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)-to-TE, TE-to-TE, TE-to-TE, and TE-to-TE converters to achieve conversion efficiencies (inter-modal crosstalk [CT] values) of >92.7% (<-27 dB), >91.7% (<-16 dB), >88.2% (<-13 dB), and >75.8% (<-10 dB), respectively, with a total transmitted power of >93%. Converter device lengths range from 16.84 to 24.61 µm for TE-to-TE to TE-to-TE, respectively. Over a broadband wavelength of 100 nm, the conversion efficiency, power transmission, and maximum inter-modal CT are almost >80%, >90%, and <-10 dB, respectively. Also, the fabrication tolerance of the proposed structure is addressed. The proposed model can not only realize arbitrary mode-order conversion but extend to other wavelength bands. To validate the feasibility of our model, the numerical results of our device operating at the wavelength of 1.55 µm are also offered and compared with those of other reports. The proposed idea may pave a new approach to designing mode converters with arbitrary geometries.