Theoretical analysis of mode conversion by refractive-index perturbation based on a single tilted slot on a silicon waveguide

We propose a compact mode converter operating at the mid-infrared wavelength of 3.4 µm, comprising an etched parallelogram slot filled with silicon nitride on a silicon-on-calcium fluoride platform. The tilted slot introduces transverse and longitudinal index perturbations on the waveguide eigenmodes, achieving mode conversion in the propagation direction. Differing from previous reports using massive parameter sweep, we provide analytical formulas to determine geometry parameters by considering the modified phase-matching condition and the profiles of coupling coefficient of coupled-mode theory. Rigorous 3D numerical examples demonstrate the transverse electric (TE) 0 -to-TE 1 , TE 0 -to-TE 2 , TE 0 -to-TE 3 , and TE 0 -to-TE 4 converters to achieve conversion efficiencies (inter-modal crosstalk [CT] values) of >92.7% (91.7% (88.2% (75.8% (93%. Converter device lengths range from 16.84 to 24.61 µm for TE 0 -to-TE 1 to TE 0 -to-TE 4 , respectively. Over a broadband wavelength of 100 nm, the conversion efficiency, power transmission, and maximum inter-modal CT are almost >80%, >90%, and