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Abstract
Over the past decades, Yb3+-doped cubic sesquioxide crystals have been considered as ideal gain materials for ultrafast laser generation, owing to their high thermal conductivity and adequate optical characteristics. The broadening of spectra by mixing host crystals to obtain short pulses has been extensively explored; however, few studies have examined the mechanism of the crystal field effect on spectral broadening. This paper describes the spectral broadening process caused by the combination of the discrete transition peaks induced by the crystal field effect and electron-phonon coupling widening based on Yb:LuxSc2-xO3 crystals. The energy level splitting induced by the crystal field effect not only determines the emission peak positions, but also broadens the emission spectra in the mixed host materials through the increasing spin-orbit coupling effect. Moreover, with the involvement of the electron-phonon coupling and the crystal field effect, the spectral broadening is much more obvious at room temperature. These results not only explain the spectral broadening mechanism of Yb3+-doped sesquioxides but also provide important insights for the improvement of new ultrafast laser materials.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
As one of the most significant branches of laser technology, ultrafast laser technology has constantly been at the forefront of development, and has been widely applied in industrial processing, medical treatment, scientific research, and other emerging fields [1–5]. The all-solid-state laser pumped by a laser diode with a high average power together with a simple and reliable structure has become a new-generation ultrafast laser source. However, the further development of all-solid-state ultrafast laser technology requires excellent laser performance in terms of peak power and pulse width, for which a crucial factor is the optical and thermal property improvement of laser gain materials [6–8]. For example, the lasing medium is required to have a wider fluorescence spectral width to create a narrower pulse [9].
The common rare-earth ion Yb3+ exhibits significant advantages for laser pulse generation. Owing to its shell structure, it has simple two-manifolds that reduce the energy loss from relaxation oscillation, resulting in a more efficient optical transition. Simultaneously, the shielding effect of the 5s25p6 to the 4f13 shell electrons is attenuated, which facilitates interaction with the lattice and broadens the emission spectrum over those of other rare-earth ions [10]. Yb3+-doped borate crystals, such as Yb:YCOB [11,12] and Yb:BOYS [13], possess sufficient emission spectrum bandwidth for ultrashort pulse generation; however, their application in high-power output is limited because of their low thermal conductivity. In contrast, the emission spectra width of crystals with high thermal conductivity, such as Yb3+-doped garnet [14] (Yb:YAG) and pure sesquioxide [15,16] crystals (Yb:Lu2O3, Yb:Sc2O3), are insufficient to generate narrow pulses. Therefore, it is critical to explore crystal materials that have a wide bandwidth and high thermal conductivity for ultrafast laser pulse generation.
The widely studied sesquioxides are multifunctional crystals with low phonon energy and high thermal conductivity that are suitable as laser gain material [17]. For example, the ultrafast laser has been achieved in a Kerr lens mode-locked (KLM) Yb:Lu2O3 thin-disk laser (TDL) oscillator with a pulse width of 95 fs, as well as the average output power of 21.1 W which is the highest in the sub-100-fs regime [18]. Although the emission spectrum bandwidth of Yb3+-doped pure sesquioxide is relatively narrow (∼12 nm), we recently showed that ligand engineering can be used to increase disorder in the form of mixed host crystal compositions and broaden its spectrum [19,20]. For instance, the shortest pulse durations of 74 fs have been realized based on the bulk Yb:LuScO3 mixed crystal [17,21]. In the Yb:LuScO3 TDL, the highest average power of 5.1 W in the sub-100-fs regime was obtained with a pulse width of 96fs [22]. Meanwhile, a pulse duration of 101 fs was obtained in the ternary composition Yb:(Lu0.33Sc0.33Y0.33)2O3 TDL, with an output power of 4.6 W [23]. However, the mechanism underlying the broadening effect requires further experimental and theoretical studies.
In this work, the crystal field parameters (CFPs) of Yb3+-doped sesquioxide crystals were fitted using the CFP fitting program CFPFit. Subsequently, the crystal field strength was calculated and its effect on the energy level splitting analyzed. Simultaneously, the vibrational modes participating in spectral broadening through electron-phonon coupling were identified using first-principles calculations of the lattice vibrations and crystalline Raman spectra. Thus, the broadening process of the emission spectrum was explained, and the contributions of energy level splitting and electron-phonon coupling were distinguished. This work is important for understanding the spectral broadening processes and may be used as a guideline for the development of ultrafast laser crystals.
2. Experimental section
Yb3+ ion-doped sesquioxide crystals were grown using the optical floating zone (OFZ) method. The crystal structures were solved using X-ray diffraction data measured by Bruker Axs D8 Advance XRD [19,20], while the crystal chemical composition was determined by X-ray fluorescence (Rigaku Zsx Primus) analysis. The absorption and emission spectra were measured at room temperature using a UH4150 Spectrophotometer and an Edinburgh Instruments FLS920 fluorescence spectrometer, respectively. Raman spectra were obtained using a LABRAM HR-800 Raman spectrometer with a scanning step size of 0.5 nm and a 532 nm laser.
The phenomenological CFPs were calculated using the CFP fitting program CFPFit [24,25]. A superposition model (SM) [26,27] was selected to obtain the initial CFP, which reduces the number of parameters needed for Yb3+ owing to its limited observed energy levels at low-symmetry sites. The detailed analysis comprised two steps: (1) The intrinsic CFPs Bk of the superposition model were fitted and used to calculate the initial values of the CFPs $B_q^k(0)$, where (0) denotes the initial parameters obtained by SM. (2) The CFPs were again fitted to the observed energy-level fitting via the numeric iteration method, and the final CFPs $B_q^k$ were obtained. The calculated energy levels were well-matched to the experimental values at this stage.
The spectral peaks corresponding to the pure electron and electron-vibration coupling transitions were obtained by decomposing the experimental emission spectra measured at room temperature with the Lorentz profile function. The densities of the phonon states and vibrational modes were calculated by first-principles calculations based on the density functional theory (DFT), as implemented in the Cambridge serial total energy package (CASTEP) code [28]. The exchange-correlation function was described using generalized gradient approximation (GGA) with Perdew-Burke-Ernzerhof (PBE). The phonons were calculated using the linear response method. Nom-conserving was selected as the pseudopotential, and the cutoff energies of the plane wave for convergence calculation were 900 eV for Sc2O3 and 990 eV for Lu2O3.
3. Results and discussion
Lutetium and scandium oxide crystals exhibit a cubic phase [29,30] and bixbyite structure at room temperature. X-ray diffraction (XRD) analysis revealed that the grown Yb:LuxSc2-xO3 crystals indeed displayed such symmetry [19], with an $\textrm{m}\bar{3}$ point group and $\textrm{Ia}\bar{3}$ space group. The symmetrical structure in Fig. 1(a) contains two cationic sites, with the centrosymmetric C3i symmetry site labeled as Re1 and the non-centrosymmetric C2 symmetry site as Re2. The cation located at the Re1 site is connected to six oxygen ions with equal bond distances and has regular octahedral ligands. In contrast, the Re2 site cations comprise irregular octahedral ligands. The Yb3+ ions will occupy the two cationic sites when they are doped into the crystal. Thus, Yb3+ ions at the non-centrosymmetric Re2 sites contribute to the electric dipole moment transition, whose strength is much larger than that of the magnetic dipole by a few orders of magnitude, while contributing to the magnetic dipole moment transition at the centrosymmetric Re1 sites [31]. Because the electric dipole transition plays a major role in luminescence and there are three times as many Re2 sites as Re1 sites in a cell, the crystal field of Yb3+ at Re2 sites was studied in this work.
Fig. 1. (a) Structure of the Yb:LuxSc2-xO3 crystal cell after deletion. The intersection of the light blue lines at the center is the Re1 site ion. (b) Coordination octahedron composed of the Re2 site ion and surrounding oxygen ions. (c) Energy levels and transitions of Yb3+ ions doped into the sesquioxide. The ground state 2F7/2 and excited state 2F5/2 of the Yb3+ ion are split into four and three Stark energy levels, marked (1)–(4) and (5)–(7), respectively, in increasing energy order.
The Re2 site is occupied by the rare-earth ions Re (Re = Lu3+, Sc3+, and Yb3+). Its ligands comprise an irregular octahedron with six oxygen ions [Fig. 1(b)], which can be divided into three groups based on their bond lengths. These bonds are labeled based on their structural positions [Fig. 1(b)]. Thus, four of the six Re2–O bonds, which are denoted as O1 and O2, are approximately in one plane, while the other two bonds have the same bond length with a bond angle of ∼139 °. The two oxygen ions with out-of-plane pair of bonds are labeled as O3. The two oxygen ions with the bonds in the plane and with a similar deviation direction as that of O3, relative to the center position, are denoted as O2, and the corresponding bond angle is ∼114 °. Finally, the remaining two oxygen ions, denoted as O1, comprise a pair of bonds with equivalent bond lengths and a bond angle of approximately 87 °.
Eleven different 5 at.% Yb3+ ion-doped LuxSc2-xO3 crystals were grown, with a gradual mixing from pure scandium to pure lutetium ions in the host crystal cationic site. The crystalline components of the grown crystals were determined by X-ray fluorescence spectroscopy. The values of the cationic site occupation (x) of the 11 LuxSc2-xO3 crystals were 0, 0.19, 0.40, 0.50, 0.76, 0.94, 1.10, 1.32, 1.52, 1.66, and 2.00.
The Yb3+ ion with the 4f13 configuration is a rare-earth ion with Kramers degeneracy. Owing to spin-orbit coupling, the energy level of the Yb3+ ion splits into 2F7/2 and 2F5/2 manifolds in the free state [32]. When the active ion is doped into the host crystal, the even terms of the crystal field result in Stark splitting of the energy levels [33]. The ground state 2F7/2 and excited state 2F5/2 of the Yb3+ ion split into four [Fig. 1(c), (1)–(4)] and three [(5)–(7)] Stark energy levels. Each energy level was deduced from the experimental absorption and emission spectral data. CFP fitting is performed at these experimental energy levels.
The Hamiltonian of Yb3+ ions doped into LuxSc2-xO3 crystals can be expressed by [34]
The superposition model assumes that the total crystal field effect experienced by the central rare-earth ion is the sum of each ligand acting alone. $B_q^k$ in Eq. (1) is expanded using the equation
where gk,q is the coordinate factor dependent on the coordination angle and distances RL and R0, which are the distances from the L-th and nearest ligands to the center rare-earth ions, respectively; Bk is the intrinsic CFP and tk is a power exponent, with values of 3, 5, and 7 for t2, t4, and t6, respectively.There are three intrinsic CFPs—B2, B4, and B6—for the site occupied by Yb3+ ions with C2 symmetry. Moreover, there are 15 mutually independent parameters in the complex $B_q^k$ for k = 2, 4, 6, with q as the even integer in –k ≤ q ≤ k. For each component of the 5 at.% Yb:LuxSc2-xO3 crystals, the ion coordinates of the structure and experimental energy levels are substituted into the SM fitting program to compute gk,q. To start the SM fitting, the initial value of (B2, B4, B6) is selected to be (10, 10, 10) based on the preliminary calculations from three parameter sets, (0, 0, 0), (10, 10, 10) and (100, 100, 100) [25]. The intrinsic CFP, residual R, and root-mean-square error σ obtained by the least method iteration are listed in Table 1. The CFPs $B_q^k(0)$ listed in Table S1 were obtained via the SM fitting program and then used as the initial parameters of the CFPFit program. The final fitted CFPs $B_q^k$ are shown in Table 2, and the corresponding experimental and calculated energy levels are shown in Table S2.
Table 1. Intrinsic crystal field parameters, residuals, and σ obtained by SM fitting.
Table 2. Crystal field parameters obtained by CFPFit (unit: cm−1).
Bk represent the net repulsion interaction between coordinated O2- ions and 4f shell electrons, which should be positive according to the previous study [26]. The B2 and B6 values first increase and then decrease with increasing x, while the B4 values vary inversely, and their inflection points all appear at x = 0.50. Speculatively, this phenomenon is due to the sudden structural distortion when Lu3+ is doped into the Sc2O3 matrix, and Bk is relatively sensitive to the induced structural change. Otherwise, the majority of the σ values are >10, indicating that the calculation accuracy is unsatisfactory; therefore, it was necessary to fit the CFPs using a second step. After the second fitting step, the calculation accuracy was significantly improved, and the residual R values were all <0.05%.
The point-charge model [34] was used for the second step fitting. This model assumes that the crystal field felt by the cation at the Re2 site is the total effect from its six coordinated O2- ions, with the $B_q^k$ parameter expression:
The conventional spherical coordinate system was selected to analyze the signs and values of the parameters. The Z’-axis of the spherical coordinate system was along the two-fold rotation axis of the ligand. Here, ZLe2 expresses the product of the charges of the L-th ligand and electron, RL is the length between the L-th ligand and the central ion, $\left\langle {{r^k}} \right\rangle$ is the radial expectation value, and $Y_k^{q \ast }({\theta _L},{\phi _L})$ is the complex conjugate operation of the spherical harmonics with the angular coordinates of the L-th ligand θL and φL. The sign for the parameters is determined by the lattice structure and selected coordinate system. Notably, the polar angle, azimuthal angle, and radial distance of the ligand ions all affect the sign of the parameters. Thus, if the Re2 coordination octahedron is an ideal polyhedron, for each $B_q^k$ parameter, the sign of the L-term corresponding to the L-th ligand in the sum will be determined with definite angles. The sign of $B_q^k$ is determined solely by θL when q = 0; in contrast, when q ≠ 0, it depends on both θL and φL [35]. For example, one term of $B_0^2$ will be positive when θL is in the range 0°–54.7° or 125.3°–180°, while for $B_0^4$, one term is negative for 30.6° ≤ θL ≤ 70.1° or 109.9° ≤ θL ≤ 149.4°. One term of $B_0^6$ is positive when the following conditions are satisfied: 0° ≤ θL ≤ 21.1°, 48.7° ≤ θL ≤ 76.1°, 103.9° ≤ θL ≤ 131.3°, or 158.9° ≤ θL ≤ 180°.
The theoretical signs of the real and imaginary parts of $B_q^k$ are obtained as shown in Tables S3 and S4, by inserting the determined structural parameters into Eq. (5). All the signs of the $B_q^k$ parameters calculated from the ideal polyhedron structure (Tables S3 and S4) are the same as those obtained by the SM fitting program (Table S1). The signs are reversed after CFPFit (Table 2) for $B_0^2$, the real parts of $B_2^4$ and $B_2^6$, and the imaginary parts of and $B_6^6$ owing to the ligand distortion caused by cationic substitution. In the meantime, some of the signs of the components differ from those of others in the same column of Table 2, especially for $B_q^6$. All the symbol changes may also be attributed to some other factors such as configuration interaction [36] and dipolar contribution [37].
Numerous factors contribute to the CFP; hence, it is difficult to provide an unambiguous interpretation of their effect in the current study. For example, the contributions to the $B_q^k$ value differ for each value of k. Considering several main factors, such as the point-charge, dipole, and shell shielding effect on the crystal field of a rare-earth-doped sesquioxide system [37,38], it can be deduced that the point-charge effect is a major contributor to $B_q^4$. Figure 2 illustrates that the absolute value of $B_q^4$ is greater than that of the other parameters, indicating that the contribution of the point charge is a significant factor affecting the crystal field.
Fig. 2. Trends of each crystal field parameter with the gradient components. (a) Five crystal field parameters with moderate variation trends and (b) four crystal field parameters with marked variation trends.
The absolute values of the CFPs listed in Table 2 are shown in Fig. 2. The trends of the parameters with the gradient components show distinct characteristics, indicating that the effects of the structure and composition on each parameter differ. The values of most of the CFPs varied gradually with increasing Lu3+ ion content [Fig. 2(a)]. For the other four parameters [Fig. 2(b)], the extrema appeared near x = 0.5 and 1, attributable to the distinct structural distortions caused by the change in the main ion composition in the matrix crystals. With the increase in x from 0 to 1, the Sc3+ ion, with its smaller radius, is the main ion, while the Lu3+ ion, with its larger radius, becomes the main ion at x >1.
The CFPs were calculated using the following formula:
Theoretically, Nυ is negatively correlated with the distance between the cations and anions according to Eq. (5) and Eq. (6), while the change in the distance is consistent with the average cationic radius. Figure 3 illustrates the linear relationship between the crystal field strength and average cationic radius. The following semi-empirical formula was obtained by fitting
where the average ionic radius rave (pm) of the cationic site was obtained by adding the products of the molar fractions and the corresponding ionic radii [39,40] of the Yb3+, Lu3+, and Sc3+ ions for each component. The radius of the Lu3+ ion is larger than that of the Sc3+ ion; therefore, the average ionic radius gradually increases with increasing Lu3+ ion content. Moreover, the Nυ value of the Yb3+ ion is larger than that of the Eu3+ ion in the cubic sesquioxide system [41], indicating that the interaction between the Yb3+ ions and the crystal field is stronger.The crystal field strength parameters intuitively express the ability of the crystal field to split the energy levels, with a stronger crystal field strength leading to larger energy splitting. The experimental and calculated splitting values of the 2F7/2 and 2F5/2 energy levels are shown in Table 3, and the trends of splitting and average energy levels with x are shown in Fig. 4. The results illustrate that the splitting extent decreases with increasing x, while the split energy level difference of the 2F7/2 ground state remains higher than that of the excited state 2F5/2. Eave is the average of all splitting energy levels, which contains the spherically symmetric parts of the free-ion and crystal field, and it decreases when the splitting weakens. Moreover, as the splitting energy increases, the difference between the ground and excited state energies decreases; hence, the emission wavelength increases. This indicates that a strong crystal field strength increases the emission wavelength, resulting in the enlargement of the spectral frame and broadening of the emission spectrum. In summary, the ionic radius effect is obvious, because the decreasing of the Lu3+ content enhances the crystal field and broadens the emission spectrum.
Fig. 4. Stark splitting energy level (left axis) under the influence of the crystal field and average energy level (right axis) versus x.
Table 3. Splitting values of 2F7/2 and 2F5/2 energy levels from experiment and calculation (unit: cm−1).
In contrast to the above inverse trend, the variation of the spin-orbit coupling strength with varying matrix composition is significant (Fig. 5). The spin-orbit coupling parameter ξ is obtained using Eq. (8) [34]
where U is the potential energy of the central field [42]. Generally, the ξ of the free Yb3+ ion is estimated at ∼2900 cm−1 [43]. Here, as presented in Fig. 5, the maximal value of ξ is calculated to be 2891.5 cm−1 when x = 1 and then decreases with the increasing component difference between Lu3+ and Sc3+. According to the fitting results, the differential dU/dr is positively correlated with r, resulting in the variation of ξ as mentioned above.The effect of the crystal field on the energy level splitting determines the peak position of the spectrum. On the other hand, the coupling of the electrons and phonons broadens the spectrum of each peak position [44], resulting in an overall widening of the emission spectrum. To determine the effect of electron-phonon coupling on spectral broadening, it is necessary to analyze the lattice vibrations; thus, Raman spectral measurements, first-principles calculations, and spectral decomposition were next performed. For simplicity, a primary cell with eight formula units was used to calculate the vibration state. The irreducible representations of the vibrational modes using group theory analysis are:
The experimental Raman spectra and calculated phonon density of states are displayed in Fig. 6 and Fig. 7, respectively. Together, the experimental and calculated data show that the high-frequency vibration (>300 cm−1) is related to the oxygen ions, while the Sc3+ and Lu3+ ions contribute in the low-frequency region. Further, the partial phonon density of states from the Re2 ion at the C2 site is greater than that of the Re1 ion at the C3i site, owing to there being more Re2 ions in one unitcell. The vibration energy is closely related to the ionic mass [45]; therefore, as component x increased from 0 to 2, the Sc3+ ion content decreased, and the vibrational states distributed in the range 150–350 cm−1 weakened. Correspondingly, as the content of the heavier Lu3+ ions increased, the vibration activity at 50–200 cm−1 also increased. Simultaneously, the vibration frequency of the strongest Raman peak gradually decreased from 415 to 392 cm−1.
The emission spectra of each component at room temperature decomposed into several peaks with Gauss and Lorentz spectral line shapes [46,47], owing to the inhomogeneous broadening of electronic transition spectra influenced by crystal fields and the homogeneous broadening caused by the vibrations, respectively. The peaks corresponding to the electronic transitions from the excited to the ground state electron energy levels and vibrational energy levels were also identified (Fig. 8). The vibrational transition peaks located from 980 to 1041 nm were the phonon sidebands of (5)-(1) energy level transitions, and the corresponding relations between the vibrational frequencies and vibrational transition peaks are listed in Table 4. Taking the Yb:Lu0.94Sc1.06O3 crystal as an example, the vibrations with frequencies of 211.0, 405.5, and 642.0 cm−1 correspond to the peaks at 995.8, 1013.3, and 1038.7 nm, respectively. The vibrational transitions peaks above 1041 nm were mainly the phonon sidebands of (5)-(2) and (3) energy levels transitions.
Fig. 8. Decompositions of the emission spectra at room temperature for x contents of (a) 0, (b) 2.00, (c) 0.94, and (d) 1.10. The electronic transition peaks have been identified as the transitions from the 2F5/2 energy levels (5)-(7) to the four 2F7/2 energy levels (1)-(4). The vibrational transitions (1), (2), and (3) corresponding to the phonon sidebands of (5)-(1), (5)-(2), and (5)-(3) energy levels transitions, respectively.
Table 4. Vibrational transition peaks (PVT) and corresponding measured vibrational frequencies (FV)
Two lattice vibrations were involved in all the vibrational transitions, corresponding to the strongest Raman intensity and vibrational energy. Both vibrational modes belong to the irreducible group representation Fg. According to the first-principles calculation results, the two types of vibrational modes of Sc2O3 and Lu2O3 crystals were next analyzed (Fig. 9). The strongest Raman modes (431 cm−1 for Sc2O3 and 331 cm−1 for Lu2O3) are opposite bond-pair stretching vibrations, while the strongest vibrations (670 cm−1 for Sc2O3 and 530 cm−1 for Lu2O3) are from O ions along with the Re2–O1 direction.
An increase in the x content from pure Sc3+ to pure Lu3+ in the mixed host decreases the crystal field strength. This causes the peak spacing of the emission spectrum to decrease because of the decrease in energy level splitting. Owing to the participation of electron-phonon coupling and other effects, the spectral broadening of each peak is most significant when the mixing ratio is equal at room temperature. Therefore, with both the crystal field and the electron-phonon coupling effects influencing the spectral broadening at room temperature, the crystal composition with the widest spectral width was determined to be Yb:Lu0.94Sc1.06O3.
4. Conclusion
In this study, the mechanism underlying emission spectrum broadening in Yb3+-doped cubic sesquioxide crystals was revealed. The intrinsic crystal field parameters Bk and CFP $B_q^k$ were obtained and analyzed successively using the CFPFit program. Thereby, the energy levels of Yb3+ were obtained and the transition wavelengths of pure electron states were identified, mainly determined by the crystal field effect. Subsequently, the density spectra of phonon states were calculated from the first principles and were confirmed by Raman experimental results, proving that the involved electron-phonon coupling also contributes to the spectral broadening in the mixed sesquioxide crystals. The results and discussions elucidate the derivation of the spectral broadening, and the Yb:Lu0.94Sc1.06O3 crystal with the widest emission spectrum has been optimized as well. This wide-spectrum Yb3+-doped cubic sesquioxide crystal shows great potential for application to ultrafast laser development.
Funding
National Key Research and Development Program of China (2016YFB1102301); National Natural Science Foundation of China (51772173, 51802307, 51902181, 52025021).
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.
Supplemental document
See Supplement 1 for supporting content.
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