Net Dispersion

Sum segment dispersion-length products and report the net dispersion sign.

Description

Net dispersion adds segment dispersion-length products.

Net dispersion adds segment dispersion-length products. The returned normal/anomalous labels follow the implementation’s sign convention for the supplied D values.^{[1, 2]}

Sum segment dispersion-length products and report the net dispersion sign.

When to use Net Dispersion

Use this tool to sum segment dispersion-length products and report the net dispersion sign.

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 Net Dispersion 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 dispersionPsPerNmKm, lengthsKilometers using the field table and calculation rules, then run the tool.
Read netDispersionPsPerNm, dispersionSign. 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
dispersionPsPerNmKm	Segment dispersion coefficients (ps/(nm·km))	list of number	Required
lengthsKilometers	Segment lengths (km)	list of number	Required

Enter nonempty aligned finite D values in ps/(nm·km) and nonnegative lengths in km. Return ps/nm and the sign label.

net=ΣD_iL_i; positive→normal; negative→anomalous; zero→zero

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
netDispersionPsPerNm	Net cavity dispersion (ps/nm)	number
dispersionSign	Net dispersion sign	string; one of "normal", "anomalous", "zero"

json

{
  "input": {
    "dispersionPsPerNmKm": [
      20,
      -10
    ],
    "lengthsKilometers": [
      1,
      0.5
    ]
  },
  "output": {
    "netDispersionPsPerNm": 15,
    "dispersionSign": "normal"
  }
}

Limitations and assumptions

D and group-velocity-dispersion β2 use different sign conventions; verify the desired physical interpretation. No higher-order dispersion or wavelength dependence is modeled.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Dispersion-Map Strength: Calculate net, absolute, and pulse-width-normalized dispersion-map strength. For a complementary task, use GDD Ripple: Summarize dispersive-mirror group-delay-dispersion ripple.

Further background: Dispersion engineering and measurement of whispering gallery mode resonators.

References

Net Dispersion — tool.io
Dispersion engineering and measurement of whispering gallery mode resonators — Nanophotonics research article

Similar or alternative tools

Dispersion-Map Strength
Calculate net, absolute, and pulse-width-normalized dispersion-map strength.
GDD Ripple
Summarize dispersive-mirror group-delay-dispersion ripple.