Temperature-Dependent Sellmeier Equations of IR Nonlinear Optical Crystal BaGa 4 Se 7

The thermal dependent principal refractive indices of a new promising IR nonlinear optical crystal BaGa4Se7 at wavelengths of 0.546, 0.5806, 0.644, 0.7065, 1.530, 1.970, and 2.325μm were measured by using the vertical incidence method within the temperature range from 25 to 150 ◦C. We derived equations of thermal refractive index coefficients as a function of wavelength that could be used to calculate the principal thermal refractive indices at different wavelengths. The temperature-dependent Sellmeier equations were also obtained and used to calculate the phase matching angles for the optical parametric process of BaGa4Se7 crystal at different temperatures.


Introduction
At present, there has been an intensive trend to explore novel mid-far IR nonlinear optical (NLO) crystals for generating mid-far IR laser sources, which have many important applications including atmospheric monitoring, laser radar, and laser guidance [1][2][3][4].In IR nonlinear optics, the chalcopyrite-type AgGaQ 2 (Q = S, Se) and ZnGeP 2 crystals have been practically used since the 1970s.However, AgGaQ 2 (Q = S, Se) has a low laser-damage threshold, and ZnGeP 2 exhibits strong two-photon absorption of the conventional 1064 nm pumping laser sources, severely limiting their applications [5][6][7].
Recently, BaGa 4 Se 7 (BGSe) was reported as a promising NLO crystal for practical applications in the mid-IR spectral range.The crystal belongs to the monoclinic space group Pc.It possesses intriguing overall properties for IR NLO applications including wide transparent range (0.47 to 18 µm), suitable birefringence, large nonlinear optical coefficients, and high laser damage threshold [8][9][10][11][12].The outstanding properties of BaGa 4 Se 7 have been exemplified by some recent laser experiments [13][14][15][16][17].Given the outstanding NLO properties and the preliminary laser experiment results, BGSe may have attractive applications in three aspects: (1) realizing mid IR output using the conventional 1 µm laser as the pumping source; (2) the generation of IR laser in the long wavelength, especially the 8-15 µm range; (3) the second-harmonic generation the CO 2 laser.
During high-power laser output process, the effect of self-heating in NLO crystal leads to variation of refractive index, and thus the phase-matching (PM) direction will be distorted, which could dramatically influence the stability of output power and the output mode of the laser cavity.To solve this problem, NLO crystal can be attached to some cooling device to obtain a stable temperature.To predict the PM angles more accurately at elevated temperature, it is of significance to determine the principal refractive indices at different temperatures and to obtain the thermal refractive index coefficients and the temperature-dependent Sellmeier equations, which are important parameters for designing a frequency-conversion device at the actual operating temperature.
In this work, we determine the principal refractive indices at different temperatures of BGSe crystal, and present its thermal refractive index coefficients and temperature-dependent Sellmeier equations for the first time.

Thermal Refractive Index Coefficients
As shown in Table 1, refractive indices n x ,n y , and n z all increase slowly with the increased temperature at different wavelengths.For a specific wavelength, the index can be assumed as a linear variation with increased temperature, which could be expressed as where n is the refractive index at temperature T, n 0 is the refractive index at T 0 , and dn/dT is the thermal refractive index coefficient.According to the measured principal indices, the relationship between dn/dT of the principal refractive indices and the wavelength λ could be fitted, shown in Equation(2): dn x /dT = (0.6837/λ 3 − 1.7607/λ 2 + 1.6316/λ + 0.0318) ×10 −4 dn y /dT = (0.2692/λ 3 − 0.3112/λ 2 + 0.2201/λ + 0.4867) × 10 −4 dn z /dT = (0.7223/λ 3 − 1.5170/λ 2 + 1.2953/λ + 0.1296) where λ is in micrometer and 0.254 µm ≤ λ ≤ 2.325 µm.The thermal refractive index coefficients for n x , n y , and n z were calculated by monadic linear regression method and are given in Table 2. Table 2 shows that these constants are all positive with magnitude level of 10 −4 .Refractive indices corresponding to different wavelengths at different temperatures were calculated by using Equations ( 1) and (2) (T 0 is 25 • C, n 0 is the experimental value of refractive index at 25 • C). Figure 1 shows the theoretical and measured values of n x , n y , and n z .The difference between the measured and calculated values was less than 2 × 10 −4 .This result verifies the reliability of Equation ( 2).The coefficients of Equation ( 2) are listed in Table 2. shows that these constants are all positive with magnitude level of 10 −4 .Refractive indices corresponding to different wavelengths at different temperatures were calculated by using Equations ( 1) and ( 2) (T0 is 25 °C, n0 is the experimental value of refractive index at 25 °C).Figure 1 shows the theoretical and measured values of nx, ny, and nz.The difference between the measured and calculated values was less than 2 × 10 −4 .This result verifies the reliability of Equation ( 2).The coefficients of Equation ( 2) are listed in Table 2.

Sellmeier Equationsof BaGa 4 Se 7 Crystal
The Sellmeier equation of given temperature can be fit as Equation (3) and the Sellmeier coefficients are listed in Table 3.The difference between the measured and calculated values was less than 3.6 × 10 −4 .

Temperature-Dependent Sellmeier Equations
The temperature-dependent Sellmeier equations of n x , n y , and n z were obtained by using the least-square-fit method, as shown in Equation (4) and Table 4, where iis x, y,or z, λ is the wavelength in micrometer, and A, B, C, D, E, F, and G are constants. (4) Average differences between calculated and experimental indices are found to be in the order of 2.8 × 10 −4 , 2.4 × 10 −4 and 2.7 × 10 −4 for n x , n y and n z , respectively.Fitting quality is also demonstrated by the fact that maximum difference (accounting for all principal indices) between theoretical and measured values is found to be 5 × 10 −4 , that is still within our experimental accuracy.

Measurement of Refractive Indices
BaGa 4 Se 7 is a biaxial crystal and belongs to the monoclinic space group Pc [8].To measure its three independent principal refractive indices n x , n y , and n z , one BaGa 4 Se 7 crystal was cut into two right-angle prisms with the sides of the right angle aligned with different directions, as shown in Figure 2. The apex angles of two prisms were approximately 14.63 • and 18.16 • , respectively.In our experiment, the refractive index could be calculated by using n = sin(α + β)/sin(α), where n is the principal refractive index, α is the apex angle of the prism, and β is the deviation angle of refractive light.When the incident light travels perpendicular to the b face of Prism 1, refractive indices n x and n z could be measured.Refractive indices n y as well as n x could also be measured when the light travels perpendicular to the c face of Prism 2.  Our experimental system is comprised ofa refractive index measurement instrument (SpectroMaster UV-VIS-IR, Trioptics, Wedel, Germany) with a high accuracy of 1 × 10 −5 and a homemade temperature-stabilized heating furnace with an accuracy of ±0.1 °C, as shown in Figure 3.In the measurement, mercury lamp at wavelengths of 0.546, 1.530, 1.970, and 2.325 μm, helium lamp at wavelengths of 0.5875 and 0.7065μm, and Chromium lamp at wavelength of 0.644 μm were used.The prisms were placed in a temperature-stabilized furnace, and heated to the target temperature (25, 50, 80, 100, 120, and 150 °C, respectively) with 30 °C/h and allowed to reach thermal equilibrium.During the measurement process, the incident angle of the central collimator beam was defined as 0°.The sample table was first adjusted to be horizontal and the accurate apex angle of the prism was measured, after which the sample was aligned square to the collimator, and the goniometer was rotated manually to find the refractive signal and measure the deviation angle using the measurement program of the instrument.At each temperature, the deviation angle was usually measured four times at different wavelengths, and the results were averaged to obtain a single determination of deviation.The measured results are listed in Table 1.

Conclusions
In summary, the thermal refractive index coefficients of BGSe crystal were measured for the first time.The temperature-dependent Sellmeier equations were fitted, and were then used to calculate PM angles for BGSe OPO crystal at different temperatures.The thermal refractive index coefficients and the temperature-dependent Sellmeier equations of BGSe crystal will be highly useful for designing a mid IR frequency conversion system based on BGSe crystal.Our experimental system is comprised ofa refractive index measurement instrument (SpectroMaster UV-VIS-IR, Trioptics, Wedel, Germany) with a high accuracy of 1 × 10 −5 and a homemade temperature-stabilized heating furnace with an accuracy of ±0.1 °C, as shown in Figure 3.In the measurement, mercury lamp at wavelengths of 0.546, 1.530, 1.970, and 2.325 μm, helium lamp at wavelengths of 0.5875 and 0.7065μm, and Chromium lamp at wavelength of 0.644 μm were used.The prisms were placed in a temperature-stabilized furnace, and heated to the target temperature (25, 50, 80, 100, 120, and 150 °C, respectively) with 30 °C/h and allowed to reach thermal equilibrium.During the measurement process, the incident angle of the central collimator beam was defined as 0°.The sample table was first adjusted to be horizontal and the accurate apex angle of the prism was measured, after which the sample was aligned square to the collimator, and the goniometer was rotated manually to find the refractive signal and measure the deviation angle using the measurement program of the instrument.At each temperature, the deviation angle was usually measured four times at different wavelengths, and the results were averaged to obtain a single determination of deviation.The measured results are listed in Table 1.

Conclusions
In summary, the thermal refractive index coefficients of BGSe crystal were measured for the first time.The temperature-dependent Sellmeier equations were fitted, and were then used to calculate PM angles for BGSe OPO crystal at different temperatures.The thermal refractive index coefficients and the temperature-dependent Sellmeier equations of BGSe crystal will be highly useful for designing a mid IR frequency conversion system based on BGSe crystal.In the measurement, mercury lamp at wavelengths of 0.546, 1.530, 1.970, and 2.325 µm, helium lamp at wavelengths of 0.5875 and 0.7065µm, and Chromium lamp at wavelength of 0.644 µm were used.The prisms were placed in a temperature-stabilized furnace, and heated to the target temperature (25, 50, 80, 100, 120, and 150 • C, respectively) with 30 • C/h and allowed to reach thermal equilibrium.During the measurement process, the incident angle of the central collimator beam was defined as 0 • .The sample table was first adjusted to be horizontal and the accurate apex angle of the prism was measured, after which the sample was aligned square to the collimator, and the goniometer was rotated manually to find the refractive signal and measure the deviation angle using the measurement program of the instrument.At each temperature, the deviation angle was usually measured four times at different wavelengths, and the results were averaged to obtain a single determination of deviation.The measured results are listed in Table 1.

Conclusions
In summary, the thermal refractive index coefficients of BGSe crystal were measured for the first time.The temperature-dependent Sellmeier equations were fitted, and were then used to calculate PM angles for BGSe OPO crystal at different temperatures.The thermal refractive index coefficients and the temperature-dependent Sellmeier equations of BGSe crystal will be highly useful for designing a mid IR frequency conversion system based on BGSe crystal.

Figure 1 .
Figure 1.Theoretical and measured values of nx, ny, and nz.

Figure 1 .
Figure 1.Theoretical and measured values of n x , n y , and n z .

n 2
(i, T) = A + B/(λ 2 − C) − Dλ 2 (I = x, y, z; T/ • C = 25, 50, 80, 100, 120, 150) (3) prisms with the sides of the right angle aligned with different directions, as shown in Figure2.The apex angles of two prisms were approximately 14.63° and 18.16°, respectively.In our experiment, the refractive index could be calculated by using n = sin(α + β)/sin(α), where n is the principal refractive index, α is the apex angle of the prism, and β is the deviation angle of refractive light.When the incident light travels perpendicular to the b face of Prism 1, refractive indices nx and nz could be measured.Refractive indices ny as well as nx could also be measured when the light travels perpendicular to the c face of Prism 2.

Figure 3 .
Figure 3.The experimental setup of measurement.

Figure 3 .
Figure 3.The experimental setup of measurement.

Figure 3 .
Figure 3.The experimental setup of measurement.

Table 5
lists the calculated phase matching angles in the xz plane for 3900 nm output OPO pumped by 1064 nm laser (1064 nm → 3900 nm + 1463 nm), based on the above Sellmeier equations.It is shown the influence of temperature on the PM angle is not obvious below 80 • C.