Crystal Growth of LiNa₅Mo₉O₃₀ Crystals of High Optical Quality

Abstract

The bulk of the LiNa₅Mo₉O₃₀ (LNM) crystals were successfully grown in the [010] and [001] directions without internal inclusions and cracks, using the Czochralski method with a low temperature gradient. The crystal grown in the [010] direction showed a tendency to twinning. The crystal grown in the [001] direction demonstrated high structural perfection (FWHM = 13″) for the (001) plane and high optical quality Δn ≈ 2 × 10⁻⁵. The laser-induced damage threshold was measured along a, b and c axes and was 12.2, 27.0 and 27.5 J/cm², respectively. The thermo-optical coefficient dn/dT was measured for the main crystallographic axes, which was −5.75 × 10⁻⁶, −20.2 × 10⁻⁶ and 3.65 × 10⁻⁶ K⁻¹ along the a, b and c axes, respectively. The second harmonic generation (SHG) was conducted in the crystalline LNM sample. The maximum efficiency value of 3.5% at a pump power of 12 W was achieved.

1. Introduction

The development of the laser industry is impossible without the development of new optical materials to improve the laser characteristics. Molybdate family crystals are widely known in laser technology.

The LiNa₅Mo₉O₃₀ (LNM) crystal was first presented in 2012 [1]. The crystal has a wide transparency window of 430–5500 μm [2], high birefringence, nonlinear optical coefficients within the values 1.4, 4.3 и 1.1 pm/V for d₃₁, d₃₂ and d₃₃, respectively [3], and a rather high radiation resistance of 2.64 GW/cm² [4]. Previously [5], we demonstrated the possibility for frequency conversion using a LNM crystal for almost the entire transparency range from UV to mid-IR.

The possibility of producing Glan polarizing prisms with a higher laser damage threshold than widely used materials such as CaCO₃, YVO₄ and α-BBO was demonstrated in [4].

LNM crystals presented in the literature were obtained using both the TSSG method [2,3,4,6] and the Czochralski method [7,8]. Crystals grown using the Czochralski method have an elongated shape along the [100] direction with pronounced planes (040). The LNM material is potentially applicable in laser optics, but no data on the measurement of thermo-optical coefficients have been reported in the literature.

In the current research, a high quality LNM crystal of 30 × 30 × 90 mm³ obtained using the Czochralski method at low temperature gradient with a mass up to 190 g is presented. Its structural perfection and optical quality are investigated. Thermo-optical coefficients dn/dT and the laser-induced damage threshold (LIDT) along three axes are measured. The first results on second harmonic generation (SHG) are obtained.

2. Experimental Section

2.1. Materials and Preliminary Preparation for Growth

Stoichiometric amounts of Na₂CO₃ (99.99%, Lenreactiv GSC, St. Peterburg, Russia), Li₂CO₃ (99.99%, Fox-Chemicals GmbH, Pfinztal, Germany), MoO₃ (99.9997%, ARMOLED Ltd., Moscow, Russia) were placed in a platinum crucible (d = 70 mm, h = 200 mm) after careful mechanical homogenization. The crucible was kept in a muffle furnace at 580 °C for 24 h to homogenize the melt. After extracting the crucible from the furnace and cooling it down, phase compositions of the preparations were determined using the PXRD method. To determine the synthesis regimes for full homogenization, TG-DTA data were used.

2.2. Crystal Growth Technique

LNM crystal growth was carried out using the Czochralski method. The setup specific feature was the 4-zone resistance furnace, which allowed the creation of a low temperature vertical gradient at the level of 5 °C/cm above the melt. We used a platinum crucible (Specmetal Ltd, Zelenograd, Russia) (d = 70 mm, h = 200 mm) with a conical lid for the growth process. Before the growth started, we superheated the melt to 650 °C and exposed it for 24 h to homogenize the melt. The growths were realized in two crystallographic directions [010] and [001] on an oriented seeds with 5 × 5 mm cross-section. The pulling speed varied from 0.3 to 1 mm/hour. The crystal rotation speed was 3–10 rpm. To the end of the growth process, the growing speed was increased to 2 mm/hour and the melt was slightly heated until the crystal broke away from the melt spontaneously. The grown crystal was cooled to room temperature at a rate of 7 °C/hour.

2.3. Crystal Characterization

Crystalline perfection was estimated via high-resolution X-ray diffraction (HRXRD) using a Malvern PANalytical Empyrean instrument (Malvern Panalytical Ltd., Worcestershire, UK) with Cu Kα radiation (λ = 1.541874 Å). The scanning range was ω = 0.6 in steps of 0.0003° at room temperature. A (001) oriented plate LNM crystal was mechanically polished on both sides and used for the HRXRD measurements.

The optical quality of the grown crystals was estimated both qualitatively and quantitatively. For the qualitative study, we used the standard Schlieren method [9]. The quantitative study of optical homogeneity was carried out using interferometry on a Mach–Zehnder interferometer [7,9].

To measure the dn/dT thermo-optic coefficient, we used the method proposed in Reference [10].

To measure the laser-induced damage threshold (LIDT), the R-on-1 method in the single pulse mode was used [11]. A fiber laser with a wavelength of 1064 nm was used for measurement; the pulse time was 5 ns, the energy in the pulse was up to 1 mJ and the beam diameter in the waist was 25 μm. This method allows the collection of a sufficient amount of statistical data from a small size area. The tested area destruction was registered by a sharp distortion of the profile of the transmitted radiation.

The experimental setup for the second harmonic generation in a crystalline LNM sample is shown in Figure 1a. Linear-polarized laser radiation at a wavelength of 1030 nm is focused via a lens system into the sample installed in a heater with a PID controller. The pulse duration is 15 ps with the repetition frequency 2 MHz, the output power is up to 25 W, the beam diameter varies from 450 to 900 μm and the beam parameter product M2 = 1.1. After nonlinear conversion, the radiation propagates through a system of dichroic dielectric mirrors, which separate radiation by wavelength. The sample (5 × 10 × 20 mm³) was cut in direction φ = 42.9°, θ = 90.0° (fsf–type) (Figure 1b).

3. Results and Discussion

3.1. LiNa₅Mo₉O₃₀ Synthesis

X-ray measurements were carried out using a Malvern PANalytical Empyrean instrument (Malvern Panalytical Ltd., Worcestershire, UK) with Cu Kα radiation (λ = 1.541874 Å) in the 2θ range from 5° to 115° at room temperature. The X-ray powder diffraction patterns of the polycrystalline LiNa₅Mo₉O₃₀ are shown in Figure 2. The experimental XRD pattern of the polycrystalline LiNa₅Mo₉O₃₀ is in good agreement with the literature data, which indicates that the pure single phase was obtained.

To determine the melt homogenization temperature, it is necessary to know the temperature at which mass loss begins. This is important to consider when working with melts containing MoO₃ due to its high volatility. According to the TG-DTA analysis data obtained using a Netzsch Jupiter STA 449 F1 instrument (NETZSCH-Gerätebau GmbH, Selb, Germany), the onset of mass loss occurs at 783 °C. This indicates that the melt homogenization occurs without changing the composition stoichiometry. The melting temperature was determined as 550 ± 1.5 °C (Figure 3), which corresponds to the literature data [3].

3.2. LNM Crystal Growth

The first experiments on LNM crystal growth were carried out on the seed oriented in the [010] direction. The plane (040) is the most stable and is pronounced on the crystals obtained in [3] and [7]. The shape of the crystals had a lamellar appearance and this is not optimal for growth technology. At the same time, the crystals grown in the [010] direction presented in the literature have defects and cracks [12].

A series of crystal growth experiments using the low temperature gradient technique of the Czochralski method in the [010] direction resulted in several crystals weighing up to 185 g (Figure 4). We did not observe any cracks and defects in the grown LNM crystals.

To investigate the optical quality of the grown crystals, 5 mm thick plates were cut parallel to the (010) crystallographic plane. During the polishing process in a slightly acidic environment (pH = 5), areas of inhomogeneity were noticed on the sample (Figure 5). An optical microscope Olympus GX53 (Olympus Corporation, Hamburg, Germany) was used to make crystal photos. Investigations of the inhomogeneity areas were carried out using the Quasi-Static Piezo d₃₃/d₃₁ Meter ZJ-6B (Beijing Jkzc Echnology Development Co., Ltd., Beijing, China). The values of the piezoelectric constant in regions 1 and 2 had the same value with the opposite signs. At the border of regions 1 and 2, the value of the constant turned to zero. Similar defects were observed along the length of the entire boule and were specific for all crystals grown in this direction.

Due to the presence of inhomogeneous areas in the [010] as-grown LNM crystals, we decided to change the growth direction to [001]. We grew a number of crystals weighing up to 190 g without visible defects in the volume and cracks were obtained (Figure 6). The crystals had a volumetric shape with a hexagon at the base and a pronounced plane (040) along the growth direction; the ratio between the [010] and [100] directions is almost 1:1. The typical diameter of the grown crystal was 30 mm. As a consequence, the bulk shape of the crystal allowed the fabrication of optical elements designed for frequency conversion tasks. The crystals shown in Figure 4 and Figure 6 were grown under the same thermal conditions, with the same growth and rotation rates.

3.3. Crystal Properties

To study the optical quality of the crystal, a 4.8 mm thick plate was cut from the central part of the boule parallel to the (001) plane. Then, a plate parallel to the (010) plane with a thickness of 3 mm was cut from the lower part of the boule. No inhomogeneities similar to Figure 5 were detected during the grinding and polishing of the samples (Figure 7).

The crystalline quality of the as-grown LNM crystal was checked using HRXRD. The FWHM for the rocking curve of the (001) diffraction plane (Figure 8) was 13″ which is the best result presented in the literature [2,3,13] (see

Table 1. The rocking curves FWHM determined using HRXRD analysis of different planes of LNM crystals.

FWHM	Plane	Reference
98″	(001)	[3]
59″	(001)	[3]
30″	(001)	[14]
17″	(100)	[2]
13″	(001)	our data

). This indicates a high structural perfection of the obtained crystal.

The optical homogeneity of the crystal was qualitatively assessed in two directions along the growth axis on the (040) plane (Figure 7B) and perpendicular to the growth axis on the (001) plane (Figure 7A).

The quantitative assessment of optical homogeneity was performed on a plate cut perpendicular to the growth axis. Figure 9 shows interferograms obtained in the infinite-width strip mode (A) and the result of processing the corresponding fragments of interferograms taken in the finite-width strip mode in the 5 × 5 mm region. The magnitude of distortions introduced into the wave front was 0.1λ. The obtained value Δn ≈ 2 × 10⁻⁵ indicates the high optical quality of the obtained crystal.

3.4. Measurement of dn/dT

The LNM material is potentially applicable in laser optics, but no data on the measurement of thermo-optical coefficients have been reported in the literature yet. To measure the thermo-optic coefficient dn/dT and LIDT, three elements of size 3 × 3 × 10 mm³ along a-, b- and c- crystallographic axes were fabricated. The measured dn/dT values are presented in

Table 2. dn/dT values obtained along the main crystallographic axes for as-grown LNM crystal.

Direction	dn/dT, K−1
along the a axis	−5.75 × 10−6
along the b axis	−20.2 × 10−6
along the c axis	3.65 × 10−6

.

The collation of the data on the thermo-optical coefficient for other nonlinear optical crystals showed that the average dn/dT value for the as-grown LNM crystal is comparable with other well-studied materials of nonlinear optics (

Table 3. dn/dT values for different nonlinear optical crystals at room temperature [15].

Direction	dn/dT, K−1
β-BBO (Ordinary)	−16.6 × 10−6
β-BBO (Extraordinary)	−9.3 × 10−6
LBO (x)	−1.8 × 10−6
LBO (y)	−13.6 × 10−6
LBO (z)	−8.4 × 10−6
LN (Ordinary)	1.4 × 10−6
LN (Extraordinary)	39.0 × 10−6
Mg:LN (Ordinary)	4.4 × 10−6
Mg:LN (Extraordinary)	54.2 × 10−6
KTP (x)	6.4 × 10−6
KTP (y)	8.5 × 10−6

). However, taking into consideration that for the as-grown LNM crystal we obtained different signs of thermo-optical coefficients along different axes, it opens up prospects to find a direction along which the thermal lens will not be formed.

3.5. Laser-Induced Damage Threshold

After measuring the thermo-optical coefficient dn/dT, destructive measurements of the laser damage threshold were performed on the same elements. The obtained measurement values are presented in Figure 10.

The graphs show the probabilistic values of the destruction of the LNM crystal when exposed to laser radiation. The graphs highlight the values obtained on the samples cut in the direction [100]. The output facet withstands lower energy exposure to radiation. Such results are probably associated with a lack of polishing quality and the need for additional verification.

The numerical values of the laser damage threshold are presented in

Table 4. Laser-induced damage threshold (LIDT) for different planes of as-grown LNM crystal.

LIDT		Plane
		a		b		c
		Input	Output	Input	Output	Input	Output
P0%	J/cm2	15.7	12.2	27.0	57.9	29.5	34.8
	GW/cm2	3.14	2.44	5.4	11.58	5.9	6.96
P50%	J/cm2	61.6	36.3	90.9	94.6	66.1	61.6
	GW/cm2	12.32	7.26	18.18	18.92	13.22	12.32

. The destruction threshold P_50% corresponds to the energy density at which the experimental probability of sample destruction is ½, while the destruction threshold P_0% corresponds to the maximum energy density at which no burnout occurred. The measured minimal (worse) values of the laser destruction threshold for the LNM crystal along a, b and c axes, determined by the P_0% level, were 2.44, 5.4 and 5.9 GW/cm², respectively. These values are 1.4 times greater than those reported in Reference [14] for the [001] direction and are in good agreement with the data [4] for the [100] direction.

The obtained values indicate that the grown LNM crystal can withstand a sufficiently high power density and be competitive in this characteristic with widely known nonlinear optic KDP, KTP, LBO, BBO, CLBO, LiNbO₃ and LiTaO₃ commercial crystals [3,5,14].

3.6. Second Harmonic Generation

Phase matching is a condition for the most effective implementation of the ability of a nonlinear medium to convert frequency. For the grown LNM crystals, we determined the optimum temperature to fulfill the phase matching condition, which was determined to be 24 °C. The dependence of the output second harmonic power P₅₁₅ on the input pump power P_in was measured, and then the conversion efficiency was calculated.

One can see (Figure 11) that the second harmonic power is the same regardless of the beam diameter in the initial part of the dependence, and then reaches different constant values. The maximum power value is achieved at a beam diameter of 900 μm with the value of 0.5 W, and the maximum efficiency value is 3.5% at 12 W pump power. In addition, during the experiment, two residual pump beams with orthogonal polarizations were observed at the output side of the sample. The angle between the beams was about 5°.

The presence of the two beams that were previously mentioned is most likely evidence of the spatial walk-off of f- and s-pump components. Theoretical estimation shows that for the chosen direction in LNM, the walk-off does take place and its angle is 5.2°, which was observed during the experiment. Due to the spatial walk-off, the interaction length of the pump components was no more than 1 cm instead of the expected 2 cm, which resulted in a significant reduction in the SH power and generation efficiency.

4. Conclusions

The LNM crystals were grown using the Czochralski method in two directions—[010] and [001]. Crystals grown in the [010] direction are prone to growth heterogeneities. When grown in the [001] direction, the crystal has a sufficiently high optical uniformity Δn ≈ 2×10⁻⁵. Six elements were made from this crystal along three crystallographic axes to measure the thermo-optical coefficients dn/dT and the LIDT. The values of dn/dT were −5.75 × 10⁻⁶, −20.2 × 10⁻⁶ and 3.65 × 10⁻⁶ K⁻¹ along the a, b and c axes, respectively. The LIDT values were measured for three crystallographic directions. The highest P_0% level of 5.9 GW/cm² was achieved for the c axis. The second harmonic generation is conducted in the crystalline LNM sample. The maximum efficiency value is 3.5% at pump power of 12 W.

Thus, the research shows the possibility of obtaining a volumetric crystal with a size of 30 × 30 × 90 mm³ and a mass of up to 190 g of high optical quality for birefringence and frequency conversion problems.