# Cavity Wavelength on Erbium-Doped Fiber Ring Laser Depending on Fabry-Perot Etalon Steering Angle
## 3 Experimental Results
The corresponding wavelengths are 1538.97 nm to 1526.04 nm in  
Figure 2: Spectral results of laser wavelength tuning through voltage change based on the structure on the left side of Figure 1 (the attached figure shows the superimposed spectrum corresponding to the main figure). Figure 4a, 1539.01 nm to 1526.04 nm in Figure 4b, 1538.99 nm to 1526.05 nm in Figure 4c, and 1539.05 nm to 1525.95 nm in Figure 4d. Obviously, the tuning of the laser wavelength ranges from 1539 nm to 1526 nm, initiated at a steering angle of 5\({}^{\circ}\) for the LC-FP. Each incremental degree of the steering angle results in a corresponding shift of approximately 1 nm towards shorter wavelengths. This relationship is illustrated in Figure 5. Figure 5a-d show the laser wavelength values and the spacing between neighboring laser wavelengths for each steering angle of the LC-FPs in Figure 4a-d, respectively. It is important to note that in the previous voltage-dependent laser wavelength tuning scheme, the right-hand side of Figure 1 was not optimal. However, it is still feasible to use this side of Figure 1 to tune the laser wavelength by adjusting the steering angle of the LC-FP. This is because the incident light is not perpendicular to the LC-FP, which increases the transmittance. In the case illustrated on the right side of Figure 1, the laser output power, based on the transmission path, is inherently suboptimal. Furthermore, the transmittance of the LC-FP structure for shorter wavelengths is significantly diminished. Consequently, a decrease in peak laser power at shorter wavelengths is evident, as depicted in Figure 4c,d. In comparison to the implementation of LC-FP voltage, regardless of whether the steering angle of the LC-FP increases in the counterclockwise or clockwise direction, the laser wavelength will consistently shift to a shorter wavelength while maintaining an adjustment range of approximately 1 nm. Notably, it is essential to highlight that, as indicated by Equation (1), an increase in the incident angle \(\theta\), with the refractive index remaining unchanged, does not result in a linear wavelength shift. Conversely, the linear shift associated with adjusting the steering angle of the LC-FP arises because variations in the angle of incidence lead to modifications in the refractive index of the LC-FP, which exhibits a nonlinear relationship concerning changes in angle [19; 20]. In the realm of fundamental physics, it is important to note that, while the nonlinear relationship between the refractive index and angle may influence measurements, the observed linear measurement shifts can also be partially ascribed to variations in the geometrical optical paths at different angles. In addition, the lack of significant laser wavelength shift for LC-FPs with steering angles between 0\({}^{\circ}\) and 5\({}^{\circ}\) is mainly attributed to the specific alignment and orientation of liquid crystal molecules at these low angles, and the effective optical path length and refractive index changes are not enough to cause wavelength shift. Figure 3: (**a**) The laser wavelengths and applied voltages for different laser wavelengths are shown in Figure 2. The pink symbols correspond to the applied voltage, the dark symbols correspond to the position of the laser wavelengths, and the light green bar is the spacing between neighboring laser wavelengths. (**b**) Stability measurements of wavelength and power for laser wavelengths of 1534.28 nm and 1527.8 nm. Square symbols correspond to wavelength, diamond symbols correspond to power; brown corresponds to the longer wavelength, and blue corresponds to the shorter wavelength.