Title of Dataset: Dataset for Figures in Robust Wave Splitters Based on Scattering Singularities in Complex non-Hermitian Systems

Author Information:

Corresponding Author:
Jared Erb, jmerb@umd.edu

Principal Investigator:
Steven Anlage, anlage@umd.edu

Funding Sources:
NSF/RINGS Grant No. ECCS-2148318
ONR Grant No. N000142312507
DARPA WARDEN Grant No. HR00112120021
Department of Energy Grant No. DE-SC0024223
US-Israel Binational Science Foundation Grant No. BSF2022158

Methodological Information:
All experimental data in Robust Wave Splitters Based on Scattering Singularities in Complex non-Hermitian Systems were collected using a Keysight model N5242B microwave vector network analyzer (VNA). The theoretical data were created using the random matrix theory model described in supplementary material section VIII of the paper. All raw data collected was the 2x2 scattering matrix S measured over many different parameters, or the voltage values measured at the receivers of the VNA. In some of the attached data files, the raw S data was processed into det(S) values by calculating the determinant of the scattering matrix for all parameter space measured, and the voltage values measured at the receivers were processed into input/output power ratios and phase differences. The data used to create each figure was saved in the corresponding .mat data file using matlab. Additional details are specified in the paper.

Once the .mat data files are downloaded, the data can be viewed natively using matlab, but python, mathematica, etc., can also process and analyze .mat files.

File List:

Fig_1_Data.mat contains the data for Figure 1. This is a .mat file, used by MATLAB to store data. The variables in this file are freq (1x32001 vector) which is the frequency over which the data was measured in GHz, Phase_Shift (1x301 vector) which is the phase shift of TM_1^{0D} over which the data was measured in Deg/GHz, and detS (32001x301 matrix) which contains the measured value of the det(S) at each (freq, Phase_Shift) value. 

Fig_2_Data.mat contains the data for Figure 2. This is a .mat file, used by MATLAB to store data. The variables in this file are Input_Power_Ratio (101x1 vector) which is the input power ratio sent into the system measured with the VNA's receivers in dB, Input_Phase_Difference (121x1 vector) which is the input phase difference sent into the system measured with the VNA's receivers in Deg, Output_Power_Ratio_Power_Sweep (101x1 vector) which is the measured output power ratio from the system as the input power ratio of the system was varied, Output_Power_Ratio_Phase_Sweep (121x1 vector) which is the measured output power ratio from the system as the input phase difference of the system was varied, Output_Phase_Difference_Power_Sweep (101x1 vector) which is the measured output phase difference from the system as the input power ratio of the system was varied in Deg, and Output_Phase_Difference_Phase_Sweep (121x1 vector) which is the measured output phase difference from the system as the input phase difference of the system was varied in Deg.

Fig_3_Data.mat contains the data for Figure 3. This is a .mat file, used by MATLAB to store data. The variables in this file are System (28x1 vector) which specifies which system the data was measured in (1=reciprocal tetrahedral graph, 2=non-reciprocal tetrahedral graph, 3=quarter bowtie billiard, 4=3D chaotic microwave cavity), Input_Power_Ratio (71x28 matrix) which is the input power ratio sent into the system measured with the VNA's receivers in dB for each of the 28 different robust splitting conditions measured, Input_Phase_Difference (121x28 matrix) which is the input phase difference sent into the system measured with the VNA's receivers in Deg for each of the 28 different robust splitting conditions measured, Output_Power_Ratio_Power_Sweep (71x28 matrix) which is the measured output power ratio from the system as the input power ratio of the system was varied for each of the 28 different robust splitting conditions measured, Output_Power_Ratio_Phase_Sweep (121x28 matrix) which is the measured output power ratio from the system as the input phase difference of the system was varied for each of the 28 different robust splitting conditions measured, Output_Phase_Difference_Power_Sweep (71x28 matrix) which is the measured output phase difference from the system as the input power ratio of the system was varied in Deg for each of the 28 different robust splitting conditions measured, and Output_Phase_Difference_Phase_Sweep (121x28 matrix) which is the measured output phase difference from the system as the input phase difference of the system was varied in Deg for each of the 28 different robust splitting conditions measured. Each column of all variables (other than system) correspond to being measured in the experimental system specified by System(column index), so the first column was measured in the first value of System which is 1 (reciprocal tetrahedral graph).

Fig_4_Data.mat contains the data for Figure 4. This is a .mat file, used by MATLAB to store data. The variables in this file are RS_Xpoints (1x482 vector) which specify the frequency of the robust splitting condition in GHz, RS_Ypoints (1x482 vector) which specify the phase shift of TM_1^{0D} of the robust splitting condition in Deg/GHz, RS_Zpoints (1x482 vector) which specify the phase shift of TM_2^{0D} of the robust splitting condition in Deg/GHz, Relative_Power (482x1 vector) which specify the output power ratio determined from the relative amplitude of the two components of the scattering matrix eigenvector corresponding to the non-zero eigenvalue, and Relative_Phase (482x1 vector) which specify the output phase difference in Deg determined from the relative phase of the two components of the scattering matrix eigenvector corresponding to the non-zero eigenvalue.

Fig_5_Data.mat contains the data for Figure 5. This is a .mat file, used by MATLAB to store data. The variables in this file are lambda_1 which is the value of the first scattering eigenvalue, lambda_2 which is the value of the second scattering eigenvalue, Input_Power_Ratio (71x1 vector) which is the input power ratio sent into the system measured with the VNA's receivers in dB, Input_Phase_Difference (121x1 vector) which is the input phase difference sent into the system measured with the VNA's receivers in Deg, Output_Power_Ratio_Power_Sweep (71x1 vector) which is the measured output power ratio from the system as the input power ratio of the system was varied, Output_Power_Ratio_Phase_Sweep (121x1 vector) which is the measured output power ratio from the system as the input phase difference of the system was varied, Output_Phase_Difference_Power_Sweep (71x1 vector) which is the measured output phase difference from the system as the input power ratio of the system was varied in Deg, and Output_Phase_Difference_Phase_Sweep (121x1 vector) which is the measured output phase difference from the system as the input phase difference of the system was varied in Deg.

Fig_6_Data.mat contains the data for Figure 6. This is a .mat file, used by MATLAB to store data. The variable in this file is S_mats (2x2x2 matrix) which contains the scattering matrices underlying the data in Figure 6a,b. The first two indices specify the components of the scattering matrix, and the third index specifies each RS condition. For example S_mats(:,:,1) specifies the 2x2 scattering matrix underlying Figure 6a, and S_mats(1,1,1) specifies the S_11 element of the scattering matrix underlying Figure 6a.

Fig_S1_Data.mat contains the data for Figure S1. This is a .mat file, used by MATLAB to store data. The variables in this file are freq (1x40001 vector) which is the frequency over which the data was measured in GHz, metasurface_voltage (1x1201 vector) which is the voltages of TM_1^{1D} over which the data was measured in V, and detS (40001x1201 matrix) which contains the measured value of the det(S) at each (freq, metasurface_voltage) value. 

Fig_S2_Data.mat contains the data for Figure S2. This is a .mat file, used by MATLAB to store data. The variables in this file are freq (1x4001 vector) which is the frequency over which the data was measured in GHz, metasurface_voltage (1x1001 vector) which is the voltages of TM_1^{2D} over which the data was measured in V, and detS (4001x1001 matrix) which contains the measured value of the det(S) at each (freq, metasurface_voltage) value. 

Fig_S3_Data.mat contains the data for Figure S3. This is a .mat file, used by MATLAB to store data. The variables in this file are RS_Xpoints (1x301 vector) which specify the frequency of the robust splitting condition in GHz, RS_Ypoints (1x301 vector) which specify the voltage of TM_1^{1D} of the robust splitting condition in V, RS_Zpoints (1x301 vector) which specify the voltage of TM_2^{1D} of the robust splitting condition in V, Relative_Power (301x1 vector) which specify the output power ratio determined from the relative amplitude of the two components of the scattering matrix eigenvector corresponding to the non-zero eigenvalue, and Relative_Phase (301x1 vector) which specify the output phase difference in Deg determined from the relative phase of the two components of the scattering matrix eigenvector corresponding to the non-zero eigenvalue.

Fig_S4_Data.mat contains the data for Figure S4. This is a .mat file, used by MATLAB to store data. The variables in this file are RS_Xpoints (1x60 vector) which specify the frequency of the robust splitting condition in GHz, RS_Ypoints (1x60 vector) which specify the voltage of TM_1^{2D} of the robust splitting condition in V, RS_Zpoints (1x60 vector) which specify the voltage of TM_2^{2D} of the robust splitting condition in V, Relative_Power (60x1 vector) which specify the output power ratio determined from the relative amplitude of the two components of the scattering matrix eigenvector corresponding to the non-zero eigenvalue, and Relative_Phase (60x1 vector) which specify the output phase difference in Deg determined from the relative phase of the two components of the scattering matrix eigenvector corresponding to the non-zero eigenvalue.

Fig_S5_Data.mat contains the data for Figure S5. This is a .mat file, used by MATLAB to store data. The variables in this file are S_mats_1D (2x2x2 matrix) which contains the scattering matrices underlying the data in Figure S5a,b, S_mats_2D (2x2x2 matrix) which contains the scattering matrices underlying the data in Figure S5c,d, S_mats_3D (2x2x2 matrix) which contains the scattering matrices underlying the data in Figure S5e,f, and S_mats_RMT (2x2x2 matrix) which contains the scattering matrices underlying the data in Figure S5g,h. For all of the variables, the first two indices specify the components of the scattering matrix, and the third index specifies each RS condition. For example S_mats_1D(:,:,1) specifies the 2x2 scattering matrix underlying Figure S5a, and S_mats_1D(1,1,1) specifies the S_11 element of the scattering matrix underlying Figure S5a.

Fig_S6_Data.mat contains the data for Figure S6. This is a .mat file, used by MATLAB to store data. The variables in this file are S_mats_1D_Ensemble_1 (2x2x100 matrix) which contains the scattering matrices underlying the 1D Ensemble 1 data, S_mats_1D_Ensemble_2 (2x2x194 matrix) which contains the scattering matrices underlying the 1D Ensemble 2 data, S_mats_2D_Ensemble (2x2x267 matrix) which contains the scattering matrices underlying the 2D Ensemble data, S_mats_3D_Ensemble (2x2x1587 matrix) which contains the scattering matrices underlying the 3D Ensemble data, S_mats_RMT_Ensemble_1 (2x2x124 matrix) which contains the scattering matrices underlying the RMT Ensemble 1 data, and S_mats_RMT_Ensemble_2 (2x2x213 matrix) which contains the scattering matrices underlying the RMT Ensemble 2 data.  For all of the variables, the first two indices specify the components of the scattering matrix, and the third index specifies each RS condition. For example S_mats_1D_Ensemble_1(:,:,i) specifies the ith 2x2 scattering matrix, and S_mats_1D_Ensemble_1(1,1,i) specifies the S_11 element of the ith scattering matrix.

Fig_S7_Data.mat contains the data for Figure S7. This is a .mat file, used by MATLAB to store data. The variables in this file are Input_Power_Ratio (71x3 matrix) which is the input power ratio sent into the system measured with the VNA's receivers in dB for each of the 3 different systems measured, Input_Phase_Difference (121x3 matrix) which is the input phase difference sent into the system measured with the VNA's receivers in Deg for each of the 3 different systems measured, Output_Power_Ratio_Power_Sweep (71x3 matrix) which is the measured output power ratio from the system as the input power ratio of the system was varied for each of the 3 different systems measured, Output_Power_Ratio_Phase_Sweep (121x3 matrix) which is the measured output power ratio from the system as the input phase difference of the system was varied for each of the 3 different systems measured, Output_Phase_Difference_Power_Sweep (71x3 matrix) which is the measured output phase difference from the system as the input power ratio of the system was varied in Deg for each of the 3 different systems measured, and Output_Phase_Difference_Phase_Sweep (121x3 matrix) which is the measured output phase difference from the system as the input phase difference of the system was varied in Deg for each of the 3 different systems measured. For all variables, the first column is data measured from a one-dimensional graph, the second column is data measured from a two-dimensional billiard, and the third column is data measured from a three-dimensional cavity. 

Fig_S8_Data.mat contains the data for Figure S8. This is a .mat file, used by MATLAB to store data. The variables in this file are freq (1x32001 vector) which is the frequency over which the data was measured in GHz, Phase_Shift_1 (1x601 vector) which is the phase shift of TM_1^{0D} over which the data was measured in Deg/GHz, Phase_Shift_2 which is the phase shift of TM_2^{0D}, and detS (32001x601 matrix) which contains the measured value of the det(S) at each (freq, Phase_Shift_1) value.

Fig_S9_Data.mat contains the data for Figure S9. This is a .mat file, used by MATLAB to store data. The variables in this file are RS_Xpoints (1x112 vector) which specify the frequency of the robust splitting condition in GHz, RS_Ypoints (1x112 vector) which specify the phase shift of TM_1^{0D} of the robust splitting condition in Deg/GHz, Time (1x112 vector) which specify the time the measurement was taken in hours, Relative_Power (112x1 vector) which specify the output power ratio determined from the relative amplitude of the two components of the scattering matrix eigenvector corresponding to the non-zero eigenvalue, and Relative_Phase (112x1 vector) which specify the output phase difference in Deg determined from the relative phase of the two components of the scattering matrix eigenvector corresponding to the non-zero eigenvalue.

Fig_S10_Data.mat contains the data for Figure S10. This is a .mat file, used by MATLAB to store data. The variables in this file are RS_Xpoints (1x182 vector) which specify the frequency of the robust splitting condition in GHz, RS_Ypoints (1x182 vector) which specify the voltage of TM_1^{1D} of the robust splitting condition in V, Time (1x182 vector)  which specify the time the measurement was taken in hours, Relative_Power (182x1 vector) which specify the output power ratio determined from the relative amplitude of the two components of the scattering matrix eigenvector corresponding to the non-zero eigenvalue, and Relative_Phase (182x1 vector) which specify the output phase difference in Deg determined from the relative phase of the two components of the scattering matrix eigenvector corresponding to the non-zero eigenvalue.

Fig_S11_Data.mat contains the data for Figure S11. This is a .mat file, used by MATLAB to store data. The variables in this file are omega (1x25001 vector) which is the frequency over which the data was simulated, x (1x1501 vector) which is the value of the parameter x over which the data was simulated, and detS (25001x1501 matrix) which contains the measured value of the det(S) at each (omega, x) value. 

Fig_S12_Data.mat contains the data for Figure S12. This is a .mat file, used by MATLAB to store data. The variables in this file are RS_Xpoints (1x301 vector) which specify the frequency of the robust splitting condition, RS_Ypoints (1x301 vector) which specify the value of the parameter x of the robust splitting condition, RS_Zpoints (1x301 vector) which specify the value of the parameter y of the robust splitting condition, Relative_Power (301x1 vector) which specify the output power ratio determined from the relative amplitude of the two components of the scattering matrix eigenvector corresponding to the non-zero eigenvalue, and Relative_Phase (301x1 vector) which specify the output phase difference in Deg determined from the relative phase of the two components of the scattering matrix eigenvector corresponding to the non-zero eigenvalue.

Supplementary_Movie.mp4 is a video which shows the dynamics and interactions of robust splitting conditions as a third parameter of the reciprocal tetrahedral microwave graph is varied. Plotted is the |det(S)| vs frequency and phase shift of TM_1^{0D} and each frame of the video is at a different fixed phase shift of TM_2^{0D}. In the video the robust splitting conditions are highlighted by the white points where |det(S)| ≤ 0.002, and we see numerous creation and annihilation events of robust splitting conditions as the phase shift of TM_2^{0D} varies. The first frame of this video is shown and described in Figure S8.