FIMMPROP

How FIMMPROP works

A modular approach to 3D optical propagation modelling

You will find here a simple description of the FIMMPROP framework.

A FIMMPROP device is composed of one or more Sections. A Section can be a straight waveguide of finite length, or a z-varying structure. This allows you to define bends, tapers, Y-junctions, periodic structures even lensed fibres in a convenient way. Each Section can be described in one of two ways:

• Planar Layout - describe an epitaxial layer structure and a lithographic mask composed of a variety of shapes. Then define an etch depth for regions that are not masked. Ideal for planar structures commonly encountered in photonics

• Cross-Section Layout - define each Section from one or more cross-sections. A taper would be defined by the cross-sections at it's ends and the structure would morph from one to another along its length in a user-defined way. Ideal for fibre tapers and fused fibre couplers but also convenient for straight planar waveguides.

We illustrate the Cross-Section Layout with the simulation of an MMI coupler. Three 2D waveguide sections are necessary to design the MMI Coupler: the input channel, the body of the MMI and the output channels.

The different Sections of a FIMMPROP device are connected with Joins, in which the overlaps between the modes of each Section are calculated. A Joint allows you to define offsets, tilts and rotations between the two Sections.

Below we have designed the 3D component by defining three straight waveguide Sections based on the 2D cross-sections and inserting Joins in between.

For each possible input mode, the transmission and coupling forward and backward through the Sections and Joins of the device is calculated in the form of a scattering matrix. The scattering matrix gives the coupling coefficient from each input mode to each output mode in a fully bi-directional way, and takes into account every possible internal reflections within the device.

It therefore also gives backward coupling from each input mode to each other input mode, from each output mode to each other input mode and from each output mode to each output mode.

The scattering matrix approach allows you to solve the problem for all inputs simultaneously, so you can for example get the response for both TE and TM polarisations in one go.

Once the scattering matrix has been calculated, it only takes a few seconds to calculate the field profile corresponding to a given input, which can be either a mode or a combination of modes of the input section.

The modular nature of the method employed is fully exploited by FIMMPROP in its flexible, modular design paradigm purposely made to take advantage of any symmetries or repetitions in the components you create.

For example, if a given cross-section is found several times along the device FIMMPROP will only need the modes to be calculated once. Similarly if a structure is periodic, the overlap integrals at the repeated joints will only be calculated once.

FIMMPROP allows you to insert each device has a sub-component of another larger device. This not only allows you to build complex structures easily, but it also enables FIMMPROP to fully exploit the symmetries and repetitions inherent in your structure, saving you computation time.

Please see here for a description of the EME method used in FIMMPROP.