs (a-b) the whole spectra are shown, where as in graphs (c-d) we show the data in a smaller range to improve the visibility of ECS data on weaker parts of the spectrum.
Figure 8, which shows the emission cross section variation in absolute units allows us to look at the process in more detail. Before discussing the details, we would like to mention that comparing the measured ECS spectra with literature, we see that our 300 K emission data is in relatively good agreement with [20,22,34,50,76], and especially a quite good match is observed with the data presented by So et al. [20]. To our knowledge, the cryogenic emission data of Tm:YLF from its 3F4 level is not reported in detail earlier. The overall spectral shape of our data is similar to the 78 K emission data reported by G. Rosa in 1988 [30], but the peak intensities are lower in [30] probably due to the limited resolution of the setup used (2.5 nm).
The E//c axis of Tm:YLF has four strong emission peaks centered around 1684 nm, 1745 nm, 1832 nm and 1880 nm at room temperature. At cryogenic temperatures, the emission around 1880 nm strongly dominates others, as this emission originate from the lowest lying Stark level of upper laser level manifold and collects most of the inverted ions. In Fig. 9 (a), we look at the variation of the 1880 nm emission in greater detail. As we can see, the 1880 nm emission line at room temperature actually originates from combination of two distinct emission lines, one centered around 1877 nm and another centered around 1888.5 nm (the peak positions are also temperature dependent). These peaks correspond to transitions 4 and 5 in Fig. 3. The stronger 1877 nm line has a peak emission cross section of 3.95 × 10−20 cm2 at 78 K, but it quickly reduces to 2.38 × 10−20 cm2 at 100 K, 1.57 × 10−20 cm2 at 125 K, and 1.09 × 10−20 cm2 at 150 K (Fig. 10 (a)). The line has a FWHM of around 2.3 nm at 78 K, which widens to 3.9 nm at 100 K, to 5.1 nm at 125 K, and to 6.6 nm at 150 K.
Fig. 9. Calculated variation of emission cross section (ECS) spectra of Tm:YLF with temperature around the main cryogenic lasing bands for the (a) E//c and (b) E//a axes. The emission peaks are located at 1877nm and 1888.5 nm for E//c axis, and at 1908nm for E//a axis.
Fig. 10. Variation of (a) measured peak emission cross section and (b) calculated peak absorption cross section values of Tm:YLF with temperature in the 78-300 K range at selected wavelengths.
The E//a axis of Tm:YLF has five distinct emission peaks centered around 1684 nm, 1744 nm, 1795 nm, 1846 nm, and 1908 at room temperature. At cryogenic temperatures, the emission around 1795 nm strongly dominates others (this peak corresponds to transition 2 in Fig. 3). The 1795 nm line has a peak ECS of 9.35 × 10−20 cm2 and a FWHM of only around 0.6 nm at 78 K (Fig. 8 (b)). The emission strength of this peak is highly temperature dependent, and the peak ECS reduces more than 10 fold to 0.88 × 10−20 cm2 at 150 K (FWHM increases to 3 nm). Due to this strong temperature dependence, it might be hard to implement this line in high power cryogenic lasing applications. On the other hand, this line might be used for in situ temperature estimation studies due to its strong temperature dependence [14,77,78].
The 1908 nm line of E//a axis, is not as strong, but as we can see from Fig. 8(d) and Fig. 9 (b), this line is relatively broadband even at cryogenic temperature and has a moderate level of strength (transition 5 & 6 in Fig. 3). This line is also quite close to the 1927 nm emission line (transition 7 in Fig. 3), which helps to broaden and smooth out the overall emission. Moreover, the strength of the 1908 nm emission line is less sensitive to temperature, and it has a peak emission cross section of 0.82 × 10−20 cm2 at 78 K, 0.74 × 10−20 cm2 at 100 K, 0.61 × 10−20 cm2 at 125 K, and 0.51 × 10−20 cm2 at 150 K (Fig. 10 (a)). The FWHM of the line is also considerably broad: around 18 nm at 78 K, which widens to 19 nm at 100 K, to 20.5 nm at 125 K, and to 22 nm at 150 K.
We close this section with Table 1, which provides equations for modeling the temperature dependence of emission cross section of Tm:YLF as a function of temperature at selected wavelengths. The following functional form:
is used to obtain a fit to the experimentally measured data, where the coefficients a0 – a4 in Eq. (7) are wavelength dependent fit parameters.
Table 1. Best fit values of the temperature coefficients in Eq. (7) for the estimation of emission cross section at different temperatures for several representative wavelengths in E//a and E//c axes of Tm:YLF.
5. Absorption cross section calculations
As mentioned earlier, McCumber relation could be used to interchange between emission and absorption cross section spectra. We could not measure absorption of Tm:YLF samples directly in this work due to lack of relevant equipment, but we have used the McCumber relation to calculate absorption cross section (ACS) spectra as a function of temperature and the results are shown in Fig. 11. Our earlier work with Yb:YLF showed that [46], this approach works quite well especially for low temperature absorption data. To confirm the validity of our calculation, we have compared the calculated ACS spectra at room temperature with the directly measured absorption cross section data in literature. We have seen that the calculated ACS at 300 K matches literature data quite well for both E//a [22,50] and E//c [50] axes (within ±10%). As the overlap of emission and absorption bands reduce at cryogenic temperatures, we expect our data to become more reliable at low temperatures. On the other hand, it is fair to state that our absorption estimate based on McCumber relation is error prone especially in the short wavelength region, and further experimental work involving direct temperature dependence of absorption is required for confirmation of the data presented here.
Fig. 11. Calculated variation of absorption cross section with temperature for Tm:YLF crystal in the 78-300 K range for (a) E//c and (b) E//a axes. The ACS data is calculated from the measured emission data using McCumber theory. (c-d) Zoomed in version to focus better on weaker parts of the spectrum with lower ACS values.
As we can see from Fig. 11, the E//c axis of Tm:YLF has three main absorption peaks at cryogenic temperatures: one around 1683 nm, a close side peak around 1690 nm, and another one around 1746 nm. The 1683 nm line has a peak ACS of around 5.2 × 10−20 cm2 and a FWHM of 5 nm at 100 K. The FWHM of the line increases to 8 nm at 150 K, at the expense of reduced peak ACS value (3.2 × 10−20 cm2). For the E//a axis, there are absorption lines around 1684 nm, 1726 nm, 1737 nm, 1745 nm and 1795 nm. Overall, compared to E//c axis, the E//a axis absorption lines of Tm:YLF are narrower and weaker at cryogenic temperatures (except the 1745 nm transition). The 1745 nm line is strong in both E//a and E//c axes, and might represent an opportunity for in band pumping using unpolarized pump sources. However, the absorption line has a width of around 1 nm at 78 K, 2 nm at 100 K, and 3 nm around 150 K. Hence, narrow linewidth pump sources are required for efficient pumping of Tm:YLF laser using the 1745 nm absorption line.
Figure 12 shows the ACS curves in logarithmic scale in a broader wavelength range. Knowledge of temperature variation of absorption cross section in the lasing region of Tm:YLF (above 1750 nm) is important in estimating laser/amplification performance. As the temperature of the Tm:YLF crystal is reduced, the absorption in this region becomes negligible, and the laser transitions from being 3-level to 4-level. At cryogenic temperatures, the main emission/lasing lines of Tm:YLF lies in the 1870-1940 nm region (Fig. 9), and temperature dependence of ACS at selected wavelengths in this region is provided in Fig. 10 (b).
Fig. 12. Calculated variation of Tm:YLF absorption cross section with temperature in logarithmic scale for (a) E//c and (b) E//a axes. The ACS data is calculated from the measured emission data using McCumber theory.
We want to close this section with Table 2, which provides equations for modeling the temperature dependence of absorption cross section of Tm:YLF as a function of temperature at selected wavelengths. Note that a similar functional form of:
has been chosen where the coefficients b0 – b3 in Eq. (8) are wavelength dependent fit parameters.Table 2. Best fit values of temperature coefficients for the calculation of absorption cross section at different temperatures for several representative wavelengths in E//a and E//c axes of Tm:YLF.
6. Gain cross section calculations
In closing, we present calculated gain cross section (GCS) spectra for Tm:YLF as a function of temperature. As in any 3-level system both the inversion and temperature have strong influence on the gain spectral shape, and one needs to look at the GCS curves both as a function of inversion and temperature to understand the full picture. To start with, Fig. 13 shows the calculated GCS of Tm:YLF in its both E//c and E//a axes, as function of inversion, for inversion levels between 10% and 75%. The data is presented at a selected temperature of 125 K, which is within the typical operation temperature range of cryogenic amplifiers [78]. As discussed earlier, for the E//c axis the gain peak of Tm:YLF is centered around 1877 nm (Fig. 9 (a)). This is in good agreement with the recent lasing report by Fangxin et al. where a free running laser wavelength of 1877 nm was reported from a cryogenically cooled system [45]. The 1877 nm line has a FWHM of around 5 nm at 125 K, which is broad enough to enable generation and amplification of 1-2 ps pulses. For the E//a axis, the main gain peak is located at 1908 nm. The gain in this transition is around 3-fold weaker compared to the 1877 nm line of E//c axis. However, the GCS curve has a FWHM of around 20 nm (125 K), and might enable generation and amplification of sub-500-fs to sub-1-ps level pulses. Note that, the E//a axis has another strong but quite narrow gain peak at 1795 nm (FWHM: 2 nm). This line strongly overlaps with the absorption lines, and hence gain in this transition is a strong function of inversion and temperature.
Fig. 13. Calculated variation of Tm:YLF gain cross section (GCS) with inversion for inversion levels between 0.1 and 0.75, at a temperature of 125 K, for (a) E//c and (b) E//a axes.
As we have mentioned earlier, it is also instructive to look at the gain spectra as a function of temperature to estimate the behavior of the laser/amplifier under thermal load. Figure 14 shows the calculated GCS spectra around the main Tm:YLF emission peaks we have discussed as a function of temperature (inversion, β, is kept at 25%, again a reasonable operating inversion level for amplifiers). The trend here is similar to the trend we have observed and discussed with the ECS curves (Fig. 9). The GCS spectra at cryogenic temperatures is in good agreement with the cw tuning range reported by Ketteridge et al. in 1997 [43]:1840-1890 nm lasing while employing the E//c configuration and 1875-1930 nm lasing while employing the E//a configuration. As we can see, the 1877 nm line of E//c axis provides higher gain compared to the 1908 nm line of E//a axis. On the other hand, the E//a axis possesses broader FWHM, and is less sensitive to temperature variation of gain cross section. As it is used for Yb:YLF in earlier studies [79], for some applications, it might be better to combine the benefits of both axes of the gain material, as they are spectrally located closely, and employing both of them in the same system might result in better performance in amplification performance especially in terms of obtainable pulsewidths.
Fig. 14. Calculated variation of Tm:YLF gain cross section (GCS) with temperature between 100 K and 300 K for an inversion level of 0.25, for (a) E//c and (b) E//a exes.
7. Conclusions and outlook
In conclusion, we have presented detailed data focusing on temperature dependence of spectroscopic properties of Tm:YLF. Carefully taken fluorescence lifetime and emission cross section data demonstrates that, it might be possible to develop cryogenic Tm:YLF amplifier systems with sub-ps pulsewidths around 1900 nm region. For this effort, the know-how already acquired with cryogenic 1018 nm Yb:YLF systems (sub-1-ps pulsewidth, up to 300 mJ energy [80], up to 500 W average power [39,79]) could ideally be transferred to this new wavelength region as the opto-mechanical properties of the YLF host should be similar. For an easier comparison of the potential of Tm:YLF, we present Table 3, which lists relevant parameters for both gain media at 150 K.
Table 3. Comparison of laser/amplifier relevant parameters of Yb:YLF and Tm:YLF. Unless specified implicitly above, the reported values are those measured at 150 K.
As we can see from Table 3, compared to Yb:YLF that is pumped at 960 nm and lase around 1018 nm, the quantum defect in pumping of Tm:YLF will be an order of magnitude larger (785 nm pumping, 1900 nm lasing). Via usage of highly-doped samples, cross-relaxation process (two-for-one pumping mechanism) could be used to reduce the quantum defect to around 20% level, but this is still around 4 times larger compared to Yb:YLF. Another attractive pumping scheme for Tm:YLF could be usage of recently developed pump diodes around 1700 nm, which could reduce the quantum defect to around 10% [35]. However, the pump power levels available from these diodes are currently limited to 10s of Watt level, and future progress in these diode systems is required for them to become attractive alternatives to their 785 nm counterpart for high power applications. Also note that, the pump absorption saturation intensity of Tm:YLF is around 40 times lower than of Yb:YLF. Hence, efficient absorption in Tm:YLF will require usage crystals with higher doping compared to Yb:YLF, which could also create additional challenges in thermal effects. In terms of emission cross section, the Yb:YLF transitions have around 1.3-1.6 times larger peak ECS values. On the other hand, Tm:YLF has a florescence lifetime that is 8-9 times longer, and as a result the small signal gain in Tm:YLF is about 5 times larger compared to Yb:YLF (comparison is made for an operation temperature of 150 K). The larger gain will relax the pressure on components of the amplifier in terms of passive losses. The longer fluorescence lifetime of Tm:YLF will also be beneficial in improving extraction efficiency of amplifiers, for repetition rates above 100 Hz, via cumulative saturation effect of neighboring pulses. At low repetition rate operation, due to its relatively large gain saturation fluence, the laser induced damage threshold barrier could still limit the achievable efficiencies in Tm:YLF based amplifies. Overall, as in most cases, Tm:YLF has its pros and cons as a laser material, and we hope that our findings presented in this work could help laser scientists and engineers to probe its potential as a cryogenic amplifier.
Funding
European Research Council (609920); Deutsche Forschungsgemeinschaft (390715994).
Acknowledgements
The authors acknowledge support from previous group members L. E. Zapata, K. Zapata for establishing the indium-bonding technology for YLF at CFEL-DESY.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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