In the recent years, infrared solid state lasers, fiber lasers, and optical amplifiers have attracted much attention due to their wide applications in telecommunications, sensors, medicine, atmosphere transmission, optical parametric oscillators, electronic vibronic lasers, and broadband communication^{[ 1], [ 2],[ 3]}. Ho³⁺ ion is one of the most important active ions applied to luminescence lasers because of its favorable energy level structure. It has been demonstrated that infrared laser emission of Ho³⁺ ion acts in the range of 1.2-4.9 μm including mid-infrared emission with transition⁵ I₇ →⁵ I₈ (2.0 μm) and⁵ I₆ →⁵ I₇ (2.9 μm) which attracted much attention in recent years^{[ 4],[ 5]}. Previous investigations about 2.0 μm emission band were mainly focused on the spectroscopic properties of Ho³⁺-doped glasses, and on the analyzing the population inversion level of those materials from the gain cross section spectra which were calculated by absorption and emission cross section and ion concentrations^{[ 6],[ 7]}. In order to achieve intense 2.9 μm mid-infrared emission for practical laser operation, co-doping of Pr³⁺ with Ho³⁺ has been used as a feasible alternative to quench efficiently the Ho³⁺:⁵ I₇ level^{[ 8]}. There are some reports about 2.9 μm emission of Ho³⁺-doped solid state materials^{[ 9],[ 10]}, but the optical gain properties at 2.9 μm emission, which is very important for laser operation to evaluate the performance of a laser media, have been rarely investigated.

Compared with fluoride glasses as host materials, the fluoride crystal LiYF₄ has been proved as a suitable laser materials from ultra-violet to mid-infrared wavelength because of their many advantages with low phonon energy, low thermal lens effect and laser threshold, and high incorporation of trivalent rare-earth ions that substitute for the Y³⁺ ions^{[ 11],[ 12]}. To our knowledge, Ho³⁺, Pr³⁺ co-doped LiYF₄ crystal has not been successfully obtained due to the difficulties of crystal growth, and the optical properties of Ho³⁺, Pr³⁺ co-doped LiYF₄ crystals around 2.9 μm have not been reported.

In this work, Ho³⁺-doped and Ho³⁺/Pr³⁺ co-doped LiYF₄ crystals were successfully prepared. Enhanced emission at 2.9 μm is realized in Ho³⁺/Pr³⁺ co-doped LiYF₄ crystal. The absorption and emission were measured, the spectroscopic investigations of 2.0 and 2.9 μm emission were carried out, and optical gain properties were analyzed.

Ho³⁺ singly doped and Ho³⁺/Pr³⁺ co-doped LiYF₄ crystals were grown by Bridgman method in a resistively heated Bridgman furnace along <001> direction. The LiF, YF₃, HoF₃, PrF₃ powders with 99.99% purity have been used as starting materials with the following molar compositions: 51.5%LiF-47.5%YF₃-1%HoF₃ and 51.5%LiF-47%YF₃-1%HoF₃-0.5%PrF₃ (mol%), respectively. Details of the growth procedure were described in literature^{[ 11],[ 12]}. The Ho³⁺ and Pr³⁺ concentrations in crystals were measured by an inductively coupled plasma (ICP) atomic emission spectrometry analysis. The Ho³⁺ and Pr³⁺ molar concentrations are 1.02% and 0.22% in Ho³⁺/Pr³⁺ co-doped LiYF₄ crystals, and 1.02% in Ho³⁺ singly doped crystal. According to the measured density of crystals, the number density was calculated to be 3.011 × 10²⁰ cm^-3 for Ho³⁺ and 0.65 × 10²⁰ cm^-3 for Pr³⁺ in Ho³⁺/Pr³⁺ co-doped LiYF₄ crystals, and 3.024 × 10²⁰ cm^-3 in Ho³⁺ singly doped crystal. The samples for spectroscopic measurements were cut from the grown LiYF₄ crystals along <001> direction and polished to 2.20 mm thickness. Structures of Ho³⁺/Pr³⁺ co-doped LiYF₄ crystal was investigated by X-ray diffraction (XRD) by using a XD-98X diffractometer (XD-3, Beijing) with Cu Kα radiation at 0.15403 nm, and the scanning 2 θ was from 10° to 90° with 0.02° increments and 6 s swept time. The absorption spectra in the range of 200-2500 nm of samples were carried out by using a U-4100 spectrophotometer. The emission spectra were tested with a Traix 320 type spectrometer (Jobin-Yvon Co., France) in the range of 1000-18,000 nm, and 1800-3020 nm excited by 640 nm light. All measurements were carried out at room temperature.

Fig. 1(a) presents the X-ray diffraction pattern for LiYF₄ sample with 1.02 mol% Ho³⁺ and 0.22 mol% Pr³⁺. Meanwhile, the peak positions in JCPD 77-0816 of LiYF₄ single crystal are listed in Fig. 1(b). It can confirm that Fig. 1(a) closely matches Fig. 1(b) and the current doping level do not cause obvious peak shift. The absorption spectra of the Ho³⁺-doped and Ho³⁺/Pr³⁺ co-doped LiYF₄ crystals are shown in Fig. 2. There are nine absorption bands located at 358, 416, 448, 472, 482, 536, 638, 1150 and 1932 nm in Ho³⁺-doped LiYF₄ crystals. They are ascribed to the transitions from the ground state⁵ I₈ to the different excited states:³ H₆,³ G₅,⁵ G₆ +⁵ F₁,⁵ F₂ +³ K₈,⁵ F₃,⁵ F₄ +⁵ S₂,⁵ F₅,⁵ I₆,⁵ I₇ of Ho³⁺ ions, respectively. Four new bands at 2300, 1530, 1443 and 592 nm, which are corresponding to the ground state³ H₄ to³ H₆,³ F₃,³ F₄ and¹ D₂ of Pr³⁺ ion, appear in Ho³⁺/Pr³⁺ co-doped LiYF₄ crystals besides above nine absorption bands of Ho³⁺ singly doped sample. A strong overlap around 2.0 μm between the⁵ I₈ →⁵ I₇ absorption transition of Ho³⁺ and the³H₄ →³F₂ absorption transition of Pr³⁺ is clearly shown in Fig. 2. It is expected that efficient energy transfer will occur from the⁵ I₇ excited state of Ho³⁺ to the³ F₂ states of Pr³⁺.

Fig. 1.

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	Fig. 1. (a) XRD pattern of the LiYF4:Ho3+/Pr3+; (b) standard line pattern of the orthorhombic phase LiYF4 (JCPD 77-0816).

Fig. 2.

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	Fig. 2. Absorption spectra of Ho3+-doped and Ho3+/Pr3+ co-doped LiYF4 crystals.

According to the framework of Judd-Ofelt theory^{[ 13],[ 14]}, the experimental oscillator strength f_exp for a transition can be determined by using the absorption spectral data and the following formula:

(1)

where N is the concentration of Ho³⁺, m and e are the mass and charge of electron, c is the velocity of light in vacuum, α( λ) = ln10·OD( λ) /d is absorption coefficient, d represents the thickness of the samples, OD( λ) is optical density, which is affected by the thickness of the samples, λ is the wavelength of the transition, Γ is the integrated absorbance for each absorption band used in calculation.

For the transitions from the ground state J to the excited states J′, the calculated oscillator strength, including both electronic dipole (ed) and magnetic dipole (md) transition component can be expressed as:

(2)

(3)

where h is the Planck constant, and J is the total angular momentum quantum number ( J = 8 in Ho³⁺). The term |<[ S, L] J|| U^{( t)}||[ S′, L′] J>|² = U_{( t)} (different with U^{( t)}) is the square of the reduced matrix element of the unit tensor operators, and can be considered independent on the host materials. Its values used in this work were quoted from literature^{[ 15]}.

(4)

According to the selection rules for magnetic dipole (md) transition in the lanthanides which are Δ L = Δ S = 0, Δ J = 0, ±1, Δ M = 0, ±1; only the⁵ I₈ →⁵ I₇ transition in all observed transitions includes a magnetic dipole component. The value of f′ was calculated by Carnall et al.^{[ 15]}. The Lorentz local field correction for the refractivity of the medium is χ_ed = ( n² + 2)/9 n and χ_md = n. n is the refractive index of the host at the mean frequency of the transition. The refractive index in LiYF₄ as light wavelength has been measured previously in literature^{[ 16]}. We fit the data to the Sellmeier formula n( λ) = A + Bλ²/( λ² - C) + Dλ²/( λ² - E) in order to determine the Sellmeier coefficients. The Sellmeier coefficients were found to be ( A = 1.1648, B = 0.2827, C = 0.0081, D = 0.1571, E = 115.7947). The root-mean-square deviation ( δ_rms) which represents the goodness of the fit between experimental and calculated line strength is defined as:

(5)

where M is the number of absorption bands which are used in the calculation. The values of δ_rms are 0.17 × 10^-6 for Ho³⁺:LiYF₄, and 0.24 × 10^-6 for Ho³⁺/Pr³⁺:LiYF₄, respectively.

Table 1 shows mean wavelength, integrated absorbance, measured and calculated oscillator strength of the Ho³⁺-doped and Ho³⁺/Pr³⁺ co-doped LiYF₄ at room temperature. From the least-square fit of measured and calculated electric dipole oscillator strength with Eq. (2), the three Judd-Ofelt intensity parameters of Ho³⁺ ions were obtained and shown in Table 2. The Ω₂, Ω₄, and Ω₆ in Ho³⁺:LiYF₄ are 2.45 × 10^-20 cm², 1.01 × 10^-20 cm², and 0.96 × 10^-20 cm², respectively, and in Ho³⁺/Pr³⁺:LiYF₄ are 1.51 × 10^-20 cm², 1.96 × 10^-20 cm², and 1.05 × 10^-20 cm², respectively. The intensity parameters Ω₂, Ω₄, Ω₆ and oscillator strength provide information on the symmetry and bonding of rare-earth polyhedra within the matrix^{[ 23]}. Ω₂ is strongly affected by covalency and Ω₆ is closely related to the rigidity of the host environment. It can be noted from Table 2 that the Ω₂ value decreases from 2.45 × 10^-20 to 1.52 × 10^-20 cm² as Pr³⁺ ion introduction into Ho³⁺:LiYF₄, indicating that the Pr³⁺ ion has an effect on the local environment of Ho³⁺.

Table 1.

Table 1.

Table 1. Mean wavelength, integrated absorbance, measured and calculated oscillator strength of the Ho3+-doped and Ho3+/Pr3+ co-doped LiYF4 at room temperature Transition J(5 I8) → J′ Ho3+:LiYF4 Ho3+/Pr3+:LiYF4 λ (nm) Γ (nm/cm) fexp × 10-6 fcal × 10-6 λ (nm) Γ (nm/cm) fexp × 10-6 fcal × 10-6 →5 I6 1150 17.498 0.497 0.521 1152 19.447 0.551 0.586 →5 F5 638 13.079 1.207 1.266 638 20.257 1.87 1.852 →5 S2,5 F4 536 15.224 1.991 1.767 534 18.917 2.493 2.246 →3 G5 416 4.847 1.052 1.076 414 8.408 1.843 2.084 →3 H5,3 H6,5 G2 358 7.105 2.083 2.051 360 7.200 2.087 2.041

Table 1. Mean wavelength, integrated absorbance, measured and calculated oscillator strength of the Ho3+-doped and Ho3+/Pr3+ co-doped LiYF4 at room temperature

Table 2.

Table 2.

Table 2. Comparison of Judd-Ofelt parameters of Ho3+ ions in Ho3+-doped and Ho3+/Pr3+ co-doped LiYF4 and other crystals Crystals Ω2 Ω4 Ω6 δrms Ref. ×10-20 cm2 ×10-6 Ho3+:LiYF4 2.45 1.01 0.96 0.17 This work Ho3+/Pr3+:LiYF4 1.52 1.96 1.05 0.24 This work Ho3+:YAG 0.04 2.67 1.89 - [17] Ho3+:LiYF4 1.16 1.62 1.60 - [18] Ho3+:LiYF4 1.03 2.32 1.93 0.13 [19] Ho3+:ZnWO4 4.61 0.16 0.48 0.25 [20] Ho3+:SrWO4 11.24 3.95 1.23 0.69 [21] Ho3+:SrMoO4 8.46 2.35 0.42 0.87 [22]

Table 2. Comparison of Judd-Ofelt parameters of Ho3+ ions in Ho3+-doped and Ho3+/Pr3+ co-doped LiYF4 and other crystals

Using Judd-Ofelt intensity parameters Ω_2,4,6, the radiative parameters, the radiative transition rates ( A), fluorescence branching ratios ( β), and radiative decay time ( τ_rad), can be obtained. The radiative decay rate including electronic and magnetic dipole transition from an excited manifold J to a lower manifold J′ can be therefore calculated by the equation:

(6)

where S_ed and S_md represent the electric and magnetic dipole line strength, respectively, and they are given by

equation(7)

(7)

(8)

The fluorescence branch ratio of a transition from an excited state J to the lower lever J′ is given by

(9)

Then the radiative lifetime of an excited state J is associated with the radiative decay rate in the relationship of

(10)

where the summation is over all transitions to every terminal state J.

The calculated radiative probabilities, radiative branching ratios and radiative lifetime of Ho³⁺-doped and Ho³⁺/Pr³⁺ co-doped LiYF₄ are listed in Table 3.The calculated radiative lifetime ( τ_rad) of the listed excited state J′ in Ho³⁺/Pr³⁺:LiYF₄ decreases by comparing with Ho³⁺:LiYF₄. Clearly, the calculated radiative rates of Ho³⁺:⁵ I₆ →⁵ I₇ transition is higher in Ho³⁺/Pr³⁺:LiYF₄, indicating that the 2.9 μm radiation tends to occur easily when Pr³⁺ is introduced.

Table 3.

Table 3.

Table 3. Calculated radiative rates, branching ratios and radiative lifetime for Ho3+:LiYF4 crystals and Ho3+/Pr3+:LiYF4 crystals Transition J → J′ λ¯ (nm) Ho3+:LiYF4 Ho3+/Pr3+:LiYF4 Aed (s-1) Amd (s-1) β τrad (ms) Aed (s-1) Amd (s-1) β τrad (ms) 5 I7 →5 I8 1960 32.1 17.41 1 20.1976 36.77 17.27 1 18.5037 5 I6 →5 I8 1175 75 0.8171 10.8955 84.43 0.825 9.7715 →5 I7 2934 7.37 9.41 0.1829 8.58 9.34 0.175 5 I5 →5 I8 900 27.23 0.3756 13.7913 32.1 0.3903 12.1603 →5 I7 1662 38.22 0.5272 42.51 0.5169 →5 I6 3831 2.93 4.12 0.0972 3.54 4.08 0.0928 5 I4 →5 I8 749 4.28 0.0789 18.4476 4.68 0.0835 17.8487 →5 I7 1211 24.06 0.4438 23.41 0.4179 →5 I6 2064 22.95 0.4235 24.55 0.4383 →5 I5 4472 2.92 0.0539 3.38 0.0604 5 F5 →5 I8 645 724.54 0.7625 1.0524 1063.52 0.7733 0.7271 →5 I7 961 177.72 0.187 252.98 0.184 →5 I6 1430 42.63 1.89a 0.0449 52.88 1.87a 0.0385 →5 I5 2282 3.39 0.0036 3.96 0.0029 →5 I4 4658 0.02 0.002 0.03 0.0014 5 S2 →5 I8 540 605.36 0.5356 0.8847 662.11 0.5314 0.8025 →5 I7 746 414.3 0.3665 453.14 0.3637 →5 I6 1000 73.81 0.0653 88.44 0.071 →5 I5 1354 18.73 0.0166 21.13 0.017 →5 I4 1942 17.9 0.0158 20.91 0.0168 →5 F5 3330 0.17 0.0002 0.30 0.0002 5 F4 →5 I8 536 1455.29 0.8168 0.5613 1915.94 0.7846 0.4095 →5 I7 738 140.2 0.0787 256.14 0.1049 →5 I6 986 108.1 0.0607 173.83 0.0712 →5 I5 1327 60.73 3.07b 0.0341 77.9 3.05b 0.0319 →5 I4 1887 9.85 0.0055 11.49 0.0047 →5 F5 3173 4.39 0.0042 3.69 0.0028 →5 S2 67,656 0.00 0.0000 0.00 0.0000 aValue is the sum of the three transitions of5 F5 →5 F5 +5 I4 +5 I5. bValue is the sum of the three transitions of5 F4 →5 I6 +5 I5 +5 I4.

Table 3. Calculated radiative rates, branching ratios and radiative lifetime for Ho3+:LiYF4 crystals and Ho3+/Pr3+:LiYF4 crystals

The emission cross section is a key parameter influencing the potential laser performance. Based on the measured absorption spectra shown in Fig. 2, the absorption and emission cross section for Ho³⁺ emissions at 2.05 μm are calculated by using Beer-Lambert equation and McCumber theory^{[ 24]}. The emission cross sections σ_em can be calculated by the following expression:

(11)

where σ_abs( λ) = α( λ)/ N represents the absorption cross sections, α( λ) is absorption coefficient and N is the number of ions in the unit volume, Z_l and Z_u are the partition functions of the lower and upper manifolds, respectively. Z_l/ Z_u can use the value of 0.8052 for the transitions⁵ I₇ →⁵ I₈ (2.05 μm) as reported in literature^{[ 19]}, and E_zl is the zero-line energy, and is defined as the energy difference between the lowest Stark level of the upper manifold and the lowest Stark level of the lower manifold. The energy levels reported for Ho³⁺:LiYF₄ in literature^{[ 25]} were used to calculate the zero-line energies for the manifolds studied. k is the Boltzmann's constant, T is the absolute temperature. The derived absorption and emission cross sections for 2.05 μm emissions are shown in Fig. 3. The maximum emission cross section of Ho³⁺:LiYF₄ crystal around 2.05 μm is 0.51 × 10^-20 cm². This value for 2.05 μm can be compared with one of some crystals: Ho³⁺:SrWO₄ (1.05 × 10^-20 cm²)^{[ 21]}, Ho³⁺:SrMoO₄ (0.271 × 10^-20 cm²)^{[ 22]}, Ho³⁺:LiYF₄ (0.39 × 10^-20 cm²)^{[ 25]}, Ho³⁺:Y₃Al₅O₁₂ (0.45 × 10^-20 cm²)^{[ 26]}. By comparing the parameters all above, the Ho³⁺:LiYF₄ crystal may be a good laser material for 2.0 μm infrared laser.

Fig. 3.

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	Fig. 3. Absorption and emission cross section line shapes for Ho3+ emissions at 2.05 μm in Ho3+:LiYF4 crystal.

Based on the above absorption and emission cross section spectra, the optical gain coefficient g( λ) can be calculated by the following equation:

(12)

where N₁ and N₂ represent the population volume-densities of upper and lower levers, respectively. The total population volume-density is N = N₁ + N₂, thus the gain cross section spectrum G( λ) can be given by:

(13)

where population inversion P = N₂/ N is assigned to the concentration ratio of Ho³⁺, and 0 ≤ P ≤ 1. The calculated gain cross sections for 2.05 μm transition of Ho³⁺ as a function of wavelength with different P values are shown in Fig. 4.It can be seen that the positive gain appears when P is around 0.3. It means that the pump threshold for obtaining 2.05 μm laser is probably lower, and this is an advantage for Ho³⁺-doped LiYF₄ infrared lasers.

Fig. 4.

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	Fig. 4. Gain cross-section spectra of Ho3+:5 I7 →5 I8 in Ho3+:LiYF4 crystal.

Fig. 5(a) shows the infrared emissions spectra of Ho³⁺:LiYF₄ and Ho³⁺/Pr³⁺:LiYF₄ crystal from 1100 to 3000 nm under the 640 nm excitation. Emission bands at 1.2, 2.05, and 2.9 μm were observed.

Fig. 5.

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	Fig. 5. (a) Infrared emission spectra of Ho3+:LiYF4 and Ho3+/Pr3+:LiYF4 crystal around 1.2 μm together with 2.05 and 2.9 μm under excitation at 640 nm, inset is the spectra around 2.9 μm; (b) simplified energy level diagram for Ho3+/Pr3+:LiYF4 crystal when pumped at 640 nm.

Under 640 nm excitation, in Ho³⁺/Pr³⁺ co-doped fluoride crystal, the intensity of three greatly enhanced mid-infrared emissions around 2841, 2888, and 2948 nm from the transition of Ho³⁺:⁵ I₆ →⁵ I₇ are quite strong which are shown in the inset of Fig. 5(a). But the intense emission intensity at 1.2 μm ascribed to the Ho³⁺:⁵ I₆ →⁵ I₈ transition was also observed, which is not beneficial to make the population inversion of the upper 2.9 μm laser level (Ho³⁺:⁵ I₆), and the corresponding transition Ho³⁺:⁵ I₆ →⁵ I₈ (1.2 μm) is only observed in low phonon energy host, such as fluoride^{[ 19]}, chalcohalide^{[ 27],[ 28]} and oxyfluoride^{[ 29]} glasses and crystals. However, a significant reduction in the emission intensity of the⁵ I₇ level at 2.0 μm is observed, which justifies that Pr³⁺ ions can be used effectively to depopulate the Ho³⁺:⁵ I₇ level. The emission at 2.0 μm is broad, which usually originates from the transition Ho³⁺:⁵ I₇ →⁵ I_8, and has been observed in many types of host including glasses^{[ 27]} and crystals^{[ 19],[ 30]} and the peak wavelength depends on the host materials^{[ 31]}. The simplified energy level diagram of the Ho³⁺, Pr³⁺ co-doped system is shown in Fig. 5(b). When the crystal is pumped by a 640 nm light, ions in⁵ F₅ level decay nonradiatively to the⁵ I₆ level, then decay radiatively to⁵ I₇ level with 2.9 μm emission or nonradiatively to⁵ I₇ level. Since the energy gap between the Pr³⁺:³ F₂ and Ho³⁺:⁵ I₇ level is very small, the energy of the Ho³⁺:⁵ I₇ level will be transferred to the Pr³⁺:³ F₂ level (ET shown in Fig. 5(b)), which depopulates the Ho³⁺:⁵ I₇ level, and makes the possibility of the 2.9 μm emission. The emission cross sections for 2.9 μm mid-infrared transition in Ho³⁺/Pr³⁺:LiYF₄ crystal are subsequently calculated by the Fuchtbauer-Ladenburg equation^{[ 32]}:

(14)

where A_rad is radiative rate, I ( λ ) is the emission spectrum intensity, I(λ)/∫λI(λ)ⅆλI(λ)/∫λI(λ)ⅆλ is the normalized line shape function of the experimental emission spectrum, c is the speed of light, n is the refractive index. By using the emission spectra data, the emission cross section for transition Ho³⁺:⁵ I₆ →⁵ I₇ in Ho³⁺/Pr³⁺ co-doped and Ho³⁺ singly doped LiYF₄ crystals were obtained and are shown in Fig. 6(a) and (b), respectively. Obviously, the maximum value of the emission cross section around 2950 nm, 0.68 × 10^-20 cm², is larger than the value of 0.53 × 10^-20 cm² in Ho³⁺ singly doped LiYF₄ crystal calculated by the same method. When the emission cross section for the transition Ho³⁺:⁵ I₆ →⁵ I₇ at 2.9 μm is known, the absorption cross section σ_abs can be derived from the calculated σ_em by using the deformation of the Eq. (12):

(15)

where E_zl is the zero-line energy defined as the energy gap between⁵ I₆ and⁵ I₇ manifolds, and the value is 3517 cm^{- 1 [ 19]}. For the Ho³⁺:LiYF₄, the value of Z_u/ Z_l is 0.98^{[ 24]}.

Fig. 6.

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	Fig. 6. Emission and absorption cross sections for the transitions Ho3+:5 I6 →5 I7 in Ho3+/Pr3+:LiYF4 (a), and in Ho3+:LiYF4 (b) crystals.

Based on the calculated absorption and emission cross-section spectra, the gain cross section G( λ) for 2.9 μm mid-infrared emission as a function of wavelength with different P values can be calculated according to the Eq. (13) and the spectra of the transition Ho³⁺:⁵ I₆ →⁵ I₇ in Ho³⁺/Pr³⁺:LiYF₄ and Ho³⁺:LiYF₄ crystal are shown in Fig. 7(a) and (b), respectively.

Fig. 7.

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	Fig. 7. Gain cross-section spectra of Ho3+:5 I6 →5 I7 in Ho3+/Pr3+:LiYF4 (a) and in Ho3+:LiYF4 (b) crystal.

Evidently, while P varies from 0.0 to 1.0 with an increasing step of 0.1, the gain cross section becomes positive once the population inversion level reaches 40% in Ho³⁺/Pr³⁺:LiYF₄ crystal, but in Ho³⁺ singly doped LiYF₄ crystal, the gain cross section does not become positive until the population inversion level reaches 50%. Obviously, with the introduction of Pr³⁺ ions, a low pumping threshold is achieved for the Ho³⁺:⁵ I₆ →⁵ I₇ laser operation.

Ho³⁺:LiYF₄ crystal and Ho³⁺/Pr³⁺:LiYF₄ single crystals with good optical quality can be grown by Bridgman method. The Pr³⁺ ion has great effect on the intensity parameters, radiative transition probabilities, radiative lifetimes and the branching ratios of Ho³⁺/Pr³⁺:LiYF₄, which result from the interaction between Ho³⁺ and Pr³⁺ ions. An enhanced mid-infrared emission at 2.9 μm as observed in Ho³⁺/Pr³⁺:LiYF₄ crystal under excitation at 640 nm is due to the energy transfer from the Ho³⁺:⁵ I₇ level to the Pr³⁺:³F₂ level. The emission cross sections emission at 2.9 μm in Ho³⁺/Pr³⁺:LiYF₄ crystal is 0.68 × 10^-20 cm² which is larger than the value of 0.53 × 10^-20 cm² in Ho³⁺ singly doped LiYF₄ crystal. The gain cross section is more likely to become positive in Ho³⁺/Pr³⁺:LiYF₄ than that in Ho³⁺ singly doped LiYF₄ crystal. All the results show that the Ho³⁺/Pr³⁺:LiYF₄ crystal may be a potential single crystal for 2.9 μm mid-infrared laser application.