pyGLLE is a Python toolkit for simulating the propagation dynamics of dissipative solitons in a variant of the Lugiato-Lefever equation (LLE). Including dispersion terms of third and fourth order, this variant is here referred to as the generalised LLE (GLLE).

The provided software implements a solver for a variant of the LLE including dispersion terms of third and fourth order. It also includes the functionality to solve for stationary solutions of the standard LLE, containing one or several localized dissipative structures.

The tools provided by the pyGLLE package require the functionality of

• numpy (>=1.8.0rc1)
• scipy (>=0.13.0b1)

Further, the figure generation scripts included with the examples require the funcality of

• matplotlib (>=1.2.1)

The repository follows a modular structure:

pyGLLE/
├── LICENSE.md
├── README.md
├── numExp01_stationarySolution
│   ├── data_stationary_solution
│   ├── main_findStationarySolution.py
│   ├── pp_figure
│   │   ├── FIGS
│   │   ├── generateFigure.sh
│   │   └── main_figure_stationarySolution.py
│   └── run.sh
├── numExp02_propagationScenarios
│   ├── data
│   ├── data_stationary_solution
│   ├── main_findStationarySolution.py
│   ├── main_propagateInitialCondition.py
│   ├── pp_figure_propagationScenarios
│   │   ├── FIGS
│   │   ├── figure_base_propagationDynamics.py
│   │   ├── generateFigures.sh
│   │   └── main_figure_propagationDynamics_stationarySolution.py
│   └── run.sh
├── scripts
│   └── pyGLLE.py
└── src
    ├── data_handler.py
    ├── solver.py
    └── stationary_solution.py

Subfolder /src contains Python modules implementing the basic functionality of the software:

• data_handler.py: provides a class, handling data accumulation and data
• ouput. Output data is stored using the numpy native npz-format.
• stationary_solution.py: provides functions allowing to obtain stationary localized solution of the standard LLE.
• solver.py: implements a solver for the numerical integration of the generalized LLE using a Runge-Kutta method.

The folder /scripts contains the main Python module implementing the interface between the user supplied code and the algorithms and data structures contained in the modules in folder \src:

• pyGLLE.py: defines the main functions findStationarySolution and propagateInitialCondition.

Further, the folders \numExp01_stationarySolution and \numExp02_propagationScenarios contain scripts that implement example workflows ranging from the specification of a propagation scenario to the visualization of the generated raw data.

The repository further contains

• LICENSE, a license file.
• Readme.md, this file.

For a more detailed description of functions, defined in the above modules, their parameters and return values we refer to the example cases and documentation provided within the code.

The pyGLLE software package is derived from our research software and is meant to work as a (system-)local software tool. There is no need to install it once you got a local clone of the repository, e.g. via

$ git clone https://github.com/omelchert/pyGLLE

We further prepared a pyGLLE compute capsule on Code Ocean, allowing to directly run and modify an exemplary simulation without the need to create a local copy of the repository.

The pyGLLE software package is described in

O. Melchert, A. Demircan, "pyGLLE: A Python toolkit for solving the generalized Lugiato–Lefever equation," SoftwareX 15 (2021) 100741, DOI: 10.1016/j.softx.2021.100741.

The presented software has been extensively used in our research work, including the study of resonant emission of multi-frequency radiation by oscillating dissipative solitons in the LLE including third order dispersion

O. Melchert, A. Demircan, A. Yulin, "Multi-frequency radiation of dissipative solitons in optical fiber cavities," Scientific Reports 10 (2020) 8849, DOI: 10.1038/s41598-020-65426-x.

and the dynamics of localized dissipative structures in the generalized LLE with negative quartic group-velocity dispersion

O. Melchert, A. Yulin, A. Demircan, "Dynamics of localized dissipative structures in a generalized Lugiato-Lefever model with negative quartic group-velocity dispersion," Optics Letters 45 (2020) 2764, DOI: 10.1364/OL.392180.

This project is licensed under the MIT License - see the LICENSE.md file for details.

This work received funding from the Deutsche Forschungsgemeinschaft (DFG) under Germany’s Excellence Strategy within the Cluster of Excellence PhoenixD (Photonics, Optics, and Engineering – Innovation Across Disciplines) (EXC 2122, projectID 390833453).