﻿ Euler Curves and Bent Tapers

# FIMMPROP

## Bend Models

#### Simulations in fully vectorial 3D with FIMMPROP software

##### Basic Bends

Basic Bends that have a constant radius of curvature are very simple to model in FIMMPROP.

However, despite being very easy to model basic bends of constant curvature have limited use due to their relative efficiency and footprint compared to other types of bend.

##### Variable Curvature Bends

FIMMPROP can be used to calculate bends of variable curvature defined either by a mathematical expression or more simply as an Euler Bend. Additionally, FIMMPROP can handle tapers that are bent, allowing transitions for to be minimised in terms of footprint.

Previously these features were only possible with a script such as python, but now are easily accessible through the graphical user interface.

Field Profile Superimposed over S-bend layout

##### Euler Bends

Euler bends are often used in photonics to minimises losses whilst also minimising chip footprint. The curvature of the bend varies along its length, typically rising linearly to a maximum and then falling back down linearly to zero as the curve straightens out. The same principle is used in civil engineering for bends in highways and on railways.

FIMMPROP allows the user to define either a Simple or S-Bend.

• Simple bends are defined by a particular angle that the bend will reach and the maximum curvature (1/µm) which the bend will reach.

• S-Bends are defined as an offset in both X and Z directions. This determines the overall length and width of the bend and FIMMPROP will apply the necessary curvature for it to be an Euler Bend.

Euler bends can typically have a significantly smaller footprint than a basic arc and still achieve the same efficiency. Consider a 90° bend as below in a typical SOI rib waveguide. If this is achieved using an arc then a length and width of 65µm is required to achieve an efficiency of 94%. For the same waveguide a 90° can be made using an Euler curve which has a much smaller footprint of 20x20µm.

##### Expression Bends

Bends can also be defined with a mathematical expression, including exponential and sinusoidal terms. This allows for almost any type of curvature.

##### Curved Tapers

S-Bend in a tapered waveguide

FIMMPROP also allows the user to define a bend which is tapered - the width of the waveguide varies as a function of length. This will allow the design of circuits which have a dramatically reduced footprint.