Longitudinal Mode Count
Calculate cavity free spectral range and longitudinal modes within a gain bandwidth.
Description
Linear-cavity round-trip time determines free spectral range.
Linear-cavity round-trip time determines free spectral range. A simple bandwidth-to-spacing tally estimates longitudinal modes.1
Calculate cavity free spectral range and longitudinal modes within a gain bandwidth.
When to use Longitudinal Mode Count
Use this tool to calculate cavity free spectral range and longitudinal modes within a gain bandwidth.
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 Longitudinal Mode Count 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 cavityLengthMeters, refractiveIndex, gainBandwidthHertz using the field table and calculation rules, then run the tool.
- Read freeSpectralRangeHertz, longitudinalModeCount, roundTripTimeSeconds. 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 |
|---|---|---|---|
| cavityLengthMeters | Cavity length (m) | number; minimum: 0 | Required |
| refractiveIndex | Cavity refractive index | number; minimum: 0 | Required |
| gainBandwidthHertz | Gain bandwidth (Hz) | number; minimum: 0 | Required |
Enter positive cavity length/index and nonnegative gain bandwidth. Return time, FSR and mode count, including one at zero bandwidth.
roundTrip=2nL/c; FSR=1/roundTrip; count=max(1,floor(bandwidth/FSR)+1) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| freeSpectralRangeHertz | Free spectral range (Hz) | number; minimum: 0 |
| longitudinalModeCount | Longitudinal mode count | integer; minimum: 1 |
| roundTripTimeSeconds | Cavity round-trip time (s) | number; minimum: 0 |
{
"input": {
"cavityLengthMeters": 1,
"refractiveIndex": 1,
"gainBandwidthHertz": 299792458
},
"output": {
"freeSpectralRangeHertz": 149896229,
"longitudinalModeCount": 3,
"roundTripTimeSeconds": 6.671281903963041e-9
}
}Limitations and assumptions
Resonance offset, dispersion and gain competition are not solved. The count assumes a mode inside the interval.
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 Harmonic Mode-Locking Rate: Calculate harmonic mode-locking pulse rate and spacing. For a complementary task, use Fabry-Pérot Linewidth: Calculate Fabry–Pérot free spectral range and linewidth from cavity length, index, and finesse.
References
-
Longitudinal Mode Count — tool.io
Similar or alternative tools
- Harmonic Mode-Locking Rate
Calculate harmonic mode-locking pulse rate and spacing.
- Fabry-Pérot Linewidth
Calculate Fabry–Pérot free spectral range and linewidth from cavity length, index, and finesse.