Research on Mid-Infrared Parametric Oscillators - Part 04

2. Theoretical Analysis of OPO

According to the quasi-phase matching condition, the energy and momentum conservation laws during the OPO nonlinear three-wave frequency conversion process are as follows:

1/λ_p = 1/λ_s + 1/λ_i                (1)

n_p/λ_p - n_s/λ_s - n_i/λ_i - 1/Λ = 0    (2)

In this equation: λ_p, λ_s and λ_i represent the wavelengths of the pump, signal, and idler light, respectively; Λ denotes the crystal poling period; n_p, n_s and n_i represent the refractive indices of the pump, signal, and idler light, respectively. The refractive indices can be calculated based on the Sellmeier equations for the refractive indices of the MgO:PPLN crystal:

    n_e² = a₁ + b₁f + (a₂ + b₂f)/[λ²-(a₃ + b₃f)²] + (a₄ + b₄f)/(λ² - a₅²) - a₆λ²  (3)

The values of the parameters in Equation (3) are shown in Table 2. Among these, f is a function of temperature t and can be expressed as:

f = (t−24.5)/(t+570.82)   (4)

Tab.2 Parameter values in Sellmeier equation

Based on Equations (1)–(4), the polarization period tuning curve for an MgO:PPLN crystal pumped by a 1.064 μm laser was simulated, as shown in Fig. 3. When the polarization period is 29.5 μm and the operating temperature is 30 °C, a mid-infrared laser output at 3.82 μm can be obtained.

Fig.3  Different  grating  period  of  MgO:PPLN-OPO  wavelength  tuning range