FDTD modeling of the second harmonic generation in transition metamaterials

On the basis of the classical Maxwell's equations the corresponding wave equations are derived for description of multiwave interactions in transition metamaterials whose refractive index varies along the sample from positive to negative values. The phenomenon of second harmonic generation is redicted in the transition layer near the point at which the refractive index turns zero, even at low intensities of the fundamental pumping wave. With the help of FDTD (finite difference time domain) mathematical modeling method it is found that the efficiency of the second harmonic generation in transition metamaterials strongly depends on the angle of incidence and the thickness of the transition layer. Specific recommendations are developed for the construction of a compact second harmonic generator based on transition metamaterials