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α-BaTeMo2O9 is a novel biaxial crystal with wide-band transmittance spectrum. The refractive index dispersion curves and birefringence of the α-BaTeMo2O9 crystal were obtained in spectral range of 0.4~5 μm. The origin of the birefringence for the crystal has been calculated and interpreted on the basis of the crystal structure combined with theoretical studies. The polarized directions and formulations of refractive index of optical waves in biaxial α-BaTeMo2O9 were investigated by solving the refractive index ellipsoid equations. Furthermore, polarized prisms based on the α-BaTeMo2O9 crystal used in spectral ranges of 0.4~2.7 μm and 0.48~4.5 μm were designed and characterized. The extinction ratios of both prisms were determined to be larger than 10000:1, which would satisfy the practical requirements. The impacts on extinction ratio for biaxial and uniaxial crystals were also discussed. To our knowledge, it is the first report about biaxial crystals for the polarized prisms, and the results show that the α-BaTeMo2O9 crystal is a promising material for polarized optical components, especially in the range of 3~5 μm.
© 2015 Optical Society of America
1. Introduction
In most optical experiments, polarized prism is one of key components. Polarized prisms made of crystals exhibit excellent properties, such as high extinction ratio, high damage threshold, wide transmittance band and so on, and have been applied in optical fiber communications, laser modulation, optical information processing, and biologic thermo-physics research [1–5]. The most widely used prism is Glan prism which serves as the polarizer or analyzer to obtain linearly polarized light. It is composed of two identical crystalline wedge plates with appropriate wedge angles [6]. There is an air gap between the two wedge plates. Crystal is the base for the high quality prisms, and large birefringence is the first requirement for prisms. To date, the most widely used crystals for prism are calcite (CaCO3), YVO4, and α-BaB2O4 (α-BBO) [7–9]. Calcite prisms possess high quality and long history. However, calcite is a kind of natural ore and hard to obtain large size crystals. Furthermore, it is difficult to be processed because of its complete cleavage and the transmittance band also limits the prism to be used only in the spectral range of 0.35~2.3 μm [10]. The prisms made of α-BBO and YVO4 crystals can expand the transmittance bands to 0.19~2.3 μm and 0.5~4.0 μm, respectively. On the other hand, prisms with longer wavelength transmittance band are also needed, thus novel crystals with wider transmission band and larger birefringence are expected for prisms. It is obviously that the widely used prism crystals are usually uniaxial crystals. Although the light propagation in biaxial is more complex than that in uniaxial crystal, the biaxial crystals are still promising for prisms due to their larger birefringence. However, rare report on biaxial crystal prisms was found.
The α-BaTeMo2O9 crystal is a novel compound synthesized by Zhang et al. in our group [11,12]. The structure analysis shows that it belongs to orthorhombic system. Its space group is Pca21 with a = 14.8683 Å, b = 5.6636 Å, c = 17.6849 Å, Z = 8. Well-developed block like α-BaTeMo2O9 single crystal with dimension up to 51 × 30 × 20 mm has been grown by using flux method. The crystal growth habit indicates that it can be easily obtained with high quality and large size which would be beneficial for the device fabrication. The physical properties have also been studied and the results show that it possesses wide transmission band (0.4~5.5 μm), high damage threshold, suitable hardness, no cleavage, stable physical and chemical properties. Especially, the large birefringence is comparable with that of YVO4. Thus the α-BaTeMo2O9 crystal is a potential excellent candidate as polarized optical material, although it is a biaxial crystal.
In this paper, the refractive index dispersion curves and birefringence of the α-BaTeMo2O9 crystal were obtained in spectral range of 0.4~5 μm. To understand the origin of the birefringence, first-principles investigations were carried out by density-functional theory. The analysis on α-BaTeMo2O9 was well performed, and the results indicate that the energy difference between Mo-O bond states along different directions plays a crucial role in the origin of the large birefringence. The polarized prisms based on the α-BaTeMo2O9 crystal for the used in spectra ranges of 0.4~2.7μm and 0.48~4.5 μm were designed and characterized. The extinction ratios of both prisms were determined to be larger than 10000:1, and it means that the α-BaTeMo2O9 crystal is a promising material for polarized optical components, especially in the range of 3~5 μm. This work is the first report about biaxial crystal prisms to our knowledge.
2. The birefringence of α-BaTeMo2O9 crystal and theory calculation
α-BaTeMo2O9 belongs to biaxial crystal with index axes X, Y, Z parallel to the crystallography axes b, c, and a, respectively [12]. The transmittance spectra of the crystal show a wide spectral range from 380 nm to 5530 nm. The refractive index determination indicates that the α-BaTeMo2O9 is a positive biaxial crystal. The refractive index in the range of 0.38 −2.3 μm have been determined and the Sellmeier equations are listed as follows [12].
On the basis of the Sellmeier equations, the refractive index dispersion curves for the crystal are explored to 5 μm. As shown in Fig. 1, the dashed lines which are marked Exp ni (i = 1, 2, 3) are consist of two parts. The dashed lines range from 0.4~2.3 μm are fitted with the determined refractive index data, and the dashed lines range from 2.3~5 μm are explored using by Sellmeier equations. The birefringence data of α-BaTeMo2O9 are listed in Table 1. It can be seen that the largest birefringence is 0.305, which is larger than that of most of crystals.
Table 1. Refractive index of polarized light in α-BaTeMo2O9 crystal and total internal reflection angles total reflection angles (α)
In order to elucidate the origin of the large birefringence, first-principles calculations are performed using a plane-wave pseudopotential total energy package CASTEP [13,14]. The single crystal structure data of α-BaTeMo2O9 reported previously was used [11]. The total energy was calculated by density functional theory using the Perdew-Burke-Ernzerh of functional for solids (PBESOL) generalized gradient approximation [15]. The interactions between the ionic cores and the electrons were described by the norm conserving pseudopotential [16]. The following orbital electrons were treated as valence electrons: Ba 5s2 5p6 6s2, Mo 4d5 5s1, Te 5s2 5p4 and O 2s2 2p4. The numbers of plane waves included in the basis sets were determined by a cutoff energy of 750 eV, and the numerical integration of the Brillouin zone was performed using a Monkhorst-Pack k-point sampling of 2?2?1. More than 120 empty bands were used during optical properties calculation. The other parameters and convergent criteria were the default values of the CASTEP code.
The linear refractive index can be evaluated from the complex dielectric function,
CASTEP calculates the imaginary part (ε2) of the dielectric constant, which is given by:
Where v and c are valance band (VB) and conduction band (CB) indices, represents the polarization of the electric field, ω is the frequency of incident light and V is the volume of cell, is the position operator, which is expressed as momentum matrix in order to cope with the crystalline boundary condition used in CASTEP package. The real and imaginary parts are linked by a Kramers-Kronig transformation, and one can obtain the real part (ε1) from this transformation.
The calculated band structure of α-BaTeMo2O9 was shown in Fig. 2, which reveals the crystal is an indirect band gap compound with a band gap of 2.689 eV, which is smaller than the experimentally observed value of 3.12 eV [11], a well-known artifact of the DFT function [18,19]. To examine the detailed electronic structure, total and partial densities of states (PDOS) analyses were performed, as shown in Fig. 3. We can see that the band structure of α-BaTeMo2O9 is divided into four regions. The strongly localized state at −35 eV is projected to be the Te 5s orbit. The lower region between −30 and −7 eV mostly arises from Ba 6s, Ba 5p, O 2s and Mo 5s. The valence band mainly consists of O 2p orbits. A small fraction of the orbits of Mo and Te atoms are also mixed in the valence band. The conduction band located at the upper region is mainly composed of 2p orbits of O, 4p orbits of Mo and 4d orbits of Te.
Fig. 2 Electron band structures of α-BaTeMo2O9 (a) in the −40.0 - 6.0 eV range and (b) in the region around the band gap energy.
Based on the calculated band structure, the refractive indexes of α-BaTeMo2O9 are calculated, which are present in Fig. 1. One can see that the calculated birefringence Δn is about 0.22-0.36 which are in very good agreement with experimental results. It is well-known that the properties of the crystal material are governed by its structure. From Eq. (2), one can recognize the contributions to optical refractive indices are mainly depends on each transition between valence and conduction states close to the band gap [17]. The upper region of the valence bands and the bottom of the conduction bands were well analyzed and the results show that these bands mainly consists of contribution of Mo 4p, Te 4d and O 2p orbitals. The large extent of hybridization among these orbitals clearly demonstrates the formation of relatively strong covalent bonds in the Mo-O and Te-O. According to this analysis, it is concluded that the electronic transitions inside the MoO6 and TeO3 anionic groups largely determine the energy band gaps as well as the refractive index of the crystal. The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) for α-BaTeMo2O9 are illustrated in Fig. 4. The MoO6 groups make the dominant contribution to the anisotropy of the refractive index in α-BaTeMo2O9, while the Ba2+cations and TeO3 groups have a very small effect on the birefringence since they do have some contributions to the refractive index. As shown in Fig. 5, the electrons around the Mo-O bonds form orbitals with strong covalent characteristics, while the charge densities located on the other cations and groups are almost spherical which lead the differences response to the incident light. The energy difference between the covalent-interaction Mo-O bond states along different directions play a crucial role in the origin of the large birefringence for α-BaTeMo2O9 crystal.
Fig. 5 Electronic charge density distribution between (a) Ba-O, (b) Mo-O and (c) Te-O in α-BaTeMo2O9.
3. The polarized directions and formulations of refractive index of optical waves in biaxial crystal
It is well known that the incident plane and principle section of the uniaxial crystal are both in the same plane for polarized prisms. Therefore, the light propagation can be easily obtained according to the polarization properties. Different from the uniaxial crystal, the light propagation in biaxial crystals is much more complex. Using the refractive index ellipsoid equation which has coordinate transformations, the formulations of refractive index of slower and faster optical waves can be given [20].
The refractive index ellipsoid equation of biaxial crystals can be expressed as:
where nx,ny, and nz are the refractive index.
As shown in Fig. 6, the direction vector (K) of incident light is (θ, φ). After the first coordinate transformation around Z, the coordinate axes in new coordinate system can be expressed as:
Then another coordinate transformation that rotates around Y’ would be taken. The relation between coordinate systems O′X′Y′Z′’and O”X”Y”Z”are listed as:
In the new coordinate system, Eq. (6) can be expressed as:
In the coordinate system O”X”Y”Z”, Z” is parallel to K, and Eq. (9) is the new refractive index ellipsoid equations. The section of refractive index ellipsoid which is perpendicular to K and through origin of coordinate is an ellipse. The directions and values of long and short axes are polarized directions and refractive indexes of the slower and faster optical waves, respectively. If the incident light propagates along one of axes, the equation can be simplified. Taking the case along Y axis as an example, the equation can be simplified with Z” = 0, as follows:
It is obviously that the long and short axes are located on the coordinate axes. It means that the polarized directions are along Z and X axes, and their refractive indexes are the values of the long and short axes of the ellipse. The above results are also fit for uniaxial crystal when the ny is instead of nx in Eqs. (9) and Eq. 10.
When the incident light propagates along Y axis of biaxial crystal, the largest birefringence Δn = nz-nx can be obtained, which is similar to that of uniaxial crystal.
4. Prisms design and characterization
According to the light propagation in biaxial crystal, the largest birefringence (Δn = nz - nx) for α-BaTeMo2O9 can be obtained when incident light propagates along Y axis. Then the total internal reflection angles (α) can be calculated following Eq. (11) as listed in Table 1.
Where n1 and n2 are the refractive index of air and polarized light in the α-BaTeMo2O9 crystal, respectively.As shown in Fig. 7, when the crystal wedge plate of α-BaTeMo2O9 with wedge angles θ = 28° for prism, all the birefringence in region from 0.4 to 3 μm are larger than 0.187. The light polarized along Z axis would be totally reflected, and the output light is polarized along X axis. For longer wavelength, the wedge angle of the crystal can be selected to be β = 28.6°. Then the wavelength can be explored to be 0.48-4.5μm, which can cover a wide spectral band from visible to 5 μm.
Then the prisms with wedge angles β = 28° and 28.6° were manufactured with air gap. The extinction ratios were determined with the setup as shown in Fig. 8. The laser source is a Nd:YAG laser operating at 1064 nm. A polarizer was used for modulating the polarized direction of light. The silicon photocell transferred the light into current, and it was detected by a galvanometer. The two extinction ratios of the prisms were determined larger than 10000:1, which can satisfy the experiment requirements.
5.Discussion
Theoretically, output light from the first wedge plate of prism would be perfect polarized light. Besides the crystal quality, the machining precision would affect the prism extinction ratios. The reduction of extinction ratio made of uniaxial crystal is demonstrated in Fig. 9. The red lines signified the optical axis direction. As shown in Fig. 7, when the incident light propagates in the first wedge plate, only the light with polarized direction perpendicular to optical axis can transmit. If there is an angle (Ψ) between the principle planes for the two wedge plates, the light can divided into two parts, with one beam polarized along the optical axis in the first plate. Then the output light from the prism is not perfect polarized light, and the extinction ratio (R) can be expressed as:
According to the analysis on the light propagation in biaxial crystals and α-BaTeMo2O9 prism design, one of the refractive index axes (X or Z) can be considered to the optical axis in uniaxial crystal. Therefore, the extinction ratio can be analyzed similar to that of uniaxial crystal, and the Eq. (12) is suitable for the biaxial crystal prism. The above discussions indicate that both the uniaxial and biaxial crystal can be used for the high quality prisms, and the factors that infect on the extinction ratio are almost the same.
In Table 2, the properties of the widely used crystals for prism are listed. It can be seen that α-BBO is usually used in ultraviolet and visible band. Limited by transmission bands, CaCO3 and YVO4 prism can only applied in the spectral band of 0.35~2.3 μm and 0.5~4 μm, and both of them cannot cover the range of 3~5 μm. Compared to these crystals, the α-BaTeMo2O9 crystal exhibits good transmittance from 0.4 ~5.0 μm which can cover 3~5 μm and most of the visible bands. The birefringence of the crystals in their transmission ranges were shown in Fig. 10. It is obviously that α-BaTeMo2O9 exhibits much larger birefringence than that of CaCO3. Even the birefringence at wavelength of 3.5μm for α-BaTeMo2O9 is still larger than 0.18 which is the largest birefringence for CaCO3. Compared to YVO4 crystal, the birefringence of α-BaTeMo2O9 is larger when the wavelength is shorter than 1064 nm. As the birefringence of α-BaTeMo2O9 changes intensely, it is a little smaller than that of YVO4 when the wavelength is longer than 1064 nm. Its wide transmission spectra, large birefringence show that α-BaTeMo2O9 crystal should be an excellent candidate for polarized prism materials in wide wavelength region, especially in 3-5 μm.
Table 2. Properties of widely used crystals for prism
6.Conclusion
In conclusion, the refractive index dispersion curves and birefringence of the α-BaTeMo2O9 crystal were obtained in spectral range of 0.4~5 μm. The theory study indicate that the energy difference between the covalent-interaction Mo-O bond states along different directions play a crucial role in the origin of the large birefringence for α-BaTeMo2O9 crystal. Wide bands prisms used in 0.4~2.7 μm and 0.48~4.5 μm have been designed and fabricated. Their extinction ratios are larger than 10000:1. To our knowledge, it is the first report about biaxial crystals for the polarized prisms, and the results show that the α-BaTeMo2O9 crystal is a promising material for polarized optical components, especially in the range of 3~5 μm.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant Nos. 61308088, 51021062, and 50802054), and the Program of Introducing Talents of Disciplines to Universities in China (111 program no. b06017).
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