Index-profile design for low-loss crossed multimode waveguide for optical printed circuit board

We present an index profile design for remarkably low loss multimode optical crossed waveguide. In this paper, we theoretically calculate the light propagation loss in crossed waveguides with step-index (SI) and graded-index (GI) square cores utilizing a ray tracing simulation. In this simulation, we focus on the index exponent values for the GI profile, which allows low crossing loss even if the number of crossing is as large as 50 or even if the crossing angle is as low as 20°. It is revealed that an index exponent of 2.0 for the GI core strongly contributes to exhibit 35 times lower loss (0.072 dB after 50-perpendicular crosses) compared to the loss of the SI-core counterpart (2.58 dB after the same crossings). The GI cores with a smaller index exponent exhibit better loss in crossed waveguides with a wide range of crossing angles from 30° to 90°. Furthermore, we discuss the effect of the refractive index profile at the intersection on the optical loss of crossed waveguides.