General Waveguide Bend Design Based on Cubic Spline Interpolation and Inverse Design

Silicon waveguide bends are key components that affect the packing density and scalability of photonic integrated circuits. Traditional bend design methods rely on well-established functions such as Euler spirals or Bezier curves, which have limited parameter spaces, limiting the discovery of compact bends with higher performance. Here, we propose a general approach to waveguide bend design. For a given radius, our method uses cubic spline interpolation with an inverse design algorithm to obtain an optimal bend geometry to support a given number of modes. We refine the particle swarm optimization algorithm to reduce the need for parameter tuning and increase its ability to avoid local optima. As a result of these modifications, the design process becomes less complicated and more efficient. To demonstrate the effectiveness of the proposed method, we design and fabricate three waveguide bends supporting one, two, and three modes with radii of 2.5
$\mu$
m, 4
$\mu$
m, and 5
$\mu$
m, respectively. The measured (simulated) insertion losses of the three bends are less than 0.012 (0.009) dB, 0.04 (0.028) dB and 0.059 (0.048) dB per 9
$^{\circ }$
, respectively. The measured (simulated) crosstalk between the modes of the latter two bends is less than −23.6 (−36.1) dB and −19.7 (−26.5) dB per 9
$^{\circ }$
, respectively. The proposed method provides an effective tool for designing compact multimode bends for future photonic integrated circuits.