## 4 Experimental Results and Discussion
### Thermally Tunable Frequency Difference
This is a lock-in phenomenon of the two frequencies [18]. It is a ubiquitous phenomenon the orthogonally  
Figure 3: The relationship between the frequency difference and temperature of 18 \({}^{\circ}\)C–24.5 \({}^{\circ}\)C (**a**) and 20.4 \({}^{\circ}\)C–21.3 \({}^{\circ}\)C (**b**). Data was measured by an F-P scanning interferometer. The minimum value of the frequency difference (in the insert of (**b**)) at 20.7 \({}^{\circ}\)C was measured by a fiber input photon detector. polarized dual-frequency lasers. Previous research on this phenomenon was focused on He-Ne lasers. The He-Ne dual-frequency laser based on the birefringent effect has a frequency difference lock-in of about 40 MHz [19]. As far as we know, there is no report on the frequency of the lock-in phenomenon in solid-state dual-frequency lasers, while a quite low beat frequency can be achieved [20]. Considering the c-cut condition of the LTO crystal, the light oscillates parallel to the optical axis in the resonant cavity, and the frequency does not split due to the same refractive index for the a and b axes of LTO. If voltage or pressure is applied to change the direction and refractive index of the crystal's optical axis, the frequency difference will increase from a small value without a significant frequency difference lock-in effect [15]. In our experiment, the electro-optic crystal was a-cut, and the optical axis was perpendicular to the direction of light propagation. Due to natural birefringence, the frequency difference between two orthogonally polarized beams split by the same longitudinal mode is large at room temperature (24 \({}^{\circ}\)C), with a magnitude of more than 10 GHz. The minimum value of the frequency difference was measured during the continuous changing of the temperature. It can be seen from the measurement results in Figure 3a that the frequency difference continuously decreased as the temperature decreased, and the two frequencies should thus coincide between 20.5 \({}^{\circ}\)C and 21 \({}^{\circ}\)C. Considering that the measurement accuracy is limited with an optical spectrum analyzer, the minimum value of the frequency difference cannot be accurately detected. Then, we switch to a RF spectrum analyzer with an InGaAs photon detector, its wavelength response range was 950-1630 nm and the bandwidth was 3.5 GHz. At 21.3 \({}^{\circ}\)C, a frequency difference of 3.0 GHz was detected, and the temperature is continuously reduced. The curve of the frequency difference showed a process of folding back in the 20.6-20.8 \({}^{\circ}\)C range, as shown in Figure 3b. This indicates that the frequency difference had passed through the minimum value of about 405 MHz. The results show that when the frequency difference dropped to 405 MHz, within a small range of temperature regulation (0.1 \({}^{\circ}\)C), the beat frequency signal disappeared. When the frequency difference was close to 405 MHz, by keeping the temperature constant and applying a voltage to change the frequency difference continuously, it was found that the beat frequency signal also disappeared below 405 MHz.