Polarized prisms have been widely used in laser modulation, optical information processing, imaging systems, and so on^[1–6]. Birefringence is one of the crystal’s physical properties and the basic requirement of polarized materials^[7]. The performance of the polarized prism is directly determined by the polarized optical crystal. Large birefringence is the most important characteristic for the polarized optical crystal influencing prism fabrication. In addition, the transmission window of the polarized crystal determines the application range of the prism. So far, the calcite (${\mathrm{CaCO}}_3$), ${\mathrm{YVO}}_4$, and $\alpha \text{-}{\mathrm{BaB}}_2{\mathrm{O}}_4$ ($\alpha \text{-}\mathrm{BBO}$) are the widely used polarized optical crystals^[8–10]. ${\mathrm{CaCO}}_3$ is a kind of natural ore with birefringence of 0.1744 at 532 nm, which is the most famous polarized optical crystal. The ${\mathrm{CaCO}}_3$ prism is of high performance, but it can only be used in the range of 0.35–2.3 µm^[11]. What is more, the ${\mathrm{CaCO}}_3$ crystal is difficult to grow due to its complete cleavage. Both ${\mathrm{YVO}}_4$ and $\alpha \text{-}\mathrm{BBO}$ crystals can be grown by the Czochralaki technique. The ${\mathrm{YVO}}_4$ crystal has a relatively large birefringence of 0.2331 at 532 nm, and the prism can be used in the range of 0.5–4 µm. The $\alpha \text{-}\mathrm{BBO}$ crystal exhibits a relatively small birefringence of 0.1241 at 532 nm, but its ultraviolet cut-off edge extends to 190 nm. Recently, biaxial crystals have been studied as polarized optical materials. The biaxial crystal $\alpha \text{-}{\mathrm{BaTeMo}}_2{\mathrm{O}}_9$ ($\alpha \text{-}\mathrm{BTM}$) prisms have been realized successfully^[6]. The $\alpha \text{-}\mathrm{BTM}$ prisms with wedge angles of 28° and 28.6° can be used in the range of 0.4–3 µm and 0.5–5 µm, respectively. It means that there is not an angle for the $\alpha \text{-}\mathrm{BTM}$ prism that is applicable for the range of 0.4–5 µm due to the refractive index dispersion of $\alpha \text{-}\mathrm{BTM}$. The $\alpha \text{-}\mathrm{BTM}$ crystal is grown by the flux method whose growth rate is much lower than the Czochralski technique. Therefore, polarized optical crystals that can be quickly grown by the Czochralski technique with large birefringence, wide transmission window, and high laser damage threshold have attracted our attention.

The ${\mathrm{LiNa}}_5{\mathrm{Mo}}_9{\mathrm{O}}_{30}$ crystal is a novel functional crystal, which was first, to the best of our knowledge, studied as a nonlinear optical crystal^[12]. It crystallizes in the orthorhombic system, with space group Fdd2 and lattice constants $a=7.2229(11)\mathrm{\AA }$ (1 Å = 0.1 nm), $b=37.150(6)\mathrm{\AA }$, $c=17.954(3)\mathrm{\AA }$, and $Z=4$. The ${\mathrm{LiNa}}_5{\mathrm{Mo}}_9{\mathrm{O}}_{30}$ crystal can be grown by the top-seeded solution growth method and Czochralski technique, and both the crystal quality and crystal growth rate can be satisfied^[12–14]. The crystal has a wide transmission band (0.31–5.35 µm), covering the whole visible, near-infrared, and mid-infrared wavelength range. The refractive index dispersion curves from 0.4502 to 1.0626 µm exhibit that the ${\mathrm{LiNa}}_5{\mathrm{Mo}}_9{\mathrm{O}}_{30}$ crystal has a large birefringence (0.2545 at 0.4502 µm), which is much larger than that of ${\mathrm{CaCO}}_3$ and $\alpha \text{-}\mathrm{BBO}$^[6,8,9,15]. The ${\mathrm{LiNa}}_5{\mathrm{Mo}}_9{\mathrm{O}}_{30}$ crystal also exhibits no dissociation and suitable hardness of 5.2^[14]. It is worth noting that the ${\mathrm{LiNa}}_5{\mathrm{Mo}}_9{\mathrm{O}}_{30}$ crystal has a high laser damage threshold, which means it can be used in high-power lasers. Therefore, we considered that the ${\mathrm{LiNa}}_5{\mathrm{Mo}}_9{\mathrm{O}}_{30}$ crystal should be a potential polarized optical crystal with wide transmission band and high laser damage threshold.

Laser damage threshold is an important parameter of the optical crystals and devices. High laser damage threshold is beneficial to high-power applications. The energy band and thermal stability of the crystal would affect its laser damage threshold. In addition, defects and impurities of the crystal could lower the laser damage threshold. Since the laser damage threshold is measured by a well-polished crystal plate, the processing quality of the crystal surface would affect this index. The surface absorption of the crystal is generally much larger than the body absorption; thus, the crystal surface damage threshold is usually much lower than the body damage threshold^[16]. Therefore, we measured the laser damage threshold of the ${\mathrm{LiNa}}_5{\mathrm{Mo}}_9{\mathrm{O}}_{30}$ crystal in this work.

In this paper, the laser damage threshold of the ${\mathrm{LiNa}}_5{\mathrm{Mo}}_9{\mathrm{O}}_{30}$ crystal was measured to be $2.64{\mathrm{GW}/\mathrm{cm}}^2$ at 1064 nm with a pulse width of 10 ns and a pulse repetition of 1 Hz. The refractive index and birefringence were determined and obtained in the range from 0.435 µm to 5 µm, and a ${\mathrm{LiNa}}_5{\mathrm{Mo}}_9{\mathrm{O}}_{30}$ prism can apply for this waveband with the wedge angle of 31.94°–32.12°. The extinction ratio of the prism we manufactured was 15,000:1, while the wedge angle was 31.09°.

In this work, a well-polished $4\mathrm{mm}\times 4\mathrm{mm}\times 1\mathrm{mm}$ (100)-faced crystal plate of ${\mathrm{LiNa}}_5{\mathrm{Mo}}_9{\mathrm{O}}_{30}$ was employed to measure the laser damage threshold. The measurement was tested by a diode-pumped $\mathrm{Nd}:{\mathrm{Y}}_3{\mathrm{Al}}_5{\mathrm{O}}_{12}$ (Nd:YAG) nano-second laser (Minilite ll, Continuum) at the wavelength of 1064 nm with a pulse width of 10 ns and a pulse repetition of 1 Hz. The pump pulse energy was operated at around 35 mJ. Under the action of the constant pulsed laser, the crystal was moved until the gray spot appeared. The result shows that ${\mathrm{LiNa}}_5{\mathrm{Mo}}_9{\mathrm{O}}_{30}$ has a high laser damage threshold of $2.64{\mathrm{GW}/\mathrm{cm}}^2$, which is much larger than that of ${\mathrm{CaCO}}_3$ ($300–600{\mathrm{MW}/\mathrm{cm}}^2$), ${\mathrm{YVO}}_4$ ($\sim 1{\mathrm{GW}/\mathrm{cm}}^2$), $\alpha \text{-}\mathrm{BBO}$ ($\sim 1{\mathrm{GW}/\mathrm{cm}}^2$), and $\alpha \text{-}\mathrm{BTM}$ ($\sim 350{\mathrm{MW}/\mathrm{cm}}^2$)^[17–20]. This means that ${\mathrm{LiNa}}_5{\mathrm{Mo}}_9{\mathrm{O}}_{30}$ is a potential material for high-power practical applications.

The refractive indices dispersion of the ${\mathrm{LiNa}}_5{\mathrm{Mo}}_9{\mathrm{O}}_{30}$ crystal was measured by the minimum deviation technique in the range of 0.435–2.325 µm at twelve discrete wavelengths. Two prisms of the ${\mathrm{LiNa}}_5{\mathrm{Mo}}_9{\mathrm{O}}_{30}$ crystal were required, as shown in Fig. 1. The prisms were designed and processed with vertex angles of 23.6° and 21.5°, respectively. The refractive index determination manifests that ${\mathrm{LiNa}}_5{\mathrm{Mo}}_9{\mathrm{O}}_{30}$ is a negative biaxial crystal. The refractive index axes X, Y, and Z are parallel to the crystallography axes $a$, $c$, and $b$, respectively. The refractive index dispersion curves at 0.435–2.325 µm are shown in Fig. 2. The Sellmeier equations are listed as follows:$$n_x^2=3.21637+0.04103/({\lambda }^2-0.06306)-0.00631{\lambda }^2,$$(1)$$n_y^2=3.82713+0.08012/({\lambda }^2-0.03836)-0.00367{\lambda }^2,$$(2)$$n_z^2=3.91313+0.08738/({\lambda }^2-0.06202)-0.01374{\lambda }^2.$$(3)

With the incident light along the Y axis of the biaxial crystal, the light will separate into components polarized along the X and Z axes, respectively. Then, the largest birefringence at certain wavelengths is obtained as $\mathrm{\Delta }n=n_z-n_x$. According to experimental data and Sellmeier equations, the refractive index, birefringence, and critical angles of ${\mathrm{LiNa}}_5{\mathrm{Mo}}_9{\mathrm{O}}_{30}$ are obtained and calculated in the range of 0.435–5 µm, as shown in Table 1. The largest birefringence is 0.26322 at 0.435 µm, which is larger than that of most crystals such as ${\mathrm{CaCO}}_3$ and $\alpha \text{-}\mathrm{BBO}.$

According to the measured data and Sellmeier equations, the total internal reflection angles ($\alpha$) are listed in Table 1 by using the following formula:$$\alpha =\arcsin \frac{n_2}{n_1},$$(4)where $n_1$ and $n_2$ are the refractive indices of the air and polarized light along the optic principal axis in the ${\mathrm{LiNa}}_5{\mathrm{Mo}}_9{\mathrm{O}}_{30}$ crystal, respectively.

As shown in Fig. 3(a), when the crystal wedge plates of ${\mathrm{LiNa}}_5{\mathrm{Mo}}_9{\mathrm{O}}_{30}$ with wedge angles $\theta =31.94°-32.12°$ were bonded by an air gap for the prism, the light polarized along the Z axis will be totally reflected, and the output light is polarized along the X axis, which would satisfy the application of 0.435–5 µm. In our experiment, the wedge angle was processed as 31.09°, as shown in Figs. 3(b) and 3(c).

As shown in Fig. 4, the extinction ratio was measured. A Nd:YAG laser operating at 1064 nm was used as laser resources. A polarizer was used to modulate the light polarization direction. The silicon photocell was used to transfer the light into current, and then the signal was detected by a galvanometer. When the direction of light propagated through the polarizer is perpendicular to the Z direction, the weakest polarized light was detected. On the contrary, the strongest polarized light was obtained with the light polarization along the X direction. The extinction ratio of the prism was measured as larger than 15,000:1, which can satisfy the experiment requirements.

The properties of the widely used polarization optical crystals are listed in Table 2. The birefringence of ${\mathrm{CaCO}}_3$ and $\alpha \text{-}\mathrm{BBO}$ crystals is smaller than that of other crystals, but both exhibit excellent ultraviolet transmission properties, especially $\alpha \text{-}\mathrm{BBO}$ crystals. In the ultraviolet-visible and near-infrared bands, ${\mathrm{CaCO}}_3$ and $\alpha \text{-}\mathrm{BBO}$ can mostly meet the requirements of the device applications. The ${\mathrm{YVO}}_4$ crystal extends the mid-infrared edge to 4 µm, and exhibits a large birefringence. The ${\mathrm{YVO}}_4$ crystal can be grown by the Czochralski technique, and its crystal growth speed is faster than that of $\alpha \text{-}\mathrm{BBO}$ and $\alpha \text{-}\mathrm{BTM}$ crystals. Unfortunately, the ${\mathrm{YVO}}_4$ crystal cannot cover the entire mid-infrared range. The $\alpha \text{-}\mathrm{BTM}$ crystal is the first polarization optical biaxial crystal, whose transmission range can cover the near- and mid-infrared range. Although the $\alpha \text{-}\mathrm{BTM}$ crystal has a wide transmission range, the $\alpha \text{-}\mathrm{BTM}$ prism should be designed with two wedge angles (28°/28.6°) to cover the application range of 0.4–3 µm and 0.5–5 µm, respectively. All of the laser damage thresholds of ${\mathrm{CaCO}}_3$, $\alpha \text{-}\mathrm{BBO}$, ${\mathrm{YVO}}_4$, and $\alpha \text{-}\mathrm{BTM}$ crystals are lower than $1\mathrm{GW}/{\mathrm{cm}}^2$, which limits their application in high-power optics.

The ${\mathrm{LiNa}}_5{\mathrm{Mo}}_9{\mathrm{O}}_{30}$ crystal not only shows larger birefringence than ${\mathrm{CaCO}}_3$ and $\alpha \text{-}\mathrm{BBO}$, but also presents a wider transmission window than ${\mathrm{CaCO}}_3$, $\alpha \text{-}\mathrm{BBO}$, and ${\mathrm{YVO}}_4$. According to our calculations, the ${\mathrm{LiNa}}_5{\mathrm{Mo}}_9{\mathrm{O}}_{30}$ crystal with wedge angles of $\theta =31.94°–32.12°$ can cover 0.435–5 µm, which is better than the $\alpha \text{-}\mathrm{BTM}$ prism. Due to the uniform melting property, high-quality ${\mathrm{LiNa}}_5{\mathrm{Mo}}_9{\mathrm{O}}_{30}$ crystal can be grown by the top-seeded solution crystal growth method and the Czochralski technique with high growth rate, which is beneficial for device applications. In addition, the ${\mathrm{LiNa}}_5{\mathrm{Mo}}_9{\mathrm{O}}_{30}$ prism is the first choice for high-power applications due to its high laser damage threshold.

In this paper, the laser damage threshold of the ${\mathrm{LiNa}}_5{\mathrm{Mo}}_9{\mathrm{O}}_{30}$ crystal was determined to be $2.64\mathrm{GW}/{\mathrm{cm}}^2$. The refractive index and dispersion curves were determined and obtained in the range from 0.435 µm to 2.325 µm. The birefringence of ${\mathrm{LiNa}}_5{\mathrm{Mo}}_9{\mathrm{O}}_{30}$ at 0.435 µm and 5 µm was determined and calculated to be 0.262322 and 0.140841, respectively. When the incident direction is along the Y axis, a prism with a wedge angle from 31.94° to 32.12° can realize light separation in the range of 0.435–5 µm. The Glan prism bonded by an air gap was designed using two ${\mathrm{LiNa}}_5{\mathrm{Mo}}_9{\mathrm{O}}_{30}$ wedges with an angle of 31.09°. The extinction ratio of the prism was determined to be larger than 15,000:1. The results provide a promising high-power polarized prism ranging from the visible to mid-infrared region.