The design and experimental demonstration of double-step, 1D amorphous germanium grating structures supporting quasi bound-states-in-continuum (quasi-BIC) resonance at 3.2 mu m wavelength and its application to third-order sum-frequency generation-based up-conversion are reported. Linear transmission measurements on the fabricated metasurface with loosely focussed excitation spanning 0-3 degrees angles show very good agreement with ideal plane-wave excitation of the periodic photonic structure. TSFG measurements performed on the same structures with tightly focusing mid-infrared signal and pump beams using a reflective-type objective with 15-40 degrees angular excitation show approximate to 375 times enhancement with significant blue-shift in the resonance feature by approximate to 300 nm. To understand this excitation angle dependence of the resonance characteristics, a generalized plane-wave expansion (PWE) model is developed by considering varying excitation angle plane-waves incident on the metasurface with a discretized angular spectrum representation used to coherently combine the resultant electric and magnetic fields to obtain the linear transmission characteristics and nonlinear TSFG spectra. The PWE method is found to be particularly effective in modeling linear and nonlinear responses under realistic illumination conditions while ensuring optimal utilization of computational resources. Good agreement is obtained between the PWE simulations, linear transmission, and nonlinear TSFG measurements by considering appropriate angular excitation. In this work, the design, fabrication, and experimental characterization of a double-step, 1D amorphous germanium sub-wavelength grating structure supporting quasi bound-states-in-continuum (quasi-BIC) resonances in the 3.2 mu m wavelength are reported and demonstrate its application for resonantly enhanced up-conversion to approximate to 605 nm wavelength using third-order sum-frequency generation process. image
