1. Introduction

There has been much recent interest in lasers emitting in the 2 µm spectral region due to a wide array of applications including atmospheric sensing [1], wind lidar [2], medical testing [3], molecular spectroscopy, and optical pumping of longer wavelength solid-state lasers. The relatively high damage resistance of the eye to 2 µm light is also an attractive benefit when dealing with potentially high-power laser emission. In the pursuit of lasers operating in this coveted spectral region, the rare-earth ion Ho³⁺ has gained significant attention in recent years for its 1.9 – 2.1 µm transition from the first excited state (⁵I₇) to the ground state (⁵I₈). Resonant pumping of the upper Ho³⁺ lasing level allows for low quantum defect operation and greatly decreased thermal loading of the laser crystal. Direct resonantly-pumped lasing of Ho³⁺ doped YAG [4], LuAG [5], YLF [6], and Y₂O₃ [7] has been demonstrated.

One of the newest host materials to demonstrate efficient Ho³⁺ laser operation is the uniaxial crystal yttrium vanadate (YVO₄). YVO₄ was previously shown to be an excellent laser host material for Nd³⁺ ions, even outperforming Nd:YAG [8]. It also has favorable chemical and mechanical properties: it is non-hygroscopic, fairly hard (Mohs hardness ~5), resistant to chemicals, and has similar thermal properties to YAG. We were the first to demonstrate a resonantly-pumped Ho:YVO₄ laser operating at 77K [9]. Most recently, we demonstrated CW dual-wavelength (~2054 and ~2068 nm) operation of a cryogenically cooled, resonantly pumped Ho:YVO₄ laser with nearly quantum-defect limited optical-to-optical slope efficiency of ~92% [10]. We surmised that the output wavelength of the laser was sensitively determined by the gain-medium temperature and the output-coupler reflectivity value. However, the exact transition point between lasing wavelengths could not be predicted accurately.

In this paper, we present spectroscopic results that explain the dual-wavelength lasing observed in those experiments.

2. Experimental details

Spectral analysis was performed on several Ho:YVO₄ crystals grown by the Czochralski method by Synoptics. In YVO₄, the Ho³⁺ ions substitute for the Y³⁺ cation and experience D_2d site symmetry. A nominally 1 at.% sample polished parallel to the c-axis was used to measure polarized transverse spectra (π and σ polarizations); and a nominally 2 at.% sample polished perpendicular to the c-axis was used to measure axial spectra. The Ho³⁺ concentrations were confirmed by analysis at Galbraith Laboratories (Knoxville, TN), giving 1.12 at.% and 2.08 at.%, respectively. The samples used in these experiments were approximately 2.75 mm thick.

Absorption measurements for the first excited Ho³⁺ manifold (⁵I₇) were taken with a Perkin Elmer Spectrum 2000 FTIR equipped with a polarizer and with a maximum resolution of 0.5 cm⁻¹. Absorption spectra of higher energy manifolds were obtained using a Varian Cary 6000i (UV-vis-nIR) spectrophotometer, also equipped with a polarizer, and with a resolution typically set to 0.1 nm. Fluorescence spectra from the ⁵I₇ manifold were taken using a Horiba iHR320 monochromator with a 1.5-micron blazed grating and equipped with a liquid nitrogen cooled extended-range InGaAs photodiode for detection. The fluorescence detection bandwidth was typically set to 0.2 nm. Excitation at 893.3 nm, into the ⁵I₅ manifold, was supplied by a Spectra Physics Tsunami Ti:sapphire laser operated in CW mode. Fluorescence lifetime measurements of the ⁵I₇ manifold were acquired by exciting the sample at ~1930 nm using a Continuum Panther EX OPO pumped by a Spectra Physics Quanta Ray PRO-230 pulsed Nd:YAG laser with a pulse duration of 7 ns and a repetition rate of 10 Hz. The decay signal was detected with a liquid nitrogen cooled InGaAs equipped with a 1700 nm long-pass filter, and was analyzed using a Tektronix TDS7104 digital oscilloscope. For all spectroscopic measurements, the samples were mounted in a CTI Cryodyne cryogenic refrigerator with temperature tunability between 8K and 300K (room temperature).

3. Experimental results

3.1 Energy levels

Proper interpretation of the laser behavior of Ho:YVO₄ requires accurate knowledge of the energy levels of the relevant manifolds, including their multiplicity. So far, there have only been a few papers dealing with the spectroscopy and energy level assignments for Ho³⁺ in YVO₄ [11–14], and the observed energy levels among these have been either contradictory or incomplete. For this reason, it was necessary to perform a careful re-examination of the spectroscopy of this material in order to get the most accurate energy level structure possible for the ground and first excited manifolds. The relevant energy levels were determined by recording low temperature absorption and emission spectra and observing how the transitions from thermally excited levels (i.e. “hot lines”) of the initial manifold grow in over fine temperature changes. The results of these investigations are collected in Table 1. The energies are relative to the lowest level of the ground manifold ⁵I₈ and the nominal uncertainty in the energy values is ± 0.2 cm⁻¹.

Table 1. Energy levels of the ⁵I₈ and ⁵I₇ manifolds of Ho³⁺ in YVO₄. Dashes indicate forbidden transitions.

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The levels of the ⁵I₈ ground manifold were determined by analyzing unpolarized fluorescence spectra taken over a range of temperatures from 7 K to 60 K. The six lowest energy levels of the ground manifold are fairly well understood in the literature [11,12]. These values were easily confirmed, using fluorescence from the ⁵I₇ manifold, including observation of the hot lines growing in as the temperature was increased. The higher energy levels of the ground manifold were determined by comparing the trends in hot line growth for fluorescence from a number of excited manifolds including ⁵I₇, ⁵I₆, ⁵F₅, and ⁵S₂. All of the high energy levels listed in Table 1 were verified by at least three different peaks observed among the various fluorescence transitions.

The energy levels of the ⁵I₇ excited manifold were obtained by analyzing unpolarized absorption spectra taken at fine temperature steps over the range from 7 K to 30 K. All 11 of the expected levels were observed in either ground-state or “hot line” absorption. In general, the energy level structure of the ⁵I₇ manifold was similar to that of Ho³⁺ in HoVO₄ published by Barakat et al [15], however, our levels were consistently several wave numbers lower than theirs. The similarity is reasonable considering that both crystals contain a tetragonal zircon structure, and also since the Y³⁺ ion has nearly the same ionic radius as Ho³⁺ [16]. There is one distinct difference between our level assignments and those of Barakat: they determined that there is a level at 5178.7 cm⁻¹ through observation of a hot line at ~5156 cm⁻¹, while we saw a similar hot line at ~5152 cm⁻¹ that we attribute to an energy level at 5199.2 cm⁻1. In the cited work, the claim was that this hot line originates from the 21 cm⁻¹ level of the ground manifold while we claim that it originates from the level at 47.1 cm⁻¹. Our rationale for this assignment is that, over the measured temperature range, the ~5156 cm⁻¹ hot line grows in at a similar rate compared to other hot lines originating from this same level.

In-depth analysis of polarized (pi, sigma, and axial) absorption and fluorescence spectra taken over a temperature range of 8 K to 100 K allowed us to determine other pertinent data regarding the ⁵I₈ and ⁵I₇ energy levels. Table 1 lists the polarization of transitions from the noted initial state to each level of those manifolds. Assignments for the ⁵I₇ manifold were obtained via absorption and assignments for the ⁵I₈ manifold were obtained via fluorescence. Using this information, along with polarization data from transitions starting on the first several excited levels and the selection rules for D_2d symmetry shown in Table 2 [17], we were able to determine the type of transition (electric dipole or magnetic dipole) and the irreducible representations of the levels. The only two levels that could not be conclusively labeled were the 5199.2 cm⁻¹ and 5214.3 cm⁻¹ levels of the ⁵I₇ manifold. Our data strongly hinted that the former was a Γ₃ and the latter a Γ₁, but there was enough uncertainty that we do not feel comfortable decisively labeling them as such.

Table 2. Selection rules for induced ED and MD transitions in D_2d symmetry [17].

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In the course of this work, the energy level structure of several other higher-level Ho³⁺ manifolds was determined from absorption spectra taken between 7 K and 30 K. The energy values for the levels of these manifolds are presented in Table 3. While our level assignments differ considerably with those presented by Golab et al [13], they show good agreement with those published by Enderle et al [12] and intermediate agreement with the results of Moncorgé et al [14] in the cases where the same manifolds were examined. Among the six manifolds presented in Table 3, only two of the expected levels are missing: one in ⁵I₄ and one in ⁵S₂. The ⁵I₄ absorption spectra were very weak compared to those of the other manifolds, and it is possible that the missing level was just buried in the noise. According to Enderle et al [12], there is an accidentally degenerate level at the ~18394 cm⁻¹ which could account for our missing level assignment in the ⁵S₂ manifold.

Table 3. Observed energy levels of the higher manifolds of Ho³⁺ in YVO₄.

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From the energy level assignments of the ⁵I₈ and ⁵I₇ manifolds shown in Table 1 and the selection rules shown in Table 2, we were able to determine the specific transitions that lead to our previously observed laser lines [10]. In terms of excitation, our Tm fiber pump laser produced unpolarized emission at ~1966 nm, which corresponds to magnetic dipole transitions between the accidentally degenerate ground levels at 47.1 cm⁻¹ and the 5136 cm⁻¹ level of the excited manifold. The observed laser peak at ~2054 nm corresponds to a π electric dipole transition from the 5136 cm⁻¹ excited level to the 263.5 cm⁻¹ level of the ground state. The observed laser peak at ~2068 nm corresponds to a σ/axial electric dipole transition from the 5129.6 cm⁻¹ excited level to the 303.4 cm⁻¹ level of the ground state. Additionally, we were able to clarify the origins of the ~2041 nm laser emission peak observed at room temperature by Li et al [18]. This π electric dipole transition starts at the bottom of the excited manifold at 5124.5 cm⁻¹ and ends on the 227.9 cm⁻¹ level of the ground state. These transitions are shown in Fig. 1.

 

Fig. 1 Simplified energy level diagram showing the relevant laser transitions between the ⁵I₇ and ⁵I₈ manifolds, and the Boltzmann populations for 80 K and 100 K.

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3.2 Cross Sections

Absorption cross sections were calculated from the observed absorption spectra using Beer’s law and the rare earth dopant concentration. Stimulated emission cross sections were obtained using a combination of the McCumber and Fuchtbauer-Ladenburg (F-L) methods. The McCumber method is used to calculate the stimulated emission cross section from the absorption cross section using the reciprocity of absorption and stimulated emission transitions between any two energy levels [19]. The reciprocity relation is written

In birefringent materials, the F-L equation requires meticulous accounting of the various polarization states of the fluorescence, which we carried out using a generalized form of that given by Payne et al [20]:

Polarized (π, σ, and axial) ground state absorption and stimulated emission cross sections of Ho³⁺ in YVO₄ were obtained for temperatures of 80 K, 100 K, and room temperature. Figure 2 shows the cross section spectra for a sample temperature of 80 K.

 

Fig. 2 Absorption (solid line) and stimulated emission (dotted line) cross sections for polarized transitions between the ground state 5I8 and first excited state 5I7 on Ho3 + in YVO4 at 80 K. Baselines have been offset for clarity.

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In general, the absorption cross sections are quite different between the various polarization states. The need to record separate σ and axial spectra, due to the presence of magnetic dipole transitions, is immediately apparent when comparing these two spectra. The maximum absorption value of 1.5x10⁻¹⁹ cm² occurs at 1956.8 nm in the σ polarized case, although there is a significant π peak centered there as well. In the long-wavelength region of the spectra, the σ and axial spectra show negligible absorption while the π spectra does exhibit some weak peaks.

In stimulated emission, the π spectrum clearly dominates in the long-wavelength region with the 2041.7 nm and 2054.2 nm peaks. The σ and axial emission shapes in the long-wavelength region are nearly identical. Of particular interest is the peak that occurs at 2068.5 nm. This, along with the aforementioned 2054.2 nm π peak, correspond to the lasing wavelengths exhibited previously [9,10] and will be very important in subsequent discussions.

The polarized absorption and stimulated emission cross section spectra for 100 K are similar to those at 80 K, and thus are not presented here. The cross sections obtained at room temperature are nearly identical to those published by Golab et al [13] and are thus similarly omitted. The cross sections at the two previously mentioned laser wavelengths are presented in Table 4 for all recorded temperatures as their values will be important in later discussions. All values were obtained directly from their respective cross section spectra except for 2068.5 nm absorption at 80 K and 100 K. In these cases, the very weak peak heights were inferred from the stimulated emission cross sections via reciprocity.

Table 4. Stimulated emission (S.E.) and absorption (Abs.)cross sections for two laser-related peaks.

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3.3 Fluorescence and Radiative Lifetimes

The fluorescence lifetime of the ⁵I₇ manifold was measured at a number of temperatures between 8 K and room temperature. These lifetime values are shown in Fig. 3. In order to minimize the effects of radiation trapping, a crystalline sample was pulverized and a thin layer (~0.3 mm) of the resultant powder was excited. The difference in measured lifetimes between the pulverized sample and a bulk crystalline sample was compared with the shapes of fluorescence spectra obtained from 1 at.% and 2 at.% bulk samples (of similar thickness) to confirm that reabsorption affected the measured lifetimes by no more than a few percent. For all temperatures, the decay waveforms exhibit a single exponential behavior as shown in the inset to Fig. 3. The measured fluorescence lifetime increased by approximately 30% between 8 K and 200 K, while higher temperatures showed the lifetime to be fairly constant at ~3.2 ms. Given that reabsorption is too weak to explain this lengthening, these results indicate that radiative transitions from the higher levels of ⁵I₇ are weaker than those from the lowest levels, resulting in a reduced radiative transition rate as temperature increases. In support of this, all states of ⁵I₇ have significant thermal population by about 200 K, by which temperature the observed lifetime has leveled off.

 

Fig. 3 Fluorescence (solid) and radiative (open) lifetimes of the ⁵I₇ manifold of Ho³⁺ in YVO₄ as a function of temperature. Inset: Fluorescence decay waveforem at 80 K.

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Radiative lifetimes of the ⁵I₇ manifold were calculated from the stimulated emission cross sections by rearranging and integrating the F-L equation, with η/τ_f replaced by 1/τ_r. The results for several temperatures are shown in Fig. 3. The values are slightly longer than the observed fluorescence lifetimes, but the overall trend with respect to temperature is similar. This supports our attribution of the observed lifetime’s temperature dependence to changes in the radiative rate. Comparison of the radiative and observed lifetimes indicates that the quantum efficiency η of this transition is calculated to be ~80% over this temperature range. Interestingly, compared to the energy gap law presented by Ermeneux et al [21], our lifetime results better fit the trend established by their “small energy gap” data even though the energy gap between the ⁵I₇ and ⁵I₈ manifolds would place our results in their “large energy gap” region.

3.4 Gain Cross Section

Gain cross section is a useful parameter in predicting the wavelength of a laser. The gain cross section is calculated from the measured absorption and stimulated emission cross sections as follows

Table 5. Parameters used in previous laser results [10].

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In this work, we focus on the behavior of the two laser peaks that we have reported previously (2054.2 nm and 2068.5 nm) [10], and we concentrate our investigations on how their gain cross sections evolve as a function of temperature. To this end, Fig. 4 presents the observed laser wavelength gain cross sections as a function of population inversion β for the temperatures of 80 K and 100 K. The horizontal line in each graph represents the point where both laser wavelengths have the same gain cross section. This line can also be interpreted as the threshold gain cross section σ_g,th associated with a given output coupler reflectivity R_oc. The σ_g,th lines depicted in the 80 K and 100 K graphs of Fig. 4 were calculated based on the laser experiment parameters presented in Table 5.

 

Fig. 4 Gain cross section as a function of population inversion β for observed laser wavelengths 2054.2 nm (dashed line) and 2068.5 nm (solid line) at 80 K and 100 K. The horizontal line in each graph denotes the point where the two wavelengths have equal gain cross section, and is labeled by the output-coupler reflectivity needed to attain lasing threshold at this point.

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At 80 K, the point at which the two laser wavelengths cross each other occurs at a gain cross section of 1.36x10⁻²² cm⁻². If thinking of that in terms of a laser gain threshold σ_g,th, it corresponds to an output coupler reflectivity R_oc = 87%. Inspection of the 80 K graph shows that for output couplers with higher reflectivity than 87%, we would expect to see the ~2068 nm peak lase while for output couplers with lower reflectivity than 87%, we would expect the ~2054 nm peak to lase.

Comparing the 80 K results to the gain curves for 100 K shown in Fig. 4, we see that as the temperature is increased the gain cross section lines shift toward higher β values. These shifts are indicative of changes in the Boltzmann population of the respective laser levels. Figure 1 shows that, while the upper laser levels do not change much in population when going from 80 K to 100 K, the lower laser levels experience a significant increase in population. Additionally, we see from Fig. 1 that the lower level of the ~2054 nm laser transition experiences a larger increase in population across this temperature range than the lower level of the ~2068 nm laser transition. This explains why, in Fig. 4, the ~2054 nm gain cross section line moves further to the right with temperature than the ~2068 nm line. This has the effect of shifting the wavelength crossover point to higher gain cross section. As a result, the crossover point at 100 K occurs for an output coupler reflectivity of only 67%. Other than this crossover shift, the overall trends remain the same: higher reflectivities yield the longer laser wavelength while lower reflectivities allow the shorter laser wavelength to dominate.

The graphs in Fig. 4 clearly show that there is much happening in the fairly short temperature range between 80 K and 100 K. In a given laser experiment, the choice of output coupler reflectivity will determine which laser wavelength achieves threshold first. However, the output wavelength is also strongly dependent on the temperature of the laser crystal. If we used an output coupler with reflectivity intermediate between 67% and 87% and started the laser experiment at a temperature of 80 K, the ~2054 nm peak would clearly dominate. However, if the temperature of the gain medium were increased (by increasing the pump power, for instance) the wavelength would switch to the ~2068 nm line before the temperature reaches 100 K.

This behavior correlates very well with the low temperature laser results we previously published [10] assuming that the temperature increase of the laser gain crystal is caused by increased pump power. With the 88% output coupler, the crossover from short to long wavelength lasing in that work occurs almost immediately after the laser threshold is reached. For the 81% output coupler, the switch takes place in the middle of the pump power range. And in the case of the 75% output coupler, the laser continues emitting at 2054.2 nm across the whole range of measured pump powers indicating that the laser crystal never reaches the crossover temperature.

4. Conclusions

In this work, we have shown that the laser output wavelength in the cryogenic temperature region between 80 K and 100 K is very susceptible to changes in the gain crystal temperature. Based solely on the stimulated emission cross sections presented in Fig. 2, one might wonder why the ~2068 nm laser emission should ever be favored over the ~2054 nm peak. Subtle changes in the Boltzmann population of the lower laser levels hold the key to understanding the observed change in wavelength. Although scarcely discernible in Fig. 2, the 80 K absorption at ~2054 nm gives sufficient loss to favor lasing at ~2068 nm if the output coupling is small, despite the much smaller stimulated emission cross section at the longer wavelength. Since the absorption at ~2054 nm increases more rapidly than that at ~2068 nm for temperatures around 80 K, lasing at the longer wavelength is favored for an increasing range of output coupling as the temperature is increased. This behavior provides a probable explanation for our published dependence of laser wavelength on output coupler and pump power [10], and it shows that efficient dual-wavelength lasing of Ho³⁺ in YVO₄ requires precise temperature control of the laser gain medium.

Additionally, we have presented the most accurate energy level scheme for the ~2µm laser-relevant ⁵I₈ and ⁵I₇ manifolds, as well as verified and clarified some of the higher-energy manifolds, of Ho³⁺ in YVO₄. Comparison of the radiative and fluorescence lifetimes indicates a quantum efficiency of ~80% for this laser transition.