Nonlinear cross-polarization generation of optical wave propagating through a nanorods-based hyperbolic metamaterial

In this study, the nonlinear orthogonal rotation of a linear polarized optical wave propagating through a nanorods-based hyperbolic metamaterial (NRHMM) was investigated numerically. This process is described by degenerate four-wave mixing (DFWM) of three strong linearly polarized pump waves and a weak generated orthogonal polarized wave, sometime called nonlinear-cross polarized wave (XPW) generation. The efficient nonlinear cross-polarization generation was created by optimal design of NRHMM structure, which made of two-dimensional periodically arrangement of subwavelength-sized indium tin-oxide (ITO) nanorods immersed in barium difluoride (BaF2) host dielectric material. Numerical results showed that the field intensity of nonlinear XPW conversion are dependent on the incident angle and the intensities of input pumping wave. By optimizing the radius and the lattice formation of ITO nanorods arrangement, the nearly perfect phase-matched condition for the nonlinear process based on hyperbolic phase-matching (HPM) method was achieved implicitly and exhibited by the intersection point of isofrequency contour of each interacting waves in wave-vector space. The intersection points would exhibit the optimal value of incident angle of pumping waves, which satisfy the phase-matched condition. Finally, the maximum conversion efficiencies at various pumping levels were obtained at this condition.