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Abstract
We present Emission and absorption cross sections of thulium doped calcium fluoride (Tm:CaF2) in the visible to short wave infrared (SWIR) wavelength range for temperatures between 80 K and 300 K. For spectral regions of high and low absorption the McCumber relation and the Fuchtbauer–Ladenburg equation have been used to give reliable results. Furthermore, an estimation for the cross relaxation efficiency is derived from the emission spectra as a function of doping concentration and temperature. In addition, nearly re-absorption-free fluorescence lifetimes for various doping concentrations were studied. It was found that a double exponential fit model is better suited than a migration model to represent the fluorescence decay curves. The measurement results are interpreted in the light of the application of Tm:CaF2 as an efficient active medium in high-energy class diode-pumped solid state lasers.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, thulium doped laser materials have attracted increasing attention as the active medium for diode-pumped solid state lasers. Absorption bands near 800 nm allow for the usage of commercially available high power laser diodes originally developed for neodymium doped laser hosts. Employing the cross relaxation process, which yields two excited ions per pump photon and a relatively low quantum defect in the range of approximately 15%, such materials allow for the realization of efficient high power short wave infrared (SWIR) laser sources [1].
Additionally, the radiative lifetime of thulium-doped gain media is very long, even when compared to ytterbium-based gain media. Especially in case of pulse-pumped operation, this promises to lead to excellent energy storage properties and therefore strongly reduced diode power requirements for a given amount of energy to be stored.
Applications of pulsed lasers in this wavelength range are widespread. Besides direct utilization in medicine e.g. for the ThuLEP treatment [2] and the endovenous laser ablation (EVLA) of varicose veins [3,4], short pulse laser sources in the range of 1.8 µm to 1.9 µm are nearly ideal pump sources for ultra-broad band Cr$^{2+}$ laser systems [5]. Cr:ZnS and Cr:ZnSe are referred to as the titanium sapphire equivalent in the mid infrared, having the potential to amplify few cycle pulses in this wavelength range to high energies.
So far, the downside of the thulium gain media has been that high doping concentrations are mandatory to ensure an efficient cross relaxation process, while at the same time – due to the low energy separation of the electronic levels – non radiative processes are becoming significant as well. Moreover, the energy transfer up-conversion process is an additional loss process especially for higher densities of excited sites.
Therefore, optimizing the doping concentration of the laser medium and the excitation density during operation is mandatory for designing thulium-based laser systems. For this task, the availability of spectral data, preferably as a function of temperature and doping concentration, are crucial. Recently, we have published similar spectral data for Tm:YAG and Tm:YAP [6].
From a general point of view materials with relatively low phonon energies should be of particular interest as hosts for the thulium ion to suppress the occurrence of multi phonon processes as efficiently as possible. Therefore, fluoride host materials such as Tm:YLF are currently in the focus of development for future high power laser systems like the Big Aperture Thulium laser (BAT) [7,8].
Recently, highly efficient operation of Tm:CaF$_2$ has been demonstrated. Here, both operation in the continuous wave regime as well as under mode locking conditions has been shown [9–12].
As a host material for thulium, CaF$_2$ leads to a similar behavior as in case of other rare earth dopants. Major properties are a relatively long radiative lifetime and broad absorption and emission bands. The latter property is mainly due to the clustering of the dopant ions [13]. This effect is of special interest with thulium as the active ion, since it influences the energy transfer mechanisms like the cross relaxation process [14]. The general effect of clustering in rare earth ion doped fluoride crystals has been investigated for many years. Since the topic is complex and not topic of this work we would like to refer the interested reader to the literature [15–20].
Though general spectroscopic data on Tm:CaF$_2$ is available in the literature [18,21,22], data for absorption [9,10,23–25] and emission cross sections [11,23,26] is quite spars, especially if it comes to temperature dependent data, which is crucial for laser design. Furthermore, data from different publications vary significantly. For example values for the fluorescence lifetime range from 3.94 ms [11] over $6.16$ ms [25] up to $14.2$ ms [23] at room temperature, which could be attributed to different measurement schemes, leading to differently strong influence e.g. of re-absorption.
The determination of the emission cross sections in general holds a significant error as all methods for their determination depend on not directly accessible quantities like the energy levels or the radiative lifetime. The radiative lifetime for example can be determined using the Judd-Ofelt theory [26,27] or Füchtbauer-Ladenburg method [28,29], where each has its own weaknesses. Hence, the available values, as well for these data as for the cross sections based on these, in the literature are bound to show a significant variation.
In this work we present a spectroscopic study on Tm:CaF$_2$ at different doping levels. Absorption and emission cross sections are determined as a function of temperature from 80 K to 300 K for the major absorption and emission bands. We also investigated the fluorescence lifetime of the $^3$F$_4$ level within the given parameter ranges.
2. Experimental setup
The setup and data processing routines used here are strongly correlated with the methods used in our previous works [30,31]. Therefore, we will only give a brief overview here and would like to refer the interested reader to the named publications.
The schematic measurement setup is shown in Fig. 1. Using only a small sample volume in the measurement layout allows us to obtain nearly re-absorption free fluorescence spectra. Since optical access points are fiber coupled, measurement devices and light sources can be exchanged without affecting the actual setup. To suppress the water vapor absorption bands in the SWIR wavelength region, the entire beam line is placed within an airtight casing, which is purged with dry nitrogen gas. In this way the relative humidity could be assured to be below 1% for all SWIR measurements.
Fig. 1. Sketch of the experimental Setup combining the measurements of absorption, emission and lifetime of the sample material. The whole setup is surrounded by an N$_2$ atmosphere to suppress disturbance by absorption of water vapor in the air. LD$\ldots$fiber coupled laser diode at 786 nm or 1120 nm wavelength, SM$\ldots$spherical mirror with 300 mm radius of curvature, PM$\ldots$parabolic mirror, M$\ldots$plane mirror, S$\ldots$mounted and cryogenically cooled sample material, P or F$\ldots$optional polarizer or filter, L$\ldots$lens, PD$\ldots$photo-diode.
To cover the full spectral region of interest ranging from about 500 nm to 2.5 µm, two optical spectrum analyzers were used. In the range up to 1.7 µm we used an AQ-6315A/B (ANDO Electric Co. Ltd.), while for wavelengths above 1.5 µm an AQ-6376 (Yokogawa Electric Corp.). The spectral range from 1.5 µm to 1.7 µm was used to adapt the absolute signal of both spectrometers to each other for full range measurements.
For the acquisition of the absorption spectra a fiber-coupled white light source WLS1000 (Bentham Instruments Ltd.) served as the illumination source. Fluorescence measurements were performed by exciting the samples with a 4 W fiber-coupled laser diode (Lu0786T04-ODD55N12A, Lumics GmbH) at 786 nm wavelength. The center wavelength was adjusted to the absorption of the samples by adapting the laser diode’s cooling temperature. The maximum pump intensity in the setup was designed to be 10 kW/cm$^2$. However, the actual intensity during the measurements was minimized to reduce the heat load inside the material but simultaneously allow for a sufficient signal.
Lifetime measurements were carried out using the same setup as for the fluorescence measurements by replacing the spectrometer with a photo-diode (DET10D/M, Thorlabs, Inc.). A long pass filter was used in the collimated part of the beam path to eliminate the influence of scattered pump light during these measurements.
Though a certain amount of re-absorption has to be considered for Tm:CaF$_2$ a fully re-absorption compensating measurement technique like the pin hole method [32] could not be implemented due to the small sample size. Nevertheless, as our measurements used a minimized measurement volume, the influence of re-absorption can be considered rather small especially given the relatively low doping concentration as it was also found in [6].
All Tm:CaF$_2$ samples under investigation were grown and prepared by the micro pulling down technique [33,34]. Stoichiometric mixtures of CaF$_2$ and TmF$_3$ powders of 4N purity (Stella Chemifa Co., Ltd.) were used to prepare the starting charge. The crystal growth was carried out using a graphite crucible with an orifice of 2 mm in diameter under Ar+CF$_4$ atmosphere. The setup was situated in a furnace with a vacuum-tight chamber that is tailored for fluoride growth [35]. An undoped CaF$_2$ crystal (Tokuyama Co., Ltd.) oriented in <111> direction was used as the seed. The growth rate was 0.1 mm/min. Following the typical baking procedure for fluoride growth the chamber was evacuated to 10$^{-4}$ Torr and the crucible was heated to approximately 900 K for about 180 min in order to remove the sources of possible oxygen impurities and moisture. After the baking procedure, the chamber was filled with Ar (99.9999%) and high-purity CF$_4$ (99.9999%) in the volume ratio of 9:1. Then the crucible was heated up to the powder melting temperature, which is around 1700 K, and the growth procedure was initiated. The doping levels of the investigated samples were 0.75, 1.5, 3, 4.5, and 7.5 at.%. The thicknesses ranged from 5.2 to 5.3 mm with a diameter of 2 to 2.5 mm. The samples were mounted in a custom optical, high-vacuum cryostat based on a ST300 flow cryostat (Janis Research Company, LLC) operated with liquid nitrogen.
3. Data processing
Since the data analysis is similar to the methods used in [30,31], we only give a short overview and refer for more details to our earlier publications.
As a reference we included the term scheme for Tm$^{3+}$-ions with all transitions discussed in this work in Fig. 2.
The Lambert-Beer’s law [36] is used to calculate the wavelength dependent absorption cross sections $\sigma _a(\lambda )$. The light intensity of the WLS transmitted trough the sample $I_{\textrm {T}}(\lambda )$ is related to the reference intensity of the WLS without passing trough the sample $I_{\textrm {R}}(\lambda )$:
The wavelength dependent emission cross sections $\sigma _{\textrm {e}}(\lambda )$ are obtained by a combination of two methods. The first is the so called McCumber (MC) or reciprocity relation, which is based on the knowledge of the previously determined absorption cross sections [37,38]:
For the energy levels we used data from the literature for Tm$^{3+}$ in the $C_{4\nu }$ sites (cf. Table 1). This should be understood as an approximation to the actual energy levels within a clustering regime, which are so far not known. Therefore, this influences the error margin of the determined emission cross sections.
Table 1. Parameters of Tm:CaF$_2$ as used in the calculation of the emission cross sections.
The second method to determine $\sigma _{\textrm {e}}$ is the so-called Füchtbauer-Ladenburg (FL) equation based on the fluorescence spectra [41]:
The spectral line function $g(\lambda )$ for Tm:CaF$_2$ is obtained from the fluorescence intensity $I_{\textrm {f}}(\lambda )$ usingTo overcome the individual limitations inherent to the two methods we combined both of them. The MC-relation is suitable in regions, in which the absorption can be measured accurately. In addition the FL-equation yields better results when the absorption is low. A valid result for the whole spectral range is therefore achieved by adjusting $\tau _{\textrm {r}}$ and thereby matching both methods in spectral regions with low but accurately measurable absorption, where both approaches yield reasonable results. Since $\tau _{\textrm {r}}$ is not temperature dependent, the final value can be found by matching multiple data sets at different temperatures to increase the reliability.
Throughout all calculations the dependencies of the refractive index $n$ on temperature and wavelength are neglected, since their contribution is very low as compared to other measurement uncertainties.
The doping concentrations given in at.% as used in this work are calculated based on the assumption that charge compensation requires a substitution of three Ca$^{2+}$-ions by two Tm$^{3+}$-ions. Hence, each unit cell in the CaF$_2$ crystal which contains one Ca$^{2+}$-ion, can only contain ${\raise0.7ex\hbox{$2$} \!\mathord{\left/ {\vphantom {2 3}}\right.}\!\lower0.7ex\hbox{$3$}}$ Tm$^{3+}$-ions. Therefore, the density of dopant ions for a doping concentration of 1 at.% is calculated by
Here, $\rho _{\textrm {CaF}_2}$ is the mass density and $m_{\textrm{EZ}}$ the mass of the unit cell for CaF$_2$.4. Spectral measurements
4.1 Absorption cross sections in the VIS to NIR region
For all available doping concentrations the absorption spectra were recorded within a spectral range between 600 nm and 1300 nm in steps of 20 K from 80 K to 300 K using the ANDO AQ-6315A/B optical spectrum analyzer. The results for selected temperatures are shown in Fig. 3. The given data was obtained with a crystal of 4.5 at. % doping concentration and 5.2 mm thickness.
Fig. 3. Absorption cross sections $\sigma _{\textrm {a}}$ for selected temperatures in Tm:CaF$_2$ for the transitions from the $^3$H$_6$ manifold to the $^3$F$_2$,$^3$F$_3$, $^3$H$_4$ and $^3$H$_5$ manifolds.
For optical pumping within the cross relaxation, the transition from $^3$H$_6$ to $^3$H$_4$ ranging from 750 nm to 800 nm is of major interest. For lower temperatures the absorption for wavelengths longer than than 795 nm is reduced, while the peak cross section close to 768 nm is increased. Due to the inhomogeneous nature of the dominating broadening mechanism the change in the line-shape is relatively small compared to e.g. Tm:YAG.
For all doping concentrations under investigation no significant dependence of $\sigma _a$ was found. The only feature in the spectral distribution of the absorption cross sections was the absorption peak at 1187 nm. This peak is assigned to centers with cubic symmetry [39]. For a temperature of $80$ K the dependencies of the absorption cross sections for this peak for different doping concentrations are shown in Fig. 4. The data show a decrease in $\sigma _a$ for higher doping concentrations, which indicates a relative reduction in the number of thulium ions in these centers in favor of clustered ions.
Fig. 4. Absorption cross sections $\sigma _a$ of the absorption peak corresponding to cubic symmetry for the measured doping concentrations. The involved transition is between the $^3$H$_6$ manifold and the $^3$H$_5$ manifold. The given values were recorded at a temperature of $80$ K.
For evaluating the pump process in a laser a convenient assessment can be attained by calculating the product of doping concentration $c_{\textrm {at}}$ (in at. %) and thickness $d$, which is needed to absorb 90 % of the pump radiation in the approximation of Lambert-Beer’s law. The pump source is assumed to have a Gaussian spectral distribution with a given $ {1}/{e^2}$-half-width $\Delta \lambda _{\textrm {p}}$ and a center pump wavelength $\lambda _{\textrm {p}}$. In Fig. 5 corresponding graphs of the $^3$H$_4$ to $^3$H$_6$ transition are shown for temperatures of 80 K and 280 K. Blue and violet colors represent areas of higher absorption, which corresponds to a smaller value of the product $d\cdot c_{at}$.
Fig. 5. Absorption characteristics of Tm:CaF$_2$ for 80 K and 280 K. Illustrated is the product of doping concentration $c_{at}$ (in at. %) and thickness $d$ needed to absorb $90$ % of the pump radiation using Lambert-Beer’s law. A Gaussian spectral distribution is assumed with a ${1}/{e^2}$-half-width $\Delta \lambda _p$ and a center pump wavelength $\lambda _p$.
Even at low temperature a bandwidth of up to approx. 5 nm still allows to use nearly the full peak absorption cross section at 768 nm. Such parameters can be fulfilled with current diode technology without the need for special measures to reduce the spectral width. In this respect the difference between room temperature and cryogenic temperature besides the actual peak value is small.
4.2 Absorption and emission cross sections in the SWIR region
In the SWIR region, spectra where recorded from 80 K to 280 K in steps of 20 K using the AQ-6376 optical spectrum analyzer (Yokogawa Electric Corp.).
In Fig. 6 on the left side the obtained absorption cross sections are presented. The peak cross sections are moderately increased for lower temperatures. For the peak cross section we found an increase by a factor of $\approx$ 1.5 when comparing the values at room temperature and 80 K. The spectral shape is mainly composed by two major absorption peaks. Similar as for the NIR absorption the spectral shape hardly changes within the measured temperature range.
Fig. 6. Absorption (left) and emission (right) cross sections $\sigma _e(\lambda )$ for selected temperatures in Tm:CaF$_2$ for the transitions between the $^3$H$_6$ and the $^3$F$_4$ manifold.
The corresponding emission cross sections are shown in Fig. 6 on the right side. The emission cross sections are composed of several individual lines, with relatively broad bandwidth forming a rather continuous band ranging from approximately 1.75 µm to more than 1.9 µm. For lower temperatures the spectrum is slightly more structured, while the peak cross sections are slightly higher.
As described in section 3, adapting results from MC-relation and FL-method, we used a radiative lifetime of $\tau _r=25$ ms independent of the temperature. As discussed in section 6, Tm:CaF$_2$ shows a special development of the lifetime at lower temperatures. Therefore, the values given for temperatures lower than $200$ K should be understood as an estimate only.
5. Cross relaxation efficiency
To estimate the efficiency of the cross relaxation process in Tm:CaF$_2$ the samples were excited in the $^3$H$_6$-$^3$H$_4$ transition while the fluorescence was measured over the full accessible spectral range. As no re-emission from the $^3$H$_5$-$^3$H$_6$ transition was found, the cross relaxation efficiency $\eta _{\textrm {CR}}$ was determined by comparing the relative integral energy content of the $^3$F$_4$-$^3$H$_6$ (SWIR) transition to the total emitted energy
The results are presented as a function of temperature for different doping concentrations in Fig. 7. For doping concentrations $\geq$ 1.5 at.% nearly all energy is transferred to the SWIR transition indicating a highly efficient cross relaxation process even at relatively low doping concentration compared to other Tm$^{3+}$-hosts. Only for the lowest doping concentration a significant amount of energy is emitted from the pump level. Additionally, the cross relaxation tends to be more efficient at higher temperatures, though the influence of the temperature is relatively small.
Fig. 7. Cross relaxation efficiency $\eta _{\textrm {CR}}$, as defined in section 5, of the $^3$F$_4$-$^3$H$_6$ transition (SWIR) as a function of the temperature for different doping concentrations.
6. Fluorescence lifetimes
To determine the fluorescence lifetimes we evaluated the temporal fluorescence decay curves under pulsed excitation. It was found that a single exponential fit could not adequately describe the measurements in the case of low temperatures. Only near room temperature a good fit could be achieved. For lower temperatures an increase in the fluorescence lifetime can be observed, which no longer follows a single exponential curve. This effect was also described by Doroshenko et al. [42]. In this work the life times of Tm:CaF$_2$ samples with doping concentrations ranging from 0.1-2 wt.%, which corresponds to doping concentrations of $1.14\cdot 10^{19}\;$cm$^{-3}$ to $2.28\cdot 10^{20}\;$cm$^{-3}$ were investigated. It was found that the decay could be described using a double exponential model indicating two optical centers. For higher doping concentrations, such behavior was attributed to the presence of clusters and another optical center with a close to tetragonal local symmetry. Others assume that the non single exponential lifetime components are due to radiation trapping in the clustered thulium optical centers [10,43]. Since so far the reason for the behavior of Tm:CaF$_2$ in this context is not entirely clear we also compared results from other decay models with the double exponential approach
as a fit to the data and compared its results to results from migration and trapping models.The so-called Inokuti–Hirayama model, expressed by the formula
In Fig. 8 the results of the double exponential fitting and the application of the Inokuti-Hirayama model are compared. The data was obtained with the $1.5$ at. % doped sample at $300$ K and $80$ K. The value for the multipole interaction parameter $s$ was found to be 10, suggesting that the effect is dominated by a quadrupole-quadrupole interaction. Even though both models show good agreement at room temperature, at $80$ K the double exponential fit is better. At room temperature the decay curve converges with a single exponential decay which is well represented by both models.
Fig. 8. Comparison between a double exponential fit and the Inokuti-Hirayamamodel at $80$ K and $300$ K for 1.5 at. % doped Tm:CaF$_2$. The value for the multipole interaction parameter $s$ in the Inokuti-Hirayama model was 10.
The resulting lifetimes are shown in Fig. 9. The two upper plots show the lifetimes of the double exponential fit and the lower plot the results from the Inokuti-Hirayama model. The double exponential fit results for the long life time component $\tau _2$ agree well with the findings of Doroshenko et al. [42,48] for temperatures down to $100$ K. For $80$ K, $\tau _2$ becomes shorter again. We also evaluated the short life time component $\tau _1$. It is in the range of $12$ ms and rather constant over the temperature $80-240$ K. Approaching room temperature the short life time component becomes less significant in the data which is then represented by a single exponential decay with the long lifetime component close to 20 ms. A significant dependence on the doping concentration was not found within the range of the measured samples, which suggests that there is no strong re-absorption present.
Fig. 9. Overview of the determined lifetimes of the $^3$F$_4$-$^3$H$_6$ transition (SWIR) as a function of temperature for different doping concentrations with different fitting models (the upper two graphs correspond to a double exponential model, while the lower graph corresponds to the Inokuti-Hirayama model).
The lowest plot in Fig. 9 shows the result for the donor life time from the Inokuti-Hirayama model. Down to $160$ K the lifetimes agree well with the results from the long life time component of the double exponential fits. For lower temperatures, however, the model tends to predict shorter lifetimes for lower concentrations, while the closest match to the double exponential results is maintained for intermediate doping levels.
Combining the results from both methods the obtained lifetime values for temperatures higher than approx. 160 K are nearly the same. Therefore, we believe that they can be assumed to be accurate. For lower temperatures it would be necessary to know the exact mechanism leading to the deviation from a single exponential decay. From our measurements this is so far not clear since neither of the applied methods leads to a perfect match of the data in this range, though the double exponential model was superior in our case.
Therefore, the determination of a radiative lifetime, which is needed to calculate the emission cross sections in the FL-method, is relatively unclear. Nevertheless, the combination of the FL-method and MC-method, as described in section 3, yielded a lifetime of $\tau _r=25$ ms, which closely matches the lifetime determined for higher temperatures. Therefore, the emission cross section in that temperature range can be given with good confidence. For the low temperature range our evaluation algorithm might no longer represent the reality in sufficient approximation. Hence, the low temperature cross sections are to be understood as an estimation.
7. Selective excitation of the $^3$H$_4$ manifold
To investigate, whether the double exponential nature at low temperature will be also visible in the fluorescence line shape, e.g. by two separate emitting centers the 1.5 at.% doped sample was excited with a tunable titanium sapphire laser and the corresponding emission spectrum was recorded for different excitation wavelengths (cf. Figure 1). As long as the spectra of different centers would be sufficiently different in emission as well as in absorption, it should be possible to selectively excite the according emission spectra, and therefore modulate the shape of the fluorescence spectrum. The Ti:Sapphire laser was operated at $760$ nm, $762$ nm, $766$ nm, $768$ nm, $776$ nm, $783$ nm and $795$ nm. The wavelengths were chosen to scan over the absorption band of the $^3$H$_6$-$^3$H$_4$ transition. The emission spectra were then normalized according to their integral. The results are shown in Fig. 10 for $80$ K (lower graph) and $300$ K (upper graph).
Fig. 10. Emission spectrum of $1.5$ at. % doped Tm:CaF$_2$ integral normalized for different excitation wavelengths of the Ti:Sapphire laser. The measurement was conducted for two different temperatures.
From the measurements neither at room temperature nor at cryogenic temperatures a significant difference in the emission line shape was found in dependence of the excitation wavelength. Therefore, it can be concluded that the excitation wavelength will not affect the output spectrum.
8. Excitation of the $^3$H$_5$ manifold
The $3$ at. % and $0.75$ at. % doped samples were excited at $1120$ nm by pumping with a $6$ W laser diode (Innolume GmbH). The spectral full width at half maximum of the diode was $1.3$ nm.
The measured emission spectra for selected temperatures are plotted in Fig. 11. Stray light from the pump laser diode at $1120$ nm was not removed from the data, and is still visible. For the samples it is evident, that there is only a very weak emission from the directly excited $^3$H$_5$-$^3$H$_6$ transition which would occur around $1200$ nm. Instead the energy is mainly transferred to the $^3$F$_4$-$^3$H$_4$ transition, indicating a fast relaxation from the $^3$H$_5$ to the $^3$F$_4$ manifold for the investigated doping concentrations. Furthermore, also a small amount of emission from the $^3$H$_4$-$^3$H$_6$ transition is detected, which is generated by up-conversion processes.
Fig. 11. Emission spectrum at selected temperatures of the $3$ at.% and $0.75$ at. % doped Tm:CaF$_2$ samples under $1120$ nm excitation. The strong line at $1120$ nm is stray light from the pump laser diode.
9. Conclusion
Absorption and emission cross sections are crucial for the design of laser systems. In this work we presented a spectroscopic investigation of Tm:CaF$_2$. For this we investigated a doping concentration series of samples ranging from 0.75 at.% to 7.5 at.% in the temperature range from 80 K to 300 K. Absorption cross sections are given for all transitions starting from the $^3$H$_6$ manifold within the spectral range from 600 nm to 2.2 µm. It was found that Tm:CaF$_2$ shows a relatively weak temperature dependence compared to e.g. Tm:YAG, since the spectral shape and bandwidth were widely maintained, though still peak cross sections were increased by a factor of approximately 1.5 from 300 K to 80 K. Therefore Tm:CaF$_2$ has the potential, independent of temperature, to be efficiently excited with standard laser diodes without the need for special line width reduction methods like the application volume Bragg gratings.
Using the cross relaxation process the samples were excited in the $^3$H$_6$-$^3$H$_4$ transition to record SWIR emission spectra. By a combination of the FL-equation and the MC-relation emission cross sections were determined for the $^3$F$_4$-$^3$H$_6$ transition. Similar as for the absorption the emission also widely maintained the line shape, while a moderate increase in peak cross sections was observed for lower temperatures. Therefore, Tm:CaF$_2$ offers a wide emission band of approximately 100 nm FWHM independent of temperature. This makes this material a very promising candidate as the active medium for ultra short pulse lasers in the SWIR as well as for applications, where a broad tunability is desired, especially for wavelengths around 1.8 µm.
The cross relaxation efficiency was estimated by a comparison of the relative energy content of the $^3$F$_4$-$^3$H$_6$ transition (SWIR) to the overall energy within the fluorescence. For doping concentrations exceeding about 1 at. % the cross relaxation process reaches an efficiency close to 100 % within the used method. This is also a promising result since the minimum doping concentration is significantly lower than for example in Tm:YAG, which simplifies the growth of high quality crystals and which is also advantageous with respect to heat conduction as the crystal lattice is less disturbed and also with respect to the reduction of concentration quenching effects.
Fluorescence lifetimes were determined as a function of temperature. It was found that independent of the actual doping concentration at lower temperatures the decay was no longer correctly described by a single exponential decay. This is in good agreement to earlier publications [42]. Therefore, we investigated the decay curves using both a double exponential decay as the so-called Inokuti-Hirayama model. For temperatures higher than approximately 160 K a consistent fluorescence lifetime in the range of 20 to 30 ms was found. For lower temperatures the double exponential model separated into two well defined lifetimes. The longer one was increased for lower temperatures up to approximately 60 ms, while a second lifetime component of approximately 10 ms independent of temperature was found. The Inokuti-Hirayama model yielded similar results as the double exponential model’s long component, though the double exponential fit overall yielded a better adaption to the data.
To investigate if the different lifetime components will also result in a different line shape in dependence of the excitation wavelength a selective excitation of the $^3$H$_4$ level with a tunable Ti:sapphire laser was tested. However, no significant change of the emission line shape was found, independent on temperature and doping concentration. Therefore within a laser setup the exact pump wavelength should have no impact on the emission spectrum.
Selective excitation of the $^3$H$_5$ level at $1120$ nm showed an energy redistribution towards the $^3$F$_4$ level. Emission at $1200$ nm was negligible. Therefore, laser operation on this band is not easily obtainable, at least within the tested range of doping concentrations.
Funding
Thüringer Ministerium für Wirtschaft, Wissenschaft und Digitale Gesellschaft (2016FE9058); LASERLAB-EUROPE (654148); Bundesministerium für Bildung und Forschung (03VNE2068D, 03Z1H531, 03ZIK445, 05P15SJFA1).
Acknowledgments
The authors would like to thank Hellma Materials GmbH in Jena for the processing and polishing of the raw Tm:CaF$_2$ crystals. Furthermore, we would like to thank Julius Irrek and Finn Kohrell for the help in the measurements of the selective excitation of the $^3$H$_4$ manifold.
Disclosures
The authors declare no conflicts of interest.
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