Topology-optimized ultra-broadband and ultra-compact mode converters with B-spline parameterization

Mode converters play a critical role in on-chip photonic mode field manipulation systems. This paper proposes a topology optimization method for mode converters based on B-spline parameterization. The initial structure's density field is represented using B-spline surfaces, with the density values determined by control coefficients. The control coefficients are iteratively optimized using the sequential quadratic programming algorithm. The optimized TE0-TE1, TE0-TE2, and TE3-TE1 mode converters, with footprints of 2 μm×1.6 μm, 2 μm×1.6 μm, and 2 μm×1.9 μm, respectively, achieve average conversion efficiencies of 93.38%, 88.39%, and 88.83% over bandwidths of 400, 290, and 340 nm. Their maximum conversion efficiencies are 98.62%, 92.45%, and 92.72%, respectively. By cascading these mode converters, arbitrary-order mode conversions among TE0, TE1, TE2, and TE3 can be realized. The method demonstrates great potential for application in nanophotonic device design, providing an effective solution for high-capacity optical communications and optical interconnects.