## 3 Experiment
The recorded output phase-locked data of the 400 DC voltage, chosen as an example, are shown in Figure 3a-c.  
Figure 2: Calibration of the amplitude of modulation phase retardation \(A_{0}\) of the photoelastic modulator (PEM). (**a**) The relationship between \(A_{0}\) and the driving voltage, (**b**) the calibration and measurement of \(A_{0}\) at \(V_{0}=85\) V.  
Figure 3a-c show that there are differences in the intensity of the incident light in the whole spectral range, and the intensity fluctuates at each wavelength. Submitting the first and second harmonics shown in Figure 3b,c, and the PEM phase retardation amplitude calibrated in Figure 2b into Equation (4), the phase retardation of the EO sample was calculated and shown in Figure 3d. The phase retardation of the EO sample decreased gradually with increasing incident light wavelength. Evident dispersion was shown, however, there was almost no fluctuation in the phase retardation at each wavelength. Thus, fluctuation of light intensity can be effectively eliminated. The refractive index of LN EO sample \(n_{0}\) can be described as \(n_{0}=\sqrt{4.9048+0.11768/(\lambda^{2}-0.04750)-0.027169\times\lambda^{2}}\) by using the Sellmeier formula [29]. By submitting the size of the LN plate \(L_{y}=7.66 nm\), \(L_{z}=17.0 mm\), the phase retardation amplitude of the PEM at different wavelengths shown in Figure 2b, and the harmonic terms shown in Figure 3b,c into Equation (5), the EO coefficients, recorded in Figure 4a, could be solved. From Figure 4, where the incident light wavelength was increased from 0.42 to 0.8 \(\upmu\)m at 20 nm increments for approximately 8 s, the EO coefficients decreased with increasing wavelength. The mean  
Figure 4: EO coefficients (with 400 V DC voltage applied to the EO sample) from 0.42 to 0.8 \(\upmu\)m, with wavelength increment of 20 nm approximately every 8 s, (**a**) experimental EO coefficients, (**b**) mean value of the EO coefficients. Figure 3: (**a**) DC term \(V_{dc}\), (**b**) first harmonic term \(V_{1f}\), (**c**) second harmonic term \(V_{2f}\), and (**d**) phase retardation of the sample \(\delta_{(\lambda,\gamma,V)}\). values and the standard deviations of the EO coefficients at various wavelengths shown in Figure 4a are illustrated in Figure 4b. The EO coefficients showed obvious dispersion characteristics over the wide wavelength range coverage. When the incident light was 0.42 \(\upmu\)m, the standard deviation of the measurement coefficient attained the maximum value, \(\max(\sigma_{y22})=1.1\times 10^{-14}\) m/V, which represented the measurement sensitivity of the system. Following the EO coefficients calculation at 400 V DC voltage, the EO coefficients at 200 V, 600 V, and 800 V DC voltage were also calculated, and the measured results are shown in Figure 5.  
The trend of the EO coefficients at various wavelengths under different applied DC voltage were consistent. The EO coefficients for the same wavelength of the incident light were very close. The mean experimental values of the EO coefficients at each wavelength of the incident light at DC voltage of 200 V, 400 V, 600 V, and 800 V were calculated, and the relationship between the resulting mean EO coefficients and the wavelength of the incident light were fitted, as shown in Figure 6.  
The measurement results demonstrate that the EO coefficients decreased with increasing light wavelength, which decreased rapidly in shorter wavelength range and slowed down gradually in longer wavelength range. The measured EO coefficients were also fitted against the light wavelength, and the dispersion of the EO coefficients with wavelength was obtained as following formula.