Second order nonlinear optical properties of Cs2TeW3O12 single crystal

Peng Zhao; Qian Wu; Chunlong Li; Shaojun Zhang; Youxuan Sun; Chengqian Zhang; Shengqing Xia; Zeliang Gao; Xutang Tao

doi:10.1364/OME.6.000451

1. Introduction

Laser has been widely applied in the fields including scientific research, industry, medical diagnosis,laser display, etc [1–3]. The lasers wavelengths are usually depended on the energy level transition of active ion, such as Nd³⁺, Yb³⁺. To extension the laser wavelength, the optical frequency conversion technology based on nonlinear crystal is one of the most effective methods. According to the output wavelength, the nonlinear crystals can be divided into three kinds: (i) deep ultraviolet-ultraviolet NLO crystals; (ii) visible-near infrared NLO crystals; (iii) mid and far-infrared NLO crystals. Ultraviolet-visible-near infrared NLO crystals have been well developed, such as BBO, LBO, KH₂PO₄ (KDP), and KTiOPO₄ (KTP) KBe₂BO₃F₂ (KBBF) [4–12]. Most of the studied mid-infrared crystals are phosphide and sulfide, such as LiInS₂, ZnGeP₂, AgGaS₂, and so on. These crystals are usually grown by Bridgman method, and hard to obtain large crystals with high optical quality. Therefore, the new mid-infrared NLO crystal and optical frequency conversion become hot research directions in materials and optical fields.

The prerequisite of a second-order NLO crystal is non-centrosymmetric (NCS) structure [13]. Since 1998, a series of new multiple oxides have been synthesized by using the ions which are susceptible to second-order Jahn-Teller (SOJT) effect. These ions consist of the d⁰ transition metals cations (Mo⁶⁺, W⁶⁺, V⁵⁺, Nb⁵⁺, etc.) and cations with stereo-chemically active lone pairs (I⁵⁺, Te⁴⁺, Se⁴⁺, Sn²⁺, etc.) [14–21]. Compounds with such structures exhibit strong powder second-harmonic generation (SHG) effects, and bulk crystals such as β-BaTeMo₂O₉ (β-BTM), Cs₂TeMo₃O₁₂ (CTM), α-BaTeMo₂O₉ (α-BTM), MgTeMoO₆ (MTM), and Na₂TeW₂O₉ (NTW) have been grown by us and others [22–26]. However, till now, only β-BaTeMo₂O₉ and Cs₂TeMo₃O₁₂ crystals have been reported with their second order nonlinear properties [27, 28]. Large-sized single crystal of CTW has been grown by us using a top-seeded solution growth method for the first time. It crystallizes in the hexagonal system with group (P6₃) and with high powder SHG effect. Its transparent range is from 0.41 to 5.31 μm, which indicates that it may be a good candidate as mid-infrared NLO crystal [29].

In this paper, the refractive indices of CTW were determined and the Sellmeier equations have been obtained. The two NLO coefficients have been determined by Maker Fringe (MF) techniques for the first time. CTW is phase matchable, and in the direction of θ = 39.6° the effective NLO coefficient is 4.0 pm/V at 1064 nm. The thermal properties of CTW are better than that of CTM. The crystal structure and magnitude of distortions of CTW have been analyzed and calculated to illustrate its good NLO properties.

2. Refractive indices and dispersion curves

The refractive index and dispersion curves are of significance in the evaluation of NLO crystal applications. CTW has two principal index n_o and n_e. In our experiment, the refractive indices were determined by minimum deviation method with a HR Spectro Master UV-VIS-IR (Trioptics, Germany). One polished prism with the vertex of 18.5° was used for the measurement. As shown in Table 1, there are ten sets of refractive indices at different wavelengths listed at temperature ranging from 20.3 °C to 21.6 °C.

Table 1. Refractive Indices for CTW Crystal

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The data show that n_e<n_o, demonstrating that CTW is a negative uniaxial optical crystal. The optical principal-axes coordinate can be established as Z∥c,and X ∥a. On the basis of the data, the Sellmeier equations are listed as follows:

n_{o}^{2} =4 .24822+ \frac{0 .10569}{λ^{2} -0 .05791} -0 {.01715λ}^{2}

n_{e}^{2} =3 .62986+ \frac{0 .0574}{λ^{2} -0 .04271} -0 {.00699λ}^{2}

where λ is the wavelength expressed in micrometers. Then, the refractive index dispersion curves for CTW are fitted and shown in Fig. 1. It is obviously that the measured values are accorded well with the fitting curves.

Fig. 1 Calculated curves from the Sellmeir fits and dispersion curves of the refractive indices for CTW crystal.

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3. Measurement of the second-order NLO coefficients

NLO coefficients, especially efficient NLO coefficient are the most important parameters for NLO applications. CTW belong to hexagonal system, space group P6₃, has totally four independent second-order NLO coefficients, d₃₂, d₃₃, d₁₄, and d₁₅ [30]. Under the Kleinman symmetry [31], d₁₄ = -d₁₄ = 0, d₃₂ = d₁₅ were obtained. Therefore there were merely two independent coefficients d₃₂ and d₃₃. MF technology is the widely used method to determine NLO coefficients. In our experiment, the coefficient d₃₆ = 0.39 pm/V in potassium dihydrogen phosphate (KDP) is selected as the reference [32]. A Q-switched Nd:Yttrium lithium fluoride laser (Sunlight 200 SGR-10) at 1053 nm with a repetition frequency of 1 Hz was used as the fundamental light source. The second harmonic signal from the sample was selectively detected by a photomultiplier tube (PMTH-S1V1-CR131), averaged by a fast-gated integrator and boxcar average (Stanford Research Systems), and then recorded by data acquisition software. All the experiments were carried out at room temperature.

The determinations of d₃₂ and d₃₃ use X-cut or Y-cut CTW samples with thickness of 0.5 mm. In our experiments, the samples are polished in the directions of pumped laser without anti-reflect coating. And their optical parallelism was processed to be less than 10”. Firstly, the reliability of MF platform was verified according to the determination of d₃₆ in KDP. Then the coefficients d₃₂ and d₃₃ can be obtained under the configurations as shown in Fig. 2. The SHG (I₂) power of CTW can be expressed as Eq. (3). According to the Maker fringe theory [33], compared with that of KDP sample, the d_ij values of CTW at θ = 0 can be calculated by Eq. (4).

I_{2} \propto f (θ) \times d_{i j}^{2} \times T

\frac{d_{i j (C T W)}}{d_{36 (K D P)}} = \sqrt{\frac{I_{2 (C T W)}}{f {(θ)}_{(C T W)}} \times \frac{f {(θ)}_{(K D P)}}{I_{2 (K D P)}} \times \frac{T_{(K D P)}}{T_{(C T W)}}}

where f(θ) is the function of the incident angle θ, T is the transmittance, and d₃₆(KDP) = 0.39 pm/V is the reference.

Fig. 2 The samples for measurements on CTW crystal by the MF technique.

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The theoretical and experimental Maker Fringes are shown in Fig. 3. It can be seen that the shapes of the experimental Maker Fringes are good agreement with that of theoretical Maker Fringes. The NLO coefficients of d₃₂ and d₃₃ are calculated to be 6.2 pm/V and 4.3 pm/V, respectively.

Fig. 3 Maker Fringes measurement for the NLO coefficients. Theoretical Maker Fringe (a) and experimental Maker Fringe (c) of d₃₂. Theoretical Maker Fringe (b) and Experimental Maker Fringe (d) of d₃₃. Note that the red curves represent the envelope curve.

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4. Phase-matching properties and effective NLO coefficients

From the refractive indices of CTW, whose phase-matching properties have been calculated, the results indicated that both the type-I and type-II PM can be realized in CTW. As a negative uniaxial crystal with point group 6, the effective NLO coefficients in the type-II PM directions is zero. Therefore, only the type-I PM angels and effective NLO coefficients are valuable. According to Eq. (5), the PM angels at different wavelengths can be calculated.

θ_{m} (I) = arc \sin {[{(\frac{n_{2}^{e}}{n_{1}^{o}})}^{2} \times \frac{{(n_{2}^{o})}^{2} - {(n_{1}^{o})}^{2}}{{(n_{2}^{o})}^{2} - {(n_{2}^{e})}^{2}}]}^{0.5}

where

n_{2}^{o}

,

n_{2}^{e}

and

n_{1}^{o}

represent the refractive indices at the fundamental and harmonic wavelengths, respectively. The PM angels in the transmission range of CTW are listed in Fig. 4. It is obviously that PM can be realized in CTW in a wide transmission range. At 1064 nm, the PM angle is shown to be 39.6 ^o.

Fig. 4 The type-I PM angels versus wavelengths of CTW crystal.

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According to [34], the effective NLO coefficient of CTW can be calculated as follows:

d_{e f f} = d_{32} \times \sin (θ)

where d_eff is the effective NLO coefficient and θ is the PM angle. The effective NLO coefficient of CTW at 1064 nm (θ = 39.6°) was calculated to be 4.0 pm/V. Table 2 listed the second-order NLO coefficients of CTW, CTM, LBO and BBO crystals [27, 35]. By comparing with the two commonly used crystals, the effective nonlinear optical coefficient of CTW crystal is 3.8 times that of LBO and 1.9 times that of BBO crystals.

Table 2. Second-order NLO coefficients and the effective NLO coefficients of CTW, CTM, and two common-used crystals at room temperature

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5. Discussion

It is worth to note that both CTW and CTM belong to the same space group, and exhibit similar transmission range and NLO properties. For NLO crystals, the thermal properties are important for both fundamental and potential applications. It is known that the thermal conductivity is closely associated with the structure. As shown in Fig. 5, CTW crystal exhibits a two-dimensional layered structure that consist of WO₆ octahedron and TeO₃ polyhedra. In the ab-plane the distorted WO₆ octahedron connect each other by the corner O atoms to form long chains, and then the TeO₄ polyhedra capping one side of three WO₆ octahedron along the c-axis. The layer stack along the crystallographic c direction and are separated by the Cs⁺ cations. The unique layered structure of CTW yields a smaller value in the c-axis (0.80 W m⁻¹ K⁻¹) than that in the a-axis (2.33 W m⁻¹ K⁻¹), as the heat is easier to diffusion in the ab-plane than that along the c-axis. The thermal conductivity of CTW is plotted in Fig. 6. Here the thermal conductivity coefficients of CTM are measured for comparison [36]. The results show that the thermal diffusivities decrease substantially with an increase in temperature along the a-direction, while the coefficients are almost constant along the c-direction. CTW exhibits a much larger thermal conductivity along the a-axis. It means that although CTW has relative smaller effective NLO coefficients than that of CTM, its large thermal property makes it be an excellent candidate of NLO crystal.

Fig. 5 Ball-and-stick diagram of CTW in ac-plane. Note that CTW exhibits a two-dimensional layered structure along the c-direction.

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Fig. 6 Thermal diffusivity coefficient versus temperature for CTW and CTM along different crystallographic directions.

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The second-order nonlinear optical properties of crystals are closely related to their structures. For CTW crystal, only one crystallographically independent Te atom and one independent W atom are discovered in the asymmetric unit [29]. The coordination environment of W and Te atoms are demonstrated in Fig. 7. Owing to the SOJT effect, the octahedron composed of W and O atoms was distorted [13]. This out-of-center distortion produced three ‘long’ (1.7469(50)-1.8467(38) Å) and three ‘short’ (2.0288(35)-2.1096(38) Å) W⁶⁺-O bonds, While Te atom is also observed in asymmetric coordination environment, attributable to the lone pair“pushing” the oxide ligands toward one side of the cation. Therefore, the lone-pair cation can be considered as “pre-distorted”, as reported by [37]. The magnitude of distortion of WO₆ was calculated by six W-O bond lengths and three trans O-W-O bond angles in the octahedron. The magnitude of the distortion can be calculated by Eq. (7):

Δ d = \frac{| (W - O_{1}) - (W - O_{2 A}) |}{| \cos θ_{1} |} + \frac{| (W - O_{2}) - (W - O_{1 A}) |}{| \cos θ_{2} |} + \frac{| (W - O_{3}) - (W - O_{4}) |}{| \cos θ_{3} |}

Where

Δ d

is the magnitude of the distortion. These bond lengths and trans bond angles in the equation are given in Fig. 7. The calculated

Δ d

of CTW is 0.7761, which belong to the moderate distortion. Our results confirm the analysis that reported in [37], which could explain the reason why CTW crystal had a larger NLO coefficient.

Fig. 7 Ball-and-stick diagram of WO₆ octahedron and TeO₄ polyhedra in CTW. Note that the red arrows indicate the direction of the distortion of WO₆ octahedron and TeO₄ polyhedra.

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6. Conclusion

In conclusion, we reported the linear and nonlinear optical properties of CTW in detail. The results show that CTW is a negative uniaxial optical crystal with a suitable birefringence, and wide range phase matching can be realized by using its birefringence. CTW has higher thermal conductivity than that of CTM. The NLO and effective NLO coefficients of CTW have been determined for the first time and which are larger than the two commonly used NLO crystals of BBO and LBO. It is expected that CTW is a good candidate for NLO applications.

Acknowledgments

This work is financially supported by the National Natural Science Foundation of China (Grant Nos. 61308088, 51321091, 51227002, and 51202128), and the Program of Introducing Talents of Disciplines to Universities in China (111 Program No. b06015).

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λ (μm)	n_e	n_o	Δn = n_o-n_e
0.480	1.98344	2.20385	0.22041
0.54608	1.96275	2.16403	0.20128
0.58756	1.95382	2.14713	0.19331
0.64385	1.94460	2.13021	0.18561
0.70652	1.93704	2.11650	0.17946
0.76819	1.93151	2.10603	0.17452
0.85211	1.92575	2.09626	0.17051
1.01398	1.91843	2.08320	0.16477
1.52958	1.90765	2.06264	0.15499
2.32542	1.89805	2.04333	0.14528

Crystal	Space group	NLO coefficients at 1064nm (pm/V)	Transmission range (μm)	Effective NLO coefficient at 1064 nm (pm/V)
CTW	P6₃	d₃₂ = 6.2, d₃₃ = 4.3 (Δ < ± 0.5)	0.41 - 5.31	4.0
CTM	P6₃	d₃₁ = 6.8, d₃₃ = 6.5	0.43 - 5.38	4.6
LiB₃O₅	Pna2₁	d₃₁ = 0.96, d₃₂ = 1.04, d₃₃ = 0.06	0.16 - 2.6	1.05
β-BaB₂O₄	R3c	d₁₁ = 2.26, d₃₁ = 0.113, d₂₂<d₃₁	0.19 - 3.5	2.067

λ (μm)	n_e	n_o	Δn = n_o-n_e
0.480	1.98344	2.20385	0.22041
0.54608	1.96275	2.16403	0.20128
0.58756	1.95382	2.14713	0.19331
0.64385	1.94460	2.13021	0.18561
0.70652	1.93704	2.11650	0.17946
0.76819	1.93151	2.10603	0.17452
0.85211	1.92575	2.09626	0.17051
1.01398	1.91843	2.08320	0.16477
1.52958	1.90765	2.06264	0.15499
2.32542	1.89805	2.04333	0.14528

Crystal	Space group	NLO coefficients at 1064nm (pm/V)	Transmission range (μm)	Effective NLO coefficient at 1064 nm (pm/V)
CTW	P6₃	d₃₂ = 6.2, d₃₃ = 4.3 (Δ < ± 0.5)	0.41 - 5.31	4.0
CTM	P6₃	d₃₁ = 6.8, d₃₃ = 6.5	0.43 - 5.38	4.6
LiB₃O₅	Pna2₁	d₃₁ = 0.96, d₃₂ = 1.04, d₃₃ = 0.06	0.16 - 2.6	1.05
β-BaB₂O₄	R3c	d₁₁ = 2.26, d₃₁ = 0.113, d₂₂<d₃₁	0.19 - 3.5	2.067

Second order nonlinear optical properties of Cs₂TeW₃O₁₂ single crystal

Abstract

1. Introduction

2. Refractive indices and dispersion curves

3. Measurement of the second-order NLO coefficients

4. Phase-matching properties and effective NLO coefficients

5. Discussion

6. Conclusion

Acknowledgments

References and links

Cited By

Figures (7)

Tables (2)

Equations (7)

Optical Materials Express