Second-Order Nonlinearity Assisted by Dual Surface Plasmon Resonance Modes in Perforated Gold Film

We have studied analytically the reflection assisted with surface plasmon through the square lattice perforated gold film. Under the excitation of the external electromagnetic field with one or two different frequencies, the second-order nonlinearity exists in this noncentrosymmetric metal-based metamaterial. We employed the two surface plasmon resonances modes with different lattice periods. With the excitation of two different plasmon resonances modes, the strong local field induces an expected increase of the second-order nonlinearity including second harmonic generation as well as the sum (difference) frequency generation. The field distributions results also indicate that the enhancement of sum frequency signals and difference frequency signals strongly depends on surface plasmon resonance effect.