Title: Data from Hermitian nonlinear wave mixing controlled by a PT-symmetric phase transition

Authors: Noah Flemens and Jeffrey Moses

Contact Information: 
		Name: Jeffrey Moses
		Institution: Cornell University
		Address: 142 Sciences Drive, Ithaca, New York, 14853, USA
		Email: moses@cornell.edu
		https://orcid.org/0000-0002-2993-0100

		Name: Noah Flemens
		Institution: Cornell University
		Address: 142 Sciences Drive, Ithaca, New York, 14853, USA
		Email: nrf33@cornell.edu
		https://orcid.org/0000-0002-5755-7913

Date of data collection: 2020/01/01 - 2022/08/24

Suggested Citation for Dataset: Noah Flemens and Jeffrey Moses. 2021. Data from: Hermitian nonlinear wave mixing controlled by a PT-symmetric phase transition [Dataset]. Cornell University eCommons Digital Repository. https://doi.org/10.7298/dra3-6774.

Related Publication: Flemens, Noah, and Jeffrey Moses. (2022) Hermitian Nonlinear Wave Mixing Controlled by a P T -Symmetric Phase Transition. Physical Review Letters, vol. 129, no. 15, Oct. 2022, p. 153901. https://doi.org/10.1103/PhysRevLett.129.153901.


Keywords: Nonlinear Optics, Three-Wave Mixing, Cascaded Nonlinear Processes, Hybridized Nonlinear Processess, Optical Frequency Conversion, PT Symmetry Breaking, Non-Hermitian Physics.


Abstract: This dataset supports the findings reported in Moses and Flemens PRL 2022 paper, 
"Hermitian nonlinear wave mixing controlled by a PT-symmetric phase transition," in which it 
is shown that coherent nonlinear interactions enable behavior associated with the PT-
symmetric phase of a non-Hermitian subsystem to control the containing Hermitian system. 
This is achieved in parametric nonlinear wave mixing where simultaneous
second harmonic generation replaces the role of loss to induce non-Hermitian behavior that persists
through a full exchange of power within the Hermitian system. These findings suggest a new
approach for the engineering of dynamics where energy recovery and sustainability are of importance
that could be of significance for photonics and laser science.


Funding: This work was supported initially by the Cornell Center for Materials Research with funding from the NSF MRSEC program (DMR-1719875), and later by the NSF under grant no. ECCS-1944653. 


License: These data are shared under a Creative Commons Attribution 4.0 International (CC BY 4.0) license (https://creativecommons.org/licenses/by/4.0/). It is free and available to be shared and adapted for re-use, but proper attribution to the original authors must be given. 


Note: Contained in this repository folder is all the figure plot data (except schematics) for the publication mentioned 
above. Each sub-folder, named after figure numbers, contains .xlsx files that include all data needed for that plot. 
The column, file, or sheet names indicate how to recreate the figures. Data for each figure is shared as a zipped bundle, named with this strategy: FlemensMoses_PRL2022_FigureY.zip We have also created an archival bundle as part of the dataset that contains CSV versions of all .xlsx workbooks and their respective sheets, and is named: FlemensMoses_PRL_2022_ExcelArchive.zip.

In detail:

 - FlemensMoses_PRL2022_Figure2 contains the simulation data for the TWM + SHG system when there is no SHG, weak SHG, 
and strong SHG. For each of these conditions, there are datasets for the three possible seeding conditions:
fields a and b seeded, a and c seeded, and b and c seeded. Each data set has a sheet representing the variables used
to generate the plots. x is a meshgrid of the radial or temporal mode coordinate with z, the propagation coordinate.
a, b, c, and d, are the fractional photon flux densities for the a, b, c, and d fields respectively.

 - FlemensMoses_PRL2022_Figure3 contains the simulation data of the a-c subsystem dynamics in the gauge transformed frames. z_j is the
propagation coordinate while RealEigen_j and ImagEigen_j are the real and imaginary parts of the eigenvalues
for the subsystem. na_j and nc_j are the fractional photon flux densities for field a and c in the gauge transformed
frame. For j = 0, 1, 2, this corresponds to eta_inf = 0.9, 1.0, 1.1.

 - FlemensMoses_PRL2022_Figure4 contains the simulation data of the photon exchange rate, rho, under the three possible seeding conditions as 
described for figure 2. For each seeding condition mn, mnSeededZ is a meshgrid of the propagation coordinate with arctan(eta_inf) 
which has a meshgrid saved in mnSeededG. The corresponding values of rho for each seeding condition are in mnSeededRho.

This readme.txt file was generated on 2022/09/22 by Noah Flemens.