Noise-resilient exceptional point sensing with immunity to undesired perturbations
Data files
Mar 03, 2026 version files 8.67 MB
-
allan_variances.mat
13.89 KB
-
frequency_sweep_data.mat
8.65 MB
-
README.md
2.94 KB
-
sensitivity_data.mat
317 B
Abstract
Exceptional point degeneracies (EPDs) are non-Hermitian singularities where eigenvalues and their corresponding eigenvectors coalesce. When a small perturbation is induced, the eigenvalue detuning from an EPD follows a root sublinear expansion, which provides a means of enhancing the sensitivity (frequency shift) of resonant-based sensors. On the downside, resonant-based sensors are susceptible to cavity imperfections, local mechanical disturbances (temperature variations, vibrations), and other experimental uncertainties. Here, we overcome this problem by experimentally implementing passive periodic microwave metamaterials with non-resonant EPDs (NR-EPD) occurring in their Bloch spectrum. We demonstrate a sublinear variation of the reflectance near NR-EPDs to a specific class of (global) perturbations and propose its usage for ultra-sensitive sensing that is immune to undesired (local) perturbations. Importantly, the sensitivity is shielded from technical or fundamental noise that typically degrades the signal-to-noise performance of resonant EPDs.
Description of files and variables
allan_variances.mat
This file contains Allan variance and Allan deviation data from five runs each for five frequency offsets, each consisting of 20,000 points collected over 3 * 192.01 seconds. The frequency offsets are:
- 1.744 GHz (50 MHz away)
- 1.784 GHz (10 MHz away)
- 1.789 GHz (5 MHz away)
- 1.792 GHz (2 MHz away)
- 1.793 GHz (1 MHz away)
Notes
- The first four frequencies lie within the sublinear scaling range.
- All measurements share the same tau values, determined by the total measurement duration.
Variables
avar_i_j
- The j-th measurement run of the Allan variance for the i-th frequency offset (in MHz from the SIP).
- Each variable is a vector over tau.
tau
- Shared across all files.
- Determined by the total measurement interval.
avar_i
- Matrix of Allan variances for frequency offset i.
- 5 rows, one per measurement run
- The number of columns is the number of tau points
avar_i_comb
- Summary statistics for the i-th frequency offset.
- Row 1: mean Allan variance across the 5 runs
- Row 2: standard deviation
adev_*
- Same structure as the corresponding
avar_*variables - Contains Allan deviations instead of variances
sensitivity_data.mat
This structured data file contains sensitivity measurements for the same five frequency offsets listed above.
Variables
- Each entry contains two elements:
- Absolute value of the sensitivity
- Standard deviation
- Values are computed from 20 frequency sweeps, see next file
frequency_sweep_data.mat
This file contains scattering matrix data collected across three experimental configurations: one unperturbed system and two defect configurations. These are denoted *_unperturbed, *_defect_1, and *_defect_2, respectively.
Frequency Sweep Details
- Each frequency sweep contains 1001 frequency steps
- Sweep range: 1 GHz to 2 GHz
Data Files
For each of the three configurations:
ave_s_mat_*.mat
- Averaged scattering matrix, computed over 20 sweeps
s_mat_total_*.mat
- Full scattering matrix data, containing all 20 trials
Defect Configurations
A 20 Ohm load is inserted at every location a cable is removed.
Defect 1
Removed cables at:
- Cable 5, between unit cells 5 and 6
- Cable 2, unit cell 10
- Cable 1, unit cell 3
Defect 2
Removed cables at:
- Cable 1, unit cell 12
- Cable 3, between unit cells 6 and 7
- Cable 6, between unit cells 2 and 3
Measurements
- Excitation is injected at port 3, corresponding to vertex 3 of unit cell 1.
- Reflection is measured from all ports, and thus the total reflection is computed as:
|S(1,3)|² + |S(2,3)|² + |S(3,3)|²
Sensitivity
The sensitivity values can be reproduced by applying a finite difference derivative.