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https://github.com/gregmoille/pyLLE

Lugiato Lefever Equation Solver in Python/Julia
https://github.com/gregmoille/pyLLE

combs frequency-comb frequency-combs julia lle python

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Lugiato Lefever Equation Solver in Python/Julia

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README 

        
# pyLLE ![NIST logo](images/NISTlogo32x32.jpg)



[![](https://img.shields.io/static/v1.svg?label=docs&message=passing&color=green&style=flat)](https://gregmoille.github.io/pyLLE/)

![](https://img.shields.io/static/v1.svg?label=version&message=4.1&color=9cf&style=flat)

[![](https://img.shields.io/static/v1.svg?label=DOI&message=10.6028/jres.124.012&color=blue&style=flat)](https://doi.org/10.6028/jres.124.012)



## What's new



A major revision, v4.0.0 introduces a lot of new stuff including:



- Complete recoding of the core with better coding and commenting which hopefully makes it easier to implement custom features

- Modification of interfacing with parameters and results through method attributes instead of bulky dictionaries

- Stability of the half step Fourier method, allowing to use a soliton solution as an original state for the LLE

- Allowing arbitrary number of driving pump, according to Taheri et al The European Physical Journal D 2017. and our paper on Nature Communication (Moille et al. Nature Communication 2021)

- **Julia compatibility with version 1.8 (current as of 05/01/2023) and above**. Previous version are no longer supported



## How to Cite Us?



Please, if you use this package and it helps you with your research and publication, cite us in your paper. Not only does it allow us to have a better idea of new things people are interested in and how to keep improving the solver, but it also helps us build a community where everybody can help maintain the solver to better suit the needs of everybody.

You can cite our paper published in the Journal of Research of the National Institute of Standards and Technology, available [here](https://doi.org/10.6028/jres.124.012), with the following BibTeX entry.:



```latex

@article{moille_pyLLE,

      author = {Gregory Moille and Qing Li and Xiyuan Lu and Kartik Srinivasan},

      title = {pyLLE: a Fast and User Friendly Lugiato-Lefever Equation Solver},

      year = {2019},

      volume = {124},

      pages = {124012},

      month = {2019-05-24},

      journal = {Journal of Research of the NIST},

       doi = {https://doi.org/10.6028/jres.124.012},

     }

```



## How to install



As pyLLE relies on a Julia back-end, please prior to installing this package be sure that Julia is installed on your machine or visit the julia [package download page](https://julialang.org/downloads/) to install it. The code should now work with any recent version of Julia.



Once Julia installed, the different packages needed to run pyLLE, either python or julia related, will be automatically downloaded and installed. Just a heads up, the installation of the package can vary in time, especially because of Julia that might rebuild the cache.



pyLLE will look by default to find the Julia binary in the `/opt/bin/julia`, which you can make it happen either in MacOS



```bash

ln -s /Applications/Julia-.app/Contents/Resources/julia/bin/julia /opt/bin/julia

```



or Linux



```bash

ln -s /bin/julia /opt/bin/julia

```



Note that if this step is skipped it is alright as an update of the pyLLE package provide a way to specify the julia binary you would like to use specifyin `solver.SolveTemporal(bin = )`



Now, one can simply automatic install, just pip it :



```bash

pip install pyLLE

```



or pip the github



```bash

pip install git+https://github.com/gregmoille/pyLLE.git

```



**For windows** the julia package have to be installed manually, using a julia console and typing the following command:



```julia

using Pkg



Pkg.add("HDF5")

Pkg.update("HDF5")



Pkg.add("FFTW")

Pkg.update("FFTW")



Pkg.add("LinearAlgebra")

Pkg.update("LinearAlgebra")



```



For a manual install, download the .zip of the repository or clone it and install with the setup.py script.



## Checking that everything works correctly



Launch a julia console and within type the commands:



```julia

using HDF5

using FFTW

using LinearAlgebra

```



if any of the previous command throw an issue, mostly it is because it is not installed. One way to fix it is to remove the installed packaged to remove the cache



- for linux and mac os user: remove everything in ~/.julia/

- for windows users: remove everything in C:\Users\\.julia\



Then enter the pacakge manager for julia by typing in the julia console:



```julia

julia>]

```



then



```julia

(v1.1) pkg>add HDF5

(v1.1) pkg>add FFTW

```



## Example [![NBviewer](https://custom-icon-badges.demolab.com/badge/jupyter-notebook-blue.svg?logo=eye&logoColor=white)](https://nbviewer.org/github/gregmoille/pyLLE/blob/master/example/TemporalDualPump.ipynb)



A complete example is available in the example directory [notebook](https://github.com/gregmoille/pyLLE/blob/master/example/TemporalDualPump.ipynb) with the corresponding file needed in the folder.

You can also access the [nbviewer](https://nbviewer.org/github/gregmoille/pyLLE/blob/master/example/TemporalDualPump.ipynb) example to have a better idea of what's going on:



## Works Using/citing pyLLE



If you want to be featured here, shoot me an email! I try to keep it up to date but this is not a priority. I would love to hear anybody who uses it!



- 2023:

  - Moille, G., Stone, J., Chojnacky, et al. Kerr-Induced Synchronization of a Cavity Soliton to an Optical Reference. Nature 624, 267–274 (2023). 

  - Moille, G., Lu, X., Stone, J., Westly, D., & Srinivasan, K. (2023). Fourier synthesis dispersion engineering of photonic crystal microrings for broadband frequency combs. Communications Physics, 6(1), 144.

  - Ren, D., Dong, C., & Burghoff, D. Integrated nonlinear photonics in the longwave-infrared: A roadmap. MRS Communications, 13(6), 942-956 (2023).

  - Ji, H., Geng, Z., Cheng, W., Wu, P., Yu, Z., Liu, Y., ... & Zhao, Q. (2023). High-power two-color Kerr frequency comb generation on the gallium phosphide-on-insulator platform at SWIR and MIR spectra. JOSA B, 40(8), 1976-1985.

  - Geng, Z., Ji, H., Yu, Z., Cheng, W., Wu, P., Li, Y., & Zhao, Q. (2023). Dispersion-flattened concentric structure for microcomb bandwidth broadening in GaP-OI resonators. JOSA B, 40(3), 673-681.

  - Moille, G., Li, C., Stone, J., Chojnacky, M., Shandilya, P., Chembo, Y. K., Dutt, A., ... & Srinivasan, K. (2023). Two-Dimensional Nonlinear Mixing Between a Dissipative Kerr Soliton and Continuous Waves for a Higher-Dimension Frequency Comb. arXiv preprint arXiv:2303.10026.

- 2022:

  - Afridi, A. A., Weng, H., Li, J., Liu, J., McDermott, M., Lu, Q., ... & Donegan, J. F. (2022). Breather solitons in AlN microresonators. Optics Continuum, 1(1), 42-50.

  - Lu, S., Liu, X., Shi, Y., Yang, H., Long, Z., Li, Y., ... & Liang, H. (2022). Mid-infrared ultra-broadband optical Kerr frequency comb based on a CdTe ring microresonator: a theoretical investigation. Optics express, 30(19), 33969-33979.

- 2021:

  - Weng, H., Liu, J., Afridi, A. A., Li, J., Dai, J., Ma, X. _et al._ "_Octave-spanning Kerr frequency comb generation with stimulated Raman scattering in an AlN microresonator_". Optics Letters, 46(3), 540-543. (2021)

  - Weng, H., Liu, J., Afridi, A. A., Li, J., Dai, J., Ma, X. _et al._ "_Directly accessing octave-spanning dissipative Kerr soliton frequency combs in an AlN microring resonator_" Photonics Research (2021)

  - Moille, G., Westly, D., Orji, N. G., & Srinivasan, K. "_Tailoring broadband Kerr soliton microcombs via post-fabrication tuning of the geometric dispersion_". Applied Physics Letters, 119(12), 121103 (2021)

  - Weng, H., Liu, J., Afridi, A. A., Li, J., Dai, J., Zhang, Y., _et al._ "_Perfect soliton crystal in an AlN microresonator"_. In CLEO: QELS_Fundamental Science (pp. JTh3A-31). Optical Society of America. (2021)

  - Moille, G., Westly, D., Simelgor, G., & Srinivasan, K. "_Impact of the precursor gas ratio on dispersion engineering of broadband silicon nitride microresonator frequency combs_". Optics

    Letters, 46(23), 5970-5973 (2021).

- 2020:

  - Schuttrups, B. (2020). "_Modelling nonlinear optical pulse propagation using pseudo-spectral methods_" (Master's thesis, University of Twente).

  - Moille, G., Chang, L., Xie, W., Rao, A., Lu, X., Davanco, M. _et al._ "_Dissipative Kerr Solitons in a III‐V Microresonator_". Laser & Photonics Reviews, 14(8), 2000022 (2020)

    -2019:

  - Gregory Moille, Xiyuan Lu, Ashutosh Rao, Qing Li, Daron A. Westly, Leonardo Ranzani, Scott B. Papp, Mohammad Soltani, and Kartik Srinivasan "_Kerr-Microresonator Soliton Frequency Combs at Cryogenic Temperatures_," Phys. Rev. Applied 12, 034057 (2019)

  - Gregory Moille, Qing Li, Travis C. Briles, Su-Peng Yu, Tara Drake, Xiyuan Lu, Ashutosh Rao, Daron Westly, Scott B. Papp, and Kartik Srinivasan "_Broadband resonator-waveguide coupling for efficient extraction of octave-spanning microcombs_," Optics Letters Vol. 44, Issue 19, pp. 4737-4740 (2019)

  - Lin Chang, Weiqiang Xie, Haowen Shu, Qifan Yang, Boqiang Shen, Andreas Boes, Jon D. Peters, Warren Jin, Songtao Liu, Gregory Moille, Su-Peng Yu, Xingjun Wang, Kartik Srinivasan, Scott B. Papp, Kerry Vahala, John E. Bowers "_Ultra-efficient frequency comb generation in AlGaAs-on-insulator microresonators_," arXiv:1909.09778 (2019)