THz Complex Conductivity
Convert complex relative permittivity to complex conductivity under an exp(-iωt) convention.
Description
Complex permittivity can be expressed as complex conductivity under a chosen harmonic time convention.
Complex permittivity can be expressed as complex conductivity under a chosen harmonic time convention. Here exp(−iωt) fixes the imaginary-part sign.1
Convert complex relative permittivity to complex conductivity under an exp(-iωt) convention.
When to use THz Complex Conductivity
Use this tool to convert complex relative permittivity to complex conductivity under an exp(-iωt) convention.
Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.
How to use THz Complex Conductivity and understand its results
- Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.
- Enter frequencyHertz, relativePermittivityReal, relativePermittivityImaginary using the field table and calculation rules, then run the tool.
- Read conductivityRealSiemensPerMeter, conductivityImaginarySiemensPerMeter. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| frequencyHertz | Frequency (Hz) | number; minimum: 0 | Required |
| relativePermittivityReal | Relative permittivity real part | number | Required |
| relativePermittivityImaginary | Relative permittivity imaginary part | number | Required |
Enter nonnegative frequency and finite signed relative-permittivity components. Use ε0=8.8541878128e−12 F/m and return S/m components. Zero frequency returns zeros.
σreal=2πf ε0 εimag; σimag=2πf ε0(1−εreal) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| conductivityRealSiemensPerMeter | Conductivity real part (S/m) | number |
| conductivityImaginarySiemensPerMeter | Conductivity imaginary part (S/m) | number |
{
"input": {
"frequencyHertz": 1000000000000,
"relativePermittivityReal": 4,
"relativePermittivityImaginary": 0.1
},
"output": {
"conductivityRealSiemensPerMeter": 5.5632502772393515,
"conductivityImaginarySiemensPerMeter": -166.89750831718055
}
}Limitations and assumptions
No material fitting, causality or sign-convention conversion is performed.
Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use THz Waveform Spectrum: Compute a direct discrete magnitude spectrum from a THz time-domain waveform. For a complementary task, use Photoconductive-Antenna Field: Calculate photoconductive-antenna bias field across the electrode gap.
References
-
THz Complex Conductivity — tool.io
Similar or alternative tools
- THz Waveform Spectrum
Compute a direct discrete magnitude spectrum from a THz time-domain waveform.
- Photoconductive-Antenna Field
Calculate photoconductive-antenna bias field across the electrode gap.