Semiconductor Non Hermitian Exceptional Point Calculator
Explicit ideal symmetric2×2PTmatrix with same real mode frequency, realκcoupling and balanced±iγgain/loss. Discriminantκ²−γ²and exact nominalκ=γequality only; no complex eigenspectrum, noise robustness or generic non-Hermitian EPdetection.
Description
An ideal balanced two-mode model compares coupling with gain/loss magnitude.
An ideal balanced two-mode model compares coupling with gain/loss magnitude.1
Exact equality describes its nominal exceptional-point condition without identifying a real device's exceptional point from noisy observations.
When to use Semiconductor Non Hermitian Exceptional Point Calculator
Use this tool to obtain signedSquaredModeSplitting, nominalExceptionalPointEquality from the supplied records using the stated calculation. Establish the device or material, operating point, units and independently applicable measurement or model calibration.
How to use Semiconductor Non Hermitian Exceptional Point Calculator and understand its results
- Establish the device or material, operating point, units and independently applicable measurement or model calibration.
- Enter callerVerifiedIdenticalModeCenterFrequency, couplingFrequencyMagnitude, balancedGainLossMagnitude, using the field meanings and rules below, then run the tool.
- Read result.signedSquaredModeSplitting, result.nominalExceptionalPointEquality. Use the units and sign conventions below, and review any unknown records separately.
- Correct any reported input issue and run again. Before using a successful result, check the stated units, signs, reference scope and observation coverage.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| callerVerifiedIdenticalModeCenterFrequency | Caller verified identical mode center frequency | number | Required |
| couplingFrequencyMagnitude | Coupling frequency magnitude | number | Required |
| balancedGainLossMagnitude | Balanced gain loss magnitude | number | Required |
Supply a finite common mode-center frequency, strictly positive coupling magnitude and nonnegative balanced gain/loss magnitude in compatible frequency units. Return coupling squared minus gain/loss squared and an exact numerical equality flag. The common center is validated as an input but does not enter either returned expression. No eigenvalues, tolerance band or experimental verification is computed.
squaredSplitting=coupling²−gainLoss²; nominalExceptionalPoint=(coupling===gainLoss) Use the matching field units and the exact boundary, ordering and reference rules above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Qualified observed calculation or explicit reference | object |
| result.signedSquaredModeSplitting | Coupling magnitude squared minus balanced gain/loss magnitude squared. | number |
| result.nominalExceptionalPointEquality | True only for exact numerical equality of the supplied coupling and gain/loss magnitudes. | boolean |
{
"input": {
"callerVerifiedIdenticalModeCenterFrequency": 10,
"couplingFrequencyMagnitude": 2,
"balancedGainLossMagnitude": 2
},
"output": {
"result": {
"signedSquaredModeSplitting": 0,
"nominalExceptionalPointEquality": true
}
}
}Limitations and assumptions
Device structure, material state, operating conditions and calibration determine applicability. The result does not infer missing physical parameters, verify a transport mechanism or validate a fabricated device model.
Missing required fields, unknown fields, wrong types and violated rules return input issues. Numeric values and outputs must be finite. Extremely large composite outputs are rejected.
Alternative or Complementary methods
For a related step, use Semiconductor Pt Symmetric Threshold Gain Calculator: An ideal PT-symmetric threshold relates calibrated coupling to gain-versus-pump slope. For a complementary comparison, use Semiconductor Plasmonic Resonator Quality Factor Vs Confinement Calculator: Plasmonic confinement and resonator quality factor describe different aspects of an optical mode.
References
Similar or alternative tools
- Semiconductor Pt Symmetric Threshold Gain Calculator
An ideal PT-symmetric threshold relates calibrated coupling to gain-versus-pump slope.
- Semiconductor Plasmonic Resonator Quality Factor Vs Confinement Calculator
Plasmonic confinement and resonator quality factor describe different aspects of an optical mode.