# A Second Harmonic Wave Angle Sensor with a Collimated Beam of Femtosecond Laser
## 3 Design of the Second Harmonic Wave Angle Sensor and Experiments  
Figure 4a exhibits the schematic setup of the proposed angle sensor, and Figure 4b shows a photograph of the experimental setup. A commercial mode-locked Fs laser (C-Fiber High Power, Menlo Systems, Planegg, Germany) was employed as the FW source with an average power of \(>\)500 mW, a pulse repetition rate of 100 MHz, a pulse width of \(<\)150 fs,  
and a spectral range from 1480 nm to 1640 nm. The emitted laser beam travels through the polarizer and the plano-convex lenses (\(f_{1}=150\) mm and \(f_{2}=75\) mm) before passing through a rotary-stage-mounted MgO:LiNbO\({}_{3}\) crystal (Castech Inc., Fujian, China) with a length \(L\) of 2 mm, cut-off angle of 47\({}^{\circ}\), a diameter of 5 mm, and 5% MgO:LN. The laser beam consists of FW and generated second harmonic wave eventually reaches a multimode fiber (M42L02, Thorlabs Japan Inc., Tokyo, Japan) connected to an optical spectrum analyzer/OSA (highest wavelength resolution of 0.02 nm, AQ6370C, Yokogawa Electric, Tokyo, Japan), in which FW and SHG spectra were recorded. The rotary stage with a travel range of \(\pm 8.5^{\circ}\) and a resolution of 0.0067\({}^{\circ}\) (KRB04017C, Suruga Seiki Co., Ltd., Shizuoka, Japan) was driven by the stepping motor controller (DS102 MS, Suruga Seiki Co., Ltd., Shizuoka, Japan) to ensure the angular shift of the target was restrained. The data was collected for every 100 pulses given to the rotary stage, which is equivalent to approximately 121 arc-second. The alignment stage (MBT613D/M, Thorlabs Japan Inc., Tokyo, Japan) was equipped with an objective lens that can be shifted independently in the XYZ axis to guide the beam to the multimode fiber. A commercial laser autocollimator (Elcomat 3000, Moller-Wedel Optical GmbH, Wedel, Germany) was employed as the external angle sensor to evaluate the angular shift of the rotary stage. As can be seen in Figure 4a, the initial position of the rotary stage was set such that the two indicator lines on the rotary plate and the surface of the stepping motor controller met. The incident laser was assumed to be perpendicular to the crystal surface at this initial position. The detection of the angular displacement was carried out by observing the evolution of the SHG spectrum with respect to the changes in the angular position of the crystal. The detection continued by varying the \(Z\)-position of the crystal. The autocollimator ensured the angular position of the crystal throughout the entire experiment. The sensitivity of the angle sensor was determined by concerning the slope of the measurement trend based on the SHG peaks changing versus respective angle shifts. As one of the first steps to produce a collimated laser beam, the initial fs laser output profile was observed. Figure 5a shows the profile of the collimated laser beam at the initial condition, which was observed at the cross-sectional \(Z\)-axis, and Figure 5b shows its cross-sectional profile. The beam width can be defined as the 1/e\({}^{2}\) value of those Gaussian-like intensities. The beam width was evaluated to be 2117 \(\upmu\)m and 2195 \(\upmu\)m along with the \(X\) and \(Y\)-directions, respectively. Figure 4: Experimental setup: (**a**) A schematic of the proposed angle sensor; (**b**) A photograph of the experimental setup. High input power is required when the Fs laser with the initial beam width is employed directly, as explained in the previous section. A reduction in the beam width is thus required. The reduction in the beam width was successfully carried out using the setup shown in Figure 4. Figure 5c shows the change in the beamwidth as the increase in observation distance. As shown in the figure, the \(X\)-directional diameter showed more consistent results than the \(Y\)-directional diameter upon the variation of observation distance. Since the dispersion angle was small at the observation distance from 10 mm to 140 mm, the produced laser was treated as a collimated laser beam.