LiNbO3-Tm3+ Crystal. Material for Optical Cooling

: The possibilities of LiNbO 3 -Tm 3+ crystals for optical cooling based on anti-Stokes luminescence in the wavelength range of 1818–2200 nm are investigated. The concentration dependences of the ﬁnal temperature of the crystal have been determined under continuous (CW) excitation at wavelengths of 1822–1977 nm with a pump intensity F p = 5 × 10 21 cm − 2 s − 1 . It was shown that signiﬁcant cooling with ∆ T = 22 K, 19 K, and 16.4 K can be achieved, respectively, with excitation at wavelengths 1977, 1967, and 1948 nm.

The optical spectra of impurity absorption and radiation of the LN: Tm 3+ crystal in the 600-2000 nm wavelength region were studied in [8,9]. In particular, in [8], the standard Judd-Ofelt analysis of the absorption spectra from the 3 H 6 ground-state manifold is carried out and the intensity parameters are defined: Ω 2 = 6.29 × 10 −20 , Ω 4 = 0.54 × 10 −20 and Ω 6 = 0.79 × 10 −20 cm 2 . The energy levels scheme of ground, 3 H 6 , and first exited, 3 F 4 , manifolds of Tm 3+ ion in LN is given on Figure 1. The main spectroscopic parameters with taking into account the transitions between Stark sublevels of 3 H 6 and 3 F 4 are calculated in [9].
In this work, based on an analysis of the energy scheme of Stark levels and the results of calculations of spectroscopic parameters, we consider the possibilities of an LN-Tm 3 + crystal for optical cooling based on ASL in the wavelength range 1818-2000 nm.

Possibilities of Using the LN-Tm 3+ Crystal in Optical Cooling Systems
The absorption and luminescence spectra of the LN-Tm 3+ crystal at = 2 × 10 cm ( is concentration of impurity Tm 3+ ions) in the wavelength range of 1600-2000 nm at room temperature are shown in Figure 2. Luminescence measurements of the samples were done by using Quanta Master 51 spectrofluorometer (Photon Technology International Inc. NJ, USA) with an InGaAs detector for NIR (Teledyne Judson Technologies, 062-8451, Mongomeryville, USA) and PMT (Hamamatzu, NJ, USA) for the visible emission. Excitation sources used are 800 nm power tunable fiber coupled Fabry Perot continuous laser diode (Thorlab, Model LM14S2, NJ, USA). For laser excitation the spot size was about 3 mm at an excitation power of 500 mW. Absorption measurements were carried out using Cary 500 UV-VIS-NIR network spectrometer with 0.1 nm resolution.
As it is known, optical cooling is caused by anti-Stokes luminescence (ASL) at wavelengths satisfying the following condition , where is the excitation wavelength and 〈 〉-is the average luminescence wavelength defined by the formula below: ( ( )-is the spectral density of the luminescence intensity). According to the emission spectrum, we obtain: = 1818.6 nm ( Figure 2). Condition (1) limits the set of wavelengths of both excitation and ASL. Thus, analysis of the absorption spectrum shows that, to gain optical cooling, excitations at wavelengths in the range 1822-1977 nm are possible. A study of the energy scheme shows that, in the indicated wavelength range, spectral absorption lines can be induced by the 17 inter-Stark transitions. The spectroscopic parameters of the corresponding spectral absorption lines are given in Table 1. The values of the absorption efficiency, determined by the formula where , -is the integral absorption coefficient at the transition ⟶ , is the energy of the j-th Stark state of the main manifold, K is the Boltzmann constant, T is the temperature.

Possibilities of Using the LN-Tm 3+ Crystal in Optical Cooling Systems
The absorption and luminescence spectra of the LN-Tm 3+ crystal at N Tm = 2 × 10 20 cm −3 (N Tm is concentration of impurity Tm 3+ ions) in the wavelength range of 1600-2000 nm at room temperature are shown in Figure 2. Luminescence measurements of the samples were done by using Quanta Master 51 spectrofluorometer (Photon Technology International Inc. NJ, USA) with an InGaAs detector for NIR (Teledyne Judson Technologies, 062-8451, Mongomeryville, PA, USA) and PMT (Hamamatzu, NJ, USA) for the visible emission. Excitation sources used are 800 nm power tunable fiber coupled Fabry Perot continuous laser diode (Thorlab, Model LM14S2, NJ, USA). For laser excitation the spot size was about 3 mm at an excitation power of 500 mW. Absorption measurements were carried out using Cary 500 UV-VIS-NIR network spectrometer with 0.1 nm resolution.
As it is known, optical cooling is caused by anti-Stokes luminescence (ASL) at wavelengths satisfying the following condition where λ ex is the excitation wavelength and λ f -is the average luminescence wavelength defined by the formula below: -is the spectral density of the luminescence intensity). According to the emission spectrum, we obtain: λ f = 1818.6 nm ( Figure 2). Condition (1) limits the set of wavelengths of both excitation and ASL. Thus, analysis of the absorption spectrum shows that, to gain optical cooling, excitations at wavelengths in the range 1822-1977 nm are possible. A study of the energy scheme shows that, in the indicated wavelength range, spectral absorption lines can be induced by the 17 inter-Stark transitions. The spectroscopic parameters of the corresponding spectral absorption lines are given in Table 1. The values of the absorption efficiency, determined by the formula where α i, f -is the integral absorption coefficient at the transition i → f , ε j is the energy of the j-th Stark state of the main manifold, K is the Boltzmann constant, T is the temperature.  The spectroscopic characteristics of the ASL spectrum at room temperature in the wavelength range of 1820-2000 nm are given in Table 2.  The spectroscopic characteristics of the ASL spectrum at room temperature in the wavelength range of 1820-2000 nm are given in Table 2. It has to be noted that excitation at a given wavelength can initiate ASL at several wavelengths satisfying condition (1). So, when excited at a wavelength of 1837 nm, ASL is possible at wavelengths of 1820, 1822, 1826, and 1829 nm. The set of ASL wavelengths satisfying condition (1) at a fixed excitation wavelength is given in Table 3. The cooling efficiency at a given excitation wavelength is estimated by the formula [10] where η is quantum yield of luminescence from the excited level, α ab is the radiation absorption coefficient at the wavelength λ ex , α ph is the background absorption coefficient of the crystal matrix, L is the length of the crystal along the optical excitation. We notice that the probability of a non-radiative intra-center multi-phonon transition from a 3 F 4 manifold is negligible, so that the lifetime of an excited manifold is due to radiative transitions. It can be assumed that the quantum yield of luminescence from the Stark level of the excited manifold coincides with the branching coefficient of luminescence. The α ab (λ) absorption coefficient in (3) is related to the integral absorption coefficient by the relation α ab = N Tm ∑ α i, f /∆λ i→ f , (N Tm -is the concentration of impurity ions, ∆λ i→ f is the width of the corresponding spectral absorption line, the summation is performed over all transitions corresponding to a given wavelength).
Considering also that the intensity of the exciting radiation is sufficiently small, so that the system is far from saturation. Then, assuming L = 0.5 cm and α ph = 0.01 cm −1 [6], according to Tables 1 and 2, we estimate the value γ for various transitions inducing ASL at each excitation wavelength. Moreover, it should be noted that for a given excitation, ASL processes at several wavelengths satisfying condition (1) are permissible. Considering that ASL-inducing transitions are mutually independent, according to Table 3, it is easy to evaluate the cooling efficiency for each excitation wavelength: γ tot (λ ex ) = ∑ γ i (λ ex ) (the summation is carried out over all admissible ASL channels at a given excitation wavelength). The results are shown in Table 3. It can be noticed that excitations at the wavelengths of 1883, 1892, 1908, 1938, 1948, 1967, and 1977 are the most effective.
To estimate the cooling temperature, ∆T = T 0 − T, we start from the energy balance equation E ph (T 0 ) − E ph (T) = ε(T 0 ) (E ph (T) is the vibrational energy of the crystal at temperature T and ε(T 0 ) is the thermal energy absorbed in result of ASL). The latter, using the Debye approximation for lattice vibrations, can be represented as where N is the concentration of atoms in the matrix of the crystal LN, T D is the Debye temperature, T 0 is the initial temperature of the crystal, δ p and δ L -the Boltzmann factors determining the populations of the initial Stark levels from which the processes of absorption and luminescence occur, h is the Planck constant, c is the speed of light, τ is the lifetime of the level 3 F 4 and F p is the photon flux density of the exciting radiation, σ p is the cross section of the excitation transition, the summation on the right-hand side of (4) is carried out over all ASL channels, satisfying condition (1) for a given excitation wavelength. Equation (4) determines the functional dependence of the cooling temperature on the concentration of N Tm impurity ions, wavelength (λ ex ), and excitation intensity (F p ).
Crystals 2021, 11, 50 6 of 8 The first integral on the right-hand side of (4) is easily calculated: I(T 0 ) = 0.100862 at T D = 503 K and T 0 = 300 K. After non-complex transformations (taking into account T < T D ), the second integral can be transformed to the form: where Q n (x) = (n + 1) 3 x 3 + 3(n + 1) 2 x 2 + 6(n + 1)x + 6. Thus, Equation (4) takes the form: where ρ = N Tm /N (N = 3.14 × 10 22 cm −3 is the concentration of atoms in the matrix of the crystal LN). Solving Equation (6), we determine the cooling temperature T and ∆T = T 0 − T. Note that the cooling value, ∆T, depends on the cross section and the population of the initial transition level that induces absorption, as well as the number of ASLs initiated. Figure 3 shows the concentration dependences of the cooling temperature at the excitation intensity F p = 5 × 10 21 cm −2 s −1 at wavelengths leading to the most efficient cooling. The temperature values ∆T = T 0 − T for N Tm = 2 × 10 20 cm −3 are given in Table 4.
where N is the concentration of atoms in the matrix of the crystal LN, TD is the Debye temperature, T0 is the initial temperature of the crystal, and -the Boltzmann factors determining the populations of the initial Stark levels from which the processes of absorption and luminescence occur, h is the Planck constant, c is the speed of light, is the lifetime of the level 3 F4 and Fp is the photon flux density of the exciting radiation, is the cross section of the excitation transition, the summation on the right-hand side of (4) is carried out over all ASL channels, satisfying condition (1) for a given excitation wavelength. Equation (4) determines the functional dependence of the cooling temperature on the concentration of impurity ions, wavelength ( ), and excitation intensity ( ). The first integral on the right-hand side of (4) is easily calculated: ( ) = 0.100862 at = 503 K and = 300 K. After non-complex transformations (taking into account < ), the second integral can be transformed to the form: where ( ) = ( + 1) + 3( + 1) + 6( + 1) + 6. Thus, Equation (4) where = ⁄ ( = 3.14 × 10 cm is the concentration of atoms in the matrix of the crystal LN). Solving Equation (6), we determine the cooling temperature T and ∆ = − . Note that the cooling value, ∆T, depends on the cross section and the population of the initial transition level that induces absorption, as well as the number of ASLs initiated. Figure 3 shows the concentration dependences of the cooling temperature at the excitation intensity = 5 × 10 cm s at wavelengths leading to the most efficient cooling. The temperature values ∆ = − for = 2 × 10 cm are given in Table 4.   Figure 3. Concentration dependences of the cooling temperature at the excitation intensity F p = 5 × 10 21 cm −2 s −1 at wavelengths leading to the most efficient cooling.