Inverse-Designed Broadband and Compact $TE_{N}$ to $TE_{0}$ Mode Converters via Optimized Bezier Curves

We present a scalable design strategy for compact, broadband mode converters capable of transforming arbitrary high-order transverse electric (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$TE\_{N}$</tex-math></inline-formula>) modes into the fundamental <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$TE\_{0}$</tex-math></inline-formula> mode on a silicon-on-insulator platform. The architecture employs a “split-phase-combine” mechanism: the higher-order mode is spatially separated into fundamental mode components, phase-synchronized, and subsequently recombined. The device comprises a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1\times (N+1)$</tex-math></inline-formula> input splitter, an adiabatic phase shifter, and a multimode interference (MMI) combiner. By parametrizing the device geometry with optimized cubic Bezier curves, we achieve a compact footprint with large operating bandwidth, while effectively maintain low losses. We validate the scalability of this approach by designing converters for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$TE\_{1}$</tex-math></inline-formula>, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$TE\_{2}$</tex-math></inline-formula>, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$TE\_{3}$</tex-math></inline-formula> modes. The optimized devices exhibit mode conversion efficiencies of 98.3%, 95.8%, and 86.8%, respectively, across a broad 100nm bandwidth (1500–1600nm). Tolerance analysis further confirms the robustness of the designs against systematic fabrication deviations of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pm 10$</tex-math></inline-formula> nm, suggesting their suitability for high-density mode-division multiplexing in next-generation optical interconnects.