# Euler waveguide bend
Efficiently routing light in a densely packed photonic chip has been a central topic in the photonic industry. This inevitably requires the use of waveguide bends of various angles and radii. Electromagnetic waves can travel in straight waveguides for a long distance with very little loss. However, when it enters a waveguide bend, significant reflection and leakage could occur.
The most common waveguide bends are circular bends. A silicon waveguide bend typically has a loss in the order of 0.01 dB. This loss is sufficiently small for many applications. However, in cases where a large number of bends are used, the total loss due to the bends can be quite large. Therefore, new methods to reduce bending loss is needed. Recently, T. Fujisawa et al. (opens new window) demonstrated that a waveguide bend following the clothoid curve, also known as the Euler bend, yields a much lower loss compared to a circular bend due to its smooth curvature transition. In this example notebook, we model a 90 degree Euler waveguide bend and compare its loss to a conventional circular bend. The loss of the Euler waveguide bend is found to be several times smaller compared to the circular bend of the same effective radius at the telecom wavelength.
To view the full example in Python, please click here (opens new window).