Nemaktis is an open-source platform including tools for propagating and visualising optical field in complex birefringent media such as liquid crystal (LC) layers. It includes three backends implementing advanced numerical methods for light propagation, as well as an easy-to-use high level interface in python allowing to quickly setup a simulation and visualize optical micrographs of a LC structure as in a real microscope.

The three backends implemented in nemaktis correspond to:

1. rt-solver, a ray-tracing C++ code allowing to automatically represent optical fields in terms of ordinary and extraordinary rays (therefore being limited to uniaxial media). This module allows to propagate rays through any media with a sufficiently regular orientational field (i.e. with C1 regularity). Optical fields can be reconstructed along rays or interpolated on a regular mesh using an advanced homotopy continuation algorithm. The main advantage of this scheme is the ability to access ray trajectories and get an intuitive feeling of how light is deflected by a liquid crystal structure, but can be inacurate when this structure is thick and/or has sharp features. For this reason, we advise to use this backend only for visualisation of light deflection, not for accurate simulation of optical field propagation (although in practice reasonable agreement can be obtained for simple structures, as explained in the Soft Matter paper cited below).

2. bpm-solver, a beam propagation C++ code which simply propagates optical fields through any birefringent layers (no limitation on the regularity of the orientational field, although only paraxial components of the optical fields will be modeled accurately). This module relies on a novel operator-splitting scheme and accurate expressions of the operators for the beam walk-off, anisotropic diffraction, and phase evolution. The main advantage of this scheme is its accuracy (1-5% of relative error in comparison to a full resolution of Maxwell equations in a system with paraxial propagation) and efficiency (parallel implementation in C++ based on sparse matrices), as explained in the Optics Express paper cited below. This scheme is particularly well suited for efficient simulation of optical micrographs as in a real transmission micrographs.

3. dtmm, a FFT-based diffractive transfer matrix python code which offer similar functionalities as bpm-solver but relies on a less accurate scheme in its default version (although the accuracy can be improved at the cost of computational efficiency using a dedicated parameter). In most cases, this scheme will show similar accuracy as bpm-solver for micrograph simulations, and will in general be faster than bpm-solver on small meshes and slower on big meshes, as expected from the computational complexity of both methods (O(N) for bpm-solver, O(N log[N]) for dtmm). We also note that the underlying python library for dtmm offer a lot of advanced features (most notably the calculation of reflection) which are currently not implemented in the bpm-solver backend.

The high-level interface corresponds to a python package named nemaktis and allows to set-up a director field for a LC sample (non-trivial shapes for the LC domain are supported), define physics constant, propagate optical fields through the sample using either the bpm-solver or dtmm backend , and recombine them as in a real microscope to obtain polarised and bright-field micrographs. A graphical user interface allows the user to quickly change settings (focalisation, polariser angles...) while visualising optical micrographs in real-time.

Note that the rt-solver backend is not interfaced in the high-level python package and have to be used directly. The reason for this is that the algorithm used to reconstruct fields is quite complex and necessitates some tweaking from the user to get the best results. In order to keep things simple in the high-level interface, we decided not to include ray-tracing support in the python package at the moment.

The first two codes and the high-level interface were written by G. Poy and are hosted on this repository, while the third code was written by A. Petelin is hosted in another repository: https://github.com/IJSComplexMatter/dtmm.

See the following page for installation instructions (you don't have to clone this repository unless you want to modify the code):

https://nemaktis.readthedocs.io/en/latest/intro/installation.html

If you are impatient, you can take a look at the examples folder to see basic usage of the high-level interface. Else, you can start reading the documentation to learn the fine details of this software:

https://nemaktis.readthedocs.io

Note that the high-level interface does not give you access to the full range of features offered by the backends. For example, dtmm supports the calculation of reflected fields, while in the high-level interface only forward-propagating fields are currently supported. If you want to use such advanced features, you will have to learn how to use directly the backends. The documentation of the backends is available in a dedicated section of the nemaktis wiki (link above).

Nemaktis is released under the MIT license, so you can use it freely. You are strongly encouraged to cite the following papers if you use this package for published research:

G. Poy, S. Žumer, Soft Matter 15, 3659-3670 (2019): https://doi.org/10.1039/C8SM02448K

G. Poy, S. Žumer, Optics Express 16, 24327-24342 (2020): https://doi.org/10.1364/OE.400984

A. Petelin et al., in preparation.