# Cavity Wavelength on Erbium-Doped Fiber Ring Laser Depending on Fabry-Perot Etalon Steering Angle
## 3 Experimental Results  
Figure 2 presents the outcomes of laser wavelength adjustments obtained by applying a 1 kHz square wave voltage to the LC-FP. Following the experimental configuration depicted on the left side of Figure 1, the steering angle of the LC-FP is maintained at 0\({}^{\circ}\). The applied voltages range from 1.138 V to 1.35 V (sequential voltage applied steps 1 to 20), as depicted on the \(z\)-axis of Figure 2, resulting in corresponding laser wavelengths that vary from 1535.38 nm to 1525.79 nm. Each incremental voltage application adjusts the laser wavelengths by approximately 0.5 nm, demonstrating a tendency toward shorter wavelengths, as indicated in the results of Figure 3a. The fixed cumulative tuning of laser wavelengths, approximately 0.5 nm, exhibits a response marked by a nonlinear change in voltage, as voltage variations display a nonlinear relationship with the refractive index of the LC-FP [18]. Furthermore, the resultant shift in the laser wavelength is inversely related to the applied voltage magnitude, which aligns with findings reported in prior  
Figure 1: Schematic of LC-FP-based fiber ring laser architecture; on the left is the reflective output scheme; on the right is the direct output scheme. The purple arrow shows the beam path emitted from the EDFA input port; the dark arrow shows the beam path emitted from the EDFA output port. (EDFA: erbium-doped fiber amplifier; LC-FP: Fabry–Pérot etalon; OSA: optical spectral analyzer). studies [14; 18]. This outcome can be illustrated through the following thin-film interference equation:  
\[2 ndcos\theta=(\text{m}-1/2)\cdot\lambda \tag{1}\]  
where the internal refractive index of the LC-FP is \(n\), the internal gap of the LC-FP is \(d\), the incidence angle is \(\theta\), the interference order is m, and \(\lambda\) is the wavelength. It follows that, if the parameters \(d\), \(\theta\), and m remain constant, a reduction in the refractive index \(n\) will necessitate a reduction in the wavelength \(\lambda\). Consequently, as the applied voltage increases, the laser wavelength is observed to decrease relative to the initial wavelength. Figure 3b illustrates the measurements of the wavelength alterations alongside the corresponding peak power values per minute when the laser wavelengths were tuned to 1534.28 nm and 1527.8 nm. The maximum observed wavelength change is approximately 0.1 nm, with a maximum power variation of about 4.5 dB. The selected wavelengths for sampling were chosen purposefully; one is situated at a shorter wavelength, while the other, at a longer wavelength, facilitates a comparative analysis of both the wavelength and peak power under these conditions. It is worth noting that the laser wavelength tuning scheme applying voltage to the LC-FP only works successfully in the left configuration of Figure 1. To use the right configuration of Figure 1, it is necessary to increase the power of the output light or try different coupler light ratios; otherwise, the results will not be satisfactory. This is mainly because the 90% reflectance of the LC-FP makes the right configuration of Figure 1 have relatively less light transmitting through the LC-FP to reach the optical spectral analyzer. Figure 4 shows the laser wavelength tuning conducted by changing the steering angle of the LC-FP perpendicular to its placement plane. Modifications to the steering angle of the LC-FP result in a corresponding change in the angle at which the beam is incident upon the LC-FP. This adjustment leads to variations in the optical path and consequently induces a shift in wavelength. Figure 4a,b present the results derived from the left side of Figure 1, while Figure 4c,d depict the outcomes based on the right side of Figure 1. The steering angle of the LC-FP is counterclockwise in Figure 4a,c, whereas it is clockwise in Figure 4b,d. The laser wavelengths in Figure 4a-d correspond to the steering angle of LC-FP from 5\({}^{\circ}\) to 18\({}^{\circ}\).