Articles techniques et présentations

Cassegrain-type reflective objectives are widely utilized when performing high resolution infrared optical micro-spectroscopy experiment. Experiments involving the mixing of two or more colors of photons, widely separated in wavelength, greatly benefit from such mirror-based objectives due to the aberration free optics construction. However, this comes at the expense of a central obscuration for the excitation angles due to the positioning of secondary mirror with respect to the primary mirror inside the objective. The effect of obscuration on the linear and non-linear response measured is important and has not been a subject of investigation. In this work, we utilize COMSOL Multiphysics’s wave optics module to model and simulate the linear and non-linear optical responses from an amorphous-germanium (a-Ge) on quartz based metasurface platform under mid-infrared wavelength illumination using a reflective objective of 13% central obscuration. COMSOL was chosen because of its versatility in modelling both linear and non-linear responses in the optical domain. Gaussian excitation conditions can mimic the operation of refractive (lens-based) objectives, but for a reflective objective with central obscuration, default Gaussian source parameters available in the commercially available software platforms cannot fully model this modified excitation conditions. Here, we adopted a novel approach to model the modified Gaussian response using a series of plane wave excitations with suitable weighing parameters. For each iteration (in angle of incidence and wavelength) the source power is scaled to match the Gaussian profile and corresponding field (both electric and magnetic) components are recorded. The fields are then coherently summed to calculate the effect of angles at a particular wavelength. The effect of obscuration can be included by simply considering the angles of interest and neglecting the rest. Poynting vector calculation is used to calculate the linear transmission spectra. The coherently summed fields are propagated through the a-Ge sub-wavelength grating-type metasurfaces used as the non-linear optical medium of interest in this study to eventually calculate the linear transmission and non-linear polarization response. We validated the model by comparing the responses of reflective objective (supporting 15 to 40 degrees) and a conventional refractive objective without obscuration (supporting 0 to 40 degrees). The modelled linear transmission response of the refractive objective was in good agreement with the Gaussian based finite area simulation results. The spectral resonance associated with the transmission spectra were found to blue-shift by ~ 300 nm due to the effect of obscuration. Similarly, non-linear responses were studied using third-order sum frequency generation (TSFG) as the underlying non-linear phenomena. The simulated TSFG spectra was in good agreement with the experimental spectra. This approach to modelling the linear and nonlinear response from photonic structures of interest can potentially offer two major advantages to electromagnetic simulations at optical frequencies. Firstly, this approach enables the modelling of source excitation with any arbitrary amplitude or phase distribution. Secondly, this approach can bring down the memory requirement and computational cost considerably by replacing perfectly matched layer-based finite area simulation with a series of plane-wave-excitation simulations at varying angles of incidence with associated periodic boundary conditions.