The characteristics of $Sreve{o}lc$ filters in $X^{(2)}$ nonlinear photonic crystals, periodically poled lithium niobate ($LiNbO_3$), were investigated by the Jones matrix method. The transmittance increases and the full width half maximum of the filter becomes narrow as the duty ratio increases. However, the filtering wavelength does not change. The transmittance at the filtering wavelength is over 95% when the duty ratio is larger than 0.35.